Mathematical description of regenerative potentials recorded from circular smooth muscle of guinea pig antrum

Regenerative potentials evoked by intracellular current injection in single bundles of circular smooth muscle taken from guinea pig antrum have the characteristics of the secondary regenerative component of the slow wave occurring in the same muscle layer. Such regenerative depolarizations might result from a mechanism that responds to membrane polarization with a delayed increase in the rate of production of unitary potentials detected in this tissue. To test this possibility, a two-stage reaction leading to the formation of an intracellular messenger was proposed. The first forward reaction was voltage-dependent, in the manner described by the Hodgkin-Huxley transient Na conductance formalism, allowing simulation of anode break excitation, stimulus threshold strength-duration characteristics, and refractory behavior. A conventional dose-effect relationship was proposed to describe the dependence of the mean rate of discharge of unitary potentials on messenger concentration. Unitary potentials were modeled as unitary membrane conductance modulations with an empirically derived amplitude distribution and Poisson-distributed intervals. The model reproduces a range of spontaneous and evoked membrane potential changes characteristic of antral circular muscle bundles.