Mesoscale model of polymer melt structure: self-consistent mapping of molecular correlations to coarse-grained potentials

Development and application of coarse-graining methods to condensed phases of macromolecules is an active area of research. Multiscale modeling of polymeric systems using coarse-graining methods presents unique challenges. Here we apply a coarse-graining method that self-consistently maps structural correlations from detailed molecular dynamics (MD) simulations of alkane oligomers onto coarse-grained potentials using a combination of MD and inverse Monte Carlo methods. Once derived, the coarse-grained potentials allow computationally efficient sampling of ensemble of conformations of significantly longer polyethylene chains. Conformational properties derived from coarse-grained simulations are in excellent agreement with experiments. The level of coarse graining provides a control over the balance of computational efficiency and retention of chemical identity of the underlying polymeric system. Challenges to extension and application of this and similar structure-based coarse-graining methods to model dynamics and phase behavior in polymeric systems are briefly discussed.     

Conformational distribution of heptaalanine: Analysis using a new Monte Carlo chain growth method

A distribution of conformations of heptaalanine is obtained using a new Monte Carlo (MC) method that grows the chain atom by atom. Resulting configurations are energy minimized and a detailed analysis is performed of the minimum-energy conformers using a method of classification that partitions ?ψ space. The MC-generated configurations are compared with those generated from high-temperature molecular dynamics (MD) simulations. It is found that the new method generates a wide distribution of low-energy conformers at least 10 times more quickly than the MD. An analysis of the generated energy minima demonstrates that they can be divided into clusters in the space defined by the five pairs of ?—ψ angles of the inner residues. The space occupied by the minima populating each cluster is restricted. © 1992 by John Wiley & Sons, Inc.     

Computer simulation of the conformational behavior of cholecystokinin fragments: Conformational families of sulfated CCK8

Summary Display methods, such as principal component analysis, and clustering methods were applied to a sample of cholecystokinin, (sulfated CCK8) conformations obtained from a Monte Carlo simulation. It is shown that six families of conformations can entirely describe the sample. Each family represents a typical conformer. These theoretical models are in agreement with recent experimental results which stress the predominance of folded conformers in aqueous medium.     

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.     

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.     

Conformational analysis of the eight-membered ring of the oxidized cysteinyl-cysteine unit implicated in nicotinic acetylcholine receptor ligand recognition.

Nicotinic acetylcholine receptors (nAChRs) are membrane-bound, pentameric ligand-gated ion channels associated with a variety of human disorders such as Alzheimer's disease, Parkinson's disease, schizophrenia, and pain. Most known nAChRs contain an unusual eight-membered disulfide-containing cysteinyl-cysteine ring, ox-[Cys-Cys], as does the soluble acetylcholine binding protein (AChBP) found in the snail Lymnaea stagnalis. The cysteinyl-cysteine ring is located in a region implicated in ligand binding, and conformational changes involving this ring may be important for modulation of nAChR function. We have studied the preferred conformations of Ac-ox-[Cys-Cys]-NH2 by NMR in water and computationally by Monte Carlo simulations using the OPLS-AA force field and GB/SA water model. ox-[Cys-Cys] adopts four distinct low-energy conformers at slightly above 0 degrees C in water. Two populations are dependent on the peptide omega2 dihedral angle, with the trans amide favored over the cis amide by a ratio of ca. 60:40. Two ox-[Cys-Cys] conformers with a cis amide bond (C+ and C-) differ from each other primarily by variation of the chi3 dihedral angle, which defines the orientation of the helicity about the S-S bond (+/- 90 degrees ). Two trans amide conformers have the same S-S helicity (chi3 approximately -90 degrees ), but are distinguished by a backbone rotation about phi2 and psi1 (T- and T'-). The ratio of T-/T'-/C+/C- is 47:15:29:9. The orientation of the pendant moieties from the eight-membered ring is more compact for the major trans conformer (T-) than for the extended conformations adopted by T'-, C+, and C-. These conformational preferences are also observed in tetrapeptide and undecapeptide fragments of the human alpha7 subtype of the nAChR that contains the ox-[Cys-Cys] unit. Conformer T- is nearly identical to the conformation seen in the X-ray structure of ox-[Cys(187)-Cys(188)] found in the unliganded AChBP, and is a Type VIII beta-turn.     

