Physiol Rev 91: 917–929, 2011
doi:10.1152/physrev.00019.2010
VOLTAGE FLUCTUATIONS IN NEURONS: SIGNAL
OR NOISE?
Yosef Yarom and Jorn Hounsgaard
Department of Neurobiology, Life Science Institute, The Edmond & Liliy Safra Centre for Brain Sciences, Hebrew
University, Jerusalem, Israel; and Institute of Neuroscience and Pharmacology, The PANUM Institute, University
of Copenhagen, Copenhagen, Denmark
L
I.
II.
III.
IV.
V.
INTRODUCTION
SOURCES OF VOLTAGE NOISE
SYNAPTIC NOISE IN NEURONS...
SPIKE TRAIN VARIABILITY
CONCLUSIONS
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I. INTRODUCTION
Nausea, the Latin root of the word noise, is a candid
expression of our inherent, sometimes emotional, reaction toward the concept of noise. These disturbing, unpredictable, and annoying events that interfere with the
natural order of things and drive us away from perfection
indeed cause a nauseous feeling. The cellular and molecular constituents of life itself are noisy. For this reason
alone, it is not surprising that living organisms are imperfect machines. Yet, can we live without noise? Is noise
the paradoxical, essential feature that derails us en route
to perfection but also distinguishes us from lifeless machines? When we refer to the living brain, this fundamental question reaches a higher dimension. The fascinating
structure of the brain, the precision of which is essential
for survival, is comprised of noisy functional elements.
The fact that the action potential, the essence of signaling
in nerve cells, is a threshold phenomenon underlines the
fundamental probabilistic nature of brain function. This
threshold feature, which emerges from the mode of operation of ion channels, is just the tip of the iceberg of
noise sources. Synaptic transmission, the mode of neuronal interactions, is quantal in nature. This notion immediately acknowledges the uncertainty in strength and timing inherent in synaptic transmission.
Given this high level of ambiguity, it is surprising to watch
the flawless performance of repeatedly executed behavioral
paradigms, knowing that the variance of the neuronal activity underlying the behaviors is higher than the variance of
the behaviors themselves. Hence, it appears either that the
neuronal activity does not fully control the behavior, an
unlikely possibility, or that the variability in neural activity
is not accidental and unavoidable noise but rather an integral element of brain function. The brain may operate with
an arsenal of solutions for each problem. A specific solution
is then recalled in a noisy, randomlike process, to handle a
particular problem. Here we examine the possibility that
uncertainty and multiple solutions produced by noisy molecular and cellular signaling elements are fundamental to
brain function and essential for the ability to find good
solutions to novel problems.
II. SOURCES OF VOLTAGE NOISE
Noise is inherent to the elementary processes that form the
foundation of brain function: the ion channels underlining
the action potentials that transmit information along nerve
fibers and synaptic transmission that enables communication between nerve cells. Recent reviews provide excellent
accounts of the properties of the noise from these sources
and the role of noise at the systems level (35, 36, 102) and
need not be repeated here. Instead, we summarize the elementary properties needed to support our view that noise is
essential for brain function. A schematic description of a
hypothetical neuronal network is shown in FIGURE 1. The
three main sites at which noise appears are marked, and the
temporal and spectral features of the noise at these sites are
summarized in the corresponding insets.
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Yarom Y, Hounsgaard J. Voltage Fluctuations in Neurons: Signal or Noise? Physiol Rev
91: 917–929, 2011; doi:10.1152/physrev.00019.2010.—Noise and variability are
fundamental companions to ion channels and synapses and thus inescapable elements
of brain function. The overriding unresolved issue is to what extent noise distorts and
limits signaling on one hand and at the same time constitutes a crucial and fundamental
enrichment that allows and facilitates complex adaptive behavior in an unpredictable world. Here
we review the growing experimental evidence that functional network activity is associated with
intense fluctuations in membrane potential and spike timing. We trace origins and consequences
of noise and variability. Finally, we discuss noise-free neuronal signaling and detrimental and
beneficial forms of noise in large-scale functional neural networks. Evidence that noise and variability in some cases go hand in hand with behavioral variability and increase behavioral choice,
richness, and adaptability opens new avenues for future studies.
NEURONAL NOISE
A. Intrinsic Noise: Stochasticity of Ion
Channel States
The source of noise in the operation of ion channels resides
in the probabilistic nature of their gating mechanisms and
the variable duration of their open state (1A). Surprisingly,
the conductance of single ion channels is, in most cases,
rather constant. Given the high density, the significant conductance in their open state, and, for some of them, a substantial driving force for the permeable ion species, one
would expect extensive and continuous fluctuations of
membrane voltage. Fortunately, most of the expected voltage changes are filtered out by the membrane capacitance
that acts as a dampening mechanism to prevent fast changes
in membrane potential. Yet, in neocortical pyramidal cells,
a nonlinear increase in voltage fluctuations was measured
when the membrane was depolarized (53). Whereas the
increase in fluctuation is to be expected, given the voltage
dependence of ionic channels, the nonlinearity has been
attributed to the activation of persistent Na current that
operates as a “noise amplifier” (53). Thus a significant voltage change can occur when occasionally a group of channels activates together, and the resultant voltage change is
amplified by a voltage-gated positive feedback.
