Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712, United States.
J Chem Theory Comput. 2021 Mar 9;17(3):1944-1954. doi: 10.1021/acs.jctc.0c01316. Epub 2021 Feb 10.
We present a theoretical method to study how changes in pH shape the heterogeneous conformational ensemble explored by intrinsically disordered proteins (IDPs). The theory is developed in the context of coarse-grained models, which enable a fast, accurate, and extensive exploration of conformational space at a given protonation state. In order to account for pH effects, we generalize the molecular transfer model (MTM), in which conformations are re-weighted using the transfer free energy, which is the free energy necessary for bringing to equilibrium in a new environment a "frozen" conformation of the system. Using the semi-grand ensemble, we derive an exact expression of the transfer free energy, which amounts to the appropriate summation over all the protonation states. Because the exact result is computationally too demanding to be useful for large polyelectrolytes or IDPs, we introduce a mean-field (MF) approximation of the transfer free energy. Using a lattice model, we compare the exact and MF results for the transfer free energy and a variety of observables associated with the model IDP. We find that the precise location of the charged groups (the sequence), and not merely the net charge, determines the structural properties. We demonstrate that some of the limitations previously noted for MF theory in the context of globular proteins are mitigated when disordered polymers are studied. The excellent agreement between the exact and MF results poises us to use the method presented here as a computational tool to study the properties of IDPs and other biological systems as a function of pH.
我们提出了一种理论方法来研究 pH 值如何改变无规卷曲蛋白质（IDP）所探索的非均相构象集合。该理论是在粗粒化模型的背景下发展起来的，这种模型能够在给定的质子化状态下快速、准确、广泛地探索构象空间。为了考虑 pH 值的影响，我们推广了分子传递模型（MTM），其中构象是使用传递自由能进行重新加权的，传递自由能是将系统的“冻结”构象在新环境中平衡所需的自由能。使用半巨正则系综，我们推导出了传递自由能的精确表达式，这相当于对所有质子化状态的适当求和。由于精确结果在计算上对于大的多聚电解质或 IDP 来说过于苛刻，因此我们引入了传递自由能的平均场（MF）近似。使用晶格模型，我们比较了传递自由能和与模型 IDP 相关的各种可观测量的精确和 MF 结果。我们发现，带电基团（序列）的精确位置，而不仅仅是净电荷，决定了结构性质。我们证明了当研究无序聚合物时，MF 理论在球状蛋白中的一些局限性得到了缓解。精确和 MF 结果之间的良好一致性使我们能够使用这里提出的方法作为一种计算工具来研究 IDP 和其他生物系统随 pH 值变化的性质。
