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5Deep turns and the dynamics ofreorientation in escape responseand free crawling of C. elegansAbstract — In the previous chapter, we developed an automated tracking algo-rithm 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 twoimportant behaviors: the escape response, and abrupt reorientations in freelycrawling worms. During the escape response, we find that the worm steers sharplyaway from the noxious stimulus by 180 on average, in a tightly controlled way.Additional reorientations before and after the turn broaden the distribution ofreorientation angles, and can be linked to known underlying neural and molec-ular mechanisms. During free crawling, we find that abrupt turns, appearing inprevious literature as ‘omega turns’, are in fact differentiated into two distinctclasses. Despite a dramatically different visual appearance, both statically anddynamically, the two turns share similar kinematics in posture space; only theamplitude of a pulse in the third postural eigenmode is a dominant distinguish-ing feature. The two classes of turns reorient the worm towards different sides:omega turns ventrally; delta turns dorsally, by over-turning through the ventralside. We show that the two turns occur independently, but with approximatelyequal rates that remain equal during adaptation. Taken together, these obser-vations suggest a shared underlying neural infrastructure, and a more diversenavigational 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 thefull 2D motor behavior of C. elegans. This algorithm is capable of trackingnot just ‘simple’ postures, but also self-occluding ones. This enables us tonow take a closer, quantitative look at behaviors of the worm that featuresuch self-occluding body shapes, and that have thus far not been fullyresolved.In the first part of this chapter, we focus on the escape response of

C. elegans. This sequence of orchestrated behavioral motifs is evoked bya 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 sharpreorientation featuring self-overlapping body shapes, is the crucial part ofthe sequence, and can now for the first time be resolved. Studying thishighly stereotyped behavior also helps us to identify quantitative patternsin 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 foodand favorable habitats, but the sharp turns that occur during this behaviorhave never been fully investigated. Here, we take the first steps towardsresolving 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 con-ditions. Its sensory neurons, most of which are connected to the outsideworld through non-motile cilia [1] [2, Ch. 3.1], can detect noxious stimuliof a chemical, mechanical, optical, or thermal nature [3]. Upon encounter-ing a sufficiently strong stimulus, the worm executes a stereotyped escaperesponse: a behavioral sequence that steers the worm away from the ob-served threat.

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Figure 5.1 | Schematic overview of the C. elegans escape response (based onref. 4). Top row shows worm body shapes extracted from tracking data: (i) forwardlocomotion and exploratory head motions; (ii) infrared laser stimulus; (iii) reversalphase; (iv) omega turn; (v) resumption of forward locomotion in opposite direction.Diagram below shows sequence of events in the C. elegans nervous system. Timeflows from left to right. RIM, SMD, and RIV designate C. elegans neurons. Green plussigns indicate stimulation; red minus signs inhibition. Inset shows the neural networkimplicated in the escape response [4, 5]. Rectangles: sensory neurons; hexagons:command neurons; circles: motor neurons. Synaptic connections are indicated bytriangles, gap junctions by bars, and extra-synaptic diffusion of tyramine by a dashedarrow. Green connections are stimulatory, red ones inhibitory. Details have beenomitted; see ref. 4 for a more in-depth overview.

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Fig. 5.1 (top) shows the timeline of the C. elegans escape response. Dur-ing normal locomotion on an agar surface (i), the worm moves by propa-gating a sinusoidal wave through the body. This snake-like motion is typ-ically accompanied by exploratory head movements. In our experiments,we elicit an escape response by applying a localized thermal stimulus tothe 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 causesthe worm to abruptly pause, and then back up (iii). During this reversalphase, head movements are suppressed, which has been suggested to in-crease the worm’s chances of escaping from the ‘snare traps’ of predatoryfungi [7]. After roughly 5 to 10 seconds of reversing, the worm executes anomega turn: a sharp reorientation manoeuvre, during which the worm’sbody briefly resembles the shape of the Greek letter Ω (iv) [5]. The turnreorients the worm away from the stimulus, and allows it to resume forwardlocomotion in the opposite direction (v).

