Abstract

Recent whole-brain calcium imaging recordings of the nematode C. elegans have demonstrated that the neural activity lives on a low-dimensional manifold. This manifold displays clustering in neural activity space, both in long-lived states and transient trajectories. Despite progress in modeling the dynamics with linear or locally linear models, it remains unclear how a single network of neurons can produce the observed features. In particular, if there are multiple clusters or fixed points in the data, then in order to capture this feature a global model must be nonlinear. We propose a global, stochastic, and parsimonious nonlinear control model which is parameterized by four parameters that match the features displayed by the low-dimensional C. elegans neural activity. In addition to reproducing the average probability distribution of the data, long and short time-scale changes in transition statistics can be explained via changes in single parameters. Some of these macro-scale transitions have experimental correlates to single neuro-modulators that seem to act as biological “global variables”, allowing this model to generate testable hypotheses about the affect of these neuro-modulators on the global dynamics. This nonlinear control framework can also be generalized to more complex systems with an arbitrary number of behavioral states