Nerve impulses are generated by voltage-gated ion channels
(10, 60). An explosion-like mechanism that uses a positivefeedback loop generates, upon reaching threshold, an allor-none response. Although the all-or-none nature of the
nerve impulse implies a noise-free unchangeable entity, the
threshold characteristics entail the fundamental probabilistic nature of impulse generation. Indeed, a transient depolarization just above threshold may increase the probability
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of spike generation so that a spike is generated on every
trial. However, the latency of spike generation may well
vary (jitter) as much as tens of milliseconds. An example is
shown in FIGURE 1C. A simulated synaptic current is injected into a neuron, and the three superimposed responses
clearly demonstrate a jitter of up to 20 ms in spike latency.
Needless to say, in a neuronal network, a jittery response
with an order of magnitude in temporal variability will
generate a substantial amount of noise.
We categorize these two manifestations of noise as intrinsic noise, that is to say, sources of noise within the neuron. This noise is expressed as random changes in the
membrane potential, voltage noise, or jitter in spike timing, temporal noise. The same two types of noise also
exist in a category of noise sources known as extrinsic or
synaptic noise.
B. Extrinsic Noise: The Probabilistic Nature
of Transmitter Release
The quantal nature of synaptic transmission is well documented (FIGURE 1B; REF. 58). Although evidence suggests that the size of a single quantum is rather constant,
the release of quanta is overly probabilistic in nature
(58). Hence, at low release probability, synaptic transmission is an all-or-none process, whereas at high release
probability, the amplitude of the postsynaptic response
varies in a random fashion with the number of quanta
released. Either way, the probabilistic nature of synaptic
transmission induces postsynaptic voltage noise. Furthermore, the probability of synaptic release has a tem-
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FIGURE 1 Origin of voltage noise in neurons.
Schematic representation of a network of four
neurons interconnected by reciprocal synapses
(axons in red, dendrites in blue). A: channel
noise illustrated by patch-clamp recording at
⫺20 mV from cerebellar Purkinje cell. The noisy
nature of channel activity is expressed by the
random steplike changes in current flow. B: synaptic noise illustrated by fluctuations in synaptic
current in loose patch recording from frog neuromuscular junction. The synaptic responses
were evoked by stimulating the motor nerve.
Arrow marks arrival of action potential at the
synaptic site. Note the variable amplitude and
onset of synaptic responses. (Records kindly
provided by H. Parnas and I. Parnas.). C: uncertain spike timing: jittery spike initiation. Three
superimposed responses to simulated synaptic
current injected in the cell body of an interneuron
from the cerebellar cortex. [From Mann-Metzer
and Yarom (71).] D: background synaptic activity recorded from cortical neuron in anesthetized rat. The bottom trace is an enlargement of
the marked line in the upper trace. (From YaronJakoubovitch et al., unpublished data.)
YOSEF YAROM AND JORN HOUNSGAARD
poral aspect; it varies in time (FIGURE 1A). Indeed, from
the arrival time of an action potential to the releasing site
at synaptic terminals (arrow in FIGURE 1B), the probability of release rises within a millisecond to a maximum
and then gradually declines to the lower probability at
rest (82). Hence, there is a certain degree of uncertainty
regarding the precise time of release. This is a significant
source of temporal noise when the release probability is
rather low.
III. SYNAPTIC NOISE IN NEURONS
EMBEDDED IN NEURAL NETWORKS
A. Background Synaptic Activity
Neurons embedded in synaptically interconnected networks invariably display rapid ongoing fluctuations in
the otherwise “resting” membrane potential of a magnitude that exceeds channel-induced noise in isolated cells
by one or two orders of magnitude (53) (see FIGURE 1D).
This is due to the background exocytosis of transmitter
from the thousands of afferent synaptic terminals that
contract most neurons. The random vesicular release unrelated to signaling (see above; Ref. 37) adds an additional dimension to the noise problem. This massive
bombardment of synaptic input occasionally causes the
membrane potential to reach threshold, generating spontaneous spike activity (see FIGURE 1D). Via recurrent connectivity, even more noise is generated (67). In addition,
spike activity never ceases completely in the normal
brain. Intrinsic pacemaker properties maintain spontaneous generation of action potentials in certain types of
neurons even in the absence of synaptic input (2, 43, 46).
In the normal brain, background synaptic noise therefore
degrades the fidelity of synaptic integration, i.e., the
translation of membrane potentials in the cell body to
impulse patterns in the axon. In their seminal work on cat
spinal motoneurons, Calvin and Stevens (21, 22) studied
the variability of the intervals between action potentials
(ISI) during steady depolarization. They established
quantitatively that background synaptic activity was the
predominant source of variability in the ISI (21, 22).
These findings also illustrate the general principle in neural transduction that firing patterns in axons are produced by ever-changing blends of synaptic input and intrinsic response properties.
