pnasresearcharticle Chen Learning is generic across species of all scales. How
does the brain flexibly learn to produce complex behavior? We focus on _C.
elegans_ to study how navigation strategies depend on olfactory learning by
utilizing precise experimental measurements and a novel statistical model. The
fitted model shows that learning alters two known navigation strategies in
worms and outperforms the classical chemotaxis metric in decoding learning
dependencies. We discover modulation of context-dependent behavior and
decrease in behavioral variability after learning. In addition, through
perturbing individual interneurons, we find that most neurons’ contribution
are distributed across strategies and are differentially altered by learning.
We expect these flexible properties in behavioral and neural computation to be
generalized to other species and behavior. K.S.C, J.W.P., and A.M.L designed
the research; K.S.C. performed research, analyzed data, and wrote the original
draft; K.S.C, J.W.P., and A.M.L wrote the paper. The authors declare no
conflict of interest. 1J.W.P. and A.M.L contributed equally to this work. 2To
whom correspondence should be addressed. E-mail<EMAIL_ADDRESS><EMAIL_ADDRESS>
# Olfactory learning alters navigation strategies and behavioral variability
in _C. elegans_

Kevin S. Chen  Princeton Neuroscience Institute, Princeton  Jonathan W.
Pillow1 Princeton Neuroscience Institute, Princeton  Andrew M. Leifer1,2
Princeton Neuroscience Institute, Princeton  Department of Physics, Princeton,
NJ, 08544

###### Abstract

Animals adjust their behavioral response to sensory input adaptively depending
on past experiences. The flexible brain computation is crucial for survival
and is of great interest in neuroscience. The nematode _C. elegans_ modulates
its navigation behavior depending on the association of odor butanone with
food (appetitive training) or starvation (aversive training), and will then
climb up the butanone gradient or ignore it, respectively. However, the exact
change in navigation strategy in response to learning is still unknown. Here
we study the learned odor navigation in worms by combining precise
experimental measurement and a novel descriptive model of navigation. Our
model consists of two known navigation strategies in worms: biased random walk
and weathervaning. We infer weights on these strategies by applying the model
to worm navigation trajectories and the exact odor concentration it
experiences. Compared to naive worms, appetitive trained worms up-regulate the
biased random walk strategy, and aversive trained worms down-regulate the
weathervaning strategy. The statistical model provides prediction with $>90\%$
accuracy of the past training condition given navigation data, which
outperforms the classical chemotaxis metric. We find that the behavioral
variability is altered by learning, such that worms are less variable after
training compared to naive ones. The model further predicts the learning-
dependent response and variability under optogenetic perturbation of the
olfactory neuron AWCON. Lastly, we investigate neural circuits downstream from
AWCON that are differentially recruited for learned odor-guided navigation.
Together, we provide a new paradigm to quantify flexible navigation algorithms
and pinpoint the underlying neural substrates.

###### keywords:

olfactory learning $|$ sensory navigation $|$ statistical inference $|$ _C.
elegans_

###### doi:

www.pnas.org/cgi/doi/10.1073/pnas.XXXXXXXXXX

This manuscript was compiled on

Learning is a fundamental property of the brain and is an important research
topic in neuroscience. In order to study how the brain learns, the first
essential step is to characterize the learning dependent behavioral outputs.
One common approach to study learning in systems neuroscience is to train
animals to perform relatively controllable but constrained tasks. While this
approach leads to the discovery of certain neural mechanisms and learning
rules (1, 2), there are growing evidence showing that learning is more
prominent in naturalistic tasks (3, 4). Animals can learn naturalistic tasks
in a few trials because it reflects the evolutionary pressure on the neural
and behavioral algorithms (5, 6). Careful characterization of learned behavior
in a naturalistic context sheds light on the flexible computation performed by
the brain.

Olfactory navigation is a naturalistic behavior that is generic across species
of different scales, has significant ethological relevance to detect long-
range signal reflecting reward or aversion in the environment, and can often
be acquired in few trials of learning. To study how animals learn to
adaptively employ olfactory navigation strategies, we focus on the nematode
worm _C. elegans_ that has a compact nervous system and well-characterized
olfactory neural circuits (7, 8, 9). The olfactory sensing mechanisms and
navigation behavior in worms have been studied in detail (9, 10). Despite the
simplicity, it has been shown that past olfactory experiences lead worms to
either seek out or avoid higher concentrations of odor (11, 12, 13). However,
it is unknown how worms’ navigation strategies are altered by learning to
achieve these feats. We aim to quantitatively characterize the learned
navigation strategy, thereby constraining our understand of the underlying
neural mechanisms.

Previous studies of navigation along salt and temperature gradients have
revealed that the worm navigates in sensory environments mainly through two
strategies: klinokinesis and klinotaxis (10, 14, 15). Klinokinesis corresponds
to a process known as a biased random walk, in which the worm produces sharp
turns called “pirouettes” with a probability that depends on local gradients
(10, 16). Klinotaxis is a process in which the worm continuously modulates its
heading to align with the local gradient. In worms, this process is also known
as “weathervaning”, as the animal biases its head direction in response to
local gradients (14). Past literature has found contributions from both
strategies in a variety of sensory-guided navigation behavior, from
temperature (15), and salt (14, 17, 18), to certain odor gradients (14, 9, 19,
20). In contrast to salt chemotaxis or thermotaxis (21, 22), airborne odor-
guided navigation in the worm has not yet been captured by well-constrained
quantitative models, in part because most experimental assays do not provide
detailed information about the odor concentration experienced by the animal as
it moves in the environment. Newly developed experimental setup to control and
monitor the odor landscape experienced by the worm (23) now make it possible
to empirically constrain models of odor guided navigation.

