Mathematical formalisms based on approximated kinetic representations for modeling genetic and metabolic pathways

Abstract

There is a renewed interest in obtaining a systemic understanding of metabolism, gene expression and signal transduction processes, driven by the recent research focus on Systems Biology. From a biotechnological point of view, such a systemic understanding of how a biological system is designed to work can facilitate the rational manipulation of specific pathways in different cell types to achieve specific goals. Due to the intrinsic complexity of biological systems, mathematical models are a central tool for understanding and predicting the integrative behavior of those systems. Particularly, models are essential for a rational development of biotechnological applications and in understanding system’s design from an evolutionary point of view. Mathematical models can be obtained using many different strategies. In each case, their utility will depend upon the properties of the mathematical representation and on the possibility of obtaining meaningful parameters from available data. In practice, there are several issues at stake when one has to decide which mathematical model is more appropriate for the study of a given problem. First, one needs a model that can represent the aspects of the system one wishes to study. Second, one must choose a mathematical only qualitative information about the dynamic of the system. Currently, SC, (log)linear and Lin-log models have less specific methods available to estimate parameter values than the power- law formalism. Additionally, the SC formalism uses at least one more parameter per equation than the other described formalisms, which implies that more information is needed to parameterize SC models. The upside is that, if such information is available, SC models are likely to have a higher range of numerical accuracy. © 2008 Taylor & Francis Group, LLC.