Navigation strategies in Caenorhabditis elegans are differentially altered by learning

Learning differentially alters olfactory navigation

We developed a protocol to train worms to associate butanone with either food (appetitive training) or starvation (aversive training) (Fig 1a). Our protocol was similar to previously reported training regimens [12,17,35] except that ours exposes the animal to multiple rounds of odor paired with starvation instead of only one, which we found increases consistency in learning (Fig A in S1 File). After training, we recorded the movement of populations of worms as they crawled in a defined odor landscape that used metal-oxide sensors to continuously monitor the odor concentration along the boundary [31] (Fig 1b; Fig B in S1 File). We recorded hundreds of locomotory trajectories per plate in this odor environment after different training conditions, for up to 13 plates per training condition. Animal’s locomotory trajectories were qualitatively different depending upon learning, with appetitive trained animals traveling up-gradient more often than naive animals, and aversive-trained animals traveling up-gradient least of all, broadly consistent with prior reports [3,12,35] (Fig 1c). We quantify the performance of traveling up the gradient using a “chemotaxis index”, , that compares the number of trajectories going up-gradient, , to the number of trajectories going down-gradient [3,35] (Fig 1d). Performance navigating up-gradients is differentially modulated by two training paradigms: chemotaxis index increases after appetitive training and decreases after aversive training compared to naive worms that undergo no training. Interestingly, even animals that undergo aversive training do not, on average, navigate down the gradient. This suggests that after learning an association between butanone and starvation, animals are indifferent or at most only still slightly attracted to butanone.

To explore whether worm navigation superficially resembles a biased random walk, we calculated a “run index”, , by computing the normalized length of a run moving up-gradient, where the run r is defined as the period between pirouettes, and subscripts _u and _d denote up- or down-gradient (Fig 1d). Similarly, to explore whether navigation superficially resembles a weathervaning strategy, we calculated a “turn index”, , that reports the fraction of turn events p that result in heading up-gradient to those heading down-gradient [23]. Additional details are described in the Methods section.

While the metrics above suggest hypotheses about how navigational strategies change due to learning, they provide little information about the dynamics of navigation, nor the sensorimotor transformations that govern these dynamics. Specifically, the metrics use only binary information about whether at the end of their track the animal traveled up- or down-gradient, and it ignore details of the sensory landscape in between and omits dynamic information like the odor concentration the animal experienced over time. The indices also provide no information about the behavioral variability across the population. To overcome these limitations, we sought a statistical model that captures temporal information, behavioral noise, and explicitly predicts how the animal changes its movement in response to sensory stimuli.

Odor-dependent mixture model of olfactory navigation

To characterize how olfactory sensory inputs are transformed to behavior under different training conditions, we developed a dynamic Pirouette and Weathervaning (dPAW) statistical model of worm olfactory navigation. The dPAW model consists of a mixture of two navigation strategies: a pirouette behavior consisting of an abrupt change in heading angle (a turn) and weathervaning which instead continuously modulates heading angle. The dPAW model describes how the worm implements and balances these two behavioral strategies depending on time-varying sensory inputs (Fig 2a). The dPAW model is an extension to a classic biased random walk, where the run intervals are replaced with weathervaning behavior. This framework explicitly models these strategies and is fit to detailed measurements of movement and odor-experience. This is to our knowledge the first statistical model that explicitly captures the detailed changes to C. elegans navigation strategies upon butanone learning.

Fig 2. dPAW captures learned olfactory navigation in worms. (a) Schematic of the dPAW model. An example measured trajectory is shown on the far left, providing time series of concentration and angle changes. Response kernels and decision functions are fitted to the time series data. The Bernoulli process β leads to two parallel strategies: biased random walk and weathervaning. (b) Chemotaxis index of simulated trajectories with inferred parameters. Error bar shows standard error of mean across 10 repeated simulation, each with 100 trajectories. (c) Example trajectories simulated from each training conditions. (d) Kernel and (e) Kernel fitted to three training conditions. Shaded area shows standard deviation of the kernel estimate. All data underlying this figure can be found at doi: 10.6084/m9.figshare.24764403.

https://doi.org/10.1371/journal.pbio.3003005.g002

The model worm samples its heading change dθ at each time step from one of two distributions: either a “weathervaning distribution” or a “pirouette distribution” . The weathervaning distribution is narrow, reflecting small changes in heading angle that result from the worm’s recent measurements of the concentration gradient. Pirouette behavior, on the other hand, corresponds to large turns that the worm makes when it receives evidence that it is going in the wrong direction. The pirouette distribution is therefore broad, with a peak at  ± π, indicating a complete reversal in direction. The concentration-dependent “decision” to produce a pirouette in between runs corresponds to a classic model known as “biased random walk” [16,22].

