5
Deep turns and the dynamics of
reorientation in escape response
and free crawling of C. elegans
Abstract — In the previous chapter, we developed an automated tracking algorithm for C. elegans 2D motor behavior that solves self-occluding body shapes.
Here, we apply that algorithm to study the dynamics of deep turning during two
important behaviors: the escape response, and abrupt reorientations in freely
crawling worms. During the escape response, we find that the worm steers sharply
away from the noxious stimulus by 180◦ on average, in a tightly controlled way.
Additional reorientations before and after the turn broaden the distribution of
reorientation angles, and can be linked to known underlying neural and molecular mechanisms. During free crawling, we find that abrupt turns, appearing in
previous literature as ‘omega turns’, are in fact differentiated into two distinct
classes. Despite a dramatically different visual appearance, both statically and
dynamically, the two turns share similar kinematics in posture space; only the
amplitude of a pulse in the third postural eigenmode is a dominant distinguishing feature. The two classes of turns reorient the worm towards different sides:
omega turns ventrally; delta turns dorsally, by over-turning through the ventral
side. We show that the two turns occur independently, but with approximately
equal rates that remain equal during adaptation. Taken together, these observations suggest a shared underlying neural infrastructure, and a more diverse
navigational repertoire than previously thought.
See the footnote at the start of Chapter 4, p. 97.
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5 Deep turns and dynamics of reorientation in C. elegans
5.1 Introduction
In the previous chapter, we have developed a tracking algorithm for the
full 2D motor behavior of C. elegans. This algorithm is capable of tracking
not just ‘simple’ postures, but also self-occluding ones. This enables us to
now take a closer, quantitative look at behaviors of the worm that feature
such self-occluding body shapes, and that have thus far not been fully
resolved.
In the first part of this chapter, we focus on the escape response of
C. elegans. This sequence of orchestrated behavioral motifs is evoked by
a noxious stimulus (in our case a localized heating of the worm’s head),
and turns the worm away from the stimulus. The ‘omega turn’, a sharp
reorientation featuring self-overlapping body shapes, is the crucial part of
the sequence, and can now for the first time be resolved. Studying this
highly stereotyped behavior also helps us to identify quantitative patterns
in the data, which will guide our analysis in the second part.
In the second part, we analyze free crawling experiments. Extensive
research has been done on the strategies used by the worm to localize food
and favorable habitats, but the sharp turns that occur during this behavior
have never been fully investigated. Here, we take the first steps towards
resolving these turns.
5.2 The C. elegans escape response
5.2.1 Introduction to the escape response
C. elegans is capable of responding to a range of potentially harmful conditions. Its sensory neurons, most of which are connected to the outside
world through non-motile cilia [1] [2, Ch. 3.1], can detect noxious stimuli
of a chemical, mechanical, optical, or thermal nature [3]. Upon encountering a sufficiently strong stimulus, the worm executes a stereotyped escape
response: a behavioral sequence that steers the worm away from the observed threat.
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5.2 The C. elegans escape response
(i)
(ii)
(iii)
(iv)
(v)
stimulus
sensory
neurons
AVB
forward
locomotion
forward
locomotion
PVC
ALM
AVM
backward
locomotion
tyramine
RIM
head
movement
extra-synaptic
tyramine
VB
VD
DD
DA
VA
SMD
AVD
RIM
DB
RMD
AVA
locomotory system
asymmetry
SMD
/ RIV
deep head
swing
time
Figure 5.1 | Schematic overview of the C. elegans escape response (based on
ref. 4). Top row shows worm body shapes extracted from tracking data: (i) forward
locomotion and exploratory head motions; (ii) infrared laser stimulus; (iii) reversal
phase; (iv) omega turn; (v) resumption of forward locomotion in opposite direction.
Diagram below shows sequence of events in the C. elegans nervous system. Time
flows from left to right. RIM, SMD, and RIV designate C. elegans neurons. Green plus
signs indicate stimulation; red minus signs inhibition. Inset shows the neural network
implicated in the escape response [4, 5]. Rectangles: sensory neurons; hexagons:
command neurons; circles: motor neurons. Synaptic connections are indicated by
triangles, gap junctions by bars, and extra-synaptic diffusion of tyramine by a dashed
arrow. Green connections are stimulatory, red ones inhibitory. Details have been
omitted; see ref. 4 for a more in-depth overview.
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5 Deep turns and dynamics of reorientation in C. elegans
Fig. 5.1 (top) shows the timeline of the C. elegans escape response. During normal locomotion on an agar surface (i), the worm moves by propagating a sinusoidal wave through the body. This snake-like motion is typically accompanied by exploratory head movements. In our experiments,
we elicit an escape response by applying a localized thermal stimulus to
the worm’s head, using an infrared laser pulse (ii) (this causes a 0.5 ◦ C
temperature increase at the head over 100 ms) [6]. The stimulus causes
the worm to abruptly pause, and then back up (iii). During this reversal
phase, head movements are suppressed, which has been suggested to increase the worm’s chances of escaping from the ‘snare traps’ of predatory
fungi [7]. After roughly 5 to 10 seconds of reversing, the worm executes an
omega turn: a sharp reorientation manoeuvre, during which the worm’s
body briefly resembles the shape of the Greek letter Ω (iv) [5]. The turn
reorients the worm away from the stimulus, and allows it to resume forward
locomotion in the opposite direction (v).
Some aspects of the escape response sequence have been teased apart at
the cellular, molecular, and genetic level. This has been greatly facilitated
by the availability of a genetic toolbox for C. elegans [8] as well as the
worm’s stereotyped development [9]. The latter means that each individual worm has the exact same body plan, in which each of its roughly 1 000
somatic cells can be named, and each cell develops from a fully predictable
lineage, starting at the fertilized egg [9]. Genetic changes can be easily introduced into the worm’s genome, and can often be made to target specific
cells [8]. As an example, using these techniques, the nociceptive ASH neurons have been found to express ion channel proteins that are implicated
in osmo- and mechanosensation [10]. This makes the ASH neurons multimodal, and downstream signaling therefore relies on signal multiplexing
[11]. As the connectivity of the C. elegans nervous system is largely known
[1], it has even been possible to partly trace the neural network that drives
the escape response (Fig. 5.1, inset) [5, 4].
The escape response is classically studied with a ‘gentle anterior touch’:
a touch to the head of the worm using a human hair [12] (typically, an eye-
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5.2 The C. elegans escape response
brow hair). In this scenario, a qualitative description of the mechanisms
that orchestrate the different phases of the escape response has emerged
from experiments (Fig. 5.1b) [4, 13], and a key element is the neurotransmitter tyramine, released by the RIM interneurons. Tyramine acts through
multiple pathways, one of which is extra-synaptic diffusion and binding to
G-protein coupled receptors (GPCRs) in distant cells. As this diffusion
process has a timescale of seconds (see Methods) — much slower than the
millisecond timescale associated with the initial synapse-mediated reversal
response [14] — it creates a time separation between the reversal and the
subsequent omega turn.
At the moment the worm is touched, the signaling cascade starts with
the sensory neurons ALM and AVM registering the touch (Fig. 5.1, diagram and inset) [4]. These neurons initiate backward locomotion (through
the AVD and AVA command neurons), while inhibiting forward locomotion (through the PVC and AVB command neurons). AVA, in turn, activates the RIM interneurons, which release the neurotransmitter tyramine.
