Locomotory state in C. elegans is regulated by a network of forward and reverse command neurons in two reciprocally connected pools, but how this network functions is poorly understood. We propose a model in which the network acts as a stochastic system. The model arises from three simple assumptions: (1) Forward neurons act as a single unit F and reverse neurons act as a single unit R. (2) Unit activation switches stochastically between two activation states: 0 and 1, corresponding to off and on, respectively. (3) The probability of a 0-1 transition is a sigmoidal function of synaptic input, i.e. the weighted sum of presynaptic activation states. Accordingly, there are four possible states of the network: (F,R) = {(0,0), (0,1), (1,0) and (1,1)}. Previous neuronal ablations suggest that the first three correspond, respectively, to locomotory pauses, forward locomotion, and reverse locomotion; we propose that the state (1,1) also corresponds to pauses, as joint activation of forward and reverse motor systems is likely to cancel out. The kinetics of the network are fully described by eight coefficients -- the rate constants K for transitions between pairs of states that differ in the activation level of one (but not both) units. Synaptic interactions in the model are fully described by just six coefficients -- the synaptic weights W, including the four possible connections among and between F and R neurons (Wfr, Wrf, Wff, Wrr), and the two connections from outside the command network (Wxf, Wxr), including sensory inputs. By Assumption 3, simple algebraic relationships can be derived such that given K, W can be computed. Thus, it is theoretically possible to infer command network connectivity from the locomotion behavior. To test such inferences, we reasoned that in strains with chronic depolarization of command neurons, such as
nmr-1::GLR-1(A/T), Wxf and Wxr should be more positive than in wild-type worms whereas, in chronically hyperpolarized strains such as
eat-4, they should be less positive. Accordingly, using a maximum likelihood approach, we obtained K for spontaneous locomotion in wild-type worms and several depolarized and hyperpolarized strains and computed W''s for each strain. As expected, Wxf and Wxr were shifted positively in depolarizing strains and negatively in hyperpolarizing strains. We conclude that the stochastic switch model provides an intuitive yet predictive representation of command neuron function. NIH MH51383.