A HIPPOCAMPAL MODEL FOR LEARNING AND
RECALLING PATHS: FROM PLACE CELLS TO PATH CELLS
Christopher R. Nolan
A thesis submitted to the University of Queensland
for the degree of Doctor of Philosophy
School of Information Technology and Electrical Engineering
November 2011
ii
c Christopher R. Nolan, 2011.
Typeset in LATEX 2ε .
iii
Declaration by author
This thesis is composed of my original work, and contains no material previously
published or written by another person except where due reference has been made in
the text.
I have clearly stated the contribution by others to jointly-authored works that I have
included in my thesis.
I have clearly stated the contribution of others to my thesis as a whole, including
statistical assistance, survey design, data analysis, significant technical procedures,
professional editorial advice, and any other original research work used or reported
in my thesis. The content of my thesis is the result of work I have carried out since
the commencement of my research higher degree candidature and does not include
a substantial part of work that has been submitted to qualify for the award of any
other degree or diploma in any university or other tertiary institution. I have clearly
stated which parts of my thesis, if any, have been submitted to qualify for another
award.
I acknowledge that an electronic copy of my thesis must be lodged with the University
Library and, subject to the General Award Rules of The University of Queensland,
immediately made available for research and study in accordance with the Copyright
Act 1968.
I acknowledge that copyright of all material contained in my thesis resides with the
copyright holder(s) of that material.
iv
Contributions
Statement of contributions to jointly authored works
contained in the thesis
Nolan, C.R., Wyeth, G., Milford, M., Wiles, J. (2011) The race to learn: Spike timing and
STDP can coordinate learning and recall in CA3. Hippocampus, 21:647-660
Initial conception for the model was primarily Nolan (80%) with contributions from Wiles.
Subsequent development of ideas was all authors Nolan (40%), Wyeth (20%), Milford (20%),
Wiles (20%). The simulations were conducted by Nolan (100%). All authors contributed to
the writing of the paper, primarily led by Nolan (50%) Wiles (30%), Milford (10%), Wyeth
(10%). Wyeth and Wiles obtained funding for the grant that supported this work.
Statement of contributions by others to the thesis as a
whole
Except as stated in the statement of contributions to the Hippocampus paper, the thesis
was wholly written by the candidate.
Statement of parts of the thesis submitted to qualify for
the award of another degree
None.
v
vi
Contributions
Published works by the author incorporated into the
thesis
Nolan, C.R., Wyeth, G., Milford, M., Wiles, J. (2011) The race to learn: Spike timing and
STDP can coordinate learning and recall in CA3. Hippocampus, 21:647-660
Additional published works by the author relevant to
the thesis but not forming part of it
Wiles, J., Ball, D., Heath, S., Nolan, C.R., Stratton, P. (2010) Spike-time robotics: a rapid
response circuit for a robot that seeks temporally varying stimuli. Australian Journal of
Intelligent Information Processing Systems, 11(1)
Acknowledgements
My sincere thanks go to the sponsors of my scholarship, the Tony Murphy Postgraduate
Award, for their support. Their generosity provided me with the freedom to focus wholeheartedly on my research, a freedom that was instrumental in seeing this research through.
This work was part of a project supported by an Australian Research Council Special Research Initiative: Thinking Systems: Navigating through real and conceptual spaces (Grant
sponsor: ARC; Grant number: TS0669699). A grant from Qualcomm assisted travel to Computational Systems Neuroscience conference (COSYNE 2010), and the NSF-funded Temporal
Dynamics of Learning Center assisted in a collaborative visit to the University of California,
San Diego. Facilities were provided by the School of Information Technology and Electrical
Engineering and the Queensland Brain Institute.
I’d like to thank my supervisors, Janet Wiles and Gordon Wyeth, for their excellent guidance.
Thanks to all my colleagues in the Thinking Systems project and at the Queensland Brain
Institute who have been there for discussion and feedback, in particular Peter Stratton,
Michael Milford and Allen Cheung. Finally thanks go to all my friends and family for their
support and their patience.
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viii
Acknowledgements
Abstract
Navigation is a foundational skill for animals. From insects to birds to mammals, many
animals have developed various strategies to search for that which they require, remember
its location, then safely return home. Discovering some of the techniques these animals use
has yielded unique solutions for the navigational problems of artificial autonomous systems.
Yet many questions remain unanswered regarding the navigational abilities that so many
animals appear to possess.
One such ability is path encoding and recall — learning a set of places in an environment and the connectivity between those places, then using the resulting graph or map for
myriad goals. Empirical data collected over the past century indicates that some animals,
and specifically rodents, are capable of behaviours difficult to reconcile with non-path-based
explanations. In more recent decades, since the discovery of spatially sensitive ‘place cells’ in
the rat brain, it has become clear that the hippocampus plays a significant role in map-based
navigation. Simultaneously developing in the field of mobile autonomous systems have been
algorithmic techniques to solve a similar map-based navigation problem, termed Simultaneous Localisation and Mapping (SLAM), which highlight the information-theoretical principles involved. The goal of this thesis has been to explore, using spiking neural modelling
techniques, how the electrophysiological and anatomical properties of the rodent hippocampus can satisfy the theoretical requirements of an online path learning and recall system.
Recognition of novelty is a key element of any memory system. In particular, it is a core
component both in learning and recognising locations and in linking locations into paths.
Existing studies have demonstrated learning mechanisms capable of developing appropriate
unique memories, and corresponding recall mechanisms capable of ignoring random variance in the input. These features are necessary for navigational memory from a theoretical
perspective, and also provide a good fit for some electrophysiological data. However these
studies have not addressed the issue of when each process, learning and recall, should occur.
The first part of this thesis extends existing models of the hippocampal network, incorporating the timing of individual spikes, and using this extra dimension to provide an internal
ix
x
Abstract
novelty signal. It demonstrates how a network that matches known hippocampal anatomy
can instigate a race between a teaching signal and recall signal, with the teaching signal winning the race only in the case of a novel input. Using this novelty signal, what constitutes
a novel input can itself be modified dynamically, without destabilising the system.
In a navigational context, individual memories can be likened to place, and sequences
of such memories to paths. The predominant interpretation of the spatial selectivity of
place cells is that these cells are ’coding for’ the location of the animal at the time of their
firing. Beyond this pure spatial selectivity, evidence demonstrates that during traversal of
a cell’s place field, its firing precesses with respect to the local theta oscillation — an effect
termed “theta phase precession” — and this precession is correlated with relative progression
through the place field. One common interpretation of this precession effect is that it provides
a greater degree of locational specificity. The remainder of this thesis explores an alternative
hypothesis that place fields and theta phase precession are evidence of a path encoding and
recall mechanism. A mechanism based on the known anatomy of CA3 is proposed that is
consistent with many dynamical properties of the region and can explain known variations
in spatial selectivity across the CA3 network. The proposed mechanism suggests that CA3
performing path encoding and recall over complete foraging ranges could be the functional
justification for anatomical and dynamical variation across the region. The thesis concludes
with a discussion of the implications of this theory on the interpretation of place cell data,
and an outline of experimental designs for its validation.
Keywords
hippocampus, neural modelling, spike timing, novelty, learning, memory, place cell
Australian and New Zealand Standard Research Classifications (ANZSRC)
060603 Animal Physiology — Systems 34%, 080110 Simulation and Modelling 33%, 170205
Neurocognitive Patterns and Neural Networks 33%
Contents
Contributions
v
Acknowledgements
vii
Abstract
ix
1 Introduction
1.1
1
Principles of navigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.1.1
A note on cues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.1.2
Reactive navigation . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.1.3
Path integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
1.1.4
Predictive navigation . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
1.2
Mechanisms of cognitive map development . . . . . . . . . . . . . . . . . . .
8
1.3
Existing theories of cognitive map development . . . . . . . . . . . . . . . .
9
1.4
Significant issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1.5
Contributions and thesis overview . . . . . . . . . . . . . . . . . . . . . . . .
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2 Neural modelling and the hippocampus
2.1
2.2
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Single cell computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
2.1.1
Neuron structure and electrophysiology . . . . . . . . . . . . . . . . .
13
2.1.2
Modelling single cells . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
2.1.3
Channels of communication . . . . . . . . . . . . . . . . . . . . . . .
16
2.1.4
Synaptic modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
2.1.5
Prediction is learning . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
2.1.6
Neuromodulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Structure of the hippocampus . . . . . . . . . . . . . . . . . . . . . . . . . .
21
2.2.1
Entorhinal cortex . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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2.2.2
Dentate gyrus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
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Contents
2.3
2.4
2.5
2.2.3
CA3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
2.2.4
CA1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
Properties of the hippocampal formation . . . . . . . . . . . . . . . . . . . .
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2.3.1
Theta rhythm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
2.3.2
Place cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
2.3.3
Grid cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
2.3.4
Non-spatial hippocampal inputs . . . . . . . . . . . . . . . . . . . . .
34
Theories and models of hippocampal function . . . . . . . . . . . . . . . . .
35
2.4.1
Dynamics of hippocampal information storage . . . . . . . . . . . . .
35
2.4.2
Hippocampus-dependent navigation . . . . . . . . . . . . . . . . . . .
42
2.4.3
Information models . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
3 A role for spike timing in learning and recognition
47
3.1
Novelty, separation and completion . . . . . . . . . . . . . . . . . . . . . . .
48
3.2
A novelty-aware microcircuit . . . . . . . . . . . . . . . . . . . . . . . . . . .
50
3.2.1
Microcircuit design . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
3.2.2
Microcircuit simulations . . . . . . . . . . . . . . . . . . . . . . . . .
52
The STSC circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
3.3.1
STSC model design . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
3.3.2
Timing is a signal of learning . . . . . . . . . . . . . . . . . . . . . .
59
3.3.3
Distinctiveness and reliability of learned responses . . . . . . . . . . .
62
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
65
3.3
3.4
4 Modulating learning and recall
4.1
4.2
4.3
4.4
71
Modulating the tendency to recall . . . . . . . . . . . . . . . . . . . . . . . .
71
4.1.1
EC2-CA3 synaptic modulation . . . . . . . . . . . . . . . . . . . . . .
72
4.1.2
Threshold modulation results . . . . . . . . . . . . . . . . . . . . . .
72
Modulating the teaching signal . . . . . . . . . . . . . . . . . . . . . . . . .
74
4.2.1
Kainate inhibition of mossy fibre synapses . . . . . . . . . . . . . . .
74
4.2.2
Kainate inhibition in the three neuron microcircuit . . . . . . . . . .
76
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
4.3.1
Tuning the learn-recall balance . . . . . . . . . . . . . . . . . . . . .
78
4.3.2
Implications of presynaptic kainate modulation . . . . . . . . . . . .
81
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
Contents
xiii
5 Temporal sequencing of memories
5.1 Place cell dynamics . . . . . . . . . . . . . . . . . . . . . .
5.1.1 Spatial field size . . . . . . . . . . . . . . . . . . . .
5.1.2 Temporal dynamics . . . . . . . . . . . . . . . . . .
5.2 Two-dimensional fields . . . . . . . . . . . . . . . . . . . .
5.2.1 Reconciling anchor and path field theory with place
5.3 Significance of anchor and path field theory . . . . . . . .
5.3.1 Calculation of position offsets and anchor fields . .
5.3.2 Notable simplifications in the theory . . . . . . . .
5.4 Validating the theory . . . . . . . . . . . . . . . . . . . . .
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6 Empirical predictions
6.1 Looking for a race . . . . . . . . . . . . .
6.2 Evidence to disambiguate path and place
6.3 Multi-segment path navigation . . . . . .
6.3.1 Experiment design . . . . . . . .
6.3.2 Predictions . . . . . . . . . . . .
6.3.3 Interpretation of results . . . . .
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7 General Discussion
7.1 Summary and contributions . . . . . . . . . . . . . . . . .
7.2 Impact of path and anchor theory on hippocampal theory .
7.2.1 Novelty and learning . . . . . . . . . . . . . . . . .
7.2.2 Place cell rate response and reliability . . . . . . .
7.2.3 Theta phase precession . . . . . . . . . . . . . . . .
7.2.4 Spatial sensitivity . . . . . . . . . . . . . . . . . . .
7.2.5 Spatial field directionality . . . . . . . . . . . . . .
7.2.6 Spatial field response with introduced barriers . . .
7.3 The theories in context . . . . . . . . . . . . . . . . . . . .
7.4 Beyond anchor and path field theory . . . . . . . . . . . .
7.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . .
7.6 Further work . . . . . . . . . . . . . . . . . . . . . . . . .
References
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xiv
Contents
1
Introduction
Spatial memory is a fundamental component of flexible and robust navigation (Tolman,
1948). Long-term storage of spatial memory in humans and in animals, particularly for
environments larger than a single sensory snapshot, is generally ascribed to a cognitive
mapping ability. The term cognitive mapping refers to the storage and cued recall of relative
locations in an environment. Understanding the neural mechanisms supporting cognitive
map development and use has many theoretical and applied benefits, such as an appreciation
of the neural basis of decision making, planning of urban environments, and way-finding for
mobile autonomous agents (Kitchin, 1994).
Navigation provides an obvious behavioural correlate of cognitive map use in animals.
Empirical evidence over the last century suggests that many animals, and rodents in particular, are capable of navigational feats explicable only by their possession of cognitive mapping
abilities. Determining the mechanistic operation of biological navigation systems through
behavioural analysis alone is difficult. This fact was eloquently described by Braitenberg
(1986) in his “law of uphill analysis and downhill invention”, a comment on the nature of a
collection of very simple interacting systems to quickly become intractable to external analysis. However, by studying the computational tasks inherent in successful navigation and by
observing and manipulating not just the behavioural task but the brain itself, mechanistic
properties can be more easily elucidated. Rodent navigation has been studied under a range
1
2
Introduction
of manipulations, for example under sensory deprivation, with selective lesions, and with
field, single-cell and multi-cell recordings (see §1.1). These studies provide data regarding
the navigational capabilities of the animals, the contributions of various brain regions to
specific behaviours, and the behavioural correlates of certain neural activity.
This thesis explores the mechanisms of spatial memory development and use in the rodent. The broad motivation for the work was to establish a theoretical framework to explain
the neural basis of the cognitive map that is computationally sufficient to fulfill the necessary processing and memory requirements of a cognitive map representation, while also
maintaining consistency with the volumes of existing experimental data concerning rodent
spatial memory. Computational modelling is a logical tool to demonstrate the computational feasibility and sufficiency of a theory, and further can ensure an appreciation of the
intricacies of the system and generate specific predictions about the modelled system (for
example Hodgkin and Huxley (1952)). Where appropriate, components of the theoretical
framework proposed in this thesis are tested through computational models, and the results
and predictions derived from these models are presented.
Rodents do not use any single navigation strategy. Behaviours resulting from the use
of a cognitive map must therefore be isolated from those derived from other strategies. In
order to identify these differentiating behaviours, one must first understand the principles
of different navigation strategies (§1.1). To understand the neural mechanisms underlying
a cognitive map, one must appreciate the theoretical processes and information required of
such a map (§1.2). This background provides context for attributing the correct behavioural
and electrophysiological evidence to cognitive map development and use. The remainder of
the chapter explores existing theories of cognitive map development and use (§1.3), discusses
the limitations of these theories (§1.4), and introduces the corresponding contributions of
this thesis (§1.5).
1.1
Principles of navigation
There are a number of different strategies an agent, whether biological or artificial, can use
to learn and navigate an environment. These strategies can be classified by the nature of
the internal representations required to facilitate them. The taxonomy used here separates
strategies into three broad classes:
Reactive navigation includes strategies for performing an action or a sequence of actions
initiated by one or more cues.
1.1 Principles of navigation
3
Path integration or dead-reckoning strategies involve maintaining a displacement vector
based on self-movement cues.
Predictive navigation includes strategies that involve path planning from a location to a
goal.
In addition to these categories, some form of action is required when lacking any information about the environment. This can occur in a novel environment, or when an agent
is disoriented in an ambiguous or cue-less scene. In this case random navigation is the best
possible strategy. Rodents show such behaviour during an exploratory phase when placed
in novel environments (Renner (1990) in Redish (1999)).
Behaviourally, these strategies are most distinguishable from each other during initial
exploration of an environment or under environmental manipulation. Drawing primarily
from data under such conditions, the following sections provide a brief overview of evidence
for the different navigation strategies in the rodent. For each strategy, key lesion and electrophysiological studies are also introduced to provide background on which brain regions
are implicated in the respective strategy.
1.1.1
A note on cues
There are two broad categories of information an animal can use to navigate. The first is the
information gleaned through feedback from self-movement, such as information from sensors
in joints and muscles. Using these internal, or idiothetic cues, an animal can keep track of its
perceived movement through an environment (which may be different to its actual movement
through the environment). The second category is the information about cues fixed in the
environment. Such information is allothetic, that is, external to the body. If the allothetic
cues are invariant relative to the observer’s position (that is, if the observer is unable to
detect that they are undergoing translational movement with respect to a cue), they can be
considered distal. An example of such a cue might be a mountain on the horizon when the
observer is attempting to localise within an acre of bushland. Distal cues can be used as a
compass to provide orientation information, but cannot provide displacement information.
Allothetic cues that can also provide displacement information are called proximal cues, for
example a nearby tree.
1.1.2
Reactive navigation
Rodents, like many other species, have the ability to directly associate actions with cues to
achieve goals. The cues can be simple, such as an odour previously laid by the animal, or
4
Introduction
more complex, such as a visual snapshot of the local scene. Similarly there are a variety of
actions that might be associated with these cues. While grouped here under the common
guise of reactive navigation, combinations of such cue-action pairings are often separated into
a more detailed taxonomy. Borrowing from one such taxonomy proposed by Redish (1999),
we can compare taxon, praxic and route strategies. Each of these strategies is discussed in
the context of a goal-oriented task, where the goal has some intrinsic reinforcing value.
Taxon navigation Otherwise known as beacon navigation, taxon navigation involves using
one or more proximal cues to approach a goal. For example, if a goal location has a
nearby proximal cue that can be partially observed from a distance, by keeping the
cue at an angle of less than 90◦ relative to its direction of movement, an animal would
continually move towards its target. Taxon navigation abilities have been demonstrated
in numerous animals, and particularly in insects (Cartwright and Collett, 1983; Wehner
et al., 2006). Rats can use taxon navigation strategies (Morris, 1981).
Praxic navigation A simple allothetic cue could initiate a complex sequence of actions.
To navigate through a maze, an animal could recognise a point in the maze and learn
a stereotyped set of left and right turns that leads to the target (relying purely on
idiothetic information after the initial allothetic stimulus). Longstanding evidence
suggests that rats are capable of praxic strategies: rats with severe sensory deficits
are capable of learning complex mazes from a fixed start point, seemingly using only
internal cues, and will run into the ends of corridors if the corridors are shortened after
training (Carr and Watson, 1908).
Route navigation Rather than relying on a single cue or snapshot, an animal might use
a sequence of such inputs to navigate a route through an environment. At any instant
the animal is following a taxon- or praxic-based strategy to reach an intermediate goal;
however the true intrinsically-reinforcing goal is reached only after the final step in the
sequence.
The key element uniting these reactive navigation strategies, and what separates this
class of strategy from others, is that the action taken for any given cue is dependent only on
the outcomes of actions taken at that cue in the past, in the context of the motivational state
of the animal. Such a binding is obvious in taxon and praxic navigation, where the success
or failure of an action is evident immediately following the action. In route navigation, an
animal executes an action or action sequence without anticipation of the following cue in
the sequence, it only anticipates the eventual reinforcement provided by the goal. Thus in
1.1 Principles of navigation
5
reactive navigation strategies, there is no sense of geometric space (as in dead-reckoning) or
in the connectedness of space (as in predictive navigation).
Learning in reactive navigation can be reduced to a specific case of the more general
animal learning concept instrumental conditioning. In the domain of reinforcement learning,
problems analogous to reactive navigation are often solved using temporal difference (TD)
learning methods (Sutton and Barto, 1998). TD learning provides a solution to the creditassignment problem (Minsky, 1961), that is, over time it enables reinforcement provided
only upon reaching a goal state to be credited to the appropriate steps in reaching the goal.
A number of models have explored how instrumental conditioning and TD learning might
contribute to rodent navigational behaviour (Brown and Sharp, 1995; Foster et al., 2000;
Joel et al., 2002). Numerous regions have been implicated in reactive navigation strategies.
The dorsolateral striatum appears to be required for taxon navigation (Devan and White,
1999), as does the parietal cortex (Kolb and Walkey, 1987; Kolb et al., 1994). A TD error
(reward prediction error) signal itself may be encoded in the release of the neuromodulator
dopamine (Schultz, 1998).
There are implications of the lack of any form of spatial representation in reactive navigation. An animal may have many different goal locations for a variety of requirements —
food, water, shelter. Without a generalised map, each requirement would require its own
set of routes from each location, resulting in a large number of stimulus-response mappings
(Scholkopf and Mallot, 1995). Furthermore, the flexibility of such a system under environmental change is poor. Consider a goal to which two routes have been mapped. If the goal
is approached by one route and is found to be devalued (e.g. if a food cache becomes depleted) there is no mechanism to update the second route, as there is no evidence that both
lead to the same location. Dead-reckoning and predictive navigation strategies use internal
representations of space to solve these issues.
1.1.3
Path integration
Rodents can perform considerably better than would be predicted if only employing reactive
strategies. Morris (1984) showed this elegantly with his development of the water maze
procedure. In this experimental paradigm, a rat is placed in a circular pool of water that
contains a submerged platform. The water is clouded using milk, and the only cues are
external to the maze. Rats prefer to stand on the platform, despite being strong swimmers,
and when placed in the maze they search for such a location. When initially placed in the
water maze they search randomly until they find the platform. If the trial is repeated with
the platform in a fixed location, the rat gradually learns to swim in a direct path to the
6
Introduction
platform, irrespective of the start location1 . This result can be achieved with a reactive
navigation strategy, pairing the external cues with approach strategies. However, if after
training the rats to navigate to one platform location the platform is then moved within
the maze, but the maze orientation with respect to the external cues remains constant,
the rats rapidly learn the new platform location, requiring many fewer trials than in the
initial training (Morris, 1984). Seemingly the rats can use their existing knowledge of the
environment to relearn more quickly — an observation that reactive learning cannot explain.
Rats must therefore have a generic representation of the environment that is independent of
task; some form of generic spatial awareness.
Path integration (also known as dead-reckoning or inertial navigation) refers to an ability
to use information about movement relative to the self2 to calculate displacement from some
starting position (Barlow, 1964). Ignoring any error in the displacement calculation, an
agent with this ability could leave a home location, walk randomly under complete external
cue deprivation and at any point navigate in a direct path back home. Evidence shows
that an enormous variety of animals have some form of path integration capability, from
desert ants in the Sahara, to bees, to a variety of rodents (Redish, 1999). Until accurate seaworthy time-pieces were invented in the 17th century, sailors used dead-reckoning strategies
to approximate longitude whilst land was out-of-sight (Sobel, 1995).
Under the above definition, the process of path integration involves transforming selfmotion into a summable quantity, rather than any ability to reverse a particular sequence
of actions. An animal using only path integration would be unable to traverse a path it
had taken in reverse, but the summed displacement vector would confer the ability to travel
relatively directly back to a starting position. This transformation into a summable quantity
implies that path integration requires a geometric model of space; an animal demonstrating
this ability must somehow maintain a spatial representation of the displacement between
itself and any relevant locations in the environment. This representation could be in the
egocentric reference frame, requiring the animal update the relative positions of all relevant
locations according to its movements, or it could be in the allocentric reference frame, requiring the animal update its own position relative to some fixed environmental positions.
Whichever reference frame is used (and recent theoretical work suggests that an allocentric
static vectorial representation is most likely (Cheung and Vickerstaff, 2010)), navigation to
a goal involves calculating the direction of the goal from the current location and moving in
that direction, much like a taxon strategy using an imagined landmark.
1
The performance of control rats with a variable platform location shows significantly less improvement,
see Morris (1984) for an explanation of the invariant improvement.
2
The term idiothetic is avoided here as external cues can be used to generate this information, possibly
making the term somewhat confusing.
1.1 Principles of navigation
7
Three particular characteristics of path integration are noted here. Firstly, as in reinforcement learning literature, path integration can be considered a planning strategy, in
that it uses a model of the environment to navigate. Secondly, spatial memory provided
by path integration is continuous, to the extent that an animal can detect its own passage
through space. Finally, any pure path integration-based navigation is a vector-based navigation strategy, in that the information represented in the model is a displacement from
the goal. Navigation derived from path integration is therefore a continuous vector-based
planning strategy 3 .
Navigation in the dark and many shortcutting abilities are afforded by a path integration
system, both of which have long been observed in the rodent (Tolman, 1948; Mittelstaedt
and Mittelstaedt, 1980). These abilities are impaired in animals with fimbria-fornix lesions
(Whishaw and Maaswinkel, 1998; Maaswinkel et al., 1999), but not in animals with specific
hippocampal lesions (Alyan and McNaughton, 1999), suggesting that a region interconnected
with the hippocampus, but not the hippocampus itself is responsible for path integration.
More recently, Hafting et al. (2005) provided evidence of a two-dimensional spatial map with
all the characteristics of a path integration centre in the medial entorhinal cortex of rats.
Some modelling work explores potential mechanisms underlying this map (Burgess et al.,
2007; Burak and Fiete, 2009), however a lack of any empirical evidence leaves the nature of
its formation an open question.
1.1.4
Predictive navigation
In an open environment, a geometric spatial memory such as that facilitated by path integration provides an efficient, flexible environmental representation. However as a vector-based
memory, it represents only total displacement, not spatial connectivity. For example, to navigate from the current location to a goal on the far side of a barrier provides a vector through
the barrier. Basic wall following behaviour may solve this problem in simple situations, but
in complex environments, a representation of intermediate points to the goal — a path —
is required4 .
3
Redish (1999) classified path integration as a form of praxic navigation. The identifying feature of
reactive navigation in the current taxonomy is that only the result of actions taken previously at a given
cue can influence future actions at the cue — equivalent to a learning strategy in reinforcement learning
nomenclature — which does not include path integration.
4
The term path here refers to any ordered set of locations (with no fixed level of positional accuracy) in
an environment. A path in this sense is not necessarily the ordered set of all locations (at any scale) between
two points, nor is it an exact sequence of cartesian coordinates traversed on a single occasion. Rather the
path is an abstract set of locations as internally represented in the memory system of an agent.
8
Introduction
Predictive navigation refers to an ability to search a route using learned spatial connectivity. The spatial memory required for this task is akin to a graph, with nodes as locations
in an environment, and edges representing navigable paths. Cueing of nodes could be based
on both allothetic and idiothetic information. Such a memory facilitates path planning; an
animal can look ahead at possible paths and evaluate which path would most likely satisfy
its current goal. Once such a graph representation were constructed, it could be both robust
to change — as a particular place would be identifiable purely based on its connectivity to
other places — and flexible under varying tasks. In this thesis, I consider a cognitive map
to mean such a graph-based spatial representation.
Similar to the geometric spatial memory facilitated by a path integration strategy, the
cognitive map provides a model of the environment, thus making predictive navigation a
planning strategy. Unlike a geometric memory however, the cognitive map is discrete rather
than continuous, in that places (or nodes) in the map represent a particular cue combination,
and it is path-based rather than vector-based, in that the route to goal is stored as a sequence
of intermediate locations (which may have associated geometric information themselves).
Predictive navigation is therefore a discrete path-based planning strategy.
Although often not explicitly noted, it is a combination of predictive navigation and
path integration skills that are commonly ascribed to rodents in spatial memory tasks. Disambiguating the two representations requires differentiating path-based from vector-based
strategies. The extensive branched mazes of Tolman (1948) among others were designed to
demonstrate path-based navigation, however such experiments failed to satisfactorily rule
out reactive navigation strategies (Jensen, 2006). Despite the lack of conclusive behavioural
evidence, electrophysiological data shows the existence of spatially selective cells in the hippocampus (O’Keefe and Dostrovsky, 1971). Beyond pure spatial selectivity, data also shows
that these cells are capable of firing in previously experienced sequences, suggestive of path
replay (Davidson et al., 2009).