Until recently, the interplay between noisiness and regularity in spike generation during functional network activity
has been out of reach. New experimental techniques and
analytical tools are now fueling progress in characterizing
how the complex dynamics of these parameters may contribute to network function in behaving animals (15). Patch
recordings from neurons in vivo in anesthetized and awake
animals reveal a complex relation between the intrinsic response properties of neurons, synaptic input, and spike patterns. Even early processing of sensory synaptic input is
superimposed on a fluctuating postsynaptic membrane potential in olfaction (23), in vision (4), in hearing (32), and in
the whisker system (19, 87). It is not yet clear to what extent
this background synaptic activity represents unavoidable
noise or the early processing of sensory information. It is
evident, however, that the character of the background synaptic activity in lamina II-III neurons in the barrel cortex
changes with the functional state of the animal. During
quiet wakefulness, the subthreshold membrane potential
undergoes slow synchronous oscillations in large populations of neurons as reflected in the local field potential and
the electroencephalogram (87). At the onset of active
whisking, the slow oscillations are replaced by rapid, lowamplitude fluctuations in membrane potential, desynchronized among neighboring neurons (87). The background
synaptic activity therefore seems to be a state-dependent
variable that integrates with the specific sensory synaptic
input even in early stages of sensory processing. The desynchronized state during a sensory stimulus, associated with
decreased variability in membrane potential fluctuations
and firing rate, is general across sensory modalities and
cortices (27). It has been proposed that irregular Poissonlike firing in the desynchronized state may be a fundamental
way to represent and process uncertainty in the brain (68).
However, the issue of variability and correlated and uncorrelated noise in population coding and how it affects information processing is well documented (5, 32) but not well
understood (6). A crucial limitation is that studies based on
patch recordings in unanesthetized animals are still few and
far apart.
One of the most convincing examples of a constructive role
of noise in information processing is demonstrated in the
work of Ferster and colleagues (4). They propose that noise
solves the problem of contrast invariance of the orientation
curve of neurons in the visual cortex. The problem of contrast invariance was first described by Sclar and Freeman
(95). They noted that the width of the orientation curve is
independent of stimulus contrast, which is correlated to the
intensity of the input. Considering the iceberg effect, one
would expect that the stronger the input, the wider is the
orientation curve. Even the feed-forward model of Hubel
and Wiesel (52) predicts that the membrane potential will
show orientation insensitivity, whereas measuring spiking
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In short, we distinguish two aspects of noise: a voltage
component and temporal component. Although this is a
somewhat artificial distinction, since the voltage noise by
definition has a temporal aspect to it, we feel that variable amplitude in essence differs from timing uncertainty.
These two types of noise can originate from intrinsic
channel noise or extrinsically from noisy transmitter release.
B. Synaptic Noise During Functional
Network Activity
NEURONAL NOISE
activity will result in widening of the curve at higher contrast. Ferster and colleagues (3, 4) found that most of the
discrepancy between the anticipated result and the experimental observations can be resolved if membrane potential
noise is taken into account. Their experiments suggest that
the noise, largely independent of the strength of the input,
operates as a linearizing device, smoothing the threshold
characteristic of spike generation. Hence, the average membrane voltage, which is orientation invariant, is linearly
translated into spike rate by the noisy fluctuations in membrane potential.
The possibility that voltage noise serves as a linearization
device that overcomes the problem of nonlinear translation
of voltage into spike trains will be discussed below.
Neurons in isolation respond to steady depolarization with
a stream of action potentials occurring in a predictable temporal sequence, i.e., with highly correlated interspike intervals. The specific pattern is determined by the intrinsic response properties of neurons that are cell specific. The specificity is determined by the density profile of voltage- and
[Ca2⫹]i-gated ion channels in the membrane along the somato-dendritic axis (66) and by the structure of the neuron
(69). However, highly irregular firing has consistently been
reported from cortical and subcortical neurons during functional network activity. This includes spontaneous firing,
firing evoked by sensory stimuli, as well as firing during
motor activity in anesthetized, decerebrate, or awake animals (20, 28 –30, 50, 70, 78, 86, 106). Irregular firing at a
constant average firing rate is a surprisingly unlikely outcome of temporal integration of random excitatory synaptic input (97, 101). The simplest and most straightforward
scenario that leads to irregular firing is high intensity of
ongoing inhibitory and excitatory synaptic activity (31, 42,
96, 97, 101). This explanation for irregular firing became
even more attractive when the implications were explored
mathematically (107, 108). The theoretical analysis showed
not only that a state of approximate balance between inhibitory and excitatory synaptic input to individual neurons
emerged naturally in simulated networks of inhibitory and
excitatory neurons, but also that such networks led neurons
to fire irregularly as predicted (107). The balanced state was
also shown to be characterized by chaotic dynamics even
with constant input and to provide networks with faster
response time than the integration time of individual neurons (107, 108). Although these high-level predictions have
not yet been tested experimentally, considerable independent evidence now suggests that the balanced state is a
widespread phenomenon in a diversity of neural networks
in both vertebrates and invertebrates (3, 9, 11, 31, 81, 94,
97, 98, 112).
