Steric hindrance effects in thin reaction zones: applications to BIAcore

Many biological and industrial processes have reactions which occur in thin zones of densely packed receptors. Understanding the rate of such reactions is important, and the BIAcore surface plasmon resonance biosensor for measuring rate constants has such a geometry. However, interpreting biosensor data correctly is difficult since large ligand molecules can block multiple receptor sites, thus skewing the kinetics. General mathematical principles are presented for handling this phenomenon, and a receptor layer model is presented explicitly. An integro-partial differential equation results. Using perturbation techniques, the problem can be simplified somewhat. In the limit of small Damköhler number, the non-local nature of the system becomes evident in the association problem, while other experiments can be modelled using local techniques. Explicit and asymptotic solutions are constructed for large-molecule cases motivated by experimental design. The analysis provides insight into surface–volume reactions occurring in various contexts. In particular, this steric hindrance effect can often be quantified with a single dimensionless parameter.