Role of solvent in determining conformational preferences of alanine dipeptide in water

Evidence from a variety of spectroscopic probes indicates that (phi, psi) values corresponding to the left-handed polyproline II helix (P(II)) are preferred for short alanine-based peptides in water. On the basis of results from theoretical studies, it is believed that the observed preference is dictated by favorable peptide-solvent interactions, which are realized through formation of optimal hydrogen-bonding water bridges between peptide donor and acceptor groups. In the present study, we address this issue explicitly by analyzing the hydration structure and thermodynamics of 16 low-energy conformers of the alanine dipeptide (N-acetylalanine-N'-methylamide) in liquid water. Monte Carlo simulations in the canonical ensemble were performed under ambient conditions with all-atom OPLS parameters for the alanine dipeptide and the TIP5P model for water. We find that the number of hydrogen-bonded water molecules connecting the peptide group donor and acceptor atoms has no effect on the solvation thermodynamics. Instead, the latter are determined by the work done to fully hydrate the peptide. This work is minimal for conformations that are characterized by a minimal overlap of the primary hydration shells around the peptide donor and acceptor atoms. As a result, peptide-solvent interactions favor "compact" conformations that do not include P(II)-like geometries. Our main conclusion is that the experimentally observed preference for P(II) does not arise due to favorable direct interactions between the peptide and water molecules. Instead, the latter act to unmask underlying conformational preferences that are a consequence of minimizing intrapeptide steric conflicts.     

Difference spatial distribution function analysis of aqueous solutions. IV. Hydration structure changes of ethylene glycol solutions throughout conformational change process from gGg' to tGg' conformers

Monte Carlo (MC) simulations were carried out for an infinitely dilute aqueous solution of two stable conformers (gGg' and tGg') and of three conformations between gGg' and tGg' conformers of ethylene glycol (EG) at 298K. Based on the spatial distribution function (SDF) goo(x,y,z), obtained from the MC simulation in the above conformations in liquid water, the high distribution of hydration water molecules could be divided into hydrogen acceptor (HA), hydrogen donor (HD), MIX (overlapped distribution of HA and HD), and hydrophobic hydration (HH) regions. The spatial orientations of hydrogen-bonded water molecules were found to be of a linear type with a triple-layer structure in the HA region and HA part (in the MIX region), and double-layer structures in the HD region and HD part (in the MIX region). In addition, it was apparent that the spatial orientations of these water molecules were of the linear type throughout the conformational change process from gGg' to tGg' conformers in liquid water. From the difference SDF (DSDF), deltagoo(x,y, z), between the SDFs of two conformations, we concluded that the distribution of hydration water molecules in the HA and HD parts of the MIX region are governed by the competition of internal hydrogen bonds between the hydrogen atom and two lone-pair electrons on the oxygen atom of an EG molecule.     

Conformational analysis of a farnesyltransferase peptide inhibitor, CVIM

The conformational states of the peptide Cys-Val-Ile-Met (or CVIM) were computed and characterized. CVIM inhibits farnesylation of the Ras oncogene product, p21^ras, at the cysteine residue of the C-terminal segment. CVIM is active in an extended conformation. A similar peptide (KTKCVFM) appears to bind the enzyme in the Type I bend conformation. In the present study, the conformations of CVIM were computed in an aqueous environment with the peptide in the zwitterionic state. Solvation free energy based on solvent accessible surface area and a distance dependent dielectric were used in the calculations. Final conformations of multiple independent Monte Carlo simulated annealing (MCSA) conformational searches were used as starting points for Metropolis Monte Carlo (MMC) runs. Conformations saved at intervals during MMC runs were analyzed. Conformers were separated by interactive clustering in dihedral angle coordinates. The four lowest energy conformers corresponding to a Type I bend, extended, AB-bend, and BA-bend were within 0.3 kcal/mol of each other, and dominant in terms of population. The Type I bend and extended conformers were supported by the binding studies. The extended conformer was the most populated. In the AB-bend conformer, `A' indicates the -helix conformation of Val, and `B' indicates the -strand conformation of Ile. The AB- and BA-bend conformations differed from the extended conformation in the value of Val and Ile , respectively, and from the Type I bend conformation in the value of Ile and Val , respectively. The four lowest energy conformers were characterized in terms of energy, density of low energy conformations (or entropy), structure, side chain rotamer fraction population, and interatomic distances.     

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.     

Molecular modelling of liquid crystal systems: An internal coordinate Monte Carlo approach

A Monte Carlo scheme is presented which is designed to provide a convenient mechanism to model accurately the internal molecular structure of liquid crystalline molecules. The technique stores atomic positions in terms of bond lengths, bond angles and dihedral angles within a Z-matrix, and the Monte Carlo scheme involves generating trial configurations from changes to the Z-matrix using the MM2 molecular mechanics potential to describe energy changes between different molecular conformations. The technique is applied to the liquid crystal molecule 4-n-pentyl-4'-cyanobiphenyl (5CB), and results are presented for the conformational populations and dihedral angle distributions of 5CB in the gas phase at 300 K. The effect of a nematic mean field on the distribution of molecular conformations is also examined via the addition of a conformation-dependent potential of mean torque to the internal energy.     

