Abstract
INTRODUCTION: This paper investigates the operational stability of lactate biosensors, crucial devices in various biomedical and biotechnological applications. We detail the construction of an amperometric transducer tailored for lactate measurement and outline the experimental setup used for empirical validation. METHODS: The modeling framework incorporates Brown and Michaelis-Menten kinetics, integrating both distributed and discrete delays to capture the intricate dynamics of lactate sensing. To ascertain model parameters, we propose a nonlinear optimization method, leveraging initial approximations from the Brown model's delay values for the subsequent model with discrete delays. RESULTS: Stability analysis forms a cornerstone of our investigation, centering on linearization around equilibrium states and scrutinizing the real parts of quasi-polynomials. Notably, our findings reveal that the discrete delay model manifests marginal stability, occupying a delicate balance between asymptotic stability and instability. We introduce criteria for verifying marginal stability based on characteristic quasi-polynomial roots, offering practical insights into system behavior. DISCUSSION: Qalitative examination of the model elucidates the influence of delay on dynamic behavior. We observe a transition from stable focus to limit cycle and period-doubling phenomena with increasing delay values, as evidenced by phase plots and bifurcation diagrams employing Poincaré sections. Additionally, we identify limitations in model applicability, notably the loss of solution positivity with growing delays, underscoring the necessity for cautious interpretation when employing delayed exponential function formulations. This comprehensive study provides valuable insights into the design and operational characteristics of lactate biosensors, offering a robust framework for understanding and optimizing their performance in diverse settings.