Stochastic Modeling of Gene Regulatory Networks

Mistry, Hitesh (2007) Stochastic Modeling of Gene Regulatory Networks. Doctoral thesis, The University of Manchester.

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Abstract

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.

Item Type: Thesis (Doctoral)
Additional Information: Dr. Mistry worked with Dr. M. Muldoon and, in his first year, with Prof. J. W. Dold.
Uncontrolled Keywords: gene regulatory networks, circadian rhythm, Gillespie algorithm, stochastic differential equations, Arabidopsis thaliana
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 34 Ordinary differential equations
MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
MSC 2010, the AMS's Mathematics Subject Classification > 92 Biology and other natural sciences
Depositing User: Dr Mark Muldoon
Date Deposited: 09 May 2007
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/794

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