1.2
Mechanisms of cognitive map development
An animal exploring an environment for the first time cannot yet know the connectivity
between locations in the environment, nor have an idea of the extent of the environment. To
construct such a connectivity map, the animal must be aware of its own location within its
developing map. The problem of constructing a map while tracking position is not specific
to animal navigation. In autonomous mobile agent research this problem is referred to as the
Simultaneous Localisation and Mapping (SLAM) problem, and is a fundamental challenge
for any agent wishing to build a flexible, reusable representation of a novel environment
1.3 Existing theories of cognitive map development
9
without access to an absolute positional ground truth.
Animal navigation research, and rodent hippocampal research in particular, has inspired
existing artificial SLAM implementations, and even resulted in the prediction of some biological phenomena (Milford et al., 2004). However these architectures do not replicate the
neural hardware in detail. Digitally-based algorithmic solutions to the SLAM problem separate the storage of the map from the processing that is required to create and use the map,
resulting in a single global map encoding to be used by any number of diverse update and access mechanisms. In contrast, by the nature of the hardware involved, a neural architecture
co-locates processing and memory in the same structure — the neurons and their connectivity — and thus any memories used for processing the current input to produce the current
behaviour must be reflected in the instantaneous behaviour of the local circuit. Mechanistically, these different underlying architectures have significantly different implementation
constraints, thus to computationally evaluate the processes underlying animal navigation a
neural simulation approach is required.
1.3
Existing theories of cognitive map development
The precise contribution of the hippocampus to spatial memory and navigation has been the
subject of many theories and models. Purely structural properties of the hippocampus have
led many (Marr, 1971; McNaughton and Morris, 1987; Treves and Rolls, 1992) to propose
that the dynamics of the region may function similarly to the attractor networks explored by
Hopfield (1982) (see §2.4.1). While some studies have demonstrated that certain dynamical
characteristics of hippocampal place cells are consistent with attractor dynamics (Wills et al.,
2005; Colgin et al., 2010), these observed characteristics are also consistent with the dynamics
of any system simultaneously performing pattern separation and completion (see §2.4.1).
Explicit electrophysiological evidence for attractor-like states in the hippocampus is lacking5
(Leutgeb et al., 2005).
Perhaps more significant than the specific network dynamics in the region is the question
of what information the hippocampus encodes. The clear correlation between the firing of
place cells and the current location (and further reinforced by the name ‘place cell’) results
in the almost universal assumption that the location in which it fires is what the cell ‘codes
for’ (for example, see the review of hippocampal models by Burgess (2007)).
5
Disambiguating attractor dynamics specifically would require evidence of activity in a single location
that began as an incomplete place code and without further external input converged to a more complete
place code (see §2.4.1 for further detail on attractor dynamics).
10
1.4
Introduction
Significant issues
Despite significant research into the neural basis of navigation, the mechanisms that endow
rats with their ability to outperform simple reactive navigation strategies remain unclear.
Although place cells provide evidence that the rat has the information with which to localise,
how this information is used in path planning is still an open question. The most common
theories claim that the localisation map encoded in the hippocampus is used offline, either
immediately prior to movement to find specific paths (Davidson et al., 2009), or to mirror
the map elsewhere over time (Johnson and Redish, 2005; Carr et al., 2011). No single theory
or model has explained how any such hypotheses may lead to a consistent explanation of
the available behavioural, lesion and electrophysiological data.
Biological neural networks are grounded in space through sensory perception, however
they are also grounded in time. Timing forms a fundamental component of learning and
memory, inseparable from the processes that form memories and modulate the system at
a multitude of scales, from neurotransmitter diffusion in the synaptic cleft to spike-timingdependent-plasticity (STDP). Relative timing is an additional dimension often ignored in
computational modelling studies and theories of network function. By considering the additional dimension provided by temporal coding, one can look beyond the simple spatial coding
assumption of place cells and question whether the observed dynamics are representative of
a more substantial role in spatial processing.
1.5
Contributions and thesis overview
The overall goal of this thesis is to demonstrate a biomimetic memory system that can
simultaneously perform localisation, path encoding and path retrieval, and that matches
behaviourally and electrophysiologically observed phenomena in the rodent hippocampus
during navigation. The brief navigation background above provides context for the remainder
of the thesis by differentiating the role of the cognitive map from other forms of navigationfacilitating memory.
Chapter 2 introduces background necessary to derive and model biologically-plausible
mechanisms for cognitive map development. This includes a brief overview of the basic
principles of neural modelling (§2.1) and the structure of the hippocampus (§2.2). The
chapter further introduces numerous dynamical properties of the hippocampus (§2.3) along
with existing theories of how such dynamics arise and how they may contribute to function
(§2.4).
1.5 Contributions and thesis overview
11
A theoretical framework for cognitive map development is developed in three parts. Chapter 3 introduces a theoretical role for spike timing in novelty detection, separating novel from
learned input stimuli. A computational model is presented that performs learning and recall
of individual memories in a single system without external cueing, using only feedforward
connections similar to hippocampal inputs.
Different conditions may require different thresholds for classification of novel stimuli.
In Chapter 4 the model is extended from the previous chapter to dynamically modulate
the balance between learning and recall. The chapter also introduces a potential synaptic
neuromodulatory process to prevent input noise from interfering with previously learned
memories without inhibiting recall.
Work to this point explains a mechanism capable of developing distinct, stable responses
to inputs, matching numerous properties of place cells. In Chapter 5 a theory is presented
to explain how the recurrent structure of the CA3 subregion of the hippocampus could
support cued sequence recall, and how such recall could represent paths while the dynamics
of individual cells exhibit place cell characteristics. This theory, if true, has significant
implications for the interpretation of place cell data, which is also discussed.
Computational models that are tightly inspired by and derived from the biology have the
potential to give rise to predictions regarding the underlying systems. The gold standard in
such studies is to produce a set of predictions that are unexplored or unexpected within the
prevailing framework. Chapter 6 contains an outline of a set of experiments and predictions
that arise from the computational perspective presented in this thesis.
In Chapter 7, I argue that the models and theories contained in the present work support
the claim that it is computationally feasible, with neurally plausible mechanisms, to perform
localisation and to learn and recall paths using only a subset of the hippocampal region and
its inputs. Further, I suggest that such an interpretation of existing data provides a unified
explanation for many observed hippocampal phenomena.
12
Introduction
2
Neural modelling and the hippocampus
There is much diversity in neuronal characteristics across the hippocampus. Understanding
firstly the range of this diversity and its functional significance is an important step to
unravelling the function of the hippocampus in its entirety. Furthermore, as the goal of
this project is to compare cell recordings as well as behaviour between animal and model,
an understanding of single cell dynamics is also a necessity. The following sections briefly
review basic neural modelling concepts, the structure and connectivity of the hippocampal
formation, and a number of significant functional proposals for the hippocampal regions1 .
Where appropriate, existing models will also be examined.
2.1
2.1.1
Single cell computation
Neuron structure and electrophysiology
The basic computational unit of the brain is the neuron (Ramon y Cajal, 1906). Morphologically, neurons consist of three broad sections, the cell body or soma, one or more
tree-branching structures called dendrites and another tree-branching structure known as
1
This chapter briefly covers some theory widely acknowledged as fact and some less well established
material. Any good neuroscience text such as Kandel et al. (2000) will provide more detail about the former
type of information, and can be referred to unless a statement in this section is specifically referenced.
13
14
Neural modelling and the hippocampus
the axon. As a general rule, the dendrites can be considered the input path to the neuron
and the axon the output. Across the mammalian brain, and even within the extent of the
hippocampal formation, there is a great diversity in the morphological characteristics of the
cells and their projections giving rise to numerous classifying labels. Two such labels of particular relevance to the hippocampus are pyramidal cells (so called for their conical-shaped
soma) and granule cells. These two morphological classes are believed to represent the primary projection neurons (those with far-reaching axons) of the hippocampus proper and the
dentate gyrus respectively. Spruston and McBain (2007) provide a comprehensive account
of properties specific to these and other hippocampal neurons.
Information is conveyed by a neuron through the generation of an action potential or
spike. An action potential is a short electrical pulse that travels the length of the axon.
The pulse is generated by the flow of ions into and out of a cell through passive voltagedependent channels on the membrane surface. Intra- and extra-cellular ion concentrations,
maintained by active pumps at the cell surface, create a potential difference across the cell
wall. At equilibrium, the voltage inside a neuron (Vm ) is generally about −70mV relative
to the extra-cellular environment. Perturbing a membrane potential a little has minimal
effect; the interaction of the ion channels restores the equilibrium. Forcing the membrane
voltage up beyond a certain threshold however initiates a cascade of positive feedback from
sodium ion (N a+) influx and produces the characteristic spike curve, generally bringing Vm
to above 30mV . After a short time the channels that initiated this cascade are inactivated
and the slower potassium ion (K+) channels open, causing an outward current and restoring
the membrane to its resting potential. Inactivation of both the sodium and potassium ion
channels after a spike generally results in a temporary desensitisation of the neuron called
the absolute refractory period, usually persisting for a few milliseconds, through which the
neuron cannot produce another action potential.
2.1.2
Modelling single cells
One of the foremost mathematical models of action potential dynamics is that of Hodgkin
and Huxley (1952). Probing and recording from a giant squid axon, the pair published
a set of four coupled differential equations with more than ten parameters modelling the
activity of three distinct types of ion channel. These equations correlate with electrophysiological recordings, allowing the replication of the many different types of spiking activity,
and provide biophysically meaningful parameters. Such models are computationally expensive however, requiring 1200 floating point operations to simulate a millisecond of a neuron’s
membrane dynamics (Izhikevich, 2004). Current consumer computing hardware would thus
15
2.1 Single cell computation
be limited to the simulation of tens to hundreds of neurons in real-time with HodgkinHuxley-type models; a severe restriction considering the CA3 region of the rat hippocampus
alone contains approximately 2.5 × 105 neurons (Amaral and Pierre, 2007).
Artificial spiking neuron models provide a solution to the computational tractability
problem. The leaky integrate and fire model uses a single equation to model the membrane
potential, requiring only four floating point operations for a millisecond of simulation, and
is solvable analytically (Izhikevich, 2004). With only a single variable however, each spike
is unavoidably independent of the next, thus the majority of cell spiking modes cannot be
replicated (e.g. a bursting neuron that takes some time to initially fire, but then continues
firing for a short time with little input). Izhikevich recently presented a model enabling
a more comprehensive set of spike responses that requires just two coupled differentials
requiring thirteen floating point operations per millisecond of simulation (Izhikevich, 2003,
2004). Two state variables are required for each neuron, the membrane potential v, and the
recovery current u. The rates of change v̇ and u̇ are given by
v̇ = 0.04v 2 + 5v + 140 − u + I
(2.1)
u̇ = a(bv − u)
(2.2)
with a reset condition
(
if v ≥ 30mV , then
v←c
u←u+d
(2.3)
where I is the sum of synaptic input currents, parameters a and b determine whether the
neuron is an integrator or a resonator and parameters c and d model the post-spike transient
behaviour due to high-threshold voltage-gated channel dynamics. There are shortcomings of
the model; it does not provide biophysically meaningful parameters, nor an approximation
of the curve between the peak spike potential and the floor of the post-spike hyperpolarisation, and it cannot be solved analytically. However with a fraction of the computational
overhead of the Hodgkin-Huxley model, this model provides a good approximation of many
documented spiking modes.
But why model the spikes at all? Historically, functional neural models have treated
neurons as transmitting their information through average firing rates, rather than considering each individual action potential a significant event. Frequency encoding underlies most
current communications technologies, thus the domain is well understood. Whilst frequency
coding is undoubtedly used in various capacities in the nervous system, and whilst frequency
analysis of electrophysiological recordings yields many information coding and behavioural
correlates, modelling purely in the frequency domain ignores any temporal significance of
16
Neural modelling and the hippocampus
precise spike timings. These relative spike timings are a potentially vast source of information in biological neural networks (Izhikevich et al., 2004; Izhikevich, 2005). A discussion
of how these timings may be established, however, first requires some discussion of neural
interactions.
2.1.3
Channels of communication
If the axon is the output of the neuron, where does the signal go? Neurons communicate with
each other at connection points, or synapses, generally between the axon of one neuron and
the dendrites of another. A single neuron can communicate with many thousands of other
neurons, and may have many synapses on each of these neurons. Synaptic characteristics
determine the nature of the connection, for example whether a presynaptic spike has an
excitatory or inhibitory effect on the postsynaptic neuron.
Action potentials provide a communication mechanism propagating down the axonal
branches to regions on the membrane surface termed active zones. At synapses, these active
zones form presynaptic terminals, which face postsynaptic terminals across a synaptic cleft.
Different neurons secrete different neurotransmitters in small spheres called vesicles, bound
to the membrane surface at the presynaptic terminals. Action potentials probabilistically
trigger the opening of the vesicles, releasing the neurotransmitter into the synaptic cleft
and providing the primary method of inter-neuron communication in the brain2 . The effect
of each neurotransmitter on the postsynaptic neuron is not constant between neurons, or
even necessarily between parts of a neuron; for each neurotransmitter there are numerous
receptors, each of which may produce profoundly different effects in the host neuron. Fast
inter-neuron communication occurs through postsynaptic receptors that mediate the opening
of channels that are selectively permeable to certain ions with the appropriate binding of
a neurotransmitter, making these channels ligand-gated as opposed to the voltage-gated
channels responsible for action potential propagation.
The magnitude of the postsynaptic effect of a presynaptic spike can be controlled by many
factors — the number of synapses, the number of receptors, the amount of neurotransmitter
released and the reuptake of the neurotransmitter are just a few — thus there is much
variability in the scale of postsynaptic responses. In the case of the pyramidal cells in CA3,
a single burst from an afferent granule cell of the dentate gyrus can be enough to cause the
cell to fire (Kullmann, 2007). Such strong connections are the exception rather than the rule
however, and generally the input of many temporally aligned presynaptic spikes is required
2
Direct electrical coupling between neurons is also present in the brain, however such synapses appear to
be a small minority.
17
2.1 Single cell computation
to effect a postsynaptic action potential.
2.1.4
Synaptic modelling
Unlike the active signal propagation in the axon of a neuron, dendrites are often modelled
as passive processes. Input integration thus occurs at the soma, and an action potential can
only be generated through a sufficient net increase of the soma potential. Not only are the
magnitudes of the synapses significant, but so too is their displacement from the soma on
the dendritic tree and the state of the separating dendritic cable. Hence to extract function
from neuroanatomical projections, the location of the synapses on the dendritic tree must
be considered.
Artificial spiking neural network models often summarise much of this synaptic complexity into a single weighted voltage increase applied directly to the postsynaptic neuron.
Such an approach is computationally efficient, however neglects potentially significant details
about the temporal proximity and duration of the events, for example:
• Presynaptic bursts will have the same postsynaptic effect for all spike occurrences.
In contrast, real synapses often show facilitation or depression at short time scales
(Markram et al., 1998).
• All postsynaptic effects are instantaneous and thus all signal integration happens at
only one time-scale, that of the membrane voltage dynamics. Electrophysiology studies show that different receptors enable currents at vastly different time-scales, some
lasting just a few milliseconds, others for hundreds of milliseconds (Dayan and Abbott,
2001).
In many circumstances these details may facilitate certain desired network behaviours.
The characteristics of certain common synapses and receptors are well described. As discussed by Dayan and Abbott (2001), the efficacy of any particular receptor type s in one
synapse can be modelled as the conductance gs by
gs = g¯s Ps Prel
(2.4)
where g¯s is the maximal conductance of that receptor type across the synapse with all channels open, Ps is the probability any particular channel is in the open state and Prel is the
probability of presynaptic transmitter release. In general a connection between two neurons
involves numerous receptors and synapses (determining the strength of the connection and
reflected by the maximal conductance variable), thus the probabilities translate to proportions, and the equation is representative of a single spike rather than temporally averaged
18
Neural modelling and the hippocampus
activity. Prel reflects the probabilistic nature of neurotransmitter release on any action potential, and is particularly significant for short-term synaptic plasticity.
The channel opening probability, Ps , is governed by the properties of a receptor. The
primary excitatory and inhibitory neurotransmitters in the mammalian brain are glutamate
and γ-aminobutyric acid (GABA) respectively. Glutamate principally binds to AMPA and
NMDA receptors, and GABA to GABAA and GABAB receptors. AMPA and the two GABA
receptors have similar properties; a presynaptic spike causes a short rise followed by the slow
decay in postsynaptic current. These receptor responses can be modelled for receptor s with
an alpha function Ps
Pmax t
exp(1 − t/τs )
(2.5)
Ps =
τs
where t is the time since the spike event and Pmax is the maximal value for Ps reached at
t = τs .
NMDA receptors are in fact both ligand- and voltage-gated. The voltage gating — Mg2+
ions bound to the receptors at membrane resting potentials — ensures that NMDA channels
are only highly conductive when a presynaptic action potential precedes a postsynaptic spike,
providing a synaptic ‘prediction’ signal. Adding an additional voltage-dependent variable
to Equation (2.4) provides this dual-dependence (equation from Jahr and Stevens (1990) in
Dayan and Abbott (2001))
gs = g¯s GNMDA (V )Ps Prel
[Mg2+ ]
GNMDA (V ) = (1 +
exp(−V /16.13mV )−1
3.57mM
(2.6)
(2.7)
where V is the membrane potential of the postsynaptic neuron at the synapse and the
extracellular concentration of Mg2+ is usually between 1 and 2 mM. These channels are
believed to play an early role in the long term synaptic modification processes discussed
below (Bi and Poo, 1998).
2.1.5
Prediction is learning
When an axon of cell A is near enough to excite cell B and repeatedly or persistently takes part in firing it, some growth process or metabolic change takes
place in one or both cells such that A’s efficiency, as one of the cells firing B, is
increased. (Donald Hebb, 1949)
Preceding the discovery of long term potentiation in the brain by more than fifteen years,
this famous quote from Hebb in his book The Organization of Behaviour (Hebb, 1949)
19
2.1 Single cell computation
Figure 2.1: An a. symmetric b. antisymmetric and c. asymmetric STDP learning window;
from Kepecs et al. (2002).
summarises his proposal that neural connections are strengthened by consistent causal firing
patterns, providing a mechanism for learning in the brain. Firm biological evidence for
this ‘Hebbian learning’ theory arrived almost 50 years later, in 1998, when Markram et al.
showed that presynaptic activity preceding a postsynaptic action potential in the granule
cells of the dentate gyrus causes a potentiation of the corresponding synapse (Markram et al.,
1997). This biological manifestation of Hebb’s postulate is known as spike timing dependent
plasticity, or STDP (Song et al., 2000).
A reasonable fit for synaptic modification data recorded from hippocampal cell cultures
over a range of pre-post synaptic activity intervals can be obtained with a model proposed
by Song et al. (2000). A function F (∆t) gives the magnitude of the synaptic change for any
particular pair of pre- and post-synaptic spikes with inter-spike interval ∆t
(
F (∆t) =
A+ exp(∆t/τ+ )
if ∆t < 0
−A− exp(∆t/τ− ) if ∆t ≥ 0
(2.8)
where A+ and A− determine the maximum amount of synaptic modification for positive and
negative ∆t respectively (on either side of t = 0) and τ+ and τ− determine the rates at which
the synaptic change declines from these maximums as the magnitude of ∆t increases. The
modelled window appears in Figure 2.1.
Applying this update rule to a synapse that predicted a postsynaptic action potential
with greater than A− /A+ probability would result in an unbounded weight growth. One
method of limiting growth is to assign a maximum synaptic weight, however there is little
experimentally observed support for such a facility. An alternate theory with greater biological plausibility proposes that the depotentiation resulting from a presynaptic spike following
a postsynaptic spike results in a depotentiation (depression) relative to the strength of the
synapse, whilst the reverse is a simple scalar additive operation (Kepecs et al., 2002). This
model also appears to agree with the more recent observation that potentiation is mediated
by processes on the postsynaptic cell whilst depression is mediated by presynaptic receptor
20
Neural modelling and the hippocampus
modifications (Rodriguez-Moreno and Paulsen, 2008).
For a single cell with numerous inputs, STDP increases the weights of all those synapses
that predict the cell’s firing. As the weights grow, fewer coincident inputs are required
to evoke a postsynaptic response, thus the postsynaptic action potential occurs with less
delay. Repetition of this process results in the weights of some number of the earliest
predictive inputs to increase and all other active input weights to decrease (Kepecs et al.,
2002). Network models with STDP synapses can learn precise temporal delays (Gerstner
et al., 1996) and activity sequences (Blum and Abbott, 1996). Pairing these abilities shows
that STDP also leads to the formation of neural groups that fire in precise spatio-temporal
patterns (Izhikevich et al., 2004).
2.1.6
Neuromodulation
Neurotransmission generally acts directly to excite or inhibit a postsynaptic cell, however
another class of receptor binds to modulatory molecules, or neuromodulators, to affect the
cell in other ways. Unlike the highly targeted release of glutamate or GABA at synapses as
discussed above, neuromodulatory transmission often spreads more diffusely. Much remains
unknown about the functional effects of the various neuromodulatory systems, however two
appear to be of particular significance for the operation of the hippocampus: acetylcholine
and dopamine.
Acetylcholine modulates learning in the hippocampus (Blokland et al., 1992; Hasselmo,
2006). Recurrent CA3 connections are directly attenuated in the presence of acetylcholine
(Vogt and Regehr, 2001), as are inputs to CA1 neurons from CA3 projections (Qian and
Saggau, 1997). Inhibitory interneuron activity in CA3 is increased due to cholinergic stimulation, which also leads to attenuation of dentate gyrus to CA3 synapses (Vogt and Regehr,
2001), however this indirect attenuation may be at a different time scale than the direct
recurrent synapse depression (see §2.3.1). Cells of the dentate gyrus are also affected, with
the modulator increasing the activity of dentate granule neurons (Vogt and Regehr, 2001).
The primary source of acetylcholine for the CA subfields and for the dentate gyrus is the
medial septal nucleus (Amaral and Pierre, 2007). Blocking the corresponding modulatory
receptors may thus impair memory formation by disabling the input selectivity of the region
and increasing noise.
Like acetylcholine, dopamine is believed to play a role in hippocampal plasticity. Early
long term potentiation (E-LTP) in CA1 is facilitated by NMDA receptors, however dopamine
appears to modulate this process (Lisman and Grace, 2005). Furthermore, the stability of
this potentiation over a longer time frame (late LTP or L-LTP) requires dopamine (Lisman
2.2 Structure of the hippocampus
21
and Grace, 2005; Pawlak and Kerr, 2008; Bliss et al., 2007). Dopaminergic innervation of the
hippocampus comes primarily from the ventral tegmental area and the substantia nigra, two
regions responsible for much of the brain’s dopamine (Amaral and Pierre, 2007). Activity in
these areas significantly increases in response to unpredicted reward and reward-predicting
stimuli, but not to known but non-rewarded stimuli (Schultz, 2002). This activity does
appear to translate to an increase in concentration of the neuromodulator in at least one
target area of these dopaminergic neurons, the nucleus accumbens of the rat (Day et al.,
2007). Thus with dopamine release modulated by unpredictable reward, and CA1 learning
rates modulated by dopamine, it seems likely that the presence of novel reward-predicting
stimuli increases CA1 plasticity.
2.2
Structure of the hippocampus
Anatomical structure provides a starting point for exploring the potential mechanisms underlying brain function. In Rhythms of the Brain, Buzsáki makes the assertion that without
a wiring diagram of the brain — in addition to an understanding of the operation of its
units — its function cannot be completely understood (Buzsaki, 2006). But what level of
detail is required of this wiring diagram to render a function tractable? With neural variation between individuals, one can assume there is a set of guiding principles, but not exact
templates, for wiring patterns between certain neurons. These principles are yet unknown.
One approach to building a model that replicates the function of a circuit is by beginning
with a gross anatomical model and adding detail as necessary to add function or to provide
additional control. This section will outline the gross hippocampal structure, and leave more
specific details to be described as required in a more functional context.
Unlike its densely recurrent cortical neighbours, the sub-regions of the hippocampal complex (depicted in Figure 2.2) are connected largely unidirectionally in an excitatory loop (see
Figure 2.3) (Amaral and Pierre, 2007). The flow of this information begins in the entorhinal
cortex, passing through the dentate gyrus, through the cornu ammonis sub-fields (CA3 to
CA1) to the subiculum and finally back to the entorhinal cortex. There are shorter paths
within this loop; the entorhinal cortex has efferent projections not just to the dentate gyrus,
but also to regions CA3 and CA1 via an axonal fibre bundle termed the perforant path. The
region CA1 also projects to the entorhinal cortex, targeting similar areas to those projections
with their origins in the subiculum. Although the subiculum forms a major output region
of the hippocampus, only the shorter entorhinal–dentate gyrus–CA3–CA1–entorhinal loop
is examined in this project. Each of these regions is discussed briefly below.
22
Neural modelling and the hippocampus
Figure 2.2: A depiction of the rat hippocampal formation, with coronal slices showing crosssections of the hippocampus. Image from Witter et al. (2004).
2.2.1
Entorhinal cortex
The entorhinal cortex can be considered the gateway to the hippocampus, as its projections
both through the dentate gyrus and directly to CA3 and CA1 form the majority of the
excitatory inputs to the structure. Similar to the cellular structure of much of the isocortex,
a six-layer scheme is generally applied to this region. Dentate gyrus and CA3 inputs arise
from the same layer II projections, whilst the fibres from layer III neurons primarily terminate
amongst the dendritic processes of CA1 and subicular cells (Amaral and Pierre, 2007). The
deeper layers V and VI provide extensive outputs to other cortical and subcortical areas,
they provide feedback to the superficial layers II and III of the entorhinal cortex and they
may innervate the hippocampus, although hippocampal connections are not as clear as those
of the superficial layers. Beyond this laminar structure, the entorhinal cortex also appears
to have two distinct subdivisions, lateral and medial (Amaral and Pierre, 2007).
2.2.2
Dentate gyrus
The rat dentate gyrus is comprised of approximately 1.2 × 106 neurons (Amaral and Pierre,
2007). Whilst this population contains numerous cell types, only the dentate granule cell
projects outside the dentate gyrus (making it the only ‘principal’ cell). Current evidence
23
2.2 Structure of the hippocampus
2
3
5EC
EC
EC
Perforant path
DG
h
Perforant path
t pa t
Perforan
Subiculum
Hilus
CA3
CA1
Excitatory
Septal
nuclei
Modulatory
Figure 2.3: Block model of the hippocampal loop. Excitatory connections use glutamate
as a neurotransmitter. Although unmarked, all regions also have inhibitory interneurons. The
modulatory septal connections consist of both cholinergic and GABAergic fibres.
suggests that these cells have anywhere from 3600 to 5600 dendritic synapses, and that
synapses closest to the cell bodies are most likely internal projections, followed more distally
by projections from the medial entorhinal cortex and finally by lateral entorhinal projections
(Spruston and McBain, 2007). Axons from these cells provide inputs to the hilus (a region
between the dentate gyrus and CA3) and terminate in CA3. Connections from dentate
granule fibres to the mossy cells of the hilus and to CA3 pyramidal cells have a low release
probability, but can be strong enough to exact a postsynaptic action potential with just
a single synaptic activation. Each dentate granule axon contributes such connections to
approximately 14 CA3 pyramidal cells (Claiborne et al., 1986), making the projections highly
targeted. Smaller and more reliable contributions from the dentate granule cells synapse on
24
Neural modelling and the hippocampus
inhibitory interneurons in both the hilus and CA3.
2.2.3
CA3
Pyramidal cells of CA3 form a recurrently excitatory network in the hippocampus. Each
pyramidal cell receives connections from an estimated 1.2 × 104 amongst a total of 2.5 × 105
other glutamatergic CA3 pyramidal cells (Amaral et al., 1990). This connection distribution
ensures that whilst the direct connection probability is only about 5%, the average shortest
path between any two neurons, assuming there is no strong connectivity bias, is via just one
other cell (Buzsaki, 2006). Connection probabilities do however vary across the axis extending from the dentate gyrus (proximal) to the CA3/CA2 border (distal) — the transverse axis
— with proximal cells projecting only to other proximal cells but cells in the more mid or
distal extent projecting across the entire axis (Amaral and Pierre, 2007). The proximal cells
are also innervated more heavily by the cells of the dentate gyrus than those more distally
located, whilst the opposite gradient applies to entorhinal inputs. Averaged across the whole
region, each pyramidal cell receives 3750 excitatory entorhinal inputs yet only 46 dentate
granule cell connections. It is unclear to what extent the spatially biased connectivity affects
the mean shortest path.
