The electrostatically driven Monte Carlo method: application to conformational analysis of decaglycine

The Electrostatically Driven Monte Carlo (EDMC) method was applied in a study of a decamer of glycine whose conformational behavior is described by the Empirical Conformational Energy Program for Peptides (ECEPP/2) potential energy model. When free neutral end groups were used, it was found that conformations that were not alpha-helical had significantly lower potential energies than fully alpha-helical ones. However, when the N- and C-termini were blocked by acetyl and methyl amide groups, respectively, the number of unsatisfied hydrogen-bond donors and acceptors at the helix termini was diminished from 8 to 6; in this case, the possibility of forming two additional alpha-helical hydrogen bonds was an important enough factor in making the alpha-helical conformation the one with the lowest energy. The EDMC method was used as a global energy optimizer since it does not often become trapped in high-energy local minima.     

On the multiple-minima problem in the conformational analysis of polypeptides. IV. Application of the electrostatically driven Monte Carlo method to the 20-residue membrane-bound portion of melittin

The conformational space of the membrane-bound portion of melittin has been searched using the electrostatically driven Monte Carlo (EDMC) method with the ECEPP/2 (empirical conformational energy program for peptides) algorithm. The former methodology assumes that a polypeptide or protein molecule is driven toward the native structure by the combined action of electrostatic interactions and stochastic conformational changes associated with thermal movements. The algorithm produces a Monte Carlo search in the conformational hyperspace of the polypeptide using electrostatic predictions and a random sampling technique, combined with local minimization of the energy function, to locate low-energy conformations. As a result of 8 test calculations on the 20-residue membrane-bound portion of melittin, starting from six arbitrary and two completely random conformations, the method was able to locate a very low-energy region of the potential with a well-defined structure for the backbone. In all of the cases under study, the method found a cluster of similar low-energy conformations that agree well with the structure deduced from x-ray diffraction experiments and with one computed earlier by the build-up procedure.     

On the multiple-minima problem in the conformational analysis of polypeptides. II. An electrostatically driven Monte Carlo method--tests on poly(L-alanine)

A new approach to the multiple-minima problem in protein folding is presented. It is assumed that the molecule is driven toward the native structure by three types of mechanism. The first one involves an optimization of the electrostatic interactions, whereby the molecule evolves toward conformations in which the charge distribution becomes energetically more favorable. The second mechanism involves a Monte Carlo–energy minimization approach, and the third one is a backtrack mechanism that acts in the opposite direction, increasing the energy—the third type of movement provides a means to perturb the molecule when it is trapped in a stable but energetically unfavorable local energy minimum. This paper describes the implementation of a model based on these mechanisms, and illustrates its effectiveness by computations on different arbitrary starting conformations of a terminally blocked 19-residue chain of poly(L -alanine) for which the global minimum apparently corresponds to the right-handed α-helix. In all cases, the global minimum was attained, even when the starting conformation was a left-handed α-helix. In the latter case, the trajectory of conformations passed through partially melted forms of the left-handed α-helix (because of electrostatic defects at the ends), and then through the formation of structures leading to the more stable right-handed α-helix.     

A prediction of tertiary structures of peptide by the Monte Carlo simulated annealing method

The Monte Carlo simulated annealing method has been applied to the prediction of three-dimensional structures of enkephalin. The low-energy conformations obtained were classified into a few groups of similar structures, which indicates that our method is effective. New low-energy structures were identified together with previously proposed structures.     

Impact of protein-protein contacts on the conformation of thrombin-bound hirudin studied by comparison with the nuclear magnetic resonance solution structure of hirudin(1-51).

The impact of protein-protein interactions on the conformation of the N-terminal hirudin domain consisting of residues 1 to 51 in the X-ray crystal structure of a hirudin-thrombin complex was investigated through comparisons with the nuclear magnetic resonance solution structure of hirudin(1-51). The close overall similarity observed between these two structures contrasts with the behavior of the C-terminal 17-residue polypeptide segment of hirudin, which is flexibly disordered in solution but exhibits a defined conformation in the complex with thrombin. Localized structural differences in the N-terminal domain include that residues 1 to 3 of hirudin in the crystalline complex form a hydrogen-bonding network with thrombin that is reminiscent of a parallel beta-sheet. Moreover, the backbone conformation of residues 17 to 20 in the complex does not contain the characteristic hydrogen bond observed for the type II' reverse turn in the solution structure, and the side-chains of Ser19 and Val21 have significantly different orientations in the two structures. Most of these structural changes can be related directly to thrombin-hirudin contacts, which may also be an important factor in the mechanism of hirudin action. In this context, it is of special interest that other residues that also make numerous contacts with thrombin, e.g. Thr4, Asp5 and Asn20, have identical conformations in free hirudin and in the complex.     