Some aspects of the escape response sequence have been teased apart atthe cellular, molecular, and genetic level. This has been greatly facilitatedby the availability of a genetic toolbox for C. elegans [8] as well as theworm’s stereotyped development [9]. The latter means that each individ-ual 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 predictablelineage, starting at the fertilized egg [9]. Genetic changes can be easily in-troduced into the worm’s genome, and can often be made to target specificcells [8]. As an example, using these techniques, the nociceptive ASH neu-rons have been found to express ion channel proteins that are implicatedin osmo- and mechanosensation [10]. This makes the ASH neurons mul-timodal, 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 drivesthe 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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brow hair). In this scenario, a qualitative description of the mechanismsthat orchestrate the different phases of the escape response has emergedfrom experiments (Fig. 5.1b) [4, 13], and a key element is the neurotrans-mitter tyramine, released by the RIM interneurons. Tyramine acts throughmultiple pathways, one of which is extra-synaptic diffusion and binding toG-protein coupled receptors (GPCRs) in distant cells. As this diffusionprocess has a timescale of seconds (see Methods) — much slower than themillisecond timescale associated with the initial synapse-mediated reversalresponse [14] — it creates a time separation between the reversal and thesubsequent omega turn.

At the moment the worm is touched, the signaling cascade starts withthe sensory neurons ALM and AVM registering the touch (Fig. 5.1, dia-gram and inset) [4]. These neurons initiate backward locomotion (throughthe AVD and AVA command neurons), while inhibiting forward locomo-tion (through the PVC and AVB command neurons). AVA, in turn, acti-vates 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 chan-nels (LGC-55) in neck muscles and head motor neurons, it additionallysuppresses head movements. Crucially, tyramine also diffuses out of thesynaptic cleft (‘synaptic spillover’), and activates GPCRs (SER-2) else-where in the worm’s body. SER-2 activation by diffusing tyramine sets upan asymmetry in the worm’s locomotory system: it disinhibits the ven-tral body wall muscles (through suppression of the VD inhibitory motorneuron). After the omega turn has been initiated by a steep ventral headswing (controlled by the SMD neuron [5]), the resulting hypercontractionof the ventral body wall muscles during the body wave produces the char-acteristic omega turn.

The construction and validation of such a description relies on classicmethods from biology. Typically, a perturbation is introduced into theworm’s locomotory system, either through genetic knockouts or cell abla-tions [15]. To assess the impact on the worm’s behavioral phenotype, one

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identifies a behavioral motif affected by the perturbation, and character-izes its temporal or physical appearance. As an example of the latter, partof the role of the SER-2 GPCR was elucidated by linking its absence toa marked decrease in ‘omega angle’, the arc angle between the head andtail during the turn [4]. Worms did not fully ‘close’ their omega turn bytouching their head to the body, evidencing a lack of disinhibition of theVD neurons.

While detailed, the existing description of the escape response is qual-itative. In this section, we take the first steps towards a quantitative de-scription of the escape response. We use the intrinsic coordinate systemfor C. elegans motor behavior that was introduced in the previous chap-ter: the low-dimensional space of body postures. Using our new trackingapproach, which also resolves self-occluding body shapes, we are, for thefirst time, able to quantify the full escape response, including the omegaturn. We show that the escape response follows stereotyped patterns inposture space, and relate this to the reorientation of the worm during theresponse. We find that the omega turn produces a tightly-controlled reori-entation of 180, but also note that pre- and post-omega phases result inadditional orientation changes, broadening the full distribution. Finally,we propose a simple model, in which the worm uses head–body touch asa 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 forquantifying the full postural dynamics of the escape response, including theself-overlapping shapes that are crucial to the reorientation. Through videotracking of the worm’s body postures, and decomposing each posture as alinear combination of postural eigenmodes (or ‘eigenworms’), we obtain adescription of the escape response as shown in Fig. 5.2. Here, a1 througha4 represent the first four eigenmodes; at each point in time, the full bodyposture of the worm can be obtained by adding together the eigenworms

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shown as insets, in the relative amounts indicated by the values of ai 1.

The different phases of the qualitative scenario described in the previoussection (also shown at the top of Fig. 5.2) correspond to distinct posturalfeatures of the time series. For larger datasets, this will allow us to auto-mate the detection of behavioral motifs in the data. What features do weobserve?

During normal, forward locomotion (segment i, t = 0 . . . 10 s), the wormcrawls by propagating a sinusoidal wave through its body. This is reflectedin 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 crawlingcorrespond to a circular trajectory in the (a1, a2) plane (Fig. 5.3; see alsoFig. 4.1f on p. 101). Based on this circular trajectory, a body wave phaseangle (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 byeye, shows up as a significant increase in the amplitude of oscillations ina3 and a4.

