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     

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.     

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     

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.     

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     

Estimating the temperature dependence of peptide folding entropies and free enthalpies from total energies in molecular dynamics simulations

The temperature dependence of thermodynamic quantities, such as heat capacity, entropy and free enthalpy, may be obtained by using well-known equations that relate these quantities to the enthalpy of the molecular system of interest at a range of temperatures. In turn, the enthalpy of a molecular system can be estimated from molecular dynamics simulations of an appropriate model. To demonstrate this, we have investigated the temperature dependence of the enthalpy, heat capacity, entropy and free enthalpy of a system that consists of a beta-heptapeptide in methanol and have used the statistical mechanics relationships to describe the thermodynamics of the folding/unfolding equilibrium of the peptide. The results illustrate the power of current molecular simulation force fields and techniques in establishing the link between thermodynamic quantities and conformational distributions.     

Empirical force-field assessment: The interplay between backbone torsions and noncovalent term scaling

The kinetic and thermodynamic aspects of the helix-coil transition in polyalanine-based peptides have been studied at the ensemble level using a distributed computing network. This study builds on a previous report, which critically assessed the performance of several contemporary force fields in reproducing experimental measurements and elucidated the complex nature of helix-coil systems. Here we consider the effects of modifying backbone torsions and the scaling of noncovalent interactions. Although these elements determine the potential of mean force between atoms separated by three covalent bonds (and thus largely determine the local conformational distributions observed in simulation), we demonstrate that the interplay between these factors is both complex and force field dependent. We quantitatively assess the heliophilicity of several helix-stabilizing potentials as well as the changes in heliophilicity resulting from such modifications, which can "make or break" the accuracy of a given force field, and our findings suggests that future force field development may need to better consider effect that vary with peptide length. This report also serves as an example of the utility of distributed computing in analyzing and improving upon contemporary force fields at the level of absolute ensemble equilibrium, the next step in force field development.     

Mixed monte carlo/molecular dynamics simulations in explicit solvent

A mixed Monte Carlo/Molecular Dynamics method using the trial moves for peptide backbone sampling known as Concerted Rotations with Angles was implemented. The algorithm was used to study polyalanine systems. Equivalent results to conventional Molecular Dynamics were obtained for simulations of Ala₆ in implicit solvent. To test the efficiency of the implemented method, several 150 ns simulations of Ala₁₂ in explicit water were performed. The results show that the present method yields significantly faster formation of secondary structure than the conventional Molecular Dynamics simulations. This opens the possibility to selectively sample alanine‐rich regions of larger peptides or proteins. It remains to be established whether hydrophilic amino acid residues can be successfully treated with the present methodology. © 2012 Wiley Periodicals, Inc.     

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     

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     

Fast and flexible gpu accelerated binding free energy calculations within the amber molecular dynamics package

Alchemical free energy (AFE) calculations based on molecular dynamics (MD) simulations are key tools in both improving our understanding of a wide variety of biological processes and accelerating the design and optimization of therapeutics for numerous diseases. Computing power and theory have, however, long been insufficient to enable AFE calculations to be routinely applied in early stage drug discovery. One of the major difficulties in performing AFE calculations is the length of time required for calculations to converge to an ensemble average. CPU implementations of MD‐based free energy algorithms can effectively only reach tens of nanoseconds per day for systems on the order of 50,000 atoms, even running on massively parallel supercomputers. Therefore, converged free energy calculations on large numbers of potential lead compounds are often untenable, preventing researchers from gaining crucial insight into molecular recognition, potential druggability and other crucial areas of interest. Graphics Processing Units (GPUs) can help address this. We present here a seamless GPU implementation, within the PMEMD module of the AMBER molecular dynamics package, of thermodynamic integration (TI) capable of reaching speeds of >140 ns/day for a 44,907‐atom system, with accuracy equivalent to the existing CPU implementation in AMBER. The implementation described here is currently part of the AMBER 18 beta code and will be an integral part of the upcoming version 18 release of AMBER. © 2018 Wiley Periodicals, Inc.     

