| The thesis investigates both mechanics and neurobiology of undulatory locomotion. Theoretically, working with Prof L. Mahadevan, I built a biomechanical model to study undulatory locomotion of slender animals such as snakes and worms. Experimentally, working with Prof Sharad Ramanathan, I developed novel optical techniques to map neural circuits in the nematode Caenorhabditis elegans.;Working with Prof Mahadevan, I first analyzed the lateral undulatory locomotion of slender organisms "swimming" on land. The governing equations for the planar lateral undulation of a thin filament interacting frictionally with its environment lead to an incomplete system. Closures accounting for the forces generated by internal muscles and the interaction of the filament with its environment lead to a nonlinear boundary value problem, which we solve using a combination of analytical and numerical methods. We find that the primary determinant of the shape of the organism is its interaction with the external environment, whereas the speed of the organism is determined primarily by internal muscular forces, consistent with prior qualitative observations. The model also allows us to pose and solve a variety of optimization problems such as those associated with maximum speed and mechanical efficiency, thus defining the performance envelope of this mode of locomotion.;Working with Prof. Ramanathan, I combined in vivo optical stimulation using light sensitive channels (ChR2, NpHR) with simultaneous calcium imaging using genetically encoded calcium indicator (GCaMP) to map neural circuits in C. elegans. Whereas most of the synaptic connections in C. elegans have been identified by electron microscopy serial reconstructions, functional connections have been inferred between only a few neurons through combinations of electrophysiology, cell ablation, in vivo calcium imaging and genetic analysis. Here we developed novel optical techniques to efficiently map functional connections. We analyzed the connections from the ASH sensory neurons and RIM interneurons to the command interneurons AVA and AVD. Stimulation of ASH or RIM using ChR2 resulted in activation of AVA neurons, evoking an avoidance behavior. Our results demonstrate that we can excite specific neurons expressing ChR2 while simultaneously monitoring GCaMP fluorescence in several other neurons, making it possible to rapidly decipher neural circuits in C. elegans. |
