A comparative study of the simulated-annealing and Monte Carlo-with-minimization approaches to the minimum-energy structures of polypeptides: [Met]-enkephalin

A comparison of two methods for surmounting the multiple-minima problem, Simulated Annealing (SA) and Monte Carlo with Minimization (MCM), is presented with applications to [Met]-enkephalin in the absence and in the presence of water. SA explores a continuous space of internal variables, while MCM explores a discrete space consisting of the local energy minima on that space. Starting from random conformations chosen from the whole conformational space in both cases, it is found that, while SA converges to low-energy structures significantly faster than MCM, the former does not converge to a unique minimum whereas the latter does. Furthermore, the behavior of the RMS deviations with respect to the apparent global minimum (for enkephalin in the absence of water) shows no correlation with the observed overall energy decrease in the case of SA, whereas such a correlation is quite evident with MCM; this implies that, even though the potential energy decreases in the annealing process, the Monte Carlo SA trajectory does not proceed towards the global minimum. Possible reasons for these differences between the two methods are discussed. It is concluded that, while SA presents attractive prospects for possibly improving or refining given structures, it must be considered inferior to MCM, at least in problems where little or no structural information is available for the molecule of interest.     

Efficiency of monte carlo minimization procedures and their use in analysis of NMR data obtained from flexible peptides

The Monte Carlo minimization (MCM) method of Li and Scheraga is an efficient tool for generating low energy minimized structures of peptides, in particular the global energy minimum (GEM). In a recent article we proposed an enhancement to MCM, called the free energy Monte Carlo minimization (FMCM) procedure. With FMCM the conformational search is carried out with respect to the harmonic free energy, which approximates the free energy of the potential energy wells around the energy minimized structures (these wells are called localized microstates). In this work we apply both methods to the pentapeptide Leu-enkephalin described by the potential energy function ECEPP, and study their efficiency in identifying the GEM structure as well as the global harmonic free energy (GFM) structure. We also investigate the efficiency of these methods to generate localized microstates, which pertain to different energy and harmonic free energy intervals above the GEM and GFM, respectively. Such microstates constitute an important ingredient of our statistical mechanical methodology for analyzing nuclear magnetic resonance data of flexible peptides. Aspects of this methodology related to the stability properties of the localized microstates are examined. © 1997 by John Wiley & Sons, Inc.     

Proton affinities of the N- and C-terminal segments arising upon the dissociation of the amide bond in protonated peptides

Dissociation of the amide bonds in a protonated peptide leads to N-terminal sequence fragments with cyclic structures and C-terminal sequence fragments with linear structures. The ionic fragments containing the N-terminus (b _n ) have been shown to be protonated oxazolones, whereas those containing the C-terminus (y _n ) are protonated linear peptides. The coproduced neutral fragments are cyclic peptides from the N-terminus and linear peptides from the C-terminus. A likely determinant of these structural choices is the proton affinity (PA) of the described peptide segments. This study determines the PA values of such segments (Pep), i.e., cyclic and linear dipeptides and a relevant oxazolone, based on the dissociations of proton-bound dimers [Pep + B _i ]H⁺ in which B _i is a reference base of known PA value (Cooks kinetic method). The dissociations are assessed at different internal energies to thereby obtain both proton affinities as well as entropies of protonation. For species with comparable amino acid composition, the proton affinity (and gas phase basicity) follows the order cyclic peptide ≪ oxazolone ≈ linear peptide. This ranking is consistent with dissociation of the protonated peptide via interconverting proton-bound complexes involving N-terminal oxazolone (O) or cyclopeptide (C) segments and C-terminal linear peptide segments (L), viz. O ⋯ H⁺ ⋯ L ⇄ C ⋯ H⁺ ⋯ L. N-terminal sequence ions (b _n ) are formed with oxazolone structures which can efficiently compete for the proton with the linear segments. On the other hand, N-terminal neutral fragments detach as cyclic peptides, with H⁺ now being retained by the more basic linear segment from the C-terminus to yield y _n .     