The omega turn itself (segment iv, gray-shaded area) is preceded bya steep head swing to the ventral side of the body. The resulting high-curvature anterior body bend, observed as peaks in a1 and a4 (red arrows),propagates head-to-tail: this implies another switch of the direction of thebody wave, and hence a return to increasing ϕ. The Ω-shaped apex of theturn is marked by a large peak in a3 (red arrow). As the worm exits theturn, the high-curvature body bend reaches the tail, causing a negativepeak in a4 (red arrow). Taken together, these quantitative features canbe used to define an omega turn: a significant peak in a3, bounded bythe low-curvature body shapes that occur before and after the turn (see

1 More formally, each eigenworm ei is a vector of tangent angles along the ‘backbone’ ofthe worm, obtained by Principle Component Analysis. The backbone tangent anglevector at time t is given by θ(t) =

∑i aiei. See the previous chapter for details.

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Figure 5.2 | Quantification of a typical escape response. Time series for thepostural eigenmode decompositions of a tracked worm. a1 to a4 represent the firstfour postural eigenmodes (also shown as the gray worm shapes in the top-left cornersof 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 areaindicates the omega turn, as defined in the Methods. Red arrows highlight featuresdiscussed in the text.

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Methods).Finally, as the turn is finished, the worm resumes its forward crawling

(v). Interestingly, the increased ‘floppiness’ of the worm (the increasedamplitude of the a3 and a4 oscillations) often remains after the omegaturn, 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 inFig. 5.3. Here, we plot the same data as a trajectory in the first threedimensions of posture space. The circular motion in the (a1, a2) plane isclearly visible. At the time of the stimulus, the direction of the body wavecircle 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 responsetrajectory. 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 atthe presence of a neural mechanism that triggers the start of the omegaturn. The kink also signals the return to a clockwise progression along thecrawling cycle.This geometric picture is potentially powerful, as it clearly visualizes

the temporal relationships between the different quantitative features ofthe escape response. It also suggests a simple decomposition of the omegaturn, as a superposition of the body wave attractor cycle and a pulse alongthe third mode.

5.2.4 Reorientation during the escape response

In order to further understand these posture space trajectories, and ex-amine their functional significance for the worm, we considered the reori-entation of the worm during the response. As the escape response serves

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Figure 5.3 | The escape response in posture space. The same data as in Fig. 5.2is 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 yellowto 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 thetilt of the body wave cycle during the reversal phase (iii).

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to turn the worm away from a perceived threat, back to known-safe terri-tory, 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 orienta-tion: the average tangent angle of the backbone, 〈θ〉. In Fig. 5.4d, we con-firm that, on average, the N = 91 tested worms change their overall orien-tation 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 theoverall orientation continuously throughout the different phases of the re-sponse. In Fig. 5.4a–c, we calculate how much each of the three phases ofthe escape response reorients the worm: (a) reversal; (b) omega turn (asdefined in the preceding sections; also see Methods); and (c) post-omegaforward crawling. The omega turn itself results in a sharp turn of around180 (−0.9π±0.4π rad, mean± SD). Pre- and post-omega phases also showsmall 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 ma-noeuvre for turning away from the stimulus, the full-response orientationchange is broadened by the pre-omega (reversal) and post-omega phases.To see if there was an underlying correlation between the pre- and post-omega phases, and hence a possible overarching mechanism controllingthe two, we simulated a histogram of full-response orientation changes byadding randomly chosen reorientation values from the three phases (seeMethods). If there were significant correlations between the pre- and post-omega 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 significantlydifferent from the data (p = 0.14). This implies that, if there are anycorrelations, they are too weak to be observed here. Therefore, the reori-entation effected by the full escape response appears to be a combination

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Figure 5.4 | Reorientation of the worm occurs during all phases of the escaperesponse. (a–c) Change of the worm’s overall orientation (∆〈θ〉) during the threedifferent 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 com-posed of independent contributions from the three phases in a–c. To show this, asimulated histogram has been computed from 10 000 random combinations of ori-entation changes from a–c, producing a statistically indistinguishable distribution(orange; Kolmogorov–Smirnov test, p = 0.14). (e,g) The mean a3 value, versus theresulting orientation change, during the reversal phase and post-omega phase, respec-tively. The orientation change is strongly correlated with the mean a3 value. (f) Peakamplitude of the a3 peak corresponding to the omega turn, versus the resulting ori-entation change. (h,j) Histogram of mean a3 values, during the reversal phase andpost-omega phase, respectively, showing similarly asymmetric distributions. (i) His-togram of a3 peak amplitudes during the omega turn. Shown is a reconstituted wormimage for an a3 value of 15.