Donnelly et al. show that tyramine further inhibits forward locomotion
(via AVB), thus prolonging the reversal. Through fast-acting ion channels (LGC-55) in neck muscles and head motor neurons, it additionally
suppresses head movements. Crucially, tyramine also diffuses out of the
synaptic cleft (‘synaptic spillover’), and activates GPCRs (SER-2) elsewhere in the worm’s body. SER-2 activation by diffusing tyramine sets up
an asymmetry in the worm’s locomotory system: it disinhibits the ventral body wall muscles (through suppression of the VD inhibitory motor
neuron). After the omega turn has been initiated by a steep ventral head
swing (controlled by the SMD neuron [5]), the resulting hypercontraction
of the ventral body wall muscles during the body wave produces the characteristic omega turn.
The construction and validation of such a description relies on classic
methods from biology. Typically, a perturbation is introduced into the
worm’s locomotory system, either through genetic knockouts or cell ablations [15]. To assess the impact on the worm’s behavioral phenotype, one
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5 Deep turns and dynamics of reorientation in C. elegans
identifies a behavioral motif affected by the perturbation, and characterizes its temporal or physical appearance. As an example of the latter, part
of the role of the SER-2 GPCR was elucidated by linking its absence to
a marked decrease in ‘omega angle’, the arc angle between the head and
tail during the turn [4]. Worms did not fully ‘close’ their omega turn by
touching their head to the body, evidencing a lack of disinhibition of the
VD neurons.
While detailed, the existing description of the escape response is qualitative. In this section, we take the first steps towards a quantitative description of the escape response. We use the intrinsic coordinate system
for C. elegans motor behavior that was introduced in the previous chapter: the low-dimensional space of body postures. Using our new tracking
approach, which also resolves self-occluding body shapes, we are, for the
first time, able to quantify the full escape response, including the omega
turn. We show that the escape response follows stereotyped patterns in
posture space, and relate this to the reorientation of the worm during the
response. We find that the omega turn produces a tightly-controlled reorientation of 180◦ , but also note that pre- and post-omega phases result in
additional orientation changes, broadening the full distribution. Finally,
we propose a simple model, in which the worm uses head–body touch as
a navigational aid to reorient by 180◦ , away from the stimulus.
5.2.2 Quantifying the escape response
The techniques presented in the previous chapter provide a method for
quantifying the full postural dynamics of the escape response, including the
self-overlapping shapes that are crucial to the reorientation. Through video
tracking of the worm’s body postures, and decomposing each posture as a
linear combination of postural eigenmodes (or ‘eigenworms’), we obtain a
description of the escape response as shown in Fig. 5.2. Here, a1 through
a4 represent the first four eigenmodes; at each point in time, the full body
posture of the worm can be obtained by adding together the eigenworms
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5.2 The C. elegans escape response
shown as insets, in the relative amounts indicated by the values of ai 1 .
The different phases of the qualitative scenario described in the previous
section (also shown at the top of Fig. 5.2) correspond to distinct postural
features of the time series. For larger datasets, this will allow us to automate the detection of behavioral motifs in the data. What features do we
observe?
During normal, forward locomotion (segment i, t = 0 . . . 10 s), the worm
crawls by propagating a sinusoidal wave through its body. This is reflected
in Fig. 5.2 as a pair of phase-locked sinusoidal oscillations in a1 and a2 .
In fact, as shown previously [16], both forward and backward crawling
correspond to a circular trajectory in the (a1 , a2 ) plane (Fig. 5.3; see also
Fig. 4.1f on p. 101). Based on this circular trajectory, a body wave phase
angle (ϕ) can be defined as the angle in the (a1 , a2 ) plane.
When the worm is stimulated by the infrared laser pulse (mark ii, t =
10 s), it immediately backs up, seen as a reversal of the direction of the
(a1 , a2 ) body wave, and thus a decrease in ϕ (iii). An increased ‘floppiness’
of the worm during the reversal, commonly observed in the movie data by
eye, shows up as a significant increase in the amplitude of oscillations in
a3 and a4 .
The omega turn itself (segment iv, gray-shaded area) is preceded by
a steep head swing to the ventral side of the body. The resulting highcurvature anterior body bend, observed as peaks in a1 and a4 (red arrows),
propagates head-to-tail: this implies another switch of the direction of the
body wave, and hence a return to increasing ϕ. The Ω-shaped apex of the
turn is marked by a large peak in a3 (red arrow). As the worm exits the
turn, the high-curvature body bend reaches the tail, causing a negative
peak in a4 (red arrow). Taken together, these quantitative features can
be used to define an omega turn: a significant peak in a3 , bounded by
the low-curvature body shapes that occur before and after the turn (see
1
More formally, each eigenworm êi is a vector of tangent angles along the ‘backbone’ of
the worm, obtained by Principle Component Analysis. The backbone tangent angle
P
vector at time t is given by θ(t) = i ai êi . See the previous chapter for details.
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5 Deep turns and dynamics of reorientation in C. elegans
(i)
(ii)(iii)
(iv)
(v)
5
a1 0
‒5
5
a2 0
‒5
a3
10
0
5
a4 0
‒5
φ
8π
0
0
5
10
15
Time (s)
20
25
30
Figure 5.2 | Quantification of a typical escape response. Time series for the
postural eigenmode decompositions of a tracked worm. a1 to a4 represent the first
four postural eigenmodes (also shown as the gray worm shapes in the top-left corners
of each graph); ϕ is the body wave phase angle, as defined in the previous chapter
(see Fig. 4.1f, p. 101). The infrared laser stimulus takes place at t = 10 s (red line).
Phases of the escape response as shown in Fig. 5.1 are shown at the top. Shaded area
indicates the omega turn, as defined in the Methods. Red arrows highlight features
discussed in the text.
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5.2 The C. elegans escape response
Methods).
Finally, as the turn is finished, the worm resumes its forward crawling
(v). Interestingly, the increased ‘floppiness’ of the worm (the increased
amplitude of the a3 and a4 oscillations) often remains after the omega
turn, as is the case in Fig. 5.2. We will come back to this point later.
5.2.3 The escape response in posture space
A geometric interpretation of the time series from Fig. 5.2 is shown in
Fig. 5.3. Here, we plot the same data as a trajectory in the first three
dimensions of posture space. The circular motion in the (a1 , a2 ) plane is
clearly visible. At the time of the stimulus, the direction of the body wave
circle reverses (iii). During the reversal phase, the previously observed
‘increased floppiness’ now shows up as a distinct tilt of the crawling cycle,
into a3 (iii, bottom). While the amount of tilting varies from worm to worm
(data not shown), it is a frequently observed feature of the escape response
trajectory. Additionally, the radius of the crawling cycle increases, until,
at (iv), the omega turn is visible as a large excursion along a3 . The abrupt
‘kink’ in the trajectory, highlighted by the black arrow in (iv), hints at
the presence of a neural mechanism that triggers the start of the omega
turn. The kink also signals the return to a clockwise progression along the
crawling cycle.
This geometric picture is potentially powerful, as it clearly visualizes
the temporal relationships between the different quantitative features of
the escape response. It also suggests a simple decomposition of the omega
turn, as a superposition of the body wave attractor cycle and a pulse along
the third mode.
