Department of Chemistry, Hankuk University of Foreign Studies, Yongin 17035, South Korea.
J Chem Phys. 2018 Jul 14;149(2):024102. doi: 10.1063/1.5028378.
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.
我们提出了一个简单的理论，解释了表面曲率如何影响扩散限制反应在球面上的反应动力学。在这个理论中，我们推导出一个二次方程，条件是速率常数分别在最低和最高曲率下满足 Hill 和 Smoluchowski 速率常数，并且在某个中间曲率下，速率常数应该有一个最大值，这是我们之前的工作中最近发现的。我们发现，我们的理论得到的结果与从数值计算得到的结果非常吻合。此外，我们表明，我们的理论可以直接应用于轴对称反应物的Šolc-Stockmayer 模型，该模型可以被认为是一个具有单个反应位点的球形反应物。此外，我们讨论了使用我们的理论来改进细胞膜上多个受体覆盖的 Berg-Purcell 配体结合模型中的速率常数公式。我们的简单理论深入了解了曲率对扩散影响反应的影响，并提供了一个有用的公式，可方便且定量地评估曲率效应。