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In several primary sensory cortical regions, the intensity of inhibitory synaptic activity scales with excitatory
synaptic activity evoked by specific sensory stimuli (3, 47,
110). In a recent study by Okun and Lampl (79), in which
the spontaneous activity of cortical neurons was studied,
the close correlation between inhibition and excitation was
unequivocally demonstrated. By simultaneously recording
from two cortical neurons, each held at different membrane
potentials, they noted that the magnitude of excitatory and
inhibitory potentials was positively correlated. Detailed experiments in slices from the somatosensory barrel cortex
provide the substrate for such correlation (57, 99). It was
found that a spike train in a layer 5 pyramidal cell, the cells
that constitute the major output of the cerebral cortex, not
only evokes monosynaptic excitation in a small number of
neighboring pyramidal cells but also activates a large number of Martinotti cells, a distinct subclass of inhibitory interneurons. These in turn form divergent and convergent
recurrent inhibitory synaptic contacts with local layer 5
pyramidal cells and Martinotti cells. In fact, this simple
organization provides a powerful feed-forward and recurrent inhibition that closely correlates with the magnitude of
excitation. The identification of a specific microcircuit
structure that automatically provides correlated changes in
the average inhibitory and excitatory activity is particularly
important in the present context. Most significantly, a circuit mechanism has been identified that readily and by design leads to a rapidly fluctuating balance of excitation and
inhibition.
2. Gain control
The noise generated in the balanced state affects the
effective gain of neurons as manifested in their current frequency curve. The slope of this curve, the “neuron gain,” is
insensitive to membrane voltage and conductance (33, 40,
49, 74, 75, 88) but effectively modulated by the level of
voltage noise. This effect has been studied by Chance et al.
(25) in layer 5 pyramidal cells in slices from the somatosensory cortex in rats. Simulated excitatory and inhibitory unit
conductances generated by independent Poisson processes
were fed into the neuron via a patch recording electrode. In
this way, the effects of synaptic noise on neuronal gain
could be explored over a wide range of parameters. This
experimental paradigm demonstrated that concurrent inhibition and excitation reduced the effective neuronal gain.
This happened because depolarizing synaptic transients
elicited action potentials from average membrane potentials
well below the spike threshold (25, 38, 48, 49).
3. Sensitivity and stability control
One of the fundamental consequences of the supralinear recruitment of inhibition with increasing excitatory syn-
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C. Balanced Inhibition and Excitation: The
High-Conductance State
1. Anatomical substrate
YOSEF YAROM AND JORN HOUNSGAARD
4. Effect on firing pattern
In vivo experiments demonstrated that concurrent
inhibition and excitation during network activity was
associated with a severalfold increase in conductance
(13, 81, 89). With such an increase in conductance, the
interspike interval is no longer determined by slow currents underlying spike afterhyperpolarizations and pacemaker potentials (1, 11, 12). Instead, action potentials in
the high-conductance state are predominantly elicited by
depolarizing transients during the noisy fluctuations in
membrane potential produced by the intense concomitant inhibitory and excitatory synaptic activity (8). In
this state fluctuations in conductance and membrane potential are crucial elements in gain modulation in contrast to invariance of orientation selectivity (3, 4, 24, 39).
Other intriguing consequences of the high-conductance state, when present, include quenching of intrinsic
response properties (1, 31), shortening of the membrane
time constant and the synaptic integration time (12), as well
as the yet unexplored recalibration of synaptic weights with
change in electrotonic cable structure.
The high variance in interspike intervals often observed in vivo cannot entirely be accounted for by random
bombardment with uncorrelated inhibitory and excitatory
synaptic activity. However, in vitro experiments by Stevens
and Zador (103) demonstrated that the high variance may
readily be obtained by assuming transient temporal correlations in synaptic input. The fundamental parameters that
determine the synaptically induced fluctuations in postsynaptic membrane potential are therefore, in addition to synaptic weights, the intensity and correlations of concurrent
excitatory and inhibitory presynaptic activity.
5. Role in functional network activity
Direct evidence for noise-driven irregular firing due
to concurrent inhibition and excitation during functional
network activity has been obtained in the spinal cord (1,
11). In the isolated carapace spinal cord preparation
from the turtle, scratch network activity can be induced
by a mechanical stimulus in the receptive field on the
carapace as illustrated in FIGURE 4 (59). Dramatic increases in synaptic input activity in motoneurons have
been reported during scratch episodes in vivo and in vitro
(1, 90). During each episode, the intensity of excitatory
and inhibitory synaptic activity is maintained in near
balance. The depolarizing waves that drive spike activity
are produced by a correlated increase in inhibitory and
excitatory synaptic activity as evidenced by the concomitant increase in average conductance and amplitude of
the fluctuations in membrane potential (1, 11, 12). For
this reason, motoneurons fire irregularly during scratching. It remains to be seen to what extent neurons in
mature spinal motor networks are driven by flexible stochastic synaptic interactions (11) rather than being
locked-in in clocklike networks of weakly coupled cellular oscillators (45).