Monte Carlo simulations of peptide solvation

To increase our understanding of peptide–water interactions, we are simulating the behavior of water molecules in the intermolecular channels of [Phe⁴Val⁶]antamanide dododecahydrate crystals. There is good overall agreement between the positions predicted using two alternative potential functions and those that have been observed by x-ray diffraction. Detailed differences between the predictions for the two potential functions are discussed.     

A multiple-start Monte Carlo docking method.

We present a method to search for possible binding modes of molecular fragments at a specific site of a potential drug target of known structure. Our method is based on a Monte Carlo (MC) algorithm applied to the translational and rotational degrees of freedom of the probe fragment. Starting from a randomly generated initial configuration, favorable binding modes are generated using a two-step process. An MC run is first performed in which the energy in the Metropolis algorithm is substituted by a score function that measures the average distance of the probe to the target surface. This has the effect of making buried probes move toward the target surface and also allows enhanced sampling of deep pockets. In a second MC run, a pairwise atom potential function is used, and the temperature parameter is slowly lowered during the run (Simulated Annealing). We repeat this procedure starting from a large number of different randomly generated initial configurations in order to find all energetically favorable docking modes in a specified region around the target. We test this method using two inhibitor-receptor systems: Streptomyces griseus proteinase B in complex with the third domain of the ovomucoid inhibitor from turkey, and dihydrofolate reductase from E. coli in complex with methotrexate. The method could consistently reproduce the complex found in the crystal structure searching from random initial positions in cubes ranging from 25 A to 50 A about the binding site. In the case of SGPB, we were also successful in docking to the native structure. In addition, we were successful in docking small probes in a search that included the entire protein surface.     

Quantitative modelling of DNA damage using Monte Carlo track structure method

This paper presents data on modelling of DNA damage induced by electrons, protons and alpha-particles to provide an insight into factors which determine the biological effectiveness of radiations of high and low linear energy transfer (LET). These data include the yield of single- and double-strand breaks (ssb, dsb) and base damage in a cellular environment. We obtain a ratio of 4–15 for ssb:dsb for solid and cellular DNA and a preliminary ratio of about 2 for base damage to strand breakage. Data are also given on specific characteristics of damage at the DNA level in the form of clustered damage of varying complexity, that challenge the repair processes and if not processed adequately could lead to the observed biological effects. It is shown that nearly 30% of dsb are of complex form for low-LET radiation, solely by virtue of additional breaks, rising to about 70% for high-LET radiation. Inclusion of base damage increases the complex proportion to about 60% and 90% for low- and high-LET radiation, respectively. The data show a twofold increase in frequencies of complex dsb from low-LET radiation when base damage is taken into account. It is shown that most ssb induced by high-LET radiation have associated base damages, and also a substantial proportion is induced by low-energy electrons. Received: 20 September 1998 / Accepted in revised form: 15 December 1998     

Tertiary structure prediction of the KIX domain of CBP using Monte Carlo simulations driven by restraints derived from multiple sequence alignments

Using a recently developed protein folding algorithm, a prediction of the tertiary structure of the KIX domain of the CREB binding protein is described. The method incorporates predicted secondary and tertiary restraints derived from multiple sequence alignments in a reduced protein model whose conformational space is explored by Monte Carlo dynamics. Secondary structure restraints are provided by the PHD secondary structure prediction algorithm that was modified for the presence of predicted U-turns, i.e., regions where the chain reverses global direction. Tertiary restraints are obtained via a two-step process: First, seed side-chain contacts are identified from a correlated mutation analysis, and then, a threading-based algorithm expands the number of these seed contacts. Blind predictions indicate that the KIX domain is a putative three-helix bundle, although the chirality of the bundle could not be uniquely determined. The expected root-mean-square deviation for the correct chirality of the KIX domain is between 5.0 and 6.2 Å. This is to be compared with the estimate of 12.9 Å that would be expected by a random prediction, using the model of F. Cohen and M. Sternberg (J. Mol. Biol. 138:321–333, 1980). Proteins 30:287–294, 1998. © 1998 Wiley-Liss, Inc.     

