Monte Carlo Simulated Annealing Research Articles

HOLE: A program for the analysis of the pore dimensions of ion channel structural models

A method (HOLE) that allows the analysis of the dimensions of the pore running through a structural model of an ion channel is presented. The algorithm uses a Monte Carlo simulated annealing procedure to find the best route for a sphere with variable radius to squeeze through the channel. Results can be displayed in a graphical fashion or visualized with most common molecular graphics packages. Advances include a method to analyze the anisotropy within a pore. The method can also be used to predict the conductance of channels using a simple empirically corrected ohmic model. As an example the program is applied to the cholera toxin B-subunit pentamer. The compatibility of the crystal structure and conductance data is established.

Characterizing large correlated fluctuations of macromolecular conformations in torsion-angle space using the multivariate wrapped-Gaussian distribution

We describe a multivariate wrapped-Gaussian distribution that can be used to model statistical distributions expressed in periodic angular variables even in the presence of significant angle-angle correlations. Using amino acid and peptide examples, we show how this distribution can be used to characterize accurately conformational fluctuations in torsion-angle space. The method permits more accurate characterization of large-scale peptide and polymer fluctuations than the standard harmonic or quasiharmonic method. This can be used to increase the efficiency of Monte Carlo sampling and simulated annealing in torsion-angle space.

Conformational analysis of two glycoproteins: a Monte Carlo simulated annealing approach using a soft-sphere potential

The Monte Carlo simulated annealing method was effectively used to predict the three-dimensional structure of the carbohydrate part of two glycoproteins: 1vsg and 2fbj from a protein data bank, utilizing a soft-sphere potential. The result was compared both to the crystal structure and to the structure of the corresponding isolated oligosaccharide structure simulated using an ECEPP/2 force field. A good agreement with crystal structure was reached. The interaction with the protein environment was found to significantly influence the structure of the carbohydrate moiety.

Generalized simulated annealing algorithms using Tsallis statistics: Application to conformational optimization of a tetrapeptide.

A Monte Carlo simulated annealing algorithm based on the generalized entropy of Tsallis is presented. The algorithm obeys detailed balance and reduces to a steepest descent algorithm at low temperatures. Application to the conformational optimization of a tetrapeptide demonstrates that the algorithm is more effective in locating low energy minima than standard simulated annealing based on molecular dynamics or Monte Carlo methods.

Simulation of the Packing of Transmembrane α-Helices

The aim of this study is to generate initial candidate models for bundles of transmembrane helices. Such models may then be further refined by eg. molecular dynamics simulations. Each helix is treated as a rigid body represented by a direction vector and the coordinates of its centre of mass. Constituent residues are mapped onto the helix axis in order to maintain the amino acid sequence dependent properties of helix. Helix packing is optimised according to a simple semi-empirical potential composed of three components: a helix-bilayer interaction potential, a helix crossing angle potential and a helix-helix distance potential. A Monte Carlo simulated annealing protocol is employed to optimise the helix bundle system, ie. to find low energy structures. A fortran program (TMH) has been developed to implement the method described.

Inter-C? atomic potentials derived from the statistics of average interresidue distances in proteins: Application to bovine pancreatic trypsin inhibitor

New effective potentials acting between pairs of residues in proteins are proposed based on statistics of average distances and standard deviations between Cα atoms of residues in protein tertiary structures. Gaussian functions are adopted as analytical forms of the potentials. A protein structure is modeled as a chain molecule with a fixed bond length connecting particles approximating the effects of amino acid residues. The potentials derived in this study are used for conformational sampling of trypsin inhibitor from bovine pancreas. Sampling is done with the Monte Carlo simulated annealing method. Sampled conformations can be classified into a few groups or structural classes, and one of these classes contains structures relatively close (with 7.8–8.7 Å root mean square [rms] deviation) to the X-ray structure. The native structure exhibits relatively low energy. These results denote a rather smooth landscape of the present potential energy surfaces. One class of classified structures contains nativelike structures, which suggests that the native structure can be predicted by further refinement of structures in this class. We discuss other properties and the effectiveness of the present potentials for description of protein structures. © 1996 by John Wiley & Sons, Inc.

