Abstract
Almost all biosensors that use ligand-receptor binding operate under equilibrium conditions. However, at low ligand concentrations, the equilibration with the receptor (e.g., antibodies and aptamers) becomes slow and thus equilibrium-based biosensors are inherently limited in making measurements that are both rapid and sensitive. In this work, we provide a theoretical foundation for a method through which biosensors can quantitatively measure ligand concentration before reaching equilibrium. Rather than only measuring receptor binding at a single time-point, the pre-equilibrium approach leverages the receptor's kinetic response to instantaneously quantify the changing ligand concentration. Importantly, by analyzing the biosensor output in frequency domain, rather than in the time domain, we show the degree to which noise in the biosensor affects the accuracy of the pre-equilibrium approach. Through this analysis, we provide the conditions under which the signal-to-noise ratio of the biosensor can be maximized for a given target concentration range and rate of change. As a model, we apply our theoretical analysis to continuous insulin measurement and show that with a properly selected antibody, the pre-equilibrium approach could make the continuous tracking of physiological insulin fluctuations possible.