Calculation of the structure of the serotonin-antibiotic lasalocid A complex by conformation analysis and the Monte Carlo method

The conformational aspects of interaction of the antibiotic X537A at complexation with serotonin, hydration of molecules and their complex were studied by the methods of theoretical conformational analysis and Monte-Carlo.     

Genome-wide tagging SNPs with entropy-based Monte Carlo method.

The number of common single nucleotide polymorphisms (SNPs) in the human genome is estimated to be around 3-6 million. It is highly anticipated that the study of SNPs will help provide a means for elucidating the genetic component of complex diseases and variable drug responses. High-throughput technologies such as oligonucleotide arrays have produced enormous amount of SNP data, which creates great challenges in genome-wide disease linkage and association studies. In this paper, we present an adaptation of the cross entropy (CE) method and propose an iterative CE Monte Carlo (CEMC) algorithm for tagging SNP selection. This differs from most of SNP selection algorithms in the literature in that our method is independent of the notion of haplotype block. Thus, the method is applicable to whole genome SNP selection without prior knowledge of block boundaries. We applied this block-free algorithm to three large datasets (two simulated and one real) that are in the order of thousands of SNPs. The successful applications to these large scale datasets demonstrate that CEMC is computationally feasible for whole genome SNP selection. Furthermore, the results show that CEMC is significantly better than random selection, and it also outperformed another block-free selection algorithm for the dataset considered.     

Stability of hirudin, a thrombin-specific inhibitor. The structure of alkaline-inactivated hirudin

Hirudin is a 65-amino acid polypeptide with three disulfide linkages. It is stable under extreme pH (1.47-12.9), high temperature (95 degrees C), and in the presence of denaturants (6 M guanidinium chloride or 8 M urea). The thrombin inhibitory activity of hirudin remains unaffected even after cleavage of an internal peptide bond (Lys36-Asn37). One condition which effectively and irreversibly inactivates hirudin is the combination of elevated temperature and alkaline pH. Structural analysis reveals that inactivation is a consequence of base-catalyzed beta-elimination of the disulfide bonds. The reaction leads to the conversion of hirudin to a mixture of highly heterogeneous polymers (from monomer to heptamer) which are intra- and intermolecularly cross-linked by cystine (20%), lanthionine (50%), and lysinoalanine (30%).     

Hydration of the left spiral of the poly-L-proline type. Study by the Monte Carlo method]

The paper exhibits results of hydration shell Monte Carlo calculations in poly-L-proline II and extended helix conformation and in alpha-helical and beta-structural conformations for comparison. It was found that left-handed helix of poly-L-proline II type as well as epsilon-helix are characterized by very favorable hydration. Therefore this conformation has preference as compared to other standard conformations of the main polypeptide chain. This determined inevitability of cold denaturation of protein.     

Conformational stability of a thrombin-binding peptide derived from the hirudin C-terminus.

The COOH-terminal region of hirudin represents an independent functional domain that binds to an anion-binding exosite of thrombin and inhibits the interaction of thrombin with fibrinogen and regulatory proteins in blood coagulation. The thrombin-bound structure of the peptide fragment, hirudin 55-65, has been determined by use of transferred NOE spectroscopy [Ni, F., Konishi, Y., & Scheraga, H. A. (1990) Biochemistry 29, 4479-4489]. The stability of the thrombin-bound conformation has been characterized further by a combined NMR and theoretical analysis of the conformational ensemble accessible by the hirudin peptide. Medium- and long-range NOE's were found for the free hirudin peptide in aqueous solution and in a mixture of dimethyl sulfoxide and water at both ambient (25 degrees C) and low (0 degrees C) temperatures, suggesting that ordered conformations are highly populated in solution. The global folding of these conformations is similar to that in the thrombin-bound state, as indicated by NOE's involving the side-chain protons of residues Phe(56), Ile(59), Pro(60), Tyr(63), and Leu(64). Residues Glu(61), Glu(62), Tyr(63), and Leu(64) all contain approximately 50% of helical conformations calculated from the ratio of the sequential dNN and d alpha N NOE's. Among the helical ensemble, active 3(10)-helical conformations were found by an analysis of the medium-range [(i,i+2) and (i,i+3)] NOE's involving the last six residues of the peptide. An analysis of the side-chain rotamers revealed that, upon binding to thrombin, there may be a rotation around the alpha CH-beta CH bond of Ile(59) such that Ile(59) adopts a gauche- (chi 1 = +60) conformation in contrast to the highly populated trans (chi 1 = -60) found for Ile(59) in the free peptide. However, the thrombin-bound conformation of the hirudin peptide is still an intrinsically stable conformer, and the preferred conformational ensemble of the peptide contains a large population of the active conformation. The apparent preference for a gauche- (chi 1 = +60) side-chain conformation of Ile(59) in the bound state may be explained by the existence of a positively charged arginine residue among the hydrophobic residues in the thrombin exosite.     