Here we focus on learned odor navigation in worms, which is particularly
interesting because it involves altering the “valance” of an external stimulus
through training. This is closer to forms of associative learning commonly
studied in other animals, including mammals. In comparison, other forms of
experience-dependent changes to behavior, such as salt chemotaxis and
thermotaxis, are altered by the specific temperature or salt concentration for
cultivation and forms a preferred “set point” memory for the environment the
worm experiences in the past (17, 15). The fact that olfactory associations
can be rapidly and flexibly learned has ethologically relevance, such as the
ability to avoiding pathological food source from past aversive experiences
(13, 24). Rapid odor learning enables the investigation of flexible neural
computation and behavioral algorithms.

Butanone provides an ideal odorant for the study of associative learning. Past
work has characterized the sensory neurons sensing butanone and demonstrated
associative learning paradigms using butanone (25, 26, 12, 11). Butanone is a
volatile organic compound that can be found in bacterial food in natural
habitats (27), so worms are intrinsically attracted to the odor. When exposed
to butanone paired with food (“appetitive training”), the worm increases its
preferences to move towards the butanone source (11, 12, 26, 8). In contrast,
when butanone is paired with starvation (“aversive training”), worms decrease
their tendency to climb up butanone gradients in comparison to worms without
exposure to butanone (“naive”) (11, 26). The chemotaxis index, defined as the
fraction of worms that move towards the butanone source in a chemotaxis assay,
is a classic measure for quantifying the effect of a learned association
between butanone and the presence or absence of food. Key molecules and genes
related to learning have been identified using this approach (26, 12). Recent
work also analyze how the neural responses to odor impulse are altered by
butanone learning (8). However, precise behavioral strategies that the worm
alters upon learned odor-navigation remain unknown.

In this study we seek to answer: (1) How are the worm’s navigation strategies
altered by olfactory learning? (2) How do the learned strategies vary across
the population? (3) What neural substrates may be involved in learned odor
navigation? To answer these questions, we combine precise experimental
measurements and a novel statistical model to rigorously characterize how
butanone associative learning alters odor navigation strategies in worms.

We investigate the worm’s odor navigation by measuring the locomotion in a
controlled butanone odor environment and use those measurements to tightly
constrain a novel generative statistical model that characterizes behavioral
strategies in worms. By fitting the model to worm navigation trajectories
after different training experiences, we find that the behavioral strategies
are bidirectionally altered by butanone learning. We characterize the
sensorimotor transformation from odor to navigation behavior by fitting the
statistical model to data. The inferred model parameters are interpretable,
better decode training conditions compared to chemotaxis index, and can also
predict response to optogenetic perturbation in the sensory neuron AWCON. We
discover that naive worms have higher behavioral variability and demonstrate
context dependent behavior. We also find that bidirectional learning effects
is dominated by the AWCON sensory neuron pathway. Lastly, we genetically down
regulate individual interneurons and find distributed contribution on
behavioral strategies that are differentially affected by learning.

Figure 1: Bidirectional olfactory learning in _C. elegans_. (a) Protocol for
butanone associative training in worms. (b) After exposure to different
training regimens in (a), worms’ olfactory navigation is measured in a
controlled odor environment. (c) Example trajectory after three different
training conditions. (d) Summary statistics of learning across three
conditions. The track index is the normalized number of tracks going up
gradient $N_{u}$ versus down $N_{d}$: $\frac{N_{u}-N_{d}}{N_{u}+N_{d}}$, which
corresponds to the chemotaxis index (CI). The run index is the normalized run
length going up gradient $r_{u}$ versus down $r_{d}$:
$\frac{r_{u}-r_{d}}{r_{u}+r_{d}}$, which quantifies biased random walk (BRW).
The turn index is the normalized probability turning up gradient $p_{u}$
versus down $p_{d}$: $\frac{p_{u}-p_{d}}{p_{u}+p_{d}}$, which quantifies
weathervaning (WV). Error bar shows standard error of mean across 9-13 plates
for each condition.

## Results

### Learning bidirectionally alters olfactory navigation

We developed a protocol to train worms to associate butanone with either food
(appetitive training) or starvation (aversive training) (Figure 1a). Our
protocol was similar to previously reported training regimens (12, 26, 8)
except it exposes the animal to multiple rounds of odor paired with starvation
instead of one, which increases consistency in learning (Fig. SI2). After
training, the movement of populations of worms was recorded in a flow chamber
with a known odor landscape (Figure 1b, Fig. SI1). We recorded hundreds of
locomotory trajectories in this odor environment after different training
conditions, per plate, for up to 13 plates per training condition.
Qualitatively, the trajectories of appetitive trained worms are biased to
travel up the butanone gradient; the trajectories of naive worms are less
biased; and aversive trained worms appear qualitatively indifferent to the
gradient (Figure 1c). We quantify the performance of traveling up the gradient
using a chemotaxis index that is calculated from the animal’s trajectory (17).
Our measurements show that animal performance navigating up gradient is
bidirectionally modulated by learning, where chemotaxis index is up-regulated
after appetitive training and down-regulated after aversive training compared
to naive condition (Figure 1d). Interestingly, even animals that undergo
aversive training do not navigate down the gradient, suggesting that after
learning an association between butanone and starvation, animal are
indifferent or still slightly attracted to butanone.

To quantify how much the worms biases the movement during a biased random
walk, we calculated a run index by computing the normalized run length moving
up-gradient. To compute how much the worms turns up gradient like a
weathervane, we calculated a turn index by computing the normalized fraction
of turns heading up-gradient (17). Our measurements show that both the run
index and the turn index are on average bidirectionally modulated by learning
with respect to naive animals, suggesting that learning alters both of these
navigational strategies.

While these indices suggest hypothesis about how navigational strategies
change due to learning, they provide little information about the dynamics
during sensorimotor transformation. Specifically, the metrics use only binary
information about whether the animal is traveling up or down gradient, but
ignore details of the sensory landscape like the concentration experienced by
the animal over time. The indices also provide no information about the
behavioral stochasticity and variability across the population. To overcome
these limitations, we sought to build a statistical model that captures
temporal information, behavioral noise, and explicitly reveals how the animal
changes its movement in response to sensory stimuli. The resulting framework
better characterizes navigational strategies by incorporating the sensorimotor
transformation from odor input to behavioral output in worms. This enables
detail comparison for changes upon olfactory learning and makes quantitative
prediction about behavioral response to sensory perturbation.

