Computational modeling of synchronization process of the circadian timing system of mammals

Abstract

This paper presents a model for the circadian temporization system of mammals which associates the synchronization dynamics of coupling oscillators to a set of equations able to reproduce the synaptic characteristics of somatodendritic membrane of neurons. The circadian timing system is organized in a way to receive information from the external and internal environments, and its function is the timing organization of physiological and behavioral processes in a circadian pattern. Circadian timing system in mammals is constituted by a group of structures which includes the suprachiasmatic nucleus, the intergeniculate leaflet and the pineal gland. In suprachiasmatic nucleus are found neuron groups working as a biological pacemaker-the so-called biological master clock. By means of numerical simulations using the Kuramoto model, we simulated the dynamics behavior of the biological pacemaker. For this we used a set of 1,000 coupled oscillators with long-range coupling, which were distributed on a 10 x 10 x 10 spherical lattice, and a new method to estimate the order parameter, which characterizes the degree of synchronization of oscillator system. Our model has been able to produce frequency responses in accordance with physiological patterns, and to reproduce two fundamental characteristics of biological rhythms: the endogenous generation and synchronization to the light-dark cycle.

Behavior of a Model for Feedback-Controlled Reverberating Circuit and Immediate Memory Function

“…Considering that, in an excitatory synapse, the neurotransmitter-receptor interaction derived from a presynaptic action potential causes an excitatory or depolarizing postsynaptic effect (E) proportional to the postsynaptic membrane potential, one can write that dE/dt = −E/τ E , where τ E is the time constant. The solution of this equation for n action potentials arriving at the synapse j in the interval t i − t 0 is given by [4,8]…”

“…Mathematical and computer modeling has been widely employed in the biological sciences field, with important application in Neuroscience. In this way, experimental and theoretical hypotheses can be combined into one single model and tested [4,7,8,23,24,26].…”

Applying Graph Theory and Mathematical-Computational Modelling to Study a Neurophysiological Circuit

“…Much knowledge has been obtained by modelling neurophysiological circuits using experimental data in the simulations to observe the behavior and limitations of the models [9] [11] [14] [15] [16].…”