Theory of curvature-dependent kinetics of diffusion-limited reactions and its application to ligand binding to a sphere with multiple receptors

The Journal of Chemical Physics
Changsun Eun

Abstract

We present a simple theory that explains how surface curvature affects the reaction kinetics of diffusion-limited reactions on spherically curved surfaces. In this theory, we derive a quadratic equation under the conditions that the rate constant satisfies the Hill and Smoluchowski rate constants at the lowest and highest curvatures, respectively, and that at a certain intermediate curvature, there should be a maximum value of the rate constant, which was recently found in our previous work. We find that the result obtained from our theory is in good agreement with the corresponding one obtained from numerical calculation. In addition, we show that our theory can be directly applied to the Šolc-Stockmayer model of axially symmetric reactants, which can be considered as a spherical reactant with a single reaction site. Furthermore, we discuss using our theory to improve the formula for the rate constant in the Berg-Purcell ligand-binding model of a cell membrane covered by multiple receptors. Our simple theory yields insight into the effect of curvature on diffusion-influenced reactions and provides a useful formula for easily and quantitatively evaluating the curvature effect.

References

Nov 1, 1977·Biophysical Journal·H C Berg, E M Purcell
Dec 1, 1975·Proceedings of the National Academy of Sciences of the United States of America·T L Hill
Aug 1, 1990·Proceedings of the National Academy of Sciences of the United States of America·R Zwanzig
Jan 7, 2005·The Journal of Chemical Physics·Alexander M BerezhkovskiiStanislav Y Shvartsman
Jan 21, 2006·The Journal of Chemical Physics·Jui-Chuang Wu, Shih-Yuan Lu
Jan 28, 2006·The Journal of Chemical Physics·Alexander M BerezhkovskiiStanislav Y Shvartsman
Dec 11, 2007·The Journal of Chemical Physics·S D Traytak, A V Barzykin
Mar 12, 2009·The Journal of Chemical Physics·Aeri KangHwangseo Park
Aug 12, 2017·The Journal of Chemical Physics·Leonardo DagdugVladimir Yu Zitserman
Sep 17, 2017·The Journal of Chemical Physics·Leonardo DagdugVladimir Yu Zitserman
Nov 17, 2017·The Journal of Chemical Physics·Changsun Eun

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