Mathematical modelling of enzyme kinetics reaction mechanisms and analytical solutions of non-linear reaction equations. (English) Zbl 1196.92020

Meena, A.; Eswari, A.; Rajendran, L.

J. Math. Chem. 48, No. 2, 179-186 (2010).

Summary: A boundary value problem in basic enzyme reactions is formulated and approximate expressions for substrate and product concentrations are presented. J.-H. He and X.-H. Wu’s [Chaos Solitons Fractals 29, No. 1, 108–113 (2006; Zbl 1147.35338)] variational iteration method is used to give approximate and analytical solutions of the nonlinear reaction equations containing a nonlinear term related to the enzymatic reaction. The relevant analytical solutions for the substrate, enzyme, substrate-enzyme and product concentration profiles are discussed in terms of dimensionless reaction diffusion parameters \(K\), \(\lambda \) and \(\varepsilon\).

MSC:

92C45	Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
37N25	Dynamical systems in biology

Keywords:

enzyme kinetics; non-linear reaction equations; variational iteration method; Michaelis-Menten kinetics

Citations:

Zbl 1147.35338

References:

[1]	Rubinow S.I.: Introduction to Mathematical Biology. Wiley, Newyork (1975) · Zbl 0314.92001
[2]	Murray J.D.: Mathematical Biology, pp. 109. Springer, Berlin (1989) · Zbl 0682.92001
[3]	Segel L.A.: Mathematical Models in Molecular and Cellular Biology. Cambridge University Press, Cambridge (1980) · Zbl 0448.92001
[4]	Roberts D.V.: Enzyme Kinetics. Cambridge University Press, Cambridge (1977)
[5]	He J.H.: J. Comput. Appl. Math. 207, 3 (2007) · Zbl 1119.65049
[6]	He J.H.: Int. J. Nonlinear Mech. 34(4), 699 (1999) · Zbl 1342.34005
[7]	Momani S., Abuasad S.: Chaos Solitons Fractals 27(5), 1119 (2000) · Zbl 1086.65113
[8]	Abdou M.A., Soliman A.A.: Nonlinear Phenomena 211(1–2), 1 (2005) · Zbl 1084.35539
[9]	He J.H., Wu X.H.: Chaos Solitons Fractals 29(1), 108 (2006) · Zbl 1147.35338
[10]	Rajendran L., Rahamathunissa G.: J. Math. Chem. 44, 849 (2008) · Zbl 1217.65233
[11]	Baronas R., kulys J.: Sensors 8, 4800 (2008)