Can we still use the Michaelis-Menten model for enzymatic microneedle sensors?

Abstract

Since the 1960s, enzymatic sensors have been vital in healthcare and environmental monitoring due to their high selectivity. Traditionally, their performance is interpreted using the Michaelis-Menten (MM) equation, which assumes idealized, homogeneous, well-mixed laboratory conditions. However, integrating these sensors with microneedle (MN) patches for wearable applications introduces challenges such as spatial and temporal variations and limited reactant availability. Applying the MM model in such scenarios can lead to dramatic errors in enzyme kinetics and biomarker estimates, risking inaccurate substrate measurements and potentially life-threatening decisions. Here, we generalize the reaction-diffusion framework for enzymatic sensors and integrate it with analytical models for MN sensors. Our approach captures time-dependent MM variables, quantifies the rate of product formation, accounts for mass transport limitations, and provides expressions for response time and active substrate levels. This physics-based framework enables a) quantification of otherwise inaccessible parameters such as active substrate levels, b) accurate response-time predictions to reach steady-state conditions, c) improved data interpretation, and d) projection of enzymatic responses across various conditions. The study highlights the need for careful application of MM model in wearable microneedle sensors, where key assumptions may not hold. Our model can also extend to sensor degradation, inactivation, and hypoxia, making it broadly applicable to enzymatic sensors in diverse environments.