5.2.4 Reorientation during the escape response
In order to further understand these posture space trajectories, and examine their functional significance for the worm, we considered the reorientation of the worm during the response. As the escape response serves
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5 Deep turns and dynamics of reorientation in C. elegans
(i)
(iii)
(iv)
(v)
a3
a1
a2
a3
a1
a2
Figure 5.3 | The escape response in posture space. The same data as in Fig. 5.2
is shown, now as a trajectory through the first three dimensions of posture space.
Time is color-coded, flowing in the direction of the arrow from blue to green to yellow
to red. The phases of the escape response from Fig. 5.1 are indicated at the top.
The bottom row shows a rotated view of the plot in the top row, highlighting the
tilt of the body wave cycle during the reversal phase (iii).
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5.2 The C. elegans escape response
to turn the worm away from a perceived threat, back to known-safe territory, one might expect a 180◦ turnaround over the course of the response.
Indeed, distributions centered around this value have been found before
[4, 6].
Our algorithm provides an easily accessible value for the overall orientation: the average tangent angle of the backbone, hθi. In Fig. 5.4d, we confirm that, on average, the N = 91 tested worms change their overall orientation by 180◦ over the course of the full escape response (−0.9π±0.5π rad,
mean ± SD; see also Methods).
Our tracking algorithm also makes it uniquely possible to track the
overall orientation continuously throughout the different phases of the response. In Fig. 5.4a–c, we calculate how much each of the three phases of
the escape response reorients the worm: (a) reversal; (b) omega turn (as
defined in the preceding sections; also see Methods); and (c) post-omega
forward crawling. The omega turn itself results in a sharp turn of around
180◦ (−0.9π±0.4π rad, mean ± SD). Pre- and post-omega phases also show
small but significant contributions (0.1π ± 0.3π rad and −0.1π ± 0.2π rad,
respectively), with distributions that are asymmetric.
Interestingly, this implies that, while the omega turn is an effective manoeuvre for turning away from the stimulus, the full-response orientation
change is broadened by the pre-omega (reversal) and post-omega phases.
To see if there was an underlying correlation between the pre- and postomega phases, and hence a possible overarching mechanism controlling
the two, we simulated a histogram of full-response orientation changes by
adding randomly chosen reorientation values from the three phases (see
Methods). If there were significant correlations between the pre- and postomega phases, these would be destroyed by the random sampling process.
The resulting distribution is shown in Fig. 5.4d (orange). A Kolmogorov–
Smirnov test showed that this simulated distribution was not significantly
different from the data (p = 0.14). This implies that, if there are any
correlations, they are too weak to be observed here. Therefore, the reorientation effected by the full escape response appears to be a combination
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5 Deep turns and dynamics of reorientation in C. elegans
Probability
0.3
Reversal
Omega turn
0.5
(a)
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0.2
Post-omega
(b)
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‒2π
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π
Orientation change (rad)
Orientation change (rad) Orientation change (rad) Orientation change (rad)
π
(e)
π/2
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‒π
‒5
Probability
0.3
0
a3 mean
(h)
10
20
30
a3 peak amplitude
a3 mean
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(g)
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(j)
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π (f)
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Full response
(d)
0.2
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0.2
0.1
0.3
0.3 (c)
0.1
5
10
15
20
25
a3 peak amplitude
0
‒5
a3 mean
Figure 5.4 | Reorientation of the worm occurs during all phases of the escape
response. (a–c) Change of the worm’s overall orientation (∆hθi) during the three
different phases of the escape response, for each of N = 91 worms (see Methods).
(d) The distribution of orientation changes across the full response (blue) is composed of independent contributions from the three phases in a–c. To show this, a
simulated histogram has been computed from 10 000 random combinations of orientation changes from a–c, producing a statistically indistinguishable distribution
(orange; Kolmogorov–Smirnov test, p = 0.14). (e,g) The mean a3 value, versus the
resulting orientation change, during the reversal phase and post-omega phase, respectively. The orientation change is strongly correlated with the mean a3 value. (f) Peak
amplitude of the a3 peak corresponding to the omega turn, versus the resulting orientation change. (h,j) Histogram of mean a3 values, during the reversal phase and
post-omega phase, respectively, showing similarly asymmetric distributions. (i) Histogram of a3 peak amplitudes during the omega turn. Shown is a reconstituted worm
image for an a3 value of 15.
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5.2 The C. elegans escape response
of uncorrelated orientation changes from the reversal, omega-turn, and
post-omega phases.
From previous work on the interpretation of the postural eigenmodes,
we know that the third eigenmode (an overall bending of the worm) is
linked to reorientation of the worm [16, 17]. We therefore tested if any
asymmetry in the fluctuations of a3 during the reversal phase could be
linked to the observed reorientations. Such asymmetry is also visible in
Fig. 5.2, as a baseline shift of the third mode during the reversal. As shown
in Fig. 5.4e, this is indeed the case: the mean a3 value during the reversal
is strongly correlated with the resulting orientation change. The opposite
correlation is observed during post-omega forward crawling (g). During
the omega turn itself, a weak correlation between a3 peak amplitude and
reorientation is observed (f). The actual distributions of mean a3 value
and a3 peak amplitude are shown in Fig. 5.4h–j.
The sum of these observations allows us to link the behavioral output of
the worm to the description of the escape response at the molecular level
from Donnelly et al. [4]. As the worm enters the reversal phase, release
of tyramine sets up an asymmetry in the worm’s body; this would appear
as a baseline shift in the fluctuations of the third mode (Fig. 5.4h). Such
a nonzero a3 mean, in turn, has been linked to orientation changes [17]
(Fig. 5.4e). After the omega turn, lingering effects of the tyramine may
produce a similar baseline shift: the distributions of mean a3 values during
the reversal and post-omega phases (Figs. 5.4h,j) are similarly asymmetric.
When the worm is moving forward instead of backward, however, this now
leads to an opposite orientation change (Fig. 5.4g). We may even speculate
as to a reason for the broadening of the orientation change distribution
by the pre- and post-omega phases, observed above: this could be an
inevitable consequence of the action of tyramine in the build-up towards
the omega turn.
A reason for the previously observed ‘increased floppiness’ of the worm
during the reversal and post-omega phases, visible as an increased amplitude of a3 and a4 oscillations, is less clear. No significant correlations
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5 Deep turns and dynamics of reorientation in C. elegans
to other quantitative properties of the escape response were found in the
currently available data (including orientation change). As ‘floppiness’
is usually observed during fast backward locomotion, additional data on
reversals may help to elucidate a mechanism for the a3 and a4 oscillations.
5.2.5 A simple model for the escape response
The preceding sections have developed a simple picture of the escape
response, as a stereotyped trajectory through posture space. The most
prominent features are the crawling cycle in the (a1 , a2 ) plane, combined
with a distinctive ‘pulse’ along the third eigenmode that corresponds to the
omega turn. A particularly striking feature of the escape-response omega
turn is how closely the worm controls its reorientation: Fig. 5.4b shows a
distribution that is tightly centered around π (180◦ ). This tight control is
mirrored in the underlying distribution of a3 peak amplitudes (Fig. 5.4i).