IV. SPIKE TRAIN VARIABILITY
A. Variability Measurements
There is a general consensus that the neural code is embedded in trains of action potentials. It is also agreed that these
trains are translated via the muscular system into specific
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aptic activity is a parallel increase in average input conductance. In this way, concurrent excitation and inhibition
leads to an efficient way of scaling input conductance with
synaptic activity. At low levels of synaptic activity, neuronal
sensitivity to individual synaptic input is high but decreases
with increased synaptic activity due to increased conductance and reduced gain. However, the ability of the neuron
to emit spikes is maintained. Over a wide range in this
regime, the magnitude of the fluctuations in subthreshold
membrane potential covaries with synaptic intensity and
average conductance (11, 62). In addition, the average
membrane potential is only moderately sensitive to synaptic
intensity in the balanced state and may remain close to
threshold. The question of stability in balanced networks
already addressed theoretically (107, 108) has also been
submitted to elegant experimental analysis (67). If many
neurons are near threshold, a single action potential in an
excitatory neuron might cause “run-away” excitation in
avalanche fashion (85). A careful analysis of this scenario
by London et al. (67) was performed in the rat barrel cortex.
Their combined computational and experimental work
shows that a single action potential in a layer V pyramidal
neuron leads to action potentials in ⬃28 postsynaptic neurons. They also show that this leads to detectable changes in
unit activity in the network for up to 100 ms. But this does
not lead to run-away excitation because the postsynaptic
cells are both excitatory and inhibitory and thus eventually
anneals the perturbation. These findings are in agreement
with spikes produced by random fluctuations in membrane
potential due to uncorrelated inhibitory and excitatory
events. If so, the brain must code by means of firing rate
rather than precise spike timing or use very large depolarizations for accurate timing. The experiments favored rate
coding because large depolarizations were rare and spikes
were readily generated in their absence (67). However, this
is not always the case. In the primary auditory cortex in
awake rats, the membrane potential in sparsely spiking neurons fluctuated in a distinctly nonrandom fashion at rest
and during auditory stimuli of short and long duration (32).
Furthermore, the occasional action potential in these neurons was triggered by isolated non-Gaussian depolarizing
events, bumps, presumably due to sudden increases in synchronized synaptic input.
NEURONAL NOISE
The most commonly used parameter is the average rate of
firing. However, even with this insensitive parameter the
results are contradictory. Chestek et al. (26) reported
long-term stability (lasting for days) of firing rates over
repeated trials, whereas Lee et al. (64) report significant
variations. Regularity of spike trains can also be use to
quantify the variable spike trains. The Fano factor (FF) is
a common measure in this respect (27, 70, 97, 104) (see
also FIGURE 4). A more refined analysis of variability is
obtained by combining the FF with CV2 (76). An alter-
native approach was used by Grana et al. (44) in which
stability and variability in spike trains in response to
natural sound stimuli was highlighted in a multi-dimensional analysis of spike-trains and discrimination matrices. The differences in spike trains can be expressed in
spike timing, in average spike rate and the instantaneous
interspike interval, as well as in the degree of regularity in
individual cells and in neuron populations (6, 7, 18, 93,
105, 109). In our opinion, however, it is not possible a
priori to decide which measure is functionally relevant,
and none of the measures gives away which part of the
variability is due to noise. Unfortunately, this question
can only be answered once the neural code is known.
Only then can the “irrelevant” information be identified.
B. Expression and Interpretation of
Variability
Regardless of the definition of noise in the nervous system,
the high variability of spike trains on one hand and the
accuracy and reproducibility of movement on the other
puzzled neuroscientists (26, 92). Three conceptually different approaches to this problem have been proposed. The
claim by the first approach is that “accurately” reproducible behavior is in fact not free of variation (see FIGURE 2).
Careful analysis will reveal minute trial by trial differences
FIGURE 2 Variable activity of neuron in the motor cortex
during hand movement. A: experimental set-up. The monkey controls movement of cursor on a video screen by a
manipulandum. B: trajectories of the cursor movements
on repeated trials. C: raster-plots of spike-timing in a neuron in the motor cortex during 30 repeated trails. Rasterplots aligned to movement onset. (Figure kindly provided by
E. Vaadia.)
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behavior. It is thus rather puzzling that the spike trains
exhibit a large degree of variability. The well-documented
inherent variability in the biophysical mechanisms that generate spikes (see above) encompasses almost all levels of
neuronal processing. An example of trial-to-trial variability
is shown in FIGURE 2. It depicts the activity recorded from a
cortical neuron in the monkey motor cortex performing a
simple and reproducible hand movement. It is obvious that
each behavioral trial is associated with a different spike
train. However, it is not equally obvious how to quantify
these differences. This is a widespread problem, since similar trial-to-trial variability appears at all stages from early
sensory processing as seen in FIGURE 3 to the final common
path in motoneurons as in FIGURE 4. The firing patterns are
not repeated in successive seemingly identical trials, sensory
or motor.
YOSEF YAROM AND JORN HOUNSGAARD
that reflect the spike train variability (26). The solution
offered by the second approach is that the average spike
train at the network level is rather invariable. Due to redundancy and extensive convergence, spike train variability of
individual neurons is eventually filtered out en route to the
output stage. The third approach assumes that spike train
variability plays a major role in information processing and
complex computation and thus has a meaning of its own
and cannot, and should not, be regarded as noise (92). We
suggest that spike train variability, which is an unavoidable
consequence of noisy processes, is an essential feature of
network activity, enabling fast and efficient adaptations to
new and unexpected environmental circumstances.
