Abagyan R, Totrov M
European Molecular Biology Laboratory, Heidelberg, Germany.
J Mol Biol. 1994 Jan 21;235(3):983-1002. doi: 10.1006/jmbi.1994.1052.
Two major components are required for a successful prediction of the three-dimensional structure of peptides and proteins: an efficient global optimization procedure which is capable of finding an appropriate local minimum for the strongly anisotropic function of hundreds of variables, and a set of free energy components for a protein molecule in solution which are computationally inexpensive enough to be used in the search procedure, yet sufficiently accurate to ensure the uniqueness of the native conformation. We here found an efficient way to make a random step in a Monte Carlo procedure given knowledge of the energy or statistical properties of conformational subspaces (e.g. phi-psi zones or side-chain torsion angles). This biased probability Monte Carlo (BPMC) procedure randomly selects the subspace first, then makes a step to a new random position independent of the previous position, but according to the predefined continuous probability distribution. The random step is followed by a local minimization in torsion angle space. The positions, sizes and preferences for high-probability zones on phi-psi maps and chi-angle maps were calculated for different residue types from the representative set of 191 and 161 protein 3D-structures, respectively. A fast and precise method to evaluate the electrostatic energy of a protein in solution is developed and combined with the BPMC procedure. The method is based on the modified spherical image charge approximation, efficiently projected onto a molecule of arbitrary shape. Comparison with the finite-difference solutions of the Poisson-Boltzmann equation shows high accuracy for our approach. The BPMC procedure is applied successfully to the structure prediction of 12- and 16-residue synthetic peptides and the determination of protein structure from NMR data, with the immunoglobulin binding domain of streptococcal protein G as an example. The BPMC runs display much better convergence properties than the non-biased simulations. The advantage of a true global optimization procedure for NMR structure determination is its ability to cope with local minima originating from data errors and ambiguities in NMR data.
要成功预测肽和蛋白质的三维结构，需要两个主要组成部分：一个高效的全局优化程序，它能够为数百个变量的强各向异性函数找到合适的局部最小值；以及一组用于溶液中蛋白质分子的自由能成分，其计算成本足够低，可用于搜索过程，同时又足够准确以确保天然构象的唯一性。我们在此发现了一种有效的方法，即在已知构象子空间（例如φ-ψ区域或侧链扭转角）的能量或统计特性的情况下，在蒙特卡罗程序中进行随机步长。这种有偏概率蒙特卡罗（BPMC）程序首先随机选择子空间，然后独立于先前位置向新的随机位置迈出一步，但要根据预定义的连续概率分布。随机步长之后是在扭转角空间中进行局部最小化。分别从191个和161个蛋白质三维结构的代表性集合中，针对不同的残基类型计算了φ-ψ图和χ角图上高概率区域的位置、大小和偏好。开发了一种快速精确的方法来评估溶液中蛋白质的静电能，并将其与BPMC程序相结合。该方法基于改进的球形镜像电荷近似，有效地投影到任意形状的分子上。与泊松-玻尔兹曼方程的有限差分解的比较表明，我们的方法具有很高的准确性。以链球菌蛋白G的免疫球蛋白结合结构域为例，BPMC程序已成功应用于12个和16个残基的合成肽的结构预测以及从NMR数据确定蛋白质结构。BPMC运行显示出比无偏模拟更好的收敛特性。用于NMR结构测定的真正全局优化程序的优势在于其能够应对源自NMR数据中的数据误差和模糊性的局部最小值。
