Exploring the energy landscape of C. elegans neural activities

Recent advances in experimental techniques and application of the maximum entropy principle have allowed us to build models for joint probability distribution of activity in groups of up to 50 neurons in Caenorhabditis elegans, a nematode with 302 neurons. These models, which are equivalent to the Boltzmann distribution for a family of Potts glasses, successfully predict the static observables of the network. The energy landscape defined by these models exhibits curious signatures of collective behavior, including a large number of energy minima, as in models for memory, and a clustering of energy barriers that is reminiscent of the dynamical transitions in disordered systems. While these models describe the distribution of network states at a single time, the observed neural dynamics are not consistent with a simple Brownian-like motion on the energy landscape. In particular, the real dynamics exhibit much longer correlation times than predicted from the heights of energy barriers alone. We will show progress towards understanding how the nematode actually explores the energy landscape of its neural network.