The evolutionary benefit of such a behavior seems obvious: it steers the
worm away from harm, back to known safety. For a ‘blind’, microscopic
organism such as C. elegans, achieving such a feat is not necessarily easy:
after all, how does one find their way back, without any visual reference
to the outside world?
Our data hints at a possible answer for this navigational issue: the
worm could use its own body as a ‘guide’ for reorientation. As shown in
Fig. 5.4i, the distribution of a3 peak amplitudes lies close to a value of 15:
the lowest a3 value that generates a self-touching body shape (inset). A
similar observation can be made for the a1 /a4 peaks that precede the a3
peak, and correspond to the deep ventral head swing (data not shown).
This suggests that the worm might coil up until it hits its own body, which
it then slides along to find its way back. Lacking a neural mechanism for
such a ‘body-touch assisted turn’, this simple model remains of course
speculative. Forward genetic screens [18] could provide a way forward for
testing this hypothesis, and for identifying further neural and molecular
substrates for this behavior. Comparison of the escape response across
different nematode species [19] may also help validate our proposed model.
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5.3 C. elegans free crawling behavior
5.3 C. elegans free crawling behavior
5.3.1 Introduction to free crawling behavior
In the first half of this chapter, we used a well-defined stimulus to elicit a
stereotyped response from C. elegans. While this approach is excellent for
teasing apart specific neural circuits within the worm’s nervous system, it
does not necessarily shed light on its full range of spontaneous behavior.
On the other side of the spectrum of behavioral assays, we can therefore let
the organism more naturally explore a more unrestricted space of behavior
[20]. An example of such an experiment is the ‘free crawling assay’.
When crawling freely on a 2D agar surface, C. elegans shows a mixture of
behavioral motifs: bouts of forward crawling are alternated with pauses,
reversals, and sharp turns (including the previously encountered omega
turn). These motifs are combined into a navigational strategy for locating
hospitable habitats, food, and mating partners. Multiple types of sensory
cues feed into this strategy: the worm responds, for example, to attractant
and repellent odorant molecules (where the type of response is encoded by
which of the sensory neurons expresses the molecule’s receptor protein
[15]). The worm also actively seeks out a preferred salt concentration [21,
22], temperature [23, 24], and oxygen concentration [25], with fascinating
evidence of adaptation [26] and associative learning [23, 27, 28].
So how does the worm actually reach, say, the peak of an attractant
chemical gradient? Interestingly, C. elegans employs two parallel mechanisms for this [29].
The first mechanism, klinokinesis, is stochastic: the worm executes a
biased random walk up the gradient. Forward crawls are interspersed with
so-called pirouettes: bursts of reversal and turning events that reorient
the worm towards the gradient [30]. The frequency of pirouette initiation
is strongly dependent on the rate of change of attractant concentration
(dC/ dt) detected by the worm. If the worm is running up the gradient,
pirouettes are suppressed; if, on the other hand, it detects a decrease, the
probability of a pirouette increases strongly [30]. The pirouette is similar
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5 Deep turns and dynamics of reorientation in C. elegans
to the bacterial tumble, used by bacteria such as E. coli to locate food
(chemotaxis) [31, 32] — albeit more efficient, as the pirouette is not a
purely random reorientation [30].
The second mechanism, klinotaxis, is a deterministic strategy. Also
called weathervaning in C. elegans, this is a gradual curving of the worm’s
trajectory towards the gradient [33]. In this case, the worm samples the
local attractant concentration during its normal undulatory head movements, using the sensory neurons in its head. It then uses this information
to bias the angle of the head during locomotion [33, 29].
Analysis of C. elegans taxis behavior is historically based on tracking
of the worm’s center-of-mass (or centroid) as it crawls around the agar
plate [30]; later generations of experiments have added increasingly sophisticated mechanisms for also tracking the worm’s body shape [34–40].
This has provided us with our current understanding of the taxis and kinesis mechanisms, but also leaves some questions unanswered. How does the
pirouette reorient the worm up the gradient? And what exactly constitutes
a pirouette?
Our tracking algorithm now makes it possible to begin filling in those
gaps: we can precisely quantify the behavioral dynamics of a freely crawling worm, even during manoeuvres that feature self-overlapping body
shapes. In the previous chapter, we showed that omega turns can actually be classified into two different classes, based on their amplitude (as
measured by the third postural eigenmode). In this section, we further
explore these two classes, and their possible role in C. elegans navigation.
5.3.2 Two types of ventral turns can be discerned during free
crawling
We previously tracked 12 worms as they crawled freely on a 2D agar surface, each for the duration of 35 minutes (see Methods). As no stimuli
or attractant/repellent gradients were present, this represents a basic experiment for studying C. elegans free crawling behavior. We applied our
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5.3 C. elegans free crawling behavior
0.1
(a)
0.1
0.08
Probability
Probability
0.08
0.06
0.04
0.06
0.04
0.02
0.02
0
0
−30
(b)
−20
−10
0
10
a3 local extremum
20
30
0
5
Ω
δ
10
15
20
25
a3 local extremum
30
Figure 5.5 | C. elegans turns during free crawling can be differentiated into
two separate, ventrally-biased classes. (a) Histogram of the amplitude of local
extrema in the time series of the third postural eigenmode a3 (for N = 12 freely
crawling worms). Colors represent the sign of the a3 amplitude, and hence the dorsal
(gray) or ventral (blue) direction of the resulting turn. Insets show reconstructed
worm shapes for the indicated a3 amplitudes. (b) As a, but with all negative a3
amplitudes plotted as positive. Two classes of turns show up on the ventral side,
corresponding to ‘classic’ Ω (omega) turns, and deep δ (delta) turns.
tracking algorithm to quantify the body postures of each worm. As our
primary interest was the ‘omega turn’, we focused on the third postural
eigenmode (a3 ). As mentioned in the previous section on the escape response, peaks in the third mode are a characteristic feature of omega turns,
and have a known role in reorientation of the worm [17].
In our earlier analysis of the same data (see previous chapter), we only
considered a3 amplitudes for turns during which the worm self-overlapped.
In Fig. 5.5, we instead look at the full distribution of a3 values for all
local extrema in the data (see Methods). In this distribution, negative a3
amplitudes correspond to dorsal turns; ventral turns have strictly positive
amplitudes.
In Fig. 5.5a, a clear asymmetry can be observed. On top of a symmetric
background distribution of shallow turns in both directions, we see, on
the ventral side, two distinct additional peaks in the histogram. Drawing
141
5 Deep turns and dynamics of reorientation in C. elegans
Ω (omega)
δ (delta)
t
Figure 5.6 | Examples of the two types of turns identified in the data. Stills
from a movie of a worm making a classical omega turn (top, yellow), and a deep
‘delta’ turn (bottom, blue). The head is marked with a red dot in the first frames.
reconstituted worm images for the center values of these two peaks, we see
that the peak at a3 ∼ 15 corresponds to a ‘classic’ Ω shape. The second
peak, at a3 ∼ 23, shows a body shape with a much higher curvature.
In Fig. 5.5b, we have ‘folded’ the dorsal side of the distribution over the
ventral side, highlighting the ventral asymmetry at high a3 amplitudes.
