Protein structure prediction with the UNRES force-field using Replica-Exchange Monte Carlo-with-Minimization; Comparison with MCM, CSA, and CFMC

Two current methods of global optimization are coupled to produce the Replica-Exchange method together with Monte Carlo-with-Minimization (REMCM). Its performance is compared with each separate component and with other global optimization techniques. REMCM was applied to search the conformational space of coarse grain protein systems described by the UNRES force field. The method consists of several noninteracting copies of Monte Carlo simulation, and minimization was used after every perturbation to enhance the sampling of low-energy conformations. REMCM was applied to five proteins of different topology, and the results were compared to those from other optimization methods, namely Monte Carlo-with-Minimization (MCM), Conformational Space Annealing (CSA), and Conformational Family Monte Carlo (CFMC). REMCM located global minima for four proteins faster and more consistently than either MCM or CFMC, and it converged faster than CSA for three of the five proteins tested. A performance comparison was also carried out between REMCM and the traditional Replica Exchange method (REM) for one protein, with REMCM showing a significant improvement. Moreover, because of its simplicity, REMCM was easy to implement, thereby offering an alternative to other global optimization methods used in protein structure prediction.     

Efficient search for all low energy conformations of polypeptides by Monte Carlo methods

The Metropolis Monte Carlo method has been added to the program FANTOM for energy refinement of polypeptides and proteins using a Newton–Raphson minimizer in torsion angle space. With this extension, different strategies for global minimization of the semiempirical energy function ECEPP/2 by various temperature schedules and restriction of conformational space were tested for locating local minimum conformations with low energy of the pentapeptide Met-enkephalin. In total, 1881 conformations below ?10 kcal/mol were found. These conformations could be represented by 77 nonidentical conformations which were analysed for their pattern of hydrogen bonds, types of tight turn, pairwise root-mean-square-deviation (rmsd), Zimmermann codes and side chain conformations. All low energy conformations below ?10.4 kcal/mol show strong similarity to the global minimum conformation in the backbone structure.     

Flexible docking simulations: Scaled collective variable Monte Carlo minimization approach using Bezier splines,and comparison with a standard Monte Carlo algorithm

An algorithm for docking a flexible ligand onto a flexible or rigid receptor, using the scaled‐collective‐variables Monte Carlo with energy minimization approach, is presented. Energy minimization is shown to be one of the best techniques for distinguishing between native‐ and nonnative‐generated conformations. Incorporation of this technique into a Monte Carlo procedure enables one to distinguish the native conformation directly during the conformational search. It avoids the generation of a large number of ligand conformers for which more sophisticated energy evaluation tools would have had to be applied to identify the nativelike conformations. The efficiency of the Monte Carlo minimization was greatly improved by incorporating a new grid‐based energy evaluation technique using Bezier splines for which the energy function, as well as all of its derivatives, can be deduced from the values at the grid points. Comparison between our ECEPP/3‐based algorithm and the Monte Carlo algorithm presented elsewhere (Hart, T. N.; Read, R. J. Prot Struct Funct Genet 1992, 13, 206–222) has been made for docking NH₂ D Phe Pro Arg COOH, the noncovalent analog of NH₂ D Phe Pro Arg chloromethylketone (PPACK), onto the active site of human α‐thrombin. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 244–252, 1999     

Conformational search using a molecular dynamics–minimization procedure: Applications to clusters of coulombic charges,Lennard–Jones particles,and waters

A new conformational search method, molecular dynamics–minimization (MDM), is proposed, which combines a molecular dynamics sampling strategy with energy minimizations in the search for low-energy molecular structures. This new method is applied to the search for low energy configurations of clusters of coulombic charges on a unit sphere, Lennard–Jones clusters, and water clusters. The MDM method is shown to be efficient in finding the lowest energy configurations of these clusters. A closer comparison of MDM with alternative conformational search methods on Lennard–Jones clusters shows that, although MDM is not as efficient as the Monte Carlo–minimization method in locating the global energy minima, it is more efficient than the diffusion equation method and the method of minimization from randomly generated structures. Given the versatility of the molecular dynamics sampling strategy in comparison to Monte Carlo in treating molecular complexes or molecules in explicit solution, one anticipates that the MDM method could be profitably applied to conformational search problems where the number of degrees of freedom is much greater. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 60–70, 1998     

