[
International Worm Meeting,
2017]
Foraging C. elegans actively modulate their search strategy to effectively sample their environment. These decisions are based on statistical distributions of food patches in the environment, sensory cues and their recent experience. Examples of C. elegans search behaviors include area restricted search, salt chemotaxis and roaming-dwelling. Studies based on centroid measures have suggested a random search framework to explain these behaviors. Within this framework, worms sample an environment by executing straight runs punctuated randomly by sharp turns made by reversals, omega turns or a combination of both. When the frequency of sharp turns is high, worms perform a diffusive search, densely sampling a small area. On the other hand when the frequency of sharp turns is small, they perform a ballistic search, going straight for a long period of time. In this study we take another look at random search in C. elegans by analyzing the continuous dynamics in the low dimensional space of C. elegans postures given by the eigenworm representation. To our surprise, we find that the randomness in random search is largely a result of deterministic chaos instead of sensory or motor noise. Thus, the chaotic nature of the dynamics implies that the behavior of the worms is not random, but predictable for a finite period of time. This prediction window is governed by a quantity called the Maximal Lyapunov Exponent (MLE), which is positive for chaotic systems. Highly chaotic systems have a small prediction window due to a large MLE, while, weakly chaotic systems have a big prediction window resulting from a small MLE. We find that for worms engaged in an area restricted search, the MLE gradually reduces with time as the worms transition from a diffusive search strategy to a ballistic search strategy. Moreover, the reversal frequency of these worms is positively correlated with the MLE, consistent with the observation that worms get more predictable as they reduce their reversal frequency. Furthermore, the variation in MLE enough to describe most of the random search behavior, suggesting the intriguing possibility that only one degree of freedom underlies control of C. elegans foraging behavior. Finally, we use this theoretical framework to probe the biology of random search by studying the roles of monoamines dopamine and serotonin in foraging. In summary, we extend past theoretical work on C.elegans random search by including detailed postural dynamics and find that deterministic chaotic dynamics underlie the apparent randomness of C.elegans search strategies. Our analysis also suggests that the MLE of the dynamics is potentially the only parameter that the worm controls to modulate its search strategy and decide how predictable or unpredictable it wants to be.
[
International Worm Meeting,
2017]
Animal behavior is often thought to be composed of discrete stereotyped motifs and stochastic transitions between them. This view has been strengthened by recent studies that utilize advances in Machine Learning to map the behavioral motifs for several different model animals, inlcuding C. elegans. However, this discrete description is only an approximation, and doesn't take into account the variability within each motif. Here, we propose an alternative description of C. elegans behavior based on the fact that it is fundamentally a continous dynamical system. The equations of any dynamical system define a flow in a phase space and the behavior of the system can be completely described by the properties of this flow. We leverage the low dimensional space of C. elegans postures to reconstruct the dynamical phase space of C. elegans locomotion and study the resulting flow. We show that the dynamics lie in a 6 dimensional phase space, which is globally composed of three sets of cyclic trajectories that form the animal's most stereotyped behaviors: forward, backward and turning locomotion. In other words, these 6 numbers tell us almost everything about worm locomotion: whether it's going forward, backward or making a turn; the speed at which it's moving, its turning rate, its wave frequency and amplitude etc. In this sense, the 6D phase space provides an almost complete description of C. elegans behavior. In contrast to the global stereotypy, we also observe substantial local variability, i.e. every body wave the animal makes is different in the detail. Surprisingly, our tests reveal that simple noise models cannot account for the observed behavioral variability. Instead, we find that the variability is due to the chaotic nature of the flow, arising from exponential divergence of neighboring trajectories in the phase space. Further analysis of the phase space flow reveals even more surprises. We find that C. elegans dynamics, although chaotic, are highly constrained. In fact, they turn out to be closely associated with Hamiltonian systems, a well understood class of dynamical systems that conserve energy. We propose that the connection with Hamiltonian dynamics might underlie the flexibility and efficiency of C. elegans behavior. In summary, we have come up with a mathematically precise description of C. elegans behavior that is not only complete but due to its geometric nature it is also simple and intuitive. Our analysis reveals that the coexistence of stereotypy and variability in C. elegans behavior is a result of chaotic dynamics and not due to stochastic flucturations. Finally, we expect that combined with remarkable progress in whole brain imaging of freely-behaving worms, this work will provide a precise and quantitative guide to neural and genetic control of behavior in C. elegans.