As indicated in Fig. 5.5b, we will refer to turns in the lower-amplitude
peak as omega turns. We will distinguish these from the higher-amplitude
delta (δ) turns in the second peak. (As for the omega turn, the name delta
turn is chosen to reflect the δ-like shape of the worm during a typical delta
turn.)
Returning to the original tracking movies, the presence of these two
classes of turns is clearly visible. In Fig. 5.6, we show movie stills for two
example turns: one omega turn, and one delta turn. During the omega
turn, the worm slides its head along its body, ending up with a roughly
180◦ reorientation — similar to the escape-response omega turn. A delta
turn, on the other hand, is much deeper: the worm completely crosses its
head over its body, resulting in an ‘over-turn’ of greater than 180◦ .
142
5.3 C. elegans free crawling behavior
5.3.3 Despite disparate appearance, delta- and omega-turn
kinematics are similar
Omega turns and delta turns are visually distinct, but how is this difference
reflected in their posture space trajectories? Most notable is the higher a3
peak amplitude of delta turns; but are they otherwise different? Taking one
particular example, shown in Fig. 5.7a, suggests that the other aspects of
the delta turn’s kinematics are actually very similar to those of the omega
turn (cf. Fig. 5.2). Just like the omega turn, the delta turn starts with a
deep ventral head swing, and corresponding peaks in a1 and a4 . This is
followed by the peak in a3 , marking the apex of the turn, and a negative
peak in a4 for the exit of the high-curvature body wave through the tail.
Averaging the eigenmode time series across N = 348 delta turns (grayshaded area in Fig 5.7a; see Methods), we obtain the average response
shown in Fig. 5.7b. Comparing this with the average omega turn for the
escape response dataset from the previous section (red dashed line), we
see that a3 amplitude is indeed the only feature that clearly separates the
delta turn from the omega turn.
5.3.4 Delta and omega turns as part of the worm’s
navigational strategy
So far, we have seen that the worm makes, in addition to shallow turns in
both the ventral and dorsal direction, two distinct types of steep ventral
turns. These omega and delta turns appear to be different only in their a3
pulse amplitude; turn kinematics are otherwise very similar. Could they
perhaps play specific roles in the worm’s navigational strategy, and could
this be linked to the difference in a3 amplitude?
We first plotted where both types of turns occur in the worm’s trajectory on the agar plate. In Fig. 5.8a,b, we show such a trajectory for
one of the twelve worms in the experiment, with omega (yellow/light) and
delta (blue/dark) turns marked. The worm starts out at position (0, 0)
(black arrow), and shows typical ‘dwelling’ behavior: a high turning fre-
143
5 Deep turns and dynamics of reorientation in C. elegans
(a)
(b)
10
10
a1 0
a1 0
−10
10
−10
10
a2 0
a2 0
−10
−10
20
a3 10
0
20
a3 10
0
5
a4 0
−5
5
a4 0
−5
0
φ −π
−3π
5
6
7
8
0.2
0.4
0.6
Normalized time
0.8
9 10 11 12 13 14
Time (s)
Figure 5.7 | Kinematics of the delta turn are similar to those of the omega
turn. (a) Typical time series for the postural eigenmodes a1..4 during a deep ‘delta’
turn; ϕ is the body wave phase angle, as defined in Fig. 4.1f (p. 101). Shaded area
indicates the delta turn, as defined in the Methods. (b) Average eigenmode time
series during a delta turn (blue, N = 348). Gray lines indicate SD. For comparison,
the average escape response omega turn is also shown (red dotted line). Time has
been normalized with respect to the total length of the turn: 6 ± 2 s (mean ± SD)
for delta turns, 7 ± 3 s for escape-response omega turns.
144
1
5.3 C. elegans free crawling behavior
(a)
(b)
Ω
δ
−14
Y (mm)
Y (mm)
10
0
−16
−10
(c)
10
X (mm)
20
8
(d)
0°
ve
nt
15
12.5
90°
d
l
sa
or
l
ra
270°
180°
Mean turning rate (min−1)
0
10
X (mm)
1.5
12
Ω
δ
1.25
1.0
0.75
0.5
0.25
10
20
Time (min)
30
Figure 5.8 | The omega and delta turns as part of the navigational strategy
of C. elegans. (a,b) Location on the agar plate of one of the 12 tracked worms over
the course of a 35-minute tracking experiment (off-food), starting at (0, 0) (black
arrow). Ventral omega turns (yellow/light) and ventral delta turns (blue/dark) are
highlighted. A blow-up of the area marked in gray is shown in b. (c) Histogram of
orientation change due to ventral omega turns (yellow/light) and ventral delta turns
(blue/dark). Omega turns dominantly lead to a re-orientation change towards the
ventral side of the animal, whereas deep delta turns cause the animal to ‘over-turn’
into the dorsal side of the compass. (d) Average turning rate (across N = 12 worms)
during the 35 minutes of the tracking experiment. Ventral omega and delta turns
are temporally independent (see text), but occur with approximately equal rate, and
show co-adaptation as the worm switches from a ‘dwelling’ to a ‘roaming’ strategy.
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5 Deep turns and dynamics of reorientation in C. elegans
quency, and an exploration of its local environment [5]. After dwelling for
some minutes without finding any food, it gradually switches to ‘roaming’
behavior, traversing a wider area of the agar plate [5, 41].
During the full course of the experiment, the two types of turns are
statistically independent. Apart from an overall modulation of the turn
frequency (discussed later), no temporal correlations are observed. We
checked this by computing the mutual information between time-binned,
time-shifted time series for both turns (see Methods). With a maximum
mutual information less than a few percent of the maximum entropy, the
turns have to be considered independent.
While independent, the turns result in a different change of orientation — following the known link between the third mode and orientation changes [17]. In Fig. 5.8c, we show how the worm reorients using
both omega (yellow/light) and delta (blue/dark) turns. The free-crawling
omega turns show a much broader distribution than the previously encountered escape-response ones (cf. Fig. 5.4d). Still, they generally reorient
the worm ventrally. In contrast, the deeper delta turns consist of the worm
‘over-turning’ and ending up reorienting towards its dorsal side.
The difference in reorientation angle may provide a hint as to why these
two distinct turns exist. In the first part of this chapter, we saw that
the neural mechanisms that produce the escape-response omega turn are
fundamentally asymmetric, producing only ventral turns (through disinhibition of the VD motor neurons) [4]. If the worm uses the same neural
infrastructure during free crawling, this would only ever allow it to reorient
itself towards its ventral side. Lacking a dorsal ‘copy’ of the same neural
infrastructure, the worm could instead hyper-activate the existing infrastructure to produce ventral over-turning’. These over-turns are what we
call delta turns, and enable the worm to also reorient towards its dorsal
side.
Evidence that both turns share at least part of the worm’s neuronal
control mechanisms is shown in Fig. 5.8d. Here, we plot the frequency of
turning events over the course of the experiment (see Methods). As the
146
5.3 C. elegans free crawling behavior
worm switches from ‘dwelling’ to ‘roaming’, in search for food in a larger
area, the turn frequency decreases significantly — a well-known adaptation [5, 28, 41]. Interestingly, both types of turns show similar frequencies,
and co-adaptation over time. This suggests that both types of turns are
regulated by a shared underlying mechanism. One possible realization of
such a mechanism is the known regulation of ‘dwelling’ behavior by the
dopamine neurotransmitter, which modulates motion-related glutaminergic signaling pathways in the worm’s nervous system [28].
