Computations that neurons perform in networks: lessons learned from a Sixteenth Century shoemaker

Abstract

Cognitive and other neural processes emerge from the interactions be- tween neurons. Major advances have been made in studying networks in which the interac- fions occur instantaneously by means ofgraded synapses (Guckenheimer and Rowat, I 997). In other networks, the interaction between neurons involves time-delayed signals (action potentials or spikes) that activate synapses on other neurons discontinuously in a pulse-like manner. These interactions can also be treated as being graded if, when appropriate, the information transmitted between neurons can be measured as the average number of spikes per unit time (Freeman, 1992); i.e., the amount ofinformation carried by individual spikes is relatively low. We refer to both ofthese types ofinteractions as "graded." There is a large armamentarium of mathematical and dynamical systems tools for studying the computa- tions that such neurons perform. There is also a complementary connection between these tools and biological experimentation. The subject of the present paper is on networks in which averaging can not be done. The generation of spikes in these neurons is significantly affècted by the temporal order of spikes sent to them by other neurons. Two input spike trains, having the saine average spikes per unit time but different temporal spacing between the spikes, produce different outputs in target neurons; i.e., the amount of information carried by individual spikes is relatively high. We refer to these networks as "spike-activated." By comparison to graded networks, there is little formal or experimental work on the general principles underlying these networks. There are many nonlinear physiological processes in spike-activated networks that need to be considered. We have begun by focusing on a single nonlinearity analysis, the threshold transition between spiking and nonspiking behavior, and use linear perturbation to examine it. The fmdings indicate that there may be an epistemological distinction be- tween graded networks and spike-activated networks. This is reminiscent of the distinction between endophysics and exophysics whose resolutions requires an external observer hav- ing information about a system and its external universe (Rössler, 1989). Interestingly, the philosophical roots of our approach and the study of dynamics more generally may be traceable to Jacob Böhme (1575-1624), a mystic and contemporary of Descartes. Böhme influenced many philosophers and scientists, and may have provided Isaac Newton the metaphorical insight into his laws of physics (Mpitsos, 1995; Yates, 1972, 1979)