Mathematical Modeling of Enzymatic Electrochemical Biosensors

Mathematical modelling of enzymatic electrochemical biosensors integrates enzyme catalysis with mass transport phenomena to predict sensor performance and guide design optimisation. Central to these models is the coupling of non-linear Michaelis–Menten kinetics with Fickian diffusion within immobilised enzyme films and through permselective membranes. Reaction–diffusion equations describe substrate consumption, product generation and mediator cycling at electrode interfaces under both transient and steady-state regimes. Analytical solutions have been derived for limiting cases of low and high substrate concentration, while numerical approaches—such as finite difference and finite element methods—address complex geometries, multi-layer architectures and boundary effects. Advances now account for competitive inhibition, concentration polarisation in the bulk solution and redox mediator dynamics, revealing non-monotonic dependencies of current response on membrane thickness, porosity and enzyme loading. Emerging strategies combine traditional reaction–diffusion frameworks with machine learning algorithms to accelerate parameter estimation and explore high-dimensional design spaces. This comprehensive modelling underpins the development of robust biosensors for medical diagnostics, environmental monitoring and industrial bioprocess control, ensuring high sensitivity, selectivity and rapid response in point-of-care and real-time applications.

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Mathematical Modeling of Enzymatic Electrochemical Biosensors publication trend

The graph below shows the total number of articles in mathematical modeling of enzymatic electrochemical biosensors across all publications each year (not limited to Nature Index journals).

Technical terms

Amperometric biosensor: A device that measures electric current produced by a redox reaction of an analyte at an electrode.

Michaelis–Menten kinetics: A model describing the rate of enzyme-catalysed reactions as a function of substrate concentration, characterised by saturation behaviour.

Reaction–diffusion equation: A partial differential equation that couples chemical reaction kinetics with spatial transport by diffusion.

Finite element method: A numerical technique for solving differential equations by discretising the domain into small, interconnected elements.

Steady-state analysis: Evaluation of system behaviour when concentrations and currents no longer vary with time.

References

1. Understanding the kinetics of catalysed reactions in microheterogeneous thin film electrodes. Journal of Electroanalytical Chemistry (2020).
2. Numerical Modeling and Investigation of Amperometric Biosensors with Perforated Membranes. Sensors (2020).
3. Mathematical Analysis of Reaction–Diffusion Equations Modeling the Michaelis–Menten Kinetics in a Micro-Disk Biosensor. Molecules (2021).
4. Further Comparisons of Finite Difference Schemes for Computational Modelling of Biosensors. Nonlinear Analysis Modelling and Control (2009).
5. Mediated Electron Transfer at Redox Active Monolayers. Part 4: Kinetics of Redox Enzymes Coupled With Electron Mediators. Sensors (2003).
6. The Influence of the Enzyme Membrane Thickness on the Response of Amperometric Biosensors. Sensors (2003).
7. Mathematical Modeling of Plate−gap Biosensors with an Outer Porous Membrane. Sensors (2006).
8. Theoretical Analysis of the Performance of Glucose Sensors with Layer-by-Layer Assembled Outer Membranes. Sensors (2012).