The effect of a receptor layer on the measurement of rate constants

Many cellular reactions involve a reactant in solution binding to or dissociating from a reactant attached to a surface. Most studies assume that the reactions occur on this surface, when in actuality the receptors usually lie in a thin layer on top of it. The effect of this layer is considered, particularly as it relates to the BIAcore(TM) measurement device, though the results are applicable to biological systems. A dimensionless parameter measuring the strength of the effect of the receptor layer is found. Asymptotic and singular perturbation techniques are used to analyse association and dissociation kinetics, though the effect of the receptor layer need not be small. Linear and nonlinear integral equations result from the analysis; explicit and asymptotic solutions are constructed for physically realizable cases. In addition, effective rate constants are derived that illustrate the combined effects of transport and the receptor layer on the measured rate constants. All these expressions provide a direct way to estimate rate constants from BIAcore(TM) binding data. (C) 2001 Society for Mathematical Biology.