On the mathematical integration of the nervous tissue based on the S-propagator formalism: II. Numerical simulations for molecular-dependent activity.

In a previous article (G. A. Chauvet, 2002), presenting a theoretical approach for integrating physiological functions in nervous tissue, we showed that a specific hierarchical representation, incorporating the novel concepts of non-symmetry and non-locality, and an appropriate formalism (the S-propagator formalism) could provide a good description of a living system in general, and the nervous system in particular. We now show that, in the framework of this theory, in spite of the complexity inherent to nervous tissue and the great number of elementary mechanisms involved, the numerical resolution of the global non-local system allows us to envisage simulations that would otherwise be impossible to realize. Here, the study is limited to one physiological function, i.e., the spatiotemporal variation of membrane potential in neuronal tissue. We demonstrate that the role of the kinetic constants at the molecular level is in agreement with the observed activity of the neuronal network. The method also reveals the critical role of the maximum density of synapses along the dendritic tree in the behavior of the network. This illustrates the great advantage of the theoretical approach in studying separately any other complementary coupled function without having to modify the computational methods used here. The application of this method to the spatiotemporal variation of synaptic efficacy, which is the basis of the learning and memory function, will be treated in a forthcoming paper.