Abstract
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.
Highlights
From the swimming motions of E. coli [1] to the mobility of human populations [2], the way in which organisms move through the world profoundly influences their experience
There is a long tradition of work which tries to make this connection through analytic approximations of the equations describing the mechanics of the organism’s interaction with the outside world
It is tempting to think of these trajectories as being approximately like those of E. coli, consisting of long, relatively straight runs punctuated by tumbles, which randomly reorient the cell [18]
Summary
From the swimming motions of E. coli [1] to the mobility of human populations [2], the way in which organisms move through the world profoundly influences their experience. There is a long tradition of work which tries to make this connection through analytic approximations of the equations describing the mechanics of the organism’s interaction with the outside world This approach is perhaps best developed for swimming and flying organisms [4,5], and there are elegant results in the limit of swimming at low Reynolds number [6,7,8]. The potentially high dimensional space of shapes or movements is not sampled uniformly under natural conditions, so that one can recognize a lower dimensional manifold that fully describes the system [9,10,11,12] In these cases it is possible to ask empirically how motions on this low dimensional manifold map into movements relative to the outside world
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