Prediction of template location via a combined Monte Carlo–simulated annealing approach

A combined Monte Carlo–simulated annealing approach has been developed to predict the location and orientation adopted by organic molecules within a zeolite host. Periodic boundary conditions were used throughout the simulations in order to permit a full treatment of organic–organic interactions within a densely packed system. This approach has been used to investigate the relationship between zeolite products and the organic template molecules used in their synthesis. The results are shown to reproduce experimentally determined locations accurately, including important disordering effects. Previous experimental work has shown that some template molecules can effect the synthesis of more than one type of zeolite framework when experimental conditions are varied and also that many zeolites can be synthesised by an apparently diverse range of templates. Our results show that both these observations can still be rationalised via the ‘templating theory’ of zeolite synthesis. A mechanism for faulting is proposed which is shown to be consistent for NU-86 and the industrially important zeolite beta.

Conformational Memories and the Exploration of Biologically Relevant Peptide Conformations: An Illustration for the Gonadotropin-Releasing Hormone

The application of a recently developed technique of conformational memories (Guarnieri, F.; Wilson, S. R. J. Comput. Chem. 1995, 16, 5, 648) to the study of peptide structure is illustrated with an analysis of the conformational populations of the decapeptide gonadotropin-releasing hormone (GnRH) and the mutant peptide Lys8-GnRH. The conformational space of the peptides is explored fully with multiple Monte Carlo simulated annealing (MC/SA) random walks using the Amber* force field and the generalized Born/surface area (GB/SA) continuum solvation model of water as implemented in the Macromodel molecular modeling package. The collective histories of all the random walks are transformed into mean field dihedral distribution functions called “conformational memories” (35 conformational memories for GnRH, one for each torsion angle). Conformational families of the peptides at 310 K are obtained from these results with the use of a biased sampling technique which explores only the areas found to be populated in the conformational memories. A large family of GnRH structures that comprises approximately 70% of the population is identified by clustering conformations according to a pairwise root mean square deviation criterion. Members of this family of conformations share a distinctive β-type turn in the backbone that involves residues 5−8. This conformation is shown to correspond to the preferred geometry of a structurally constrained analog of GnRH that binds to the GnRH receptor with high affinity. In contrast, GnRH analogs such as Lys8-GnRH, for which we find that the major conformational family exhibits an extended backbone, seem to belong to the group of low-affinity ligands. The results suggest a correlation between high affinity at the GnRH receptor and the ability of the peptides to have a large population of conformations that exhibit the characteristic secondary structure of a β-type bend. Thus, the method of conformational memories is shown to provide a powerful and reliable tool for the computational exploration of structure−function relations of flexible peptides.

Theoretical Studies on the Bioactive Conformation of Nerve Growth Factor Using VBMCA Novel Variable Basis Monte Carlo Simulated Annealing Algorithm for Peptides

Nerve Growth Factor (NGF) is an important neurotrophic protein implicated in Alzheimer's disease, epilepsy, and pain. Although the amino and carboxyl termini enable an NGF's recognition by its TrkA receptor, their conformations have not been resolved in recent crystallographic studies. Variable Basis Monte Carlo simulated annealing calculations are utilized to study low-energy conformational space of the NGF termini of three highly active and three inactive NGF analogues in order to determine their bioactive conformation. The complex of the NGF termini splits into two distinct moieties: a rigid region (residues 9-11 and 112‘-118‘) and a flexible loop (residues 1-8). The geometry of the rigid region, which is maintained by electrostatic interaction between Glu11 and Arg118‘, is conserved in active molecules only. The separation of the flexible loop from the rigid region is necessary in order to eliminate an influence of the loop on the biologically active conformation of the rigid region. Experimentally o...

An automated method for dynamic ligand design.

An automated method for the dynamic ligand design (DLD) for a binding site of known structure is described. The method can be used for the creation of de novo ligands and for the modification of existing ligands. The binding site is saturated with atoms (sp3 carbon atoms in the present implementation) that form molecules under the influence of a potential function that joins atoms to each other with the correct stereochemistry. The resulting molecules are linked to precomputed functional group minimum energy positions in the binding site. The generalized potential function allows atoms to sample a continuous parameter space that includes the Cartesian coordinates and their occupancy and type, e.g., the method allows change of an sp3 carbon into an sp2 carbon or oxygen. A parameter space formulated in this way can then be sampled and optimized by a variety of methods. In this work, molecules are generated by use of a Monte Carlo simulated annealing algorithm. The DLD method is illustrated by its application to the binding site of FK506 binding protein (FKBP), an immunophilin. De novo ligands are designed and modification of the immunosuppressant drug FK506 are suggested. The results demonstrate that the dynamic ligand design approach can automatically construct ligands which complement both the shape and charge distribution of the binding site.

