Statistical analysis and reverse engineering of large biochemical networks

Many important problems in biology and medicine, such as diseases regarding the immune system, like AIDS, sepsis, and cancer, are hard to analyze using regular methods, mainly due to the large size of such systems. There are many difficulties involved with system-level approaches in biology: (1) Obtaining complete and accurate data on such a large scale; and construct an accurate model based on incomplete or inaccurate data is extremely difficult. (2) There is a lack of mathematical tools for analysis of such models. (3) Interpreting mathematical results of analysis into useful knowledge is a challenging task.; In this thesis, we address some of these questions. Motivated by the recent experimental results regarding the existence of universal statistical properties in living systems, and the success of similar approaches in other fields, we take a statistical approach in analyzing large biochemical networks. We construct artificial biochemical reaction networks and study the temporal evolution of the Abundance Distribution Function (ADF). Surprisingly, ADF is insensitive to many dramatic changes in the reaction network, and our simulation results agree with experimental results. Unfortunately we found that there is no Fokker-Planck type PDE with time independent coefficients, which govern the evolution of ADF.; We further present an algorithm that automatically constructs a model of a biological system using experimental results. The experimental results are the temporal response of the system to perturbations, such as creating a change in the concentration of a specific molecule in the system. We test this algorithm using large size artificial reaction networks, and in most cases, we are able to recover %85 of the system accurately.; We also investigate the relation between system response to perturbations, and the connectivity of the network. Real life biochemical systems have scale-free connectivity distribution. However, a random graph has a normal connectivity distribution by central limit theorem. We find that the response to perturbations is very local in systems with normal connectivity; however the response is global and system wide in systems with scale-free connectivity.