Examples



mdbootstrap.com



 
Статья
2018

Kinetic Mechanism for Modelling of Electrochemical Mediatedenzyme Reactions and Determination of Enzyme Kinetics Parameters


O. M. Kirthiga O. M. Kirthiga , L. Rajendran L. Rajendran , Carlos Fernandez Carlos Fernandez
Российский электрохимический журнал
https://doi.org/10.1134/S1023193518110034
Abstract / Full Text

The non-steady state current density for reversible electrochemical coupled with a homogeneous enzyme reaction and a constant potential is presented in this manuscript for the first time. The model is based on non-stationary diffusion equations with semi infinite boundary condition containing a nonlinear term related to the kinetics of an enzymatic reaction. The nonlinear differential equation for the mediator is solved for reversible homogeneous enzyme reaction. Approximate analytical expressions for the concentration of the mediator and corresponding current for non-steady state conditions are derived. Kinetic parameters are also determined such as Michaelis–Menten constants for substrate (KMS) and mediator (KMM) as well as catalytic rate constant (kcat). Upon comparison, we found that the analytical results of this work are in excellent agreement with the numerical (Matlab program) and existing limiting case results. The significance of the analytical results has been demonstrated by suggesting two new graphical procedures for estimating the kinetic parameters from the current densities.

Author information
  • Department of Mathematics, Sethu Institute of Technology, Kariapatti, 626115, India

    O. M. Kirthiga & L. Rajendran

  • Department of Analytical Chemistry, School of Pharmacy and Life Sciences, Robert Gordon University, Aberdeen, UK

    Carlos Fernandez

References
  1. Nicholson, R.S. and Shain, I., Theory of stationary electrode polarography. single scan and cyclic methods applied to reversible, irreversible, and kinetic systems, Anal. Chem., 1964, vol. 36, p. 706.
  2. Leypoldt, J.K. and Gough, D.A., Model of a two-substrate enzyme electrode for glucose, Anal. Chem., 1984, vol. 56, p. 2896.
  3. Bartlett, P.N. and Whitaker, R.G., Electrochemical immobilisation of enzymes. Part I. Theory, J. Electroanal. Chem., 1987, vol. 224, p. 27.
  4. Bartlett, P.N. and Whitaker, R.G., Electrochemical immobilisation of enzymes. Part II. Glucose oxidase immobilised in poly-n-methylpyrrole, J. Electroanal. Chem., 1987, vol. 224, p. 37.
  5. Rusling, J.F. and Ito, K., Voltammetric determination of electron-transfer rate between an enzyme and a mediator, Anal. Chim. Acta, 1991, vol. 252, p. 23.
  6. Bartlett, P.N. and Pratt, K.F.E., Modeling of processes in enzyme electrodes, Biosens. Bioelectron., 1993, vol. 8, p. 451.
  7. Britz, D., Digital Simulation in Electrochemistry, 2nd ed., Berlin: Springer-Verlag, 1988.
  8. Mell, L.D. and Maloy, J.T., A model for the amperometric enzyme electrode obtained through digital simulation and applied to the immobilized glucose oxidase system, Anal. Chem., 1975, vol. 47, p. 299.
  9. Bergel, A. and Comtat, M., Theoretical evaluation of transient responses of an amperometric enzyme electrode, Anal. Chem., 1984, vol. 56, p. 2904.
  10. Lucisano, J.Y. and Gough, D.A., Transient response of the two-dimensional glucose sensor, Anal. Chem., 1988, vol. 60, p. 1272.
  11. Battaglini, F. and Calvo, E.J., Digital-simulation of homogeneous enzyme-kinetics for amperometric redox-enzyme electrodes, Anal. Chim. Acta, 1992, vol. 258, p. 151.
  12. Martens, N. and Hall, E.A.H., Model for an immobilized oxidase enzyme electrode in the presence of two oxidants, Anal. Chem., 1994, vol. 66, p. 2763.
  13. Osman, M.H., Shah, A.A., Wills, R.G.A., and Walsh, F.C., Mathematical modelling of an enzymatic fuel cell with an air-breathing cathode, Electrochim. Acta, 2013, vol. 112, p. 386.
  14. Do, T.Q.N., Varničić, M., Hanke-Rauschenbach, R., Vidaković-Koch, T., and Sundmacher, K., Mathematical modeling of a porous enzymatic electrode with direct electron transfer mechanism, Electrochim. Acta, 2014, vol. 137, p. 616.
  15. Picioreanu, C., Head, I.M., Katuri, K.P., van Loosdrecht, M.C.M., and Scott, K., A computational model for biofilm-based microbial fuel cells, Water Res., 2007, vol. 41, p. 2921.
  16. Eswari, A. and Rajendran, L., Mathematical modeling of cyclic voltammetry for ec reaction, Russ. J Electrochem., 2011, vol. 47, p. 181.
  17. Eswari, A. and Rajendran, L., Mathematical modeling of cyclic voltammetry for ec2 reaction, Russ. J Electrochem., 2011, vol. 47, p. 191.
  18. Eloul, S. and Compton, R.G., Voltammetric sensitivity enhancement by using preconcentration adjacent to the electrode: simulation, critical evaluation, and insights, J. Phys. Chem. C, 2014, vol. 118, p. 24520.
  19. Molina, A., Serna, C., Li, Q., Laborda, E., Batchelor-McAuley, C., and Compton, R.G., Analytical solutions for the study of multielectron transfer processes by staircase, cyclic, and differential voltammetries at disc microelectrodes, J. Phys. Chem. C, 2012, vol. 116, p. 11470.
  20. Kenji, Y., Satoshi, K., and Yoshihiro, K., Cyclic Voltammetric simulation of electrochemically mediated enzyme reaction and elucidation of biosensor behaviors, Anal. Bioanal. Chem., 2002, vol. 372, p. 248.
  21. Rajendran, L. and Saravankumar, K., Analytical expression of transient and steady-state catalytic current of mediated bioelectrocatalysis, Electrochim. Acta, 2014, vol. 147, p. 678.
  22. Kenji, Y. and Yoshihiro, K., Cyclic voltammetric simulation for electrochemically mediated enzyme reaction and determination of enzyme kinetic constants, Anal. Chem., 1998, vol. 70, p. 3368.
  23. He, J.H. and Mo, L.F., Comments on “Analytical solution of amperometric enzymatic reactions based on homotopy perturbation method,” Electrochim. Acta, 2013, vol. 102, p. 472.
  24. Rajendran, L. and Anitha, S., Reply to “Comments on analytical solution of amperometric enzymatic reactions based on homotopy perturbation method,” by Ji-Huan He, Lu-Feng Mo, Electrochim. Acta, 2013, vol. 102, p. 474.
  25. Kirthiga, O.M. and Rajendran, L., Approximate analytical solution for non-linear reaction diffusion equations in a mono-enzymatic biosensor involving michaelis–menten kinetics, J. Electroanal. Chem., 2015, vol. 751, p. 119.
  26. Danckwerts, P.V., Absorption by simultaneous diffusion and chemical reaction into particles of various shapes and into falling drops, Trans Faraday Soc., 1951, vol. 47, p. 1014.
  27. Rahamathunissa, G., Basha, C.A., and Rajendran, L., The theory of reaction-diffusion processes at cylindrical ultramicroelectrodes, J. Theor. Comput. Chem., 2007, vol. 6, p. 301.
  28. Rasi, M., Rajendran, L., and Sangaranarayanan, M.V., Enzyme-catalyzed oxygen reduction reaction in biofuel cells: Analytical expressions for chronoamperometric current densities, J. Electrochem. Soc., 2015, vol. 162, p. H671.