### Odor-dependent mixture model of olfactory navigation

To understand the how sensory inputs are transformed to behavior under
different training conditions, we developed a new statistical model of worm
olfactory navigation. The dynamic Pirouette and Weathervaning (dPAW) model
consists a mixture of two navigation strategies —biased random walk through
pirouette behavior and weathervaning—and describes how the worm alternates
between two behavioral strategies depending on the time-varying sensory inputs
(Figure 2a). dPAW explicitly models these strategies and fits to the full
chemotaxis data. This is to our knowledge the first rigorous statistical model
that captures the details of navigation strategies, which can better
characterize how the worm’s behavior changes with learning.

In our model, the worm samples its heading change $d\theta$ at each time step
from one of two distributions: either a “weathervaning distribution”
$P_{wv}(d\theta)$ or a “pirouette distribution” $P_{pr}(d\theta)$. 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
$\pm\pi$, indicating a complete reversal in direction. The concentration-
dependent “decision” to produce pirouettes behavior forms a biased random
walk.

We model the worm’s decision to pirouette or weathervane on each time step
with a Bernoulli generalized linear model (GLM) that takes the filtered
history of the odor concentration $C_{1:t-1}$ and the worm’s own movement
history $d\theta_{1:t-1}$ as inputs. The output of this GLM is a binary
variable $\beta_{t}$ that indicates the presence of a pirouette. Thus, the
worm samples its heading change from the pirouette distribution
$P_{pr}(d\theta)$ if $\beta_{t}=1$ and the weathervaning distribution
$P_{wv}(d\theta)$ if $\beta_{t}=0$. The full model can be written:

$P(d\theta_{t}|C_{1:t-1},dC_{1:t-1}^{\perp},d\theta_{1:t-1})=\\\
P(\beta_{t}=1)P_{pr}(d\theta)+P(\beta_{t}=0)P_{wv}(d\theta\mid
dC^{\perp}_{1:t-1}),$ (1)

where

$P(\beta_{t}=1)=m+\frac{M-m}{1+\exp(K_{C}\cdot\mathbf{C}_{1:t-1}+K_{h}\cdot|\mathbf{d\theta}_{1:t-1}|)}$
(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 $K_{C}$ and $K_{h}$ corresponding to filters on past odor
concentration $\mathbf{C}_{1:t-1}$ and the past absolute angular change
$|\mathbf{d\theta}_{1:t-1}|$ vectors, respectively. The pirouette and
weathervaning distributions are in turn given by

$\displaystyle P_{pr}(d\theta)$ $\displaystyle=\alpha
U[-\pi,\pi]+(1-\alpha)f(\pi,\kappa_{pr}),$ (3) $\displaystyle
P_{wv}(d\theta\mid dC^{\perp}_{1:t-1})$
$\displaystyle=f(-K_{dC^{\perp}}\cdot\mathbf{dC}_{1:t-1}^{\perp},\kappa_{wv})$
(4)

where $U$ is uniform in the circular heading and $f$ is a von Mises
distribution with mean and precision parameter $\kappa$. In the pirouette
distribution, scalar $\alpha\in[0,1]$ is the weight on the uniform
distribution and $\kappa_{pr}$ 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
$dC^{\perp}_{1:t-1}$ and the precision parameter $\kappa_{wv}$ determines the
noise around the head angle.

Figure 2: dPAW captures learned olfactory navigation in worms. (a) Schematic
of the dPAW model. An example data 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
$\beta$ leads to two parallel strategies: biased random walk and
weathervaning. (b) Kernel $K_{C}$ and (c) Kernel $K_{dC^{\perp}}$ fitted to
three training conditions. Shaded area shows standard deviation of the kernel
estimate. (d) Chemotaxis index of simulated trajectories with inferred
parameters. Error bar shows standard error of mean across 10 repeated
simulation, each with 100 trajectories. (e) Example trajectories simulate from
each training conditions.

We fit dPAW to the experimental measurements, including the time varying
headings $d\theta_{t}$, the concentration along the locomotion path $C_{t}$,
and the concentration perpendicular to the locomotion path $dC^{\perp}_{t}$.
All model parameters in dPAW are jointly inferred through maximum-likelihood
method. To validate that parameters can be reliably inferred, we simulated
example chemotaxis trajectories from pre-defined parameters, fit them to the
model, and confirmed that we accurately recovered the parameters (Fig. SI3).
In the rest of the paper we use this model to interpret how navigation
strategies change with learning, to quantify variability across behavioral
trajectories, and to decode the animal’s past experience.

### Model captures navigation strategies altered by olfactory learning

We seek to characterize how olfactory learning alter navigation strategies. We
fit dPAW to trajectories measured in the butanone odor environment after
different training conditions. The result shows that the kernels corresponding
to both weathervaning and biased random walk strategies are altered by
learning (Figure. 2b,c). The weathervaning kernel $K_{dC^{\perp}}$ has lower
weights after aversive training compared to appetitive trained or naive
animals (Figure 2c), suggesting that the animal’s heading angle is less
tightly dependent upon the concentration difference perpendicular to its path.
In the kernel for pirouette decision $K_{C}$, the amplitude is significantly
increased after appetitive training compared to naive animals, suggesting that
the animal’s pirouette probability strongly depends on the concentration
change along the navigation path. After aversive training, the kernel $K_{C}$
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 not be responding as much to downward changes in concentration
(Figure 2b). Collectively, these changes in the sensing kernels provide
insights into how the worms flexibly alters their sensorimotor transformations
locally to achieve the observed learned chemotaxis (Figure 1d). This precise
effect on the way worms compute local odor concentration is not apparent from
an analysis of chemotaxis index alone.

