Mathematical Model of Synaptic Facilitation and Depression During and Following Repetitive Stimulation

Abstract

A mathematical model of facilitation and depression of postsynaptic potential amplitude (PSP) during and following repetitive stimulation is proposed. The model uses first-degree linear equations to simulate the interactions of different presynaptic physiological mechanisms that may influence and control the amount of transmitters liberated outside the nerve terminal. These mechanisms are: (1) vesicle movement toward the presynaptic membrane, (2) transmitter release, (3) vesicle recycling within the synapse, and (4) transmitter synthesis. When submitted to the same frequencies and durations of stimulation as used in a variety of electrophysiological studies of synaptic facilitation and depression, the model successfully reproduces all the variations of PSP amplitude obtained in these studies. The analysis of the internal functioning of the model during the process of simulation also allows a better understanding of the dynamics of diverse phenomena characterizing facilitation and depression during and following the administration of a tetanus. The main conclusion of this study is that both facilitation and depression may be explained in terms of the dynamics of a single synaptic system.

Key Words:

• mathematical model
• synaptic transmission
• neuromuscular junction
• synaptic depression
• synaptic facilitation