Stochastic formulation for a partial neural circuit of C. elegans

We present a stochastic formulation for a partial neural circuit of Caenorhabditis elegans. This study is concerned with how to reduce the degree of freedom in a large neural circuit. In the presented formulation, neurons in the whole neural circuit are divided into two complementary groups. One is the neurons which are mainly associated with a certain behavior, and the other is the remaining neurons of C. elegans. In an ordinary study on a partial neural circuit, the influence of the latter (the remaining neurons) on the former (the associated neurons) is completely neglected. In the presented formulation, however, the influence is expressed by a stochastic variable. The structure of the ensemble for the stochastic variable is appropriately evaluated by the neural connectivity of C. elegans since the neural connectivity of C. elegans has been completely determined. In this way, the degree of freedom is effectively reduced. We apply the presented formulation to determine the synaptic signs in the touch sensitivity circuit of C. elegans. The synaptic signs are determined to satisfy the locomotory behaviors in C. elegans. We find that the influence of the remaining neurons on the touch sensitivity circuit is important to determine the synaptic signs.