Modelling of amperometric biosensor used for synergistic substrates determination

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

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.

Modeling microelectrode biosensors: free-flow calibration can substantially underestimate tissue concentrations

Microelectrode biosensors are typically calibrated in a free-flow environment where the concentrations at the biosensor surface are constant. However, when in tissue, the analyte reaches the biosensor via diffusion and so analyte breakdown by the biosensor results in a concentration gradient and consequently a lower concentration around the biosensor. This effect means that naive free-flow calibration will underestimate tissue concentration. We develop mathematical models to better quantify the discrepancy between the calibration and tissue environment and experimentally verify our key predictions.

Microelectrode amperometric biosensors are widely used to measure concentrations of analytes in solution and tissue including acetylcholine, adenosine, glucose, and glutamate. A great deal of experimental and modeling effort has been directed at quantifying the response of the biosensors themselves; however, the influence that the macroscopic tissue environment has on biosensor response has not been subjected to the same level of scrutiny. Here we identify an important issue in the way microelectrode biosensors are calibrated that is likely to have led to underestimations of analyte tissue concentrations. Concentration in tissue is typically determined by comparing the biosensor signal to that measured in free-flow calibration conditions. In a free-flow environment the concentration of the analyte at the outer surface of the biosensor can be considered constant. However, in tissue the analyte reaches the biosensor surface by diffusion through the extracellular space. Because the enzymes in the biosensor break down the analyte, a density gradient is set up resulting in a significantly lower concentration of analyte near the biosensor surface. This effect is compounded by the diminished volume fraction (porosity) and reduction in the diffusion coefficient due to obstructions (tortuosity) in tissue. We demonstrate this effect through modeling and experimentally verify our predictions in diffusive environments.

NEW & NOTEWORTHY Microelectrode biosensors are typically calibrated in a free-flow environment where the concentrations at the biosensor surface are constant. However, when in tissue, the analyte reaches the biosensor via diffusion and so analyte breakdown by the biosensor results in a concentration gradient and consequently a lower concentration around the biosensor. This effect means that naive free-flow calibration will underestimate tissue concentration. We develop mathematical models to better quantify the discrepancy between the calibration and tissue environment and experimentally verify our key predictions.

Catalytic and inhibitory kinetic behavior of horseradish peroxidase on the electrode surface

Enzymatic biosensors are often used to detect trace levels of some specific substance. An alternative methodology is applied for enzymatic assays, in which the electrocatalytic kinetic behavior of enzymes is monitored by measuring the faradaic current for a variety of substrate and inhibitor concentrations. Here we examine a steady-state and pre-steady-state reduction of H(2)O(2) on the horseradish peroxidase electrode. The results indicate the substrate-concentration dependence of the steady-state current strictly obeys Michaelis-Menten kinetics rules; in other cases there is ambiguity, whereby he inhibitor-concentration dependence of the steady-state current has a discontinuity under moderate concentration conditions. For pre-steady-state phases, both catalysis and inhibition show an abrupt change of the output current. These anomalous phenomena are universal and there might be an underlying biochemical or electrochemical rationale.