Han Rongsheng, Leo-Macias Alejandra, Zerbino Daniel, Bastolla Ugo, Contreras-Moreira Bruno, Ortiz Angel R
Bioinformatics Unit, Centro de Biología Molecular "Severo Ochoa" (CSIC-UAM), Universidad Autónoma de Madrid, Cantoblanco, Madrid, Spain.
Proteins. 2008 Apr;71(1):175-88. doi: 10.1002/prot.21672.
The structural refinement of protein models is a challenging problem in protein structure prediction (Moult et al., Proteins 2003;53(Suppl 6):334-339). Most attempts to refine comparative models lead to degradation rather than improvement in model quality, so most current comparative modeling procedures omit the refinement step. However, it has been shown that even in the absence of alignment errors and using optimal templates, methods based on a single template have intrinsic limitations, and that refinement is needed to improve model accuracy. It is thought that failure of current methods originates on one hand from the inaccuracy of the effective free energy functions adopted, which do not represent properly the energetic balance in the native state, and on the other hand from the difficulty to sample the high dimensional and rugged free energy landscape of protein folding, in the search for the global minimum. Here, we address this second issue. We define the evolutionary and vibrational armonics subspace (EVA), a reduced sampling subspace that consists of a combination of evolutionarily favored directions, defined by the principal components of the structural variation within a homologous family, plus topologically favored directions, derived from the low frequency normal modes of the vibrational dynamics, up to 50 dimensions. This subspace is accurate enough so that the cores of most proteins can be represented within 1 A accuracy, and reduced enough so that Replica Exchange Monte Carlo (Hukushima and Nemoto, J Phys Soc Jpn 1996;65:1604-1608; Hukushima et al., Int J Mod Phys C: Phys Comput 1996;7:337-344; Mitsutake et al., J Chem Phys 2003;118:6664-6675; Mitsutake et al., J Chem Phys 2003;118:6676-6688) (REMC) can be applied. REMC is one of the best sampling methods currently available, but its applicability is restricted to spaces of small dimensionality. We show that the combination of the EVA subspace and REMC can essentially solve the optimization problem for backbone atoms in the reduced sampling subspace, even for rather rugged free energy landscapes. Applications and limitations of this methodology are finally discussed.
蛋白质模型的结构优化是蛋白质结构预测中的一个具有挑战性的问题（Moult等人，《蛋白质》，2003年；53（增刊6）：334 - 339）。大多数优化比较模型的尝试导致模型质量下降而非提高，因此当前大多数比较建模程序都省略了优化步骤。然而，已经表明，即使在没有比对错误且使用最优模板的情况下，基于单个模板的方法也存在内在局限性，并且需要进行优化以提高模型准确性。人们认为，当前方法的失败一方面源于所采用的有效自由能函数不准确，其不能恰当地表示天然状态下的能量平衡，另一方面源于在寻找全局最小值时，难以对蛋白质折叠的高维且崎岖的自由能景观进行采样。在此，我们解决第二个问题。我们定义了进化与振动谐波子空间（EVA），这是一个降维采样子空间，它由进化偏好方向和拓扑偏好方向组合而成，进化偏好方向由同源家族内结构变异的主成分定义，拓扑偏好方向则来自振动动力学的低频正常模式，维度高达50维。这个子空间足够精确，以至于大多数蛋白质的核心部分能够以1埃的精度表示，同时又足够低维，使得可以应用复制交换蒙特卡罗方法（Hukushima和Nemoto，《日本物理学会杂志》，1996年；65：1604 - 1608；Hukushima等人，《国际现代物理杂志C：物理计算》，1996年；7：337 - 344；Mitsutake等人，《化学物理杂志》，2003年；118：6664 - 6675；Mitsutake等人，《化学物理杂志》，2003年；118：6676 - 6688）（REMC）。REMC是目前可用的最佳采样方法之一，但其适用性仅限于低维空间。我们表明，EVA子空间和REMC的结合能够基本上解决降维采样子空间中主链原子的优化问题，即使对于相当崎岖的自由能景观也是如此。最后讨论了该方法的应用和局限性。