Helix‐coil and beta sheet‐coil transitions in a simplified,yet realistic protein model

A reduced model of polypeptide chains and protein stochastic dynamics is employed in Monte Carlo studies of the coil‐globule transition. The model assumes a high‐resolution lattice representation of protein conformational space. The interaction scheme is derived from a statistical analysis of structural regularities seen in known three‐dimensional protein structures. It is shown that model polypeptides containing residues that have strong propensities towards locally expanded conformations collapse to β‐like globular conformations, while polypeptides containing residues with helical propensities form globules of closely packed helices. A more cooperative transition is observed for β‐type systems. It is also demonstrated that hydrogen bonding is an important factor for protein cooperativity, although, for systems with suppressed hydrogen bond interactions, a higher cooperativity of β‐type proteins is also observed.     

Protein structure prediction aided by geometrical and probabilistic constraints

Database-assisted ab initio protein structure prediction methods have exhibited considerable promise in the recent past, with several implementations being successful in community-wide experiments (CASP). We have employed combinatorial optimization techniques toward solving the protein structure prediction problem. A Monte Carlo minimization algorithm has been employed on a constrained search space to identify minimum energy configurations. The search space is constrained by using radius of gyration cutoffs, the loop backbone dihedral probability distributions, and various secondary structure packing conformations. Simulations have been carried out on several sequences and 1000 conformations have been initially generated. Of these, 50 best candidates have then been selected as probable conformations. The search for the optimum has been simplified by incorporating various geometrical constraints on secondary structural elements using distance restraint potential functions. The advantages of the reported methodology are its simplicity, and modifiability to include other geometric and probabilistic restraints.     

Computer simulations of ligand–protein binding with ensembles of protein conformations: A Monte Carlo study of HIV‐1 protease binding energy landscapes

We present the results of molecular docking simulations with HIV‐1 protease for the sb203386 and skf107457 inhibitors by Monte Carlo simulated annealing. A simplified piecewise linear energy function, the standard AMBER force field, and the AMBER force field with solvation and a soft‐core smoothing component are employed in simulations with a single‐protein conformation to determine the relationship between docking simulations with a simple energy function and more realistic force fields. The temperature‐dependent binding free energy profiles of the inhibitors interacting with a single protein conformation provide a detailed picture of relative thermodynamic stability and a distribution of ligand binding modes in agreement with experimental crystallographic data. Using the simplified piecewise linear energy function, we also performed Monte Carlo docking simulations with an ensemble of protein conformations employing preferential biased sampling of low‐energy protein conformations, and the results are analyzed in connection with the free energy profiles. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 73–84, 1999     

Comparing three stochastic search algorithms for computational protein design: Monte Carlo,replica exchange Monte Carlo,and a multistart,steepest‐descent heuristic

Computational protein design depends on an energy function and an algorithm to search the sequence/conformation space. We compare three stochastic search algorithms: a heuristic, Monte Carlo (MC), and a Replica Exchange Monte Carlo method (REMC). The heuristic performs a steepest‐descent minimization starting from thousands of random starting points. The methods are applied to nine test proteins from three structural families, with a fixed backbone structure, a molecular mechanics energy function, and with 1, 5, 10, 20, 30, or all amino acids allowed to mutate. Results are compared to an exact, “Cost Function Network” method that identifies the global minimum energy conformation (GMEC) in favorable cases. The designed sequences accurately reproduce experimental sequences in the hydrophobic core. The heuristic and REMC agree closely and reproduce the GMEC when it is known, with a few exceptions. Plain MC performs well for most cases, occasionally departing from the GMEC by 3–4 kcal/mol. With REMC, the diversity of the sequences sampled agrees with exact enumeration where the latter is possible: up to 2 kcal/mol above the GMEC. Beyond, room temperature replicas sample sequences up to 10 kcal/mol above the GMEC, providing thermal averages and a solution to the inverse protein folding problem. © 2016 Wiley Periodicals, Inc.     

