Sample volume as a key design parameter in affinity-based biosensors

Abstract

Affinity-based biosensors have become indispensable in modern diagnostics and health monitoring. While considerable research has focused on optimizing analyte transport and binding kinetics, a fundamental parameter - sample volume - remains largely underexplored in biosensor design. This is critical because biosensor performance depends on the absolute number of target molecules present, not solely their concentration, making volume a key consideration where sample availability is limited. To address this gap, we developed a mathematical two-compartment model integrating simplified mass transport, Langmuir binding kinetics, and mass conservation under finite volume constraints. The model accurately simulates biosensor binding kinetics and predicts equilibration time and required volume compared to finite-element simulations, whilst achieving more than 100-fold reduction in computational time. From the framework, we derived analytical expressions for biosensor equilibration time and required volume as a function of the Damk\"ohler number, ranging from reaction-limited to transport-limited systems. These analytical solutions predict equilibration time and required volume for a biosensors, providing rapid estimates from first-order biosensor parameters without numerical simulation. We validated this framework experimentally by optimizing flow rate parameters for a quartz crystal microbalance (QCM) biosensor and retrospectively applied optimization guidelines on a published biosensor. The open-source model and analytical expressions allow researchers to gain mechanistic insights, optimize device performance, and make informed design decisions tailored to specific healthcare contexts, including point-of-care testing and resource-constrained environments.