To validate that dPAW captures biologically plausible navigation behavior, we
use it to simulate chemotaxis behavior with the fitted parameters from animals
in the same odor environment previously exposed to three training conditions.
dPAW with fitted parameters produces macroscopic behavior similar to the
measurements (Figure 2d). Similar to the measurements, the model-generated
behavior has a chemotaxis index that is bidirectionally modulated by training
conditions. Example model-generated chemotaxis trajectories also appear
similar to experimental observations (Figure 2e). We show that the simulated
trajectories capture other statistics measured in experiments, including the
heading distribution, pirouette rate, perpendicular concentration difference,
and the tangential concentration distributions (Fig SI 4,5).

Figure 3: Learning alters pirouette decision and and behavioral noise. (a) The
top panel shows decision function $P(\beta=1|C,d\theta)$ of three training
conditions as a function of filtered signal: $K_{C}\cdot
C+K_{h}\cdot|d\theta|$. 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, $\kappa_{wv}$ 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 10 sampled batches of trajectories.

To understand how the animal alters its preference for continuing to
weathervane versus interrupting weathervaning with pirouettes, we compared the
decision function in equation 2 inferred from our measurements before and
after learning. We found that learning alters the input-output statistics for
producing the pirouette behavior (Figure 3a, bottom). This is clear from
inspecting the distribution of the filtered signal (related to odor
concentration and past behavior), where appetitive training and aversive
training pushes the tail of the distribution in opposite directions with
respect to naive condition.

Passing the filtered signal (Figure 3a, bottom) through the nonlinear decision
function (equation 2 and Figure 3a, top), we find that aversive trained worms
have higher baseline turning rate $m$ and appetitive trained worms have a
lower one (Figure 3a, right). Both aversive and appetitive trained worms have
higher maximum pirouette rate $M$ compared to naive worms. The parameters $M$
and $m$ are not simply reflecting the overall pirouette rate. The fitted model
parameters “explain” the pirouette behavior differently – an observed
pirouette behavior is more likely to be spontaneous for aversive trained worms
and is more likely to be an odor-driven event in appetitive trained worms.
Inspecting these output distributions in a log scale (Fig 3a right, inset), 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, possibly indicating a more efficient strategy for chemotaxis.

To confirm that the model accurately captures the empirical pirouette
frequency, we compared model predictions and the classic threshold-crossing
method to detect sharp turns in experimental measurements (10). The model
estimation agrees with empirical pirouette rate across training conditions
(Fig. SI4). Together, the result shows that dPAW captures the pirouette
decision and reveals that learning alters both the processing of sensory input
and the probabilistic behavioral output. The model also helps us understand
how pirouettes are more or less often odor-driven under different training
conditions.

Analysis of the kernel amplitude reveals that weathervaning was down-regulated
after aversive training (Figure 2c). One hypothesis for a disrupted
weathervaning behavior is that the worm is uncoordinated and randomizes its
heading direction more during weathervaning, such that the weathervaning
process itself becomes more similar to a continuous random walk. We show that
this is not the case. On the contrary, the worm’s trajectory after aversive
training has a longer persistence length. This is shown from the inferred
precision parameter for the weathervaning process $\kappa_{wv}$, which is
larger after aversive training (Figure 3b).

We further investigate the functional contribution of two strategies with dPAW
by investigating two types of alternative models that omit key information. In
the first, we set the two sensing kernels separately to zero and find that the
$K_{C}$ that affects the pirouette decision is highly informative across all
training conditions (Fig. SI5a). In the second type of null model we remove
odor dependence entirely, but preserve the average pirouette rate. dPAW with
the concentration-dependent strategies on average provides $0.3-0.6$ bits/s
more information compared to the null model without any olfactory sensing
mechanisms (Figure 3c).

### Model-based decoding of learned experience

How much do the worms’ navigation strategies differ after learning? To address
this question, we performed model-based decoding of the past training
experiences. We first fit separate dPAW models to measured trajectories from
each training conditions
$\gamma\in\\{\textrm{appetitive},\textrm{naive},\textrm{aversive}\\}$ giving
the corresponding fitting parameters $\Theta_{\gamma}$. Then we make maximum
likelihood predictions of the condition given held-out test trajectories:
$\textrm{argmax}_{\gamma}P(\vec{d\theta}|\vec{C},\vec{dC^{\perp}};\Theta_{\gamma})$.
On held out data, the fitted model correctly predicts past training condition
with a performance above 90$\%$, which is significantly above the 33.3$\%$
chance level (Figure 4a). We compare the performance with a classical
chemotaxis metric – the fraction of tracks that go up gradient. This metric
can be formulated as a binomial model that estimates the probability of
observing tracks going up gradient. The chemotaxis metric reaches only 80$\%$
accuracy at decoding and is continuously outperformed by our dPAW model for
finite testing data.

Why might dPAW perform better? dPAW derives its power in part from using the
animal’s combined concentration experience and behavior history, what we call
its navigation trajectory. Together, this contains more information than, for
example, the binary outcome of up or down gradient. We found that predicting
learning experiences from concentration alone – without behavioral information
– performs worse, suggesting that its not the full concentration history alone
that trivially provides all the needed information (Figure 4a). For instance,
the distribution of concentration change along all tracks in each condition is
not separable enough to reach $90\%$ predictive performance (Fig. SI7). Even
if we take the concentration trajectory and compute the difference of
concentration in the beginning and ending of each trajectory, the predictive
performance is only around 50$\%$. This suggests that combining moment-by-
moment concentration information with behavior information is necessary for
optimal decoding.

Similarly, dPAW also outperforms models or metrics that rely only on behavior
and without the animal’s experienced concentration. When considering a model
that only captures the behavioral statistics but neglects the odor
concentration, the predictive performance plateaus around the 60$\%$
performance. We note that because this is above chance, it indicates that
learning alters the overall behavioral statistics as well. In other words, we
demonstrate that even without knowing any aspect of the sensory environment,
simply observing the statistics of motion provides information about the
animals learning. Together, the results show that the detailed sensorimotor
transformation between odor concentration and navigation behavior is important
for decoding. The learned parameters in dPAW better characterizes how the
worms learned to navigate and can generalize to make predictions on
trajectories measured in new experiments.