Examination of the distribution of synapses on the dendritic tree of CA3 pyramidal
neurons shows a clear ordering to the input. Dentate granule neurons provide synapses very
close to the soma, and distal from the soma to these synapses are the recurrent synapses from
other CA3 cells (Amaral and Pierre, 2007). Entorhinal cortex projections via the perforant
path terminate most distally from the soma in a similar pattern as in the dentate gyrus;
medial then lateral (Amaral and Pierre, 2007). The reliability of this input ordering across
the region suggests that it has some functional significance.
The only major output from CA3/CA2 is via the Schaffer collaterals to CA1. Some of
these fibres also project to the lateral septal nucleus (Amaral and Pierre, 2007).
2.2.4
CA1
With few traces of the excitatory recurrence that so characterises the CA3 network, the
slightly larger CA1 region comprised of 4 × 105 neurons receives heavy innervation from
both CA3 and from the entorhinal cortex (Amaral and Pierre, 2007). Inputs via the Schaffer
collaterals terminate in an inverted pattern on the transverse axis with respect to their point
of origin; proximal CA3 cells project to distal CA1 cells, and distal CA3 cells to proximal
CA1 cells. Entorhinal input via the perforant path — originating from layer III rather than
layer II as in the dentate gyrus and CA3 — also differentiates across this axis with medial
2.3 Properties of the hippocampal formation
25
entorhinal input terminating proximally and the lateral entorhinal projections terminating
distally. Unlike the distinct separation of inputs in the dentate gyrus and CA3 dendritic
trees, the CA1 inputs do not appear to organise in dendritic layers.
Extrinsic connections from CA1 are primarily to the subiculum and to the deeper layers
(V and VI) of the entorhinal cortex. The latter connections are organised in a spatially
reciprocal fashion to the input to the entorhinal regions; proximal to medial and distal to
lateral. Finally, principal cells of CA1, like those of CA3, project to the lateral septal nucleus.
2.3
2.3.1
Properties of the hippocampal formation
Theta rhythm
One pronounced characteristic of hippocampal neurons is the oscillatory cell firing that
occurs in the frequency range of 4–12 Hz. Since Jung and Kornmuller (1938) provided evidence of this oscillation in the rabbit, its electrophysiological basis has been the topic of
much research, as has its possible functional role. Vanderwolf contributed correlations between behavioural data and coarse electroencephalographic (EEG) recordings showing the
rhythm (Vanderwolf, 1969). He continued with Kramis and Bland to show that this oscillatory activity in fact consists of two components, a faster (7–12 Hz) movement-correlated
rhythm and a slower (4–7 Hz) arousal-dependent rhythm (Kramis et al., 1975). The two
components can be separated both behaviourally and chemically, the latter through the application of drugs that affect cholinergic synapses. Evidence implicates the slower rhythm
in attentional processes; it is observed when rats are placed in novel environments but not
in known environments. Decreasing the sensitivity of the CA3 region to neuromodulation
by acetylcholine3 attenuates or eradicates this component of the rhythm entirely (Villarreal
et al., 2007; Buzsaki, 2002). It is often referred to as type 2 theta (Kramis et al., 1975)
or a-theta (O’Keefe, 2007). The faster component of the rhythm is correlated in rats with
movements that modify the position of the head with respect to the environment (thus including both translation and rotation). Whilst this component is unaffected by acetylcholine
receptor antagonists4 , there is some evidence that it depends on both serotonin modulation
and extrinsic excitatory glutamateric afferent projections (O’Keefe, 2007). This faster theta
is referred to as type 1 theta (Kramis et al., 1975) or t-theta (O’Keefe, 2007).
What are the sources of this oscillatory activity? Evidence clearly shows that both the
3
by application of atropine that selectively blocks muscarinic receptors (one of two broad types of acetylcholine receptor, the other being the nicotinic receptor)
4
both muscarinic and nicotinic
26
Neural modelling and the hippocampus
medial septum-diagonal band of Broca (MS-DBB) and the supra-mammillary region are
critical for theta generation, as lesions of either of the regions eradicates theta oscillations
across all cortical areas (Buzsaki, 2002; Thinschmidt et al., 1995). These regions project both
directly to the hippocampus and to the entorhinal cortex via cholinergic and GABAergic
fibres. In vivo recordings of these regions shows periodic activity phase-locked with the global
theta rhythm signal from the hippocampus (Stewart and Fox, 1990). Whilst muscarinic
receptors5 in the hippocampus act too slowly to function alone as a generator of theta rhythm,
their activation results in a general depolarisation of both pyramidal cells and inhibitory
interneurons (Cole and Nicoll, 1983; Hasselmo and Fehlau, 2001). In concert with this slow
pyramidal cell depolarisation, the GABAergic input to the local interneurons disinhibits the
pyramidal neurons and allows excitatory input to increase activity across the region on a
shorter timescale (Hasselmo and Fehlau, 2001). If the entorhinal cortex is lesioned, theta
rhythm is still observed in the hippocampus, however that which remains is both atropine
sensitive and dependent on the recurrent CA3 network (Buzsaki, 2002). When slices of CA3
are extracted and observed in a solution containing a muscarinic agonist, bursts of activity at
theta frequencies are observed (Konopacki et al., 1988). These observations suggest that type
1 theta is a result of extrinsic excitation from the entorhinal cortex, and that type 2 theta
is intrinsically generated through the interaction of periodic septo-hippocampal projections
with the internally recurrent CA3 network.
The hippocampus is strongly implicated in memory function (see §2.4), thus it is of little
surprise that the role of theta activity has also been linked to the acquisition of memories. There has been evidence for some time that the extrinsic perforant path and intrinsic
recurrent inputs to CA3 pyramidal cells are differentially attenuated through theta phase
(Hasselmo et al., 1995; Vogt and Regehr, 2001). Models have proposed functional roles for
such modulation, often to separate encoding and retrieval of memory sequences (Hasselmo
et al., 2002a). More recently this differential attenuation has been shown to be active only in
novel environments and subject to inactivation with the application of atropine (Villarreal
et al., 2007). It thus seems plausible that the phase-dependent efficacy changes are in fact a
function of type 2 theta and are required for memory formation, but not for memory retrieval
in a known environment.
2.3.2
Place cells
One of the most prominent electrophysiologically observed properties of the hippocampus
is the spatial selectivity shown by some cells (O’Keefe and Dostrovsky, 1971). Section 1.1.4
5
or more specifically muscarinic M1 receptors (Buzsaki, 2002)
2.3 Properties of the hippocampal formation
27
Figure 2.4: An example field of one place cell on a linear track. a. The experimental setup. b.
The firing field averaged over multiple eastward runs, colour coded for frequency. In the periphery
of the field the response is weak, gradually increasing towards the centre of the field. c. Firings of
the same cell over a single eastward run, plotted above the simultaneously recorded EEG. The EEG
signal shows prominent theta-frequency oscillations, and the place cell exhibits bursting behaviour
at approximately this frequency. Adapted from Huxter et al. (2003).
introduced the concept that rodents build a connectivity map of their environment. Initial
evidence for this map came from recordings of CA1 complex-spike cells (i.e. those that fire
non-rhythmically) showing a correlation between the location of animals on a linear track
and the firing rate of the cells. Across the majority of the environment the activity of these
cells is low. As the animal approaches a particular point in the environment — a different
point for each cell — the firing rate of that cell rises. O’Keefe termed such cells place cells
and the locations in which they displayed an elevated firing rate their place field (O’Keefe
and Dostrovsky, 1971).
The typical response of a place cell in its firing field is one of rhythmic bursting, as
shown in Figure 2.4. As an animal approaches the centre of the place field, the strength
of each burst typically increases and as the animal moves away from the centre the burst
strength typically decreases. There is no absolute strength value (on each pass through
the field the average firing rate may be different), however the burst magnitude peak and
bidirectional falloff is a robust phenomenon (Huxter et al., 2003). The inter-burst frequency
approximately matches that of the population-based theta rhythm.
Many studies are devoted to the observation and analysis of these place cells (see Redish
(1999) and O’Keefe (2007) for review). This section attempts to summarise some of the
28
Neural modelling and the hippocampus
interesting points most relevant to the methods by which cells might acquire place fields and
thereafter be used for goal-directed navigation. Unless otherwise documented, the referenced
experiments were performed in the CA1 region.
Place fields can be directional or non-directional
When an animal predominantly approaches a location from a limited set of directions the
corresponding CA1 place fields tend to be directional, firing only when the animal approaches
with the same trajectory. This effect is quite clear on a linear track (O’Keefe and Recce,
1993). Conversely, in open field environments where each location can be reached from any
direction a majority of place cells exhibit omni-directional firing (Muller et al., 1994; Huxter
et al., 2008). One might question, does the same process underlie the development of all
these fields, or are some cells predisposed to being uni- and others multi-directional, either
universally or in a context-dependent manner?
Radial arm mazes — mazes with thin arms extending radially from a central chamber
— evoke both directional and non-directional responses (McNaughton et al., 1983; Muller
et al., 1994). Muller found one cell amongst the 11 he isolated that responded with unique
place fields in two different arms (Figure 2.5). This cell was responsive only when the rat
was travelling away from the centre for one of the fields, whilst responding invariantly with
direction for the other, showing that cells can be conditioned simultaneously as direction
sensitive and insensitive (Muller et al., 1994). Whether unidirectional cells conditionally
acquire direction insensitivity after repeated exposure to a field from many directions, or
whether omni-directional cells develop directly as such is as yet unknown (O’Keefe, 2007).
Place fields are learned and refined
There is little consensus on the spatial selectivity of complex-spike cells in a novel environment. One example in Figure 2.6 shows the firing characteristics of a CA1 pyramidal cell in
a novel two-dimensional environment, showing a clear growth in firing field activity over the
20 minutes of exposure. Other evidence suggests both that strong place fields are present
immediately in a new environment, or take anywhere from a few minutes to four hours to
develop (Redish, 1999; O’Keefe, 2007). It is plausible that these disagreements are merely
due to different environmental or experimental conditions. Tanila et al. (1997) observed that
cells appear to develop and refine fields at vastly different rates, thus place fields may be
developing over numerous time scales simultaneously.
The place field of Figure 2.4 appears to be elongated, exhibiting a longer and slower
rate increase upon entering the field than the firing rate decrease upon leaving. Mehta
2.3 Properties of the hippocampal formation
29
Figure 2.5: One cell from a radial arm maze exhibiting two firing fields. Any single cell does not
necessarily have uni-directional or omni-directional fields, the cell here has one direction-sensitive
field (northern arm) and one direction-insensitive field (south-eastern arm). Darker colours indicate
increasing activity. Taken from Muller et al. (1994).
and colleagues examined this effect in two linear track analyses in a familiar environment,
showing firstly that CA1 place fields asymmetrically expand due to experience by lengthening
in the opposite direction to motion (Mehta et al., 1997), and secondly that this expansion
also introduces a negative skew to the field such that the firing rate upon entry to the
field is low and the firing rate upon exit from the field is high (Mehta et al., 2000). This
work was performed over multiple sessions in trained rats, thus it is of considerable note
that these fields began each session without observable asymmetries. Why would a healthy
animal relearn the same information every trial — because it is uninteresting and thus
forgettable, because the CA1 network is being used only temporarily and the persistent
memory is elsewhere, or even because it is a side-effect of a phylogenetically uncharacteristic
environment?
30
Neural modelling and the hippocampus
Figure 2.6: Development of a two-dimensional place field in a novel environment in an experiment from Wilson and McNaughton (1993), demonstrating that firing field activity increases
with exposure to the environment. Each panel represents averaged cell activity through one of four
different experimental phases, represented in ascending order from left to right. In the first and
fourth phases the rat was blocked from visiting or seeing the bottom half of the field. During the
second and third phases, both 10 minutes long, the animal was given free access to the entire arena.
Colour code from low to high activity: blue, green, yellow, red.
The field expansion effect was subsequently corroborated and extended showing that
whilst expansion occurs in CA1 in a known environment, modifying the environment significantly increases expansion (Lee et al., 2004). The same experiment produced trial-by-trial
skewness adjustments in CA1 only under a modified environment (Lee et al., 2004).
Place field remapping describes the modification of a place code under environmental
manipulation. Bostock et al. (1991) demonstrated that by replacing significant cues in
known environments, the place code in the modified environment eventually diverges from
the place code in the original environment.
Place fields come in many sizes
Evidence suggests that the size of places fields varies on a gradient over the septo-temporal
extent of the hippocampus, beginning small at the septal end (dorsal hippocampus) and
growing towards the temporal extent (ventral hippocampus)6 (O’Keefe, 2007). Recent data
suggests that place fields in the ventral hippocampus of the rodent have a limit of approximately 10 metres, however this has yet to be confirmed in other environments and under
alternative task conditions (Kjelstrup et al., 2008).
Particularly interesting are two anatomically significant variations corresponding to the
size differences along the dorso-ventral axis. The first of these is an increase in packing
6
This axis is referred in this work as both the septo-temporal axis and the dorso-ventral axis. When
referring to computational theory, the term septo-temporal axis is used predominantly, as it is a more fitting
description of the length-wise axis that would result if the hippocampus were ‘unwound’ from its seahorse or
horn-like shape. The dorso-ventral axis is often used for anatomical and electrophysiological work in which
stereotaxic coordinates are required.
2.3 Properties of the hippocampal formation
31
density of CA3 pyramidal cells and a decrease in dentate granule cell density, together
changing the cell ratio between these interconnected regions from approximately 12 : 1 to
2 : 3 at the septal and temporal poles respectively (Amaral and Pierre, 2007). The second is a
connectivity bias amongst the CA3 recurrent connections, resulting in the average recurrent
projection being directed ventro-proximally (Amaral and Pierre, 2007).
Place cell activity precesses in theta phase during firing field traversal
As a rodent actively traverses the field of a place cell, the cell bursts at a frequency slightly
higher than the theta rhythm of the surrounding population. Temporally this observation
manifests itself as a precession of the exact timing of the cell’s firing with respect to the
local theta oscillations. O’Keefe and Recce first observed this phase precession in 1993 on
a linear track (O’Keefe and Recce, 1993) and the effect was verified and extended to open
field environments by Skaggs et al. (1996). On the linear track there is a strong correlation
between the animal’s location within the place field and the phase at which the cell is
spiking (Huxter et al., 2003; Dragoi and Buzsaki, 2006). This effect is also observed, albeit
less obviously, in an open field environment (Skaggs et al., 1996; Huxter et al., 2008).
Phase variance is greater at the end of a place field traversal when averaged over multiple
runs, however during any given run phase precession is evident (Huxter et al., 2003). This
variance does however result in a lesser (though still significant) correlation between phase
and position in the portion of the place field beyond the burst frequency peak (early in theta)
when compared to the correlation earlier in the field (late in theta) (Dragoi and Buzsaki,
2006).
Observation of phase precession in cells with overlapping place fields leads to a prediction of temporal ordering of place cell firing (see Figure 2.7). Recent studies have sought
to extricate a causal relationship between place cell firings from recordings of many such
cells to establish whether phase precession is a result only of afferent variation (the ‘pacemaker’ model) or whether sequences are explicitly encoded in the network (the ‘coordinated
assembly’ model) (Dragoi and Buzsaki, 2006; Foster and Wilson, 2007). Dragoi and Buzsáki
inferred causality by showing covariance in firing rates between certain cells within each theta
cycle, and the lack of such covariance between others, declaring such pairs dependent and
independent respectively (Dragoi and Buzsaki, 2006). Separating by this classification, they
showed that dependent pairs exhibit a greater spatial-temporal correlation than independent
pairs.
32
Neural modelling and the hippocampus
Figure 2.7: Firing rate (top) and phase (bottom) vs. distance along track of five cells (colour
coded) with overlapping place fields. Phase plot lines are linear regression slopes, suggesting that
firing order is well maintained throughout field progression. Adapted from Dragoi and Buzsaki
(2006).
Place cells have varying characteristics between CA3 and CA1
Place cell activity is predominantly recorded in the CA1 region, however some recent papers
document the activity differences between CA1 and CA3 neurons. In one such account,
Dragoi and Buzsáki show that place fields on a linear track are less directional in CA3
than in CA1 (Dragoi and Buzsaki, 2006). Leutgeb and colleagues examined the differences
in CA1 and CA3 place representations in different environments by comparing the overlap
between the population of active cells in each environment (Leutgeb et al., 2004). They
found that that the overlap in CA1 place cell populations is dependent on the similarity of
environments, whereas place cell populations in CA3 overlap only as expected by chance,
irrespective of cue similarities. Lee et al. studied changes in place fields on a linear track due
to distal cue changes (Lee et al., 2004). Their results show that persistent centre-of-mass
changes occur in place fields in the opposite direction to motion, however that these changes
take place over different time scales in CA1 and CA3. Place fields of cells in CA3 begin
to shift immediately and become stable quickly. CA1 fields begin to change more slowly
and continue to change over a longer period, eventually stabilising with approximately the
same total shift as the CA3 cells. Conversely, there is also evidence showing that in novel
environments, place representations stabilise more quickly in CA1 than in CA3 (Leutgeb
et al., 2004). Much remains unclear about the precise differences in place field development
2.3 Properties of the hippocampal formation
33
between these two regions, however it does seem likely that their roles are distinct.
Place cells are not restricted to CA3 and CA1
Early place cell recordings found the units in both CA3 and CA1 (O’Keefe and Dostrovsky,
1971; O’Keefe and Nadel, 1978). Subsequent experimentation showed cells with place fields
outside these CA fields, including the subiculum (Sharp and Green, 1994) and the dentate
gyrus (Jung and McNaughton, 1993). These extra-hippocampal place cells can however be
differentiated from the observed hippocampal cells. Place fields of subicular cells are in
general larger than those in the hippocampus proper and more often show multiple firing
rate peaks within a single environment (Sharp and Green, 1994). Dentate gyrus place cells
also show multiple firing rate peaks within a single environment, however exhibit on average
smaller place fields than other regions (Jung and McNaughton, 1993; Leutgeb et al., 2007).
Most complex spike cells in CA3 and CA1 have place fields
Analysing the proportion of recorded cells that are active in one of a number of test environments with the lesser proportion that are active in many of the environments suggests that
most complex spike cells of the hippocampus will display spatial selectivity (O’Keefe, 2007).
Whilst complex-spiking hippocampal cells can have multiple place fields in a single environment, current estimates suggest that only 5 − 10% of cells show such responses (O’Keefe,
2007).
2.3.3
Grid cells
Place cells, as noted above, generally fire in a single location in any particular environment,
thus their firing is non-metric: they make no determination about the dimensionality of
the space that they represent. In contrast, Hafting et al. (2005) have shown clear evidence
of a two-dimensional map centred in the medial entorhinal cortex. In small environments,
cells in this region appear to display characteristics indicative of place cells. However when
Hafting and colleagues tested similar cells in environments of up to two metres in diameter,
they found that these cells have a triangular tessellated firing field, as in Figure 2.8, and
termed these grid cells. Their data showed that spatially proximal cells shared a common
orientation, field size and field spacing, but varied freely in vertex location. It also showed
that the grid cell field size and spacing co-varied, increasing along the dorsoventral axis, and
that orientation varied over the entire 60◦ range without any discernible pattern.
Layer II of the dorsomedial entorhinal cortex contributes input to the dentate gyrus and
CA3, thus grid cells provide the hippocampus with a two-dimensional spatially grounded
34
Neural modelling and the hippocampus
Figure 2.8: Plots of paths and corresponding cell activity (left) and average firing rates (right)
of three cells in the dorsomedial entorhinal cortex of the rat. Regularly spaced firing fields form a
triangular tessellation across the environment. Adapted from Hafting et al. (2005).
signal. But does the hippocampus provide feedback to the grid cell network? Evidence from
the initial report suggests that grid cells are sensitive to orienting sensory cues: in a known
environment if such cues are rotated the grid cell response likewise rotates. Although some
place cells in the hippocampus are orientation-sensitive, the grid-cell network also receives
information from orientation-carrying regions in the postsubiculum and parahippocampal
structures (Taube et al., 1990; van Groen and Wyss, 1990; Amaral and Pierre, 2007). Furthermore, allothetic information is not required for the operation of the cells, as vestibular
information appears to maintain grid cell firing even in the dark despite a decrease in spatial
correlation of the grid fields (Hafting et al., 2005). More recent evidence shows that grid cells
have a non-contiguous representation across certain boundaries, such as between different
rooms, thus a contextual ‘reset’ cue in such situations may be provided by hippocampal
place cell activation (Hafting et al., 2005; Fyhn et al., 2007). Empirical results are yet to
show which regions are required to maintain normal grid cell orienting behaviour.
2.3.4
Non-spatial hippocampal inputs
Compared to the medial entorhinal cortex, little is known about the behavioural correlations
of lateral entorhinal cortex activity. Unlike the strong spatial selectivity present in the
grid cells in mEC, the activity of lEC cells has little correlation to position (Hargreaves
et al., 2005), even in cue-rich environments (Yoganarasimha et al., 2010). One theory of
the information encoded by lEC cells is that they form the end of a pathway from the
perirhinal cortex representing object identity (the ‘what’ pathway). The lEC may therefore
be providing the hippocampus with non-spatial information regarding individual items or
sets of items in an environment (Yoganarasimha et al., 2010). In support of this hypothesis,
2.4 Theories and models of hippocampal function
35
Deshmukh and Knierim (2011) have shown that lEC cells are significantly more responsive
to objects than mEC cells. Such object-sensitive cells could explain the conjunctive objectplace coding evident in the hippocampus (Manns and Eichenbaum, 2009; Komorowski et al.,
2009).
2.4
Theories and models of hippocampal function
Thus far this chapter has examined the anatomical and electrophysiological properties of
the hippocampus, and their correlates with behaviour. The current section will introduce
existing theories of hippocampal function, focusing on how hippocampal cells develop their
behavioural correlates, why such properties are useful and what function they may facilitate.
2.4.1
Dynamics of hippocampal information storage
One approach to gaining a better understanding of place cells has been to understand what
computations are theoretically required to produce their characteristics. The resulting class
of model does not aim to produce predictions regarding the structure or dynamics of specific
elements of the neural systems, but rather attempts to concern itself solely with the relationship between the inputs and the outputs of the system: how modification of the input
modifies the output, and what the relative significance of the input elements are given such
modifications (Zipser, 1985).
Returning again to Braitenberg’s law of ‘uphill analysis and downhill invention’, this
approach is tractable for sufficiently simple systems. As complexity increases and the number
of possible input-output states increases, the approach rapidly becomes more difficult to
analyse. By employing knowledge of how neural structures and dynamics affect computation,
anatomical and electrophysiological data provide constraints with which to further limit
the range of possible implementations. The following sections summarise the predominant
theories of such hippocampal dynamics, and how they may result in the observed correlations
with space.
Numerous place field characteristics can be demonstrated using solely the feedforward
connectivity of the hippocampal circuitry: stability under cue removal, field rotation, partial
remapping (Bostock et al., 1991) and field scaling (Sharp, 1991) to name a few. One hypothesis of particular note — derived from models of the feedforward input to CA3 — is that
these connections can explain observations that hippocampal place fields are uni-directional
in linear track-like environments and omni-directional in open fields. Sharp (1991) suggested that all fields begin uni-directionally, paired with particular sensory snapshots, and
36
Neural modelling and the hippocampus
that when a location is observed only in two orientations 180 degrees offset, then the sensory
snapshots are sufficiently different to evoke different place cell responses. However in a two
dimensional environment, where all orientations are available, the smaller average sensory
differences between these orientations create a ‘cluster’ of view responses for that location,
most sharing much greater similarity than in the 180 degree case, resulting in one place cell
being likely to respond to many different orientations.
Again using the remapping of place fields as evidence, Barry et al. (2006) proposed
that place fields could arise via conjunctive activation from input cells tuned to respond
preferentially to the barriers within and surrounding an environment. Their model posits
the existance of ‘boundary vector cells’ (BVCs) upstream of the hippocampus, each such
cell having a Gaussian response peaked at a particular distance and allocentric direction
from a barrier. While each BVC would respond along the extent of a barrier, and along
other similarly aligned barriers, the conjunctive activation of BVCs responding to barriers at
different distances and orientations could provide place cells with the input necessary to evoke
their characteristic spatial fields. Barry et al. demonstrate that the BVC model is consistent
with data showing the remapping of place fields due to geometric environmental deformation,
environmental expansions and the insertion and removal of barriers within an environment.
Although directly downstream of hippocampal CA fields, evidence suggests that the dorsal
subiculum contains cells with BVC-like characteristics (Barry et al., 2006; Lever et al., 2009).
How these subicular cells may contribute to the formation and maintenance of place fields
remains an open question.
Pattern separation and completion
Place cells in the rodent hippocampus acquire their characteristic spatial selectivity during
initial exploration of an unknown environment (see §2.3.2). Within a single environment,
these cells develop fields that individually select only a fraction of the space, but together
cover the whole space, despite potentially sharing a large number of sensory cues. Once
learned however, place fields can remain stable even during significant cue removal. That is,
with respect to allothetic cues, the cells can be both highly discriminatory during learning yet
robust to variation in a known environment. Extending this evidence to the cell population,
one might expect that during learning, as two sensory snapshots diverge in similarity, the
similarity of the place cell codes — the set of place cells responding for each location —
diverges more rapidly (Figure 2.9, left). During recall the inverse seems likely: as two
sensory snapshots diverge in similarity, the similarity of the place cell codes diverges less
rapidly (Figure 2.9, middle). The former condition is known as pattern separation, the
2.4 Theories and models of hippocampal function
37
Figure 2.9: Pattern separation and completion. Each graph shows a transfer function from
input (x-axis) to output (y-axis). Each axis measures the similarity of a pattern to a reference
pattern. The y=x line (dotted) shows when the output similarity would be the same as the input
similarity. When the transfer function (solid line) is below the y=x line, then output patterns will
be less similar than their input patterns (separation). When the transfer function is above the y=x
line, then output patterns will be more similar than their input patterns (completion). The left
graph shows a pattern separation function, the middle graph a pattern completion function, and
the right graph shows a combination of both, with a similarity measure of 0.5 in the input set as
the threshold required to switch from pattern separation to completion.
latter as pattern completion.
Pattern separation and completion in neural systems have been the subject of many
theoretical and computational modeling studies (Fuhs and Touretzky, 2000; Hopfield, 1982;
Marr, 1971; McNaughton and Morris, 1987; McClelland et al., 1995; O’Reilly and McClelland, 1994; Rolls, 1996; Treves and Rolls, 1992). Many of these theoretical models are similar
in network structure to that of the hippocampus, some by design (Marr, 1971; McNaughton
and Morris, 1987; Rolls, 1996; Treves and Rolls, 1992) and others seemingly by chance (Hopfield, 1982). This similarity, along with the observations that the hippocampus appears to
be required for episodic memory formation in humans (Scoville and Milner, 1957) and for
complex spatial memory tasks (locale navigation) in animals (Morris, 2007), supports the
hypothesis that the region may be performing separation and completion.
Modelling studies show how pattern separation and completion can account for the various properties of place cells. A simple network, involving only feedforward connections from
the entorhinal cortex to the hippocampus, demonstrates that such a structure can act as a
pattern classifier (Sharp, 1991). With appropriate assumptions regarding sensory and idiothetic input, the spatial rate responses of individual place units learned by such a model
provide a reasonable approximation to those of real place cells: fields are stable over time,
robust to cue removal, and scale with field expansion. One obvious issue with such a model
is that the similarity in the place code learned in two different locations will be correlated
with the similarity of the locations. Place cells in the hippocampus do not appear to exhibit
such correlation.
38
Neural modelling and the hippocampus
An alternative mechanism allowing separation and completion in a single neural region
— initially proposed by Treves and Rolls (1992) and based on known hippocampal anatomy
— suggests that the disynaptic (indirect) pathway from layer two of the entorhinal cortex
(EC2) to CA3 via DG and the monosynaptic (direct) pathway from EC2 to CA3 fulfill
pattern separation and completion roles respectively. Substantial experimental data now
supports this proposal: activity in DG suggests a role of pattern separation for the region
(Leutgeb and Leutgeb, 2007) and activity in CA3 suggests that inputs sufficiently similar
to a previously learned input evoke the same learned response (completion) but that below
some input similarity threshold, the response rapidly decorrelates from the learned response
(separation) (see Figure 2.9, right) (Leutgeb and Leutgeb, 2007; Vazdarjanova and Guzowski,
2004). Furthermore, disruption of the indirect pathway interferes with the encoding of new
memories but not the retrieval of existing memories and disruption of the direct pathway
interferes with retrieval but not encoding (Lee and Kesner, 2004). Downstream CA1 activity
is similar to that in CA3, but with less environmental specificity (more completion) (Leutgeb
et al., 2004; Vazdarjanova and Guzowski, 2004). Although this evidence is largely from
rodent studies, new imaging studies suggest that a similar functional distinction between
regions may be present in humans (Bakker et al., 2008).