CABS‐NMR—De novo tool for rapid global fold determination from chemical shifts,residual dipolar couplings and sparse methyl‐methyl noes

Recent development of nuclear magnetic resonance (NMR) techniques provided new types of structural restraints that can be successfully used in fast and low‐cost global protein fold determination. Here, we present CABS‐NMR, an efficient protein modeling tool, which takes advantage of such structural restraints. The restraints are converted from original NMR data to fit the coarse grained protein representation of the C‐Alpha‐Beta‐Side‐group (CABS) algorithm. CABS is a Monte Carlo search algorithm that uses a knowledge‐based force field. Its versatile structure enables a variety of protein‐modeling protocols, including purely de novo folding, folding guided by restraints derived from template structures or, structure assembly based on experimental data. In particular, CABS‐NMR uses the distance and angular restraints set derived from various NMR experiments. This new modeling technique was successfully tested in structure determination of 10 globular proteins of size up to 216 residues, for which sparse NMR data were available. Additional detailed analysis was performed for a S100A1 protein. Namely, we successfully predicted Nuclear Overhauser Effect signals on the basis of low‐energy structures obtained from chemical shifts by CABS‐NMR. It has been observed that utility of chemical shifts and other types of experimental data (i.e. residual dipolar couplings and methyl‐methyl Nuclear Overhauser Effect signals) in the presented modeling pipeline depends mainly on size of a protein and complexity of its topology. In this work, we have provided tools for either post‐experiment processing of various kinds of NMR data or fast and low‐cost structural analysis in the still challenging field of new fold predictions. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

Conformational search of peptides and proteins: Monte Carlo minimization with an adaptive bias method applied to the heptapeptide deltorphin

The energy function of a protein consists of a tremendous number of minima. Locating the global energy minimum (GEM) structure, which corresponds approximately to the native structure, is a severe problem in global optimization. Recently we have proposed a conformational search technique based on the Monte Carlo minimization (MCM) method of Li and Scheraga, where trial dihedral angles are not selected at random within the range [-180 degrees,180 degrees ] (as with MCM) but with biased probabilities depending on the increased structure-energy correlations as the GEM is approached during the search. This method, called the Monte Carlo minimization with an adaptive bias (MCMAB), was applied initially to the pentapeptide Leu-enkephalin. Here we study its properties further by applying it to the larger peptide with bulky side chains, deltorphin (H-Tyr-D-Met-Phe-His-Leu-Met-Asp-NH(2)). We find that on average the number of energy minimizations required by MCMAB to locate the GEM for the first time is smaller by a factor of approximately three than the number required by MCM-in accord with results obtained for Leu-enkephalin.     

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.     

蒙特卡洛模拟退火与距离限制相结合的方法在多肽溶液构象分析中的应用

多维核磁共振技术的飞速发展议得其在生物大分子结构测定方面的应用已经达到可以与【射线晶体学并驾齐驱的地步．蛋白质结构堆积紧密，较适合于用核磁共振方法给出确定的结构．与蛋白质不同的是多肽的柔性较大，在溶液中可能存在多种构象，核磁共振实验给出的只是平均信息＊．利用核磁，（振数据构建分子结构模型常用的方法有距离几何、分子动力学等，在由核磁共振NOESZ得到的距离信息足够多时可以给出较好的结果问．由于多肽本身的特点：柔性较大，由核磁共振得到的距离信息较少等，利用距离几何、分子动力学方法进行构象搜索时容易陷入…     

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.     

Molecular mechanics conformational analysis of tylosin

The conformations of the 16-membered macrolide antibiotic tylosin were studied with molecular mechanics (AMBER* force field) including modelling of the effect of the solvent on the conformational preferences (GB/SA). A Monte Carlo conformational search procedure was used for finding the most probable low-energy conformations. The present study provides complementary data to recently reported analysis of the conformations of tylosin based on NMR techniques. A search for the low-energy conformations of protynolide, a 16-membered lactone containing the same aglycone as tylosin, was also carried out, and the results were compared with the observed conformation in the crystal as well as with the most probable conformations of the macrocyclic ring of tylosin. The dependence of the results on force field was also studied by utilizing the MM3 force field. Some particular conformations were computed with the semiempirical molecular orbital methods AM1 and PM3.     