Determination of side‐chain‐rotamer and side‐chain and backbone virtual‐bond‐stretching potentials of mean force from AM1 energy surfaces of terminally‐blocked amino‐acid residues,for coarse‐grained simulations of protein structure and folding. I. The method

In this and the accompanying article, we report the development of new physics‐based side‐chain‐rotamer and virtual‐bond‐deformation potentials which now replace the respective statistical potentials used so far in our physics‐based united‐reside UNRES force field for large‐scale simulations of protein structure and dynamics. In this article, we describe the methodology for determining the corresponding potentials of mean force (PMF's) from the energy surfaces of terminally‐blocked amino‐acid residues calculated with the AM1 quantum‐mechanical semiempirical method. The approach is based on minimization of the AM1 energy for fixed values of the angles λ for rotation of the peptide groups about the C^α ··· C^α virtual bonds, and for fixed values of the side‐chain dihedral angles χ, which formed a multidimensional grid. A harmonic‐approximation approach was developed to extrapolate from the energy at a given grid point to other points of the conformational space to compute the respective contributions to the PMF. To test the applicability of the harmonic approximation, the rotamer PMF's of alanine and valine obtained with this approach have been compared with those obtained by using a Metropolis Monte Carlo method. The PMF surfaces computed with the harmonic approximation are more rugged and have more pronounced minima than the MC‐calculated surfaces but the harmonic‐approximation‐and MC‐calculated PMF values are linearly correlated. The potentials derived with the harmonic approximation are, therefore, appropriate for UNRES for which the weights (scaling factors) of the energy terms are determined by force‐field optimization for foldability. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Cages, baskets, ladders, and tubes: conformational studies of polyhedral oligomeric silsesquioxanes

The conformational flexibility of a series of cage, basket, ladder, and tube polyhedral oligomeric silsesquioxanes (POSS) has been examined using the Low Mode:Monte Carlo conformational search method in conjunction with the MM3/GBSA(CHCl3) surface. An ensemble of low energy structures was generated and used to explore the molecular shape and flexibility of each system. The results indicate that, except for the ladder molecule, the incompletely condensed systems that are studied are relatively rigid. Even in cases where the molecule is able to adopt numerous low energy conformations, the overall shape remains cage-like and the conformations differ only by small angles or substituent orientations. The ladder molecule is the most flexible and this ensemble clusters into two families: one that is cage-like and the other that is more open and ladder-like. The conformational flexibilities in the gas and solvent phases, as approximated using the GBSA continuum solvent model, are very similar.     

Multicanonical Monte Carlo calculation of the free‐energy map of the base–amino acid interaction

The specific interactions between base pairs and amino acids were studied by the multicanonical Monte Carlo method. We sampled numerous interaction configurations and side‐chain conformations of the amino acid by the multicanonical algorithm, and calculated the free energies of the interactions between an amino acid at given C_α positions and a fixed base pair. The contour maps of free energy derived from this calculation represent the preferred C_α position of the amino acid around the base, and these maps of various combinations of bases and amino acids can be used to quantify the specificity of intrinsic base–amino acid interactions. Similarly, enthalpy and entropy maps will provide further details of the specific interactions. We have also calculated the free‐energy map of the orientations of the C_α C_β bond vector, which indicates the preferential orientation of the amino acid against the base. We compared the results obtained by the multicanonical method with those of the exhaustive sampling and canonical Monte Carlo methods. The free‐energy map of the base–amino acid interaction obtained by the multicanonical simulation method was nearly identical to the accurate result derived from the exhaustive sampling method. This indicates that a single multicanonical Monte Carlo simulation can produce an accurate free‐energy map. Multicanonical Monte Carlo sampling produced free‐energy maps that were more accurate than those produced by canonical Monte Carlo sampling. Thus, the multicanonical Monte Carlo method can serve as a powerful tool for estimating the free‐energy landscape of base–amino acid interactions and for elucidating the mechanism by which amino acids of proteins recognize particular DNA base pairs. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 954–962, 2000     