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of uncorrelated orientation changes from the reversal, omega-turn, andpost-omega phases.

From previous work on the interpretation of the postural eigenmodes,we know that the third eigenmode (an overall bending of the worm) islinked to reorientation of the worm [16, 17]. We therefore tested if anyasymmetry in the fluctuations of a3 during the reversal phase could belinked to the observed reorientations. Such asymmetry is also visible inFig. 5.2, as a baseline shift of the third mode during the reversal. As shownin Fig. 5.4e, this is indeed the case: the mean a3 value during the reversalis strongly correlated with the resulting orientation change. The oppositecorrelation is observed during post-omega forward crawling (g). Duringthe omega turn itself, a weak correlation between a3 peak amplitude andreorientation is observed (f). The actual distributions of mean a3 valueand a3 peak amplitude are shown in Fig. 5.4h–j.

The sum of these observations allows us to link the behavioral output ofthe worm to the description of the escape response at the molecular levelfrom Donnelly et al. [4]. As the worm enters the reversal phase, releaseof tyramine sets up an asymmetry in the worm’s body; this would appearas a baseline shift in the fluctuations of the third mode (Fig. 5.4h). Sucha nonzero a3 mean, in turn, has been linked to orientation changes [17](Fig. 5.4e). After the omega turn, lingering effects of the tyramine mayproduce a similar baseline shift: the distributions of mean a3 values duringthe reversal and post-omega phases (Figs. 5.4h,j) are similarly asymmetric.When the worm is moving forward instead of backward, however, this nowleads to an opposite orientation change (Fig. 5.4g). We may even speculateas to a reason for the broadening of the orientation change distributionby the pre- and post-omega phases, observed above: this could be aninevitable consequence of the action of tyramine in the build-up towardsthe omega turn.

A reason for the previously observed ‘increased floppiness’ of the wormduring the reversal and post-omega phases, visible as an increased am-plitude of a3 and a4 oscillations, is less clear. No significant correlations

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to other quantitative properties of the escape response were found in thecurrently available data (including orientation change). As ‘floppiness’is usually observed during fast backward locomotion, additional data onreversals 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 escaperesponse, as a stereotyped trajectory through posture space. The mostprominent features are the crawling cycle in the (a1, a2) plane, combinedwith a distinctive ‘pulse’ along the third eigenmode that corresponds to theomega turn. A particularly striking feature of the escape-response omegaturn is how closely the worm controls its reorientation: Fig. 5.4b shows adistribution that is tightly centered around π (180). This tight control ismirrored 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’, microscopicorganism such as C. elegans, achieving such a feat is not necessarily easy:after all, how does one find their way back, without any visual referenceto 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 inFig. 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). Asimilar observation can be made for the a1/a4 peaks that precede the a3peak, 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, whichit then slides along to find its way back. Lacking a neural mechanism forsuch a ‘body-touch assisted turn’, this simple model remains of coursespeculative. Forward genetic screens [18] could provide a way forward fortesting this hypothesis, and for identifying further neural and molecularsubstrates for this behavior. Comparison of the escape response acrossdifferent nematode species [19] may also help validate our proposed model.

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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 astereotyped response from C. elegans. While this approach is excellent forteasing apart specific neural circuits within the worm’s nervous system, itdoes not necessarily shed light on its full range of spontaneous behavior.On the other side of the spectrum of behavioral assays, we can therefore letthe 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 ofbehavioral motifs: bouts of forward crawling are alternated with pauses,reversals, and sharp turns (including the previously encountered omegaturn). These motifs are combined into a navigational strategy for locatinghospitable habitats, food, and mating partners. Multiple types of sensorycues feed into this strategy: the worm responds, for example, to attractantand repellent odorant molecules (where the type of response is encoded bywhich 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 fascinatingevidence of adaptation [26] and associative learning [23, 27, 28].

So how does the worm actually reach, say, the peak of an attractantchemical gradient? Interestingly, C. elegans employs two parallel mecha-nisms for this [29].

The first mechanism, klinokinesis, is stochastic: the worm executes abiased random walk up the gradient. Forward crawls are interspersed withso-called pirouettes: bursts of reversal and turning events that reorientthe worm towards the gradient [30]. The frequency of pirouette initiationis 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, theprobability of a pirouette increases strongly [30]. The pirouette is similar

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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 apurely 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’strajectory towards the gradient [33]. In this case, the worm samples thelocal attractant concentration during its normal undulatory head move-ments, using the sensory neurons in its head. It then uses this informationto bias the angle of the head during locomotion [33, 29].

