The shallow turn of a worm

When crawling on a solid surface, the nematode Caenorhabditis elegans (C. elegans) moves forward by propagating sinusoidal dorso-ventral retrograde contraction waves. A uniform propagating wave leads to motion that undulates about a straight line. When C. elegans turns as it forages or navigates its environment, it uses several different strategies of reorientation. These modes include the well-known omega turn, in which the worm makes a sharp angle turn forming an Omega-shape, and the reversal, in which the worm draws itself backwards. In these two modes of reorientation, C. elegans strongly disrupts its propagating sinusoidal wave, either in form or in direction, leading to abrupt directional change. However, a third mode of reorientation, the shallow turn, involves a gentler disruption of the locomotory gait. Analyzing the statistics of locomotion suggests that the shallow turn is by far the most frequent reorienting maneuver in navigation in the absence of food. We show that the worm executes a shallow turn by modulating the amplitude and wavelength of its curvature during forward movement, and provide a minimal description of the process using a three-parameter mathematical model. The results of our study augment the understanding of how these parameters are controlled at the neuromotor circuit level.