The role of CA3 recurrence
One striking characteristic of the CA3 hippocampal subfield is the significant excitatory projection between pyramidal cells. The modelling literature is dominated by the hypothesis
that these recurrent collaterals enable an attractor landscape to form, providing an associative memory function. No existing evidence rules out alternatives however, and one key
alternative is that the recurrent connections encode sequences.
Considering again the directionality of place fields, the model presented by Sharp (1991)
predicted that fields at the centre of a radial 8-arm maze should be omni-directional. Evidence collected since suggests that a significant number of such fields are directional (Markus
et al., 1995). Brunel and Trullier (1998) proposed that the recurrent CA3 synapses, rather
than the feedforward EC2 to CA3 synapses, could explain the two cases. In their model,
strengthening of recurrent synapses between cells with similar positional and directional
preferences initially causes an increase in the directionality of cell firing. In open field environments, this increase is followed by a decrease of directionality as synapses between cells of
similar positional but varied directional properties are also potentiated, due to the temporal
proximity of their activations.
2.4 Theories and models of hippocampal function
39
The attractor hypothesis
Not all studies define separation and completion the same way. In Figure 2.9, consistent
with O’Reilly and McClelland (1994) and Fuhs and Touretzky (2000) among others, pattern
separation is defined as the process by which an input with a particular similarity to a
reference input generates an output of a lower similarity to the corresponding reference
output and pattern completion as an increase in output similarity with respect to input
similarity. An alternative definition for pattern completion is that it is the ability for a noisy
or partially cued input to produce an output arbitrarily close to 100% similarity to a reference
output, such as in the classic Hopfield (1982) model. In this latter sense, pattern completion
is most commonly achieved using recurrent auto-associative networks with attractor states7 .
One dominant hypothesis is that the basic recurrent structure of CA3 produces attractorlike dynamics in the region. Numerous studies have explored the development of attractor
dynamics in CA3 as a generalised memory (Marr, 1971; McNaughton and Morris, 1987;
Treves and Rolls, 1992). More recent work examines how an attractor network may account
for the specific properties of place cells (Samsonovich and McNaughton, 1997; Kali and
Dayan, 2000) (discussed further below). But what information do these attractors encode,
and how is this information used?
Prior to the discovery of grid cells in the medial entorhinal cortex (see §2.3.3), one theory postulated that hippocampal place cells were responsible for creating a two-dimensional
geometric map of space, enabling hippocampally-mediated path integration (McNaughton
et al., 1996). As grid cells appear to form such a map, it now seems less likely that the hippocampus is principally involved in its storage (McNaughton et al., 2006). It is theoretically
possible to maintain position in such a map using idiothetic cues with sensory-based resetting to correct drift (Fuhs and Touretzky, 2006), which has been demonstrated in principle
in robotic experiments (Milford and Wyeth, 2009). Recent models explore the potential
mechanisms underpinning grid cells (Fuhs and Touretzky, 2006; Burgess et al., 2007; Burak
and Fiete, 2009).
As the medial entorhinal cortex projects directly to CA3, any CA3 attractors may be
receiving both sensory information and two-dimensional geometric position. Place cells in
CA3 have been proposed as a conjoint representation of these two sources (Touretzky and
Redish, 1996). A further filtering step, also advantageous for localisation, is the connectivity
of the environment. Although two locations may be adjacent in a two-dimensional coordinate
sense, if there is some form of barrier between them, they may be distant in a path planning
7
although hetero-associative networks with feedback from the output back to the input are similarly
capable
40
Neural modelling and the hippocampus
sense. By encoding past transitions between locations in an environment, an animal could
apply an additional filter to estimate the likelihood of a particular transition occurring. In
an attractor landscape, this likelihood can be encoded as lower-energy transitions between
adjacent, navigable locations, thus forming a continuous attractor along previously traversed
paths (Rolls, 2007).
Isolating specific evidence for attractor dynamics in the hippocampus is difficult. Wills
et al. (2005) found that place cells in CA1 sharply transitioned from active to non-active,
as would be expected in an attractor-like pattern completion network. Declaring this as
evidence for attractor dynamics may be premature however, as the same effect may arise
through different means (as discussed in the following section). In the context of the CA3
network as an attractor network, theta phase precession is often considered a side-effect of
pattern completion (Yamaguchi et al., 2007), or as a coding scheme for providing position
within a place field (Burgess et al., 1994; Tsodyks et al., 1996). Again, attractors are not
the sole explanation for these observations.
Beyond the continuous attractor theory, Blum and Abbott (1996) suggested that LTP
between cells involved in adjacent attractor states in CA3 may cause the cells representing
locations slightly ahead of the rat to fire. In this sense, their model is not performing
localisation but is rather performing a limited form of path planning — the active CA3
attractor fires for the next location as formed from previous experiences. Exploring further
the potential role of CA3 in path planning, the next section considers alternatives to the
notion of CA3 as network implementing stable attractor dynamics.
The sequence hypothesis
Stable attractor models primarily ascribe a localisation function to CA3, albiet at times a
slightly predictive localisation. While localisation is certainly necessary for navigation, it is
not sufficient — current position is only interesting in its relation to other known positions.
If a place cell fires solely in the location for which it codes then it provides only localisation,
and it cannot be responsible for path planning (even if some kind of map exists in the network
to improve localisation ability).
Reciprocal connections tend to promote the formation of stable attractors (Amit, 1989).
Anatomical studies show that connectivity in CA3 is about 5%. Reciprocal connections
would be uncommon if connectivity in the network was random, leading instead to an asymmetric connectivity structure. Such an asymmetric structure is not well suited to maintaining stable attractor states, effectively decreasing the capacity of the network by more
often resulting in chaotic trajectories (Amit, 1989). Asymmetric networks are demonstrably
2.4 Theories and models of hippocampal function
41
capable of sequence learning (Tsodyks et al., 1996; Levy, 1996; Wallenstein and Hasselmo,
1997; Lisman and Otmakhova, 2001).
Modelling studies have explored how well such a structure may suit the encoding and
retrieval of sequences of memories. As an animal traverses an environment, direct responses
to individual locations form codes in CA3. Cells responsive in locations sufficiently proximate would fire within the window of LTP, and any connection between these cells would be
strengthened. Perhaps the simplest explanation from an encoding perspective of how a cognitive map may form is that the weight of the CA3-CA3 synapses themselves encode the map
(Muller et al., 1996), but have very little effect on the activity during navigation. Variation
in CA3 firing phase under this model would be dependent solely on afferent variation, thus
would be supported by evidence supporting the ‘pacemaker’ model of theta phase precession. Furthermore, because the CA3 cells are responding primarily to external input (rather
than recurrent input) during navigation, retrieval of the map from the synaptic weights in
this scheme must occur while the animal is at rest. Evidence from place cell recordings in
rodents suggest that place cells do fire at rest, either in the order experienced or in reverse
(Kudrimoti et al., 1999; Diba and Buzsaki, 2007; Carr et al., 2011). Using such an ‘offline’
path planning solution for navigation requires that the desired path is somehow remembered
during movement, a complication often overlooked.
Although some evidence suggests that the efficacy of CA3 recurrent synapses can be
down-regulated by neuromodulatory processes, specifically by acetylcholine (Vogt and Regehr,
2001), there is little reason to suppose that this occurs constantly during navigation. On the
contrary, cholinergic antagonists do not seem to disrupt retrieval in CA3 during navigation
(Rogers and Kesner, 2003), indicating that the recurrent connections are uninhibited in this
state. Active, asymmetric recurrent collaterals may thus be playing a role in the ongoing
activity of CA3 during navigation.
At any particular location, numerous place cells with overlapping fields will fire. On average the phase of the theta rhythm at which each of these cells fire is related to the percentage
of their field traversed. Those cells firing earliest in theta are those whose fields the animal
is about to leave. If the CA3 recurrent synapses did produce some postsynaptic effect during movement, the earliest firing place cells could bias the subsequent activity towards cells
with nearby fields due to the LTP induced in previous exploration. This bias would result in
causal sequences that could provide a path look-ahead function to anticipate the locations at
the place field edges of currently active place cells. Evidence for the ‘coordinated assembly’
model of phase precession would support such a model (such as Dragoi and Buzsaki (2006),
see §2.3.2). The theta-gamma model of CA3 sequence learning explores the effect of causal
firing of place cells within strongly modulated oscillations. The active cells of each step are
42
Neural modelling and the hippocampus
directly responsible for the activation of cells in the following step, thus during encoding the
time between each step is limited by the time window of LTP. This model suggests that
approximately one second of route anticipation from approximately seven predictive steps
could be expected based on commonly observed place cell and hippocampal dynamics data
(Tsodyks et al., 1996). Further modelling efforts with similar architectures have demonstrated likely roles for GABA (Wallenstein and Hasselmo, 1997) and acetylcholine (Lisman
and Otmakhova, 2001) in the timing and control of sequence recall.
One second of anticipation is insufficient for most route planning scenarios. In principle,
the basic recurrent architecture of the hippocampus may support more complex planning
tasks (Levy, 1996). A gap remains, however, in understanding the biophysical mechanisms
that may support more complex sequence learning. More extended route planning has been
proposed as one function of a hippocampal phenomenon known as ‘sharp wave ripples’
(SWRs) (O’Keefe and Nadel, 1978; Buzsaki et al., 1983). SWRs are spontaneous, fast (approximately 150 Hz) oscillations that occur in the hippocampus while an animal is at rest
or asleep, but not during navigation (Wilson and McNaughton, 1994; Foster and Wilson,
2006). Place cells have been observed to fire in sequence during these ripples, both in the
order in which the place fields were experienced (Foster and Wilson, 2006; Diba and Buzsaki,
2007), and in reverse (Diba and Buzsaki, 2007). Sleep replay is often considered a mechanism
for memory consolidation (Lee and Wilson, 2002). Reverse replay in awake rodents often
follows immediately after a period of navigation (Foster and Wilson, 2006; O’Neill et al.,
2006), leading investigators to the idea that this phenomenon may link traversed paths to
their outcomes (providing a solution to the credit assignment problem in reactive navigation). Forward replay often occurs prior to movement, potentially contributing to planning
(Johnson and Redish, 2007). Under this form of planning, some form of short-term memory
buffer would still be required to execute movements along a trajectory, perhaps by potentiation of links within the hippocampus, or perhaps by buffering in a region external to the
hippocampus.
2.4.2
Hippocampus-dependent navigation
In contrast to the myriad theories of place cell development and information content, theories
regarding the contribution of place cells to navigation are relatively sparse. Such sparsity
is perhaps not unexpected when considering that in order to formulate a theory about the
latter (i.e. hippocampus-dependent navigation), a theory about the former is required (i.e. an
assumption about the nature of the information encoded). One puzzle, related in particular
to the common definition of place cells as providing primarily localisation information, is
2.4 Theories and models of hippocampal function
43
that during navigation, the hippocampus cannot provide information regarding locations
except that which an animal is currently occupying (Morris, 1991). If one begins with this
assumption, then the implication is that an animal wishing to navigate to a remote location
cannot rely on any map encoded in the hippocampal place cells while navigating a route.
Many of the models discussed below do make such an assumption. Furthermore, many of the
same models predated the discovery of grid cells, and assume that place cells form the basis
of a metric map. While metric navigation is unlikely to be a direct result of hippocampallybased spatial memory, such strategies may be driven by a combination of place cell and grid
cell activity, and are thus briefly discussed here.
Brown and Sharp (1995) demonstrated a model in which a form of stimulus-response
encoding allowed a simulated rat to perform similarly to real rats in the hidden platform
Morris water maze task. Place cells in these simulations functioned as unique locations for
contextual input to a set of associative learning cells in the nucleus accumbens that paired
movement responses with current head direction. Learning in this model relied on a slowly
decaying trace signal for each action on a path to the goal that was reinforced upon reaching
the goal. As every location on the path to each goal is reinforced, this method is slow to
learn optimal paths. Furthermore, the learned actions are specific for the goal location: for
any new goal an entirely new set of actions must be learned (there is no latent learning,
but see Gerstner and Abbott (1997) for a description of how goal-specific maps could be
learned).
Foster et al. (2000) improved on pure stimulus-response models using a temporal difference learning mechanism (see Sutton and Barto (1998)). An action-reinforcement mechanism
based on the actor-critic architecture replaced the decaying trace used by Brown and Sharp
(1995), which allowed updating of the value of each location based on the current value of
nearby locations, rather than by propagating rewards back only upon reaching the goal. This
solution to the credit-assignment problem converges on appropriate values for each location
more quickly than the decaying trace method, however still provides no latent learning abilities. To solve the latent learning problem, Foster et al. (2000) added a coordinate-learning
mechanism driven by the place cells and a path-integration module providing estimated selfmotion cues. Over time, this coordinate system would provide a globally-consistent position
within the environment, eventually allowing new goal locations to be learned in a single
trial. Combined with the actor-critic model, performance on the watermaze in both static
goal location and in modified goal location scenarios were demonstrably similar to that of
rodents. However it is unclear where in the hippocampus the biological implementation
of the coordinate-learning mechanism may be manifested. Furthermore, the model cannot
account for more complex maze behaviours (discussed further below).
44
Neural modelling and the hippocampus
As an alternative to an action-reinforcement or coordinate-framework model, Burgess
et al. (1994) suggested that goal cells immediately downstream of the subiculum could provide a one-shot learning ability, similar to that demonstrated by rodents in a familiar environment (Steele and Morris, 1999). In its simplest form, when visiting a goal location, synapses
between place cells and goal cells active in that location could be potentiated (Burgess and
O’Keefe, 1996). Assuming place fields are distributed uniformly, the subsequent activity of
the goal cell would decay with the distance from the goal, to the limit of the size of the place
fields. This simple scheme relies on gradient ascent to navigate, requiring brief exploration
to determine the direction to the goal. Incorporating head-direction cells and directional
goal cells removes this requirement by providing an innate awareness of the direction to the
goal (Burgess et al., 1994).
The metric models mentioned above facilitate latent learning and shortcutting, both
of which are abilities observed in rodent experiments (Buxton, 1940; Tolman, 1948). It is
their intrinsic encoding of the direction to the goal that provides these models with such
abilities. As a result of this direction-to-goal basis for navigation, if reaching the current
goal involves a choice point with two directions of possible motion, an animal following a
direction-based model would choose the option closest to the direction of the goal, even if
that option had been experienced previously and did not lead to the goal, or was a longer
route than the alternative. Rodents do not exhibit such behaviour: they are capable of
making decisions that take them away from their goal in a metric displacement sense, but
towards the goal along a navigable path (Buxton, 1940). That this behaviour is evident in
latent learning experiments suggests that such path following cannot be accounted for by
the stimulus-response learning suggested by Foster et al. (2000) among others.
The navigation models above are all examples of reactive navigation systems or deadreckoning navigation systems (see §1.1.2 and §1.1.3). Fewer models have considered how
predictive navigation (see §1.1.4) may involve the hippocampus. One hypothesis is that
mapping information is transferred from the hippocampus to the cortex during periods of rest
or sleep (Buzsaki, 1986; Wilson and McNaughton, 1994). During navigation, this external
map could be activated not based on the current sensory information, but by the current goal.
Reverse replay of paths could occur in the cortical map during navigation, simultaneously
stimulating a region (perhaps CA1) downstream of the predominantly localising CA3 cells,
resulting in activation of cells corresponding to the next location on the path to the goal in
the downstream region.
Another hypothesis is that animals explore the possible outcomes at choice points via
a vicarious trial-and-error process (Tolman, 1938). Johnson and Redish (2007) provided
some evidence for mental exploration in CA3 at decision points in a T-maze task. Such
2.5 Summary
45
vicarious exploration has since been shown to be specific to a choice requiring model-based
evaluation (i.e. a planning strategy) (van der Meer et al., 2010). This forward lookahead
occurs during SWR events (§2.4.1) and is a specific form of replay, which as noted previously,
requires some form of short-term memory to store the appropriate path once selected. It
is unclear how pre-movement replay interacts with the goal-modulation of CA1 cells during
active navigation (Ainge et al., 2007).
The predictive navigation theories above contain an underlying assumption that the
hippocampal place cell network encodes sequences of locations. Viewing the hippocampus as
a cognitive graph (Muller et al., 1996) rather than a metric map means that any navigation
algorithm must translate the output into either relations to detectable allothetic cues, or
map the graph nodes back to a metric representation. The general theory mapping from
node to metric space is theorised by Touretzky and Redish (1996), and further developed
by functioning models of navigation in Arleo and Gerstner (2000) and Milford and Wyeth
(2009). Furthermore, metric information is used only for identity in sequence-based models,
thus novel (previously un-traversed) shortcutting is unlikely to result from such a model.
As a metric representation is available in the entorhinal cortex however, such shortcutting
could be a function added at the convergence of path and metric information.
2.4.3
Information models
Some models do not fit any specific genre, for example Becker (2005) is a major paper that
addresses a broad range of issues from the functional role of specific regions, through to
detailed implementations of these regions. Like other papers, it has a connectivity between
each of these regions, however unlike other papers, it doesn’t present a specific theory about
the functional role of each region in navigational tasks. Instead, the generic functional goal
of each region is to reconstruct the input to the system.
2.5
Summary
This chapter has provided a brief summary of key hippocampal and neural modelling literature. Despite the large volume of literature and experimental results on this topic, current
experimental techniques lack the ability to provide conclusive evidence for how such results
fit together. Through a synthesis of anatomical, dynamical and behavioural data into functional, computable systems, network models provide a good domain for testing potential
theories of hippocampal function.
The prevailing view of the hippocampal role in navigation, ascribing a pure localisation
46
Neural modelling and the hippocampus
role to the highly recurrent CA3 network, appears to ignore the flexibility provided by a
temporal dimension in such a network. Hence whilst some models have proposed potential mechanisms for the formation of place fields, they tend to separate field development
and path development (Burgess et al., 1994; Burgess and O’Keefe, 1996; Kali and Dayan,
2000). Certain other models do explore potential path storage in the hippocampus, but
ignore the establishment of the place fields themselves, thereby also sidestepping the complications of their simultaneous development and sequencing (Hasselmo and Eichenbaum,
2005; Samsonovich and Ascoli, 2005; Blum and Abbott, 1996). The remainder of this thesis
is dedicated to developing a novel model of CA3 as a path-based spatial memory system,
capable of storing and recalling locations and paths during behaviour. The proposed model
shares some elements with previous models (in particular (Lisman and Otmakhova, 2001)),
however there are specific mechanistic contributions derived from the model regarding novelty detection and modulation. Furthermore, the model demonstrates how much of the
existing data is consistent with the theory that the CA3 hippocampal subfield is not merely
performing localisation during navigation, but is also performing extensive path recall.
3
A role for spike timing in learning and
recognition
A cognitive map stores information about the connectivity of locations in the environment,
which requires an ability to learn and thereafter recognise specific locations. The system
must therefore be able to decide whether any particular location is novel, to be learned and
integrated into the map, or whether it is familiar. Evidence from many electrophysiological studies suggest that complex spiking cells in the hippocampus exhibit spatially-sensitive
characteristics suggestive of some role in representing spatial location (reviewed in §2.3.2).
This chapter deals with the critical role of novelty in cognitive map development and maintenance, and proposes a millisecond time scale race between hippocampal inputs that enables
a mechanism intrinsic to the circuit to mediate the learn-recall balance. The resulting cell
dynamics are consistent with many observed hippocampal spatial field characteristics. Later
chapters explore how the novelty-detection mechanism can be modulated to maintain stability with changing and noisy input characteristics (Chapter 4) and how the receptive fields
of the cells can develop beyond their initial responses to encode the relationships between
fields (Chapter 5).
47
48
A role for spike timing in learning and recognition
3.1
Novelty, separation and completion
An internal representation of location may be cued by environmental elements, but these
elements are not the identity of the location. Rather location identity is either a coordinate
in space (in a dead-reckoning sense) or a node on a graph (in a cognitive map sense). Some
mechanism must transform sensory data into this internal representation. Assuming that the
result of such a transformation is hippocampal place cells then there are certain observations
that constrain the possible nature of such a transformation process. Some of the place cell
properties of particular note are restated here (see §2.3.2 for an overview).
• Individual cells are responsive in zero or one locations in any continuous environment.
• For any particular location in an environment there are numerous cells active.
• In a novel environment, cells acquire spatial sensitivity over time.
• Active place cells in similar-looking environments overlap with a likelihood no greater
than chance.
• Once an environment is known, the cues can be modified to some extent without
disrupting which place cells are active.
With the above assumptions and observations, there are a number of possible conclusions
one might draw:
• The internal representation is learned over time.
• There is little relation between which cells become associated with a particular input and the input itself — during learning, the representations of similar inputs are
separated.
• Once learned, the internal representations become robust to input variation — similar
inputs evoke the same learned representation.
The aforementioned characteristics of place cells present a problem of competing requirements: how does an animal distinguish between a sensory stimulus that is ’close enough’ to
something it has experienced before, and one that is novel and must be learned? On one
hand, distinct memories can be formed from similar novel inputs, implying some form of
pattern separation is involved. On the other hand, a pattern completion effect is observed
on known inputs, allowing variation in the input without equivalent variation internally. As
3.1 Novelty, separation and completion
49
discussed in §2.4.1, Treves and Rolls (1992) demonstrated a mechanism by which two distinct
pathways from EC2 to CA3 could fulfill pattern separation and pattern completion roles.
This hypothesis, and the supporting data collected since, begins to explain what processes
are facilitating memory storage and where these processes occur, but it remains unclear precisely when each process is occurring, that is, when new details should be learned and when
known details should be recalled.
Determining when to learn and when to recall requires a mechanism to detect when an
input is novel. Intuitively, it seems as though such a decision should depend on the patterns
stored within the hippocampus itself, thereby requiring that the structure mediate its own
novelty signal. Treves and Rolls (1992) identified the mechanistic consequences of novelty
on learning and recall that were required for their aforementioned dual pathway hypothesis. During learning, the indirect input should be strong in comparison with other CA3
inputs (for example the direct input and recurrent connections) to allow new associations
to be learned. During retrieval, the indirect input should be rendered effectively inactive
to avoid spurious separation noise — input noise amplified by the separation properties of
the dentate gyrus — interfering with retrieval and potentially disrupting learned memories.
Although these requirements are recognised, their underlying biological mechanisms remain
unclear. Experimental data from Hasselmo et al. (1995) implicates the septo-hippocampal
cholinergic system in down-regulation of the CA3-CA3 recurrent synapses during learning,
however this modulation operates at a multi-second timescale (Hasselmo and Fehlau, 2001).
This multi-second time scale may be too slow for the purposes of online learning and recall,
leading Hasselmo et al. (2002b) to propose that pattern-by-pattern learning may be accounted for by explicitly modulating between completion and separation in separate phases
of the hippocampal theta rhythm. However, with an explicit learning phase, separation
noise interferes even with well-known patterns. None of these models internally generate
a pattern-by-pattern novelty signal, and use that signal as a basis for switching between
learning and recall. The question arises: what mechanism supports such a signal, and could
it be generated within the hippocampus itself?
The remainder of this chapter will detail a novel mechanism capable of deciding when
to learn a novel input pattern and when to recall by completing to a previously learned
pattern, using a decision criterion based on patterns currently stored in the system. This
is demonstrated through a new computational model of the dual-pathway circuit formed by
layer II of the entorhinal cortex (EC2), DG and CA3 that implicitly performs pattern-bypattern novelty detection. I term this model the Spike-Timing Separation and Completion
(STSC) model. The model incorporates spike time as an integral aspect of neurons, which
enables it to distinguish between patterns that have been previously seen, and patterns that
50
A role for spike timing in learning and recognition
are new and should be learned. Spike timing not only provides the ability to discriminate
between known and unknown patterns through spike-timing-dependent-plasticity (STDP)
(Levy and Steward, 1983; Markram et al., 1997; Song et al., 2000), but also inherently
drives the mechanism to effect or suppress learning. This pattern-by-pattern suppression
ensures that even in unfamiliar situations, already known patterns are not re-learned, while
in familiar situations, unknown patterns can be learned. The timing mechanism is first
outlined in a three-neuron network to illustrate the principle of using spike-timing as a
correlate of learning in a dual-pathway network. This principle is then extended to the
complete STSC model, showing that a larger network based on EC2-DG-CA3 anatomical
details correlates learning and timing, and that the network learns patterns that are both
reliable and distinct. Finally, the model produces a number of predictions regarding the
underlying biology, and in particular regarding the timing of activity in the hippocampus,
which conclude this chapter.
3.2
A novelty-aware microcircuit
STDP is a biological manifestation of Hebb’s theoretical learning rule (Song et al., 2000).
In its most commonly observed form, synapses connected to a cell are strengthened when
they fire in a time window prior to the cell firing, and are weakened when they fire in a time
window after the cell fires. This temporal dependence means that afferent synapses that
predict a cell’s firing will have a greater postsynaptic effect on their next activation. If a cell
is activated after (but independently of) the activation of a particular set of synapses, the cell
will gradually spike earlier with respect to the activation of the synapses (Guyonneau et al.,
2005). Furthermore, assuming this synaptic set is sufficiently large, the cell will eventually
fire in response to the predictive synapses alone. This behavior was elegantly demonstrated
by Izhikevich (2007) using a conditioning paradigm, in which the cells originally activated
by an unconditioned stimulus were eventually activated by synapses receiving input due to
a conditioned stimulus. In Izhikevich’s model, spike timing encodes whether a response has
been learned, with a shorter latency between input and response indicating a well known
input.
STDP requires that the postsynaptic cell be active to learn active inputs. In the conditioning scenario of Izhikevich (2007), the unconditioned stimulus activated the cells that
the conditioned stimulus predicted. In the context of generalised memory, the same sensory
stimuli can be considered as both the target to be learned (conditioned stimulus) and the cue
that is triggering learning (unconditioned stimulus). A mechanism is thus required whereby
a novel input can evoke a pattern of activity in a target cell population that can then be
51
3.2 A novelty-aware microcircuit
associated with the input. The dual-pathway architecture (already discussed) provides such
a mechanism: the indirect pathway does not undergo associative plasticity, and enables novel
input to evoke baseline activity; the direct pathway is subject to associative LTP, thus pairing presynaptic and postsynaptic activity. By modelling with spiking neurons, I investigated
the effect of the temporal dynamics of STDP in a highly simplified dual-pathway model.
Consistent with previous dual-pathway models, synapses from the two pathways differ in
strength and plasticity, however in the current model they also differ in the latency of their
initial activation following a given input stimulus. Simulation results show that the distinction between a fixed and learned response is retained in the response of the target cell if the
temporal dynamics are considered.
3.2.1
Microcircuit design
The network consists of three neurons, each one representative of one region (see Figure 3.1a).
Individual neurons are modelled as point devices following the model presented by Izhikevich
(2003, 2004) given in equation 2.1. The synaptic input current for each neuron is the sum
of the currents given by each individual synapse. Each STDP synapse is modelled as a
single-state Is representing the current injection to its postsynaptic neuron, with its rate of
change I˙s given by
I˙s = −Is /τs + δ(t − ts )w
(3.1)
where τs is the decay time constant of synapse s, δ is the Dirac delta function, ts is the
vector of presynaptic spike times, t is time, and ws is the current synaptic weight. Synapses
subject to STDP follow the model of (Song et al., 2000). For each pair of presynaptic and
postsynaptic spikes, the change in synaptic weight ∆w is given by
∆w = max (min (F (∆t) , wmax − w) , −w)
(3.2)
where F (∆t) is governed by Equation (2.8).
For simplicity in this study, the synaptic current Is for static synapses is given by
Is =
X
gr (v − Er )
(3.3)
r∈R
where R is a set of receptor types, in this case containing only AMPA, v is the membrane
potential of the postsynaptic neuron, Er is the reversal potential of the receptor and gr is
52
A role for spike timing in learning and recognition
the current conductance of the receptor given by
ġ = −g/τr + δ(t − ts )ws
(3.4)
in which τr is the decay time constant of the receptor (Dayan and Abbott, 2001). See
Table 3.1 for neuron parameter values and descriptions, Table 3.2 for synaptic parameter
descriptions and Table 3.3 for synaptic parameter values.