The worm’s decision to initiate a pirouette or to continue to weathervane on each time step is modeled with a Bernoulli generalized linear model (GLM) that takes the filtered history of the odor concentration and the worm’s own movement history as inputs. The output of this GLM is a binary variable that indicates the presence of a pirouette. Thus, the worm samples its heading change from the pirouette distribution if and the weathervaning distribution if . The full model can be written:

(1)

where

(2)

is the mixing probability over the two distributions, with parameters m and M for the minimum and maximum probability of a pirouette on a single time bin, and and corresponding to filters on past odor concentration and the past absolute angular change vectors, respectively. The pirouette and weathervaning distributions are in turn given by

(3)(4)

where U is uniform in the circular heading and f is a von Mises distribution with mean and precision parameter κ. In the pirouette distribution, scalar α ∈ [ 0 , 1 ]  is the weight on the uniform distribution and is the precision parameter that determines the sharpness of the pirouette. In the weathervaning distribution, the mean is altered according to the perpendicular concentration change and the precision parameter determines the noise around the head angle. (Note we have made a simplification by allowing the model access to the instantaneous perpendicular odor concentration. In reality, the animal is thought to compute from sequential measurements in time as it swings its head through space.) The full dPAW model has 13 parameters, which includes all the mixture parameters in Eqs 2–4 and all parameters needed to prescribe the shape of the kernels. Model setting and inference is described in the Methods section.

We fit dPAW to measurements of animal movement in the odor arena, including the time varying headings , the concentration along the locomotion path , and the concentration perpendicular to the locomotion path . All model parameters in dPAW are jointly inferred through a maximum-likelihood method. To validate that parameters are reliably inferred, we simulated example chemotaxis trajectories from pre-defined parameters, fit them by the model, and confirmed that the model accurately recovered the pre-defined parameters (Fig C in S1 File). In the rest of the paper we fit the model to measurements to explore how navigation strategies change with learning.

Model captures navigation altered by olfactory learning

To characterize how olfactory learning alters navigation strategies, we fit the dPAW model to trajectories measured in the butanone odor environment after different training conditions. We first confirmed that the model captures key aspects of the animal’s navigation. We confirmed that the fitted model’s estimate of pirouette frequency matches that measured empirically [16] (Fig Db in S1 File). We also used the model to simulate chemotaxis behavior in the odor environment and confirmed that model-generated trajectories have a chemotaxis index that agrees with measurement and is similarly differentially modulated by training conditions (Fig 2b). Model-generated trajectories also appear visually similar to experimental observations (Fig 2c). And in further agreement, trajectories simulated from the model recapitulate sensory and behavioral statistics measured in experiments, including the measured distribution of the worm’s heading angle, pirouette rate, experienced perpendicular odor concentration difference, and tangential odor concentration (Fig D and Fig E in S1 File).

Agreement between model and measurement was not due to chance. The dPAW model on average captures 0 . 3 to 0 . 6 bits/s more information about navigation behavior than a null model that lacks any olfactory sensing mechanisms (Fig 4c). For comparison to additional null models see Fig E in S1 File.

Sensorimotor kernels change upon learning

We hypothesize that the sensorimotor temporal kernels, and , should change upon learning [16,18,35]. An alternative hypothesis is that changes to baseline pirouette rate and trajectory curvature alter the chemotaxis index without having to change the kernel governing its sensorimotor response. To test this, we inspected the inferred kernels fit to animals that had underwent different training conditions. Kernels corresponding to both weathervaning and biased random walk strategies were altered by learning (Fig 2d and 2e). The weathervaning kernel had lower weights after aversive training compared to appetitive trained or naive animals (Fig 2d), suggesting that the animal’s heading angle is less tightly dependent upon the concentration difference perpendicular to its path. In other words, aversive trained worms don’t pay as much attention to perpendicular concentration when choosing their heading angle. There are two extreme ways these worms could not pay attention to the sensory cue: the worm could be uncoordinated and randomly select a heading direction, or alternatively, it could keep its existing heading. We observe the latter. We found that aversive-trained worms decrease their behavioral noise and are more likely to preserve their existing heading and exhibit higher persistent length during their runs, as indicated by higher fitted precision parameter of weathervaning (Fig 4b).