Comparative analysis of nucleotide translocation through protein nanopores using steered molecular dynamics and an adaptive biasing force

The translocation of nucleotide molecules across biological and synthetic nanopores has attracted attention as a next generation technique for sequencing DNA. Computer simulations have the ability to provide atomistic‐level insight into important states and processes, delivering a means to develop a fundamental understanding of the translocation event, for example, by extracting the free energy of the process. Even with current supercomputing facilities, the simulation of many‐atom systems in fine detail is limited to shorter timescales than the real events they attempt to recreate. This imposes the need for enhanced simulation techniques that expand the scope of investigation in a given timeframe. There are numerous free energy calculation and translocation methodologies available, and it is by no means clear which method is best applied to a particular problem. This article explores the use of two popular free energy calculation methodologies in a nucleotide‐nanopore translocation system, using the α‐hemolysin nanopore. The first uses constant velocity‐steered molecular dynamics (cv‐SMD) in conjunction with Jarzynski's equality. The second applies an adaptive biasing force (ABF), which has not previously been applied to the nucleotide‐nanpore system. The purpose of this study is to provide a comprehensive comparison of these methodologies, allowing for a detailed comparative assessment of the scientific merits, the computational cost, and the statistical quality of the data obtained from each technique. We find that the ABF method produces results that are closer to experimental measurements than those from cv‐SMD, whereas the net errors are smaller for the same computational cost. © 2014 The Authors Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Essential dynamics/factor analysis for the interpretation of molecular dynamics trajectories

Subject of this work is the analysis of molecular dynamics (MD) trajectories of neurophysins I (NPI) and II (NPII) and their complexes with the neurophyseal nonapeptide hormones oxytocin (OT) and vasopresssin (VP), respectively, simulated in water. NPs serve in the neurosecretory granules as carrier proteins for the hormones before their release to the blood. The starting data consisted of two pairs of different trajectories for each of the (NPII/VP)2 and (NPI/OT)2 heterotetramers and two more trajectories for the NPII2 and NPI2 homodimers (six trajectories in total). Using essential dynamics which, to our judgement, is equivalent to factor analysis, we found that only about 10 degrees of freedom per trajectory are necessary and sufficient to describe in full the motions relevant for the function of the protein. This is consistent with these motions to explain about 90% of the total variance of the system. These principal degrees of freedom represent slow anharmonic motional modes, clearly pointing at distinguished mobility of the atoms involved in the protein's functionality.     

Temperature‐shuffled parallel cascade selection molecular dynamics accelerates the structural transitions of proteins

Parallel cascade selection molecular dynamics (PaCS‐MD) is an enhanced conformational sampling method for searching structural transition pathways from a given reactant to a product. Recently, a temperature‐aided PaCS‐MD (Vinod et al., Eur. Biophys. J. 2016, 45, 463) has been proposed as its extension, in which the temperatures were introduced as additional parameters in conformational resampling, whereas the temperature is fixed in the original PaCS‐MD. In the present study, temperature‐shuffled PaCS‐MD is proposed as a further extension of temperature‐aided PaCS‐MD in which the temperatures are shuffled among different replicas at the beginning of each cycle of conformational resampling. To evaluate their conformational sampling efficiencies, the original, temperature‐aided, and temperature‐shuffled PaCS‐MD were applied to a protein‐folding process of Trp‐cage, and their minimum computational costs to identify the native state were addressed. Through the evaluation, it was confirmed that temperature‐shuffled PaCS‐MD remarkably accelerated the protein‐folding process of Trp‐cage compared with the other methods. © 2017 Wiley Periodicals, Inc.     

Comparative analysis of molecular interactions in quaternary fluid system performed by classical and ab initio molecular dynamics

Molecular interactions in the quaternary fluid system acetic acid–n-propanol–n-propyl acetate–water were analyzed by classical and ab initio molecular dynamics methods. It was shown that ab initio molecular dynamics simulation can reproduce the molecular mobility tendency and structural features of a multicomponent system without empirical parameters.     

