A computational model of insect campaniform sensilla predicts encoding of forces during walking

Control of forces is essential in both animals and walking machines. Insects measure forces as strains in their exoskeletons via campaniform sensilla (CS). Deformations of cuticular caps embedded in the exoskeleton excite afferents that project to the central nervous system. CS afferent firing frequency (i.e. 'discharge') is highly dynamic, correlating with the rate of change of the force. Discharges adapt over time to tonic forces and exhibit hysteresis during cyclic loading.In this study we characterized a phenomenological model that predicts CS discharge, in which discharge is proportional to the instantaneous stimulus force relative to an adaptive variable. In contrast to previous studies of sensory adaptation, our model (1) is nonlinear and (2) reproduces the characteristic power-law adaptation with first order dynamics only (i.e. no 'fractional derivatives' are required to explain dynamics). We solve the response of the system analytically in multiple cases and use these solutions to derive the dynamics of the adaptive variable. We show that the model can reproduce responses of insect CS to many different force stimuli after being tuned to reproduce only one response, suggesting that the model captures the underlying dynamics of the system. We show that adaptation to tonic forces, rate-sensitivity, and hysteresis are different manifestations of the same underlying mechanism: the adaptive variable. We tune the model to replicate the dynamics of three different CS groups from two insects (cockroach and stick insect), demonstrating that it is generalizable. We also invert the model to estimate the stimulus force given the discharge recording from the animal. We discuss the adaptive neural and mechanical processes that the model may mimic and the model's use for understanding the role of load feedback in insect motor control. A preliminary model and results were previously published in the proceedings of the Conference on Biohybrid and Biomimetic Systems.