Operational stability study of lactate biosensors: modeling, parameter identification, and stability analysis

Area of Science:

• Biomedical Engineering
• Biotechnology
• Chemical Kinetics

Background:

• Lactate biosensors are vital for biomedical and biotechnological applications.
• Understanding their operational stability is crucial for reliable performance.
• Existing models may not fully capture the complex dynamics influenced by delays.

Purpose of the Study:

• To investigate the operational stability of lactate biosensors.
• To develop and analyze a mathematical model incorporating kinetic and delay elements.
• To provide insights into factors affecting biosensor performance and reliability.

Main Methods:

• Construction of an amperometric transducer for lactate measurement.
• Development of a modeling framework using Brown and Michaelis-Menten kinetics with distributed and discrete delays.
• Application of nonlinear optimization for parameter ascertainment.
• Stability analysis via linearization and quasi-polynomial root scrutiny.

Main Results:

• Discrete delay models demonstrate marginal stability, existing between stable and unstable states.
• Criteria for verifying marginal stability based on characteristic quasi-polynomial roots were established.
• Increasing delays induce transitions from stable focus to limit cycles and period-doubling.

Conclusions:

• The discrete delay model offers a nuanced understanding of lactate biosensor dynamics.
• Delay significantly influences biosensor behavior, leading to complex dynamic phenomena.
• Limitations include potential loss of solution positivity with increasing delays, necessitating cautious model application.