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IMA Journal of Applied Mathematics Advance Access published online on November 1, 2007
IMA Journal of Applied Mathematics, doi:10.1093/imamat/hxm041
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© The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Steric hindrance effects in thin reaction zones: applications to BIAcore

David A. Edwards{dagger}

Department of Mathematical Sciences, University of Delaware, Newark, DE 19716-2553, USA

{dagger} Email: edwards{at}math.udel.edu

Received on August 15, 2006; Revision received July 27, 2007. 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.

Keywords: biomolecular reactions; rate constants; asymptotics; integrodifferential equations; steric hindrance effects; BIAcore.


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