On the calculation of absolute macromolecular binding free energies

The standard framework for calculating the absolute binding free energy of a macromolecular association reaction A + B → AB with an association constant K(AB) is to equate chemical potentials of the species on the left- and right-hand sides of this reaction and evaluate the chemical potentials from theory. This theory involves (usually hidden) assumptions about what constitutes the bound species, AB, and where the contribution of the solvent appears. We present here an alternative derivation that can be traced back to Bjerrum, in which the expectation value of K(AB) is obtained directly through the statistical mechanical method of evaluating its ensemble (Boltzmann-weighted) average. The generalized Bjerrum approach more clearly delineates: (i) the different contributions to binding; (ii) the origin of the much-discussed and somewhat controversial association entropy term; and (iii) where the solvent contribution appears. This approach also allows approximations required for practical evaluation of the binding constant in complex macromolecular systems, to be introduced in a well defined way. We provide an example, with application to test cases that illustrate a range of binding behavior.

用于计算缔合常数K(AB)的大分子缔合反应A + B → AB的绝对结合自由能的标准框架，是令该反应左右两侧各物种的化学势（chemical potential）相等，并基于理论推导各物种的化学势。该理论通常隐含了关于结合物种AB的定义，以及溶剂贡献来源的相关假设。本文提出一种可追溯至比耶鲁姆（Bjerrum）的替代推导方法，通过统计力学方法直接求取缔合常数K(AB)的期望值——即对其系综（玻尔兹曼加权）平均进行计算。该广义比耶鲁姆方法能够更清晰地阐明：(i) 结合作用的不同贡献组分；(ii) 广受讨论且存在一定争议的结合熵项的起源；(iii) 溶剂贡献的具体位置。该方法还允许以严谨规范的方式，引入复杂大分子体系中缔合常数实际计算所需的近似处理。本文提供了一个应用实例，通过一系列测试案例展示了不同类型的结合行为特征。