Figure 4: Model-based decoding of learning. (a) Model-based classification as
a function of mean data length. Four models are compared and error bars show
standard error of mean across 7-fold cross validation and 10-fold sampling
across data length. w/o concentration: model that only captures behavioral
statistics and does not account for odor input. w/o behavior: model for
concentration difference along each trajectory and does not account for
behavioral output. Chance level is shown in grey dash line. b dPAW-based
decoding as a function of data length, for each training conditions calculated
separately.

Model-based prediction characterizes how well the fitted parameter generalize
to new test data. Given variable behavioral data, such analysis can guide
experimenter to repeat more variable conditions to gain better estimates of
the behavioral strategies. Specifically, trajectories from naive worms show
the lowest predictive performance with finite data when decoding is done for
each training conditions separately (Figure 4b). This is consistent with lower
information rate and variable parameter estimates shown in Figure 2b and
Figure 3c. Empirically, this result indicates that more measurements are
required to capture navigation behavior in naive worms.

### The same computations govern natural and artificial odor stimuli

We investigated response to optogenetic induced odor sensation after olfactory
learning. The motivation for using optogenetics is to probe casual sensory
motor responses that are not confounded by the correlations in the odor
stimuli experienced by the animal in a naturalistic environment. For example,
the worms in our arena always experience temporally correlated and slowly
varying odor responses, but with optogenetics we can probe the animal’s
response to arbitrary stimulation, including impulses (26, 28). We wondered
whether the underlying computations that govern the animals response to
natural odor stimuli were similar to those governing its response to
optogenetic-induced sensory stimuli. We therefore included optogenetic
perturbation in the experiments and adopted our model to incorporate such
stimuli.

Figure 5: Optogenetic perturbation in the context of learned odor navigation.
(a) Experimental setup that combines optogenetic perturbation with the odor-
flow chamber. (b) Absolute change in angular speed upon optogenetic impulse
across thee training conditions. Change is computed between the average
response during the 5s impulse and 5s before it. Within each training
conditions, measurements are further separated into trajectories going up or
down gradient. We record from 4-7 plates per condition. Error bar shows
standard error of mean across over 1000 impulses per condition. (c) Temporal
kernels for odor $K_{C}$ and optogenetic $K_{opto}$ fitted to each training
conditions. The grey area shows standard deviation around the estimated
kernels. (d) Time-varying absolute angular speed aligned to the optogenetic
stimuli. Three panels show different training conditions. Solid line and dash
line indicate up and sown gradient trajectories. The grey area shows standard
error of mean across traces.

We presented optogenetic stimulation to worms expressing channelrhodopsin in
AWCON, a sensory neuron known to sense butanone and play an important role in
learning (26, 8, 12). AWCON was optogenetically stimulated in worms as they
navigated in the odor arena, therefore they received both optogenetic-induced
and natural odor stimuli simultaneously (Figure 5a). The absolute angular
change in response to an optogenetic impulse was bidirectionally modulated by
learning. This is similar to results shown in (26), but note that here we use
the exact same naive control to compare with appetitive and aversive training
conditions (Figure 5b,c). We extend our model so that light intensity
contributes to the biased random walk strategy and the pirouette probability
during navigation:

$P(\beta_{t}=1)=\frac{M-m}{1+\exp(K_{odor}\cdot\mathbf{C}_{1:t-1}+K_{opto}\cdot\mathbf{I}_{1:t-1})}+m$
(5)

where kernels $K_{odor}$ and $K_{opto}$ are weights on vectors of odor
concentration $\mathbf{C}_{1:t-1}$ and light intensity $\mathbf{I}_{1:t-1}$,
respectively. Since there is no difference along the tangential direction in
optogenetic signal, this model is simplified with kernels weighting the
tangential concentration and neglecting the perpendicular concentration for
weathervaning. Surprisingly, 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 (Figure 5d; Fig. SI8). Our
result provides empirical evidence that sensorimotor computation inferred from
freely moving animals can predict the response to external perturbations. The
inversion can partly be explained by the biophysics of AWC neuron: it
hyperpolarizes when odor is present and depolarizes when odor is removed,
therefore we expect optogenetic stimulation to have an opposite effect as odor
presentation. 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. Similarly, we can leverage
optogenetics to probe behavioral variability during odor navigation.

### Learning modulates behavioral variability in response to sensory
perturbation

Sensory processing and navigation behavior can be intrinsically noisy in worms
(29). We first sought to characterize the variable navigation behavior across
the worm population by analyzing sub-sampled tracks during natural odor
stimuli (Fig. SI6). We found that the biased random walk kernel $K_{C}$ in
naive and aversive trained conditions are more variable across ensembles. To
better identify the source of the variability, we again turn to an optogenetic
approach to probe behavioral response in the context of navigation and
learning.

Surprisingly, we discovered that one source of variability was the context of
gradient direction. We found that naive and aversive trained worms respond to
optogenetic impulse differently depending on whether the navigation trajectory
is going up or down gradient (Figure 5b). Appetitive trained worms respond
consistently to optogenetic impulse regardless to the context of gradient
direction, whereas naive and aversive trained worms respond more strongly in
the context of moving up gradient. This indicates that learning alters
behavioral variability, which in turn can be context-dependent along the
navigation trajectory. The result that naive worms exhibit more variability in
their odor guided navigation is consistent across three different analyses:
(1) naive worm produce trajectories that have less bits per seconds captured
by the model (Figure 2b and 3e), (2) the decoding performance of naive worms
is lower with finite data (Figure 4b), and (3) naive worms’ response to
optogenetic stimulation is more variable (Figure 5d) and context-dependent
(Figure 5b). Together, this shows that naive worms have more heterogeneous
navigation strategies and sensorimotor responses. And at least some of that
variability can be explained by its context-dependent interpretation of odor
stimuli, depending on whether it travels up or down gradient.