Atomic short-range order and alloy ordering tendency in the Ag-Au system

Accurate information of energetics is essential to map out the temperature versus composition phase diagram of a binary substitutional A1-xBx alloy. Since it is computationally prohibitive to calculate the total energies of all 2N configurations obtained by occupying N sites by A and B atoms, we map instead the ab initio calculated total energies of only O(10) simple structures (with <or=8 atoms/cell) onto a generalized Ising model (including pair and many-body interactions) finding that for Ag-Au a close reproduction (within approximately 2 meV/atom) of LDA energies of arbitrary structures can be achieved by including relatively short-ranged interactions. Subjecting these Ising interaction parameters to a Monte Carlo simulated annealing treatment, we obtain (i) the structures having T=0 minimum energy ('ground states'); (ii) the order-disorder phase transition temperatures; (iii) the mixing enthalpy for the disordered alloy; and (iv) the high-temperature atomic short-range order (SRO). While the predicted ordering temperatures for the ground state structures are too low to enable direct growth into the ordered phase, the calculated mixing enthalpy and the SRO parameters for Ag-Au agree quantitatively with experiment and dearly indicate a tendency for ordering, not phase separation.

Effects of electrostatic field on the phase properties of mixed-stack organic charge-transfer compounds.

We have studied the effects of an external electric field on the phase properties of mixed-stack organic charge-transfer complexes through illustrative calculations based on the ionic crystal model, paying special attention to the roles of electrostatic energy. The ground-state charge configurations of tetrathiafulvalene-p-chloranil (TTF-CA) under electric fields have been explored mainly by the Monte Carlo simulated annealing method in the cases of one-dimensional chain, three-dimensional bulk crystal, and thin film. It has been found for TTF-CA bulk crystals at room temperature and ambient pressure that the applied electric field beyond approximately ${10}^{6}$ V/cm would induce a transition from the neutral phase to the charge-separated phase in which positively and negatively charged donor-acceptor pairs, ${\mathit{D}}^{+}$${\mathit{A}}^{0}$ and ${\mathit{D}}^{0}$${\mathit{A}}^{\mathrm{\ensuremath{-}}}$, separately appear near both ends of DA stack chains. Investigating the phase structure of charge-transfer complexes through the variations in ionization energy, Madelung energy, and external field, we have also found that the applied field can cause a neutral-ionic transition of mixed-stack organic charge-transfer compounds in the close vicinity of neutral-ionic phase boundary. We then discuss the feasibility of this electric-field-induced neutral-ionic transition in actual organic-complex systems in terms of employing compounds other than TTF-CA or of varying temperature, pressure, and film thickness to approach the systems to the neutral-ionic phase boundary.

Short- and long-range order of the binary Madelung lattice.

We discuss the influence of point-ion electrostatics on the long- (LRO) and short-range order (SRO) in binary fcc-, bcc-, and simple-cubic-based (sc) alloys. The electrostatic problem is studied by a combination of (a) a model for the distribution of point charges on lattice sites, motivated by recent first-principles calculations, (b) a mapping of the infinite-ranged Coulomb interaction onto a rapidly convergent series of effective interactions, and (c) Monte Carlo simulated annealing of the ensuing Ising-like expansion. This provides a means to identify the lowest energy structures (``ground states'') at zero temperature and the dominant wave vectors of the SRO at high temperatures, which are stabilized by ionic interactions. (i) We confirm previous results that the three ground states of the fcc Madelung lattice are the D${0}_{22}$ (${\mathit{A}}_{3}$B and ${\mathit{AB}}_{3}$) and ``40'' (AB) structures, which can all be described as 〈210〉 superlattices. We further find that the ground states of the bcc and sc Madelung lattices are CsCl and NaCl, respectively. (ii) Despite the fact that the structure ``40'' has the lowest electrostatic energy of any fcc-type compound, this structure is very rare in nature. We find that this rarity could imply that a highly ionic fcc AB compound will transform to the bcc structure CsCl that is electrostatically more stable for the same charge distribution. The exception is when the energy required to promote the elemental solids A+B from fcc to bcc is larger than the gain in electrostatic energy. (iii) Monte Carlo and mean-field calculations both demonstrate that the dominant wave vectors of LRO and SRO coincide for the bcc and sc Madelung lattices.However, for compositions x\ensuremath{\lesssim}0.33 and x\ensuremath{\gtrsim}0.67 on the fcc lattice, mean-field calculations incorrectly predict SRO peaks at the 〈11/20〉 points, whereas Monte Carlo calculations show SRO peaks at the 〈100〉 points. Thus, in describing fcc electrostatics, the mean-field theory of SRO is seen to qualitatively fail. (iv) Electrostatic point-ion interactions lead to significant SRO correlations. Near the transition temperature, these correlations account for a \ensuremath{\gtrsim}60% change in the energy of the random alloy.

