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  Far East Journal of Applied Mathematics  
 ISSN: 0972-0960
 
 
 

     Far East Journal of Applied Mathematics
    Volume 30, Issue 1, Pages 115 - 124 (January 2008)


SIMULATION OF TIME-DEPENDENT ENZYME KINETICS BY AN EXPLICIT NUMERIC-ANALYTIC TECHNIQUE

I. Hashim (Malaysia) and M. S. Selamat (Malaysia)

Received August 7, 2007

References:



[1] O. Abdulaziz, N. F. M. Noor, I. Hashim and M. S. M. Noorani, Further accuracy tests on Adomian decomposition method for chaotic systems, Chaos, Solitons and Fractals doi:10.1016/j.chaos.2006.09.007, (in press).

[2] G. Adomian, Nonlinear Stochastics Systems Theory and Application to Physics, Kluwer, Dordrecht, 1988.

[3] G. Adomian, Solving Frontier Problems of Physics, The Decomposition Method, Kluwer, Boston, 1994.

[4] J. S. Aranda, E. Salgado and A. Munoz-Diosdado, Multifractality in intracellular enzymatic reactions, J. Theor. Biol. doi:10.1016/j.jtbi.2005.09.005, (in press).

[5] G. A. Baker, Essentials of Padé Approximants, Academic Press, New York, 1975.

[6] D. Barton, I. M. Willers and R. V. M. Zahar, The Best Computer Papers of 1971, Auerbach, New Jersey, 1971.

[7] D. Barton, On Taylor series and stiff equations, ACM Trans. Math. Software 6 (1980), 280-294.

[8] S. Ghosh, A. Roy and D. Roy, An adaptation of Adomian decomposition for numeric-analytic integration of strongly nonlinear and chaotic oscillations, Comput. Methods Appl. Mech. Engrg. 196 (2007), 1133-1153.

[9] S. Guellal, P. Grimalt and Y. Cherruault, Numerical study of Lorenz’s equation by Adomian method, Comput. Math. Appl. 33 (1997), 25-29.

[10] J. E. Haag, A. V. Wouwer and M. Remy, A general model of reaction kinetics in biological systems, Bioprocess Biosyst. Eng. 27 (2005), 303-309.

[11] I. Hashim, M. S. M. Noorani, R. Ahmad, S. A. Bakar, E. S. Ismail and A. M. Zakaria, Accuracy of the Adomian decomposition method applied to the Lorenz system, Chaos, Solitons and Fractals 28 (2006), 1149-1158.

[12] R. Lall and E. O. Voit, Parameter estimation in modulated, unbreached reaction chains within biochemical systems, Comput. Bio. Chem. doi:10.1016/ j.compbiolchem.2005.08.001, (in press).

[13] N. Leksawasdi, Y. Y. S. Chow, M. Breuer, B. Hauer, B. Rosche and P. L. Rogers, Kinetic analysis and modelling of enzymatic (R)-phenylacetylcarbinol batch biotransformation process, J. Biotech. 111 (2004), 179-189.

[14] L. Michaelis and M. L. Menten, Die kinetik der invertinwirkung, Biochem. Z. 49 (1913), 333-369.

[15] H. Luz Neto, J. N. N. Quaresma and R. M. Cotta, Integral transform solution for natural convection in three-dimensional porous cavities, Aspect ratio effects, Int. J. Heat Mass Transfer 49 (2006), 4687-4695.

[16] M. S. M. Noorani, I. Hashim, R. Ahmad, S. A. Bakar, E. S. Ismail and A. M. Zakaria, Comparing numerical methods for the solutions of the Chen system, Chaos, Solitons and Fractals 32 (2007), 1296-1304.

[17] S. Olek, An accurate solution to the multispecies Lotka-Volterra equations, SIAM Rev. 36 (1994), 480-488.

[18] A. Répaci, Nonlinear dynamical systems, on the accuracy of Adomian’s decomposition method, Appl. Math. Lett. 3 (1990), 35-39.

[19] J. Ruan and Z. Lu, A modified algorithm for Adomian decomposition method with applications to Lotka-Volterra systems, Math. Comput. Modelling (accepted).

[20] S. Schnell and C. Mendoza, Closed form solution for time-dependent enzyme kinetics, J. Theor. Biol. 187 (1997), 207-212.

[21] S. Schnell and P. K. Maini, Enzyme kinetics far from the standard quasi-steady-state and equilibrium approximations, Math. Comput. Modelling 35 (2002), 137-144.

[22] S. Schnell, M. J. Chappell, N. D. Evans and M. R. Roussel, The mechanism distinguishability problem in biochemical kinetics, The single-enzyme, single-substrate reaction as a case study, C. R. Biologies 329 (2006), 51-61.

[23] A. K. Sen, An application of the Adomian decomposition method to the transient behavior of a model biochemical reaction, J. Math. Anal. Appl. 131 (1988), 232-245.

[24] D. Shanks, Nonlinear transformations of divergent and slowly convergent series, J. Math. Phys. 34 (1955), 1-42.

[25] N. Shawagfeh and D. Kaya, Comparing numerical methods for the solutions of systems of ordinary differential equations, Appl. Math. Lett. 17 (2004), 323-328.

[26] J. R. Sonnad and C. T. Goudar, Solution of the Haldane equation for substrate inhibition enzyme kinetics using the decomposition method, Math. Comput. Modelling 40 (2004), 573-582.

[27] P. Vadasz and S. Olek, Convergence and accuracy of Adomian’s decomposition method for the solution of Lorenz equation, Int. J. Heat Mass Transfer 43 (2000), 1715-1734.

Keywords and phrases: Adomian decomposition method, nonlinear ODEs, biochemical reaction.

 


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