Mathematical theory of chemical synaptic transmission

Abstract

Mathematical theory of chemical synaptic transmission is suggested in which the modes of operation of chemical synapses are given as consequencies of some fundamental theoretical principles presented in the form of systems of quantum and macroscopic postulates. These postulates establish transmitter transfer rules between 3 component parts -- cytoplasmic, vesicular and external pools of neurotransmitter. The main features of the transfers are determined by special properties of the dividing membranes (synaptic and vesicle) which show high selectivity towards the direction of the transmitter quantum transfer. The formulation of a previously unknown effect of transmitter quantum transfer from the vesicular pool into the cytoplasmic one is introduced: it is postulated that each arriving presynaptic impulse not only releases a constant fraction of the current contents of the cytoplasmic pool into the synaptic cleft (external pool), but also realizes practically simultaneous transmitter transfer from the vesicular pool into the cytoplasmic one. Zone structure of the vesicular pool is postulated. In accordance with basic equations of the theory a nonlinear control system (dynamic synaptic modulator -- DYSYM) of transmitter release from the terminal is constructed. Depending on the parameters relation two types of synapses are classified -- those with rapid and slow demobilization. Analytical dependencies of the transmitter pools sizes on the stimulation frequency are introduced. By fitting the frequency dependencies to the empirical data model parameters are determined corresponding to a set of experimentally studied synaptic junctions. Different aspects of the chemical synapse behaviour under the influence of presynaptic stimulation are simulated.