### Downstream interneurons deferentially contribute to learned chemotaxis

Measured behavior under optogenetic stimulation shows that driving AWCON
neuron is sufficient to recapitulate the effects of bidirectional learning.
Past work has also shown the importance of AWCON in terms of odor sensing (9),
navigation (30, 31, 32), and learning (11, 26). We further investigated the
downstream circuit that implements this sensorimotor computation by ablating
or down-regulating specific interneurons in worms, and then characterized
defects in the learned odor navigation using dPAW. Following known anatomical
connections (7) (Figure 6a), we focused on five interneurons with direct
synaptic inputs (chemical or electrical connections) from AWC: AIB, AIZ, AIY,
RIA, and AIA.

We compared the chemotaxis performance and behavioral strategies in mutants to
wild-type worms, and conducted significance test with sub-sampled data (Figure
6b; Fig. SI9, Fig. SI10). Without learning, naive worms with individual
disrupted interneurons can still climb up gradient, except for AIZ(-) worms.
AIZ(-) condition eliminates gradient climbing behavior across all three
training conditions. RIA(-) worms have down-regulated chemotaxis indices for
both appetitive and naive conditions, but show increased chemotaxis index in
aversive conditions. This indicates that in RIA(-) defective mutants there is
no bidirectional change to navigation upon learning. AIA(-), AIB(-), and
AIY(-) worms have less difference between naive and aversive training
conditions, but still preserve up-regulated chemotaxis performance after
appetitive training conditions.

Figure 6: 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 (CI), biased-random walk
(BRW), and weathervaning (WV) indices computed from the inferred dPAW for all
mutants across three training conditions. The circles show value from wild-
type N2 worms and arrow shows the modulation in mutant worms. We record 3-5
plates for each stain and condition, resulting in 200-500 tracks in each
measurement. (c) Weights in the neuron-behavior matrix $\mathbf{W}$ across
three training conditions. The two rows are for different behavioral
strategies and the columns are for different mutant worms.

We systematically quantified the effects of interneuron perturbation with a
linear model (Figure 6c): $\mathbf{B}=\mathbf{W}\mathbf{A}$, where
$\mathbf{B}$ is the matrix with behavior readout along the rows and ablation
conditions along the columns, $\mathbf{W}$ is an unknown weight matrix from
neuron to behavior, and $\mathbf{A}$ is the ablation matrix with binary
elements. In our experimental design, if we assume that each transgenic line
is specific enough to perturb one interneuron at a time, the diagonal elements
would be zero and all off-diagonal elements are one. This matrix is full-rank
and makes the linear model solvable. We normalized the rows in $\mathbf{B}$ to
better compare weights across behaviors.

We studied $\mathbf{W}$ (Figure 2c) and found that AIA contributes strongly to
biased random walk in aversive trained conditions, which agrees with
observation in (26) showing that AIA is required for aversive learning and
alters turning responses. AIB and AIY contribute to both behavioral strategies
(31), but the contribution differs depending on the training conditions: the
contribution of AIB is enhanced for appetitive condition and the contribution
of AIY is enhanced for aversive condition. AIZ contributes to weathervaning in
all conditions and is significantly higher in naive condition. Our result is
consistent with the finding showing that ablating AIZ destroys salt chemotaxis
behavior reported in (14). Lastly, RIA has negative weights in the aversive
condition, possibly reflecting the importance of regulating weathervaning in
the aversive condition shown in Figure 2c, and in agreement with RIA’s known
role in controlling head motion (33). Overall, the weight matrices
$\mathbf{W}$ are more similar between appetitive and naive conditions than
aversive. Our analysis shows that the contribution on behavioral strategies
are distributed across interneurons for all training conditions.

## Discussion

We combined precise experimental measurements and a novel statistical model,
dPAW, to characterize learned olfactory navigation in worms. The results show
that (1) navigation strategies are bidirectionally altered by learning, (2)
dPAW decodes the animal’s past training conditions based on the observed
navigation behavior and outperforms a classic chemotaxis metric, (3) behavior
is more variable in naive worms and some of this variability can be explained
by a context-dependent response to odor, and (4) interneurons downstream from
AWCON contribute to learned navigation strategies differently depending on
learning .

Worms respond to a range of sensory input in a experience-dependent manner
(34, 17). Previous studies show how neural responses are altered by learning
or sensory adaptation (17, 15, 26). Specifically, butanone learning has been a
major focus in the previous literature (11, 26, 8, 35). Butanone learning was
first proposed to bidirectionally modulate chemotaxis index (11). However,
learning and chemotaxis results can vary depending on the regime of butanone
concentration used (11, 8, 36) and might produce variable chemotaxis indices
across different repeated assay (8, 35). Therefore, later studies mostly focus
on one of the two valances (appetitive vs naive, or aversive vs naive), with
specific concentrations (12, 26). When appetitive and aversive learning are
compared, past work has tested them at non-comparable odor concentration
ranges (26, 8). In contrast, here we design a bivalent training protocol
(aversive and appetitive) that shows clear effects even when tested in the
same odor concentration range. To accomplish this our protocol is asymmetric
with multiple exposures repeats aversive training and only a single exposure
during appetitive training. We then conduct tests in an identical, controlled
sensory environment enabled by our recently developed odor delivery system
(23). The sensorimotor transformation altered by learning can then be directly
compared through this approach (Figure 1).

Characterization of sensorimotor transformation in small animals such as _C.
elegans_ sheds light on the underlying neural computation (9, 15, 17) and
navigation algorithms (37). Specifically, past studies have pinpointed neural
circuits related to both biased random walk and weathervaning strategies for
salt and thermal navigation (14, 17, 15). In contrast to only counting the
number of worms ending up gradient, which is the classical calculation for
chemotaxis index, we can better characterize sensorimotor transformation along
the chemotaxis trajectories with the full tracking data. Moreover, as shown
from simulation work, coarse measurements such as the chemotaxis index is
often degenerate (22), since an agent can climb up gradient with different
kinematics and strategies but result in similar chemotaxis index. It is
therefore important to study how the worm respond to odor concentration along
the navigation path.

