Monte Carlo Simulated Annealing Algorithm Research Articles

Ab initio predictions for 3D structure and stability of single- and double-stranded DNAs in ion solutions.

The three-dimensional (3D) structure and stability of DNA are essential to understand/control their biological functions and aid the development of novel materials. In this work, we present a coarse-grained (CG) model for DNA based on the RNA CG model proposed by us, to predict 3D structures and stability for both dsDNA and ssDNA from the sequence. Combined with a Monte Carlo simulated annealing algorithm and CG force fields involving the sequence-dependent base-pairing/stacking interactions and an implicit electrostatic potential, the present model successfully folds 20 dsDNAs (≤52nt) and 20 ssDNAs (≤74nt) into the corresponding native-like structures just from their sequences, with an overall mean RMSD of 3.4Å from the experimental structures. For DNAs with various lengths and sequences, the present model can make reliable predictions on stability, e.g., for 27 dsDNAs with/without bulge/internal loops and 24 ssDNAs including pseudoknot, the mean deviation of predicted melting temperatures from the corresponding experimental data is only ~2.0°C. Furthermore, the model also quantificationally predicts the effects of monovalent or divalent ions on the structure stability of ssDNAs/dsDNAs.

Could network structures generated with simple rules imposed on a cubic lattice reproduce the structural descriptors of globular proteins?

Abstract A direct way to spot structural features that are universally shared among proteins is to find analogues from simpler condensed matter systems. In the current study, the feasibility of creating ensembles of artificial structures that can automatically reproduce a large number of geometrical and topological descriptors of globular proteins is investigated. Towards this aim, a simple cubic (SC) arrangement is shown to provide the best background lattice after a careful analysis of the residue packing trends from 210 globular proteins. It is shown that a minimalistic set of rules imposed on this lattice is sufficient to generate structures that can mimic real proteins. In the proposed method, 210 such structures are generated by randomly removing residues (beads) from clusters that have a SC lattice arrangement such that all the generated structures have single connected components. Two additional sets are prepared from the initial structures via random relaxation and a reverse Monte Carlo simulated annealing algorithm, which targets the average radial distribution function (RDF) of 210 globular proteins. The initial and relaxed structures are compared to real proteins via RDF, bond orientational order parameters and several descriptors of network topology. Based on these features, results indicate that the structures generated with 40% occupancy closely resemble real residue networks. The structure generation mechanism automatically produces networks that are in the same topological class as globular proteins and reproduce small-world characteristics of high clustering and small shortest path lengths. Most notably, the established correspondence rules out icosahedral order as a relevant structural feature for residue networks in contrast to other amorphous systems where it is an inherent characteristic. The close correspondence is also observed in the vibrational characteristics as computed from the Anisotropic Network Model, therefore hinting at a non-superficial link between the proteins and the defect laden cubic crystalline order.

Dense skyrmion crystal stabilized through interfacial exchange coupling: Role of in-plane anisotropy

A Monte Carlo simulated-annealing algorithm was used to study the magnetic state in an in-plane helimagnet layer on triangular lattice that exchange couples to an underlayer with strong out-of-plane anisotropy. In the single helimagnet layer with in-plane anisotropy (K), the formation of labyrinthlike domains with local spin spirals, instead of parallel stripes, is favored, and these domains rapidly transform into dense skyrmion crystals with increasing interfacial exchange coupling (J′), equivalent to a virtual magnetic field, and finally evolve to an out-of-plane uniform state at large enough J′. Moreover, with increasing K, the skyrmion crystal state can vary from regular 6-nearest-neighboring circular skyrmion arrangement to irregular squeezed skyrmions with less than 6 nearest neighbors when the in-plane anisotropy energy is higher than the interfacial exchange energy as the skyrmion number is maximized. Finally, we demonstrated that the antiferromagnetic underlayer cannot induce skyrmions while the chirality inversion can be achieved on top of an out-of-plane magnetization underlayer with 180° domain walls, supporting the experimental findings in FeGe thin film. This compelling advantage offers a fertile playground for exploring emergent phenomena that arise from interfacing magnetic skyrmions with additional functionalities.

Automated assignment of NMR spectra of macroscopically oriented proteins using simulated annealing

An automated technique for the sequential assignment of NMR backbone resonances of oriented protein samples has been developed and tested based on 15N-15N homonuclear exchange and spin-exchanged separated local-field spectra. By treating the experimental spectral intensity as a pseudopotential, the Monte-Carlo Simulated Annealing algorithm has been employed to seek lowest-energy assignment solutions over a large sampling space where direct enumeration would be unfeasible. The determined sequential assignments have been scored based on the positions of the crosspeaks resulting from the possible orders for the main peaks. This approach is versatile in terms of the parameters that can be specified to achieve the best-fit result. At a minimum the algorithm requires a continuous segment of the main-peak chemical shifts obtained from a uniformly labeled sample and a spin-exchanged experimental spectrum represented as a 2D matrix array. With selective labeling experiments, groups of chemical shifts corresponding to specific locations in the protein backbone can be fixed, thereby decreasing the sampling space. The output from the program consists of a list of top-score main peak assignments, which can be subjected to further scoring criteria until a consensus solution is found. The algorithm has first been tested on a synthetic spectrum with randomly generated chemical shifts and dipolar couplings for the main peaks. The original assignments have been successfully recovered for as many as 100 main peaks when residue-type information was used even in the presence of substantial spectral peak overlap. The algorithm was then applied to assigning two sets of experimental spectra to recover and confirm the previously established assignments in an automated fashion. For the 20-residue transmembrane domain of Pf1 coat protein reconstituted in magnetically aligned bicelles, the original assignment by Park et al. (2010) was recovered by the automated algorithm with additional input from 5 selectively labeled amino acid spectra. The second case considered was the 46 residue Pf1 bacteriophage from Thiriot et al. (2005) and Knox et al. (2010), of which 38 residues were fit. Automated fitting resulted in several possible assignments but not exactly the original assignment. By using a post-fitting filtering procedure based on the number of missed cross peaks and Pf1 helical structure, a consensus spectroscopic assignment is proposed covering 84% of the original assignment. While the automated assignment works best in spectra with well-resolved crosspeaks, it also tolerates substantial spectral crowding to yield reasonable assignments in the cases where ambiguity and degeneracy of possible assignment solutions are inevitable.

