Mathematical modeling for evolution of heterogeneous modules in the brain

Abstract

Modular architecture has been found in most cortical areas of mammalian brains, but little is known about its evolutionary origin. It has been proposed by several researchers that maximizing information transmission among subsystems can be used as a principle for understanding the development of complex brain networks. In this paper, we study how heterogeneous modules develop in coupled-map networks via a genetic algorithm, where selection is based on maximizing bidirectional information transmission. Two functionally differentiated modules evolved from two homogeneous systems with random couplings, which are associated with symmetry breaking of intrasystem and intersystem couplings. By exploring the parameter space of the network around the optimal parameter values, it was found that the optimum network exists near transition points, at which the incoherent state loses its stability and an extremely slow oscillatory motion emerges.

Keywords: Coupled-oscillator; Evolution; Information flow; Modularity; Symmetry breaking; Transfer entropy.