Mathematical models of synaptic plasticity: I. Posttetanic potentiation

A mathematical model of post-tetanic potentiation is proposed. The model uses differential equations and is based upon physiological postulates of the electrical, metabolic, and neuroendocrine activities that are related to synaptic connectivity. These activities may modify some important parameters in synaptic function. In the proposed model these parameters are restricted to the presynapse in view of the physiological evidence indicating that posttetanic potentiation is probably due to presynaptic mechanisms. The model takes into consideration the size of the transmitter pool available for release, the mobilization of transmitter from and to this pool, and the fraction of transmitter released. Based upon the above postulates, we have simulated different phases of the phenomenon of posttetanic potentiation, and we have presented the results of several preparations in which this event has been studied. This work represents a successful attempt to reproduce the dynamics of posttetanic potentiation based upon physiological results with a mathematical model.