C. Noisy Sensory Motor Transduction
Variability is an integral element in spike generation and
synaptic transmission. In principle, transmission of spike
patterns from cell to cell and from layer to layer through
a network should therefore unavoidably be degraded by
the accumulation of noise at each step (6). This prediction is confirmed by a detailed analysis of the sequential
sensory motor transduction for pressure-induced local
bending in the leech. In this system, mechanical sensory
stimuli as well as the resulting motor behavior can be
recorded with great accuracy (84, 111) and related to the
spike activity in nerve cells in the intercalated central
nervous system (113). Local bending is primarily elicited
by skin indentations that activate the mechanosensory P
cells (61, 65, 113). P-cell firing is highly reproducible in
response to direct depolarization (84) and to tactile mechanical stimulation of the skin (112). Not surprisingly,
P-cell firing displays much lower variance than the bending behavior elicited. On the other hand, the dozen or so
cells in the leech ganglion that respond to activation of a
P cell show higher spatial and temporal variability than
the local bending they produce. A key observation may
explain how variability in behavior is contained. Action
potentials in the coactivated interneurons in the ganglion
turn out to be poorly pairwise correlated and exhibit a
high degree of statistical independence. It is this property, combined with ensemble averaging and long integration time in muscles, that secures a smooth and reproducible motor behavior despite the irregular and variable
activity of the motoneurons. The stochastic properties of
synaptic transmission, the low release probability in
many synapses, and the massive convergent and divergent connectivity is probably the main source of uncorrelated noise in neurons (35). For this reason, the finding
that highly reliable spike trains in early sensory processing degrades in neurons at later stages in the CNS en
route to behavioral output may apply to nervous systems
in general. Unfortunately, systematic investigations in
large-scale nervous systems, such as in mammals, are not
yet feasible. From the trial-to-trial variance of spike
counts and spike timing in a few, randomly chosen units
during behavior, it is not really possible to extract the
underlying neuronal algorithms.
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FIGURE 3 Context-dependent responses of auditory
neuron to the same tone. A: raster-plots of spiketiming during tone presentations in six different contexts (color codes). B: average spike frequency during
each of six different contexts. The response to the test
tone is favored in contexts in which the tone is presented in few trials, and the tones presented in the
other trial have distinctly different frequencies. Test
tone was presented in 5% of trials in conditions 1, 2,
3, and 6 (yellow, dull green, green, and red). In these
four conditions, the response to the test tone is favored by silent trials (green) or trials with very different
tones (yellow). Test tone in many trials [50% in condition 4 (black), 95% in condition 5 (blue)] depresses the
response. (Figure kindly provided by N. Ta’aseh and I.
Nelken.)
NEURONAL NOISE
D. Noise, Variability, Choice, and Decision
Making
Organisms continuously respond and adjust to their environment. In animals this capacity to adapt is greatly enhanced by brain function. Brains provide a wide selection of
often very different behavioral responses to seemingly identical stimuli. Recent experiments provide evidence that neuronal noise and variability play a fundamental role in how
behavioral choice is made (16). In a reduced preparation of
the leech, activation of mechanosensory neurons can lead to
swimming or crawling network activity in the ganglionic
motor network. In this preparation, more than 80% of the
neurons in one of the ganglia involved in the behavior can
be monitored simultaneously (17). Under experimental
conditions, in which the chance of either behavioral response to the stimulus is equal, the activity of the neurons
monitored was followed from the application of the stimulus until the onset of clearly identifiable swim or crawl network activity (16). The first striking observation is that a
very large fraction of the neurons were activated immediately after the stimulus in the build-up period before the
onset of the behavior. Next, only ⬃5% of the active neurons fired in a manner that predicted the behavioral outcome, and a particular ensemble from this subgroup predicted the outcome much earlier than any of the neurons
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individually. Taken together, this suggested that the decision mechanism is preceded by a general arousal of the
network, followed by the expression of activity patterns
that gradually diverge into either a swim or a crawl. It could
not be decided from the experiments whether the statistical
nature of the behavioral choice to the same stimulus was
due to the stochastic nature of the decision-making network
activity or depended on trial-to-trial differences in welldefined but unknown state variables in the preparation. It
was also unclear if the predicting neurons were causally
involved in the decision-making mechanisms or merely reflected it (15). Manipulating the activity of any one of the
predicting neurons during the arousal and decision-making
period by hyperpolarization or depolarization did not bias
the behavioral choice. However, such a biasing effect was
obtained in another neuron not belonging to the early predictor neurons. The statistical nature of choice was illuminated by the fact that although the bias was statistically
significant, the activity of the neuron was overruled in some
trials. It is interesting to note that network activity in the
leech is associated with widespread feed-forward inhibition
which clearly mediates gain modulation (9). It remains to be
seen if this concurrent excitation and inhibition also underlie statistical decision making (15) and the high spatial and
temporal firing variability (83, 113) in network neurons
during local bending.
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FIGURE 4 High variability across trials: Fano factor. A: intracellular recording from motoneuron
during one of seven consecutive scratch episodes.