Previous calculation for pirouette strategy (10) and weathervaning strategy
(14, 17) rely on regressing the worm’s locomotion with respect to estimates of
the sensory environment. This requires choosing a time window to calculated
gradients, and defining behavior with hand-tuned parameters. Moreover, these
regression approaches often omit quantification of uncertainty and noise. dPAW
provides a framework to jointly fit navigation parameters and their
uncertainties to data. Through statistical inference with dPAW, we find that
learning might not only alter the baseline behavioral statistics (Figure 3)
but also the temporal kernels for odor input. For instance, appetitive
training sharpens the tangential concentration kernel (Figure 2). By contrast,
classical approaches implicitly have static kernels, and therefore would have
missed this important change. dPAW includes parameter that control the noise
level of behavioral output, which is an advantage over past works (14, 22).
Our finding shows that learning alters not only the sensing mechanism but also
the behavioral statistics, which is consistent with recent work showing that
starvation or neuromodulation can alter multiple behavioral traits (38, 39).
Future work is needed to pinpoint the source of stochasticity, such as noise
in the sensory or motor circuits, and its potential functional roles in
navigation and exploration (40).

Statistical modeling and inference methods have been widely adopted in
computational neuroscience, particularly in the study of sensory encoding (41,
42). Recent work has extended similar frameworks to characterize sensorimotor
transformation in small animals (34, 28). These experiments conduct
optogenetic stimulation in odor sensing neurons to characterize neural
dynamics (30) or behavioral output (26). While these results focus on the
elements of odor navigation, the mapping to sensorimotor transformation during
a navigation task is still less clear. To deliver olfactory impulses,
experimenters often have to either construct transgenic strains to
optogenetically stimulate the sensory neurons or develop apparatus to deliver
controlled odor impulse, which are both relatively challenging. In our work,
we show that by applying statistical inference directly to navigational
trajectories, the noninvasive method can indeed qualitatively recover
sensorimotor transformation upon optogenetic perturbation (Figure 5). The
result also shows that the variability in optogenetic response can be
predicted by sensing kernels inferred from navigation across odor landscapes.

As shown in multiple studies (43, 44, 45), the result of associative learning
is often heterogeneous across animals or non-stationary in time. Our result
shows an opposite effect, where naive worms are more variable and the learning
better “synchronizes” behavioral strategies across worms. Surprisingly, we
further find that the variation across optogenetic responses in naive worms
can in part be explained by the context in an odor environment, up or down the
gradient. While recent work show population representation of odor stimuli in
worms (25), our result shows that the AWC pathway is sufficient to capitulate
learning effects and is causally altering navigation behavior.

The biophysics of the AWCON neuron (30, 32) and its circuit connection (31,
26, 8) has been studied in detail. Importantly, many connections to the first
layer of interneurons are shared with salt sensing neurons ASER/L and thermal
sensing neuron AFD. In the five interneurons we focused on, AIB has been shown
to play a role in temperature learning (15). AIB, AIY, and AIZ all seem to be
involved in learned salt chemotaxis strategies (17). Our findings agree with
these results in showing that all three interneurons have non-zero and
learning-dependent weights for both behavioral strategies. Through optogenetic
control (46) and calcium imaging (33), AIY and RIA have been shown to support
weathervaning behavior. Interestingly, we find that weathervaning in worms
with ablated AIY and RIA increase their weathervaning index after appetitive
and aversive trained conditions, respectively. This indicates that there might
be compensatory effects from other circuits performing weathervaning in an
experience-dependent manner. To date, the most comprehensive work on the
neural circuits underlying butanone learning also shows that neural activity
in steering neurons such as AIY and RIA are altered by learning (8). Our
finding shows how they are deferentially modulated by learning, supporting
that RIA is crucial for bidirectional learning. In addition, imaging results
show that a population of sensory neurons are affected by learning (8). While
we demonstrate that the driving the AWCON neuron is sufficient to recover
learning-dependent behavior, analysis on the neural population level and its
corresponding behavior would be an important extension.

To understand the underlying neural mechanisms that supports learned odor
navigation in worms, potential future directions include imaging the neural
population dynamics (25, 8) _during_ odor navigation and study temporal
progression of learning effects (47). Despite having high spatiotemporal
resolution in neural recording, whole-brain imaging experiments are inherently
low throughput. Typical neural imaging are on the order of 10 minutes and one
worm at a time, oppose to chemotaxis with 100 worms with the same training
procedure and recorded for 30 minutes in parallel. In the limit of finite
data, our result show quantitative model comparisons and indicate that dPAW
can better decode for training conditions with finite behavioral data. The
fact that these behavioral variables are more informative about training
conditions would guide our search for learning-dependent neural
representations.

In this work we utilize a controlled odor environment and an innovative model
to characterize learned odor navigation in worms. The combined approach of
precisely delivered sensory stimuli, behavior quantification and navigational
modeling continues to be a powerful approach (48, 49, 50) that can be
generalized to other sensory modalities and species to study adaptive sensory
navigation.

### Worm strains and preparation

We used N2 wild type worms for experiments shown in Figure 1 to Figure 4. The
strain for optogenetics was integrated from the strain in (26). All strains
were maintained on nematode growth medial (NGM) agar plates and fed with OP50
food. For interneuron perturbation, we integrated strains from (17) and used
strains from (15). Detailed genetics and transgenic protocol are shown in
supplementary information. Before chemotaxis experiments, we bleached batches
of worms to synchronize the next generation. For optogenetic strains, worms
were plated on 1ml OP50 food with 10$\mu$l all-trans retinal at L1 stage. For
interneuron perturbation, miniSOG strains were treated with 2.16 mW/mm2 450 nm
blue light at 1 Hz for 30 minutes at L1 stage.

