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首页> 美国卫生研究院文献>Proceedings of the National Academy of Sciences of the United States of America >Systematic derivation of partition functions for ligand binding to two-dimensional lattices
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Systematic derivation of partition functions for ligand binding to two-dimensional lattices

机译：配体结合的分配函数的系统推导 到二维晶格

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摘要

The Ising problem consists in finding the analytical solution of the partition function of a lattice once the interaction geometry among its elements is specified. No general analytical solution is available for this problem, except for the one-dimensional case. Using site-specific thermodynamics, it is shown that the partition function for ligand binding to a two-dimensional lattice can be obtained from those of one-dimensional lattices with known solution. The complexity of the lattice is reduced recursively by application of a contact transformation that involves a relatively small number of steps. The transformation implemented in a computer code solves the partition function of the lattice by operating on the connectivity matrix of the graph associated with it. This provides a powerful new approach to the Ising problem, and enables a systematic analysis of two-dimensional lattices that model many biologically relevant phenomena. Application of this approach to finite two-dimensional lattices with positive cooperativity indicates that the binding capacity per site diverges as Na (N = number of sites in the lattice) and experiences a phase-transition-like discontinuity in the thermodynamic limit N → ∞. The zeroes of the partition function tend to distribute on a slightly distorted unit circle in complex plane and approach the positive real axis already for a 5×5 square lattice. When the lattice has negative cooperativity, its properties mimic those of a system composed of two classes of independent sites with the apparent population of low-affinity binding sites increasing with the size of the lattice, thereby accounting for a phenomenon encountered in many ligand-receptor interactions.
机译：Ising问题在于，一旦指定了元素之间的相互作用几何，就可以找到晶格分配函数的解析解。除一维情况外，没有通用的解析解决方案可用于此问题。使用位点特定的热力学，表明配体结合至二维晶格的分配函数可以从具有已知溶液的一维晶格获得。通过应用涉及较少步骤的接触变换，递归地降低了晶格的复杂性。通过对与之关联的图的连接矩阵进行运算，计算机代码中实现的转换解决了晶格的分区函数。这为解决伊辛问题提供了一种有力的新方法，并能够对建模许多生物学相关现象的二维晶格进行系统分析。这种方法在具有正合作性的有限二维晶格上的应用表明，每个位点的结合能力随着 N a （N = 数量的晶格）并经历类似相变的过程 热力学极限N→∞不连续。的 分区函数的零趋于稍微分布 使复平面中的单位圆变形并逼近正实 轴已经有一个5×5方格。当晶格为负数时 合作性，其性质模仿了由两个组成的系统的性质 具有明显人口数量的独立站点类别 低亲和力结合位点随晶格大小的增加而增加， 从而解释了许多配体受体中遇到的现象 互动。

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