State Key Laboratory of Genetic Engineering, School of Life Sciences, Fudan University, Shanghai 200433, China.
Protein Cell. 2012 Mar;3(3):230-8. doi: 10.1007/s13238-012-2035-4. Epub 2012 Mar 31.
Protein folding, stability, and function are usually influenced by pH. And free energy plays a fundamental role in analysis of such pH-dependent properties. Electrostatics-based theoretical framework using dielectric solvent continuum model and solving Poisson-Boltzmann equation numerically has been shown to be very successful in understanding the pH-dependent properties. However, in this approach the exact computation of pH-dependent free energy becomes impractical for proteins possessing more than several tens of ionizable sites (e.g. > 30), because exact evaluation of the partition function requires a summation over a vast number of possible protonation microstates. Here we present a method which computes the free energy using the average energy and the protonation probabilities of ionizable sites obtained by the well-established Monte Carlo sampling procedure. The key feature is to calculate the entropy by using the protonation probabilities. We used this method to examine a well-studied protein (lysozyme) and produced results which agree very well with the exact calculations. Applications to the optimum pH of maximal stability of proteins and protein-DNA interactions have also resulted in good agreement with experimental data. These examples recommend our method for application to the elucidation of the pH-dependent properties of proteins.
蛋白质的折叠、稳定性和功能通常受 pH 值的影响。而自由能在分析这种依赖于 pH 值的性质方面起着至关重要的作用。基于静电的理论框架，使用介电溶剂连续体模型和数值求解泊松-玻尔兹曼方程，已被证明在理解 pH 值依赖性性质方面非常成功。然而，在这种方法中，对于具有几十个以上可离子化位点的蛋白质（例如 >30 个），精确计算依赖于 pH 值的自由能变得不切实际，因为精确评估分配函数需要对大量可能的质子化微态进行求和。在这里，我们提出了一种方法，该方法使用通过成熟的蒙特卡罗采样程序获得的可离子化位点的平均能量和质子化概率来计算自由能。关键特征是通过质子化概率来计算熵。我们使用这种方法来研究一种研究充分的蛋白质（溶菌酶），并得到了与精确计算非常吻合的结果。将该方法应用于蛋白质最大稳定性的最适 pH 值和蛋白质-DNA 相互作用也得到了与实验数据的良好一致。这些例子推荐我们的方法应用于阐明蛋白质的 pH 值依赖性性质。
