Comparative analysis of the conformational profile of substance P using simulated annealing and molecular dynamics

The present study describes an extensive conformational search of substance P using two different computational methods. On the one hand, the peptide was studied using the iterative simulated annealing, and on the other, molecular dynamics simulations at 300 and 400 K. With the former method, the peptide was studied in vacuo with a dielectric constant of 80, whereas using the latter study the peptide was studied in a box of TIP3P water molecules. Analysis of the results obtained using both methodologies was carried out using an in-house methodology using a cluster analysis method based on information theory. Comparison of the two sampling methodologies and the different environment used in the calculations is also analyzed. Finally, the conformational motifs that are characteristic of substance P in a hydrophilic environment are presented and compared with the experimental results available in the literature.     

The flexible alignment of molecular structures using simulated annealing with weighted Lagrangian multipliers

A framework for superimposing small molecules is presented. The proposed method consists of a simple atom‐based, flexible alignment. The optimization procedure used in the alignment is based on a recently published variant of the simulated annealing whereby nonlinear constraints are accommodated using Lagrangian multipliers. It differs from other published superposition algorithms in that any number of nonlinear constraints can be readily imposed on the structural alignment directly through the objective function without assuming an a priori trade‐off between competing conditions. These can include equality and equality constraints on distances, angles, and energy states. Examples illustrating the use of the proposed approach are also provided. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

Protein structure predictions by parallel simulated annealing molecular dynamics using genetic crossover

We propose a conformational search method to find a global minimum energy structure for protein systems. The simulated annealing is a powerful method for local conformational search. On the other hand, the genetic crossover can search the global conformational space. Our method incorporates these attractive features of the simulated annealing and genetic crossover. In the previous works, we have been using the Monte Carlo algorithm for simulated annealing. In the present work, we use the molecular dynamics algorithm instead. To examine the effectiveness of our method, we compared our results with those of the normal simulated annealing molecular dynamics simulations by using an α-helical miniprotein. We used genetic two-point crossover here. The conformations, which have lower energy than those obtained from the conventional simulated annealing, were obtained.     

Efficiency of simulated annealing for peptides with increasing geometrical restrictions

Simulated annealing (SA) is a popular global minimizer that can conveniently be applied to complex macromolecular systems. Thus, a molecular dynamics or a Monte Carlo simulation starts at high temperature, which is decreased gradually, and the system is expected to reach the low-energy region on the potential energy surface of the molecule. However, in many cases this process is not efficient. Alternatively, the low-energy region can be reached more effectively by minimizing the energy of selected molecular structures generated along the simulation pathway. The efficiency of SA to locate energy-minimized structures within 5 kcal/mol above the global energy minimum is studied as applied to three peptide models with increasing geometrical restrictions: (1) The linear pentapeptide Leu-enkephalin described by the ECEPP potential, (2) a cyclic hexapeptide described by the GROMOS force field energy E_GRO alone, and (3) the same cyclic peptide with E_GRO combined with a restraining potential based on 31 proton–proton restraints obtained from nuclear magnetic resonance (NMR) experiments. The efficiency of SA is compared to that of the Monte Carlo minimization (MCM) method of Li and Scheraga, and to our local torsional deformations (LTD) method for the conformational search of cyclic molecules. The results for the linear peptide show that SA provides a relatively weak guidance towards the most stable energy region; as expected, this guidance increases for the cyclic peptide and the cyclic peptide with NMR restraints. However, in general, MCM and LTD are significantly more efficient than SA as generators of low-energy minimized structures. This suggests that LTD might provide a better search tool than SA in structure determination of protein regions for which a relatively small number of restraints are provided by NMR. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1659–1670, 1999     

Combining genetic algorithm and simulated annealing: a molecular geometry optimization study

