Mathematical model of competence regulation circuit

Abstract

Gene expression regulatory networks are molecular networks which describe interactions among gene products in terms of biochemical reactions. This helps us understand the molecular mechanisms underlying important biological processes as well as cell functioning as a whole. For instance, the phenomenon of bacterial competence, whereby a bacterium enters a transiently differentiated state, incorporating DNA fragments from its environment into its genome, has been studied with the help of such gene regulatory circuits (Suel et al., 2006; Maamar and Dubnau, 2005). As a result, a genetic circuit has been taken into account in order to describe the transition from a vegetative state to a transient state of competence and vice versa. In this work, we are going to study a genetic circuit presented by Suel et al. (2007) to describe this dynamical behaviour. The authors introduce model reduction techniques to study the behaviour of stochastic chemical system of X species by means of an adiabatic two dimensional model. While the adiabatic model helps us understand about the dynamics near the steady state, it gives an incorrect description of the time-scales of the competent state. For this reason, it is necessary to build up a model which better describes the system realistically. In the thesis, I propose an approximate two-dimensional model of the full high-dimensional system and from that, the dynamics of the system can be simulated more accurately compared to that of Suel et al. (2007). I then show how to put the noise back into the approximate model to be able come up with a stochastic model which can mathematically describe the dynamical behaviour of the original high dimensional system. I also found out that the evolution of the system is not well approximated by a Langevin process. This leads to a gap between the real behavior which is described by Gillespie's stochastic simulation and the Langevin approximation. To overcome this, I have fixed the stochastic Langevin model by incorporating empirically tunable noise into the model so as to obtain a similar behaviour as observed in the original system. I also introduce the chemical Fokker-Planck equation aimed to estimate the probability density function of species concentrations which are involved in the biochemical system.

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