We expect that our observation of the existence of both omega and
delta turns will be highly relevant for future investigations of C. elegans
‘pirouettes’. The definition of what exactly constitutes a pirouette has
varied from publication to publication [5, 33, 38, 30], but always features a
series of one or more omega turns as the course-adjusting motif. We have
now shown that these turns are, in fact, two distinct turns, each producing
a different reorientation. How the two turns are combined to produce the
known reorientation towards an attractant gradient [30], is an interesting
avenue for further investigation.
5.3.5 Conclusions and outlook
In this chapter, we have taken the first steps towards opening up the
‘black box’ of self-overlapping body shapes that occur during navigation
in C. elegans.
During the C. elegans escape response, the signature omega turn is
the central behavioral motif that steers the worm away from the noxious
stimulus. The turn contributes around 180◦ of the reorientation observed
across the response, and appears to be highly stereotyped, with a tightly
controlled amplitude. The characteristics of the escape response can be
linked to previously found mechanisms at the neural and molecular level.
A tyramine-mediated build-up of asymmetry in the worm’s locomotory
system is quantitatively visible as a baseline shift in the oscillations of the
third postural eigenmode a3 . This occurs during the reversal phase, and
lingers after the omega turn has completed, resulting in a broadening of
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5 Deep turns and dynamics of reorientation in C. elegans
the distribution of orientation changes across the full response. Finally,
we have proposed a simple hypothesis that the worm, lacking visual cues,
uses its own body to ‘guide’ itself backwards.
In free crawling, a distinction can be made between two separate populations of deep turns: omega turns, featuring the classic Ω shape, and a novel
class of deep turns, which we here call ‘delta’ (δ) turns. We show that,
despite their distinct visual appearance, the posture space trajectories of
delta and omega turns are very similar. Their only clear distinguishing feature is the amplitude of the pulse in the third postural eigenmode a3 , which
seems to drive a difference in resulting reorientation. Taken together, this
generates a picture of omega and delta turns as a way for the worm to make
sharp turns in the ventral and dorsal direction, respectively. The turns are
temporally uncorrelated, although their overall frequency appears to be
controlled by a shared mechanism.
Our first glance into the ‘black box’ of self-overlapping body shapes of
C. elegans is of course just that: a first glance. Some important questions
remain, as yet, unanswered. For example, posture space trajectories for
sharp turns, while geometrically similar, still show significant variability. It
remains unclear what the source of this inter- and intra-individual variance
is. To answer such questions, a principled way of quantifying differences
between trajectories through posture space, and relating those differences
to behavioral output, would be needed.
Our tracking algorithm could also provide a way forward for elucidating
the neural and molecular pathways that drive turning behavior in C. elegans. Behavioral defects induced by genetic mutations or cell ablations
are typically detected manually [5, 4]; automated tracking would allow for
increased throughput, and detection of more subtle defects than might be
detected by eye.
Finally, work on other nematodes has shown interesting differences in
the way these species modulate their navigational strategies, in this case
between a ‘roaming’ and a ‘dwelling’ strategy [19]. Whether omega and
delta turns are conserved across species, and contribute similarly to es-
148
5.4 Methods
Molecule
Molecular weight
(g/mol)
Free diffusion constant
(10−10 m2 /s)
Source
norepinephrine
dopamine
leucine
threonine
169
153
131
119
5.5
6.0
6.0
7.5
[42]
[42]
[43]
[44]
Table 5.1 | Diffusion constants of some small molecules (neurotransmitters and
amino acids) that are similar in molecular weight to tyramine (MW = 137 g/mol).
cape response and foraging behavior, could be an interesting future line of
investigation.
5.4 Methods
Tyramine diffusion. During the escape response, extra-synaptic diffusion of
tyramine is thought to temporally separate the initial reversal of the worm and
the omega turn (see ‘Introduction to the escape response’, p. 126) [4]. We can
make a rough, back-of-an-envelope estimate of the time needed for tyramine to
diffuse, and show that this is consistent with the reversal phase duration typically
observed in our experiments.
To our knowledge, no diffusion constant has been published for tyramine. Instead, we can estimate the relevant order of magnitude by considering other molecules with a similar molecular mass. From the data in Table 5.1, we can derive
a conservative estimate of the tyramine diffusion constant of D ∼ 5 · 10−10 m2 /s.
Using the diffusion equation, h(∆x)2 i = 2Dt, for a length scale that we estimate to be a tenth of the worm’s full-grown length of 1 mm [3] (since the distance
between the RIM and VD neurons is far less than 1 mm), we arrive at a typical
timescale of t ∼ (10−4 m2 )2 /(2 · 5 · 10−10 m2 /s) ∼ 10 s. This is consistent with
the typical reversal time of 5 s observed in our escape response data.
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5 Deep turns and dynamics of reorientation in C. elegans
Data collection. Two datasets were used in this chapter: one with C. elegans
escape responses evoked by a thermal stimulus; and one with free crawling assays.
The collection of both of these datasets, including the postural tracking, was
described in the Methods of the previous chapter (see p. 115).
As C. elegans crawls on its side [5], worms can have one of two possible orientations during experiments. Dorsal/ventral orientation was recorded during
the experiments by noting the position of the vulva, and results for worms with
a right-handed orientation were mirrored. Surprisingly, we found two worms in
the free-crawling dataset that changed their dorsal/ventral orientation during the
experiment. Both worms showed the asymmetry in a3 peak amplitude that was
noted in Fig. 5.5, but this asymmetry switched sign half-way during the recording. Inspecting the movies, we found that the time of switching corresponded to
moments when the worms moved off or into the agar, escaping the 2D constraints
of the experiment. This was corrected for by mirroring tracking results for only
the relevant part of the experiment.
Reorientation during escape response. For the analysis of the worm’s reorientation during the escape response (Fig. 5.4), N = 91 escape responses were
analyzed. Each 30-second recording was segmented by first finding the omega
turn, as described below. After identification of the omega turn, the reversal
phase was simply defined as the first frame after the stimulus with a negative
body wave phase velocity dϕ/ dt, up until the start of the omega turn. The
‘post-omega’ phase was any data after the end of the omega turn until the end
of the recording at t = 30 s.
To generate the simulated histogram for the orientation change of the full
response, we picked a random worm for the reversal phase, a random worm
for the omega turn (possibly the same), etc. The orientation changes of these
three phases were summed, and added to the simulated distribution. If any of
the chosen recordings did not have a successfully detected omega turn, this was
skipped. A total of 106 iterations were performed.
Definition of omega and delta turn. For the escape response data, the
largest peak in a3 between t = 10 s (the time of the stimulus) and t = 29 s
was identified as the apex of the omega turn. To locate the end of the omega
turn, the first root (zero) of a4 after the apex was found; any point after that
root that had a3 < 3 was considered to be the end of the omega turn. This
ensured that the negative peak in a4 , representing a high-curvature state of the
150
5.4 Methods
tail at the end of the omega turn, had finished, and that the worm had reached
a relatively ‘straight’ shape. For such straight shapes, the overall orientation hθi
has a straightforward, intuitive interpretation. The same criterion was used, in
the opposite direction, to find the start of the omega turn. If no starting point
and/or end point of the omega turn could be found, the recording was excluded
from the analysis. (In the escape response dataset, this was the case for 15 out
of 91 recordings).
