Nonlinear Analytics for Electrochemical Biosensor Design Using Enzyme Aggregates and Delayed Mass Action

Area of Science:

• Biochemistry
• Chemical Kinetics
• Mathematical Modeling

Background:

• Enzyme kinetics models often simplify time delays.
• Brown's model provides a foundation for enzyme kinetic analysis.
• Incorporating distributed delays enhances model realism.

Purpose of the Study:

• To extend Brown's enzyme kinetics model to include distributed delays.
• To develop and validate a model for multi-substrate, multi-inhibitor systems.
• To compare the chemical adequacy of discrete versus distributed delay models.

Main Methods:

• Construction of a multi-substrate, multi-inhibitor model with discrete and distributed delays.
• Development of a parameter identification algorithm.
• Experimental validation using solution conductivity data and Kohlrausch's law.
• Optimization procedures for model and experimental parameters.

Main Results:

• An algorithm for parameter identification was successfully developed and tested.
• The distributed delay model demonstrated greater chemical adequacy than the discrete delay model.
• Model and Kohlrausch's law parameters were estimated through optimization.

Conclusions:

• Distributed delays offer a more chemically adequate representation in enzyme kinetics compared to discrete delays.
• The developed methodology is applicable to complex multi-component systems.
• Further generalization to multi-substrate, multi-inhibitor scenarios is feasible.