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Modular Gene Dynamics and Network Theory at Mesoscopic Scale

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arXiv ID: 0901.2870
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Complex dynamical systems are often modeled as networks, with nodes representing dynamical units which interact through the network's links. Gene regulatory networks, responsible for the production of proteins inside a cell, are an example of system that can be described as a network of interacting genes. The behavior of a complex dynamical system is characterized by cooperativity of its units at various scales, leading to emergent dynamics which is related to the system's function. Among the key problems concerning complex systems is the issue of stability of their functioning, in relation to different internal and external interaction parameters. In this Thesis we study two-dimensional chaotic maps coupled through non-directed networks with different topologies. We use a non-symplectic coupling which involves a time delay in the interaction among the maps. We test the stability of network topologies through investigation of their collective motion, done by analyzing the departures from chaotic nature of the isolated units. The study is done on two network scales: (a) full-size networks (a computer generated scalefree tree and a tree with addition of cliques); (b) tree's characteristic sub-graph 4-star, as a tree's typical dynamical motif which captures its topology in smallest possible number of nodes and is suitable for time-delayed interaction. We study the dynamical relationship between these two network structures, examining the emergence of cooperativity on a large scale (trees) as a consequence of mesoscale dynamical patterns exhibited by the 4-star. (FULL ABSTRACT INSIDE THE TEXT)


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