Analysis of a simple gene expression model
Date
2012
Authors
Chipindirwi, Simbarashe
Journal Title
Journal ISSN
Volume Title
Publisher
Lethbridge, Alta. : University of Lethbridge, Dept. of Chemistry and Biochemistry, c2012
Abstract
Gene expression is random owing to the low copy numbers of molecules in a living cell
and the best way to study it is by use of a stochastic method, specifically the chemical
master equation. The method is used here to derive analytically the invariant probability
distributions, and expressions for the moments and noise strength for a simple gene model
without feedback. Sensitivity analysis, emphasizing particularly the dependence of the
probability distributions, the moments, and noise strength is carried out using Metabolic
Control Analysis, which uses control coefficients that measure the response of observables
when parameters change. Bifurcation analysis is also carried out. The results show that the
number of mRNA molecules follows a hypergeometric probability distribution, and that
noise decreases as the number of these molecules increases. Metabolic Control Analysis
was successfully extended to genetic control mechanisms, with the obtained control coefficients
satisfying a summation theorem. The system undergoes stochastic bifurcations as
parameters change.
Description
xii, 86 leaves : ill. ; 29 cm
Keywords
Gene expression -- Research , Gene expression -- Mathematical models , Stochastic analysis , Markov processes , Dissertations, Academic