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     

Single molecule spectroscopy as a probe for dye-polymer interactions

Experimental (Single Molecule Spectroscopy) and theoretical (quantum-chemical calculations and Monte Carlo and molecular dynamics simulations) techniques are combined to investigate the behavior and dynamics of a polymer-dye molecule system. It is shown that the dye molecule of interest (1,1'-dioctadecyl-3,3,3',3'-tetramethylindo-dicarbocyanine) adopts two classes of conformations, namely planar and nonplanar ones, when embedded in a poly(styrene) matrix. From an in-depth analysis of the fluorescence lifetime trajectories, the planar conformers can be further classified according to the way their alkyl side chains interact with the surrounding poly(styrene) chains.     

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.     

Monte Carlo simulation and molecular theory of tethered polyelectrolytes

We investigate the structure of end-tethered polyelectrolytes using Monte Carlo simulations and molecular theory. In the Monte Carlo calculations we explicitly take into account counterions and polymer configurations and calculate electrostatic interaction using Ewald summation. Rosenbluth biasing, distance biasing, and the use of a lattice are all used to speed up Monte Carlo calculation, enabling the efficient simulation of the polyelectrolyte layer. The molecular theory explicitly incorporates the chain conformations and the possibility of counterion condensation. Using both Monte Carlo simulation and theory, we examine the effect of grafting density, surface charge density, charge strength, and polymer chain length on the distribution of the polyelectrolyte monomers and counterions. For all grafting densities examined, a sharp decrease in brush height is observed in the strongly charged regime using both Monte Carlo simulation and theory. The decrease in layer thickness is due to counterion condensation within the layer. The height of the polymer layer increases slightly upon charging the grafting surface. The molecular theory describes the structure of the polyelectrolyte layer well in all the different regimes that we have studied.     

Structure and free energy of complex thermodynamic systems

Biological systems are intrinsically complex, involving many degrees of freedom, heterogeneity, and strong interactions among components. For the simplest of biological substances, e.g., biomolecules, which obey the laws of thermodynamics, we may try to investigate them by means of a statistical mechanical approach. Even for these simplest many-body systems, assuming all microscopic interactions are completely known, current physical and chemical methods of characterizing the overall structure and free energy face the fundamental challenge of an exponential amount of computations as the number of degrees of freedom of these systems increases. As a response to this problem, two general procedures have been developed to compute the structure (Monte Carlo-minimization method) and free energy (Monte Carlo recursion method) of a complex thermodynamic system. The Monte Carlo-minimization procedure has been applied to determine the structure of a pentapeptide Met-enkephalin, leading consistently to a stable β-bend structure, starting from random initial conformations. The Monte Carlo recursion method has been applied to a Lennard-Jones fluid, with results in agreement with previously published values of the free energy obtained from other procedures.     

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].     

Solid-State CP/MAS 13C-NMR Spectra of Oligolides derived from 3-hydroxybutanoic acid

The solid-state CP/MAS ¹³C-NMR spectra (cross-polarization/magic-angle spinning ¹³C-NMR) of eight lower cyclic and one linear oligomers and several polymers of (R)-3-hydroxybutanoic acid (3-HB) are reported. The polymeric samples of different origin and molecular weight give remarkably similar and well resolved spectra, indicating considerable similarity in the conformations of the molecules and homegeneity in the solid-state environment. The crystalline cyclic oligomers 1 – 8 containing 3–9 units of 3-HB give very well resolved spectra. The number of nonequivalent positions in the solid state can be identified and is in accord with structures from X-ray diffraction where these were determined. The spectra of the oligolides become increasingly similar to those of the polymer as the ring size increases. This spectral evidence supports the view of a homogeneous and well defined conformation for the polymeric material (as proposed previously, based on other experiments).     

Conformation Controls Mobility: 2H-Tetranaphthylporphyrins on Cu(111)

The adsorption behavior and the mobility of 2H-Tetranaphthylporphyrin (2HTNP) on Cu(111) was investigated by scanning tunneling microscopy (STM) at room temperature (RT). The molecules adsorb, like the structurally related 2HTPP, in the “inverted” structure with the naphthyl plane restricted to an orientation parallel to the Cu surface. The orientation of the four naphthyl groups yields altogether 16 possible conformations. Due to the existence of rotamer pairs, 10 different appearances are expected on the surface, and all of them are identified by STM at RT. Most interestingly, the orientation of the naphthyl groups significantly influences the diffusion behavior of the molecules on Cu(111). We identify three different groups of conformers, which are either immobile, medium or fast diffusing at RT. The mobility seems to decrease with increasing size of the footprint of the conformers on the surface.