The kernels corresponding to pirouette decisions, , change for both aversive and appetitive training compared to naive animals (Fig 2e). The amplitude is increased after appetitive training compared to naive animals, suggesting that appetitive trained animal’s pirouette probability depends more strongly on the concentration change along the navigation path than for naive animals. After aversive training, the kernel has a longer time delay and forms a tri-phasic shape, markedly different from the biphasic shape observed in naive animals, suggesting that aversive trained animals may be less responsive to downward changes in concentration (Fig 2e).

Collectively, we show that C. elegans alter their chemotaxis upon learning by changing the kernels that govern their sensorimotor response.

Fig 3. dPAW model captures bidirectional salt chemotaxis. (a) Worms are grown on 50 mM salt environments. (b) Salt chemotaxis are conducted in two types of linear salt gradient plates. (c) Example trajectory for navigation in a 0-50 mM (left) and 50–100 mM (right) linear salt gradient. (d) Summary statistics of measured chemotaxis, reported as in Fig 1d but for salt chemotaxis in two environments. Error bar shows standard error of mean across 10 resampled trajectories from 2–3 salt chemotaxis plates. (e) Kernel and (f) Kernel calculated by fitting dPAW to navigation in two linear salt gradients. (g) Example of 11 trajectories simulated for 0–50 mM (left) and 50–100 mM (right) linear salt gradient environments. (h) Chemotaxis index of simulated trajectories with inferred parameters from salt chemotaxis. Error bar shows standard error of mean across 10 repeated simulations, each with 100 trajectories. All data underlying this figure can be found at doi: 10.6084/m9.figshare.24764403 .

https://doi.org/10.1371/journal.pbio.3003005.g003

Model also captures bidirectional salt chemotaxis

To gain confidence in dPAW’s ability to extract meaningful sensorimotor kernels and parameters, we also challenged dPAW to capture changes to sensorimotor transformations in a different context, namely context-dependent changes to salt chemotaxis (Fig 3a– 3c). Navigation strategies in a salt environment have been characterized previously—worms navigate towards the concentration they were raised at by employing both biased random walk and weathervaning strategies [18,23] (Fig 3d). We repeated a series of experiments previously reported in [23]: animals raised at 50 mM salt concentration were evaluated on linear salt gradients of different concentration regimes (0 to 50 mM, and 50 mM to 100 mM). In each case dPAW was fit to measurements of the animal’s locomotory trajectories. As expected, the dPAW model captured positive and negative salt chemotaxis, depending on the environment the animals were tested on. (The paradigm commonly used for salt chemotaxis differs from that of butanone—for salt the animal’s experience stays the same but the arena varies, while for butanone the experience varies but the arena stays the same.) Reassuredly, simulations from dPAW fitted to salt chemotaxis trajectories nicely agreed with the observed positive and negative chemotaxis indices (Fig 3g and 3h). Sensory kernels had not previously been reported for salt chemotaxis, but one would expect their kernels’ sign to switch depending on whether the worm was in a higher or lower salt concentration landscape. Indeed, dPAW’s inferred salt sensorimotor kernels for both biased random walk () and weathervaning () had opposite signs in the high- and low-concentration contexts, as expected (Fig 3e and 3f). The dPAW model’s ability to extract expected parameters and generate trajectories that match observations for salt chemotaxis demonstrates its capacity to generalize across different sensory modalities, environmental landscapes, and concentration levels.

Fig 4. Learning alters pirouette decision and behavioral noise. (a) The top panel shows decision function P ( β = 1 | C , dθ )  of three training conditions as a function of filtered signal: . The distribution of the filtered signal is shown in the bottom panel. The right panel shows the distribution of the output pirouette rate, with inset showing the same distribution in log scale. (b) The precision parameter for weathervaning, across three training conditions. (c) The information rate given fitted model parameters and data across three training conditions. Error bar shows standard error of mean across 7 batches of testing trajectories using cross-validation. All data underlying this figure can be found at doi: 10.6084/m9.figshare.24764403.

https://doi.org/10.1371/journal.pbio.3003005.g004

Decision function governing pirouettes changes upon odor learning

To understand how the animal alters its preference for continuing to weathervane versus interrupting weathervaning with pirouettes during odor learning, we compared the pirouette decision function in Eq 2 inferred from our measurements before and after learning.

We found that learning alters the input-output statistics governing the initiation of a pirouette. This is clear from inspecting the distribution of the filtered signal (Fig 4a, bottom, related to odor concentration and past behavior) that serves as input to the decision function. Appetitive training and aversive training push the tail of the filtered signal probability distribution in opposite directions with respect to naive condition, which changes the statistics of pirouettes. This could reflect either changes to the kernels, or changes to the environment that those animals prefer to explore.

