Mathematical modeling to optimize the product in enzyme kinetics

• Autorzy: Nandi S. , Ghosh M. K. , Bhattacharya R. , Roy P. K.
• Języki publikacji: EN

Abstrakty

EN

Optimization of product in enzyme kinetics is successful by the showers of mathematical analysis with control measures. Enzymes are an important functional aspects of all biochemical processes, as they catalyze numerous reaction taking place within living organisms. With this view, optimization and quantification of product is stressed upon and in such a context, optimal control approaches have been applied in our study. In this article, we have formulated a mathematical model of enzymatic system Dynamics with control measures with a view to optimize the product as well as process conditions. Here, Pontryagin Minimum Principle is used for determination of optimal control with the help of Hamiltonian. We discuss the relevant numerical solutions for the concentration of substrate, enzyme, complex and product with respect to a specified time interval by varying control factors.

Słowa kluczowe

EN

enzyme kinetics; optimization; optimal control approach; reversible reaction

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2013
• Tom: Vol. 42, no. 2
• Strony: 431--442
• Opis fizyczny: Bibliogr. 16 poz., wykr.

Twórcy

autor

Nandi S.

• Narula Institute of Technology, Kolkata 700109, India

autor

Ghosh M. K.

• Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India

autor

Bhattacharya R.

• Narula Institute of Technology, Kolkata 700109, India

autor

Roy P. K.

• Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India

Bibliografia

• 1. ALICEA, R. M. (2010) A mathematical model for enzyme kinetics: multiple timescale analysis. Asymptotics and Perturbations 2A, 1-9.
• 2. BONNANS, J. F. and HERMANT, A. (2009) Revisiting the analysis of optima control problems with several state constraints. Control and Cybernetics 38(4A).
• 3. BONNARD, B. and SUGNY, D. (2009) Geometric optimal control and twolevel dissipative quantum systems. Control and Cybernetics 38(4A).
• 4. BROWN, A. J. (1902) Enzyme action. J. Chem. Soc. Trans. 81, 373–386.
• 5. FISTER, K. R., LENHART, S. and MCNALLY, J. S. (1998) Optimizing Chemotherapy in an HIV Model. Electronic Journal of Differential Equations 1998(32), 1-12.
• 6. FLEMING, W. H. and RISHEL, R. W. (1975) Deterministic and Stochastic Optimal Control. Springer Verlag.
• 7. KIRSCHNER, D., LENHART, S. and SERBIN, S. (1997) Optimal control of the chemotherapy of HIV. J. Math. Biol. 35, 775–792.
• 8. MURRAY, J. D. (1989) Mathematical Biology. Springer, Berlin, 109-113.
• 9. PONTRYAGIN, L. S., BOLTYANSKII, V. G., GAMKRELIDZE, R. V. and MISHCHENKO, E. F. (1986) Mathematical Theory of Optimal Processes. Gordon and Breach Science Publishers 4.
• 10. ROBERTS, D. V. (1977) Enzyme Kinetics. Cambridge University Press.
• 11. RUBINOW, S. I. (1975) Introduction to Mathematical Biology. Dover Publications.
• 12. SEGEL, L. A. (1980) Mathematical Models in Molecular and Cellular Biology. Cambridge University Press.
• 13. SHARPE, F. R. and LOTKA, A. J. (1923) Contributions to the analysis of malaria epidemiology. IV. Incubation log. Amer. J. Hyg. 3 (Suppl.1), 96–112.
• 14. TZAFRIRI, A. R. and EDELMAN, E. R. (2004) The total quasi-steady-state approximation is valid for reversible enzyme kinetics. Journal of Theoretical Biology 226, 303-313.
• 15. VARADHARAJAN, G. and RAJENDRAN, L. (2011) Analytical solution of coupled non-linear second order reaction differential equations in enzyme kinetics. Natural Science 3(6), 459-465.
• 16. VASIC-RACKI, D., KRAGL, U. and LIESE, A. (2003) Benefits of enzyme kinetics modelling. Chem. Biochem. Eng. Q. 17(1), 7-18.