Gene regulatory networks set a second order approximation to genetics understanding, where the first order is the knowledge at the single gene activity level. With the increasing number of sequenced genomes, including humans, the time has come to investigate the interactions among myriads of genes that result in complex behaviors. These characteristics are included in the novel discipline of Systems Biology. The composition and unfolding of interactions among genes determine the activity of cells and, when is considered during development, the organogenesis. Hence the interest of building representative networks of gene expression and their time evolution, i.e. the structure as the network dynamics, for certain development processes. The complexity of this kind of problems makes imperative to analyze the problem in the field of network theory and the evolutionary dynamics of complex systems.All this has led us to investigate, in a first step, the evolutionary dynamics in generic networks. Thus, the results can be used in experimental researches in the field of Systems Biology. This research aims to decode the transformation rules governing the evolutionary dynamics in a network. To do this, a genetic algorithm has been implemented in which, starting from initial and ending network states, it is possible to determine the transformation dynamics between these states by using simple acting rules. The network description is the following: (a) The network node values in the initial and ending states can be active or inactive; (b) The network links can act as activators or repressors; (c) A set of rules is established in order to transform the initial state into the ending one; (d) Due to the low connectivity, frequently observed, in gene regulatory networks, each node will hold a maximum of three inputs with no restriction on outputs. The "chromosomes" of the genetic algorithm include two parts, one related to the node links and another related to the transformation rules.The implemented rules are based on certain genetic interactions behavior. The rules and their combinations are compound by logic conditions and set the bases to the network motifs formation, which are the building blocks of the network dynamics.The implemented algorithm is able to find appropriate dynamics in complex networks evolution among different states for several cases.
Evolutionary Dynamics of Stochastic SEIR Models with Migration and Human Awareness in Complex Networks
