Mathematical Systems Biology: Genomic Cybernetics

The purpose of mathematical systems biology is to investigate genome expression and regulation through mathematical modeling and systems theory in particular. The principal idea is to treat gene expression and regulatory mechanisms of the cell cycle, morphological development, cell differentiation and environmental responses as controlled dynamic systems. Although it is common knowledge that cellular systems are dynamic and regulated processes, to this date they are not investigated and represented as such. The kinds of experimental techniques, which have been available in molecular biology, largely determined the material reductionism, which describes gene expression by means of molecular characterization. Instead of trying to identify genes as causal agents for some function, role, or change in phenotype we ought to relate these observations to sequences of events. In other words, in systems biology, instead of looking for a gene that is the reason, explanation or cause of some phenomenon we seek an explanation in the dynamics (sequences of events ordered by time) that led to it. In mathematical systems biology we are aiming at developing a systems theory for the dynamics of a cell. In this text we first define the concept of complexity in the context of gene expression and regulation before we discuss the challenges and problems in developing mathematical models of cellular dynamics, and provide an example to illustrate systems biology, its challenges and perspectives of this emerging area of research.