RECEPTOR CLUSTERING ON A CELL-SURFACE .1. THEORY OF RECEPTOR CROSS-LINKING BY LIGANDS BEARING 2 CHEMICALLY IDENTICAL FUNCTIONAL-GROUPS
RECEPTOR CLUSTERING ON A CELL-SURFACE .1. THEORY OF RECEPTOR CROSS-LINKING BY LIGANDS BEARING 2 CHEMICALLY IDENTICAL FUNCTIONAL-GROUPS
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DOI：
10.1016/0025-5564(80)90017-6
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发表时间：
1980-01-01
影响因子：
4.3
通讯作者：
DELISI, C
中科院分区：
文献类型：
--
作者：
PERELSON, AS;DELISI, C
本文对含有两个相同反应基团的二价配体与细胞表面受体相互作用问题进行了一般的数学分析。这种配体与细胞的初始结合之后是在表面上的进一步反应，导致配体-受体簇的形成。如果受体是单价的，则最多2个受体可以通过配体交联。如果受体是二价的（或多价的），则可以形成大的细胞表面聚集体，簇的大小是分布的。配体结合和受体交联的数学分析是基于等效位点假设，并包括平衡和动力学方面的问题。原则上，簇形成动力学的数学描述需要解耦合的非线性微分方程的无限系统。在没有配体-受体环的情况下，获得作为时间的函数的整个聚集体尺寸分布的问题可以简化为2个非线性微分方程的解。这些方程的近似解是通过奇异摄动方法。当模型中包括成环时，需要求解附加方程。当闭环速率常数与链长成反比时，描述线性聚集体生长所需的无穷微分方程组可化为3个积分微分方程组。为了确定环的浓度，必须对每个感兴趣的环尺寸求解附加方程。数学的发展是普遍的，并可能适用于一些生物学问题的分析，包括组胺从嗜碱性粒细胞和肥大细胞的释放，B[骨髓衍生]-细胞触发，和激素的作用，如胰岛素和表皮生长因子。
A general mathematical analysis of the problem of bivalent ligands, containing 2 identical reactive groups, interacting with cell surface receptors is presented. The initial binding of such ligands to a cell is followed by further reactions on the surface, leading to the formation of ligand-receptor clusters. If the receptors are monovalent, at most 2 receptors can be cross-linked by ligand. If the receptors are bivalent (or multivalent), large cell surface aggregates can form, the clusters being distributed in size. Mathematical analysis of ligand binding and receptor cross-linking is based upon the equivalent-site hypothesis and encompasses equilibrium and kinetic aspects of the problem. In principle, the mathematical description of cluster formation kinetics requires the solution of an infinite system of coupled nonlinear differential equations. In the absence of ligand-receptor rings, the problem of obtaining the entire aggregate size distribution as a function of time can be reduced to the solution of 2 nonlinear differential equations. Approximate solutions to these equations are developed via singular perturbation methods. When ring formation is included in the model, additional equations need to be solved. When the rate constant for ring closure varies inversely with chain size, the infinite system of differential equations needed to describe the growth of linear aggregates can be reduced to a system of 3 integral and integrodifferential equations. To determine the concentration of rings, an additional equation must be solved for each ring size of interest. The mathematical development is general and may be applicable to the analysis of a number of biological problems, including histamine release from basophils and mast cells, B[bone marrow-derived]-cell triggering, and the action of hormones, such as insulin and epidermal growth factor.