At present there is no general solution for the dynamic equations describing an arbitrary system of enzyme-catalyzed reactions. The reasons are three-fold. First, available methods of kinetic analysis are inadequate for obtaining the complete rate law of complex reactions. Second, even if the methods were available, the amount of experimental data required for such an analysis might be prohibitive. In addition, the general solution of the complete rate-equations represents an enormous nonlinear problem. These difficulties have been largely circumvented by utilizing a suitable approximation procedure that is based on the nonlinear nature of the rate law and yet is sufficiently simple to treat mathematically. In this paper the approximate dynamic equations are developed in matrix form, and a general program for the solution of an n chemical system using conventional numerical methods is described. Sample solutions are also presented to show that the equations resulting from the simplifying approximation retain the capability of describing many of the more interesting behavior patterns associated with biological systems.
ASJC Scopus subject areas
- Agricultural and Biological Sciences(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Immunology and Microbiology(all)
- Applied Mathematics
- Modeling and Simulation
- Statistics and Probability