Receptor heterogeneity in optical biosensors

Scientists measure rate constants associated with biochemical reactions in an optical biosensor-an instrument in which ligand molecules are convected through a flow cell over a surface to which receptors are immobilized. We quantify transport effects on such reactions by modeling the associated convection-diffusion equation with a reaction boundary condition. In experimental situations, the full PDE model reduces to a set of unwieldy integrodifferential equations (IDEs). Employing common physical assumptions, we may reduce the system to an ODE model, which is more useful in practice, and which can be easily adapted to the inverse problem of finding rate constants. The results from the ODE model compare favorably with numerical simulations of the IDEs, even outside its range of validity.