Biomechanical analysis of gait adaptation in the nematode Caenorhabditis elegans

Abstract

To navigate different environments, an animal must be able to adapt its locomotory gait to its physical surroundings. The nematode Caenorhabditis elegans, between swimming in water and crawling on surfaces, adapts its locomotory gait to surroundings that impose approximately 10,000-fold differences in mechanical resistance. Here we investigate this feat by studying the undulatory movements of C. elegans in Newtonian fluids spanning nearly five orders of magnitude in viscosity. In these fluids, the worm undulatory gait varies continuously with changes in external load: As load increases, both wavelength and frequency of undulation decrease. We also quantify the internal viscoelastic properties of the worm's body and their role in locomotory dynamics. We incorporate muscle activity, internal load, and external load into a biomechanical model of locomotion and show that (i) muscle power is nearly constant across changes in locomotory gait, and (ii) the onset of gait adaptation occurs as external load becomes comparable to internal load. During the swimming gait, which is evoked by small external loads, muscle power is primarily devoted to bending the worm's elastic body. During the crawling gait, evoked by large external loads, comparable muscle power is used to drive the external load and the elastic body. Our results suggest that C. elegans locomotory gait continuously adapts to external mechanical load in order to maintain propulsive thrust.

Fig. 1.

The kinematics of an undulating worm. (A) Diagram of a worm moving in a viscous fluid. Body coordinate s describes path length along worm body, starting from the head. Posture y(s,t) describes lateral displacement of worm body centerline. θ_a describes angle of each body component with respect to direction of movement. (B) Worm body is modeled as a rod with elasticity (represented by spring), internal damping (represented by dashpot), and active muscular torque M(s,t).

Fig. 2.

Modulation of C. elegans locomotion. Dark field images and time-dependent curvature patterns of adult worms (A) swimming in NGM buffer with viscosity 1 mPas, (B) in dextran solutions with viscosity 980 mPa·s, (C) in dextran solution with viscosity 28,000 mPa·s, (D) crawling on 2% agarose surface. The worm head is to the left in all images. Body curvature as a function of time (in seconds) and normalized body coordinate (varying from 0 at the head to 1 at the tail). Body curvature is represented using the nondimensional product of curvature (the inverse of radius of curvature) and body length.

Fig. 3.

Locomotory parameters. (A) Mean wavelength of undulation scaled by worm body length L in different viscous solutions; (B) mean undulatory frequency; (C) mean curvature amplitude of undulation scaled by reciprocal of body length; (D) peak angle of attack, in degrees.

Fig. 4.

Measurements of internal elasticity and viscosity. (A) Images from a video sequence in which worm position decays from deformed posture in NGM medium (viscosity 1 mPa·s). (B) Normalized worm bending angle for three viscosities. Lines show least-squares exponential fit for each viscosity. (C) Decay time scaled with fourth power of length of worm outside pipette, as function of viscosity. Data represents 15 decays from a total of five worms. Line: least-squares linear fit y = Mη + B; fit parameter estimates M = 5.71 ± 0.65, B = 4.82 ± 7.13 in the units of the figure.

Fig. 5.

(A) Estimated external viscous power, peak internal elastic power, and peak total power as a function of viscosity. (B) Maximum torque as a function of viscosity, from Eq. 3. (C) Phase difference between torque and curvature as a function of viscosity, from Eq. 7.