Analysis of C. elegans taxis behavior is historically based on trackingof the worm’s center-of-mass (or centroid) as it crawls around the agarplate [30]; later generations of experiments have added increasingly so-phisticated mechanisms for also tracking the worm’s body shape [34–40].This has provided us with our current understanding of the taxis and kine-sis mechanisms, but also leaves some questions unanswered. How does thepirouette reorient the worm up the gradient? And what exactly constitutesa pirouette?Our tracking algorithm now makes it possible to begin filling in those

gaps: we can precisely quantify the behavioral dynamics of a freely crawl-ing worm, even during manoeuvres that feature self-overlapping bodyshapes. In the previous chapter, we showed that omega turns can ac-tually be classified into two different classes, based on their amplitude (asmeasured by the third postural eigenmode). In this section, we furtherexplore these two classes, and their possible role in C. elegans navigation.

5.3.2 Two types of ventral turns can be discerned during freecrawling

We previously tracked 12 worms as they crawled freely on a 2D agar sur-face, each for the duration of 35 minutes (see Methods). As no stimulior attractant/repellent gradients were present, this represents a basic ex-periment for studying C. elegans free crawling behavior. We applied our

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Figure 5.5 | C. elegans turns during free crawling can be differentiated intotwo separate, ventrally-biased classes. (a) Histogram of the amplitude of localextrema in the time series of the third postural eigenmode a3 (for N = 12 freelycrawling worms). Colors represent the sign of the a3 amplitude, and hence the dorsal(gray) or ventral (blue) direction of the resulting turn. Insets show reconstructedworm 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 ourprimary interest was the ‘omega turn’, we focused on the third posturaleigenmode (a3). As mentioned in the previous section on the escape re-sponse, 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 onlyconsidered 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 alllocal extrema in the data (see Methods). In this distribution, negative a3amplitudes correspond to dorsal turns; ventral turns have strictly positiveamplitudes.

In Fig. 5.5a, a clear asymmetry can be observed. On top of a symmetricbackground distribution of shallow turns in both directions, we see, onthe ventral side, two distinct additional peaks in the histogram. Drawing

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reconstituted worm images for the center values of these two peaks, we seethat the peak at a3 ∼ 15 corresponds to a ‘classic’ Ω shape. The secondpeak, 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 theventral side, highlighting the ventral asymmetry at high a3 amplitudes.As indicated in Fig. 5.5b, we will refer to turns in the lower-amplitudepeak as omega turns. We will distinguish these from the higher-amplitudedelta (δ) turns in the second peak. (As for the omega turn, the name deltaturn is chosen to reflect the δ-like shape of the worm during a typical deltaturn.)

Returning to the original tracking movies, the presence of these twoclasses of turns is clearly visible. In Fig. 5.6, we show movie stills for twoexample turns: one omega turn, and one delta turn. During the omegaturn, the worm slides its head along its body, ending up with a roughly180 reorientation — similar to the escape-response omega turn. A deltaturn, on the other hand, is much deeper: the worm completely crosses itshead over its body, resulting in an ‘over-turn’ of greater than 180.

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5.3.3 Despite disparate appearance, delta- and omega-turnkinematics are similar

Omega turns and delta turns are visually distinct, but how is this differencereflected in their posture space trajectories? Most notable is the higher a3peak amplitude of delta turns; but are they otherwise different? Taking oneparticular example, shown in Fig. 5.7a, suggests that the other aspects ofthe delta turn’s kinematics are actually very similar to those of the omegaturn (cf. Fig. 5.2). Just like the omega turn, the delta turn starts with adeep ventral head swing, and corresponding peaks in a1 and a4. This isfollowed by the peak in a3, marking the apex of the turn, and a negativepeak in a4 for the exit of the high-curvature body wave through the tail.

Averaging the eigenmode time series across N = 348 delta turns (gray-shaded area in Fig 5.7a; see Methods), we obtain the average responseshown in Fig. 5.7b. Comparing this with the average omega turn for theescape response dataset from the previous section (red dashed line), wesee that a3 amplitude is indeed the only feature that clearly separates thedelta turn from the omega turn.

