Input-output relations in computer-simulated nerve cells. Influence of the statistical properties, strength, number and inter-dependence of excitatory pre-synaptic terminals.

This communication examines, in digital computer simulated networks, the input-output relation established at synaptic level. It is restricted to excitatory junctions and analyzes the changes in post-synaptic discharge which occur when the number of pre-synaptic terminals increases while the EPSP size decreases, when the statistical structure or “form” (as measured by the interspike interval mean, standard deviation, histogram and by the autocorrelogram) of the spike train in each pre-synaptic fiber changes, and/or when the interdependence between pre-synaptic fibers varies from complete independence to strong dependence. 1Independent Pre-synaptic Terminals. When the number of pre-synaptic terminals increases and the EPSP size decreases proportionally (while the input form remains constant), the post-synaptic interspike interval mean increases slightly, the standard deviation decreases markedly, the histogram becomes sharp and narrow and the autocorrelogram becomes periodic. When, on the other hand, the pre-synaptic form varies (while the number of terminals and the EPSP size remain constant), the effect upon the post-synaptio output depends upon the given number of terminals and EPSP size. If terminals are few and EPSP's large, the output varies with the pre-synaptic form. The post-synaptic coefficient of variation is linearly related to the pre-synaptic coefficient of variation, the slope decreasing as the number of inputs increases. If terminals are numerous and weak, the pre-synaptic form ceases to be influential and the post-synaptic cell generates the same output regardless of the detailed structure of the corresponding input. The output common to any combination of independent weak input forms is a very regular train of evenly spaced spikes. (This conclusion is valid unless pre-synaptic terminals fire at extremely low rates.) Such results are mathematically predictable in a simple and realistic model of membrane potential and threshold dynamics (see Appendix). As the EPSP size increases, all other variables being equal, the post-synaptic interval mean decreases monotonically. The decrease is smooth or in steps depending on whether the pre-synaptic form is Poisson or pacemaker, respectively. Post-synaptic spikes are effectively blocked by relatively small numbers of inhibitory terminals. 2Dependent Pre-synaptic Terminals. When there is a physiological amount of interdependence between the presynaptic terminals that impinge upon the post-synaptic cell, the activity of the latter is a function of the statistical form of the input channels, even when the latter are numerous and weak. This happens when interdependence involves only a proportion of all terminals or only the terminals within separate and independent groups. In order to understand the transactions that take place in the nervous system, it is necessary to identify the presynaptic statistics that influence the corresponding post-synaptic discharge. When pre-synaptic terminals produce large PSP's their influence is dominant and exerted by way of the precise statistical form of the discharge. When terminals produce small PSP's their influence is contingent on their degree of interdependence. If they are uncorrelated, they act exclusively by way of their mean rates and provide a smooth adjustment of the post-synaptic membrane potential and firing rate. If terminals are correlated, they act by way of several statistical features and assume a dominant role that determines a precise relation between pre-synaptic timing and post-synaptic firing. The degree of inter-terminal correlation is thus a functionally significant variable.