A balance-evolution artificial bee colony algorithm for protein structure optimization based on a three-dimensional AB off-lattice model

Protein structure prediction is a fundamental issue in the field of computational molecular biology. In this paper, the AB off-lattice model is adopted to transform the original protein structure prediction scheme into a numerical optimization problem. We present a balance-evolution artificial bee colony (BE-ABC) algorithm to address the problem, with the aim of finding the structure for a given protein sequence with the minimal free-energy value. This is achieved through the use of convergence information during the optimization process to adaptively manipulate the search intensity. Besides that, an overall degradation procedure is introduced as part of the BE-ABC algorithm to prevent premature convergence. Comprehensive simulation experiments based on the well-known artificial Fibonacci sequence set and several real sequences from the database of Protein Data Bank have been carried out to compare the performance of BE-ABC against other algorithms. Our numerical results show that the BE-ABC algorithm is able to outperform many state-of-the-art approaches and can be effectively employed for protein structure optimization.     

Protein structure optimization using improved simulated annealing algorithm on a three-dimensional AB off-lattice model

This paper proposed an improved simulated annealing (ISA) algorithm for protein structure optimization based on a three-dimensional AB off-lattice model. In the algorithm, we provided a general formula used for producing initial solution, and designed a multivariable disturbance term, relating to the parameters of simulated annealing and a tuned constant, to generate neighborhood solution. To avoid missing optimal solution, storage operation was performed in searching process. We applied the algorithm to test artificial protein sequences from literature and constructed a benchmark dataset consisting of 10 real protein sequences from the Protein Data Bank (PDB). Otherwise, we generated C_α space-filling model to represent protein folding conformation. The results indicate our algorithm outperforms the five methods before in searching lower energies of artificial protein sequences. In the testing on real proteins, our method can achieve the energy conformations with C_α-RMSD less than 3.0 Å from the PDB structures. Moreover, C_α space-filling model may simulate dynamic change of protein folding conformation at atomic level.     

Modeling flexible amphiphilic bilayers: a solvent-free off-lattice Monte Carlo study

We present a simple, implicit-solvent model for fluid bilayer membranes. The model was designed to reproduce the elastic properties of real bilayer membranes. For this model, we observed the solid-fluid transition and studied the in-plane diffusivity of the fluid phase. As a test, we compute the elastic-bending and area-compressing moduli of fluid bilayer membranes. We find that the computed elastic properties are consistent with the available experimental data.     

Modeling of composite latex particle morphology by off-lattice Monte Carlo simulation

Composite latex particles have shown a great range of applications such as paint resins, varnishes, water borne adhesives, impact modifiers, etc. The high-performance properties of this kind of materials may be explained in terms of a synergistical combination of two different polymers (usually a rubber and a thermoplastic). A great variety of composite latex particles with very different morphologies may be obtained by two-step emulsion polymerization processes. The formation of specific particle morphology depends on the chemical and physical nature of the monomers used during the synthesis, the process temperature, the reaction initiator, the surfactants, etc. Only a few models have been proposed to explain the appearance of the composite particle morphologies. These models have been based on the change of the interfacial energies during the synthesis. In this work, we present a new three-component model: Polymer blend (flexible and rigid chain particles) is dispersed in water by forming spherical cavities. Monte Carlo simulations of the model in two dimensions are used to determine the density distribution of chains and water molecules inside the suspended particle. This approach allows us to study the dependence of the morphology of the composite latex particles on the relative hydrophilicity and flexibility of the chain molecules as well as on their density and composition. It has been shown that our simple model is capable of reproducing the main features of the various morphologies observed in synthesis experiments.     

