Stochastic Modeling of Gene Regulatory Networks

Gene Regulatory Networks (GRNs) describe how chemical species within a cell interact with one another, thereby governing the rates at which key genes are expressed. This thesis is concerned with modeling a particular GRN, Arabidopsis thaliana Circadian Clock, by considering three different approaches; discrete stochastic, continuous stochastic and parameter variation. By considering these different methods we will see if the desired behavior required from our network is robust to biological noise. Through employing stochastic approaches we found the GRN under question is robust to biological noise to a point; the results of our study led to a couple of interesting questions to people within the field. When the number of molecules involved in the reactions were reduced sufficiently the biological noise in the system destroyed the desired circadian rhythm. To the biologists we would ask how low are the molecule numbers involved in such reactions and to the modelers how appropriate is it to use Michaelis-Menten type kinetics for low molecule numbers.