B: raster-plot of spike timing in seven consecutive
scratch episodes (episode from A included) shows
irregular spiking during depolarizing waves within
and across scratch episodes. C: counting spikes
within a fixed time window is a measure of the
variability of synaptic input. The Fano factor is the
fraction of variability in spike count over the mean
spike count across trials. “*” is the Fano factor for
individual cycles, and “o” is the accumulated Fano
factor for cycles. The steady increase in the accumulated Fano factor suggests long-range correlations on a time scale exceeding single cycles (10 –
11). The average single cycle Fano factor is close to
1, which is the expected value for a Poission process (1–2). Table of Fano factors for single cycles
averaged over cycles and single scratch episodes in
10 motoneurons. [This is Figure S5 from supporting online material from Berg et al. (11).]
YOSEF YAROM AND JORN HOUNSGAARD
V. CONCLUSIONS
Inherent to the basic mechanisms of the neuronal machinery, noise is an inevitable element of brain function. The
stochastic nature of electric signaling in neurons implies
that uncertainty is inescapable in functional network activity and behavior. However, one can argue that the stochasticity of ion channels and synaptic release may only be noticeable as threshold phenomena under special circumstances, i.e., when small voltage changes activate just a few
channels or at low levels of synaptic efficacy when transmitter quanta are released in a Poisson manner. Only under
these conditions will stochasticity emerge at the macroscopic level to induce random-like events that we tend to
perceive as noise. However, when stimuli are of significant
intensity, the brain will respond in a reliable and reproducible manner. What remains to be discussed, then, is which
of these states predominate in neural circuits during brain
function. Is functional network activity a purposeful mode
of action where robust input overcome the uncertainty or is
it by design a low-efficiency regime in which stochasticity
lets unique states or solutions emerge? The fact is that most
experimental observations favor the latter possibility. Lowamplitude synaptic potentials are often encountered (80),
and jitter and failures are common in spiking responses to a
given input. Nevertheless, specific examples to the contrary
exist. Most prominently, the climbing fiber input to cerebellar Purkinje cells is a robust all-or-none synaptic input
that produces a reliable and identical response for each
stimulus (34). Similarly, the calyx of Held exemplifies efficient and high-fidelity synaptic transmission. These “excep-
tions that confirm the rule” occur at very specific sites at
which uncertainty should be avoided at all costs. The climbing fiber input delivers error signals (100) in situations
where fast and efficient correction is essential for survival.
Efficient and reliable transmission in the calyx of Held ensures that small time differences can be accurately detected
(14) without disturbing jitter and failure.
However, these exceptions apart, it seems that neurons in
the brain at large predominantly operate near the firing
threshold receiving synaptic input of low power and fidelity
that produce modest elementary voltage changes. In this
regime, uncertainties in time and voltage are bound to occur. Therefore, there is a pressing need for models and concepts that can account for the high macroscopic reliability
of brain function on one hand and the high degree of microscopic uncertainty and variability on the other. There
are several conceptually different approaches to this dilemma. The simplest of all is to challenge the fidelity and
reliability of brain function. Indeed, careful analysis of repeated movements, the real and only output of brain function, reveal variability (see FIGURE 2 and Ref. 26). The
trajectories of even the simplest movements are not identical, and kinematic parameters display considerable variation (91). To what extent these variations reflect variations
in the electrical activity of single neurons are yet to be demonstrated.
The second approach to resolve the issue takes advantage of
population dynamics. In this view, which is supported by
experimental observations, movements reflect and are generated by the ensemble activity of an entire population of
neurons. Movement direction can be accurately predicted
from population vectors extracted from unit activity in relevant territories of the motor cortex (41). This suggests that
each neuron in the motor cortex is directionally tuned, i.e.,
when a particular neuron is active the movement will be
biased in a particular direction. The direction of movement
is thus determined by the direction of the average vectorial
summation of all the active neurons at that particular movement. It follows that variability in activity of individual
neurons is averaged out with a reasonably large ensemble
size. Similar concepts can be demonstrated in sensory areas
of the brain where, for example, perceiving the orientation
of visual input is the average orientation of all orientationsensitive cells that were activated by the stimulus (51). Indeed, the average response can always overcome the large
variability observed in single-cell activity. However, for an
average response to emerge requires mechanisms to extract
the population activity. But for read out, the ensemble activity needs to converge on a small number of neurons
whose inherent variability will again distort the fidelity of
the execution. Furthermore, recent work with brain machine interfaces demonstrates that prediction of movement
direction or force can be reached by analyzing the activity of
a small number of neurons. It also turns out that accurate
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Irregular firing and trial-by-trial variability has been observed in neurons during functional network activity in organisms ranging from leech and Aplysia (94, 112) to behaving monkeys (97). Is this an unavoidable disturbing byproduct of neuronal signaling that the nervous system must
deal with or could it be a fundamental part of brain function
that enables decision making and adaptive behavior? A recent radical proposal suggests that the Poisson-like variability in neuronal firing implements a simple way of performing Bayesian inference in population coding neural circuits
(68). It is implied that variable firing in neurons in sensory
systems expresses the inevitable ambiguity about the external physical reality represented by sensory stimuli. Fluctuating spike rate and trial-to-trial variability in the population of neurons affected by the stimulus is taken to represent
genuine uncertainty about the external world. In such population coding networks, new theoretical insight shows that
noisy correlated and uncorrelated firing can have consequences ranging from increase to decrease in the information content in the network (6). Therefore, the question we
started out with is still with us. The role of variable and
noisy firing of neurons in brain function may turn out to be
a tractable and meaningful question only in the context of
known neural codes.
