G. VARADHARAJAN ET AL.
1144
3
an d
are derived using the HPM. The primary result
of this work is simple approximate calculations of con-
centrations for all values of dimensionless parameters
12 3
, , and
. The HPM is an extremely simple
method and it is also a promising method to solve other
non-linear equations. This method can be easily extended
nds of system of coupled non-linear equations in
multi-substrate systems and networks of coupled enzyme
reactions.
6. Acknowledgements
This work was supported by the Council of Scientific
and Industrial Research (CSIR No.01 (2442)/10/EMR-II),
Governmen
to all ki
urai, In
t of Indi
dia for their
ui
ens, J. C. Ma
a. The authors also thank Secretary,
and Principal, Head of the
The Madura College, Ma-
constant encouragement.
, pp. 1123-
z, M. B. Amao, A. N. P Hiner, F.
rtins, E. Brosens, K. Van Belle, D. M.
The Madura College Board
Department of Mathematics,
d
7. References
[1] M. P. Deutscher, “Rat Liver Glutamyl Ribonucleic Acid
Synthetase. I. Purification and Evidence for Separate En-
zymes for Glutamic Acid and Glutamine,” Journal of
Biological Chemistry, Vol. 242, No. 6, 1967
1131.
2] J. Hernadez-R[ Gar-
cia-Canovas and M. Acosta, “Catalase-Like Activity of
Horseradish Peroxidase: Relationship to Enzyme Inacti-
vation by H2O2,” Biochemical Journal, Vol. 354, No. 2,
2001, pp. 107-114.
[3] J. Mess
Jacobs, R. Willem and L. Wyns, “Kinetics and Active
Site Dynamics of Staphylococcus Aureus Reductase,”
Journal of Biological Inorganic Chemistry, Vol. 7, 2002,
pp. 146-156. doi:10.1007/s007750100282
[4] S. Ho and G. S. Mittal, “High Voltage Pulsed Electrical
Field for Liquid Food Pasteurization,” Food Reviews In-
ternational, Vol. 16, No. 4, 2000, pp. 395-434.
doi:10.1081/FRI-100102317
[5] C. P. Yao and R. H Levy, “Inhibition-Based Metabolic
Drug-Drug Interactions: Predictions from in Vitro Data,”
Journal of Pharmaceutical Sciences, Vol. 91, No. 9, 2002,
pp. 1923-1935. doi:10.1002/jps.10179
[6] S. G. Waley, “Kinetics of Suicide Substrates,”
mical Journal, Vol. 185, 1980
Bioche-
, pp. 771-773.
e Kinetik der In-
2-3, 2007, pp. 269-274.
[7] S. G. Waley, “Kinetics of Suicide Substrates. Practical
Procedures for Determining Parameters,” Biochemical
Journal, Vol. 227, 1985, pp. 843-849.
[8] L. Michaelis and M. L. Menten, “Di
vertinwirking,” Biochemische Zeitschrift, Vol. 49, 1913,
pp. 333-369.
[9] G. E. Briggs and J. B. S. Haldane, “A Note on the Kinet-
ics of Enzyme Action,” Biochemical Journal, Vol. 19, No.
2, 1925, pp. 338-339.
[10] S. Schnell and S. M. Hanson, “A Test for Measuring the
Effects of Enzyme Inactivation,” Biophysical Chemistry,
Vol. 125, No.
doi:10.1016/j.bpc.2006.08.010
[11] S. J. Li and Y. X. Liu, “An Improved Approach to
Nonlinear Dynamical System Identification Using PID
Z. Nturforsch, “Applica-
pplied Mechanics and Engineering, Vol.
Neural Networks,” International Journal of Nonlinear
Sciences and Numerical Simulation, Vol. 7, No. 2, 2006,
pp. 177-182.
[12] M. M. Mousa, S. F. Ragab and
tion of the Homotopy Perturbation Method to Linear and
Nonlinear Schrödinger Equations,” Zeitschrift für Natur-
forschung, Vol. 63, 2008, pp. 140-144.
[13] J. H. He, “Homotopy Perturbation Technique,” Computer
Methods in A
178, 1999, pp. 257-262.
doi:10.1016/S0045-7825(99)00018-3
[14] J. H. He, “Homotopy Perturbation Method: A New
Nonlinear Analytical Technique,” Applied Mathematics
and Computation, Vol. 135, No. 1, 2003, pp. 73-79.
doi:10.1016/S0096-3003(01)00312-5
[15] J. H. He, “A Simple Per
Equation,” Applied Mathematics and
turbation Approach to Blasius
Computation, Vol.
140, No. 2-3, 2003, pp. 217-222.
doi:10.1016/S0096-3003(02)00189-3
[16] J. H. He, “Some Asymptotic Methods for Stro
Nonlinear Equations,” International J
ngly
ournal of Modern
Physics B, Vol. 20, No. 10, 2006, pp. 1141-1199.
doi:10.1142/S0217979206033796
[17] J. H. He, G. C. Wu and F. Austin
tion Method Which Should Be Fol
, “The Variational Itera-
lowed,” Nonlinear
lems,”
r Mechanics, Vol. 35,
Science Letters A, Vol. 1, No. 1, 2010, pp. 1-30.
[18] J. H. He, “A Coupling Method of a Homotopy Technique
and a Perturbation Technique for Non-Linear Prob
International Journal of Non-Linea
No. 1, 2000, pp. 37-43.
doi:10.1016/S0020-7462(98)00085-7
[19] D. D. Ganji, M. Amini and A. Kolahdooz, “Analytical
jendran, “Mathematical Model-
erometric Immobi-
Investigation of Hyperbolic Equations via He’s Methods,”
American Journal of Engineering and Applied Sciences,
Vol. 1, No. 4, 2008, pp. 399-407.
[20] S. Loghambal and L. Ra
ing of Diffusion and Kinetics of Amp
lized Enzyme Electrodes,” Electrochimica Acta, Vol. 55,
No. 18, 2010, pp. 5230-5238.
doi:10.1016/j.electacta.2010.04.050
[21] A. Meena and L. Rajendran, “Mathematical Modeling of
Amperometric and Potentiometric Biosensors and System
of Non-Linear Equations—Homotopy Perturbation Ap-
proach,” Journal of Electroanalytical Chemistry, Vol.
644, No. 1, 2010, pp. 50-59.
doi:10.1016/j.jelechem.2010.03.027
[22] A. Eswari and L. Rajendran, “Analytical Solution of
Steady State Current an Enzyme Modified Microcylinder
Electrodes,” Journal of Electroanalytical Chemistry, Vol.
648, No. 1, 2010, pp. 36-46.
doi:10.1016/j.jelechem.2010.07.002
Copyright © 2011 SciRes. AM