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