Stable structures of Na(H2O)n (n = 1-3) clusters by ab initio simulated annealing

Minimum-energy structures of clusters of one sodium atom and as many as three water molecules have been calculated by combining the method of ab initio Monte Carlo simulated annealing with conventional optimization methods. 6-31G* basis sets have been employed, and each structure was optimized at the MP2 (frozen core) level of theory. © 1995 John Wiley & Sons, Inc.

Article

The sequence-specific assignment of resonance is considered to be a requirement for the determination of the three-dimensional (3D) structure of a protein in solution by nuclear magnetic resonance methods. The main source of structural information is the nuclear Overhauser effect spectroscopy (NOESY) spectrum, which contains information about spatially close pairs of protons. Currently, various J-correlated spectra must be recorded in order to obtaine the sequence-specific assignments necessary to interpret the NOESY spectra. In this work, a novel procedure to determine the 3D structure and the sequence-specific assignments of a protein using only data from 13C and 15N-separated multidimensional NOESY spectra is described. No information for J-correlated spectra is required. The algorithm is called ANSRS (Assingment of NOESY Spectra in Real Space) and is based on an inversion of the traditional strategy. A 3D real-space structure of detected, but unassigned, 1H spins is calculated from the nuclear Overhauser effect (NOE) distance restraints using a dynamical simulated annealing procedure. The sequence-specific assngments are then determined by searching among the 1H spin in the 3D real-space structure for plausible residue assingments. The search uses a Monte Carlo simulated annealing algorithm based on assignment probabilities derived from the 1H, 15N and 13C chemical shifts, various spatial constraints, and the known sequence of the protein. The procedure has been tested on semi-synthetic data sets comprising published experimental chemical shifts and NOE distance restraints derived from the known 3D structures of the two proteins GAL4 (residues 9 to 41) and bovine pancreatic trypsin inhibitor. The ANSRS procedure was able to determine the sequence-specific assignments for more than 95% of the spins, and was faily robust with respect to missing NOE data. The potential of the ANSRS approach with respect to automated assignment, reduction of the number of NMR spectra required for a structure determination, assignment of homologous and mutant proteins, and the possibility of analysing spectra recorded at high pH is discussed.

Dynamics of Formation and Evaporation of Mixed Alkali Halide Nanocrystals: A Case of Comparable Lattice Energies

Abstract : The relative intensity distribution of the (Rb(n)K(14-n)I(13)(+) mixed nanocrystals containing a 'magic' number of 14 metal cations and 13 iodide anions is examined. These nanocrystals were generated through sputtering of mixed RbI/KI solids using fast atom bombardment, and analyzed by use of a double-focusing sector-field mass spectrometer. The relative intensities of the observed peaks is found to have a 'bimodal' distribution with a maximum near n=7. This observation is explained by assuming: (a) a rate of formation that is proportional to the number of isomers that can be formed for each mixed nanocrystal, and (b) a rate of dissociation that is insensitive to the composition of the mixed nanocrystal. The later assumption leads to the conclusion that the internal energies of these mixed nanocrystals are similar and independent of their composition. The conclusion is supported by the results of Monte Carlo simulation annealing as well as by the similarity of the known lattice energies of KI and RbI bulk crystals.

Unequal wave vectors in short- versus long-range ordering in intermetallic compounds.