### Olfactory learning protocol

Synchronized young adult worms were removed from food and washed three times
with S. Basal solution (9). Appetitive trained 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 $\mu$l of
butanone dropped on the lid. The butanone droplets were distributed across
three agar plugs and the petri dish is sealed with parafilm. Aversive trained
worms were suspended in 10 ml of S. Basal with 1 $\mu$l butanone added. The
tube was sealed and placed on the shaker for 1 hour. We empirically found that
aversive training does not work without repetition, so we interleaved the
session by plating the worms back on food for 30 minutes, then repeating the
training for three times (Figure 1a). Naive worms were removed from food and
washed for three times before testing directly. More details for the protocol
and empirical observations are included in supplementary information.

### Odor flow chamber setup and chemotaxis experiments

Following the different training protocols, worms were tested in the same odor
flow chamber. This odor flow chamber enables continuous control through
odorized air flow and monitor odor concentration through metal-oxide-based
sensor arrays. Given a fixed flow parameter, we measured the steady-state odor
landscape across the two-dimensional sensor array. This odor landscape was
then used to infer odor concentration the worm experiences as it navigates
along the same stationary odor environment. The assembling details of this
apparatus is reported in (23). For chemotaxis experiments, we used 1.6 $\%$
agar with salt content matching S. Basal in a 9 cm square plate. We used 11 mM
butanone dissolved in water as the odor reservoir and moisturized clean air as
the background flow. The background airflow is 400 ml/min and the butanone
odor flow is 33-35 ml/min. After the pre-equilibration protocol (23) 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 were record for 30 minutes.

### Behavioral imaging and optical setup

Worm navigation behavior were recorded with a CMOS camera fixed above the odor
flow chamber. Each image is $2500\times 3000$ pixels, with each pixel as
$32\mu$m, and acquired at 14 Hz. Images were captured with custom written
Labview program and analyzed with Matlab scripts (23). Worms were illuminated
with 850 nm LED strip surrounding and above the agar plate. For optogenetic
experiments, a long-pass filter is fixed in front of the camera lens to block
the 525 nm stimuli. Three 525 nm LEDs were fixed on top of the flow chamber to
deliver stimulation. The intensity was calibrated in the field of view with a
photometer, with 85 $\mu W$/mm2 for each uniform light impulse. Each pulse
last for 5 seconds and were delivered every 30 seconds. Here we analyzed
1220-3060 pulses delivered to worms treated with retinal in each training
conditions.

### Behavioral analysis and dPAW inference

With the behavioral analysis pipeline (23), we tracked the location of the
worm’s centroid and fit a centerline to its posture. We smoothed the
navigation trajectories with a third-order polynomial with a 0.5 second time
window. We removed trajectories that are shorted than 1 minute or have
displacement less than 3 mm across the recordings. In addition, trajectories
that started above 70$\%$ for the maximum odor concentration were also removed
to prevent double-counting worms that have made it up gradient. This results
in 270-1,140 animal hours of chemotaxis trajectory per training condition for
model fitting. For each processes navigation trajectories, we computed the
displacement vectors every 5 time bins (5/14 seconds) and compute the angle
between consecutive vectors to obtain $d\theta_{t}$. We computed the odor
concentration it passes through using the two-dimensional odor landscape
measured in the flow chamber $C_{t}$. The perpendicular concentration
difference $dC^{\perp}$ 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.

With the ensembles of trajectories, we fit dPAW by maximizing the log-
likelihood:

$argmax\Sigma_{n}^{N}\Sigma_{t}^{T}\log
P(d\theta_{n,t+1}|C_{n,:t},dC^{\perp}_{n,:t},d\theta_{n,:t})-\lambda|K_{C}|^{2}$
(6)

where $N$ is the number of trajectories, $T$ is the time steps, and $\lambda$
is the regularization term. To imposes smoothness on kernels, $K_{C}$ is
parameterized with 4 raised-cosine basis function, $K_{dC^{\perp}}$ and
$K_{h}$ 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. We show that the
inference procedure works with simulated data and recovers the ground truth
parameters. Uncertainty about the inferred parameters are characterized by
numerically computing the Hessian of the log-likelihood function. For model-
based decoding, we perform 7-fold cross validation with all measured
trajectories. To test with finite data, we subsample 10 ensembles of
trajectories to test for performance in Figure 4.

To generate chemotaxis trajectories from inferred parameters shown in Figure
2, we conduct agent-based simulation by measuring concentration in the same
odor landscape and drawing angular change $d\theta_{t}$ from dPAW. We simulate
two-dimensional navigation trajectories with:

$\displaystyle x_{t+1}$ $\displaystyle=x_{t}+v_{t}\cos(\theta_{t})$ (7)
$\displaystyle y_{t+1}$ $\displaystyle=y_{t}+v_{t}\sin(\theta_{t})$ (8)
$\displaystyle\theta_{t+1}$ $\displaystyle=\theta_{t}+d\theta_{t}$ (9)

where $v_{t}$ is speed drawn from Gaussian fit to the empirical distribution.

For information rate (Fig. 3) and model companions (Fig. 4), we construct null
models to compare with dPAW. The random walk model has similar statistical
structure for behavior but is independent to odor concentration:

$P(d\theta_{t})=P(\beta=1)P_{pr}(d\theta)+P(\beta=0)P_{run}(d\theta)$ (10)

Note that different from dPAW, the turning probability is time-independent, so
$\beta$ does not have a time subscript $t$. The pirouette behavior has the
similar sharp angle, but now 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 dPAW and this model is normalized by $\log(2)$
per time to compute the bit rate. We also used this model to compute behavior-
only model prediction in figure 4. The chemotaxis model is formulated with a
binomial distribution with expected fraction of track going up gradient
$\hat{p}$. The estimation for chemotaxis index is then $2\hat{p}-1$. Lastly,
the concentration change model takes $C_{final}-C_{initial}$ for all tracks
and uses naive Bayes classifier for prediction.

We thank the Leifer lab and Pillow lab for helpful discussions. This work was
supported by the National Institutes of Health National Institute of
Neurological Disorders and Stroke under New Innovator award (DP2-NS116768),
the Simons Foundation under award SCGB (543003), an NSF CAREER Award to AML
((NSF PHY-1748958), and through the Center for the Physics of Biological
Function (PHY-1734030).

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