Bieler Noah S, Hünenberger Philippe H
Laboratory of Physical Chemistry, ETH Zürich, CH-8093 Zürich, Switzerland.
J Chem Phys. 2015 Apr 28;142(16):165102. doi: 10.1063/1.4918548.
Estimating the relative stabilities of different conformational states of a (bio-)molecule using molecular dynamics simulations involves two challenging problems: the conceptual problem of how to define the states of interest and the technical problem of how to properly sample these states, along with achieving a sufficient number of interconversion transitions. In this study, the two issues are addressed in the context of a decaalanine peptide in water, by considering the 310-, α-, and π-helical states. The simulations rely on the ball-and-stick local-elevation umbrella-sampling (B&S-LEUS) method. In this scheme, the states are defined as hyperspheres (balls) in a (possibly high dimensional) collective-coordinate space and connected by hypercylinders (sticks) to ensure transitions. A new object, the pipe, is also introduced here to handle curvilinear pathways. Optimal sampling within the so-defined space is ensured by confinement and (one-dimensional) memory-based biasing potentials associated with the three different kinds of objects. The simulation results are then analysed in terms of free energies using reweighting, possibly relying on two distinct sets of collective coordinates for the state definition and analysis. The four possible choices considered for these sets are Cartesian coordinates, hydrogen-bond distances, backbone dihedral angles, or pairwise sums of successive backbone dihedral angles. The results concerning decaalanine underline that the concept of conformational state may be extremely ambiguous, and that its tentative absolute definition as a free-energy basin remains subordinated to the choice of a specific analysis space. For example, within the force-field employed and depending on the analysis coordinates selected, the 310-helical state may refer to weakly overlapping collections of conformations, differing by as much as 25 kJ mol(-1) in terms of free energy. As another example, the π-helical state appears to correspond to a free-energy basin for three choices of analysis coordinates, but to be unstable with the fourth one. The problem of conformational-state definition may become even more intricate when comparison with experiment is involved, where the state definition relies on spectroscopic or functional observables.
使用分子动力学模拟来估计（生物）分子不同构象状态的相对稳定性涉及两个具有挑战性的问题：一是如何定义感兴趣状态的概念性问题，二是如何恰当地对这些状态进行采样，以及实现足够数量的相互转换跃迁的技术问题。在本研究中，通过考虑十丙氨酸肽在水中的310螺旋、α螺旋和π螺旋状态，在十丙氨酸肽于水中的背景下解决了这两个问题。模拟依赖于球棍局部提升伞形采样（B&S-LEUS）方法。在该方案中，状态被定义为（可能是高维的）集体坐标空间中的超球体（球），并通过超圆柱体（棍）连接以确保跃迁。这里还引入了一个新对象“管道”来处理曲线路径。通过与三种不同对象相关联的约束和（一维）基于记忆的偏置势，确保在如此定义的空间内进行最优采样。然后使用重加权根据自由能分析模拟结果，可能依赖两组不同的集体坐标进行状态定义和分析。对于这些坐标集考虑的四种可能选择是笛卡尔坐标、氢键距离、主链二面角或连续主链二面角的成对和。关于十丙氨酸的结果强调，构象状态的概念可能极其模糊，并且其作为自由能盆地的初步绝对定义仍然依赖于特定分析空间的选择。例如，在所采用的力场范围内，并且取决于所选的分析坐标，310螺旋状态可能指的是构象的弱重叠集合，其自由能相差高达25 kJ·mol⁻¹。再比如，对于三种分析坐标的选择，π螺旋状态似乎对应一个自由能盆地，但对于第四种选择则不稳定。当涉及与实验的比较时，构象状态定义的问题可能会变得更加复杂，因为此时状态定义依赖于光谱或功能观测值。