Synthesis of a Type-VIβ-Turn Peptide Mimetic and Its Incorporation into a High-Affinity Somatostatin Receptor Ligand

The synthesis of a cis-Phe-Pro dipeptide mimetic is described, which adopts a type-VIβ-turn conformation. In this mimetic, the α-positions of Phe and Pro are joined by a CH₂CH₂ bridge, thereby forming a fused bicyclic system, and fixing a geometry similar to that seen in cis-Phe-Pro units in protein crystal structures. The dipeptide mimetic 20 was synthesized in optically pure form starting from (R)-α-allylproline ( 6 ; Schemes 1, 3, and 4), with a free carboxylic acid and an Fmoc-protected N-terminus, thereby allowing its incorporation into linear and cyclic peptides using standard solid-phase methods. The mimetic 20 was incorporated into the cyclic somatostatin analogue cyclo(-Phe = Pro-Phe-D -Trp-Lys-Thr-), where Phe = Pro represents the mimetic. This analogue shows a high affinity (pIC₅₀ 8.6) for somatostatin receptors on rat-brain cortex membranes. Based on NMR studies in aqueous solution, likely low-energy conformations for this analogue were deduced using restrained dynamic simulated annealing. The conformations found, which include a distorted type-II′ turn at D -Trp-Lys, are similar to low-energy conformations deduced elsewhere for cyclo(-Phe-Pro-Phe-D -Trp-Lys-Thr-), as well as to those seen in crystal structures of the somatostatin analogue octreotide.     

蒙特卡洛模拟退火与距离限制相结合的方法——在多肽溶液构象分析中的应用

Distance geometry and molecular dynamics are currently employed in determining molecular structures with interatomic distances from NMR NOESY experiment. Because of the flexibility of peptide, distances obtained from NMR are usually not sufficient to confine its structure. Both distance geometry and molecular dynamics will bias in the conformational space at this circumstance. Constraint Monte Carlo simulated annealing was established to solve this problem. Distance constraints were included into the ECEPP/2 force field by introducing a harmonic energy term. Conformational analysis of a pentapeptide with eight interatomic distances from NMR was carried out as a test. By comparison of the 100 conformers obtained from constraint simulated annealing and the 100 conformers from distance geometry calculation, it was found that constraint simulated annealing can cover the outcomes of distance geometry and at the same time give more con-formers fitting to the experimental data. The result shows that constraint Monte-Carlo simulated annealing is more valid in constructing peptide structures from NMR distances than currently employed methods when no sufficient distances from NMR are available.     

Low-mode conformational search elucidated: Application to C39H80 and flexible docking of 9-deazaguanine inhibitors into PNP

We previously described a new conformational search method, termed low-mode search (LMOD), and discussed its utility for conformational searches performed on cycloalkanes and a cyclic penta-peptide. 1 In this report, we discuss a rigorous implementation of mode following (c-LMOD) for conformational searching, and we demonstrate that for a conformational search involving cycloheptadecane, this rigorous implementation is capable of finding all of the previously known structures. To the best of our knowledge, this is the first computational proof that mode following can be used for conformational searches conducted on a complex molecular system. We show, however, that, as expected, it is generally inefficient to perform a conformational search in this manner. Nonetheless, c-LMOD has been shown to be an excellent method for conducting conformational analyses involving conformational interconversions, where the location of saddle points is important. We also describe refinement to our original LMOD procedure (l-LMOD) and discuss its utility for a difficult conformational search problem, namely locating the global minimum energy conformation of C₃₉H₈₀. For this search, l-LMOD combined with limited torsional Monte Carlo movement was able to locate the lowest energy structures yet reported, and significantly outperformed a pure torsional Monte Carlo and a genetic algorithm-based search. Furthermore, we also demonstrate the utility of l-LMOD combined with random translation/rotation of a ligand for the extremely difficult problem of docking flexible ligands into flexible protein binding sites on a system that includes 9-deaza-guanine-based inhibitors docked into the flexible biding site of PNP. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1671–1684, 1999     

Monte Carlo simulation of liquid hydroxylamine using ab initio intermolecular potential functions

A potential model for intermolecular interactions between hydroxylamine (NH₂OH) molecules based on ab initio quantum mechanical calculations is reviewed and critically assessed by analyzing results from a Monte Carlo simulation of liquid hydroxylamine. The liquid structure is studied in detail using radial, energy, and angular distribution functions, coordination numbers, and their distribution. Results indicate a large first solvation shell (5.3 Å), which contains 13 molecules, out of which only 4 are truly bonded by nonlinear, low-energy hydrogen bonds. These are of either the OH…O or the OH…N type, as NH…O and NH…N linear bonds are considerably suppressed, and no cyclic dimers are found. The dependence of the structural and physical properties on the simulation characteristics has also been investigated.     