5.3.4 Delta and omega turns as part of the worm’snavigational strategy

So far, we have seen that the worm makes, in addition to shallow turns inboth the ventral and dorsal direction, two distinct types of steep ventralturns. These omega and delta turns appear to be different only in their a3pulse amplitude; turn kinematics are otherwise very similar. Could theyperhaps play specific roles in the worm’s navigational strategy, and couldthis be linked to the difference in a3 amplitude?

We first plotted where both types of turns occur in the worm’s tra-jectory on the agar plate. In Fig. 5.8a,b, we show such a trajectory forone of the twelve worms in the experiment, with omega (yellow/light) anddelta (blue/dark) turns marked. The worm starts out at position (0, 0)

(black arrow), and shows typical ‘dwelling’ behavior: a high turning fre-

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Figure 5.7 | Kinematics of the delta turn are similar to those of the omegaturn. (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 areaindicates the delta turn, as defined in the Methods. (b) Average eigenmode timeseries 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 hasbeen 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.

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Figure 5.8 | The omega and delta turns as part of the navigational strategyof C. elegans. (a,b) Location on the agar plate of one of the 12 tracked worms overthe course of a 35-minute tracking experiment (off-food), starting at (0, 0) (blackarrow). Ventral omega turns (yellow/light) and ventral delta turns (blue/dark) arehighlighted. A blow-up of the area marked in gray is shown in b. (c) Histogram oforientation change due to ventral omega turns (yellow/light) and ventral delta turns(blue/dark). Omega turns dominantly lead to a re-orientation change towards theventral 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 turnsare temporally independent (see text), but occur with approximately equal rate, andshow co-adaptation as the worm switches from a ‘dwelling’ to a ‘roaming’ strategy.

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quency, and an exploration of its local environment [5]. After dwelling forsome 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 arestatistically independent. Apart from an overall modulation of the turnfrequency (discussed later), no temporal correlations are observed. Wechecked this by computing the mutual information between time-binned,time-shifted time series for both turns (see Methods). With a maximummutual information less than a few percent of the maximum entropy, theturns have to be considered independent.

While independent, the turns result in a different change of orienta-tion — following the known link between the third mode and orienta-tion changes [17]. In Fig. 5.8c, we show how the worm reorients usingboth omega (yellow/light) and delta (blue/dark) turns. The free-crawlingomega turns show a much broader distribution than the previously encoun-tered escape-response ones (cf. Fig. 5.4d). Still, they generally reorientthe 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 thesetwo distinct turns exist. In the first part of this chapter, we saw thatthe neural mechanisms that produce the escape-response omega turn arefundamentally asymmetric, producing only ventral turns (through disin-hibition of the VD motor neurons) [4]. If the worm uses the same neuralinfrastructure during free crawling, this would only ever allow it to reorientitself towards its ventral side. Lacking a dorsal ‘copy’ of the same neuralinfrastructure, the worm could instead hyper-activate the existing infra-structure to produce ventral over-turning’. These over-turns are what wecall delta turns, and enable the worm to also reorient towards its dorsalside.

Evidence that both turns share at least part of the worm’s neuronalcontrol mechanisms is shown in Fig. 5.8d. Here, we plot the frequency ofturning events over the course of the experiment (see Methods). As the

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worm switches from ‘dwelling’ to ‘roaming’, in search for food in a largerarea, the turn frequency decreases significantly — a well-known adapta-tion [5, 28, 41]. Interestingly, both types of turns show similar frequencies,and co-adaptation over time. This suggests that both types of turns areregulated by a shared underlying mechanism. One possible realization ofsuch a mechanism is the known regulation of ‘dwelling’ behavior by thedopamine neurotransmitter, which modulates motion-related glutaminer-gic 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 hasvaried from publication to publication [5, 33, 38, 30], but always features aseries of one or more omega turns as the course-adjusting motif. We havenow shown that these turns are, in fact, two distinct turns, each producinga different reorientation. How the two turns are combined to produce theknown reorientation towards an attractant gradient [30], is an interestingavenue 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 navigationin C. elegans.During the C. elegans escape response, the signature omega turn is

the central behavioral motif that steers the worm away from the noxiousstimulus. The turn contributes around 180 of the reorientation observedacross the response, and appears to be highly stereotyped, with a tightlycontrolled amplitude. The characteristics of the escape response can belinked to previously found mechanisms at the neural and molecular level.A tyramine-mediated build-up of asymmetry in the worm’s locomotorysystem is quantitatively visible as a baseline shift in the oscillations of thethird postural eigenmode a3. This occurs during the reversal phase, andlingers after the omega turn has completed, resulting in a broadening of

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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 popula-

tions of deep turns: omega turns, featuring the classic Ω shape, and a novelclass of deep turns, which we here call ‘delta’ (δ) turns. We show that,despite their distinct visual appearance, the posture space trajectories ofdelta and omega turns are very similar. Their only clear distinguishing fea-ture is the amplitude of the pulse in the third postural eigenmode a3, whichseems to drive a difference in resulting reorientation. Taken together, thisgenerates a picture of omega and delta turns as a way for the worm to makesharp turns in the ventral and dorsal direction, respectively. The turns aretemporally uncorrelated, although their overall frequency appears to becontrolled by a shared mechanism.