Aversive-trained worms have higher baseline turning rate m than appetitive trained worms, as seen in the output probability (Fig 4a, right), which is the result of passing the filtered odor signal (Fig 4a, bottom) through a nonlinear decision function (Eq 2 and Fig 4a, top). Both aversive- and appetitive-trained worms have higher maximum pirouette rate M compared to naive worms, reflecting a change to the decision function itself.

It is interesting to note that appetitive (but not aversive) trained animals spend more time with their pirouette probabilities in the most sensitive range of the sigmoid (Fig 4a right, inset), possibly indicating a more efficient strategy for chemotaxis. Capturing these details is one of the ways that dPAW is able to better detect changes in learning.

Model outperforms other metrics at decoding learned experience

The changes to sensorimotor processing detected by the dPAW model all provide information about the animal’s past experience. We therefore wondered whether the model could accurately predict the training (aversive, appetitive or naive) that a population of worms had experienced. To test this we inspected dPAW models fit to measured trajectories from each training conditions γ ∈ Halo  corresponding to fitting parameters and made maximum likelihood predictions of the training condition given held-out test trajectories: . On held out data, the fitted model correctly predicted training condition with a performance well above 90%, significantly above chance levels (Fig 5a), given sufficiently long recordings.

The inferred kernels and decision function within better reflect the worm’s learning than either a classic chemotaxis index that captures the fraction of trajectories that go up-gradient (Fig 5a), or the concentration difference along the track Fig G in S1 File. Indeed, on average dPAW always outperforms the chemotaxis index at decoding past training, for any tested amount of finite data. The model’s predictive power is derived from observing both the odor-history experienced by the animal and the corresponding behavior responses. Models supplied with either odor-history or behavior but not both fail to perform as well.

Some training conditions are more challenging for dPAW to decode than others. Naive worms show the lowest predictive performance with finite data when decoding is performed for each training condition separately (Fig 5b). This is consistent with our estimate of lower information exhibited by the trajectories of naive worms than trained worms (Fig 4c). Practically, this means more measurements are required to capture navigation behavior in naive worms than in trained worms.

Fig 5. Model-based decoding of learning. (a) Model performance at classifying the prior training of a population of worms (aversive, appetitive or naive) as a function of mean chemotaxis data length. Four models are compared and error bars show standard error of mean across 7-fold cross-validation, each with 10 sampled ensembles across the data length. w/o concentration: model that only captures behavioral statistics and does not account for odor input. w/o behavior: model is given concentration difference along each trajectory and does not have access to behavioral measurements. Chance level, 33%, is shown in grey dashed line. (b) dPAW-based decoding as a function of data length as in (a), but here performance for each training condition is reported separately. All data underlying this figure can be found at doi: 10.6084/m9.figshare.24764403

https://doi.org/10.1371/journal.pbio.3003005.g005

The same computations govern natural and optogenetic odor stimuli

We wondered whether the same underlying computations that governed the animal’s response to natural odor stimuli also govern its response to optogenetic-induced sensory stimuli. Optogenetics stimuli are not bound by the same natural statistics that the worm encounters when exploring a physical odor arena. For example, worms in our arena always experience temporally correlated and slowly varying odor responses. This introduces potentially confounding temporal correlations that can be avoided by using optogenetic stimuli [35,37–39]. We therefore investigated the animal’s behavioral response to optogenetic induced odor sensation after learning and adapted our model to incorporate both forms of stimuli.

Fig 6. Response to optogenetic induced odor sensation is altered by learning and depends on odor gradient context. (a) Optogenetic stimulation is delivered to animals expressing Channelrhodopsin-2 (ChR2) in AWC^ON as they crawl in an odor-flow chamber. (b) Change in the absolute heading  | dθ |  upon optogenetic impulse across the three training conditions. This change is defined as the average absolute heading during the 5s impulse minus the value during the 5s preceding the impulse. We record from 4-7 plates per condition. Error bar shows standard error of mean across over 1000 impulses per condition. The results of t-test comparison between training conditions are shown with  ∗ ∗ ∗  for p p  and optogenetic fitted to each training conditions. The grey area shows standard deviation around the estimated kernels. All data underlying this figure can be found at doi: 10.6084/m9.figshare.24764403 .