Prodock: Software package for protein modeling and docking

A new software package, Prodock , for protein modeling and flexible docking is presented. The protein system is described in internal coordinates with an arbitrary level of flexiblity for the proteins or ligands. The protein is represented by an all-atom model with the Ecepp /3 or Amber IV force field, depending on whether the ligand is a peptidic molecule or not. Prodock is based on a new residue data dictionary that makes the programming easier and the definition of molecular flexibility more straigthforward. Two versions of the dictionary have been constructed for the Ecepp /3 and Amber IV geometry, respectively. The global optimization of the energy function is carried out with the scaled collective variable Monte Carlo method plus energy minimization. The incorporation of a local minimization during the conformational sampling has been shown to be very important for distinguishing low-energy nonnative conformations from native structures. To make the Monte Carlo minimization method efficient for docking, a new grid-based energy evaluation technique using Bezier splines has been incorporated. This article includes some techniques and simulation tools that significantly improve the efficiency of flexible docking simulations, in particular forward/backward polypeptide chain generation. A comparative study to illustrate the advantage of using quaternions over Euler angles for the rigid-body rotational variables is presented in this paper. Several applications of the program Prodock are also discussed. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 412–427, 1999     

Torsional flexing: Conformational searching of cyclic molecules in biased internal coordinate space

A new stochastic (Monte Carlo) procedure, termed torsional flexing, has been devised for searching the conformational space of cyclic molecules. Torsional flexing causes a local, torsion angle-biased, distortion of a ring bond in a cyclic molecule. Because torsional flexing does not cause large atomic movements, even when it is applied to several bonds simultaneously, subsequent energy minimization generally proceeds rapidly. Nevertheless, the torsional flexing method is prone to generate structures that cross energy barriers so that the structure resulting after energy minimization is frequently a different conformer of the cyclic molecule. Conformational searches on cycloheptadecane, oxobrefeldin A, cyclopenta-L -alanine, and rifamycin SV based upon torsional flexing indicated that torsional flexing is among the best methods yet devised for searching the conformational space of flexible cyclic molecules. © 1993 John Wiley & Sons, Inc.     

Monte Carlo sampling algorithm for searching a scale-transformed energy space of polypeptides

A Monte Carlo sampling algorithm for searching a scale-transformed conformational energy space of polypeptides is presented. This algorithm is based on the assumption that energy barriers can be overcome by a uniform sampling of the logarithmically transformed energy space. This algorithm is tested with Met-enkephalin. For comparison, the entropy sampling Monte Carlo (ESMC) simulation is performed. First, the global minimum is easily found by the optimization of a scale-transformed energy space. With a new Monte Carlo sampling, energy barriers of 3000 kcal/mol are frequently overcome, and low-energy conformations are sampled more efficiently than with ESMC simulations. Several thermodynamic quantities are calculated with good accuracy.     

Implementation of the ECEPP algorithm,the Monte Carlo minimization method,and the electrostatically driven Monte Carlo method on the Kendall square research KSR1 computer

In this article the adaptation of the Empirical Conformational Energy Program for Peptides (ECEPP/3) and two conformational search methods [viz., the Monte Carlo minimization (MCM) method and the electrostatically driven Monte Carlo (EDMC) method] to the Kendall Square Research KSR1 computer is described. The MCM and EDMC methods were developed to surmount the multiple-minima problem in protein folding. Parallelization of these codes led to substantial speedups (expressed as the ratio between the mean time per energy evaluation in one processor and the mean time per energy evaluation in a set of processors) over the serial versions of these codes. A comparison of the performance of these algorithms on the KSR1 and on the IBM ES9000 computers is presented. © 1995 by John Wiley & Sons, Inc.     