Our first glance into the ‘black box’ of self-overlapping body shapes ofC. elegans is of course just that: a first glance. Some important questionsremain, as yet, unanswered. For example, posture space trajectories forsharp turns, while geometrically similar, still show significant variability. Itremains unclear what the source of this inter- and intra-individual varianceis. To answer such questions, a principled way of quantifying differencesbetween trajectories through posture space, and relating those differencesto 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. el-egans. Behavioral defects induced by genetic mutations or cell ablationsare typically detected manually [5, 4]; automated tracking would allow forincreased throughput, and detection of more subtle defects than might bedetected by eye.Finally, work on other nematodes has shown interesting differences in

the way these species modulate their navigational strategies, in this casebetween a ‘roaming’ and a ‘dwelling’ strategy [19]. Whether omega anddelta turns are conserved across species, and contribute similarly to es-

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5.4 Methods

Molecule Molecular weight Free diffusion constant Source(g/mol) (10−10 m2/s)

norepinephrine 169 5.5 [42]dopamine 153 6.0 [42]leucine 131 6.0 [43]

threonine 119 7.5 [44]

Table 5.1 | Diffusion constants of some small molecules (neurotransmitters andamino acids) that are similar in molecular weight to tyramine (MW = 137 g/mol).

cape response and foraging behavior, could be an interesting future line ofinvestigation.

5.4 Methods

Tyramine diffusion. During the escape response, extra-synaptic diffusion oftyramine is thought to temporally separate the initial reversal of the worm andthe omega turn (see ‘Introduction to the escape response’, p. 126) [4]. We canmake a rough, back-of-an-envelope estimate of the time needed for tyramine todiffuse, and show that this is consistent with the reversal phase duration typicallyobserved in our experiments.

To our knowledge, no diffusion constant has been published for tyramine. In-stead, we can estimate the relevant order of magnitude by considering other mo-lecules with a similar molecular mass. From the data in Table 5.1, we can derivea conservative estimate of the tyramine diffusion constant of D ∼ 5 · 10−10 m2/s.

Using the diffusion equation, 〈(∆x)2〉 = 2Dt, for a length scale that we esti-mate to be a tenth of the worm’s full-grown length of 1 mm [3] (since the distancebetween the RIM and VD neurons is far less than 1 mm), we arrive at a typicaltimescale of t ∼ (10−4 m2)2/(2 · 5 · 10−10 m2/s) ∼ 10 s. This is consistent withthe typical reversal time of 5 s observed in our escape response data.

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Data collection. Two datasets were used in this chapter: one with C. elegansescape responses evoked by a thermal stimulus; and one with free crawling assays.The collection of both of these datasets, including the postural tracking, wasdescribed 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 ori-entations during experiments. Dorsal/ventral orientation was recorded duringthe experiments by noting the position of the vulva, and results for worms witha right-handed orientation were mirrored. Surprisingly, we found two worms inthe free-crawling dataset that changed their dorsal/ventral orientation during theexperiment. Both worms showed the asymmetry in a3 peak amplitude that wasnoted in Fig. 5.5, but this asymmetry switched sign half-way during the record-ing. Inspecting the movies, we found that the time of switching corresponded tomoments when the worms moved off or into the agar, escaping the 2D constraintsof the experiment. This was corrected for by mirroring tracking results for onlythe relevant part of the experiment.

Reorientation during escape response. For the analysis of the worm’s re-orientation during the escape response (Fig. 5.4), N = 91 escape responses wereanalyzed. Each 30-second recording was segmented by first finding the omegaturn, as described below. After identification of the omega turn, the reversalphase was simply defined as the first frame after the stimulus with a negativebody 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 endof the recording at t = 30 s.

