Stochastic modeling of chemical reactions and gene regulatory networks

Living cells are characterized by small populations of key components (for example, proteins and mRNAs), which make bio-chemical reactions inherently noisy. This thesis outlines new computational techniques for quantifying noise in such bio-chemical reactions. These techniques include a novel moment closure procedure that provides the time evolution of all lower order statistical moments (for example, means and standard deviations) for the number of molecules of different species involved in the reaction. Striking features of this moment closure procedure is that it is independent of the reaction parameters (reaction rates and stoichiometry) and its accuracy can be improved by incurring more computational cost.;This thesis also proposes a new small noise approximation that provides analytical formulas relating the steady-state statistical moments to the parameters of the chemical reaction. Unlike the well-known linear noise approximation, these formulas not only predict the stochastic fluctuations about the mean but also the deviation of the mean from the solution of the corresponding chemical rate equation (i.e., deterministic model).;Using the above computational techniques this thesis investigates the noise suppression properties of various gene network motifs. One such common network motif is an auto-regulatory negative feedback loop, where the protein expressed from a gene inhibits its own expression. In this network, stochastic fluctuations in protein levels are attributed to two factors: intrinsic noise (i.e., the randomness associated with protein expression and degradation) and extrinsic noise (i.e., the noise caused by fluctuations in cellular components such as enzyme levels and gene-copy numbers). This thesis shows that although negative feedback loops attenuate both components of noise, they are much more efficient in reducing the extrinsic component of noise than the intrinsic component. It further shows that in these auto-regulatory networks, the protein noise levels are minimized at an optimal level of feedback strength. Analytical expressions for this highest level of noise suppression and the amount of feedback that achieves this minimal noise are provided. These theoretical results are shown to be consistent and explain recent experimental observations.;Finally, this thesis examines other common network motifs such as gene cascades, which can act as noise attenuators or noise magnifiers depending upon the amount of intrinsic and extrinsic noise present.