Enzyme kinetics for a two-step enzymic reaction with comparable initial enzyme-substrate ratios
- 189 Downloads
We extend the validity of the quasi-steady state assumption for a model double intermediate enzyme-substrate reaction to include the case where the ratio of initial enzyme to substrate concentration is not necessarily small. Simple analytical solutions are obtained when the reaction rates and the initial substrate concentration satisfy a certain condition. These analytical solutions compare favourably with numerical solutions of the full system of differential equations describing the reaction. Experimental methods are suggested which might permit the application of the quasi-steady state assumption to reactions where it may not have been obviously applicable before.
Key wordsMichaelis Menten approximation Quasi-steady state assumption Scaling Singular perturbations Fast and slow timescales
Unable to display preview. Download preview PDF.
- 1.Michaelis, L., Menton, M. L.: Die Kinetik der Invertinwirkung. Biochem. Z. 49, 333–69 (1913)Google Scholar
- 2.Murray, J. D.L. Lectures on nonlinear-differential-equation models in biology. Oxford: 1977 Clarendon PressGoogle Scholar
- 3.Laidler, K. J., Bunting, P. S.; The chemical kinetics of enzyme action, Oxford: Clarendon Press 1973Google Scholar
- 4.Segel, L. A., Slemrod, M.: The quasi-steady state assumption: a case study in perturbation. SIAM Review (to appear)Google Scholar
- 5.Sols, A., Marco, R.: Concentrations of metabolites and binding sites. Implications in metabolic regulation. In: Horecker, B., Stadman E. (eds.) Current topics in cellular regulation, vol. 2, pp. 227–273 New York, Academic Press 1970Google Scholar
- 6.Kevorkian, J., Cole, J. D.: Perturbation methods in applied mathematics. Berlin Heidelberg New York: Springer 1981Google Scholar
- 7.Lin, C. C. Segel, L. A.: Mathematics applied to deterministic problems in the natural sciences. New York: Macmillan 1974Google Scholar