Abstract
In this paper, we describe the problem of describing the transport and catalytic kinetics at immobilized enzymes in an electronically conductive polymer thin film where substrate inhibition is important. Here, the enzyme kinetics are not well described by the Michaelis-Menten equation. We describe a mathematical procedure based on the recently developed Akbari-Ganji method (AGM) which facilitates a full analytical solution of the boundary value problem which is valid for all values of substrate concentration. Closed form expressions for both the substrate concentration in the film and the steady-state amperometric current response are presented. Limiting kinetic cases are identified and are expressed pictorially in parameter space using a kinetic case diagram.
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References
Andrieux CP, Dumas-Bouchiat JM, Saveant JM (1982) Catalysis of electrochemical reactions at redox polymer electrodes: kinetic model for stationary viltammetric techniques. J Electroanal Chem 131:1–15
Andrieux CP, Saveant JM (1982) Kinetics of electrochemical reactions mediated by redox polymer films: irreversible cross-exchange reactions. Formulation in terms of characteristic currents for stationary techniques. J Electroanal Chem 134:163–166
Saveant JM (2006) Elements of molecular and bimolecular electrochemistry: an electrochemical approach to electron transfer chemistry. Wiley Interscience, Hoboken 485pp
Albery WJ, Hillman AR (1984) Transport and kinetics in modified electrodes. J Electroanal Chem 170:27–49
Lyons MEG (1996) Transport and kinetics in electroactive polymers. In: Prigogine I, Rice SA (eds) Advances in chemical physics, Vol. XCIV. Wiley, New York, pp 297–624
Costentin C, Saveant JM (2015) Cyclic voltammetry of electrocatalytic films. J Phys Chem C 119:12174–12182
Costentin C, Saveant JM (2017) Catalysis of electrochemical reactions by surface active sites: analysing the occurrence and significance of volcano plots by cyclic voltammetry. ACS Catal 7:4876–4880
Amarasinghe S, Chen TY, Moberg P, Paul HJ, Tinoco F, Zook LA, Leddy J (1995) Models for mediated reactions at film modified electrodes: controlled electrode potential. Anal Chim Acta 307:227–244
Costentin C, Saveant JM (2014) Multielectron multistep molecular catalysis of electrochemical reactions: benchmarking of homogeneous catalysts. ChemElectroChem. 1:1226–1236
Costentin C, Passard G, Saveant JM (2015) Benchmarking of homogeneous electrocatalysts: overpotential, turnover frequency, limiting turnover number. J Am Chem Soc 137(16):5461–5467
Costentin C, Robert M, Saveant JM (2012) Turnover numbers, turnover frequencies and overpotential in molecular catalysis of electrochemical reactions. Cyclic voltammetry and preparative scale electrolysis. J Am Chem Soc 134(27):11235–11242
Lyons MEG, Greer JC, Fitzgerald CA, Bannon TB, Bartlett PN (1996) Reaction/diffusion with Michaelis-Menten kinetics in electroactive polymer films. Part 1. The steady state amperometric response. Analyst 121:715–731
Lyons MEG, Bannon TB, Hinds G, Rebouillat S Reaction diffusion with Michaelis-Menten kinetics in electroactive polymer films. Part 2. The transient amperometric response. Analyst 123:1947–1959
Lyons MEG, Bannon TB, Rebouillat S (1998) Reaction/diffusion at conducting polymer ultramicroelectrodes. Analyst 123:1961–1966
Rebouillat S, Lyons MEG, Flynn A (1999) Heterogeneous redox catalysis at conducting polymer ultramicroelectrodes. Analyst 124:1635–1644
Rebouillat S, Lyons MEG, Flynn A (2000) Mediated electron transfer at conducting polymer ultramicroelectrodes. Analyst 125:1611–1628
Lyons MEG (2020) Understanding the kinetics of catalysed reactions in microheterogeneous thin film electrodes. J Electroanal Chem Submitted for publication JELECHEM-D-20-00043
Manimozhi P, Subbiah A, Rajendran L (2010) Solution of steady state substrate concentration in the action of biosensor response at mixed enzyme kinetics. Sensors Actuators B 147:290–297
Noggle JH (1996) Physical chemistry, 3rd edn. Harper Collins, New York, pp 576–582
Dharmalingam KM, Veeramuni M (2019) Akbari-Ganji’s method (AGM) for solving non-linear reaction-diffusion equation in the electroactive polymer film. J Electroanal Chem 844:1–5
Acknowledgements
This paper is dedicated to the excellent colleague and electrochemist Professor Dr. Fritz Scholz on the occasion of his 65th birthday. It is my wish that Fritz continues to contribute to electrochemical science into the far future, as indeed he has done so successfully, and with such aplomb, in the past. The author wishes to thank Trinity College Dublin for support of this work.
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This paper is dedicated to Professor Dr Fritz Scholz on the occasion of his 65th birthday.
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Lyons, M.E.G. Transport and kinetics in electrocatalytic thin film biosensors: bounded diffusion with non-Michaelis-Menten reaction kinetics. J Solid State Electrochem 24, 2751–2761 (2020). https://doi.org/10.1007/s10008-020-04576-4
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DOI: https://doi.org/10.1007/s10008-020-04576-4