https://doi.org/10.1371/journal.pbio.3003005.g006

The animal’s behavioral response to optogenetic stimulation was differentially altered by learning (Fig 6; Fig H and Fig I in S1 File). We measured the animal’s absolute change in heading angle  | dθ |  in response to optogenetic stimulation of neuron AWC^ON expressing ChR2 (Fig 6b). AWC^ON is a butanone sensitive neuron known to play an important role in olfactory learning [12,17,35,39]. We measured behavior response to optogenetic stimuli two ways: we delivered pulses of optogenetic stimuli to animals experiencing odor in the arena (Fig 6; Fig H in S1 File), and we delivered time-varying intensity white noise optogenetic stimuli to animals off odor (Fig I in S1 File). In both cases (Fig 6e; Fig I in S1 File) the animal’s turning behavior was more tightly coupled to optogenetic stimuli for appetitive trained animals than naive worms, and less so for aversive trained animals. A change in behavior response is consistent with prior reports [35,39], but note that here we make a more stringent comparison by comparing both appetitive and aversive trained animals against the same naive control condition.

We extended our model so that light intensity contributes to the pirouette probability during navigation:

(5)

where kernels and are weights on vectors of odor concentration and light intensity , respectively. Since there is no difference along the perpendicular direction for this five second long spatially uniform optogenetic pulse, this model is simplified with kernels weighting the tangential concentration and neglecting the perpendicular concentration for weathervaning.

Across different training conditions, the optical kernel is close to the mirror image of the odor kernel, most strikingly demonstrated in the naive and aversive conditions (Fig 6e). Therefore the sensorimotor computation inferred from freely moving animals is predictive of the response to external perturbations. The inversion is expected and can partly be explained by the biophysics of the AWC^ON neuron: it hyperpolarizes when odor is present and depolarizes when odor is removed. This gives us confidence that our findings about sensorimotor processing derived from natural odor stimuli should be relevant to the larger literature based on more artificial stimulation. We therefore will leverage optogenetics to probe behavioral variability during odor navigation.

Learning modulates behavioral variability in response to sensory perturbation

We sought to characterize the variability in learned odor-guided navigation, because variability is a known feature of sensory processing in worms [40]. We observe variability across collections of trajectories in learned navigation. For example, the kernel that governs the timing of pirouettes varies across subsamples of our data, and seems to vary more for aversive-trained than appetitive-trained or naive animals (Fig F in S1 File).

Surprisingly, we discovered that animals respond to stimuli differently depending on whether they are traveling up or down an odor gradient and that this contributes to variability (Fig 6c and 6d). Naive worms respond more strongly to optogenetic impulses delivered when traveling up an odor gradient, than when traveling down the gradient (Fig 6c). Appetitive trained worms, by contrast, respond consistently to optogenetic impulses regardless of their direction of travel along the odor gradient. Aversive trained worms show weak response to optogenetic impulse regardless of the gradient context. This indicates that learning alters behavioral variability, and that a response to stimuli can be context-dependent along the navigation trajectory.

Downstream interneurons differentially contribute to learned chemotaxis

We investigated interneurons that may be involved in implementing learned changes to navigation strategy. We focused on interneurons downstream of the odor-sensing neuron AWC^ON because optogenetically induced activity in AWC^ON recapitulates aspects of learned navigation (Fig 6b) and AWC^ON is known to play an important role in odor sensing [11], navigation [41–43], and butanone learning [3,35]. We selected five interneurons subtypes with direct synaptic inputs (chemical or electrical connections) from AWC^ON [10,13]: AIA, AIB, AIZ, AIY, and RIA, several of which are known to be involved in navigation [18,19,23,35,42,44]. For each neuron subtype we compared learned odor-guided navigation in wild type animals to that of transgenic strains for which the neuron subtype was genetically ablated (via miniSOG, Methods Table 1) or down-regulated (via expressing activated potassium channel), as described in methods, Fig 7.

Ablating or down-regulating the downstream interneurons had wide-ranging and statistically significant effects on chemotaxis performance and inferred model parameter, including after learning (Fig 7b; Fig J and Fig K in S1 File). Here we characterize chemotaxis performance with a weighted chemotaxis index (wCI) that differs from the chemotaxis index in Fig 1d by more heavily weighting trajectories that experience a large change in odor concentration and de-emphasizing tracks that experience little odor change (described in the methods). To capture changes in inferred model parameters we report a stimuli-normalized magnitude of the kernels and which correspond to the extent to which the animal uses the biased random walk (BRW) or weathervaning strategies (WV), respectively, Fig 7b. Normalization is performed by dividing the L2 norm of kernels by the standard deviation of the corresponding sensory signal (described in the methods).

