Identification of synaptic interactions

This paper studies the influence exerted by the presynaptic spike train on the postsynaptic one. It applies to synaptic exploration a novel method for characterization of point-process systems (Brillinger, 1974, 1975a), and draws from it physiologically meaningful conclusions. The departure point was a large data set of action potential trains from an Aplysia network whose neurons are connected by monosynaptic inhibitory or excitatory PSP's, and either discharged spontaneously or were driven by intracellular pulses. First, a sequence of “kernels” is estimated, each with a physiological connotation relevant to synaptic transmission. The kernel independent of time — of zero-order — measures the postsynaptic rate with no presynaptic discharge. That of a single time argument — of first-order — relates to the rate effect of the average PSP. Those of two, three, or more time arguments — of second, third or higher-order — relate to interactions between two, three, or more postsynaptic potentials (e.g. to facilitation) and/or spikes (e.g. to refractoriness). Then successive models are constructed recursively and based on the kernel of zero-order, on the kernels of zero and first order, on those of zero, first and second order, and so forth, until a desired approximation is achieved. The plausibilities of each kernel estimate and of each model are evaluated separately by way of spectra and coherences. The “linear” model based upon the zero and first-order kernel was tested (after that based exclusively on the zero-order one was proven inadequate). When presynaptic discharges are very irregular and at intermediate or low rates, it provides satisfactory description and prediction, and the first-order kernel is an uncontaminated display of the rate effects of the average presynaptic spike: this constitutes the “linear” domain. When presynaptic discharges are bursty, regular or very fast, the linear model is unsatisfyctory: this is referred to as “non-linear” domain. Reasons for non-linearity lie in PSP facilitation and anti-facilitation, conversion of membrane current into firing rate, after-spike excitability oscillations, and special pacemaker interactions. The model can be extended to three-neuron networks where partial coherences exract interactions between followers, even while submitted to a common driver. The basic and ubiquitous issues of spike train description and stability were discussed. The counting and the interval statistic of spike trains provide equivalent descriptions and their current opposition is conceptually meaningless. Concomitant short-term fluctuations in spike generation intensity at preand postsynaptic levels have funciional significance beyond changes in the overall average rate or interval: they are made precise by parameters whose definition, estimation and physiological interpretation are presented here. Some stability of the experimental preparation is presupposed by investigators, but variations (e.g. from cycles or deterioration) always exist. Hence, decisions as to the preparation's evolution and as to tolerable changes must be made, and based upon pre-existing knowledge, educated guesses and practical considerations. This study provided basic knowledge of the individual synapse considered the elementary building block of the nervous system when viewed as a network of interacting nerve cells. It also contributed generally applicable mathematical techniques which were illustrated by application to relatively well studied and simple networks.