NEURONAL NOISE
movements can be achieved with a relatively small number
of neurons that propel a robotic arm to a designated target
(77). A logic interpretation of such observations is that even
a small group of neurons can provide enough information
to perform accurate motor tasks. In this light it seems
wastefully inefficient to overcome the variability of single
neurons by population coding.
What then controls the process by which the brain converges on a particular solution? It is easy to imagine that this
is a kind of random process that reflects the state of the
system at the time of the demand and the voltage noise
inherent to constituents, the neurons, and the functional
structure, the connectivity.
This seemingly imaginary scenario is actually supported
by recent reports. The most notable is that of Rokni et al.
(92; see also Ref. 54). In a theoretical study they try to
account for a continuous shift in motor presentation of
cortical neurons. They show that many different combinations of connection weights will produce the same output in redundant neural networks. They concluded that a
network with a noisy learning mechanism can provide
many possible solutions for any given calculation. Another study supports the idea that noise and variability
may reflect increased behavioral choice and accuracy. In
a face recognition task in children and young adults, the
relation between behavioral performance and cortical
electroencephalogram (EEG) was investigated (73). The
experiments showed that increasing behavioral accuracy
and decreasing response time in adults was accompanied
by increased EEG variability. This surprising finding was
interpreted to suggest that better performance is achieved
because more solutions are available and actively
searched. In the present context this supports the view
that noise and variability are crucial for behavioral richness and adequate and accurate performance.
926
In closing, we note that this review has focused on the
expressions of noise and variability in the electrical activity
of the nervous system. The empirical data have so far provided no clues that can resolve the question we posed: “voltage fluctuations in neurons: signal or noise?” Does randomness distort signaling, or is it helpful and even crucial for
normal brain function? There are good theoretical reasons
for believing that brains evolved to exploit “good noise” in
the neural code and contain the detrimental effects that
corrupt and distort signaling (72). An immediate and major
goal is therefore to develop testable theoretical predictions
and experimental paradigms that can distinguish and resolve the roles of noise and variability in brain function.
ACKNOWLEDGMENTS
Address for reprint requests and other correspondence: J.
Hounsgaard, Institute of Neuroscience and Pharmacology,
The PANUM Institute, Bldg. 12–5-9, Univ. of Copenhagen,
Blegdamsvej 3, DK-2200 Copenhagen N, Denmark (e-mail:
[email protected]).
GRANTS
We acknowledge funding by The Gatsby Charitable Foundation and The Israel Science Foundation (to Y. Yarom)
and by The Lundbeck Foundation and The Danish Council
for Independent Research (to J. Hounsgaard).
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Accepting the possibility that motor tasks can be specified
by the activity of a small number of neurons leads to the
third approach to reconcile fidelity of brain function with
neuronal variability. It is conceivable that there are many
ways to perform the same task. In the most simplistic way,
once a need to perform is imposed on the brain it is imaginable that frantic activity goes into the search for immediate solutions. There are quite a few solutions to choose from
if only a few neurons are needed for each. In fact, it is not
unrealistic to predict that there are a very large number of
good solutions. It follows that a part of the behavioral variability observed may represent the variety of solutions
available to any given problem that confronts the brain.
Hence, variation does not necessarily reflect noise or uncertainty. It may also be alternative versions of adaptive goaldirected responses in the execution of accurate performance
albeit in different ways with each repetition.
As a case in point, experiments in song birds have revealed
that neuronal circuits in the basal ganglia through neuromodulation act as tunable sources of noise that let social
context regulate song variability (63). Zebra finch males
court females by songs gradually learned during maturation. When directed at a female, the song by an adult male
is repeated stereotypically with very little variability. In the
absence of females, however, males sing the same songs in
much more variable and explorative ways reminiscent of
how songs evolve in juveniles. For the present purpose, it is
particularly interesting to note that the increased richness
and variability induced by social context depends on the
lateral magnocellular nucleus (LMAN), a subcompartment
of the nidopallium. Although LMAN is not involved in song
production, the ability to enter the variable song mode is
lost after LMAN lesions. In intact males, individual LMAN
neurons fire in a characteristic relation to particular elements of the song. During stereotypical female directed
songs, LMAN neurons fire more regularly than in the absence of females (56). Likewise, microstimulation in LMAN
during singing in the intact male induces variability in the
amplitude and frequency of particular components of the
song (55). For this reason, it is proposed that the neuronal
circuit in LMAN serves as a switch to let the motor network
that generates stereotypically goal-directed courting song
enter an explorative mode that enables improvement and
development through vocal plasticity and reinforcement
learning.
YOSEF YAROM AND JORN HOUNSGAARD
DISCLOSURES
24. Carandini M. Melting the iceberg: contrast invariance in visual cortex. Neuron 54:
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No conflicts of interest, financial or otherwise, are declared
by the authors.
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SI, Churchland MM, Shenoy KV. Single-neuron stability during repeated reaching in
macaque premotor cortex. J Neurosci 27: 10742–10750, 2007.
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