Systems Biology, BST & S-systems
BST is an acronym for Biochemical Systems Theory, one of the established formalisms in a scientific field now called Systems Biology. This theory was proposed in the late 1960 by Michael A. Savageau and has since been elaborated in several hundred scientific treatises, chapters, proceedings articles and books. Initially targeting biochemical systems, BST has since been applied to biomedical topics ranging from generic design patterns in gene regulation and prokaryotic metabolism to questions in forestry, immunology, and health risk assessment, to name but a few. Beyond biology, BST has led to insights in metabolic engineering, control theory, and computational statistics.
The two key ingredients of BST are the the description of biological and other phenomena as systems of ordinary differential equations and the representation of the processes governing these systems as products of power-law functions. S-systems constitute one class of BST models, in which each equation has a particularly simple format: The change in a system variables is given as one set of influxes minus one set of effluxes, and each set is collectively written as one product of power-law functions. This form has very interesting mathematical properties. Foremost, it is easy to compute steady states. This feature is very consequential for a variety of systes analyses and facilitates a spectrum of diagnostic and exploratory methods and techniques. For instance, it permits the optimization of very complex systems in a straightforward manner, a fact that is useful in metabolic engineering, where the goal is to steer a microorganism toward producing some desired organic compound.
Generic Model Description and Two Main Types of BST Representations
While BST models may seem very restricted by their exclusive reliance on power-law functions, this perception is not true: Two decades ago we have shown with mathematical rigor that virtually any nonlinearity that can be expressed as a set of ordinary differential equations can also be expressed as an S-system model or as any of the other variants within BST.
To learn more about S-systems and BST, click here or here or check out the introductory text Computational Analysis of Biochemical Systems. A Practical Guide for Biochemists and Molecular Biologists (Cambridge University Press, 2000) by E.O. Voit.