Dependence on the dielectric model and pH in a synthetic helical peptide studied by Monte Carlo simulated annealing

Monte Carlo simulated annealing is applied to the tertiary structure prediction of a 17-residue synthetic peptide, which is known by experiment to exhibit high helical content at low pH. Two dielectric models are considered: sigmoidal distance-dependent dielectric function and a constant dielectric function (? = 2). Starting from completely random initial conformations, our simulations for both dielectric models at low pH gave many helical conformations. The obtained low-energy conformations are compared with the nuclear Overhauser effect spectroscopy cross-peak data for both main chain and side chains, and it is shown that the results for the sigmoidal dielectric function are in remarkable agreement with the experimental data. The results predict the existence of two disjoint helices around residues 5–9 and 11–16, while nmr experiments imply significant α-helix content between residues 5 and 14. Simulations with high pH, on the other hand, hardly gave a helical conformation, which is also in accord with the experiment. These findings indicate that when side chains are charged, electrostatic interactions due to these charges play a major role in the helix stability. Our results are compared with the previous 500 ps molecular dynamics simulations of the same peptide. It is argued that simulated annealing is superior to molecular dynamics in two respects: (1) direct folding of α-helix from completely random initial conformations is possible for the former, whereas only unfolding of an α-helix can be studied by the latter; (2) while both methods predict high helix content for low pH, the results for high pH agree with experiment (low helix content) only for the former method. © 1994 John Wiley & Sons, Inc.     

The structure of polymer chains in confinement. A Monte Carlo study

A coarse-grained model of polymer star chains confined in two parallel impenetrable surfaces, which were attractive for polymer beads was studied. The flexible homopolymer chains were built of united atoms whose positions in space were restricted to vertices of a simple cubic lattice. The chains were modeled in good solvent conditions and, thus, there were no long-range specific interactions between polymer beads—only the excluded volume was present. The influence of the polymer density and the distances between the confining surfaces on the properties of star-branched polymers was studied. It is shown that the chains adsorbed on one surface could change their position so that they swap between both surfaces with frequency depending on the size of the slit and on the density of the system only. The increase of the polymer density diminished the frequency of jumps and caused that chains became only partially adsorbed. The analysis of structural elements of chains showed that the increase of the density of the system leads to increase of the number of bridges connecting the two adsorbing surfaces, thus, the frequency of jumps between them decreases.     

A Monte Carlo method for combined segregation and linkage analysis.

We introduce a Monte Carlo approach to combined segregation and linkage analysis of a quantitative trait observed in an extended pedigree. In conjunction with the Monte Carlo method of likelihood-ratio evaluation proposed by Thompson and Guo, the method provides for estimation and hypothesis testing. The greatest attraction of this approach is its ability to handle complex genetic models and large pedigrees. Two examples illustrate the practicality of the method. One is of simulated data on a large pedigree; the other is a reanalysis of published data previously analyzed by other methods.     

Modeling of phototransduction processes in the photoreceptor disk membranes by the Monte Carlo method

The Monte Carlo method was used to model the diffusion behaviors of functionally important proteins of the phototransduction system in retinal rod outer segment disk membranes. The results expand our knowledge of the mechanisms of inactivation of the main phototransduction heterotrimeric GTP-binding protein transducin.