Luo Hengbin, Sharp Kim
Department of Biochemistry and Biophysics, University of Pennsylvania, Philadelphia, PA 19104-6059, USA.
Proc Natl Acad Sci U S A. 2002 Aug 6;99(16):10399-404. doi: 10.1073/pnas.162365999. Epub 2002 Jul 29.
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.
计算大分子缔合反应A + B --> AB的绝对结合自由能（其缔合常数为K(AB)）的标准框架是使该反应左右两侧物种的化学势相等，并从理论上评估化学势。该理论涉及（通常是隐含的）关于什么构成结合物种AB以及溶剂贡献出现在何处的假设。我们在此给出一种可追溯到比耶鲁姆（Bjerrum）的替代推导方法，其中K(AB)的期望值是通过评估其系综（玻尔兹曼加权）平均值的统计力学方法直接获得的。广义的比耶鲁姆方法更清晰地界定了：(i) 对结合的不同贡献；(ii) 备受讨论且有些争议的缔合熵项的起源；以及(iii) 溶剂贡献出现在何处。这种方法还允许以明确的方式引入复杂大分子系统中结合常数实际评估所需的近似值。我们给出一个示例，并应用于测试案例，这些案例说明了一系列的结合行为。
