Diffusion-controlled reaction rates for clusters of binding sites on a cell

David E. Shoup; David E. Shoup

doi:10.3934/biophy.2016.4.522

AIMS Biophysics

2016, Volume 3, Issue 4: 522-528. doi: 10.3934/biophy.2016.4.522

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Diffusion-controlled reaction rates for clusters of binding sites on a cell

David E. Shoup ^,

Mathematics and Science Department, Lincoln Land Community College (Retired), 5250 Shepherd Rd. P.O. Box 19256 Springfield, Illinois 62794, USA

Received: 26 August 2016 Accepted: 17 October 2016 Published: 26 October 2016

The Berg-Purcell expression for the diffusion-controlled binding rate to N sites uniformly distributed on the surface of a sphere is generalized to clusters of receptors located at the poles of a cell. By replacing a partially reactive surface with one that is covered with N circular sites that act independently, one can derive analytic expressions for the diffusion-controlled rate constant for clusters of binding sites. This has application to systems where the reactive sites are located in a specific region or regions on the surface of the protein or cell. These include peptide hormones reacting with target receptors, protein-ligand reactions and bacterial chemotaxis. Multiple sensory receptors both at one and two poles of a sphere are studied.
- diffusion-controlled; ligand binding; binding site; receptor clusters; cell kinetics
Citation: David E. Shoup. Diffusion-controlled reaction rates for clusters of binding sites on a cell[J]. AIMS Biophysics, 2016, 3(4): 522-528. doi: 10.3934/biophy.2016.4.522

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Abstract

The Berg-Purcell expression for the diffusion-controlled binding rate to N sites uniformly distributed on the surface of a sphere is generalized to clusters of receptors located at the poles of a cell. By replacing a partially reactive surface with one that is covered with N circular sites that act independently, one can derive analytic expressions for the diffusion-controlled rate constant for clusters of binding sites. This has application to systems where the reactive sites are located in a specific region or regions on the surface of the protein or cell. These include peptide hormones reacting with target receptors, protein-ligand reactions and bacterial chemotaxis. Multiple sensory receptors both at one and two poles of a sphere are studied.

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