In the free crawling dataset, the same quantitative criterion was used to find
both omega and delta turns.
Local extrema in a3 . For the free crawling dataset, we analyzed the amplitudes of local minima and maxima in the third postural eigenmode a3 (Fig. 5.5).
As the tracking was originally performed on a segmented version of this data,
tracking data first had to be ‘stitched together’ again.
Segmentation of the 33 600-frame movies was described in the ‘Methods’ of
the previous chapter. Briefly, each segment of a movie was chosen such, that it
contained a consecutive series of non-crossed frames, followed by a consecutive
series of crossed frames (a turn), followed by another series of non-crossed frames.
The last series of non-crossed frames in segment j overlapped with the first series
of non-crossed frames in segment j +1. This facilitated the stitching process: two
segments could be joined together at a frame that occurred in both segments j
and j + 1, and that had the exact same tracking solution in both segments within
a given margin of error (0.1).
Tracking errors could cause violations of this margin of error. All such stitching
problems were manually inspected; if a tracking error was found, that segment of
the data was excluded from the analysis. In total, across all twelve worms, 878
out of 936 segments (94%) produced tracking results of sufficient quality.
For detection of local extrema in a3 , a standard peak-finding algorithm was
used to detect both minima and maxima (based on MATLAB’s findpeaks function, which defines a peak as a data point with a greater value than its immediate
neighbors). Only extrema with a minimum prominence of 0.5 were kept. Some
a3 peaks featured smaller sub-peaks in their shoulders; such sub-peaks were discarded.
Average delta-turn eigenmode time series. To generate Fig. 5.7b, delta
turns as defined above were cut from the free crawling dataset (N = 348). Each
five-dimensional time series (modes a1...5 ) for each delta turn was mapped onto
151
5 Deep turns and dynamics of reorientation in C. elegans
a 50-point, linearly-spaced ‘normalized time’ axis (tN ∈ [0, 1]), using linear interpolation of the time series where necessary. This normalized time corresponded
to an actual duration of the delta turns of 6 ± 2 s (mean ± SD). Data across
delta turns was then averaged per normalized-time point, giving the trajectories
shown in the Figure.
The same procedure was followed for omega turns in the escape response
dataset (N = 91). For this data, the normalized time axis corresponds to an
actual duration of the omega turns of 7 ± 3 s (mean ± SD).
Mutual information between omega and delta turns. For calculating the
mutual information between the omega and delta turns during free crawling,
we followed the procedure from ref. 45. We created binarized time series for
each type of turn, by binning turning events into bins of 2, 4, 10, or 20 s. The
mutual information was calculated for different time shifts, ranging from −60 to
+60 s. Mutual information across time shifts never exceeded 3% of the maximum
entropy of each time series, hence precluding a significant correlation between the
two types of turns.
Turn frequency adaptation. In Fig. 5.8d, we show how the average turn
frequencies for omega and delta turns change over the course of the 35-minute
free-crawling experiments. Turns were detected in the stitched data by using the
peak detection algorithm outlined above (see ‘Local extrema in a3’ before). Using
the boundaries identified in Fig. 5.5b, a3 extrema with an absolute value between
10 and 20 were classified as ‘omega turns’, while extrema with an absolute value
greater than 20 were considered to be ‘delta turns’. We also distinguished between ventral turns, with a positive amplitude, and dorsal turns, with a negative
amplitude.
For the Figure, we counted the average number of turns per unit time, across
the 12 experiments, in a 10-minute sliding window, shifted across the data in
5-minute increments. The first 200 seconds of each experiment were discarded,
as the worms showed signs of adaptation to their new environment (the agar
plate without food): the average turn frequency, somewhat erratically, increased
during this period.
The population of ‘omega turns’ thus found consists, as can be seen in Fig. 5.5b,
of two sub-populations: a tail of the symmetric distribution of ‘shallow turns’,
and the actual population of ventrally-biased omega turns. We therefore counted
the number of a3 peaks with an amplitude between −20 and −10 in each time
152
5.5 References
window, and subtracted this from the total number of a3 peaks with an amplitude
between +10 and +20. This gave us the number of ‘true’, ventrally-biased omega
turns. This number showed excellent agreement with the number of delta turns
(Fig. 5.8d).
5.5 References
[1] J. G. White, E. Southgate, J. N. Thomson, and S. Brenner. The Structure of the
Nervous System of the Nematode Caenorhabditis elegans. Philosophical Transactions of the Royal Society B: Biological Sciences, 314(1165):1–340, 1986.
[2] B. Prevo. Kinesin Illuminated. PhD thesis, VU University Amsterdam, 2015.
[3] Z. Altun and D. Hall. Nervous system, general description. In WormAtlas. 2011.
[4] J. L. Donnelly, C. M. Clark, A. M. Leifer, J. K. Pirri, M. Haburcak, M. M. Francis, A. D. T. Samuel, and M. J. Alkema. Monoaminergic orchestration of motor
programs in a complex C. elegans behavior. PLoS Biology, 11(4):e1001529, 2013.
[5] J. M. Gray, J. J. Hill, and C. I. Bargmann. A circuit for navigation in Caenorhabditis elegans. Proceedings of the National Academy of Sciences of the United States
of America, 102(9):3184–91, 2005.
[6] A. Mohammadi, J. Byrne Rodgers, I. Kotera, and W. S. Ryu. Behavioral response of Caenorhabditis elegans to localized thermal stimuli. BMC Neuroscience,
14(1):66, 2013.
[7] S. M. Maguire, C. M. Clark, J. Nunnari, J. K. Pirri, and M. J. Alkema. The
C. elegans Touch Response Facilitates Escape from Predacious Fungi. Current
Biology, 21(15):1326–1330, 2011.
[8] T. Boulin and O. Hobert. From genes to function: The C. elegans genetic toolbox.
Wiley Interdisciplinary Reviews: Developmental Biology, 1(1):114–137, 2012.
[9] J. Sulston, E. Schierenberg, J. White, and J. Thomson. The embryonic cell lineage
of the nematode Caenorhabditis elegans. Developmental Biology, 100(1):64–119,
1983.
[10] D. M. Tobin and C. I. Bargmann. Invertebrate nociception: Behaviors, neurons
and molecules. Journal of Neurobiology, 61(1):161–174, 2004.
[11] J. E. Mellem, P. J. Brockie, Y. Zheng, D. M. Madsen, and A. V. Maricq. Decoding
of polymodal sensory stimuli by postsynaptic glutamate receptors in C. elegans.
Neuron, 36(5):933–944, 2002.
[12] M. Chalfie, J. E. Sulston, J. G. White, E. Southgate, J. N. Thomson, and S. Brenner. The neural circuit for touch sensitivity in Caenorhabditis elegans. Journal of
Neuroscience, 5(4):956–964, 1985.
[13] J. K. Pirri, A. D. McPherson, J. L. Donnelly, M. M. Francis, and M. J. Alkema.
153
5 Deep turns and dynamics of reorientation in C. elegans
A Tyramine-Gated Chloride Channel Coordinates Distinct Motor Programs of a
Caenorhabditis elegans Escape Response. Neuron, 62:526–538, 2009.
