A Simple Mathematical Model of Second-Messenger Mediated Slow Excitatory Postsynaptic Potentials

We have developed a novel and simple mathematical model of a slow excitatory postsynaptic potential (EPSP) based on an abstraction of the processes of activation, inactivation, and summation of a cAMP, protein kinase A (PKA)-dependent second-messenger cascade. The model describes the activation of receptors, G-proteins, and production of cAMP as the first stage and uses first-order, non-rate-limited kinetics. The second stage corresponds to the release of active, PKA catalytic subunit and can use first- or higher-order kinetics. The third stage represents simple phosphorylation of ion channels and is limited by the number of channels available. The decay of each stage is based on first-order, mass-action kinetics. These equations and some variations were solved numerically and values of the parameters were determined by fitting to a variety of experimental data from myenteric neurons of the guinea-pig ileum. The model produced a slow EPSP with a nonlinear stimulus-response relationship that resulted from the underlying kinetics of the signaling cascade. This system of equations is suitable for incorporation into a large-scale computer simulation, and the methodology should be generalizable to other pathways.