Proton Transverse Relaxation as a Sensitive Probe for Structure Determination in Solid Proteins

Solid‐state nuclear magnetic resonance (NMR) spectroscopy has been successfully applied to elucidate the atomic‐resolution structures of insoluble proteins. The major bottleneck is the difficulty to obtain valuable long‐distance structural information. Here, we propose the use of distance restraints as long as 32 Å, obtained from the quantification of transverse proton relaxation induced by a methanethiosulfonate spin label (MTSL). Combined with dipolar proton–proton distance restraints, this method allows us to obtain protein structures with excellent precision from single spin‐labeled 1 mg protein samples using fast magic angle spinning.     

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.     

NMR structure of a cyclic polyamide-DNA complex

The solution structure of a cyclic polyamide ligand complexed to a DNA oligomer, derived from NMR restrained molecular mechanics, is presented. The polyamide, cyclo-gamma-ImPyPy-gamma-PyPyPy-, binds to target DNA with a nanomolar dissociation constant as characterized by quantitative footprinting previously reported. 2D (1)H NMR data were used to generate distance restraints defining the structure of this cyclic polyamide with the DNA duplex d(5'-GCCTGTTAGCG-3'):d(5'-CGCTAACAGGC-3'). Data interpretation used complete relaxation matrix analysis of the NOESY cross-peak intensities with the program MARDIGRAS. The NMR-based distance restraints (276 total) were applied in restrained molecular dynamics calculations using a solvent model, yielding structures with an rmsd for the ligand and binding site of approximately 1 A. The resulting structures indicate some distortion of the DNA in the binding site. The constraints from cyclization lead to altered stacking of the rings in the halves of the cyclic ligand relative to unlinked complexes. Despite this, the interactions with DNA are very similar to what has been found in unlinked complexes. Measurements of ligand amide and DNA imino proton exchange rates indicate very slow dissociation of the ligand and show that the DNA can undergo opening fluctuations while the ligand is bound although the presence of the ligand decreases their frequency relative to the free DNA.     

Rb + CH3I: Empirically determined potential and predicted cross sections for reactive scattering

We have fitted a 6-atom potential to results of low-energy molecular beam studies of Rb + CH₃I → RbI + CH₃, using Monte Carlo trajectory methods. We used it to predict the cross section versus reactant translational energy over the range 0–2 eV. An auxiliary calculation for the analogous K reaction is also presented.     

Structure of protonated water clusters: low-energy structures and finite temperature behavior

The structure of protonated water clusters H+(H2O)n (n=5-22) are examined by two Monte Carlo methods in conjunction with the OSS2 potential [L. Ojamae, I. Shavitt, and S. J. Singer J. Chem. Phys. 109, 5547 (1998)]. The basin-hopping method is employed to explore the OSS2 potential energy surface and to locate low-energy structures. The topology of the "global minimum," the most stable low-energy structure, changes from single ring to multiple ring to polyhedral cage as the cluster size grows. The temperature dependence of the cluster geometry is examined by carrying out parallel tempering Monte Carlo simulations. Over the temperature range we studied (25-330 K), all water clusters undergo significant structural changes. The trends are treelike structures dominating at high temperature and single-ring structures appearing in slightly lower temperatures. For n> or =7, an additional transition from single ring to multiple rings appears as the temperature decreases. Only for n> or =16 do polyhedral structures dominate the lowest temperature range. Our results indicate very dynamic structural changes at temperature range relevant to atmospheric chemistry and current experiments. The structures and properties of medium-sized protonated clusters in this temperature range are far from their global minimum cousins. The relevance of these findings to recent experiments and theoretical simulations is also discussed.     

Molecular mobility in rubbery composites: Effect of filler particle size

We have measured proton NMR T₂ relaxation spectra in Arco R45M OH-terminated poly-butadienes (PBs) cured with isophorone diisocyanate and filled with 65 wt % SiO₂ particles of each of six different average sizes. Identifying the short T₂ component with the gel, we find that the gel fraction is displaced from nominal NCO/OH stoichiometry, probably as a result of water adsorbed on filler particle surfaces. Near effective stoichiometry and in the presence of filler, molecular and segmental mobilities decrease, most strongly in specimens with the smallest filler particles. Comparison with parallel Monte Carlo simulations of the PB matrix geometry indicates that segmental mobility and sol migration decrease uniformly in a wide vicinity of the filler particles. Thus the rigidification of the matrix measured via NMR has a range of approximately 1-3 μm from nearby filler particle surfaces, representing the rms diffusion distance of the light components of the sol during the T₂ relaxation. © 1993 John Wiley & Sons, Inc.