In the example microcircuit, synaptic weights are set such that a single spike from neuron
A is capable of causing a spike in neuron B, and in turn a single spike from cell B is capable
of causing a spike in neuron C. The weights from A to B and from B to C are static, that
is, unaffected by activity. The direct synapse from A to C has a small initial weight, but is
modified according to the above STDP rule, such that a fully potentiated synapse can evoke
an action potential in C.
3.2.2
Microcircuit simulations
The simulation protocol involved stimulating input neuron A 28 times at 7 Hz and recording
membrane voltages of neurons B and C (see Figure 3.1b-c). The 7 Hz stimulation frequency
was chosen as a typical theta rhythm frequency in the hippocampus and the entorhinal
cortex. Initially the direct input had little impact on the membrane potential of cell C,
which spiked only after it received input from neuron B. Over repeated presentations, the
direct synapse was potentiated, and eventually became strong enough to directly evoke an
action potential in cell C. At this stage, when the corresponding input from neuron B arrived
the cell was still partially hyperpolarised, as a result of which the indirect input was no longer
sufficient to cause a postsynaptic potential.
The timing of the spikes of cell C relative to those of cell A indicates whether the postsynaptic action potential is caused by the direct stimulation through the A-C synapse or
the indirect stimulation through the B-C synapse. If cell C fires after the input from cell
B arrives, the stimulus can be considered unknown, and thus requires the input from B to
enable learning. If cell C fires before cell B, the stimulus is known, and any input via the
indirect pathway can be ignored. Furthermore, when cell C fires before cell B it does not
also fire after cell B (due to hyperpolarisation), demonstrating that the circuit intrinsically
selects between learning and recall for each individual input. The relative timing of firing
between cell A and cell C inherently coordinates two functions: (1) it encodes the novelty
of the association between cells A and C, and (2) it controls whether the A-C synapse is
modified by the B-C input. These results indicate that the dual-pathway architecture, when
3.2 A novelty-aware microcircuit
a
53
b
Static synapse
STDP synapse
A
B
C
c
Figure 3.1: How timing can signify the distinction between novel and familiar inputs. (a)
Schematic illustration of a three-field network with two paths from A to C, an indirect path A-B-C
and a direct path A-C. (b) The latency of the response of cell B relative to cell A is fixed (see
dotted line), the response of cell C relative to cell A has a latency that is a function of the strength
of the A-C synapse (see solid line). With a novel input (A-C weight < 2.03 × 10−9 ), the signal
travels via the indirect path A-B-C and the latency of C is longer than that of B (the solid line
above the dotted line indicates that A is novel). With a known input (A-C weight > 2.03 × 10−9 ),
the signal travels via the direct path A-C and C’s latency is shorter than that of B (the solid line
below the dotted line indicates that A has previously been learned). Between these two conditions
(A-C weight = 2.03 × 10−9 ), the two pathways contribute equally to the timing of cell C’s action
potential. The latency therefore indicates which path, A-B-C or A-C, is dominant. (c) Three panels
show snapshots of the behavior for novel, near-threshold and known weights during a learning trial:
for low A-C weights, the response of C depends entirely on the input from B (c, left). As the
A-C weight approaches a threshold (2.03 × 10−9 ), less input from B is required as the membrane
potential of C is still elevated due to the direct input from A, and thus the time of C’s response is
closer to that of B (c, middle). Beyond this threshold, cell C is responding before cell B, showing
that the direct A-C synapse is solely responsible for C’s response and signifying that the input is
known (c, right).
54
A role for spike timing in learning and recognition
implemented with a spiking neural input and STDP, provides a conceptually simple, integrated mechanism to distinguish novel from known input. To similarly signal when to learn
based on a network of inputs however, this mechanism must be expanded to detect novelty
of not just a single cell input, but a pattern of active cells. In the next section, the threecell network is expanded to model the EC-DG-CA3 circuit, demonstrating how spike timing
can control when subsets of CA3 neurons learn new patterns, and when they recall known
patterns.
3.3
The STSC circuit
Like the hypothesised dual-pathway architecture of Treves and Rolls (1992), anatomical
data suggests that cells in CA3 receive external excitatory input from EC2 both directly via
the perforant path and indirectly through DG and its mossy fibre system (Amaral, 1993).
The projections from DG to CA3 are sparse: each dentate granule cell forms synapses on
approximately 14 CA3 neurons (Claiborne et al., 1986). Dynamic facilitation in the mossy
synapses on CA3 cells allows a burst from even a single dentate granule cell to evoke a
postsynaptic action potential (Henze et al., 2002). The direct synapses from EC2 to CA3
number in the thousands per CA3 cell, but each individual synapse has a much smaller
effect on the postsynaptic potential than the DG inputs. Plasticity characteristics also differ
between the two synaptic paths: although LTP is evident in the DG to CA3 synapses, they
show little evidence of associative modification (Chattarji et al., 1989), whereas associative
LTP is evident in perforant path inputs to both DG (Bliss and Lomo, 1973) and to CA3 (Do
et al., 2002). The CA3 cells are also self-connected through the recurrent collateral pathway.
Like the perforant path, recurrent collateral synapses exhibit associative LTP (Chattarji
et al., 1989; Martinez et al., 2002), and although numerous, are individually weak.
Pattern separation requires the pre-wired, sparse connections in the DG-CA3 pathway
to provide an index into the CA3 population. Activation in EC2 evokes a response in DG,
which in turn causes strong activation of a small number of CA3 cells. Hebbian-like direct
synapses connecting active EC2 cells to the most active neurons are potentiated, as are
recurrent links between active CA3 neurons. The EC2-CA3 connections learn to associate
EC2 stimuli with patterns in CA3, while the recurrent CA3-CA3 connections learn to selfassociate patterns in CA3. The recurrent connections provide pattern completion for partial
or noisy stimuli from EC2. Fuhs and Touretzky (2000) demonstrated in a computational
model that a similar effect can be achieved with competitive inhibition in CA3 instead of
excitatory recurrence.
In the previously described models, the pre-wired DG-CA3 connections bias CA3 activity
3.3 The STSC circuit
55
both when learning new patterns and when recalling familiar patterns. The activity of the
CA3 population contains no information about the contribution of the direct EC2-CA3
path relative to that of these pre-wired DG-CA3 connections. Hasselmo et al. (2002b)
hypothesised that theta half-cycles might alternately facilitate learning and recall in CA1.
This idea has since been explored in more detailed modeling scenarios in both CA3 (Kunec
et al., 2005) and in CA1 (Cutsuridis et al., 2009).
The ABC-AC network of the previous section suggests an alternative solution to the
problem of mediating between learning and recall in the hippocampal circuit. If the three
regions A, B and C are considered analogous to EC2, DG and CA3 respectively, the two
pathways (indirect EC2-DG-CA3 and direct EC2-CA3) could act to simultaneously learn
and cue memories by virtue of their relative timing. If the direct pathway evokes a sufficient
response, the indirect response can be safely ignored. If instead the direct pathway fails
to evoke a direct response, the indirect pathway can activate a novel set of CA3 neurons
which can be associated with the input. The dual-pathway guarantees not only that a set of
neurons will be activated in CA3, but also that the relative timing of the response determines
whether the active set corresponds to a familiar pattern that is being reactivated or a novel
memory that needs to be learned. The network thus acts simultaneously as a memory system
and as a novelty detector.
In order to investigate the capability of a race in a spiking network to mediate the
learning of new patterns and the recall of known patterns, the following sections explore the
design and simulations of the STSC model of the hippocampus that incorporates many of
the known anatomical and functional details of the EC-DG-CA3 circuit. Two key questions
are addressed by this expanded model:
• Does a larger network based on EC2-DG-CA3 anatomical details show the same clear
correlation between learning and timing that was seen in the three-cell network?
• Can the network learn patterns that are both reliable and distinct? Reliability ensures that pattern completion is stable, and distinctiveness provides a measure of the
network’s discriminative power.
3.3.1
STSC model design
The architecture of the STSC model is similar to that of existing models in terms of the
functional roles of each region (Fuhs and Touretzky, 2000; Kali and Dayan, 2000; Treves
and Rolls, 1992) (see Figure 3.2). Regional cell numbers are proportional to estimated
numbers of cells in the adult rat brain (Amaral et al., 1990), reduced by a factor of 1000
56
A role for spike timing in learning and recognition
Figure 3.2: Network architecture showing main regions, cell types, and the fan-in/fan-out
connectivity (* indicates full connectivity). Open semicircles indicate plastic excitatory synapses,
filled semicircles indicate fixed excitatory synapses and filled diamonds indicate fixed inhibitory
synapses. The CA3 region is the primary component of associative memory storage in the system.
It receives input from EC2 via two pathways: one is a direct excitatory path, the other is indirect
via DG.
(110 EC2, 1200 DG, 250 CA3). Network input was provided via direct stimulation of the
EC2 neurons. Each stimulus activated a specific subset of the EC2 neurons (11/110) at a
random time within a 5 ms window. Stimuli were presented at theta frequency (7.0 Hz). In
addition to the activity generated by this stimulation, the EC2 input neurons were activated
probabilistically at each time step (probability calculated for an average baseline activity of
0.5 Hz).
Connectivity between the regions was assigned so as to achieve sparse activation of the
CA3 cell population via the DG-CA3 mossy fibre system. For modelling convenience, all
synapses on the indirect pathway (EC2-DG and DG-CA3) were non-plastic. Each CA3 cell
was connected to ten DG cells, randomly distributed but ensuring that each DG cell was
connected to two or three CA3 cells. The DG-CA3 synapses had static weights set such
that two synapses active in a 5 ms window provided sufficient input to evoke a postsynaptic
action potential.
Combinatorial analysis provides one method of estimation for fan-in and fan-out connections and the synaptic strength of each connection. Let Nr be the set of all neurons in
region r, and Srv ⊂ Nr the set of neurons in region r responding to a particular stimulus
57
3.3 The STSC circuit
v. Using the example of EC to DG connections (the same process applies to the DG-CA3
path), let nch be the number of EC cells forming synapses to any particular DG cell, and
nreq the number of active synapses required for a postsynaptic response in DG. The chance
v
P v (nch , nreq ) that any particular DG cell has connections to exactly enough cells in SEC
to
allow a postsynaptic response can then be given by
P e (nch , nreq ) =
v
C(nch , nreq )C((|NEC | − nch ), (|SEC
| − nreq ))
v
C(|NEC |, |SEC |)
(3.5)
where the function C(n, k) is the standard combinatorial: the number of non-ordered sets of
size k in a set of size n, given by
C(n, k) =
n!
k!(n − k)!
(3.6)
Because equation 3.5 specifies the exact number of connections, the probability for any
postsynaptic cell to have at least enough input is
v
Ptot
(nch , nreq ) =
v
SEC
|X
|
P v (i, nch )
(3.7)
i=nreq
Assuming all synapses produce the same post-synaptic response (PSR) when activated,
v
with increasing nreq , Ptot
will fall, increasing the input specificity of the cells. Conversely,
with increasing nch , the input specificity of cells will fall. Extending this to determine the
probability of a certain number of DG cells responding to a particular pattern gives
v
v
PnvDG (nch , nreq ) = Ptot
(nreq , nch )nDG (1 − Ptot
(nreq , nch ))|NDG |−nDG
(3.8)
Using this analysis (see Figure 3.3 for the connectivity statistics for the EC2-DG link),
excitatory connectivity for the indirect pathway was calculated to ensure that for greater
than 99% of possible stimuli, in the absence of noise, at least one CA3 neuron would respond.
The corresponding minimum active DG cell numbers per stimulus was calculated to achieve
this CA3 response. In order to ensure that this required minimum number of DG cells
responded, each dentate granule cell received weighted input from 50% (55) of the EC2 cells
such that a minimum number (nDG
req ) of active synapses caused any particular DG cell to fire
(in this simulation, the minimum number of active synapses was nine). All combinatorial
calculations were tested and refined in isolated feedforward network simulations prior to full
network simulations.
58
A role for spike timing in learning and recognition
a.
b.
1200
50
nch = 11
1000
n
ch
40
= 33
n
600
n
= 33
n
= 44
ch
= 55
30
nresp
ch
nch = 22
ch
nch = 44
800
nresp
nch = 11
nch = 22
nch = 55
20
400
10
200
0
2
4
6
nreq
8
10
0
2
4
6
nreq
8
10
Figure 3.3: Average number of DG cells firing for various values of nreq and nch . The total
range of DG responses in (a) is zoomed to the response range of interest (around 35) in (b). The
desired DG response range was derived using a similar calculation between DG and CA3, with the
CA3 target as the smallest possible CA3 response such that 99% of inputs produced some response.
Each EC neuron was connected to all CA3 neurons. Initially the efficacies of the direct
EC2 synapses were sufficiently low that none of the presented patterns in EC2 caused activity
in CA3. Perforant path inputs were subject to STDP, such that if any one EC2 neuron
consistently fired before a particular CA3 cell, the synapse directly connecting them was
potentiated. Because the CA3 network is small, any particular novel stimulus may activate
only a few CA3 cells. In this situation, all active cells must be capable of learning the input.
The 100% connectivity for EC2-CA3 is necessary due to these scaling issues.
Two different types of inhibitory neurons were included. Six inhibitory cells in DG
received excitatory input from all EC2 cells. Each of these cells was calibrated to fire when
i
greater than a given number of inputs (nDG
req ) were active within a 5 ms window, where each
cell required a different minimum number of active inputs ranging from 11 to 16. The effect
of this graded inhibition was to restrict the activity of DG despite the varying levels of EC
activity in the presence of noise. An inhibitory cell in CA3 received input from the local
pyramidal cells, and acted to suppress further CA3 network activity after approximately
i
three action potentials in a 5 ms window (nCA3
req ). The purpose of the CA3 inhibitory
cell was two-fold. Firstly, it ensured that small variations in DG activity (variations not
normalised by inhibition in DG) did not cause large variation in the CA3 activation levels
(which would then contribute to synaptic plasticity). Secondly, it acted as a threshold; if
sufficient CA3 cells responded to a pattern directly, the CA3 inhibitory cell would signal the
pattern as known. The CA3 inhibitory cell was designed to act as a regional equivalent to the
3.3 The STSC circuit
59
hyperpolarisation of cell C in the ABC-AC network; if it fired before the indirect pathway
caused a response then it attenuated any such response, thereby enabling the circuit to again
intrinsically select between learning and recall for each individual input.
DG and CA3 cells were modelled as spiking neurons with parameters chosen to match
the cell properties characterised in a recent review by Spruston and McBain (2007), who describe that a somatic current injection into CA3 pyramidal cells elicits a bursting response,
whereas a similar stimulus in a dentate granule cell causes spike trains exhibiting spike frequency adaptation. For the current model, dentate granule cells were implemented with
regular spiking dynamics, CA3 pyramidal cells were implemented with intrinsically bursting
dynamics, and all inhibitory cells were implemented with fast-spiking dynamics (neuronal
models were as described for the three-neuron model, neuronal parameters were chosen according to the suggestions of Izhikevich (2003); see Table 3.1, Table 3.2 and Table 3.3 for
parameter values). Although likely not essential to the operation of the model, the dynamics
of the different neurons do enhance the timing differences in the model, as the faster membrane response times of the CA3 neurons over those of dentate granule neurons exaggerate
the timing differences between novel and learned inputs. Furthermore, the fast-spiking characteristics of the inhibitory interneurons enables feedforward inhibition to reach the dentate
granule and CA3 pyramidal cells before the EC2 activity induces action potentials in these
cells, thereby allowing the inhibition to aid in normalising activity levels under variations in
input activity levels.
As in the three-neuron model (ABC-AC), both static and plastic excitatory synapses were
modelled with a single time constant in the range of AMPA channel dynamics (equation 7)
and plastic excitatory synapses were modified according to STDP (equation 4). Inhibitory
synapses were modelled according to equation 7 but with time constants and reversal potentials in the range of GABAA channel dynamics, and the CA3 inhibitory feedback interneuron
had an additional channel with a longer effect akin to the time course of GABAB . This second time course was intended to ensure that, like the C cell in the three-neuron model, all
CA3 neurons were hyperpolarised upon arrival of the indirect input if a known pattern was
presented.
3.3.2
Timing is a signal of learning
The timing between the stimulus and response provides a clear marker of learning for a single
neuron. To investigate the relationship between learning and timing in a network structure,
the STSC system was trained to respond to varied and noisy stimuli. Each unique EC2
stimulus (as described previously) was presented 28 times sequentially at theta frequency
60
A role for spike timing in learning and recognition
Cell
DG dentate granule - regular spiking
CA3 pyramidal - intrinsically bursting
Inhibitory interneurons - fast spiking
Parameter Value
a
0.02
b
0.2
c
-65.0
d
8.0
a
0.02
b
0.2
c
-55.0
d
4.0
a
0.1
b
0.2
c
-65.0
d
2.0
Table 3.1: Neural parameter values. Values as suggested by Izhikevich (2003).
Parameter
w
winit
wmax
A+
A−
rev
rev
rev
, EGABAB
EAMPA
, EGABAA
τAMPA , τGABAA , τGABAB
τs
τ+
τ−
τgap
Description
The synaptic weight. For STDP synapses, a current (in
Amps) to inject into the postsynaptic neuron after a presynaptic spike. For static glutamate and GABA synapses, the
conductance increase for that synapse for each presynaptic
spike.
The initial weight of an STDP synapse.
The maximum weight of an STDP synapse.
Maximal positive change in weight due to STDP.
Maximal negative change in weight due to STDP.
Reversal potentials of the relevant receptors (Volts).
Time constants of the relevant receptors (seconds).
Time constant for the single exponential decay STDP
synapses (seconds).
Time constant for pre-before-post STDP modification (seconds).
Time constant for post-before-pre STDP modification (seconds).
Minimum pre-before-post or post-before-pre time difference
required to evoke STDP (seconds).
Table 3.2: Synaptic parameter descriptions.
3.3 The STSC circuit
Parameter Synaptic connection
w
EC2(input)—DG(granule)
EC2(input)—DG(basket)
winit
wmax
A+
A−
rev
EAMPA
rev
EGABAA
rev
EGABAB
τAMPA
τGABAA
τGABAB
τs
τ+
τ−
τgap
DG(basket)—DG(granule)
DG(granule)—CA(pyramidal)
CA3(pyramidal)—CA3(chandelier)
CA3(chandelier)—CA3(pyramidal)
EC(input)—CA3(pyramidal)
EC(input)—CA3(pyramidal)
EC(input)—CA3(pyramidal)
EC(input)—CA3(pyramidal)
All excitatory non-STDP
All inhibitory
All inhibitory
All excitatory non-STDP
All inhibitory
All inhibitory
EC(input)—CA3(pyramidal)
EC(input)—CA3(pyramidal)
EC(input)—CA3(pyramidal)
EC(input)—CA3(pyramidal)
61
Value(s)
2.2 × 10−9
{4.8 × 10−9 , 4.25 × 10−9 , 3.92 × 10−9 ,
3.64 × 10−9 , 3.40 × 10−9 , 3.19 × 10−9 }
(weights to each of the six basket neurons respectively)
6.0 × 10−9
3.31 × 10−8
2.86 × 10−8
3.0 × 10−8
1.0 × 10−11
2.26 × 10−10
1.5 × 10−10
−1.8 × 10−10
0.0
−7.0 × 10−2
−9.0 × 10−2
5.0 × 10−3
6.0 × 10−3
1.5 × 10−1
3.0 × 10−3
4.0 × 10−2
4.0 × 10−2
2.0 × 10−3
Table 3.3: Synaptic parameter values. Synaptic connections are specified as presynaptic region
— postsynaptic region, with cell type in parentheses.
(7.0 Hz). Action potentials from the CA3 network were recorded for ten sets of ten different
stimuli. As the number of learned stimuli increases, the potential for crosstalk between the
weights for these different stimuli increases, and ultimately affects classification performance.
The current study was not intended to evaluate network capacity, thus each of ten networks
learned only ten stimuli each. The difference between the time of each CA3 spike and
the mean time of the most recent input stimulus was recorded and grouped for each perstimulus trial number, that is, for the first instance of each stimulus, the second instance of
each stimulus and so on.
Qualitative results of the network being trained to the first three stimuli over 10 seconds
demonstrate the typical behavior of the network (see the raster plot of Figure 3.4a). During
the first second, no stimuli are presented, and without coordinated input activity, the DG
and CA3 networks are silent. In subsequent seconds, the stimulus is applied to EC2. The
62
A role for spike timing in learning and recognition
DG response clearly precedes the CA3 response at the first presentation of each stimulus
(see Figure 3.4b), showing that DG input is initially required to cause CA3 activity. By the
final presentation of the same stimulus (see Figure 3.4c), the temporal order has reversed
and the response of the CA3 region precedes the DG response.
The progressive change in spike timing during repeated presentation of a stimulus follows a characteristic pattern (see Figure 3.4d). Across the range of trials, the variance of
the responses initially increases. Between trials 10 and 14 there is a median shift showing
the transition between post-DG and pre-DG response. The variance of the response timing
— increasing as the response is first learned then gradually decreasing — suggests a consolidation of neural responses. Noise causes variation in the activity of the dentate granule
cells, which initially causes corresponding variation in the instantaneous CA3 response. Over
several presentations, synapses between the most consistently responsive EC2 and CA3 neurons are strengthened enough to directly effect a postsynaptic action potential. When few
CA3 neurons respond directly, the variance in response times is high. As more CA3 neurons
respond directly and reliably to the EC2 stimulation, the variance in response times falls.
The apparent increase in outliers is a side-effect of the reliability of the early spikes (see
Figure 3.5).
3.3.3
Distinctiveness and reliability of learned responses
Although the preceding results show that learning reduces the time of the CA3 response
to EC2 stimulation, they do not show whether the patterns that are learned are in fact
distinct and reliably re-activated. Ideally, the network should demonstrate a capability to
learn distinct responses for different input, and furthermore activate these responses reliably
Figure 3.4:(following page): CA3 response timing distinguishes learned from novel inputs: At
the start of a presentation, the input is novel, and CA3 cells are slow to activate, not responding
until activated by the indirect link through DG. After repeated presentations, CA3 cells start
responding faster, activated directly by the EC2 input and eventually respond before the arrival of
the indirect signal. (a) Operation of the network over nine seconds. During the first second noise
was injected. Three distinct input patterns were chosen, and stimulated 28 times sequentially (7 Hz
for 4 seconds) in the EC cells with 5 ms jitter in spike timing. (b-c) Boxed areas from a, showing
the first and last presentation of the third pattern. While the CA3 cells initially respond only to
the indirect DG pathway, after multiple presentations the CA3 cells respond directly to the EC2
input prior to the DG response. The left-most vertical line shows the mean time of the jittered
input stimulus, the two right-most vertical lines show the median of the CA3 and DG responses
within the theta cycle. (d) Over the course of 28 presentations, the median response reduces from
39 ms to 19 ms, indicating that CA3 cells initially activated by the EC2-DG-CA3 pathway learn
to respond to the direct EC2 input.
3.3 The STSC circuit
63
64
A role for spike timing in learning and recognition
Figure 3.5: Spike latency histograms for CA3 responses at four different presentations (top left:
#1, top right: #10, bottom left: #14, bottom right: #28). The distribution of spike timing begins
unimodal, becomes bimodal during learning, but unimodal again once the stimulus is known.
when presented with sufficiently similar input.
In order to investigate the distinctiveness and reliability of the learned responses, the
network was trained with a set of three distinct stimuli, each of which activated 10% of EC2
(i.e. 11 out of 110 EC2 neurons). During training, each stimulus was presented 28 times.
After training, synaptic plasticity was disabled. Distinct test input patterns were generated
for each of the trained patterns, such that none of the neurons active in the trained pattern
were also active in the test patterns. A set of 200 distinct test input patterns were chosen in
this fashion for each of the three stimuli. In order to vary the similarity of the input pattern
to the trained patterns, testing consisted of stimulating the network with a combination of
the trained pattern and the current test pattern. Initially, the whole trained pattern was
presented, giving 100% similarity to the trained EC2 stimulus. On each subsequent trial,
one neuron from the trained pattern was removed from the active stimulus and replaced by
a neuron from the current test pattern, reducing the similarity to the trained input until all
neurons corresponded to the test pattern giving 0% similarity. This process was repeated
for each of the 600 test patterns (three stimuli × 200 test patterns each). All input patterns
were also subject to noise (as described previously), creating further variation in similarity
of the input pattern with the trained pattern.
3.4 Discussion
65
The separation of responses was determined by comparisons between the sets of responsive cells in CA3 for different input stimuli in EC2. The EC2 stimulus and the CA3 responses
can be represented as vectors, where each element in the vector corresponds to a neuron in
the respective regions. Elements in the vector were set to one if the associated neuron fired
between one stimulus and the next, and set to zero otherwise. The similarity between learned
and test responses was determined by correlating the respective response vectors (calculated
as the normalised dot product).
For each level of EC2 similarity, the similarity of the CA3 responses was averaged (see
Figure 3.6). The response curve shows that the EC2-DG-CA3 network is acting as a strong
pattern separator, and only performs limited pattern completion. For input patterns with
less than 50% input similarity to the trained patterns, the CA3 response had a low similarity
to the learned response (< 5%). However, once the input pattern was sufficiently similar to
a training pattern, the CA3 response matched the learned response. The improvement of
separation and completion when filtering the results according to CA3 spike latency shows
that ignoring inputs after learned responses prevents the highly separated input (which also
amplifies noise) from interfering with already known memories. Such improvement also
shows that the self-inhibition of CA3 is not fulfilling this role perfectly.
The results demonstrate a core property of a memory system: the CA3 region accurately
reactivates its previous response when a familiar pattern is presented, and activates a new and
distinct pattern in response to a novel input. As temporal filtering of the results substantially
improves the separation-completion curve, and the current self-inhibition in CA3 silences
the region for the remainder of the theta-cycle, an alternate method for attenuating the
separation signal seems likely in practice. Additionally, the curve here is heavily biased
towards separation, but a family of curves with different threshold intercepts that would be
useful in different contexts is plausible. Chapter 4 explores these issues in more detail.
3.4
Discussion
The goal of this experiment was to explore a mechanism to determine when to learn and
when to recall in the hippocampus. Simulation results show that spike timing can act as an
indicator of novelty to distinguish the two functions in the CA3 network (exemplified in the
three-neuron model and demonstrated in the STSC model).
The race model shows that the elapsed time from the stimulation of EC2 to a response
in CA3 can act as an indicator of the novelty of the stimulation pattern. The system has
functionally different behaviors for familiar and novel stimuli: EC2 patterns that are highly
similar to a familiar pattern will directly evoke patterns in CA3 that reflect the high input
66
A role for spike timing in learning and recognition
Figure 3.6: Learning and recall of patterns with and without consideration of timing. The
dotted line (y = x) indicates the boundary between separation and completion: the farther below
the line, the greater the separation; the farther above the line, the greater the completion. EC2
input vs. CA3 similarity comparison in the simulated hippocampal network shows that for low EC2
similarity, CA3 similarity approaches zero; only for the highest levels of EC2 similarity does CA3
similarity significantly rise above zero. The cross markers show the CA3 response overlap which
includes all CA3 cell responses within a single theta cycle, with CA3 response to the indirect input
only attenuated by the action of the inhibitory interneuron. Both separation and completion are
improved if the timing of the response is taken into account: The plus markers show the average
CA3 similarity responses which were active earlier than the median DG response within each
theta cycle. Short latency responses provide reliable completion for known inputs before indirect
stimulation, such that subsequent attenuation of the indirect input can prevent spurious separation
noise.
similarity; EC2 patterns that have low or moderate similarity are insufficient to evoke a direct
response in CA3, and instead activate CA3 through the indirect EC2-DG-CA3 pathway. The
DG input to CA3 itself is active for both novel and familiar patterns, however a sufficiently
familiar EC2 pattern activates CA3 via the direct path before the corresponding DG input
arrives, separating learned and novel responses temporally and allowing CA3 to suppress the
DG input (in the STSC model, this is through GABAB inhibition of CA3). Unlike previous
models that modulate between learning and recall over numerous pattern presentations with
a multi-second timescale (Hasselmo et al., 1995; Kali and Dayan, 2000), each presentation
of a pattern in the STSC model is learned or recalled depending on its individual novelty, a
process taking a fraction of each theta cycle.
