Global optimization using bad derivatives: Derivative-free method for molecular energy minimization

A general method designed to isolate the global minimum of a multidimensional objective function with multiple minima is presented. The algorithm exploits an integral “coarse-graining” transformation of the objective function, U, into a smoothed function with few minima. When the coarse-graining is defined over a cubic neighborhood of length scale ϵ, the exact gradient of the smoothed function, 𝒰_ϵ, is a simple three-point finite difference of U. When ϵ is very large, the gradient of 𝒰_ϵ appears to be a “bad derivative” of U. Because the gradient of 𝒰_ϵ is a simple function of U, minimization on the smoothed surface requires no explicit calculation or differentiation of 𝒰_ϵ. The minimization method is “derivative-free” and may be applied to optimization problems involving functions that are not smooth or differentiable. Generalization to functions in high-dimensional space is straightforward. In the context of molecular conformational optimization, the method may be used to minimize the potential energy or, preferably, to maximize the Boltzmann probability function. The algorithm is applied to conformational optimization of a model potential, Lennard–Jones atomic clusters, and a tetrapeptide. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1445–1455, 1998     

Some recent applications of ab initio electronic structure methods to metal,semimetal, and molecular clusters

Recent experimental and theoretical cluster studies are reviewed. Areas of current and developing interest in theoretical and computational chemistry are identified. Some promising methods applied to metal clusters, main group clusters, molecular clusters, spectroscopy, and models of cluster-molecule reactions are indicated. Results of calculations on small hydrogenated lithium clusters and hydrated sodium clusters are discussed in some detail.     

Investigation of the binding of a carbohydrate-mimetic peptide to its complementary anticarbohydrate antibody by STD-NMR spectroscopy and molecular-dynamics simulations

Saturation transfer difference (STD)‐NMR spectroscopy was used to probe experimentally the bioactive solution conformation of the carbohydrate mimic MDWNMHAA 1 of the O‐polysaccharide of Shigella flexneri Y when bound to its complementary antibody, mAb SYA/J6. Molecular dynamics simulations using the ZymeCAD? Molecular Dynamics platform were also undertaken to give a more accurate picture of the conformational flexibility and the possibilities for bound ligand conformations. The ligand topology, or the dynamic epitope, was mapped with the CORCEMA‐ST (COmplete Relaxation and Conformational Exchange Matrix Analysis of Saturation Transfer) program that calculates a total matrix analysis of relaxation and exchange effects to generate predicted STD‐NMR intensities from simulation. The comparison of these predicted STD enhancements with experimental data was used to select a representative binding mode. A protocol that employed theoretical STD effects calculated at snapshots during the entire course of a molecular dynamics (MD) trajectory of the peptide bound to the Fv portion of the antibody, and not the averaged atomic positions of receptor–ligand complexes, was also examined. In addition, the R factor was calculated on the basis of STD (fit) to avoid T1 bias, and an effective R factor, R_eff, was defined such that if the calculated STD (fit) for proton k was within error of the experimental STD (fit) for proton k, then that calculated STD (fit) for proton k was not included in the calculation of the R factor. This protocol was effective in deriving the antibody‐bound solution conformation of the peptide which also differed from the bound conformation determined by X‐ray crystallography; however, several discrepancies between experimental and calculated STD (fit) values were observed. The bound conformation was therefore further refined with a simulated annealing refinement protocol known as STD‐NMR intensity‐restrained CORCEMA optimization (SICO) to give a more accurate representation of the bound peptide epitope. Further optimization was required in this case, but a satisfactory correlation between experimental and calculated STD values was obtained. Attempts were also made to obtain STD enhancements with a synthetic pentasaccharide hapten, corresponding to the O‐polysaccharide, while bound to the antibody. However, unfavorable kinetics of binding in this system prevented sufficient STD build‐up, which, in turn, hindered a rigorous analysis via full STD build‐up curves.     

Ab initio structure predictions using a hierarchical approach applied to 434 cro and the Drosophila homeodomain

A discrete-state ab initio protein structure prediction procedure is presented, based on the assumption that some proteins fold in an hierarchical way, where the early folding of independent units precedes and helps complete structure formation. It involves a first step predicting, by means of threading algorithms and local structure prediction methods, the location of autonomous protein subunits presenting favorable local and tertiary interactions. The second step consists of predicting the structure of these units by Monte Carlo simulated annealing using several database-derived potentials. In a last step, these predicted structures are used as starting conformations of additional simulations, keeping these structures frozen and including the complete protein sequence. This procedure is applied to two small DNA-binding proteins, 434 cro and the Drosophila melanogaster homeodomain that contain 65 and 47 residues, respectively, and is compared to the nonhierarchical procedure where the whole protein is predicted in a single run. The best predicted structures were found to present root-mean-square deviations relative to the native conformation of 2.7 ? in the case of the homeodomain and of 3.9 ? for 434 cro; these structures thus represent low-resolution models of the native structures. Strikingly, not only the helices were correctly predicted but also intervening turn motifs. Received: 6 July 2000 / Accepted: 8 September 2000 / Published online: 21 December 2000     

Stochastic molecular optimization using generalized simulated annealing

We propose a stochastic optimization technique based on a generalized simulated annealing (GSA) method for mapping minima points of molecular conformational energy surfaces. The energy maps are obtained by coupling a classical molecular force field (THOR package) with a GSA procedure. Unlike the usual molecular dynamics (MD) method, the method proposed in this study is force independent; that is, we obtain the optimized conformation without calculating the force, and only potential energy is involved. Therefore, we do not need to know the conformational energy gradient to arrive at equilibrium conformations. Its utility in molecular mechanics is illustrated by applying it to examples of simple molecules (H₂O and H₂O₃) and to polypeptides. The results obtained for H₂O and H₂O₃ using Tsallis thermostatistics suggest that the GSA approach is faster than the other two conventional methods (Boltzmann and Cauchy machines). The results for polypeptides show that pentalanine does not form a stable α-helix structure, probably because the number of hydrogen bonds is insufficient to maintain the helical array. On the contrary, the icoalanine molecule forms an α-helix structure. We obtain this structure simulating all Φ, Ψ pairs using only a few steps, as compared with conventional methods. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 647–657, 1998     

基于支持向量机方法的HERG钾离子通道抑制剂分类模型

对human ether-a-gō-gō related genes(HERG)钾离子通道(钾通道)抑制剂,计算了表征分子组成、电荷分布、拓扑、几何结构及物理化学性质等特征的1559个分子描述符.采用Fischer Score(F-Score)排序过滤和Monte Carlo模拟退火法相结合从中筛选与HERG钾通道抑制剂分类相关的分子描述符.采用支持向量机(SVM)方法,分别以IC50=1.0、10.0μmol·L-1为分类标准,建立了三个分类预测模型.对367个训练集分子,用五重交叉验证.得到正、负样本的平均预测精度分别为84.8%-96.6%、80.7%-97.7%,其总的平均预测精度为87.1%-97.2%,优于其它文献报道结果.对97个外部测试集分子,所建三个模型的总样本预测精度在67.0%-90.1%之间,接近或优于其它文献报道结果.