From modes to movement in the behavior of Caenorhabditis elegans

Organisms move through the world by changing their shape, and here we explore the mapping from shape space to movements in the nematode Caenorhabditis elegans as it crawls on an agar plate. We characterize the statistics of the trajectories through the correlation functions of the orientation angular velocity, orientation angle and the mean-squared displacement, and we find that the loss of orientational memory has significant contributions from both abrupt, large amplitude turning events and the continuous dynamics between these events. Further, we discover long-time persistence of orientational memory in the intervals between abrupt turns. Building on recent work demonstrating that C. elegans movements are restricted to a low-dimensional shape space, we construct a map from the dynamics in this shape space to the trajectory of the worm along the agar. We use this connection to illustrate that changes in the continuous dynamics reveal subtle differences in movement strategy that occur among mutants defective in two classes of dopamine receptors.