Mathematical and Statistical Computing Laboratory, Division of Computational Bioscience, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892, USA.
J Chem Phys. 2013 Sep 28;139(12):121910. doi: 10.1063/1.4816105.
The role of diffusion in the kinetics of reversible ligand binding to receptors on a cell surface or to a macromolecule with multiple binding sites is considered. A formalism is developed that is based on a Markovian master equation for the distribution function of the number of occupied receptors containing rate constants that depend on the ligand diffusivity. The formalism is used to derive (1) a nonlinear rate equation for the mean number of occupied receptors and (2) an analytical expression for the relaxation time that characterizes the decay of equilibrium fluctuations of the occupancy of the receptors. The relaxation time is shown to depend on the ligand diffusivity and concentration, the number of receptors, the cell radius, and intrinsic association/dissociation rate constants. This result is then used to estimate the accuracy of the ligand concentration measurements by the cell, which, according to the Berg-Purcell model, is related to fluctuations in the receptor occupancy, averaged over a finite interval of time. Specifically, a simple expression (which is exact in the framework of our formalism) is derived for the variance in the measured ligand concentration in the limit of long averaging times.
本文考虑了扩散在配体与细胞表面受体或具有多个结合位点的大分子之间可逆结合的动力学中的作用。建立了一种基于马氏主方程的形式体系，用于描述受体占据数的分布函数，其中包含依赖于配体扩散系数的速率常数。该形式体系用于推导出（1）占据受体的平均数量的非线性速率方程，以及（2）用于描述受体占据平衡波动衰减的弛豫时间的解析表达式。结果表明，弛豫时间取决于配体扩散系数和浓度、受体数量、细胞半径以及内在的结合/解离速率常数。然后，根据 Berg-Purcell 模型，利用该结果来估计细胞对配体浓度测量的准确性，该模型与受体占据的波动有关，这些波动是在有限的时间间隔内平均得到的。具体而言，针对长时间平均的极限情况，推导出了用于测量的配体浓度方差的简单表达式（在我们的形式体系中是精确的）。