Fig 7. Learned odor navigation in worms with disrupted interneurons. (a) Five interneurons connected to the AWC sensory neuron. Schematic generated from nemanode.org. (b) Weighted chemotaxis index (wCI), biased random walk (BRW), and weathervaning (WV) indices computed from the inferred dPAW for all transgenic strains across three training conditions. BRW and WV correspond to the norm of kernels and in dPAW. The circles show value from wild-type N2 worms and arrow shows the modulation in transgenic worms. We record 3-5 plates for each stain and condition, resulting in 200-500 tracks in each measurement. All data underlying this figure can be found at doi: 10.6084/m9.figshare.24764403.

https://doi.org/10.1371/journal.pbio.3003005.g007

Ablation of neuron subtype AIZ was most severe and eliminated gradient climbing behavior across all three conditions (wCI close to zero), consistent with its reported role in the context of salt chemotaxis [18]. In general, though, neuron subtypes contributed differently to chemotaxis performance, learning, or had different contributions to the inferred kernels corresponding to each navigation strategy. For instance, AIA and AIB defective animals showed little difference between naive and aversive training conditions, but did increase chemotaxis performance after appetitive training. In other words, AIA and AIB are less involved in appetitive behavior but important to maintain naive and aversive behavior. The AIY defective animals show an interesting increase in their use of weathervaning after appetitive training and an increase in their use of biased random walk in naive conditions. This suggests that the recruitment of AIY for different strategies may be learning-dependent. The RIA defective animals have similar chemotaxis performance upon appetitive and aversive learning, suggesting that RIA is involved in fine-tuning the animal’s heading angle in response to learning. Interestingly, RIA defect results in much lower gradient climbing performance for naive animals. This suggests that, in addition to its role in learning, RIA may also be important for sensory adaptation, including of naive animals, as they perform odor navigation.

In general, we do not observe a simple one-to-one mapping of neuron sub-populations to chemotaxis strategies. This suggests that even though weathervaning and biased random walk strategies are mathematically and behaviorally distinct, they do not segregate cleanly into different neuron types. Instead the neural basis for learning-dependent weathervaning and biased random walks are both distributed across the neural population.

In our investigation, we apply the same model to multiple transgenic strains. This has not commonly been done in the past because it can be challenging to find a model that is general enough to accommodate differences across strains. A potential confound can arise if the transgenic strains’ behavior differs from wild-type in such a way as to be poorly captured by the model. And, indeed, we do observe some differences in the behavior of different strains, for example their speed distributions differ (Fig Jb in S1 File). Reassuredly, several strands of evidence suggest that the differences dPAW infers in navigation across transgenic strains in Fig 7 reflect differences in navigation strategies, and can not be trivially explained by model mismatch. First, dPAW’s cross-validated fit for transgenic strains is not dramatically different from those of wild-type worms (Fig La in S1 File), suggesting that the model is doing a decent job capturing transgenic strains’ behavior. Second, an analysis of heading distributions further shows reasonable agreement between model and measurements (Fig Lb in S1 File). Finally, the model’s microscopic description of transgenic strains’ behavior does a reasonable job recapitulating the worms’ observed macroscopic chemotaxis index (Fig M in S1 File). When considering all strains across all learning conditions, the model’s predicted chemotaxis index correlated to the measured chemotaxis index (). Taken together, we conclude that perturbations to individual neurons in the analyzed strains do result in changes to navigation strategies.

Worm strains and preparation

All worms were maintained at 20 C on nematode growth medium (NGM) agar plates seeded with E. coli (OP50). We used N2 bristol as wild type worms. A detailed strain list is provided in Table 1. Strain AML105 used for optogenetics experiments was integrated using strain CX14418 from [35] employing UV irradiation and was outcrossed six times before testing. AIB(-) strain is from [31] and AIA(-), AIY(-), AIZ(-) and RIA(-) strains are from [? ]. All worm strains used in this work are shown in Table 1.

Before chemotaxis experiments, we bleached and centrifuged batches of worms to synchronize the next generation as described in [61]. L1 synchronized worms were plated to seeded NGM plates on the next day. Experiments were conducted 3 days after seeding, which corresponds to synchronized 1-day-old adult worms. For optogenetic strains, L1 stage worms were plated onto 9 cm NGM agar plates seeded with 1ml OP50 food with 10 μl all-trans retinal (from 100 mM stock). For interneuron perturbation, miniSOG strains were treated with square wave pulses of 2.16 mW/mm² 450 nm blue light at 1 Hz for 30 minutes at L1 stage and then allowed to recover before testing. The combination of strains and perturbations used in this work are detailed in Table 2.

