Modelo energético auto-organizado para a atividade coletiva em tecidos de animais simples

Abstract

Since the end of the twentieth century and the beginning of the twenty-first century, many scientists have become interested in the study of the dynamics of complex systems and in critical systems. This class of non-linear systems has properties described by power laws. Critical phenomena is characteristics of complex systems that has properties not well described by the laws of thermodynamics. The present work presents a self-organized critical (SOC) energy model, created to explain spontaneous collective activity in a given animal tissue without the necessity of a muscular control or central nervous system. This prototype model introduces a cuboid epithelial tissue formed by a single layer of cells, such as the internal digestive cavity of some primitive animals. The tissue is composed of cells that absorb nutrients and store energy, with probability p, to participate in a collective tissue motion. Each cell can be in two states: the high-energy state able to become active or low-metabolic and at rest. Any cell can be activated spontaneously, with a very low probability, and starts a collective activity with its neighbors that share enough energy. The tissue cells that participate in the oscillation consume all their energy. It is observed a power law relation, P(s) α sγ, for the probability of having a collective motion with s cells. The construction of this model is analogous to the Forest Fire SOC model. This approach naturally produces a critical condition for the oscillation of the animal tissue, in addition, it explains self-sustaining activities in a living animal tissue without feedback control.