Model Checking Tap Withdrawal in C. Elegans
We present what we believe to be the first formal verification of a biologically realistic (nonlinear ODE) model of a neural circuit in a multicellular organism: Tap Withdrawal (TW) in C. Elegans, the common roundworm. TW is a reflexive behavior exhibited by C. Elegans in response to vibrating the surface on which it is moving; the neural circuit underlying this response is the subject of this investigation. Specially, we perform reach-tube-based reachability analysis on the TW circuit model of Wicks et al. (1996) to estimate key model parameters. Underlying our approach is the use of Fan and Mitra’s recently developed technique for automatically computing local discrepancy (convergence and divergence rates) of general nonlinear systems.
The results we obtain are a significant extension of those of Wicks et al. (1996), who equip their model with fixed parameter values that reproduce the predominant TW response they observed experimentally in a population of 590 worms. In contrast, our techniques allow us to much more fully explore the model’s parameter space, identifying in the process the parameter ranges responsible for the predominant behavior as well as the non-dominant ones. The verification framework we developed to conduct this analysis is model-agnostic, and can thus be re-used on other complex nonlinear systems.
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