To generate the simulated histogram for the orientation change of the fullresponse, we picked a random worm for the reversal phase, a random wormfor the omega turn (possibly the same), etc. The orientation changes of thesethree phases were summed, and added to the simulated distribution. If any ofthe chosen recordings did not have a successfully detected omega turn, this wasskipped. A total of 106 iterations were performed.

Definition of omega and delta turn. For the escape response data, thelargest 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 omegaturn, the first root (zero) of a4 after the apex was found; any point after thatroot that had a3 < 3 was considered to be the end of the omega turn. Thisensured that the negative peak in a4, representing a high-curvature state of the

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tail at the end of the omega turn, had finished, and that the worm had reacheda relatively ‘straight’ shape. For such straight shapes, the overall orientation 〈θ〉has a straightforward, intuitive interpretation. The same criterion was used, inthe opposite direction, to find the start of the omega turn. If no starting pointand/or end point of the omega turn could be found, the recording was excludedfrom the analysis. (In the escape response dataset, this was the case for 15 outof 91 recordings).

In the free crawling dataset, the same quantitative criterion was used to findboth omega and delta turns.

Local extrema in a3. For the free crawling dataset, we analyzed the ampli-tudes 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’ ofthe previous chapter. Briefly, each segment of a movie was chosen such, that itcontained a consecutive series of non-crossed frames, followed by a consecutiveseries 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 seriesof non-crossed frames in segment j+1. This facilitated the stitching process: twosegments could be joined together at a frame that occurred in both segments jand j+1, and that had the exact same tracking solution in both segments withina given margin of error (0.1).

Tracking errors could cause violations of this margin of error. All such stitchingproblems were manually inspected; if a tracking error was found, that segment ofthe data was excluded from the analysis. In total, across all twelve worms, 878out of 936 segments (94%) produced tracking results of sufficient quality.

For detection of local extrema in a3, a standard peak-finding algorithm wasused to detect both minima and maxima (based on MATLAB’s findpeaks func-tion, which defines a peak as a data point with a greater value than its immediateneighbors). Only extrema with a minimum prominence of 0.5 were kept. Somea3 peaks featured smaller sub-peaks in their shoulders; such sub-peaks were dis-carded.

Average delta-turn eigenmode time series. To generate Fig. 5.7b, deltaturns as defined above were cut from the free crawling dataset (N = 348). Eachfive-dimensional time series (modes a1...5) for each delta turn was mapped onto

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a 50-point, linearly-spaced ‘normalized time’ axis (tN ∈ [0, 1]), using linear inter-polation of the time series where necessary. This normalized time correspondedto an actual duration of the delta turns of 6 ± 2 s (mean ± SD). Data acrossdelta turns was then averaged per normalized-time point, giving the trajectoriesshown in the Figure.

The same procedure was followed for omega turns in the escape responsedataset (N = 91). For this data, the normalized time axis corresponds to anactual duration of the omega turns of 7± 3 s (mean ± SD).

Mutual information between omega and delta turns. For calculating themutual information between the omega and delta turns during free crawling,we followed the procedure from ref. 45. We created binarized time series foreach type of turn, by binning turning events into bins of 2, 4, 10, or 20 s. Themutual information was calculated for different time shifts, ranging from −60 to+60 s. Mutual information across time shifts never exceeded 3% of the maximumentropy of each time series, hence precluding a significant correlation between thetwo types of turns.

Turn frequency adaptation. In Fig. 5.8d, we show how the average turnfrequencies for omega and delta turns change over the course of the 35-minutefree-crawling experiments. Turns were detected in the stitched data by using thepeak detection algorithm outlined above (see ‘Local extrema in a3’ before). Usingthe boundaries identified in Fig. 5.5b, a3 extrema with an absolute value between10 and 20 were classified as ‘omega turns’, while extrema with an absolute valuegreater than 20 were considered to be ‘delta turns’. We also distinguished be-tween ventral turns, with a positive amplitude, and dorsal turns, with a negativeamplitude.

For the Figure, we counted the average number of turns per unit time, acrossthe 12 experiments, in a 10-minute sliding window, shifted across the data in5-minute increments. The first 200 seconds of each experiment were discarded,as the worms showed signs of adaptation to their new environment (the agarplate without food): the average turn frequency, somewhat erratically, increasedduring 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 countedthe number of a3 peaks with an amplitude between −20 and −10 in each time

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window, and subtracted this from the total number of a3 peaks with an amplitudebetween +10 and +20. This gave us the number of ‘true’, ventrally-biased omegaturns. This number showed excellent agreement with the number of delta turns(Fig. 5.8d).

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