Metabolic control analysis in enzymes kinetics

Mathematical modelling of metabolic pathway provides us a wide variety of information about behaviour of the system. The kinetic approach to the modelling of the systems is sometimes hampered by the fact that kinetic properties are imperfectly know that makes the structural approach more attractive. In order to make kinetic analysis of a metabolic pathway, construction of mathematical model describing its kinetics is a major part of the work. In the framework of metabolic kinetic theory, it is assumed that the rate of changes in the concentration x _i of a metabolite X _i is the sum of the r reaction rates, each weighted by corresponding stoichiometric coefficient of X _i. Using v and x to denote the rate vector and concentration vector respectively, mathematical model for kinetics of a system can be written as dx/dt = Nv where N is stoichiometric matrix which represents how the metabolites involved in the system combine. Derivation of conservation relationship which mainly depends on decomposition of stoichiometric matrix N plays important roles in constructing mathematical model of the system.