We introduce a new hybrid approach to determine the ground state geometry of molecular systems. Firstly, we compared the ability of genetic algorithm (GA) and simulated annealing (SA) to find the lowest energy geometry of silicon clusters with six and 10 atoms. This comparison showed that GA exhibits fast initial convergence, but its performance deteriorates as it approaches the desired global extreme. Interestingly, SA showed a complementary convergence pattern, in addition to high accuracy. Our new procedure combines selected features from GA and SA to achieve weak dependence on initial parameters, parallel search strategy, fast convergence and high accuracy. This hybrid algorithm outperforms GA and SA by one order of magnitude for small silicon clusters (Si₆ and Si₁₀). Next, we applied the hybrid method to study the geometry of a 20-atom silicon cluster. It was able to find an original geometry, apparently lower in energy than those previously described in literature. In principle, our procedure can be applied successfully to any molecular system.     

Exploring the similarities between potential smoothing and simulated annealing

Simulated annealing and potential function smoothing are two widely used approaches for global energy optimization of molecular systems. Potential smoothing as implemented in the diffusion equation method has been applied to study partitioning of the potential energy surface (PES) for N‐Acetyl‐Ala‐Ala‐N‐Methylamide (CDAP) and the clustering of conformations on deformed surfaces. A deformable version of the united‐atom OPLS force field is described, and used to locate all local minima and conformational transition states on the CDAP surface. It is shown that the smoothing process clusters conformations in a manner consistent with the inherent structure of the undeformed PES. Smoothing deforms the original surface in three ways: structural shifting of individual minima, merging of adjacent minima, and energy crossings between unrelated minima. A master equation approach and explicit molecular dynamics trajectories are used to uncover similar features in the equilibrium probability distribution of CDAP minima as a function of temperature. Qualitative and quantitative correlations between the simulated annealing and potential smoothing approaches to enhanced conformational sampling are established. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 531–552, 2000     

Protein structure optimization using improved simulated annealing algorithm on a three-dimensional AB off-lattice model

This paper proposed an improved simulated annealing (ISA) algorithm for protein structure optimization based on a three-dimensional AB off-lattice model. In the algorithm, we provided a general formula used for producing initial solution, and designed a multivariable disturbance term, relating to the parameters of simulated annealing and a tuned constant, to generate neighborhood solution. To avoid missing optimal solution, storage operation was performed in searching process. We applied the algorithm to test artificial protein sequences from literature and constructed a benchmark dataset consisting of 10 real protein sequences from the Protein Data Bank (PDB). Otherwise, we generated C_α space-filling model to represent protein folding conformation. The results indicate our algorithm outperforms the five methods before in searching lower energies of artificial protein sequences. In the testing on real proteins, our method can achieve the energy conformations with C_α-RMSD less than 3.0 Å from the PDB structures. Moreover, C_α space-filling model may simulate dynamic change of protein folding conformation at atomic level.     

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     

An efficient molecular docking using conformational space annealing

Molecular docking falls into the general category of global optimization problems because its main purpose is to find the most stable complex consisting of a receptor and its ligand. Conformational space annealing (CSA), a powerful global optimization method, is incorporated with the Tinker molecular modeling package to perform molecular docking simulations of six receptor-ligand complexes (3PTB, 1ULB, 2CPP, 1STP, 3CPA, and 1PPH) from the Protein Data Bank. In parallel, Monte Carlo with the minimization (MCM) method is also incorporated into the Tinker package for comparison. The energy function, consisting of electrostatic interactions, van der Waals interactions, and torsional energy terms, is calculated using the AMBER94 all-atom empirical force field. Rigid docking simulations for all six complexes and flexible docking simulations for three complexes (1STP, 3CPA, and 1PPH) are carried out using the CSA and the MCM methods. The simulation results show that the docking procedures using the CSA method generally find the most stable complexes as well as the native-like complexes more efficiently and accurately than those using the MCM, demonstrating that CSA is a promising search method for molecular docking problems.     