Systematic stepsize variation: Efficient method for searching conformational space of polypeptides

A new and efficient method for overcoming the multiple minima problem of polypeptides, the systematic stepsize variation (SSV) method, is presented. The SSV is based on the assumption that energy barriers can be passed over by sufficiently large rotations about rotatable bonds: randomly chosen dihedral angles are updated starting with a small stepsize (i.e., magnitude of rotation). A new structure is accepted only if it possesses a lower energy than the precedent one. Local minima are passed over by increasing the stepsize systematically. When no new structures are found any longer, the simulation is continued with the starting structure, but other trajectories will be followed due to the random order in updating the torsional angles. First, the method is tested with Met-enkephalin, a peptide with a known global minimum structure; in all runs the latter is found at least once. The global minimum conformations obtained in the simulations show deviations of ±0.0004 kcal/mol from the reference structure and, consequently, are perfectly superposable. For comparison, Metropolis Monte Carlo simulated annealing (MMC-SA) is performed. To estimate the efficiency of the algorithm depending on the complexity of the optimization problem, homopolymers of Ala and Gly of different lengths are simulated, with both the SSV and the MMC-SA method. The comparative simulations clearly reveal the higher efficiency of SSV compared with MMC-SA. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1470–1481, 1998     

StreaMD: Advanced analysis of molecular dynamics using R

Gromacs is one of the most popular molecular simulation suites currently available. In this contribution we present streaMD , the first interface between Gromacs trajectory files and the statistical language R . The amount of data created due to ever increasing computational power renders fast and efficient analysis of trajectories into a challenge. Especially as standard approaches such as root‐mean square fluctuations and the like provide only limited physical insight. In our streaMD package integration of the Gromacs I/O libraries with advanced, graph‐based analysis methods as the java library Stream leads to both: improved speed and analysis depth. We benchmark our results and highlight the applicability of the package by an interesting problem in RNA design, namely the interaction of tetracycline with an aptamer. © 2018 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.     

Molecular modeling of the human vasopressin V2 receptor/agonist complex

The V2 vasopressin renal receptor (V2R), which controls antidiuresis in mammals, is a member of the large family of heptahelical transmembrane (7TM) G protein-coupled receptors (GPCRs). Using the automated GPCR modeling facility available via Internet (http://expasy.hcuge.ch/swissmod/SWISS-MODEL.html) for construction of the 7TM domain in accord with the bovine rhodopsin (RD) footprint, and the SYBYL software for addition of the intra- and extracellular domains, the human V2R was modeled. The structure was further refined and its conformational variability tested by the use of a version of the Constrained Simulated Annealing (CSA) protocol developed in this laboratory. An inspection of the resulting structure reveals that the V2R (likewise any GPCR modeled this way) is much thicker and accordingly forms a more spacious TM cavity than most of the hitherto modeled GPCR constructs do, typically based on the structure of bacteriorhodopsin (BRD). Moreover, in this model the 7TM helices are arranged differently than they are in any BRD-based model. Thus, the topology and geometry of the TM cavity, potentially capable of receiving ligands, is in this model quite different than it is in the earlier models. In the subsequent step, two ligands, the native [arginine⁸]vasopressin (AVP) and the selective agonist [d-arginine⁸]vasopressin (DAVP) were inserted, each in two topologically non-equivalent ways, into the TM cavity and the resulting structures were equilibrated and their conformational variabilities tested using CSA as above. The best docking was selected and justified upon consideration of ligand-receptor interactions and structure-activity data. Finally, the amino acid residues were indicated, mainly in TM helices 3-7, as potentially important in both AVP and DAVP docking. Among those Cys¹¹², Val¹¹⁵-Lys¹¹⁶, Gln¹¹⁹, Met¹²³ in helix 3; Glu¹⁷⁴ in helix 4; Val²⁰⁶, Ala²¹⁰, Val²¹³-Phe²¹⁴ in helix 5; Trp²⁸⁴, Phe²⁸⁷-Phe²⁸⁸, Gln²⁹¹ in helix 6; and Phe³⁰⁷, Leu³¹⁰, Ala³¹⁴ and Asn³¹⁷ in helix 7 appeared to be the most important ones. Many of these residues are invariant for either the GPCR superfamily or the neurophyseal (vasopressin V2R, V1aR and V1bR and oxytocin OR) subfamily of receptors. Moreover, some of the equivalent residues in V1aR have already been found critical for the ligand affinity [Mouillac et al., J. Biol. Chem, 270 (1995) 25771].