Excursions in stochastic dynamics of complex biological systems

With rapid advances in sequencing and annotation of many entire genomes, the task of understanding the associated regulatory networks became a task of large importance. Accumulation of genomic data, which include not only sequences but also information on schemes of protein-protein interactions, regulatory and metabolic networks provide us with "wiring" diagrams of possible interactions among the variety of components. While obtaining such diagrams and combining different interactions together is important for qualitative understanding of genetic regulation, this knowledge is not enough to provide us with quantitative predictions. Due to the complexity of pathway interactions and the large number of components involved, it is almost impossible to intuitively understand the behavior of cellular networks. It is also unrealistic to assume that many of the details of interactions between individual components will be obtained with great resolution. Hence, it would be worthwhile to focus on principles of general validity rather then specific details of interaction. Systems biology brings ideas from engineering disciplines such as signal processing and control theory into the modeling of biological phenomena at the level of interaction networks and pathways.; Interior of a typical prokaryotic or eukaryotic cell represents a very unusual environment from the point of view of traditional chemical engineering. Average cell is not just a simple small "chemical plant" where well mixed substances engage in different first or second order reaction processes taking place in a sequence or in parallel. An important aspect of modeling and understanding of cellular networks is the occurrence of stochastic or random events. In addition, chemical signals are emitted and captured at spatially separated points and propagation of these signals in space may induce additional stochasticity in the downstream pathways. In principle, computer simulations are ideal for studying how biochemical networks reliably process information and deal with intracellular noise on a systems level but non-classical aspects of cellular environment significantly limit the computational efficiency and even applicability of many simulation techniques extensively used by engineering community.; This thesis reexamines some existing theoretical and computational concepts of statistical mechanics and chemical kinetics of gene expression and cell signal transduction and can provide with new computational techniques capable of analyzing the heterogeneous and highly multi-scale stochastic bio-chemical systems.