Once a pattern is known, the network reliably and directly generates a response in CA3
before indirect activation via DG. The transition from a novel to a known input is facilitated
through STDP at the CA3 synapses; if a CA3 neuron fires shortly after a presynaptic EC2
neuron, the synapse connecting them is potentiated. At the tested rate of one presentation
per 7 Hz theta cycle, patterns are learned by the network after 10–20 presentations of a
3.4 Discussion
67
stimulus (see Figure 3.4), corresponding to 1.5 to 3 seconds of real time. This time frame
(1–3 seconds) is critical for many psychological phenomena including learning, memory and
attention.
The 7 Hz stimulation frequency ensures that there is no significant learning due to the
response of the CA3 cells to one input and any subsequent stimulations of EC2 cells (due to
the STDP time window and the maximum relative time of CA3 responses to EC2 stimuli,
as shown in the ABC-AC case in Figure 3.1b). As the race model does not incorporate
the recurrent connections of CA3 and hence requires no particular minimum stimulation
frequency to facilitate CA3 to CA3 synaptic plasticity, lower stimulation frequencies would
be unlikely to modify the model’s behavior. While the results presented here did not include
simulations with greater stimulation frequencies, rates beyond approximately 12 Hz would
cause significant interference in CA3 responses by subsequent inputs.
The STSC model does not incorporate plasticity in the synapses of the indirect path —
neither the associative LTP from EC2 to DG nor the non-associative LTP from DG to CA3.
While the former in particular may result in a latency reduction along the indirect route,
similar to the operation of STDP on the direct route, the delay introduced by the extra cell
(the DG cell) in the indirect path makes it unlikely that a known input will reach a CA3
cell via the indirect path before the direct input causes a CA3 response. Importantly, the
prerequisite for the correct isolation of novel and known responses is the relative timing of
the first responses of CA3 cells and the synaptic input from DG; so long as the first CA3
responses precede the DG input, the CA3 cells have some capability to ‘ignore’ the DG input.
In the simple ABC-AC network, once cell C learns the input from A, hyperpolarisation of
the cell after the direct response ensures that the input from B is ignored, resulting in a
response only to the learned pathway — recall. In the STSC model, a response is known if
a small subset of CA3 neurons respond directly and cause an inhibitory feedback neuron to
attenuate further incoming signals for a short time, also resulting in recall by using only the
learned pathway. Although the dynamics of the fast-acting global inhibition do achieve this
suppression in the current model, it seems likely that attenuation of the indirect pathway
would occur at the mossy fibre synapses rather than solely via GABAB inhibition of the CA3
cells (as modelled here), so as to allow other inputs to CA3 to drive the network’s behavior
(e.g. the CA3 recurrent connections) until the following EC2 input.
Based on the timing produced by the STSC model, one can predict that in vivo recordings
from DG and CA3 in response to stimulation of EC2 would show a population of spikes in
CA3 preceding DG activity (representing recall of cues) and a population of spikes in CA3
following DG activity (representing cues yet to be learned). A study by Yeckel and Berger
(1990) recorded the responses of DG, CA3 and CA1 to the stimulation of axons of entorhinal
68
A role for spike timing in learning and recognition
cortex in an anesthetised rabbit. Responses in CA3 were shown to occur at times both before
and after responses in DG, with the majority of responses in CA3 occurring with low latency
before a response in DG. Yeckel and Berger commented that the responses in CA3 with longer
latency than the latency in DG “did not follow more than the first few trains of continuous
stimulation” of the perforant path, although this effect was not quantified in the paper.
The results and the observation are consistent with predictions made by the race model,
although the exact latencies to the two CA3 responses differ. Based on the assumption that
artificial stimulation of EC is an unfamiliar pattern for the system, the STSC model predicts
that the initial stimulation will produce a long latency CA3 response through DG. After a
few trains of stimulation, the learned connections from EC2 would result in a lower latency
response in CA3. As the magnitude of the earlier direct response increases, the magnitude
of the later indirect response should decrease — an effect seen clearly in the STSC model
(see Figure 3.4d).
The spike timing method of combining learning and recall is also consistent with recent
data demonstrating that the phase in theta of pyramidal activity in CA1 increases with
environmental novelty (Lever et al., 2010). Lever et al. interpret their data as support for the
hypothesis that half-phases of theta are alternately used for encoding and retrieval. However
the data is equally consistent with an interpretation that the initial longer latency responses
correspond to the untrained stimuli through the trisynaptic pathway (EC2-DG-CA3-CA1),
and the shorter latencies result from the learned stimuli through the monosynaptic pathway
(EC3-CA1). The 33 degree theta phase shift observed by Lever et al. would correspond to
approximately half a gamma cycle, which could be due to the different delays in the pathways.
Assuming a theta rhythm of approximately 6 Hz, the Lever et al. data is consistent with
that of Yeckel and Berger (1990). In contrast to the Hasselmo et al. (2002b) theta phase
account of separation and completion, the STSC model makes a strong prediction about
how learning would affect the phase shift in CA regions relative to EC: namely the STSC
model predicts that, relative to the phase shift between the EC inputs, the magnitude of the
phase shift due to learning would be lower in CA3 than in CA1. This prediction is explored
further as a potential experimental study in Chapter 6.
Novelty in the STSC model is a localised phenomenon. The CA3 region learns a particular
response to a particular input from EC2, and using this is capable of regulating its own
learning. A region with inputs from both EC2 and CA3 may be capable of distinguishing
novel from known responses using the same timing signal. However it is unclear if the
knowledge of what is novel to CA3 is useful elsewhere. For example, CA3 itself is a major
input to CA1, along with EC3, therefore it seems logical that CA1 should also regulate its
own learning for its unique set of inputs. The precise mechanism of such regulation may
3.4 Discussion
69
differ substantially between regions; the complexity of the CA3 mechanism is required for
its dual pattern separation and pattern completion role, which downstream regions may not
require. The current work remains primarily focused on novelty, encoding and retrieval in
CA3 specifically.
70
A role for spike timing in learning and recognition
4
Modulating learning and recall
Dynamic environments require dynamic learning; a difference between two inputs that in
one context is insignificant may be highly significant in another. Although spike-timing may
signal the novelty of an individual input, additional processing is required to make use of
this temporal encoding. Neural processes are not limited to direct excitatory and inhibitory
transmission from pre- to post-synaptic neuron, a multitude of other processes regulate
and modulate the operation of all elements of the network. Two particular extracellular
neuromodulatory processes are considered in the current chapter as candidates for functional
control over the learn-recall balance. The first study explores the modulation of EC2-CA3
synaptic efficacy to control the degree of similarity between a given input and a previously
learned input that will recall the learned CA3 pattern (§4.1). The second study explores a
potential modulatory role for kainate receptors to allow the timing distinction between novel
and known inputs to prevent interference during recall without inhibiting all CA3 activity
(§4.2).
4.1
Modulating the tendency to recall
The STSC model in Chapter 3 required the test input to exceed a certain degree of similarity
to the learned input in order to complete the learned output representation. In earlier models
71
72
Modulating learning and recall
this similarity threshold was fixed and as low as 30 percent (Marr, 1971; Treves and Rolls,
1992). Furthermore, knowledge of the threshold in these earlier models was available only
via external analysis; the models were either trained offline and in a recall-only state during
testing, or they learned online but provided no distinction between learning and recall states.
Without an internal representation of the threshold, any modification to the learn-recall
balance would occur in the absence of feedback. In contrast, the race for activation in CA3
between direct and indirect pathways in the STSC model does distinguish novel from known
input. Assuming the novel vs. known statistics can be averaged, the ability to change the
similarity threshold enables the system to be modulated to maintain a particular threshold
given the current context. One simple mechanism for modulating this similarity threshold
is introduced below.
4.1.1
EC2-CA3 synaptic modulation
To investigate the effect of varying the threshold between completion and separation, a
modulatory input µ is introduced to the perforant path synapses. This input directly modifies
the efficacy of the synapse, such that I˙s is calculated as in Equation (3.1) but with the
postsynaptic effect of a presynaptic spike also multiplied by the current modulatory value:
I˙s = −Is /τs + δ(t − ts )wµ
(4.1)
where τs is the decay time constant of the synapse, δ is the Dirac delta function, ts is the
vector of presynaptic spike times, t is the current time, ws is the current synaptic weight
and µ is the current modulation value.
At baseline efficacy (µ = 1.0), the synapses act as in Chapter 3 (as Equation (3.1)
and Equation (4.1) are equal). Increasing µ increases the postsynaptic potential evoked by
presynaptic spikes, thereby decreasing the total number of active synapses required to evoke
an action potential in CA3. Consequently the specificity required to activate any particular
neuron also decreases. By varying µ, we sought to test whether the network could correctly
complete test input patterns with lower similarity to learned input patterns.
4.1.2
Threshold modulation results
The stimulation and recording procedure closely followed that of the previous experiment.
The network was trained with a set of three stimuli presented 28 times, and tested with 200
distinct sets of input patterns and related variations for each of the stimuli. The testing phase
was executed five times, starting at baseline modulation but increasing µ on each repetition
4.1 Modulating the tendency to recall
73
Figure 4.1: Modulation of the EC2-CA3 synapses affects the balance between pattern separation and completion. At baseline modulation (µ = 1.0), separation dominates over completion,
resulting in a network that is highly selective. As the modulatory input is increased (µ = 1.09) ,
the balance shifts from separation towards completion. At intermediate values (µ = 1.23, 1.38), the
functions are approximately equally balanced, with areas equal above and below the separationcompletion boundary. At the highest level of modulation (µ = 1.84), the network is strongly biased
towards recall.
such that one fewer fully potentiated synapse would be required to cause a postsynaptic
action potential. The specific values of µ were determined by finding the threshold of single
neurons with input similar to the EC2 input in the STSC model (for the exact µ values
see the supplementary material). Using the normalized dot product to compare network
responses, input / output overlap relations were generated for each test stimulus against the
network response to the appropriate trained stimulus. Results were grouped by modulatory
input level.
The network response at baseline modulation was no different from that in the previous
tests of distinctiveness, that is, the network was highly selective (see Figure 4.1). As the
modulatory value was increased, the level at which the output correlation exceeded the input
correlation decreased, that is, the network completed more patterns.
74
Modulating learning and recall
Figure 4.2: Effect of varied concentrations of KA and K+ on the PSPs at mossy fibre synapses.
From Schmitz et al. (2001).
4.2
Modulating the teaching signal
As discussed in Chapter 3, if the dentate gyrus acts as a pattern separator then it will
amplify input noise, which, left unchecked, will result in modifications to the corresponding
CA3 pattern. Early activation of CA3 for learned inputs provides a time window before the
arrival of DG input in which the network state might be modulated to curb the influence
of the DG input. One method of suppressing the indirect contribution, used in the STSC
model to this point, is to have all CA3 cells inhibited following their activation by the direct
pathway. While this does prevent the cells’ activation via the indirect pathway, it also
prevents their activation through any other means, such as through CA3 recurrent synapses.
To facilitate a functional role for the recurrent synapses during navigation (see Chapter 5),
an alternative method is required. One candidate mechanism is presynaptic modulation of
mossy fibre synapses via kainate receptors.
4.2.1
Kainate inhibition of mossy fibre synapses
Kainate receptors have a modulatory effect on mossy fibre inputs to CA3. High concentrations of kainate (KA) (> 100nM) appear to transiently attenuate the EPSP at mossy fibre
synapses (Schmitz et al., 2000, 2001). Low concentrations of KA (< 100nM) transiently
facilitate mossy fibre synapses (Schmitz et al., 2001; Ji and Staubli, 2002). At associationalcommissural (A/C) synapses, KA appears to have only an inhibitory effect, even at low
concentrations (Ji and Staubli, 2002). The excitability of the mossy fibres themselves is also
affected by KA (Figure 4.2, filled triangles) however unlike the dose-dependent facilitation
or depression at the synapses, the activity of the fibres appears to monotonically increase
with KA up to high (> 500nM) concentrations.
Glutamate release from A/C synapses near mossy fibres can affect the operation of the
75
4.2 Modulating the teaching signal
mossy fibre synapses (Schmitz et al., 2001). DG input could thus be regulated by CA3
activity; low levels of CA3 activity would increase the DG input and high levels of CA3
activity would decrease the DG input.
Evidence suggests that the effect of KA is presynaptic, and it interacts with paired pulse
facilitation (Schmitz et al., 2001; Ji and Staubli, 2002). Markram et al. (1998) describe a
model of short term synaptic dynamics where the effect of a presynaptic spike at a synapse,
EPSP , is given by
EPSP = A · R · u
(4.2)
where A is the absolute synaptic efficacy, R represents the relative volume of neurotransmitter available for release and u is a facilitatory variable representing the amount of remaining
neurotransmitter to be released. At spike event index n, the relative volume of neurotransmitter Rn can be calculated with1
Rn = Rn−1 (1 − un−1 ) exp
−∆t
τrec
+ 1 − exp
−∆t
τrec
(4.3)
where ∆t is the elapsed time since the previous spike, τrec is the recovery time constant and
where un is given by
un = un−1 exp
−∆t
τfacil
−∆t
+ U 1 − un−1 exp
τfacil
(4.4)
where τfacil is the time constant for facilitation, U is the proportion of available neurotransmitter to release at steady-state and the initial conditions are set as
R0 = 1
(4.5)
u0 = U
(4.6)
To allow KA-dependent modulation, we modify the model of short-term dynamics to
replace the constant U with a variable U KA dependent on the KA concentration. The effect
of KA on the EPSP (Figure 4.2, left, open circles) can be approximated with a simple model
assuming the presence of two KA receptors (KARs), one facilitating neurotransmitter release
(KAR1) and one interfering with neurotransmitter release (KAR2):
KA KAR1
KA KAR2
U KA = U + Ū KA − U · 1 − e−µ /
· e−µ /
(4.7)
1
The equation for Rn refers to un−1 ; this is inconsistent with the original Markram et al. (1998) description
(which uses un ) but is consistent with the operation of the model.
76
Modulating learning and recall
Figure 4.3: Model of U KA as a function of KA concentration µKA . The action of a facilitatory
receptor (KAR1) ensures that low levels of KA rapidly increase the relative amount of neurotransmitter released by a presynaptic action potential (beyond any existing facilitatory amounts). The
counteraction of a second receptor sensitive to greater levels of KA (KAR2) reverses this enhancement at 200nM and further increases of KA inhibit further facilitation.
where Ū KA is the upper bound for U KA , µKA is the current extracellular concentration of
KA, and KAR1 and KAR2 are constants determining the effect of KA concentration on
the KA-sensitive facilitating and interfering receptors respectively. Solving Equation (4.7)
for the points provided by Schmitz et al. (2001) (Figure 4.2) gives the best fit constants
U = 0.35, Ū = 1.0, KAR1 = 71ms and KAR1 = 193ms. The resulting function is visualised
in Figure 4.3.
There is no evidence to suggest whether one or both KA receptors affect the presynaptic
facilitation itself. Here I take a simple approach, letting the presynaptic facilitation depend
on the amount of extracellular glutamate. The consequent facilitation is dependent on the
activation of KARs at the time of presynaptic stimulation
un = un−1 exp
4.2.2
−∆t
τfacil
+U
KA
1.0 − un−1 exp
−∆t
τfacil
(4.8)
Kainate inhibition in the three neuron microcircuit
The effect of kainate inhibition can be demonstrated in the simple three neuron microcircuit
used to explain the race model (see §3.2). Structurally the network is similar to the initial
A-B-C microcircuit (Figure 3.1a), with three modifications. Firstly, the synapse from the
DG neuron to the CA3 neuron (or neuron B to neuron C in Figure 3.1a) is enhanced with
the kainate short term dynamics introduced above. Secondly, the CA3 neuron projects back
to an extracellular glutamate pool surrounding the DG-CA3 synapse, providing the value for
µKA in Equation (4.7) (Figure 4.4b). The glutamate concentration in this pool decays over
time to mimic uptake dynamics. Finally, the weight of the DG-CA3 synapse is increased to
77
4.2 Modulating the teaching signal
a.
b.
EC2 stimulation
EC2 stimulation
Extracellular
glutamate
DG stimulation
DG stimulation
CA3
CA3
CA3
Figure 4.4: CA3 structures for inhibition of separation responses on known input. a. Structure
used for the initial STSC model, using an inhibitory interneuron that fires with enough CA3
input, and inhibits the CA3 pyramidal cells. b. Alternate structure using KA modulation, where
glutamate spillover from proximal recurrent synapses (in blue) and mossy fibre synapses (in red)
add to the extracellular glutamate concentration, which in turn modulates the mossy fibre synapses.
Although the structure here depicts two CA3 neurons, in the microcircuit model there is only one
CA3 neuron, thus the recurrent synapse is configured as a self-exciting synapse with zero weight,
but that still produces extracellular glutamate.
highlight the kainate-derived inhibition.
During learning, the KA-modulated microcircuit behaviour is similar to the behaviour
of the non-modulated circuit. Initially, the CA3 neuron fires only after the input from DG
arrives (Figure 4.5, left panel). As before, after enough stimulations of the EC2 cell, the EC2CA3 path is potentiated and the CA3 cell generates an action potential in direct response
to the EC2 input (Figure 4.5, right panel). The corresponding activity in the CA3 recurrent
collaterals produces extracellular glutamate near the mossy fibre synapses. With the weight
increase of the DG-CA3 synapse, a CA3 cell without kainate modulation of its DG input
will, after responding to the direct input from EC2, also spike in response to the indirect
DG input (Figure 4.5, right panel, middle trace). A CA3 cell with kainate modulation of
its DG input will not respond to the same indirect input due to a presynaptic inhibition of
the mossy fibre synapse (Figure 4.5, right panel, bottom trace). In this simple model, the
inhibition occurred on a synapse to the same cell as responded to the EC2 input, however in
a larger network, all synapses near the active CA3 recurrent collaterals would be modulated
by the glutamate release.
78
Modulating learning and recall
Figure 4.5: Relative firing times and number of spikes for each region of the model with and
without kainate modulation. The spike times relative to the EC input (vertical green line) are
shown before learning (left panel) and after learning (right panel). Cells in DG fire after a small
constant delay (red spikes on top line); cells in CA3 are initially slower to respond and fire after
DG (blue spikes in left panel middle and lower lines). After learning, cells in CA3 learn to respond
to the direct EC input and fire faster than DG (blue spikes in right panel middle and lower lines).
The effects of kainate suppression of the DG-CA3 synaptic transmission are seen in the difference
between the middle and lower right panel. A CA3 cell without kainate modulation responds to
both the EC and DG inputs (seen in the middle right panel — CA3 ctrl — as two spikes). A CA3
cell with kainite modulation responds to the EC input alone (lower right panel — CA3 KA), as
the extracellular glutamate from the auto-associative connections presynaptically down-regulates
the DG-CA3 synapse. (See Nolan et. al. 2010 for further details.)
4.3
4.3.1
Discussion
Tuning the learn-recall balance
The dentate gyrus in the STSC model acts as a delayed pathway for the purpose of novelty
detection, but it also performs an orthogonalization role similar to previous models (Treves
and Rolls, 1992). Differences between EC2 stimulation patterns are enhanced by the indirect
pathway. Small differences between EC2 stimuli lead to larger differences between baseline
CA3 responses before learning. As a consequence, the CA3 patterns that are evoked by the
indirect pathway are inherently distinct (as shown in Figure 3.6).
Because small differences in the EC2 layer are further separated in DG, input noise is
also amplified. Computational models to date have worked around this issue via different
means, for example by using explicit learning and recall modes (Kali and Dayan, 2000),
by designating separate sub-phases of the theta rhythm for learning and recall (Hasselmo
et al., 2002b), or by permitting remapping of known inputs in partially known environments
4.3 Discussion
79
(Hasselmo et al., 1995). The STSC model selectively suppresses the effect of highly separated
input from DG for known EC2 patterns on a pattern-by-pattern basis, intrinsically ensuring
that any patterns that are sufficiently well known will not be relearned. This intrinsic novelty
detection operates without regard for the level of input pattern to learned pattern correlation,
or for the corresponding correlation of evoked responses in DG. Modifying the correlation
level required to elicit a learned response will therefore not negate the separation-suppression
effect of the novelty detection process.
A mechanism was proposed (§4.1) for tuning the rate of perceived novelty of a pattern,
and hence the ratio of learning over recall by modulating the synaptic strength between EC2
and CA3. The results show that increased synaptic efficacy in CA3 will cause CA3 cells
to fire more frequently before DG input reaches the region, increasing the rate of pattern
completion, which in turn will prevent the encoding of a new pattern (Figure 4.1). An
equivalent modulatory effect is visible even at a single CA3 synapse, where modulation affects
the weight at which that synapse will become strong enough to evoke a postsynaptic spike
(see Figure 4.6). As modulation is increased over baseline (µ > 1.0), the mean EC2-CA3
synaptic weight required for a CA3 cell to respond to the EC2 input decreases. Completion
occurs when a CA3 cell responds with a lower latency than the response of DG. Thus the
greater the modulation value, the lower the required similarity between the current input
and the learned pattern. However as the strongest learned weights still respond most quickly
(d∆t/dw is always negative), and the CA3 response is attenuated once a certain number of
CA3 cells respond, then irrespective of the level of modulation, only the memory that best
matches the input will be activated.
Acetylcholine has previously been proposed as a modulator of the novelty detection
threshold — the threshold at which an input is similar enough to a previously learned
input to be considered known (Hasselmo and Schnell, 1994; Hasselmo and Wyble, 1997). In
support of this theory, Rogers and Kesner (2003) have shown that an infusion of scopolamine
(a cholinergic antagonist) in CA3 prevents encoding of new patterns, but does not impair
retrieval during a rat navigation task. Evidence suggests that associational / commissural
(A/C) connections in the stratum oriens of CA3 are attenuated in the presence of acetylcholine (Vogt and Regehr, 2001), potentially ensuring that the pattern separation mechanism
through the indirect EC2-DG-CA3 path is free from interference during encoding (Hasselmo
et al., 1995). Furthermore, in high-acetylcholine environments, long term potentiation (LTP)
is elevated in the stratum oriens of CA1 (Huerta and Lisman, 1995; Ovsepian et al., 2004;
Shinoe et al., 2005), although there appear to be no experiments to date testing for a similar
effect in CA3.
Dopamine is similarly implicated in hippocampal function, leading to a proposal that it
80
Modulating learning and recall
Novel
Known
Figure 4.6: Modulation in the response latency of a single neuron. For low EC2-CA3 weights
the delay is high. Initially the modulation has little effect; at a synaptic weight of 5.0 × 10−10 the
CA3 response time is at its ceiling (∼35 ms), a value determined by latency of the indirect path. For
weights between approximately 1.0 × 10−9 and 2.1 × 10−9 , the CA3 response time depends strongly
on the modulation level of the synapses, which determines the EC2-CA3 weight at which the CA3
cell responds to the direct stimulation before the indirect stimulation arrives. For weights beyond
approximately 2.1 × 10−9 , the modulatory value has little functional difference as the direct path
evokes responses irrespective of modulation level, and the response latency decreases monotonically
with the weight, ensuring that so long as µ is equal across all cells, the cells latencies are ordered
according to their strength (and hence how close the input is to that cell’s learned input).
may likewise modulate the novelty detection threshold in the region (Lisman and Otmakhova,
2001). Like acetylcholine in the stratum oriens, elevated concentrations of dopamine appear to selectively attenuate the effect of perforant path inputs in the stratum lacunosummoleculare of CA1 (Otmakhova and Lisman, 1999). Dopaminergic neurons, including those
in the region afferent to the hippocampus, are highly active for unpredicted reward (Schultz,
2002) and LTP is elevated at perforant path synapses to CA1 pyramidal cells with dopamine
receptor activation (Otmakhova and Lisman, 1996; Lisman and Grace, 2005). Although
dopamine is generally implicated in reward learning, evidence suggests it is also involved
in the attentional or motivational scenarios required of a signal for novelty detection (Lisman and Otmakhova, 2001). It thus appears that acetylcholine and dopamine selectively
attenuate and up-modulate learning in internal and external inputs respectively.
Similar to the view of Hasselmo et al. (1995), I suggest here that acetylcholine release
in CA3 may not directly signal learning, but rather that neuromodulation of CA3 via both
4.3 Discussion
81
acetylcholine and dopamine may encode uncertainty by affecting the probability that any
afferent stimulation will be perceived as novel and hence will be learned. Increased neuromodulatory release would imply greater uncertainty: decreasing the strength of the direct
EC2-CA3 ‘recall’ path, thereby increasing the similarity threshold required to reactivate
previously learned representations and resulting in more patterns being classed as novel and
therefore being learned. Decreased modulatory release would imply less uncertainty and
have the inverse effect, resulting in fewer novel experiences and less learning.
A prediction from the STSC model is that neuromodulation of CA3 under novelty should,
in addition to its effect on the A/C fibers, also have some effect on the perforant path inputs
to CA3. Presynaptic stimulation of the perforant path should have a postsynaptic somatic
effect that varies with the concentration of some neuromodulator. Given the evidence of
dopaminergic attenuation of perforant path synapses in CA1, dopamine is proposed here as
the most likely candidate for this modulation in CA3. In the STSC model the efficacy of
perforant path synapses increased with the modulatory parameter µ. One would then expect
µ to vary inversely with dopamine concentration, such that as the concentration of dopamine
rose, the efficacy of the perforant path would fall, and potentially the rate of STDP would rise
(an effect omitted in the present work, but one that could operate as described by Izhikevich
(2007)). Modulation could alternatively be achieved by direct cholinergic effect or by indirect
means similar to the GABAergic innervation suggested by Vogt and Regehr (2001) at mossy
fiber synapses. For example, the stratum oriens-lacunosum moleculare (O-LM) interneurons
are enhanced by activation of M1 and M3 muscarinic acetylcholine receptors (Lawrence
et al., 2006) and their axons terminate among the CA3 dendrites receiving perforant path
stimulation (Gulyas et al., 1993).
4.3.2
Implications of presynaptic kainate modulation
It is well established that presynaptic kainate receptors modulate the efficacy of glutamate
release (Schmitz et al., 2000, 2001; Ji and Staubli, 2002). High levels of principal cell activity
in CA3 and in the corresponding A/C synapses seems likely to lead to high volumes of
glutamate release and increased synaptic spillover, capable of modulating nearby mossy
fibre synapses (Schmitz et al., 2001). Simulations of the synaptic regulation effect in the
three neuron microcircuit demonstrate that it can prevent a postsynaptic response to input
arriving within approximately 10 ms of an initial action potential (Figure 4.5).
The original STSC model implemented a global inhibitory feedback mechanism that limited the total amount of activity in CA3. After reaching some threshold, a single inhibitory
neuron projecting to all pyramidal cells would fire, forcing all these cells into a hyperpolarised
82
Modulating learning and recall
state. When direct EC2 input evoked enough CA3 activity to reach this threshold, CA3 cells
would not respond to the ensuing input from DG, however they were also non-responsive to
further input from EC2, or to input from the recurrent A/C synapses. Ignoring the DG input
for known inputs is important as it prevents noisy pattern separation input interfering with
existing memories in CA3. Kainate modulation provides an alternative mechanism to ignore
DG input without inhibiting the CA3 cells, thereby allowing CA3 to continue to respond to
other input. In the context of a larger network, the functional role of kainate proposed here
is to temporarily and selectively ignore pattern separation input to CA3.
Although a high concentration of glutamate presynaptically inhibits mossy fibre synapses,
in lower doses it has the opposite effect, facilitating transmission instead (Schmitz et al., 2001;
Ji and Staubli, 2002). A small number of active A/C synapses should therefore increase the
EPSPs generated by DG input. Likewise, glutamate spillover from neighbouring mossy
fibre synapses may also contribute to kainate modulation. All such activity seems likely to
increase the synchronisation of the ensuing CA3 activity.