A coarse-grained model with implicit salt for RNAs: predicting 3D structure, stability and salt effect.

To bridge the gap between the sequences and 3-dimensional (3D) structures of RNAs, some computational models have been proposed for predicting RNA 3D structures. However, the existed models seldom consider the conditions departing from the room/body temperature and high salt (1M NaCl), and thus generally hardly predict the thermodynamics and salt effect. In this study, we propose a coarse-grained model with implicit salt for RNAs to predict 3D structures, stability, and salt effect. Combined with Monte Carlo simulated annealing algorithm and a coarse-grained force field, the model folds 46 tested RNAs (≤45 nt) including pseudoknots into their native-like structures from their sequences, with an overall mean RMSD of 3.5 Å and an overall minimum RMSD of 1.9 Å from the experimental structures. For 30 RNA hairpins, the present model also gives the reliable predictions for the stability and salt effect with the mean deviation ∼ 1.0 °C of melting temperatures, as compared with the extensive experimental data. In addition, the model could provide the ensemble of possible 3D structures for a short RNA at a given temperature/salt condition.

Joint Bayesian Decomposition of a Spectroscopic Signal Sequence

This letter addresses the problem of decomposing a sequence of spectroscopic signals: data are a series of (energy or electromagnetic) spectra and we aim to estimate the peak parameters (centers, amplitudes, and widths). The key idea is to perform the decomposition of the whole sequence and to impose the parameters to evolve smoothly through the sequence. The problem is set within a Bayesian framework whose posterior distribution is sampled using a Markov chain Monte Carlo simulated annealing algorithm. Simulations conducted on synthetic data illustrate the performance of the method.

Tackling the protein folding problem by a generalized-ensemble approach with Tsallis statistics

We review uses of Tsallis statistical mechanics in the protein folding problem. Monte Carlo simulated annealing algorithm and generalized-ensemble algorithm with both Monte Carlo and stochastic dynamics algorithms are discussed. Simulations by these algorithms are performed for a penta peptide, Met-enkephalin. In particular, for generalized-ensemble algorithms, it is shown that from only one simulation run one can find the global-minimum-energy conformation and obtain probability distributions in canonical ensemble for a wide temperature range, which allows the calculation of any thermodynamic quantity as a function of temperature.

Sampling protein conformations using segment libraries and a genetic algorithm

We present a new simulation algorithm for minimizing empirical contact potentials for a simplified model of protein structure. The model consists of backbone atoms only (including Cβ) with the φ and ψ dihedral angles as the only degrees of freedom. In addition, φ and ψ are restricted to a finite set of 532 discrete pairs of values, and the secondary structural elements are held fixed in ideal geometries. The potential function consists of a look-up table based on discretized inter-residue atomic distances. The minimization consists of two principal elements: the use of preselected lists of trial moves and the use of a genetic algorithm. The trial moves consist of substitutions of one or two complete loop regions, and the lists are in turn built up using preselected lists of randomly-generated three-residue segments. The genetic algorithm consists of mutation steps (namely, the loop replacements), as well as a hybridization step in which new structures are created by combining parts of two “parents’’ and a selection step in which hybrid structures are introduced into the population. These methods are combined into a Monte Carlo simulated annealing algorithm which has the overall structure of a random walk on a restricted set of preselected conformations. The algorithm is tested using two types of simple model potential. The first uses global information derived from the radius of gyration and the rms deviation to drive the folding, whereas the second is based exclusively on distance-geometry constraints. The hierarchical algorithm significantly outperforms conventional Monte Carlo simulation for a set of test proteins in both cases, with the greatest advantage being for the largest molecule having 193 residues. When tested on a realistic potential function, the method consistently generates structures ranked lower than the crystal structure. The results also show that the improved efficiency of the hierarchical algorithm exceeds that which would be anticipated from tests on either of the two main elements used independently.

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.

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.

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.

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.

Ab initio Monte Carlo simulated annealing method

The major difficulty in computer simulations of metal and semiconductor clusters is the description of the many-body interactions. The pair-wise approximation commonly used to describe the system does not work well for covalent and metallic systems where many-body interactions play a crucial role. We present an ab initio Monte Carlo simulated annealing algorithm that describes the many-body interactions in metal and semiconductor clusters in terms of an ab initio correlated method at the level of second-order MΦller—Plesset perturbation theory. We apply the method to the mixed lithium—hydrogen cluster, Li 5H, as a test case for small clusters.