Stochastic processes in biological systems : selected problems

Abstract

Majority of biological processes can not be described deterministically. Multple levels of regulation contribute to the noise in the observable properties of the cells: fluctuations are ubiquitous in biological networks and in their spatial organization. In this thesis we consider several examples from three broad categories. Firstly, we study two problems that highlight connection between network topologies and manifestations of stochastic fluctuation in networks of chemical reactions that are meant to represent biological networks in the coarse-grained way. We show that specific network structure can have profound consequences on the steady-state probability distribution function of corresponding chemical system. Secondly, we study effects of spatial organization of the proteins on the membrane surface of T-cells on the initialization of signal propagation. We show that coordinated diffusion of proteins is critical for signal-enhancing properties of co-receptors CD4 and CD8. In third part of the thesis we attempt to reconstruct network topology based on incomplete information about specific interactions between the network nodes and some information about "macroscopic" behavior of the system governed by the network in question. The matter of the Part III, however, is one scale larger than the corresponding objects considered in Part II and I. Specifically, we consider transformations of cells between different cell types and molecular origins that underlie cell transformations (such as differentiation/de-differentiation). Our model suggests specific structure of the master-regulatory network of genes and makes testable predictions.