Theory of multivalent binding in one and two-dimensional lattices
Theory of multivalent binding in one and two-dimensional lattices
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DOI：
10.1016/s0301-4622(96)02178-3
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发表时间：
1996-10-30
影响因子：
3.8
通讯作者：
Kong, Y
中科院分区：
文献类型：
--
作者：
DiCera, E;Kong, Y
根据压缩配分函数理论，讨论了在一般的协作性和结合所覆盖的点数m条件下，配位体与N个点阵的结合。系统的配分函数服从递归关系，该递归关系导致生成函数，该生成函数为任何感兴趣的情况提供精确的解析解。晶格的特定于位置的性质是由解析表达式的简单变换得到的。McGhee-von Hippel模型是在极限N-->；无穷远处的一个特例。推导过程简单明了，不涉及任何组合论证。对于非合作结合到长度为N的二维环面的情形，还导出了配分函数和特定于位置的性质，该环面包含S位置，总共有SN个位置。该环为配体与双链DNA(S=2)或蛋白质螺旋(S=3，4)的结合提供了相应的模型。证明了当m=S时，二维环面的非合作束缚可以模拟一维线性晶格的协同束缚，晶格的维度嵌入及其相互作用位的几何形状对确定实验测量所能获得的体系的束缚性质起着至关重要的作用。因此，在用一维McGhee-von Hippel模型解释Scatchard图时必须谨慎，特别是当m小于或等于4并且系统的几何形状明显是二维的时候。
Ligand binding to a linear lattice composed of N sites, under general conditions of cooperativity and number of sites covered upon binding, m, is approached in terms of the theory of contracted partition functions. The partition function of the system obeys a recursion relation leading to a generating function that provides an exact analytical solution for any case of interest. Site-specific properties of the lattice are derived from simple transformations of the analytical expressions. The McGhee-von Hippel model is obtained as a special case in the limit N --> infinity. The derivation is straightforward and involves no combinatorial arguments. Partition functions and site-specific properties are also derived for the case of non-cooperative binding to a two-dimensional torus of length N, containing s sites in its section for a total of sN sites. The torus provides a relevant model for ligand binding to double-stranded DNA (s = 2) or protein helices (s = 3,4). It is proved that non-cooperative binding to the two-dimensional torus can mimic cooperative binding to a one-dimensional linear lattice when m = s. The dimensional embedding of the lattice and the geometry of interaction of its sites play a crucial role in defining the binding properties of the system accessible to experimental measurements. Hence, caution must be exercised in the interpretation of Scatchard plots in terms of the one-dimensional McGhee-von Hippel model, especially when m less than or equal to 4 and the geometry of the system is clearly two-dimensional.