Model Checking Tap Withdrawal in C. Elegans

TL;DR

This paper applies formal verification and reachability analysis to a nonlinear ODE model of the Tap Withdrawal neural circuit in C. Elegans, providing insights into parameter ranges for different behaviors.

Contribution

It introduces the first formal verification of a biologically realistic neural circuit model in C. Elegans using reachability analysis and discrepancy computation techniques.

Findings

Parameter ranges for different behaviors identified

Results agree with experimental data

Method characterizes behavior variability

Abstract

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 \emph{C. Elegans}, the common roundworm. TW is a reflexive behavior exhibited by \emph{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. Specifically, we perform reachability analysis on the TW circuit model of Wicks et al. (1996), which enables us to estimate key circuit 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. We show that the results we obtain are in agreement with the experimental results of Wicks et al. (1995). As opposed to the fixed parameters found in most biological models, which can only produce the predominant behavior, our techniques characterize ranges of parameters that produce (and do not produce) all three observed behaviors: reversal of movement, acceleration, and lack of response.