基于分子模拟技术煤焦分子模型构建

煤、焦是过程工业的重要原料。因此,有必要深入了解煤、焦分子结构以揭示其反应性。采用Materials Studio 7.0软件,从分子层次研究煤、焦的分子结构。根据已报道的文献,构建煤、焦的初始结构;基于分子力学原理对这些结构进行优化,使得模型物性与煤、焦物性相符;基于退火模拟算法对模型进行优化,从而使得模型密度、元素分析数据与真实值吻合;基于能量最小化原理,对煤、焦模型再次优化,从而获得其稳定、真实的分子构型。由计算结果发现,模型的估算密度、元素组成与已报道一致,说明构建的模型是有效、合理的;在模型优化过程中,相对于其他能量而言,库伦能和范德华能起着重要的作用。因此可以推断在煤、焦热加工过程中,弱键占据主要地位。另外,本文采用分子模拟技术构建煤、焦模型的方法对于构建其他复杂大分子结构有着重要的借鉴作用。     

Exploration of the (ethanol)4–water heteropentamers potential energy surface by simulated annealing and Ab initio molecular dynamics

A DFT electronic structure study of the (ethanol)₄–water heteropentamers at the B3LYP/6‐31+G(d) model chemistry was carried out. To get determine possible configurations, the potential energy surface (PES) was explored with two methods: simulated annealing and ab initio molecular dynamics. The results suggest that the PES is very flat. A total of 81 stable structures were determined. These structures were classified into 16 different geometric patterns according to geometric criteria like the number of hydrogen bonds and their spatial arrangement: cyclic, bicyclic, or lineal patterns. Thermodynamic stability was used for defining the order of such classification. Hydrogen bonds are mutually disturbed due to the existence of cooperative effects. Cooperativity affects the nature of the hydrogen bonds and the overall stability of the ethanol–water system given that the strongest interactions are markedly covalent and the most stable geometric pattern corresponds to the pentagonal arrangement. These observations were supported by the analysis of the loss of atomic charge of the hydrogen atoms involved in hydrogen bonds. These hydrogen bonds were classified as primary and secondary hydrogen bonds: O? H ··· O and C? H ··· O, respectively. For comparative purposes, some (ethanol)₅, (methanol)₅, and (methanol)₄–water clusters were characterized in this study. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Evolution of defect states in doped polythiophene: A study based on the method of simulated annealing

A modified Su–Schrieffer–Heeger Hamiltonian‐based model is used to compute the electronic and geometric structures of fairly long polythiophene (PT) chains, neutral as well as doped. The geometry optimization is carried out by the simulated annealing method. Both Metropolis and Glauber functions are used for sampling. It is shown that a bipolaron can be structurally represented by a fragment of the PT chain containing 14 thiophene units. As a series of bipolaronic defects are introduced in a long PT chain (50–100 rings), the highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) gap energy (Δ) becomes vanishingly small, a feature not present in the PT chains of similar sizes containing polaronic defects. The Fermi energy level (E_F) also moves into the valency band and nonzero density of states at ? = E_F are created. Once again, this feature is shown to be missing in PT chains containing polaronic defects. Implications of these findings are analyzed. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

A heuristic and parallel simulated annealing algorithm for variable selection in near‐infrared spectroscopy analysis

A new heuristic and parallel simulated annealing algorithm was proposed for variable selection in near‐infrared spectroscopy analysis. The algorithm employs a parallel mechanism to enhance the search efficiency, a heuristic mechanism to generate high‐quality candidate solutions, and the concept of Metropolis criterion to estimate accuracy of the candidate solutions. Several near‐infrared datasets have been evaluated under the proposed new algorithm, with partial least squares leading to improved analytical figures of merit upon wavelength selection. Improved robust and predictive regression models were obtained by the new algorithm. The method could also be helpful in other chemometric activities such as classification or quantitative structure‐activity relationship problems.     

