Dynamics of molecular fluctuations in gene regulatory networks

Abstract

The components that are central to cellular processing are proteins, whose production is regulated by other proteins known as transcription factors. Proteins are products of genes that regulate the expression of one another, thereby forming large gene regulatory networks that perform specific cellular functions. The complex connectivity between genes of a network could result in various behaviours that are interesting. The assumption then is that tracking subnetwork behaviour helps understand the characteristics of the larger networks they are embedded in. For example, the structure of a subnetwork could say a lot about its biological role. Theoretical models of such systems and their deterministic dynamical properties have been the focus of study in the past. However, the dynamics of transcriptional control involves small numbers of molecules and result in significant fluctuations in protein and mRNA concentrations. Hence the recent shift in focus has been towards stochastic modelling approaches. Experimentally, the issues regarding average molecular numbers over a cell population draw our attention towards single-cell techniques where these fluctuations in the numbers are captured. On understanding the fluctuation properties of the smaller networks, one could study or design a combination of these networks leading to more complex regulatory networks.
The objective of this thesis is to characterize small subnetworks of genes, based on the properties of their internal fluctuations. The correlations between these intrinsic fluctuations then offer, via the fluctuation dissipation relation, the possibility of capturing the system’s response to external perturbations, and hence the nature of the regulatory activity itself. Therefore we do a stochastic analysis and derive time-dependent noise correlation functions between molecular species of the networks, and using these functions we study simple networks by varying three of its factors. One is the type of regulatory activity that is present between two genes or proteins, whose correlations we are interested in. We show that the regulatory mechanism of activation, repression either by monomers or dimers, produces different correlations. We also study the dependence of the correlations on the values of the rate constants for the ingredient processes. We demonstrate the influence of various rate constants on the protein correlations. Finally, we analyze regulatory networks of different motifs such as cascades and feedforward loops and explore the extent to which fluctuation correlations report on the network structure. The distinct correlated fluctuations could then possibly be used as signatures for identifying the regulatory mechanism present between two genes of a network. To that end, in this thesis we present analytical and numerical results on features such as the magnitudes and time delays in dynamic correlations between proteins within smaller networks, and the dependence of these features on rate constants and regulatory and network mechanisms.

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