Mjolsness Eric
Department of Computer Science, University of California, Irvine, CA 92617, USA.
Brief Bioinform. 2007 Jul;8(4):226-33. doi: 10.1093/bib/bbm034. Epub 2007 Jul 18.
An overview is presented of the construction and use of algebraic partition functions to represent the equilibrium statistical mechanics of multimolecular complexes and their action within a larger regulatory network. Unlike many applications of equilibrium statistical mechanics, multimolecular complexes may operate with various subsets of their components present and connected to the others, the rest remaining in solution. Thus they are variable-structure systems. This aspect of their behavior may be accounted for by the use of 'fugacity' variables as a representation within the partition functions. Four principles are proposed by which the combinatorics of molecular complex construction can be reflected in the construction of their partition functions. The corresponding algebraic operations on partition functions are multiplication, addition, function composition and a less commonly used operation called contraction. Each has a natural interpretation in terms of probability distributions on multimolecular structures. Possible generalizations to nonequilibrium statistical mechanics are briefly discussed.
本文概述了代数配分函数的构建与应用，其用于表示多分子复合物的平衡统计力学及其在更大调控网络中的作用。与平衡统计力学的许多应用不同，多分子复合物可能在其部分组分存在并与其他组分相连的情况下运行，其余组分则留在溶液中。因此，它们是可变结构系统。其行为的这一方面可以通过在配分函数中使用“逸度”变量来描述。提出了四条原则，通过这些原则，分子复合物构建的组合学可以反映在其配分函数的构建中。配分函数相应的代数运算为乘法、加法、函数复合以及一种较少使用的称为收缩的运算。每种运算在多分子结构的概率分布方面都有自然的解释。文中还简要讨论了对非平衡统计力学的可能推广。