Pure component spectral reconstruction from mixture data using SVD, global entropy minimization, and simulated annealing. Numerical investigations of admissible objective functions using a synthetic 7-species data set

A combination of singular value decomposition, entropy minimization, and simulated annealing was applied to a synthetic 7-species spectroscopic data set with added white noise. The pure spectra were highly overlapping. Global minima for selected objective functions were obtained for the transformation of the first seven right singular vectors. Simple Shannon type entropy functions were used in the objective functions and realistic physical constraints were imposed in the penalties. It was found that good first approximations for the pure component spectra could be obtained without the use of any a priori information. The present method out performed the two widely used routines, namely Simplisma and OPA-ALS, as well as IPCA. These results indicate that a combination of SVD, entropy minimization, and simulated annealing is a potentially powerful tool for spectral reconstructions from large real experimental systems.     

Effect of molecular vibrations on the MD/QC‐simulated absorption spectra

Effect of molecular vibrations on the absorption spectra simulated via a sequential approach combining molecular dynamics (MD) with quantum‐chemical calculations has been investigated. Simulated spectra have been obtained from the time‐dependent density functional theory results averaged over series of molecular geometries retrieved from Born–Oppenheimer MD trajectories. Distributions of bond lengths have been analyzed and related to the features of calculated spectra. For NVE simulations of small systems, absorption spectra exhibit bimodal bandshape as a result of classical treatment of vibrations. For NVE trajectories of larger systems or simulations in the NVT ensemble calculated absorption bands are symmetric, however, they may not agree with the results of Franck–Condon analysis. These results are practical manifestations of effects predicted theoretically from general principles. Consequences for the modeling of absorption spectra have been discussed. © 2013 Wiley Periodicals, Inc.     

On the use of mass scaling for stable and efficient simulated tempering with molecular dynamics

Simulated tempering (ST) is a generalized‐ensemble algorithm that employs trajectories exploring a range of temperatures to effectively sample rugged energy landscapes. When implemented using the molecular dynamics method, ST can require the use of short time steps for ensuring the stability of trajectories at high temperatures. To address this shortcoming, a mass‐scaling ST (MSST) method is presented in which the particle mass is scaled in proportion to the temperature. Mass scaling in the MSST method leads to velocity distributions that are independent of temperature and eliminates the need for velocity scaling after the accepted temperature updates that are required in conventional ST simulations. The homogeneity in time scales with changing temperature improves the stability of simulations and allows for the use of longer time steps at high temperatures. As a result, the MSST is found to be more efficient than the standard ST method, particularly for cases in which a large temperature range is employed. © 2016 Wiley Periodicals, Inc.     

Conformational selection of protein kinase A revealed by flexible-ligand flexible-protein docking

Protein kinases have high structural plasticity: their structure can change significantly, depending on what ligands are bound to them. Rigid-protein docking methods are not capable of describing such effects. Here, we present a new flexible-ligand flexible-protein docking model in which the protein can adopt conformations between two extremes observed experimentally. The model utilized a molecular dynamics-based simulated annealing cycling protocol and a distance-dependent dielectric model to perform docking. By testing this model on docking four diverse ligands to protein kinase A, we found that the ligands were able to dock successfully to the protein with the proper conformations of the protein induced. By imposing relatively soft conformational restraints to the protein during docking, this model reduced computational costs yet permitted essential conformational changes that were essential for these inhibitors to dock properly to the protein. For example, without adequate movement of the glycine-rich loop, it was difficult for the ligands to move from the surface of the protein to the binding site. In addition, these simulations called for better ways to compare simulation results with experiment other than using the popular root-mean-square deviation between the structure of a ligand in a docking pose and that in experiment because the structure of the protein also changed. In this work, we also calculated the correlation coefficient between protein-ligand/protein-protein distances in the docking structure and those in the crystal structure to check how well a ligand docked into the binding site of the protein and whether the proper conformation of the protein was induced.