In the kainate-modulated microcircuit (§4.2.2), the modulation occurred on the synapse
from DG to the same cell as responded to the EC2 input. In a larger network, all mossy
fibre synapses near the active CA3 recurrent collaterals would be modulated by glutamate release. Kainate modulation is not limited to mossy fibre synapses however; the A/C synapses
themselves are also inhibited by extracellular glutamate (Ji and Staubli, 2002). The time
course of glutamate diffusion and uptake regulate the range in which synapses are affected
and for what duration. Existing data is inconclusive, suggesting only that glutamate levels
may remain elevated from tens to hundreds of milliseconds after a significant release event
(Clements, 1996; Hires et al., 2008). The function of the kainate receptors in the model here
predicts that the effect of the extracellular glutamate on mossy fibre synapses would be of
long enough duration to attenuate the DG input for any stimulus that evoked a direct response — a duration in the low tens of milliseconds. This duration is also suitable to restore
the effect of A/C synapses by the next gamma cycle, fitting with the theorised function of
CA3 recurrence in the following chapter.
4.4
Summary
This chapter extended the pattern separation and completion network of Chapter 3 with
mechanisms to control the balance between learning and recall and to prevent remapping
of known stimuli. In the context of a cognitive map, with appropriate input (for example
input from a path integration system and some form of sensory input) the memory system
described thus far is capable of learning and recognising places. The significance of the
4.4 Summary
83
particular implementation proposed here is that this function occurs in a short time — a
fraction of a theta cycle — following an input. The next chapter explores how the anatomy
and dynamics of CA3 support a model in which the remaining time in the theta cycle fulfills
the path encoding and recall aspects of a cognitive mapping memory system.
84
Modulating learning and recall
5
Temporal sequencing of memories
Using a cognitive map to facilitate predictive navigation requires both the ability to localise
within an environment and the ability to recall paths to remote locations. Evidence from
lesion-based one-shot learning and latent learning experiments implicates the hippocampus
in the predictive navigation abilities of rodents (Steele and Morris, 1999; Stouffer and White,
2007). At a cellular dynamics level, the strong spatial correlation of hippocampal principal
cell activity is generally assumed as evidence that these cells ‘code for’ the location in which
they fire during navigation. This assumption has led to a widely accepted conjecture that
the hippocampus primarily plays a localisation role during navigation. How and where path
recall occurs, however, remains an open question.
Both localisation and path recall abilities require a map detailing the connectedness of
the environment. If the localisation hypothesis is true, the map necessarily encoded by the
hippocampus must either be used prior to navigation to recall and store a navigable path
in some form of short-term memory, or the map must be replicated entirely elsewhere to be
used simultaneously during navigation. Although these options are theoretically possible,
this chapter explores an alternative that I argue is simpler and provides an explanation
encompassing a greater number of observed hippocampal phenomena. Underlying the theory
presented here is a modification of the localisation conjecture of the hippocampus: in addition
to localisation, the hippocampus is implicitly performing path recall throughout navigation.
85
86
Temporal sequencing of memories
To describe this new theory, new definitions are required for certain spatial concepts,
for example the region where a cell responds directly to external input I term the anchor
field of that cell. Based on an extended role for hippocampal cells, I propose a CA3 model
incorporating path recall that explains how the traditional understanding of place cells needs
to change, to reinterpret their firing fields as path fields that lead to the cell’s anchor field.
To illustrate the mechanisms by which the anatomical and dynamical properties of the CA3
network support such a function, I describe the expected behaviour of CA3 place cells for an
animal running on a linear track, showing how a path is represented by the firing of cells with
overlapping yet ordered fields at successive points along the path (§5.1). This linear track
case is extended to two-dimensional fields and compared with existing interpretations of
place cell data (§5.2). This chapter concludes with a discussion of how the presented theory
differs from typical place field theory, looking particularly at the information encoded by the
hippocampus (§5.3).
5.1
Place cell dynamics
Chapters 3 & 4 demonstrated a mechanism by which CA3 principal cells could develop and
maintain stable spatial fields. The corresponding model CA3 population dynamics provide
unique codes for locations within the environment. In the race model, each of these CA3
codes is cued directly by the sensory footprint of the location in which it was created, via
the projections from EC2 and DG, and without any contribution from the characteristic
CA3 recurrent synapses. Spatial fields that are cued directly from the current sensory input
are referred to here as anchor fields. Regardless of the connectivity of the environment, the
anchor field of the cell remains constant. Under the localisation hypothesis for CA3 function,
a cell’s anchor field would be equivalent to its entire place field.
Although often modelled as a homogeneous randomly connected network, the CA3-toCA3 synapses have a spatial bias in their connectivity (Amaral and Pierre, 2007). Cells
distal from the dentate gyrus project farther on the septo-temporal axis than proximal cells.
Furthermore, projections are more proximal to cells located temporally than the originating
cell, and more distal to cells located septally. These facts suggest that a cell located septodistally of another is less likely to receive a projection from that cell than it is to project to
that cell (Figure 5.1). In the extreme case, such a connection structure forms a series of cell
groups with feedforward connectivity between groups.
Although the connectivity between these networks is feedforward, each individual pool
receives direct input from EC21 (Amaral and Pierre, 2007). Each individual pool could thus
1
There is however a gradient across the transverse axis of CA3, with proximal cells receiving less EC2
87
5.1 Place cell dynamics
on
cti
roj
e
ren
tp
Re
cur
Temporal - septal
Place field size increases
sb
ias
CA3
Proximal - distal
Figure 5.1: CA3 connectivity bias. Septo-distal CA3 cells on average project more temporally
and proximally than tempero-proximal CA3 cells project septally and distally. Electrophysiologically, an obvious correlate of this distribution is the spatial field size of the cells, which grows from
the septal (dorsal) to temporal (ventral) extents of the region.
develop individual direct spatial responses for a particular sensory input. During initial
exposure to an environment, cholinergic antagonists prevent novelty-specific modulation,
suggesting acetylcholine is present in the region in novel environments (Villarreal et al., 2007).
Acetylcholine causes a decrease in the efficacy of the CA3-CA3 synapses (Vogt and Regehr,
2001), but increases LTP in these synapses (Buchanan et al., 2010; Boddeke et al., 1992).
If the codes for adjacent locations are stimulated in quick succession during navigation,
the group-to-next-most-temporal-group CA3 connections between cells coding for adjacent
locations will be potentiated via STDP (Figure 5.2).
5.1.1
Spatial field size
As the direct spatial responses are learned by the CA3 cells, that is, once these cells acquire
their anchor fields, it seems likely that the activity level in the region would increase. Because
CA3 projects to the lateral septum, which in turn inhibits the medial septum (Amaral
and Pierre, 2007), increased CA3 activity may decrease medial septum activity and hence
decrease acetylcholine release in the hippocampus. If the resulting up-regulation of the
previously potentiated CA3-CA3 synapses is strong enough to cause the next most temporal
layer’s adjacent code to fire, the spatial field of those cells would broaden to include their
input than distal cells (Amaral and Pierre, 2007)
88
Temporal sequencing of memories
a.
A
B
C
D
E
F
G
A
B
C
D
E
F
G
CA3
Temporal - septal
EC2
b.
CA3
Temporal - septal
EC2
Figure 5.2: Theorised potentiation of CA3 to CA3 synapses during initial traversal of a linear
track. A set of seven EC2 cells represent locations A-G on a linear track, each cell responding in
only one location; each of these cells represents some unique combination of sensory and idiothetic
data as used in previous chapters. Each of these cells projects to one cell in each CA3 group,
each CA3 cell representing a unique CA3 code for that group. These pre-wired CA3 fields assume
the learning steps of previous chapters have already yielded unique direct responses for each EC2
input, that is, each EC2 cell has synapses with many different CA3 cells, but for each EC2 cell
only one synapse per CA3 group is potentiated. Each EC2 and CA3 cell is coloured to indicate
the location to which it directly responds, matching the colours on the linear track (top right of
each figure). Currently responsive cells and connections are highlighted (filled triangles: active
cell; empty triangles: inactive cell; black line: active connection; grey line: inactive connection).
Each CA3 cell in one group is connected to every CA3 cell in the next-most-temporal-group, but
the synapses are initially weak (dotted grey lines). a. At location A, all the synapses from one
CA3 group to its efferent group are activated (dotted black lines), but have no direct effect. b. At
location B, all projections from cells responsive to location B are still weak, however the betweengroup synapse from an A-sensitive to a B-sensitive cell is potentiated due to STDP (solid grey
line).
5.1 Place cell dynamics
89
adjacent location. Importantly however, without significant cholinergic modulation, the
plasticity of EC2-CA3 synapses would be lowered. Thus while the spatial fields of the cells
would grow, their anchor fields would remain constant. At the most septal (dorsal) layer,
the spatial field of each cell would consist only of the cell’s anchor field, but in the layer more
temporal (ventral), each cell’s field would include its anchor field and the anchor fields of any
cells in the afferent layer that fired immediately prior during initial exploration. The firing
fields of the more temporal cells would thus extend backwards along the explored paths
that lead to their anchor fields. In a simple unidirectional environment such as a linear
track, spatial field expansion would thus occur in one direction only (as in the learned links
in Figure 5.2). The more temporal cells thus begin to fire predictively before the animal
reaches their anchor fields, gaining what I define here as a path field.
Spatial field expansion during recall is dependent on the cells in one layer receiving
input through previously potentiated synapses from cells with adjacent anchor fields in the
next-most-septal layer, its afferent-adjacency cells (Figure 5.3). Ignoring other influences,
a cell’s spatial field will thus include its anchor field, plus the entire spatial fields of its
afferent-adjacency cells. The magnitude of the spatial fields of each cell will consequently
depend upon the septo-temporal location of the cell: the most septal cells will have spatial
fields limited to their anchor fields, and the more temporal, the greater the size of the
spatial field (see shaded bands in Figure 5.4, in particular the field size of the cell coding for
location G in each cell group). This progressive spatial field size increase will occur despite
potentiation of synapses only occurring between proximal layers. A correlation of field size
to septo-temporal (dorso-ventral) extent is well characterised in existing electrophysiology
experiments (Kjelstrup et al., 2008).
5.1.2
Temporal dynamics
In addition to the field size order in the cells, a temporal structure to the firing of the cells
would also be expected. Because the firing of a cell in its extended spatial field is consequent
on the firing of its afferent-adjacency cells, the activity of the former will occur after the
latter. In the current simplified structure, the farther away from its own anchor field, the
later a cell fires with respect to the firing of the cells currently in their anchor fields. Thus as
an animal navigates, the activity of each cell precesses (in the linear track case in Figure 5.4,
each individual cell can be seen precessing at each consecutive location from left to right).
Such precession has been observed with respect to theta rhythm in the hippocampus —
theta phase precession.
90
Temporal sequencing of memories
A
B
C
D
E
F
G
CA3
Temporal - septal
EC2
Figure 5.3: Activity of CA3 cells after training on a linear track under the proposed theory.
Although there is full connectivity between each group of CA3 cells in the septo-temporal direction,
only those synapses that have been potentiated via STDP are shown here. The animal is in location
A, causing direct activation of the corresponding cells in each CA3 group (as in Figure 5.2, filled
triangles: active cell; empty triangles: inactive cell; black line: active connection; grey line: inactive
connection). Due to the potentiation of synapses between each cell and its afferent-adjacency cell,
cells with direct responses to locations ahead of the animal’s current position are also activated.
Each step in the temporal (ventral) direction sees activation of another step forward on the track.
91
5.1 Place cell dynamics
Position
A
B
C
D
E
F
G
1
Cell group
3
4
5
6
Cell responses in theta phase and resulting place fields
2
7
Figure 5.4: Anchor fields, path fields and theta phase precession on a linear track. The diagram
shows a rat running through seven locations on a linear track (A-G). The vertical axis corresponds
to the septo-temporal axis in CA3, and shows seven cell groups (1-7) as in Figure 5.3, each group
containing one cell per location (49 cells total), coloured to match the location of the cell’s anchor
field. Most septally located cells have small place fields, each place field consisting solely of the
anchor field. Moving temporally, place field size increases, but the size of the anchor fields remains
constant (anchor fields in dark shading, non-anchor in light shading). In this diagram, the rat
traverses each location A-G over a single theta-cycle (grey sine wave). The relative timing of each
spike with respect to theta is given in the raster overlayed on the corresponding cell’s place field.
The anchor field fires in early theta. The region of the place field outside the anchor field shows
theta phase precession as the rat traverses the field (late theta on field entry precessing to early
theta at the anchor field).
92
5.2
Temporal sequencing of memories
Two-dimensional fields
Moving beyond the simple linear track environment, consider the dynamics of the outlined
CA3 structure in an open field. In this case, during learning, an animal would approach the
anchor field of a cell from many different directions. The resulting spatial field would extend
backward in every direction, with the path field surrounding the anchor field. Once learned,
as the animal entered the extended field from any direction, the cell would begin firing. In
the linear track example, because of the non-symmetry of experience, the cell would cease
firing after the animal passed the anchor field. If such asymmetry persisted even in the open
field scenario (other alternatives are discussed in §5.3.2), a cell would cease firing once the
animal passed through its anchor field, not firing while the animal traversed the path field
travelling away from the anchor field. Summed over many field traversals in many directions
(as with typical place field plots), the resulting two-dimensional field would appear spatially
symmetric, although on any single traversal the cell would appear to fire in approximately
half the field.
The temporal dynamics in the open field scenario also provide distinct characteristics.
Again assuming the linear track asymmetry persists in the open field, then spikes on the
perimeter of a cell’s spatial field all occur just as the cell begins to fire on anchor field
approach. Thus all perimeter spikes occur with maximal latency (minimal precession) with
respect to the firing of cells currently in their anchor fields. Thoughout the approach to the
centre of spatial field from any direction, the relative firing of the cell precesses, creating
a concentric ring gradient of firing phase precession from the field perimeter to the cell’s
anchor field (Figure 5.5, right).
5.2.1
Reconciling anchor and path field theory with place field
plots
The dynamics of two-dimensional place fields described above do not match the typical
plots from electrophysiology experiments. Experimentally derived place fields tend to show
firing throughout the field on individual passes through the field. As a consequence of this
spatial difference and the nature of theta phase precession, there is no absolute correlation
between firing phase and field position; the field perimeter has both minimally and maximally
precessed firings depending on the direction of travel, while firing at the field centre is in
general partially precessed. On initial inspection, the anchor and path field model proposed
above is inconsistent with the two-dimensional field data. However if one considers that the
typical place field plots are one particular analysis of the data, then the anchor and path
5.2 Two-dimensional fields
93
Figure 5.5: Diagrammatic characterisation of theta-phase and position interpreted using a
theory of place fields vs. a theory of anchor fields. By definition a place field is the region of the
environment that the cell fires. (a) The traditional interpretation is that the perimeter of a place
field is delimited by the onset and offset of a cell’s firing irrespective of the trajectory through the
field. This interpretation of position is a consequence of place field sizes being minimised during
analysis. (b) The proposed anchor and path field theory states that spatially-sensitive cells respond
both directly and indirectly to the location in the environment. The subset of these regions of the
environment that cause a direct response I term “anchor fields”. In practice, these anchor fields
could be determined by examining the location when the cell fires at maximum theta precession.
When an animal’s path passes through the anchor field, this will coincide with the offset of the cell.
When an animal’s path does not pass through the anchor field, the cell never reaches its maximal
phase precession.
field model is not necessarily inconsistent with the data itself, but rather with the model
upon which typical place field analysis is based. That is, the conflict is with the typical place
field interpretation of cell firings.
Analysis of place fields is typically based on the assumption that the location a cell
represents is the same as the location in which it responds. As a result of this assumption,
it is further assumed that the cell represents such information with optimal accuracy and
quality. The analytic consequence of these assumptions is that the locations of the spikes
are offset by the fixed amount that minimises the firing area of the cell in two-dimensions,
potentially with a consideration to also minimise the field’s patchiness and maximise its
coherence (Muller and Kubie, 1989). This offset can be interpreted as adjusting the location
at which the animal perceives itself to be located, as a displacement from the location sampled
by the animal tracking system (usually the location of LEDs on the headstage affixed to the
animal).
Different offsets produce different place fields. Skaggs et al. (1996) outlined the effects
94
Temporal sequencing of memories
of using various different offsets for the analysis of one particular place field (Figure 5.6).
If the reference point is at the rat’s eyes, the field is tight with a mixed-phase perimeter as
described above (Figure 5.6, middle). Using a reference point near the rat’s nose results in
a larger field with a late-firing centre and a precessed-firing perimeter (firing onset as the
rat enters the field centre, Figure 5.6, bottom). Finally, if the reference point is near the
back of the rat’s head, the field is similarly large, but with a late-firing perimeter and a
precessed-firing field centre (Figure 5.6, top). The first offset provides the typical place field
theory analysis, and the final offset matches the expected field characteristics of the anchor
and path field theory.
Open field data from cells with similarly sized fields cannot disambiguate between the two
theories. Alternate experiments to obtain a variety of field sizes in an open field arena would
enable the testing of fixed offsets to determine whether any particular offset maintains the
consistency of field characteristics across field size (see §6.2). In lieu of such disambiguating
evidence, anchor and path field theory provides a functional purpose for firing precession and
varying field sizes, fitting with an operational explanation of how the known anatomy could
lead to the known dynamics — a consistent explanation that place field theory seemingly
lacks.
5.3
Significance of anchor and path field theory
What information does an anchor and path field provide that a place field does not? In
the classical interpretation, when a CA3 spatially-sensitive cell first fires (late in the theta
cycle), it provides information that the rat is at a point along the perimeter of the place
field. As it passes through the field, the phase correlates well with distance through the field
(O’Keefe and Recce, 1993), until at the final firing (early in the theta cycle) the rat is once
again at a point on the field perimeter.
In the anchor and path field interpretation, when a CA3 spatially-sensitive cell fires in
an open field it provides similar spatial correlations as the place field interpretation, merely
shifted backwards along the trajectory. However it also provides information regarding the
accessibility of the cell’s anchor field: a cell’s firing signals that the anchor field of that cell
is accessible from the current location. Causal firing between cells with nearby anchor fields
produces sequences that correspond to paths. When a CA3 cell is maximally precessed, it
indicates that the animal is in the anchor field of the cell. Thus under the anchor and path
field interpretation, CA3 is performing both localisation and path recall.
5.3 Significance of anchor and path field theory
95
Figure 5.6: Spatial field characteristics of a rat hippocampal cell using different position offsets.
With the reference point near the back of the rat’s head (top), the field is large with the cell
firing late around the perimeter of the field and early in the centre. When the reference point is
at approximately the rat’s eyes (middle), the field is tight, with the firing latency intermingled
throughout the field. When the reference point is around the tip of the rat’s nose (bottom), the
field is again large, but with the cell firing late in the centre of the field, and early around the
perimeter. Adapted from Skaggs et al. (1996).
5.3.1
Calculation of position offsets and anchor fields
As discussed in §5.2.1, place fields are typically calculated to optimise size, patchiness and
coherence measures. These measures are based on the position and firing rates of the cells,
but not the phase of firing. Calculating a cell’s spatial field under anchor and path field
theory involves optimising the phase gradient over the field. Across all cells, the appropriate
offset should be calculated by minimising the area in which the most-precessed spikes occur.
This area forms the anchor field of the cell. Although the anchor fields of different cells may
be different sizes, a single offset should give late-perimeter and early-centre firing for all cells.
The remainder of the spatial field for each cell forms the path field of that cell. In an open
field environment, there should be a gradient of increasing phase with increasing distance
from the anchor field within the path field.
96
5.3.2
Temporal sequencing of memories
Notable simplifications in the theory
Theta oscillations and path recall
Anchor and path field theory is not intrinsically dependent on the theta rhythm, the explanation in this chapter merely uses it as an index for precession. However if the path
recall system is reset on each theta cycle, it provides a simple mechanism for fixed-time
search, allowing continuous planning during movement. Such fixed-time search limits the
scope of planning, although to what degree it is limited requires further experimental and
theoretical work, particularly relating to the differences in scale and synchronisation across
the hippocampus.
Discrete sets of cells connected in a feedforward manner, as described for the model in this
chapter to illustrate the potential mechanism behind the development of spatial fields, is a
simplification of CA3 anatomy. Continuous connectivity, including the transverse (distal-toproximal) bias across the field is likely to produce more complex dynamics than suggested by
the theoretical model above. Furthermore, in addition to the additional internal complexity,
the external projections are not homogenous across the region. Input from EC2 is greater at
the distal than the proximal extent, and the strength of the input from DG has the reverse
gradient (Amaral and Pierre, 2007). On the septo-temporal axis, the external input at the
septal pole is dominated by input from lateral and caudal EC2 (both lEC2 and mEC2), while
at the temporal pole there is a greater contribution from more medial extents of the EC2
subdivisions (Witter, 1993). Although not specified by anchor and path field theory itself,
the effect of this additional anatomical detail may play a role in minimising the impact of
the fixed-time search by allowing multi-scale searches to plan local paths in fine detail (in
the septal extent) and longer paths more approximately (in the temporal extent). A parallel
planning mechanism such as this would also provide an explanation for the complete phase
precession found even in the dorsal (septal) hippocampus.
Why directional planning?
In the open field scenario there are two possibilities for the location of the cessation of firing.
If the dynamics were such that both the location of field entry and the direction of motion
were irrelevant, then the cell would fire until the animal exited the extended spatial field. In
this case, the phase of firing would precess in both directions, reversing at the field centre.
Electrophysiological data demonstrates that this is not occurring: under the anchor and path
field interpretation of the data, cells fire only on anchor field approach. Such behaviour would
prune path search to exclude paths through recently visited locations. How the directional
bias is introduced is unclear; it is possible that some path trace or direction of motion is
5.4 Validating the theory
97
encoded in the CA3 network, or a sensory bias from the EC2 input could partially potentiate
cells currently in their path fields with similar sensory footprints.
5.4
Validating the theory
There are three significant elements to the theory proposed here, each requiring testing.
Firstly, there is the assertion that rodents are capable of path planning, a fact often assumed
to be true, and one much discussed (Thistlethwaite, 1951) but never satisfactorily resolved
(Jensen, 2006). Assuming rodents are capable of path planning, anchor and path field theory
asserts that the hippocampus is involved in more than merely localisation — that it is also
responsible for performing path planning. Finally, there is the proposed mechanism by which
the hippocampus may encode and recall paths, the concept of anchor fields as the space a
cell represents and the path field as the space a cell responds.
While it is possible that the anchor and path field representation is the spatial information
storage mechanism in the hippocampus even if rodents are not capable of path planning,
it does remove the functional justification for the mechanism — there seems to be little
reason to perform forward path search if it confers none of the behavioural advantages.
The strongest possible result for anchor and path field theory is if all three elements are
empirically validated. The following chapter presents the design of a series of experiments
to support or falsify these elements.
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Temporal sequencing of memories
6
Empirical predictions
The gold standard in computational modelling is to make novel predictions that can be
tested empirically. A prediction should be falsifiable, and ideally should be interesting and
even counter-intuitive given the current prevailing views. The previous sections identified
theoretical issues that arose from the modelling work. This chapter presents three proposals
to translate these issues into empirically testable designs. The race theory predicts that
timing in CA3 should change relative to the timing of EC2 stimuli. This prediction can
be tested through relative timing studies (see §6.1). The path and anchor theory predicts
that path field size will vary while anchor field size will remain relatively constant over the
dorso-ventral axis of CA3. This prediction can be tested by simultaneously recording twodimensional fields in CA3 from different points on this axis (see §6.2). A second prediction
from the anchor and path theory is that rodents are capable of performing multi-segment
path navigation, and that this occurs using path replay within CA3 theta cycles. This
prediction requires a complex maze paradigm (see §6.3). The study designs for the first two
predictions are given as outline sketches, and for the third prediction a complete experimental
design has been prepared. These three studies have been discussed with electrophysiologists
and plans are being developed for their execution.
99
100
6.1
Empirical predictions
Looking for a race
The race described in the STSC model (Chapter 3) (Nolan et al., 2011) demonstrates that the
time at which CA3 cells fire in response to perforant path and mossy fibre inputs could encode
the novelty of the EC2 stimulus. Finding explicit direct evidence for the race mechanism
would require simultaneously recording units in EC2, DG and CA3 that were connected
via both the disynaptic and the monosynaptic pathway, perhaps by establishing a likely
causal connection similar to Dragoi and Buzsaki (2006). Simultaneously recording cells in
three separate regions connected in such a fashion seems unlikely, however other experiments
may provide some evidence of the race. Experimental evidence suggests that EC2 spikes fire
preferentially at some local theta phase (Mizuseki et al., 2009), thus were the race hypothesis
true, one would predict that during learning, the responses of place cells in CA3 precess
slightly with respect to EC2 theta. Such precession should be greater than any similar effect
observed in the granule cells in the dentate gyrus.
Testing the model requires LFP recordings from EC2 with simultaneous multi-unit recordings from CA3 and DG during exposure to a novel environment. For the purposes of this
experiment, novel would be defined as any environment for which the majority of CA3 place
cells do not yet have stable fields, for example a new box in a familiar room or an unexplored
chamber in an existing box. As the fields increase in stability, the average firing phase of
CA3 place cells (i.e. the CA3 principal cell population response in figure 6.1) should precess,
while the average firing phase of dentate granule cells should remain constant or decrease by
a lesser amount.
6.2
Evidence to disambiguate path and place interpretations
A practical question in processing the data collected from place cell experiments is determination of where to attribute a rat’s location given the recorded position of the rat’s
headstage. The majority of studies minimise the size of the place field, potentially also
minimising patchiness and maximising coherence as suggested by Muller and Kubie (1989).
The prediction from path and anchor field theory is that an accurate analysis of place cell
information can only be gained by a different process, one that determines the location of
the anchor field.
In order to discriminate between these two possibilities, different sized fields are required.
A basic open field task can be used to test the relative sizes of fields while recording from both
6.3 Multi-segment path navigation
101
Figure 6.1: Hippocampal (top) and entorhinal (bottom) principal cell responses across EC3
theta (from Mizuseki et al. (2009)). Both EC2 and CA3 are strongly modulated by theta, with
CA3 at its quietest shortly after the peak of EC2 activity. DG activity is modulated by theta to
a lesser extent. The data does not distinguish novel from known responses. A prediction from the
race theory is that in novel environments the CA3 response would initially further lag the EC2
response (creating a greater phase difference from one EC2 peak to the following CA3 peak), and
would shift to the timing pictured here in familiar environments.
dorsal and ventral CA3. The traditional analysis would predict that the headstage offset
required to minimise different sized fields would be constant across the size of the field,
whereas anchor and path field theory predicts that the offset would vary systematically with
the size of the field. Anchor and path field theory also predicts a different structure to
the phase-position relationship within a field. The periphery of the field should contain
late-theta spikes, with the spike phase gradually precessing to the centre of the field, which
should contain primarily early-theta spikes. This is in contrast to traditional analysis, which
has early and late theta spikes on the periphery, and mid-theta spikes in the centre.
6.3
Multi-segment path navigation
Rodent navigation experiments tend to focus on whether an animal knows where it is in a
previously explored environment, or how well the animal can estimate its spatial location (i.e.
102
Empirical predictions
its dead reckoning abilities). There has been little work in the last half century establishing
how effectively rodents can actively plan routes from previously learned sub-sections. The
task outlined here is intended to elucidate whether rodents are capable of planning routes
by combining sections previously traversed independently.
It is an open question how place cells participate in path planning. Any cells involved
in planning a route to a particular location should be active not just in the destination, but
also in locations from which such planning is taking place. Such cells would appear to have
place fields spanning some distance from the location they are ’coding’ for, with the field
size determined by the scale of the prediction. In a straight corridor, a cell that coded for
the end of the corridor, but was predictive from a distance greater than the length of the
corridor would fire throughout the corridor.
Place fields in CA3 vary in size from the dorsal (septal) to ventral (temporal) extent
(O’Keefe, 2007). In addition to testing whether rats can mentally connect subsections of a
route to achieve a behavioural outcome, we also consider what evidence would be required
to determine whether place field size variance is due to a greater degree of prediction, that
is, whether place cells are in fact involved in path planning.
6.3.1
Experiment design
Rats should be implanted with multi-unit tetrodes targeting the intermediate to ventral
CA3. The target cells are those with place fields approaching the size of the testing arena.