[14] T. H. Lindsay, T. R. Thiele, and S. R. Lockery. Optogenetic analysis of synaptic
transmission in the central nervous system of the nematode Caenorhabditis elegans.
Nature communications, 2(May):306, 2011.
[15] E. R. Troemel, B. E. Kimmel, and C. I. Bargmann. Reprogramming chemotaxis responses: Sensory neurons define olfactory preferences in C. elegans. Cell,
91(2):161–169, 1997.
[16] G. J. Stephens, B. Johnson-Kerner, W. Bialek, and W. S. Ryu. Dimensionality and dynamics in the behavior of C. elegans. PLoS Computational Biology,
4(4):e1000028, 2008.
[17] G. J. Stephens, B. Johnson-Kerner, W. Bialek, and W. S. Ryu. From modes to
movement in the behavior of Caenorhabditis elegans. PLoS One, 5(11):e13914,
2010.
[18] E. M. Jorgensen and S. E. Mango. The art and design of genetic screens:
Caenorhabditis elegans. Nature Reviews Genetics, 3(5):356–369, 2002.
[19] S. J. Helms, L. Avery, G. J. Stephens, and T. S. Shimizu. Modeling the ballistic-todiffusive transition in nematode motility reveals low-dimensional behavioral variation across species. 2015, arXiv:1501.00481.
[20] G. J. Stephens, L. C. Osborne, and W. Bialek. Searching for simplicity in the
analysis of neurons and behavior. Proceedings of the National Academy of Sciences
of the United States of America, 108 Suppl:15565–71, 2011.
[21] S. Ward. Chemotaxis by the nematode Caenorhabditis elegans: identification of
attractants and analysis of the response by use of mutants. Proceedings of the
National Academy of Sciences of the United States of America, 70(3):817–821,
1973.
[22] C. I. Bargmann and H. R. Horvitz. Chemosensory neurons with overlapping functions direct chemotaxis to multiple chemicals in C. elegans. Neuron, 7(5):729–42,
1991.
[23] E. M. Hedgecock and R. L. Russell. Normal and mutant thermotaxis in the nematode Caenorhabditis elegans. Proceedings of the National Academy of Sciences of
the United States of America, 72(10):4061–4065, 1975.
[24] D. A. Clark, C. V. Gabel, H. Gabel, and A. D. T. Samuel. Temporal activity
patterns in thermosensory neurons of freely moving Caenorhabditis elegans encode
spatial thermal gradients. Journal of Neuroscience, 27(23):6083–90, 2007.
[25] J. M. Gray, D. S. Karow, H. Lu, A. J. Chang, J. S. Chang, R. E. Ellis, M. A.
Marletta, and C. I. Bargmann. Oxygen sensation and social feeding mediated by
a C. elegans guanylate cyclase homologue. Nature, 430(6997):317–322, 2004.
[26] A. J. Chang, N. Chronis, D. S. Karow, M. A. Marletta, and C. I. Bargmann. A
154
5.5 References
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
[40]
distributed chemosensory circuit for oxygen preference in C. elegans. PLoS Biology,
4(9):e274, 2006.
M. Gomez, E. De Castro, E. Guarin, H. Sasakura, A. Kuhara, I. Mori, T. Bartfai,
C. I. Bargmann, and P. Nef. Ca2+ signaling via the neuronal calcium sensor-1
regulates associative learning and memory in C. elegans. Neuron, 30(1):241–248,
2001.
M. de Bono and A. Villu Maricq. Neuronal Substrates of Complex Behaviors in
C. elegans. Annual Review of Neuroscience, 28(1):451–501, 2005.
S. R. Lockery. The computational worm: spatial orientation and its neuronal basis
in C. elegans. Current Opinion in Neurobiology, 21(5):782–90, 2011.
J. T. Pierce-Shimomura, T. M. Morse, and S. R. Lockery. The fundamental
role of pirouettes in Caenorhabditis elegans chemotaxis. Journal of Neuroscience,
19(21):9557–69, 1999.
E. F. Keller and L. A. Segel. Model for chemotaxis. Journal of Theoretical Biology,
30(2):225–34, 1971.
H. C. Berg and D. A. Brown. Chemotaxis in Escherichia coli analysed by threedimensional tracking. Nature, 239(5374):500–504, 1972.
Y. Iino and K. Yoshida. Parallel use of two behavioral mechanisms for chemotaxis
in Caenorhabditis elegans. Journal of Neuroscience, 29(17):5370–80, 2009.
J. H. Baek, P. Cosman, Z. Feng, J. Silver, and W. R. Schafer. Using machine
vision to analyze and classify Caenorhabditis elegans behavioral phenotypes quantitatively. Journal of Neuroscience Methods, 118(1):9–21, 2002.
Z. Feng, C. J. Cronin, J. H. Wittig, P. W. Sternberg, and W. R. Schafer. An
imaging system for standardized quantitative analysis of C. elegans behavior. BMC
Bioinformatics, 5(1):115, 2004.
C. J. Cronin, J. E. Mendel, S. Mukhtar, Y.-M. Kim, R. C. Stirbl, J. Bruck, and
P. W. Sternberg. An automated system for measuring parameters of nematode
sinusoidal movement. BMC Genetics, 6:5, 2005.
E. Fontaine, J. Burdick, and A. Barr. Automated tracking of multiple C. elegans.
In Engineering in Medicine and Biology Society, 2006. EMBS ’06. 28th Annual
International Conference of the IEEE, volume 2, pages 3716–3719, 2006.
L. C. M. Salvador, F. Bartumeus, S. A. Levin, and W. S. Ryu. Mechanistic
analysis of the search behaviour of Caenorhabditis elegans. Journal of the Royal
Society Interface, 11(92):20131092, 2014.
N. Roussel, J. Sprenger, S. J. Tappan, and J. R. Glaser. Robust tracking and quantification of C. elegans body shape and locomotion through coiling, entanglement,
and omega bends. Worm, 3(4):e982437, 2014.
S. Nagy, M. Goessling, Y. Amit, and D. Biron. A generative statistical algorithm
for automatic detection of complex postures. PLoS Computational Biology, 2015
(in press).
155
5 Deep turns and dynamics of reorientation in C. elegans
[41] N. Srivastava, D. A. Clark, and A. D. T. Samuel. Temporal analysis of stochastic
turning behavior of swimming C. elegans. Journal of Neurophysiology, 102(2):1172–
9, 2009.
[42] G. Gerhardt and R. N. Adams. Determination of diffusion coefficients by flow
injection analysis. Analytical Chemistry, 54(14):2618–2620, 1982.
[43] A. Polson. On the diffusion constants of the amino-acids. Biochemical Journal,
31(10):1903–1912, 1937.
[44] Y. Ma, C. Zhu, P. Ma, and K. T. Yu. Studies on the Diffusion Coefficients of
Amino Acids in Aqueous Solutions. Journal of Chemical & Engineering Data,
50(4):1192–1196, 2005.
[45] S. Strong, R. Koberle, R. de Ruyter van Steveninck, and W. Bialek. Entropy and
Information in Neural Spike Trains. Physical Review Letters, 80(1):197–200, 1998.
156