A dynamical model of C. elegans thermal preference reveals independent excitatory and inhibitory learning pathways

Caenorhabditis elegans is capable of learning and remembering behaviorally relevant cues such as smells, tastes, and temperature. This is an example of associative learning, a process in which behavior is modified by making associations between various stimuli. Since the mathematical theory of conditioning does not account for some of its salient aspects, such as spontaneous recovery of extinguished associations, accurate modeling of behavior of real animals during conditioning has turned out difficult. Here, we do this in the context of the dynamics of the thermal preference of C. elegans. We quantify C. elegans thermotaxis in response to various conditioning temperatures, starvation durations, and genetic perturbations using a high-resolution microfluidic droplet assay. We model these data comprehensively, within a biologically interpretable, multi-modal framework. We find that the strength of the thermal preference is composed of two independent, genetically separable contributions and requires a model with at least four dynamical variables. One pathway positively associates the experienced temperature independently of food and the other negatively associates with the temperature when food is absent. The multidimensional structure of the association strength provides an explanation for the apparent classical temperature-food association of C. elegans thermal preference and a number of longstanding questions in animal learning, including spontaneous recovery, asymmetric response to appetitive vs. aversive cues, latent inhibition, and generalization among similar cues.