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

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 × 10 × 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.