Biochemical systems theory
is a mathematical modelling
framework for biochemical systems
, based on ordinary differential equations
(ODE), in which biochemical processes
are represented using power-law
expansions in the variables of the system
. This framework, which became known as Biochemical Systems Theory, is developed since the 1960s
by Michael Savageau and other groups for systems analysis
of biochemical processes
. They regard this as a general theory
of metabolic control
, which includes both metabolic control analysis and flux-oriented theory as special cases.
The dynamics of a specie is represented by a differential equation with the structure:
where Xi represents one of the nd variables of the model (metabolite concentrations, protein concentrations or levels of gene expression). j represents the nf biochemical processes affecting the dynamics of the specie. On the other hand, ij (stoichiometric coefficient), j (rate constants) and fik (kinetic orders) are two different kinds of parameters defining the dynamics of the system.
The principal difference of power-law models with respect to other ODE models used in biochemical systems is that the kinetic orders can be non-integer numbers. A kinetic order can have even negative value when inhibition is modelled. In this way, power-law models have a higher flexibility to reproduce the non-linearity of biochemical systems.
Models using power-law expansions have been used during the last 35 years to model and analyse several kinds of biochemical systems including metabolic networks, genetic networks and recently in cell signalling.
- M.A. Savageau, Biochemical systems analysis: a study of function and design in molecular biology, Reading, MA, Addison–Wesley, 1976.
- E.O. Voit (ed), Canonical Nonlinear Modeling. S-System Approach to Understanding Complexity, Van Nostrand Reinhold, NY, 1991.
- E.O. Voit, Computational Analysis of Biochemical Systems. A Practical Guide for Biochemists and Molecular Biologists, Cambridge University Press, Cambridge, U.K., 2000.
- N.V. Torres and E.O. Voit, Pathway Analysis and Optimization in Metabolic Engineering, Cambridge University Press, Cambridge, U.K., 2002.
- M.A. Savageau, Biochemical systems analysis: I. Some mathematical properties of the rate law for the component enzymatic reactions in: J. Theor. Biol. 25, pp. 365-369, 1969.
- M.A. Savageau, Development of fractal kinetic theory for enzyme-catalysed reactions and implications for the design of biochemical pathways in: Biosystems 47(1-2), pp. 9-36, 1998.
- M.R. Atkinson et al, Design of gene circuits using power-law models, in: Cell 113, pp. 597–607, 2003.
- F. Alvarez-Vasquez et al, Simulation and validation of modelled sphingolipid metabolism in Saccharomyces cerevisiae, Nature 27, pp. 433(7024), pp. 425-30, 2005.
- J. Vera et al, Power-Law models of signal transduction pathways in: Cellular Signalling doi:10.1016/j.cellsig.2007.01.029), 2007.
- Eberhart O. Voit, Applications of Biochemical Systems Theory, 2006.