APPROXIMATING THE EFFECTS OF DIFFUSION ON REVERSIBLE-REACTIONS AT THE CELL-SURFACE - LIGAND-RECEPTOR KINETICS
APPROXIMATING THE EFFECTS OF DIFFUSION ON REVERSIBLE-REACTIONS AT THE CELL-SURFACE - LIGAND-RECEPTOR KINETICS
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DOI：
10.1016/s0006-3495(95)80298-5
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发表时间：
1995-04-01
影响因子：
3.4
通讯作者：
DEMBO, M
中科院分区：
文献类型：
--
作者：
GOLDSTEIN, B;DEMBO, M
我们考虑的问题，确定的时间依赖性的结合配体浓度的可逆结合的扩散单价配体的受体均匀分布在一个球形细胞的表面。我们首先制定一个边界值问题，捕捉这种情况下的基本物理。然后，我们介绍了一个系统的近似计划的基础上的加权残值法。通过这种方法，我们把初边值问题转化为一个简单的问题，只需要解决少量的常微分方程。我们展示了如何，在最低阶的近似，该方法可以用来获得修改后的化学速率方程，而不是基本的速率常数，有效的速率系数出现。这些速率系数是配体扩散系数、细胞半径、受体密度和其他变量的函数。我们比较了精确解和近似解，并讨论了在什么条件下可以使用近似方程。我们还应用加权残差法获得结合动力学的近似描述，当（1）有两种不同的细胞表面受体群体结合配体和（2）细胞分泌的配体可以结合回细胞上的受体（自分泌结合）。
We consider the problem of determining the time dependence of the bound ligand concentration for the reversible binding of a diffusing monovalent ligand to receptors uniformly distributed over the surface of a spherical cell. We start by formulating a boundary Value problem that captures the essential physics of this situation. We then introduce a systematic approximation scheme based on the method of weighted residuals. By this means we convert the initial boundary Value problem into a simpler problem that requires solving only a small number of ordinary differential equations. We show how, at the lowest order of approximation, the method can be used to obtain modified chemical rate equations where, in place of fundamental rate constants, effective rate coefficients appear. These rate coefficients are functions of the ligand diffusion coefficient, the cell radius, the receptor density and other variables. We compare exact and approximate solutions and discuss under what conditions the approximate equations can be used. We also apply the method of weighted residuals to obtain approximate descriptions of the binding kinetics when (1) there are two different cell surface receptor populations that bind the ligand and (2) the cell secretes a ligand that can bind back to receptors on the cell (autocrine binding).