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.     

Probing the conformational space available to inhibitors in the thermolysin active site using Monte Carlo/energy minimization techniques

The conformational space available to four inhibitors of the bacterial enzyme thermolysin has been searched in the enzyme binding site using a method that combines Monte Carlo type techniques with energy minimization for exploration of the conformational potential energy hypersurface. Molecular mechanics methodology using the AMBER force field was employed for computation of the molecular energetics. Solvation energies were also included in the calculations by employing a technique that estimates hydration energies based on the exposed solvent accessible surface area for each atom of the inhibitor and active site. It was found that in each case, the crystallographically observed conformation was among the low energy conformers discovered. In fact, in three of the calculations it was the lowest energy conformation. The methodology described in this article is expected to be quite useful for studies involving computer aided design and evaluation of enzyme inhibitors.     

Exploring hierarchical refinement techniques for induced fit docking with protein and ligand flexibility

We present a series of molecular‐mechanics‐based protein refinement methods, including two novel ones, applied as part of an induced fit docking procedure. The methods used include minimization; protein and ligand sidechain prediction; a hierarchical ligand placement procedure similar to a‐priori protein loop predictions; and a minimized Monte Carlo approach using normal mode analysis as a move step. The results clearly indicate the importance of a proper opening of the active site backbone, which might not be accomplished when the ligand degrees of freedom are prioritized. The most accurate method consisted of the minimized Monte Carlo procedure designed to open the active site followed by a hierarchical optimization of the sidechain packing around a mobile flexible ligand. The methods have been used on a series of 88 protein‐ligand complexes including both cross‐docking and apo‐docking members resulting in complex conformations determined to within 2.0 Å heavy‐atom RMSD in 75% of cases where the protein backbone rearrangement upon binding is less than 1.0 Å α‐carbon RMSD. We also demonstrate that physics‐based all‐atom potentials can be more accurate than docking‐style potentials when complexes are sufficiently refined. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

A Monte Carlo pharmacophore generation procedure: Application to the human PAF receptor

Summary A novel pharmacophore definition procedure is described, which uses a Monte Carlo method to superimpose molecules. Pharmacophore space is searched by a technique similar to high temperature annealing. Subsequent refinement of candidate pharmacophores by energy minimization produces low-energy conformations that may be involved in receptor binding. The method has been applied to compounds that bind to the human platelet-activating factor (PAF) receptor. Alternative binding site models for the PAF receptor are presented and discussed.A preliminary account of this work has been published elsewhere [1].     

A pose prediction approach based on ligand 3D shape similarity

Molecular docking predicts the best pose of a ligand in the target protein binding site by sampling and scoring numerous conformations and orientations of the ligand. Failures in pose prediction are often due to either insufficient sampling or scoring function errors. To improve the accuracy of pose prediction by tackling the sampling problem, we have developed a method of pose prediction using shape similarity. It first places a ligand conformation of the highest 3D shape similarity with known crystal structure ligands into protein binding site and then refines the pose by repacking the side-chains and performing energy minimization with a Monte Carlo algorithm. We have assessed our method utilizing CSARdock 2012 and 2014 benchmark exercise datasets consisting of co-crystal structures from eight proteins. Our results revealed that ligand 3D shape similarity could substitute conformational and orientational sampling if at least one suitable co-crystal structure is available. Our method identified poses within 2 Å RMSD as the top-ranking pose for 85.7 % of the test cases. The median RMSD for our pose prediction method was found to be 0.81 Å and was better than methods performing extensive conformational and orientational sampling within target protein binding sites. Furthermore, our method was better than similar methods utilizing ligand 3D shape similarity for pose prediction.