The animals will be tested in a cued navigation task on a T-maze with corridors attached
to the end of each arm, with the arms themselves warped such that at the junction the
end chambers are not visible (see Figure 6.2, which has been modified from a more classic
two-tiered T-maze task seen in Figure 6.3 to simplify the learning task). The walls of the
maze should be plain, avoiding any unique visual cues, and high enough to prevent rearing
from providing any topological clues. Each chamber at the end of the arms of T-maze and
associated corridors should have a unique textural and visual cue. During all phases of
training and testing, a reward should be present but inaccessible in each chamber to control
for scent. The maze apparatus should be easily rotated. Global cues should be minimised,
and during the task the area outside the maze itself should be kept as dark as possible. This
could be achieved as in Roberts et al. (2007), by restricting illumination in the maze and
the experimental room to single small LEDs in the walls of each chamber. As the maze will
be rotated, global cues will not directly affect the task, however they may interfere with
training through the introduction of local-global cue conflicts.
Training takes place in two stages. In the first stage, the door from chamber B to chamber
6.3 Multi-segment path navigation
103
D is closed, as is the door from chamber C to chamber E (Figure 6.2a). The rat is cued
to either chamber B or chamber C by placing the animal in the chamber with food and
allowing it to feed briefly. A black shroud is then placed over the rat, and the rat is lifted
out of the chamber. While keeping the rat stationary, the maze is rotated under the rat
such that chamber A is close to the previous position of the destination chamber. The rat
is then placed in chamber A with the door closed. After a few seconds, the door is opened
and the rat is allowed to run to either chamber B or chamber C. Once the rat moves from
the junction point to a position at which it has a line of sight to a destination chamber,
the return path is blocked and the rat must continue to the chosen chamber1 . If the animal
makes the correct choice, it is allowed to feed and then is removed from the maze. If the
animal makes the incorrect choice it is merely removed from the maze. Upon removal from
the maze, the rat is returned to the home cage, and the maze is wiped down and rotated
randomly before the next trial2 . This task is repeated so the rat can run to the correct
chamber between B or C after being cued to that chamber, and until CA3 complex spiking
cells have stable fields. A set of cells with fields for the A-B-C T-maze should be identified.
The second stage of training is similar to the first, except that the doors from chambers
B and C permitting access to chamber A are closed, and the other door to each chamber
is opened (Figure 6.2b). Here rats are divided into control and test groups. For control
rats, the visual and textural cues in chambers B and C are modified (denoted B’ and C’),
while test rats have B and C unmodified. Rats are then trained as in the first phase to the
corridors B-D (or B’-D) and C-E (or C’-E). Thus for the B-D (or B’-D) corridor, the rat is
cued to D then placed in chamber B (or B’) to begin each training run. Further sets of B-D
(or B’-D) and C-E (or C’-E) CA3 cells should be identified (the cells of interest are those
that respond over a large amount of one and only one of the corridors).
For the test, the doors in chambers B and C are both open (Figure 6.2c). For the control
animals, chambers B and C are restored to their initial cues. The animal is cued to one
of location D or E, then placed in location A with the door closed. After a few seconds,
the door is open. The behavioural test point is at the junction of the first T-maze between
chambers B and C.
1
Cueing by placing in the target chamber has been demonstrated by Roberts et al. (2007). A possible
alternative would be to provide each chamber with unique scents in place of unique textures, so long as these
scents were masked such that they were non-distinguishable to the animal at the choice point of the maze.
2
The rat could be allowed an initial period to freely explore the maze if this accelerates the training. The
requirement at this stage is that the rat learns the connectedness of chambers A, B and C, and is familiar
with the cueing task itself.
104
Empirical predictions
a.
Training (stage 1)
b.
Open
door
Open
door
B
D
Closed door
Training (stage 2)
C
A
Closed
door
B
D
E
Closed door
Start
Closed
door
Goal
A
Open
door
Start
C
E
Open
door
Goal
Goal
c.
Testing
?
Open
door
Open
door
Choice
point
D
Goal
B
A
Start
C
E
Goal
Figure 6.2: The layout of the maze. Each chamber A-E has a unique texture, and each is
individually lit. The corridors between are dark and unmarked. Dotted lines represent an open
door and solid lines represent a closed door. a. In the first training phase, the doors from chambers
B and C to the corridors leading to chambers E and F are closed, and the animals explore only the
areas between chambers A, B and C. b. In the second training phase, the doors from chambers
B and C back to chamber A are closed, and those to chambers D and E are open. During this
phase, animals are only exposed to the B-D and C-E corridors in isolation. Control animals have
the texture and appearance of chambers B and C modified from those learned in the first phase.
c. During the test phase, all doors between chamber A and chambers D and E are opened. The
choice point is marked.
6.3.2
Predictions
Reward estimation techniques, including latent learning-based reward, rely on reassignment
of the value of an action after a given stimulus depending on the outcome of that action. As
the rat has not previously traversed the test point between chambers B and C en route to
chambers D or E, and has thus been given no chance to assign value to either a left or right
turn in that particular context, any performance above control can be attributed solely to
an active path planning ability. To make the correct choice between chambers B and C, the
rat must internally ‘look-ahead’ to connect chamber A to chambers B and C, then chambers B and C to chambers D and E respectively. The behavioural and electrophysiological
predictions from this experiment follow:
Prediction 1 Despite never having travelled through the junction of chambers A, B and C
to reach chambers D and E, the test rats outperform the control rats, demonstrating that they
are looking ahead to connect the choice location with the cued location.
105
6.3 Multi-segment path navigation
a.
b.
Training (stage 1)
D
E
B
Training (stage 2)
D
G
F
E
F
B
C
G
C
A
A
c.
Testing
E
D
B
F
?
G
C
A
Figure 6.3: The layout of an equivalent, traditional two-tiered T-maze design. The procedure
for this original maze would be similar to that described in the text, with two complete T-mazes
trained for the second phase of training. There is no benefit in the extra end-points in the double
T-maze task, as to avoid having a stimulus-response confound in the form of a left-turn or right-turn
strategy, only chambers E and F could be used for testing.
Prediction 2 CA3 complex spiking cells are coding not for current location, but for future
locations, thus some cells that during training were responsive only within one of the B-D or
C-E corridors but not the A-B-C maze will become active for the entire run from A to the
destination.
6.3.3
Interpretation of results
On the first test trial, even with prior knowledge of the task requirements, a rat requires
some form of look-ahead to perform above chance. After the first trial, look-ahead is no
longer the only solution, thus for the purposes of prediction 1, the first test trial is the only
significant trial. However the entire experiment can be repeated as often as the animals can
learn the new individual environments by modifying the cues at each of the locations.
Although only the first test trial provides information for prediction 1, repeated test trials
provide information for prediction 2 for the duration of any changes to the path cells.
106
Empirical predictions
7
General Discussion
7.1
Summary and contributions
The overarching goal of this thesis was to demonstrate the feasibility of a single system
that exhibited similar characteristics to those observed in the rodent hippocampus, and
that was capable of learning and recalling paths through an environment. A theoretical
solution meeting these criteria was developed in three stages. Firstly a spike-timing based
method was demonstrated that identifies which individual inputs are sufficiently novel to be
learned (Chapter 3). As “sufficiently novel” is a context-dependent term, an online method
of controlling what constitutes novelty was developed, along with a mechanism to prevent
learning new responses for known inputs (Chapter 4). The learned patterns in this model
were likened to places in a cognitive map. An mechanism was then outlined to link these
patterns together, enabling them to be replayed in observed order after curing from a single
input, while exhibiting spatiotemporal firing characteristics similar to those of cells in the
hippocampus of an awake behaving rodent (Chapter 5). This final result is akin to the
recall of a path from a given sensory snapshot, thus demonstrating the model satisfies the
aforementioned thesis goal.
The network model developed in the current work supports the claim that the spatially
sensitive cells in CA3 have the computational ability to perform more than mere localisation.
107
108
General Discussion
The key ability that extends beyond traditional CA3 place cell interpretations is that of
path encoding, a function required for predictive navigation (§1.1.4), but often ascribed to
structures outside the hippocampus (§2.4.2). Exactly how purely localising hippocampal
cells would contribute to a route navigation system is an open question. By considering the
temporal dynamics of neural behaviour, using these dynamics to reduce the localisation
aspect of route navigation to a fraction of a cycle in a local oscillation, and using the
remaining cycle time for path replay, the model integrates localisation and path functions.
A good theory should explain both how the system reaches the state in which any experiments observe it, and why that state is functionally useful. In the case of the hippocampal
place cell system, a theory should thus explain how the properties of these spatially sensitive
cells might develop, and why a cell that responds in such a manner is useful for navigation.
Anchor and path field theory provides a single explanatory framework for how and why many
of the phenomenological properties of CA3 complex spiking cells might come to exist. These
properties have more than one plausible explanation however, and numerous existing theories provide alternative justifications for these phenomena. In general, existing explanations
begin with an assumption that spatially sensitive hippocampal cells fire to represent their
entire spatial field, or some defined offset from that field, and explore how other properties,
such as phase precession or field deformation due to cue change might arise given the spatial
coding assumption. The theory presented in this thesis begins with the assumption that a
cell that encodes a node in a graph-like map is useful only if that information is accessible from some location other than that encoded by the cell, requiring a biological SLAM
implementation. Many of the electrophysiological observations of CA3 cells can be directly
explained by this one reinterpretation (see §7.2).
Comparative simplicity is a second desirable property of a theory. Any neural theory has
some degree of biological fidelity and some degree of biological abstraction. The aforementioned criteria of function helps to determine what is required for inclusion. Standard place
field theory posits a conceptually simple explanation for the information content of the place
cells, however substantial complexity is introduced when attempting to extract this information for navigational purposes. Bearing witness to this is the inconsistency in theories of
this nature, and their general inability to explain the predictive planning abilities of rodents
— the navigational task in which the hippocampus is most strongly implicated (see §2.4.2).
Anchor and path field theory may initially seem complex in comparison to standard place
field theory, however it obviates the need for a separate system to perform path learning and
replay.
A useful theory is also testable and falsifiable. An initial set of experiments were outlined to test the basic aspects of anchor and path field theory. The dominant hypothesis for
7.2 Impact of path and anchor theory on hippocampal theory
109
localisation dynamics in CA3 is via an attractor network, for which evidence is scarce. One
experiment detailed in the current work proposes a test of the race model as an alternative
localisation mechanism that results in the development of anchor fields. Evidence for any
mechanisms of hippocampal-dependent predictive navigation has seemingly remained elusive, however anchor and path field theory suggests that many of the common hippocampal
phenomena provide such evidence. Further experiments proposed in this thesis attempt both
to test whether rodents use predictive navigation strategies, and to clarify the correct spatial binding for hippocampal complex spiking cells. Together these experiments will either
provide significant support for anchor and path field theory, or they will falsify part or all of
it.
The major contribution of this thesis is a theory of hippocampal function that is simple,
falsifiable, and is consistent with a large body of behavioural and electrophysiological data.
This theory includes a larger computational role for CA3 in navigation than is typically
ascribed to the region, and a greater capability in learning and memory functions in general.
The expanded computational capability is derived from a set of mechanisms incorporating
spike timing into their processing and memory functions. Such mechanisms should be detectable by comparing spike times with appropriate reference frames, which may be intrinsic
oscillations, other spiking activity, or any temporally significant event.
7.2
Impact of path and anchor theory on hippocampal
theory
Larger place fields in the ventral hippocampus may also provide information
about the broader spatial context. Nonetheless, we would expect that only cells
whose place fields overlap the animal’s current location will be activated at these
times. (Carr et al., 2011)
Many of the ideas forming the basis of path and anchor field theory have been conveyed
in previous work, yet the prevailing view of the information content of place cells has remained the same: that they are responding to represent the location the animal current
occupies, or the location that the rat will shortly occupy. Although the passage from Carr
et al. (2011) above is logically correct — the fields of place cells are defined as firing only
when overlapping the animal’s current location — there remains an accompanying implication that the cell’s firing represents the current location. There are significant conceptual
differences between such an interpretation and the alternative “path encoding and retrieval”
interpretation illustrated in this thesis where the place field of a cell includes its immediate
110
General Discussion
location-responsive anchor field and its predictive planning field. The major contribution of
this thesis in this regard is in highlighting how these conceptual differences could result in
an alternative interpretation of place cell data.
In many ways, path and anchor field theory pieces together existing theories in a single
unified structure. Feedforward models, particularly those treating the subject of pattern
separation and completion in the disynaptic pathway, have similar dynamics to the dynamics
of the initial creation of anchor fields in the current model (Bostock et al., 1991; Sharp, 1991;
Marr, 1971; O’Reilly and McClelland, 1994; Fuhs and Touretzky, 2000). Encoding proximity
in the recurrent CA3 synapses, as suggested by Muller et al. (1996), is required to achieve the
sequence-like path fields in the current model, as it was in the sequence models proposed by
numerous others (Tsodyks et al., 1996; Levy, 1996; Wallenstein and Hasselmo, 1997; Lisman
and Otmakhova, 2001). The earlier proposal of guiding navigation through simultaneous
activation of place cells and goal cells (Burgess et al., 1994; Burgess and O’Keefe, 1996) is a
specific case in the current theory of two place cells, one firing in its anchor field and one in
its path field (although the goal cells are not formed in the same manner).
Others have proposed mechanisms that share features with the anchor and path field
interpretation but differ in their mechanistic explanations. Mehta et al. (2000) proposed
that an asymmetric expansion of CA1 place fields (skewness) with experience during a
linear track experiment could be indicative of a coding of between-location relationships.
Although the coding is seemingly similar conceptually to anchor and path field coding, the
mechanisms of this coding differ substantially. The skewness model suggests that betweenlocation relationships form in the synapses between CA3 and CA1, and that theta phase
precession results from an increase in net excitatory input to CA1 cells from their CA3
afferents during field traversal. The model presented with anchor and path field theory
suggests that between-location relationships are formed in asymmetric connections between
CA3 cells, and that phase precession results from ordered firing chains of these CA3 cells,
with the first activated cell in the chain moving forward during field traversal.
Numerous other theories do not fit consistently with path and anchor field theory. The
concept of specific phases of theta for learning and recall, as proposed by Hasselmo et al.
(2002b), is difficult to reconcile with the idea that hippocampal cells fire in their path fields
through the theta cycle (and the race model provides an alternative). Attractor models, such
as that of Treves and Rolls (1992), have fundamentally different structural and dynamical
requirements of the underlying network than path and anchor field theory; for example,
activity within the network must converge on a stable point, rather that diverge from a
cued point as suggested in the current work. Numerous models of hippocampus-dependent
navigation suggest the presence of metric information in place cells (Foster et al., 2000;
7.2 Impact of path and anchor theory on hippocampal theory
111
Burgess et al., 1994; Burgess and O’Keefe, 1996). While place cells in the current theory
have anchor fields that are potentially partially established and cued by upstream, geometricbased grid fields, their corresponding path fields are purely sequence-based and thus nonmetric1 . The experimental designs of Chapter 6 provide methods for establishing supporting
evidence to distinguish between these alternatives.
7.2.1
Novelty and learning
Novelty detection has long been accepted as a fundamental ability of an adaptive system
(O’Keefe and Nadel, 1978). Multiple brain regions rely on a novelty signal, and it seems likely
that multiple regions also generate such a signal (Frank et al., 2004). Different sites have been
hypothesised to account for different categories of novelty, for example a new unique object
(stimulus novelty) versus a unique configuration of well known objects (spatial associative
novelty) (Kumaran and Maguire, 2007). Despite recognition of this issue even in relation to
the specific hippocampal anatomy and function (Treves and Rolls, 1992), many hippocampal
models do not incorporate an explicit mechanism for classifying inputs as novel or known.
A variety of means have been used to work around this novelty detection issue such as using
separate theta phases for learning and recall (Cutsuridis et al., 2009; Hasselmo et al., 2002b;
Kunec et al., 2005), or relying on a universal average threshold between the two functions
(Marr, 1971; Treves and Rolls, 1992).
The STSC model in this thesis demonstrates a mechanism that supports the emergence and stability of anchor fields using only the inputs from EC2 and DG. Field stability
is achieved by differentiating novel inputs from known inputs with the race between two
pathways. The race permits simple and elegant control mechanisms for the learning-recall
dilemma, obviating the need for an externally-based novelty signal. Relying only on an internal classification is significant, as novelty is relative to the memory in question, suggesting
that all novelty detection is best achieved by the memory system in which it is used. Although specifically addressed with respect to spatial navigation in the current work (a form
of associative novelty in Kumaran and Maguire (2007)), a similar race mechanism could also
function for other forms of novelty detection in other regions.
1
For the purposes of navigation, binding abstract places back to a geometric map seems plausible. An
alternative is mapping to relations to allothetic cues, however this would require some kind of “hunting”
behaviour, evidence for which is scarce.
112
7.2.2
General Discussion
Place cell rate response and reliability
As noted in the attractor modelling literature review (§2.4.1), the response rate in different
parts of a cell’s spatial field is a challenging issue. Namely, attractor models are inconsistent
with the gradual dropoff of place cell activity (Touretzky and Redish, 1996), whereas the
model presented here provides a coherent explanation for this observation. Specifically, the
anchor field has the highest rate response, as it is directly driven from the available sensory
cues. This makes its input reliable. In contrast, at the edge of a cell’s spatial field, its firing
is dependent on the chain of associations to the cells currently firing in their anchor fields,
with each step in the chain decreasing the reliability and hence the strength of the signal.
7.2.3
Theta phase precession
On initial characterisation, theta phase precession was noted to correlate well with position
through a cell’s spatial field (O’Keefe and Recce, 1993), leading to a theory that phase encoded within-field position (O’Keefe and Recce, 1993; Jensen and Lisman, 2000; O’Keefe and
Burgess, 2005). A second theory suggested that the phenomenon is a side-effect of directionof-motion encoding (Burgess et al., 1994; Burgess and O’Keefe, 1996). These correlations
were observed by pooling the phase precession over many field traversals, however pooled
phase precession data belies the variability in single trial phase precession (Schmidt et al.,
2009). On a single trial, any particular phase does not provide a good correlation with a
particular field position.
Along with other sequence theories (Wallenstein and Hasselmo, 1997; Lisman and Otmakhova, 2001; Yamaguchi et al., 2007), anchor and path field theory suggests that phase
precession is a side-effect of the prediction occurring in the network. Sequence theories are
consistent with position and direction being somewhat correlated with phase, and are also
consistent with the phase-position correlation being relative to the the initial phase of firing
or to the phase of other cell firings on any single run. Furthermore, sequence models are
consistent with the observation that early theta better predicts position than late theta, and
late theta better predicts direction than early theta (Huxter et al., 2008). Sequence theories
predict that the activity of some CA3 place cells will be causally related to other place cell
firings, a demonstrated phenomenon (Dragoi and Buzsaki, 2006).
Aside from the precise locations encoded by the cells, anchor and path field theory
differs with other sequence theories in the retrieval dynamics. Two previously hypothesised
mechanisms of path replay are via retrieval over multiple theta cycles (Yamaguchi et al.,
2007), or via sharp-wave ripples (Davidson et al., 2009; Carr et al., 2011). Although there
is some evidence of phenomena that support these theories, they generally occur while an
7.2 Impact of path and anchor theory on hippocampal theory
113
animal is at rest. Both therefore require paths to be kept in some form of short-term memory
for navigation (see §2.4.1). Anchor and path field theory instead suggests that within each
theta cycle and across the septo-temporal axis of CA3, entire paths can be retrieved.
7.2.4
Spatial sensitivity
Place cell spatial scale appears to increase systematically from the septal to temporal poles of
the hippocampus (Jung et al., 1994; O’Keefe, 2007; Kjelstrup et al., 2008) (see §2.3.2). Little
modelling work has focused on this variation in spatial scale, although since the discovery of
grid cells in mEC, the systematic variation in grid spacing in this region has been proposed
as the cause of place field scale (Kjelstrup et al., 2006). Anchor and path field theory instead
relies on the systematic anatomical variations present across CA3 to reproduce the variation
in spatial scale. More importantly, this theory provides a functional justification for such
variation, namely that it is a phenomenon arising from the region’s role in path encoding
and retrieval.
7.2.5
Spatial field directionality
The striking difference between the uni-directionality of place fields in linear track-like environments and their omni-directionality in open arenas has been explored in numerous
modelling studies (see §2.4). Sharp (1991) proposed that competitive inhibition between
place cells may create separate “clusters” in the feedforward input for different views of the
same location if the views were sufficiently different, but one large “cluster” if the views
from a single location were similar. Brunel and Trullier (1998) suggested instead that the
potentiation of recurrent CA3 to CA3 synapses, first those of similar position and orientation, then those of similar position alone, resulted in a closer match to the available data.
Another alternative is the theory that multiple different “charts” of attractors, each “chart”
intrinsically non-directional, are switched based on context, with the direction on a linear
track providing sufficient contextual difference (Redish and Touretzky, 1997).
Mechanistically, the anchor fields of place cells in the current work could operate as
suggested by either Sharp (1991) or Brunel and Trullier (1998), or some combination of
both. In a linear track-like environment the anchor field would thus be expected to be unidirectional. The directionality of the path field then arises as the cell only fires after cells
with anchor fields earlier on the track, resulting in an expansion in only one direction along
the track. Furthermore, as the path field is predicting the anchor field, the cell should only
fire in the path field if the animal is heading towards the cell’s anchor field — rendering the
entire field directional in the linear track case. In an open field, the anchor field develops
114
General Discussion
omni-directionality, as in existing models. As any one cell fires on approach of its anchor
field from any direction, after cells with anchor fields earlier on all these approach directions,
the path field of the cell expands in every direction, allowing omni-directional prediction of
the anchor field.
7.2.6
Spatial field response with introduced barriers
One interesting distinction between typical place field theory and anchor and path field
theory is the difference in expected deformation of fields with introduced barriers. Assuming
the introduction of the barrier was insufficient to disrupt the pattern completion ability of the
location, place field theory has little to say about the nature of such a change. In contrast,
anchor and path field theory would suggest that the introduction of such a barrier would
result in an update to the accessibility of the anchor field from locations on the opposite side
of the barrier. Regions near the edge of the barrier would thus have an increased phase and
a decreased response rate, deforming the field on the barrier side (Figure 7.1, right). Using
typical place field analysis, this effect would appear as a more general rate decrease on the
barrier side of the field (Figure 7.1, left).
There is little data available on the effect of fields into which a barrier is introduced. One
experiment does show the effect of a barrier placed directly through the centre of a field,
with controls to demonstrate that the sensory characteristics of the barrier do not appear
to play a role in field modification (i.e. firing changes are not due to an inability to pattern
complete) (Muller and Kubie, 1987). The mid-field barriers seem to disrupt the majority
of place field activity (Figure 7.2). Under anchor and path field theory it seems likely that
they bisected the anchor field itself, thus it is difficult to draw any further significance from
these specific experiments. Although not detailed in this work, further experiments on field
changes due to barriers may provide a fruitful line of research for examining the information
content of place cells.
7.3
The theories in context
This project began as a study into how the hippocampus, and in particular place cells,
could contribute to rodent navigation. Rationalising observed hippocampal dynamics with
observed behaviour under hippocampal manipulations during navigation tasks led to the
development of anchor and path field theory, and hence to an alternative interpretation of
the existing hippocampal dynamics data. In short, the current work provides a mechanistic
7.3 The theories in context
115
Figure 7.1: Hypothesised place cell responses near barriers under anchor and path field theory.
Using a traditional interpretation of place cell data, the field of the cell will be weaker, but still
present on the side of the barrier away from the centre of the field, primarily due to the low
reliability of early-field (late-theta) place cell firings (left). The explanation of this effect lies in the
anchor and path field interpretation: the cell fires while the centre of the field is still within the
path recall range of the animal, but stops firing once the animal diverges from all routes through
the cell’s anchor field (right).
framework for spatial memory encoding and retrieval that challenges many existing models of the same (e.g. Burgess et al. (1994); Kali and Dayan (2000); Foster et al. (2000)),
while agreeing with elements of models of sequence encoding and episodic memory (e.g.
Samsonovich and Ascoli (2005); Lisman and Otmakhova (2001)).
Although predominantly grounded in the spatial aspects of hippocampal memory, parts
of the current work also fit with other literature. Temporal structure in neural dynamics
of learning and memory has come to prominence in recent years. In part this prominence
is due to an increased understanding of inherently time-based phenomena such as STDP
(Markram et al., 1997; Song et al., 2000; Izhikevich, 2007), in part it is due to an appreciation
of the increase in computational power of a temporally sensitive network (Izhikevich, 2005;
Maass et al., 2002), and in part it is due to new models incorporating different timescales
of plasticity for different purpose (Aimone et al., 2009). The models and theories in this
thesis demonstrate possible functions in three distinct timescales in CA3, using inherently
time-based mechanisms and the enhanced representational ability provided by the temporal
dimension. In the milliseconds to tens of milliseconds range the race model detects the
novelty of sensory input and learns or recalls as appropriate. In the tens of milliseconds to
116
General Discussion
Figure 7.2: The effect of adding a barrier in the spatial field of a place cell. Prior to the barrier’s
insertion, the response is one of a typical spatial response in a two dimensional environment (left).
After the barrier is introduced, the response is largely abolished (right). Under anchor and path
field interpretation, the barrier would bisect the cell’s anchor field if it were in the centre of the
spatial field, confounding the problem of path replay to that location. Image adapted from Muller
and Kubie (1987).
a hundred milliseconds range, anchor and path field theory provides a mechanism for path
recall. In the hundreds of milliseconds to seconds range, the model of extracellular synaptic
modulation controls what constitutes novelty in the system. Appropriate temporal dynamics
thus enables CA3 to fulfill roles that typically appeared separately in either competing models
of the region, or in models of multiple different regions.
7.4
Beyond anchor and path field theory
The current work explores a place and path encoding and replay function in the CA3 subfield
of the hippocampus. Simply remembering and replaying paths is only one step in enabling
predictive navigation however; a path must be selected based on an animal’s current motivation, and this path must then be transformed into the appropriate locomotive movements.
As the primary afferent of CA3, the CA1 subfield is a logical candidate for filtering
an appropriate path from the set of all available paths replayed in CA3. To achieve such
a filter, the CA1 cells would require both path and motivational sensitivity. In addition
to input from CA3, CA1 also receives strong projections from layer III of the entorhinal
cortex (EC3) (Amaral and Pierre, 2007). If CA1 was acting as a motivation-based filter on
paths, one would expect EC3 activity to reflect motivational state, and CA1 place and path
7.5 Conclusions
117
activity to depend on the eventual goal. Existing research does not make clear any particular
distinguishing characteristics of EC3 activity, however there is some evidence that CA1 is
modulated by intended goal (Ainge et al., 2007).
Path planning is still not sufficient for predictive navigation, the path must somehow be
used to navigate. Memory recall and pattern completion in this work is used to refer to
the process of matching a sensory snapshot to an internal, abstract representation that was
learned from an amalgamation of responses to various slightly different sensory snapshots.
Chains of these abstract representations form paths, but alone they have no real-world
meaning. Reattaining this real-world meaning requires a mapping of abstract representation
back to the physical world. This would likely involve the projections from CA1 back to the
entorhinal cortex, to the subiculum, or both. Functionally, it may involve mapping abstract
place back into the geometric space afforded by grid cells, and into the sensory view to enable
localised beacon- or view-based navigation.
7.5
Conclusions
The claim of this thesis is that the CA3 network alone is computationally sufficient to
learn places and paths in a system while simultaneously supporting cued recall in the same
system. This work demonstrated how microtiming can signal the difference between familiar
and novel, and through this, impact on the role of CA3 in learning new memories. It
provided a rigorous demonstration of the computational feasibility of this timing signal, and
how neuromodulatory signals could be used to control the stability and the balance of the
system. The thesis introduced a simple, falsifiable theory that implies a reinterpretation of
existing data is required in light of the expanded computational ability of a spike-timing
based network. Finally, a series of empirical studies was presented to test many of the
ensuing electrophysiological and behavioural predictions. Each model, theory, prediction
and experiment has advanced or aims to advance our understanding of the importance of
timing in neural processing.
7.6
Further work
The computational and theoretical studies in this thesis make numerous predictions regarding the neural underpinnings of rodent navigation. Specific rodent experiments, both
behavioural and electrophysiological, were outlined in Chapter 6 that would enable testing of
118
General Discussion
some of these predictions. These experiments aim to provide evidence for predictive navigation in rodent behaviour, test whether stimulus response timing in CA3 provides a signal of
stimulus novelty, and test the spatial information representation of place cells. Contact has
been made with researchers at the University of California San Diego, at the Kavli Institute
for Systems Neuroscience and Centre for the Biology of Memory and at the Queensland
Brain Institute to run the outlined experiments.
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