Genetic regulation networks: circuits, regulons and attractors

Abstract

We deal in this paper with the concept of genetic regulation network. The genes expression observed through the bio-array imaging allows the geneticist to obtain the intergenic interaction matrix W of the network. The interaction graph G associated to W presents in general interesting features like connected components, gardens of Eden, positive and negative circuits (or loops), and minimal components having 1 positive and 1 negative loop called regulons. Depending on parameters values like the connectivity coefficient K(W) and the mean inhibition weight I (W), the genetic regulation network can present several dynamical behaviours (fixed configuration, limit cycle of configurations) called attractors, when the observation time increases. We give some examples of such genetic regulation networks and analyse their dynamical properties and their biological consequences.

On the Analysis of “Simple” 2D Stochastic Cellular Automata

“…One explanation would be the absence of central nervous system implying that the aperture has to be chosen by local consensus in a rather slow process (more than five hours). than half of its neighbors (including itself) express it, and that otherwise it stops expressing it, leads to the Minority rule [4]. If cells are assembled into a two-dimensional grid, it yields 2D Minority.…”

“Immunetworks”, intersecting circuits and dynamics

“…Since then, these conjectures have been proven in different frameworks [20,21,22,23,24,25,26,27,28,29]. As for intersecting circuits, we will argue here that beyond the impact that circuits have on the dynamical behaviour of a network, the interactions of circuits via their intersections also account significantly for certain dynamical properties of networks.…”

“…Edges of G can then be turned into arcs, by choosing uniformly between one orientation, the other or both. This yields digraphs of connectivity c [26,57].…”

Structural Sensitivity of Neural and Genetic Networks

“…Note that the interaction graph contains only one connected component having at least one (here two) positive circuit of interactions (a circuit is positive if its number of inhibiting edges is even). Hence, from [16,17,18,19,20,21,22], we can expect only 2 1 = 2 fixed configurations for the network dynamics and an upper bound for this number of 2 2 . On Table 3, we see that, if the state of p27 and miRNA 159 are not fixed to particular values, then this number is in reality 2, plus one (resp.…”