Olfactory learning protocol

The olfactory learning protocol was adapted, with modifications, from previously described protocols [3,12,17,35]. Synchronized young adult worms were removed from food and washed three times with S. Basal solution [11]. For appetitive training, worms were suspended in 10 ml of S. Basal solution on a shaker to starve for 1 hour. After starvation, worms were placed on a 9 cm NGM agar plate with 1 ml of OP50 and 12 μl of pure butanone (2-Butanone, +99%, Extra Pure, Thermo Scientific) dropped on the interior of the lid and sealed with Parafilm. To fixate butanone droplets on the lid, we placed 3 agar plugs on the lid and dropped 4 μl of butanone onto each plug. To conduct aversive training, worms were suspended in 10 ml of S. Basal with 1 μl butanone added. The tube was sealed and placed on the shaker for 1 hour. We found that aversive training was most robust with repetition (Fig A in S1 File), so we interleaved the session by plating the worms back on food for 30 minutes, then repeating the training for three times (Fig 1a). Worms were washed three times with S. Basal solution and centrifuged between each transfer during the training protocol. For naive condition, worms were directly removed from food and washed for three times before testing.

Odor delivery system and chemotaxis experiments

We used the odor flow delivery system and experimental protocols developed in [31] to measure chemotaxis trajectories after different training conditions. In short, this system incorporates controlled odorized airflow and continuously measures odor concentration along the boundary of an agar plate during animal experiments. As in [31], we calibrated the full array of metal-oxide based sensors with a downstream photo-ionization detector (Fig Ba in S1 File) to characterize the steady-state spatial profile (Fig Bb in S1 File). During animal experiments, we swapped out sensors in the middle of the arena to place in worms on an agar plate and continued to measure the boundary condition to confirm that the odor landscape is controlled and stable across the arena (Fig Bc in S1 File), as in [31] .

For butanone chemotaxis experiments, we used 1.6 % agar with salt content matching S. Basal solution in a 10 cm square plate lid. We used 11 mM butanone dissolved in water as the odor reservoir and provided moisturized clean air as the background flow. The background airflow was 400 ml/min and the butanone odor flow was 33–36 ml/min. After the pre-equilibration protocol [31] that brings the agar plate to steady-state in the odor environment, 50–100 worms were placed in the middle of agar plate and dried with kimwipes. Each chemotaxis sessions was recorded for 30 minutes.

Behavioral imaging and optical setup

Worm behavior imaging was performed as described in [31]. Briefly, a CMOS camera measured worm behavior at 14 Hz. Worms were illuminated with 850 nm light. Images were captured with custom written Labview program and analyzed with Matlab scripts. An important difference from [31] is that here we added the ability to deliver optogenetic stimulation. Three 455 nm LEDs (M455L4, Thorlabs) were fixed on top of the flow chamber to deliver stimulation. The intensity was calibrated in the field of view with a photometer, such that 85 μW/mm² intensity light was uniformly delivered. Each pulse lasts for 5 seconds and were delivered every 30 seconds. Here we analyzed 1220 to 3060 pulses delivered to worms treated with retinal in each training condition.

Chemotaxis assay in linear salt gradients

We conducted salt chemotaxis experiments following established methods [23]. We constructed linear salt gradient in the same 10 cm square plate lids used for odor delivery. Worms grown on standard NGM plates with 50 mM salt concentration were washed off food with M9 solution, then placed in the middle of either the 0–50 mM or 50–100 mM linear gradient. We then imaged behavior in the same odor flow chamber and imaging setup without applying airflow.

Behavioral analysis and dPAW inference

We tracked the location of the worm’s centroid and fit a centerline to its posture as described in [31]. We removed trajectories that are shorter than 1 minute or have displacement less than 3 mm across the recordings. In addition, trajectories that started above 70% of the maximum odor concentration were also removed to prevent double-counting worms that may have already started or traveled up-gradient. This results in 270 to 1,140 animal hours of chemotaxis trajectory per training condition for model fitting.

We characterized chemotaxis performance and strategies with indices in Fig 1d and Fig 3b. The chemotaxis index is , where and are the number of tracks going up- and down-gradient, respectively. The run index is , where and are run lengths. The turn index is , where and are the number of turn events turning up- or down-gradient , respectively.