The sign of the formation energy [Delta][ital H][sub [ital F]] of a compound indicates if the low-temperature long-range order (LRO) corresponds to compound formation (when [Delta][ital H][sub [ital F]][lt]0) or to phase-separation (when [Delta][ital H][sub [ital F]][gt]0). However, [Delta][ital H][sub [ital F]] by itself does not tell us what type (ordering or clustering) of high-temperature short-range order (SRO) can be expected. The reason is that [Delta][ital H][sub [ital F]] contains two [ital types] of contributions: an elastic,'' volume-deformation energy [ital G]([ital x]) that reflects the energy invested in deforming the constituents [ital A] and [ital B] to the volume [ital V]([ital x]) of the [ital A][sub 1[minus][ital x]][ital B][sub [ital x]] alloy, and a chemical'' energy [var epsilon] that reflects [ital A]-[ital B] interactions (charge transfer and atomic relaxations) at a [ital fixed] [ital V]([ital x]). We show that the LRO and the SRO have the same behavior only when the signs of [Delta][ital H][sub [ital F]] and [var epsilon] are the same: ordering tendencies ( type I'') when both [Delta][ital H][sub [ital F]][lt]0 and [var epsilon][lt]0, or phase-separating/clustering tendencies ( type III'') when both [Delta][ital H][sub [ital F]][gt]0 and [var epsilon][gt]0. However, type II'' systems ([Delta][ital H][sub [ital F]][gt]0;more » [var epsilon][lt]0) can exhibit a phase-separating LRO and an ordering-type SRO. Direct self-consistent local-density calculations of the total energy coupled with Monte-Carlo simulated annealing calculations of the ensuing Ising-like cluster expansion illustrate these type I, II, and III behaviors in Ni-V, Ni-Au, and Pd-Rh, respectively.« less

The Origins of Protein Secondary Structure: Effects of Packing Density and Hydrogen Bonding Studied by a Fast Conformational Search

Globular proteins fold to create compact structures rich in α-helices and β-sheets. While studies of cubic lattice models of simplified polypeptide chains have concluded that, secondary structure is a necessary consequence of chain compactness, different conclusions have been reached from studies of off-lattice models of simplified chains. In an attempt to resolve this controversy, we study an all-atom off-lattice model of a protein subject to a variety of simplified energy functions. A Monte Carlo simulated annealing algorithm is used to search conformational space quickly. The algorithm uses pivot-type moves in which a residue is selected at random and the values of its main-chain dihedral angles are changed. The energy function used to accept or reject moves is taken to be either a term proportional to the volume occupied by a structure (to mimic the hydrophobic effect), a term proportional to the energy of main-chain hydrogen bonding, or a combination of these two terms. Secondary structure content is evaluated using several different definitions. For all the definitions used, compactness alone produces a 10% increase in secondary structure content. However, this is a small fraction of the secondary structure observed in native protein structures. Structures produced by minimizing the hydrogen bond energy have extensive secondary structure but are not densely packed. Structures having both the high density of native structures and extensive secondary structure are produced by minimizing combinations of the volume and hydrogen bond energy terms.Our results emphasize the close relationship between secondary structure and the geometry of main-chain hydrogen bonding. The results are consistent with a description of protein folding in which the hydrophobic effect favors dense packing while hydrogen bonding determines the specific local geometry which generates secondary structure. To make an analogy with lattice studies of packing density and secondary structure, it seems that hydrophobicity provides the packing density while hydrogen bonding provides the lattice.

Long- versus short-range order in Ni3V and Pd3V alloys.

Measurements of the short-range-order (SRO) diffuse scattered intensity show peaks at the 〈11/20〉 and 〈100〉 points in ${\mathrm{Ni}}_{3}$V and ${\mathrm{Pd}}_{3}$V, respectively, although the stable ground state in both systems (D${0}_{22}$) is a 〈11/20〉-type structure. Mean-field theory predicts 〈11/20〉 SRO in both materials, in contradiction with experiment for ${\mathrm{Pd}}_{3}$V. The 〈100〉-type SRO in ${\mathrm{Pd}}_{3}$V has been explained previously as a non-mean-field effect. Via a combination of first-principles total-energy calculations and Monte Carlo simulated annealing, we show that non-mean-field effects are insufficient to explain the observed SRO of ${\mathrm{Pd}}_{3}$V. However, the inclusion of electronic excitations leads to a temperature dependence in the interaction energies which correctly explains both the SRO and phase stability in ${\mathrm{Pd}}_{3}$V and ${\mathrm{Ni}}_{3}$V.

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 (epsilon = 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 alpha-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 changes 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 alpha-helix from completely random initial conformations is possible for the former, whereas only unfolding of an alpha-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.