  We model intracellular regulatory dynamics with threshold-type
state-dependent delay and investigate the effect of the state-dependent
diffusion time. A general model which is an extension of the classic
differential equation models with constant or zero time delays is developed to
study the stability of steady state, the occurrence and stability of periodic
oscillations in regulatory dynamics. Using the method of multiple time scales,
we compute the normal form of the general model and show that the
state-dependent diffusion time may give arise to both supercritical and
subcritical Hopf bifurcations. Numerical simulations of the prototype model of
genetic regulatory dynamics are also given to illustrate the general results.