To analyze the time series of navigation, for each processed navigation trajectory, we computed the displacement vectors every 5 time bins (5/14 seconds) and computed the angle between consecutive vectors to obtain . We computed the odor concentration it passes through using the two-dimensional odor landscape measured in the flow chamber . The perpendicular concentration difference is calculated with unit vectors that are orthogonal to each displacement vector. We also recorded the length of each displacement vector to form the empirical speed distribution.

We fit dPAW to the ensemble of trajectories by maximizing the log-likelihood:

(6)

where N is the number of trajectories, T is the time steps, and λ is the regularization term. To impose smoothness on kernels, is parameterized with 4 raised-cosine basis function [50], and are parameterized with an exponential form. Optimization was performed with constrained optimization in Matlab, where the constrains are positivity of the precision parameters and sigmoid probabilities. All together, there are 13 parameters in the full dPAW model shown in the schematic of Fig 2a, including the nonlinearity and mixture parameters shown in Eqs 2–4, 4 coefficients on the bases for , scale and scale parameters for both and exponential kernels. All fitted parameters across conditions and strains are included in the folder: 10.6084/m9.figshare.24764403.

Uncertainty about the inferred parameters are characterized by numerically computing the Hessian of the log-likelihood function around the maximum likelihood estimation. For model-based decoding, we perform 7-fold cross-validation with all measured trajectories. To analyze effects with finite data, we subsample 10 ensembles of trajectories to test for performance in Fig 5.

To validate the accuracy of maximum likelihood inference for dPAW model parameters, we simulated behavioral time series from dPAW with a fixed set of ground-truth parameters. The model generated simulated trajectories using Gaussian random white noise for concentration time series and . The time series has 50,000 data points, which is in the same scale of our data length ( ∼  300 animal hours of recording at 5 ∕ 14 Hz sampling frequency). We confirmed that the inference procedure works with simulated data and recovers the ground truth parameters (Fig C in S1 File).

To generate chemotaxis trajectories from inferred parameters shown in Fig 2, we conducted agent-based simulation by measuring concentration in the same odor landscape and drawing angular change from dPAW. We simulated two-dimensional navigation trajectories with:

(7)(8)(9)

where is speed drawn from Gaussian fit to the empirical distribution.

For information rate (Fig 4) and model comparison (Fig 5), we constructed null models to compare with dPAW. The random walk model has similar statistical structure for behavior but is independent of odor concentration:

(10)

Note that in this null model, the turning probability is time-independent, so β does not have a time subscript t. The pirouette behavior has the similar sharp angle as the full model, but now in the null model the weathervaning is changed to “runs” that have zero-mean and do not take perpendicular concentration change into account. This model was fitted to the same ensemble of trajectories, and the log-likelihood difference between the full dPAW and this null model was normalized by log ⁡  ( 2 )  per time to compute the bit rate. We also used this model to compute behavior-only model predictions in Fig 5. The chemotaxis model is formulated with a binomial distribution with expected fraction of tracks going up-gradient . The estimation for chemotaxis index is then . Lastly, the concentration change model takes for all tracks and uses naive Bayes classifier for prediction.

Statistical analysis for chemotaxis in transgenic worms

We computed the concentration weighted chemotaxis index (wCI) as follows,: , where N is the number of tracks going up- or down-gradient and ΔC is computed for every track. We find the maximum and minimum concentration across the full observed odor landscape, then define for tracks going up-gradient and for tracks going down-gradient, with ending concentration .

To conduct statistical tests between indices in Fig 7, we re-sampled chemotaxis trajectories in each condition (Fig K in S1 File). For the weighted chemotaxis index, we sampled 50 tracks for 20 times to compute the standard deviation from mean. For the biased random walk strategy, we computed to quantify the weights on concentration C and normalized by the standard deviation of the time series itself to compare across strains that experience different concentration inputs. For the weathervaning strategy, we computed to characterize how much the worm weights and corrects for the heading in response to . To conduct statistical tests on the behavioral strategies, we sampled 100 times from the posteriors of these kernels, with Gaussian approximation around the maximum likelihood estimate shown in Fig 2 b,c. For each transgenic strain and training condition, we computed the standard deviation of the metrics and conducted t-tests between the transgenic strain and wild type worms (Fig K in S1 File).

Measuring the behavior-triggered average with optogenetics

For behavior triggered averages (Fig I in S1 File) we delivered time varying LED light stimuli drawn from N ( 30 , 30 )  (μW/mm²) at 14Hz with 0.5s correlation time and bounded between 0-60 μW/mm². This serves as a white noise stimulus. We computed the behavior triggered average (BTA) for reversals following methods applied to touch sensation in worms [61].