An off-lattice, self-learning kinetic Monte Carlo method using local environments

We present a method called local environment kinetic Monte Carlo (LE-KMC) method for efficiently performing off-lattice, self-learning kinetic Monte Carlo (KMC) simulations of activated processes in material systems. Like other off-lattice KMC schemes, new atomic processes can be found on-the-fly in LE-KMC. However, a unique feature of LE-KMC is that as long as the assumption that all processes and rates depend only on the local environment is satisfied, LE-KMC provides a general algorithm for (i) unambiguously describing a process in terms of its local atomic environments, (ii) storing new processes and environments in a catalog for later use with standard KMC, and (iii) updating the system based on the local information once a process has been selected for a KMC move. Search, classification, storage and retrieval steps needed while employing local environments and processes in the LE-KMC method are discussed. The advantages and computational cost of LE-KMC are discussed. We assess the performance of the LE-KMC algorithm by considering test systems involving diffusion in a submonolayer Ag and Ag-Cu alloy films on Ag(001) surface.     

Biopolymer structure simulation and optimization via fragment regrowth Monte Carlo

An efficient exploration of the configuration space of a biopolymer is essential for its structure modeling and prediction. In this study, the authors propose a new Monte Carlo method, fragment regrowth via energy-guided sequential sampling (FRESS), which incorporates the idea of multigrid Monte Carlo into the framework of configurational-bias Monte Carlo and is suitable for chain polymer simulations. As a by-product, the authors also found a novel extension of the Metropolis Monte Carlo framework applicable to all Monte Carlo computations. They tested FRESS on hydrophobic-hydrophilic (HP) protein folding models in both two and three dimensions. For the benchmark sequences, FRESS not only found all the minimum energies obtained by previous studies with substantially less computation time but also found new lower energies for all the three-dimensional HP models with sequence length longer than 80 residues.     

Re-examination of structure optimization of off-lattice protein AB models by conformational space annealing

The global structural optimization is carried out for off-lattice protein AB models in two and three dimensions by conformational space annealing. The models consist of hydrophobic and hydrophilic monomers in Fibonacci sequences. To accelerate the convergence, we have introduced a shift operator in the internal coordinate system, and effectively reduced the search space by forming a quotient space. With this, we significantly improve our previous results on AB models, and provide new low energy conformations. This work provides insights on exploring complicated energy landscapes by exploiting the advantages and limitations of CSA.     

An efficient sampling algorithm for variational Monte Carlo

We propose a new algorithm for sampling the N-body density mid R:Psi(R)mid R:(2)R(3N)mid R:Psimid R:(2) in the variational Monte Carlo framework. This algorithm is based upon a modified Ricci-Ciccotti discretization of the Langevin dynamics in the phase space (R,P) improved by a Metropolis-Hastings accept/reject step. We show through some representative numerical examples (lithium, fluorine, and copper atoms and phenol molecule) that this algorithm is superior to the standard sampling algorithm based on the biased random walk (importance sampling).     

Monte Carlo simulation of an inhomogeneous dielectric continuum model for B-DNA

Thermodynamic and structural properties of the counterion atmosphere surrounding B-DNA are calculated by Monte Carlo simulation in a spatially inhomogeneous, but piecewise uniform, dielectric continuum cell model - the "barbarous" model. A boundary element formulation is implemented to study the sensitivity of these properties with respect to perturbations in the location of discontinuous dielectric boundaries relative to fixed and mobile charges. High concentrations are considered corresponding to the liquid crystalline hexagonally ordered phase of DNA. Primitive model results are verified against other simulation reports and a comparison of barbarous model predictions with experimental data is discussed. The internal energy, osmotic coefficient, radial distributions and the population ratio of counterions in the geometrically resolved major and minor grooves are all found to strongly depend on the dielectric boundary position. This suggests that a self-consistent development of the model should consider a free surface problem where the boundary is not specified a priori.     

Heuristic-based tabu search algorithm for folding two-dimensional AB off-lattice model proteins

The protein structure prediction problem is a classical NP hard problem in bioinformatics. The lack of an effective global optimization method is the key obstacle in solving this problem. As one of the global optimization algorithms, tabu search (TS) algorithm has been successfully applied in many optimization problems. We define the new neighborhood conformation, tabu object and acceptance criteria of current conformation based on the original TS algorithm and put forward an improved TS algorithm. By integrating the heuristic initialization mechanism, the heuristic conformation updating mechanism, and the gradient method into the improved TS algorithm, a heuristic-based tabu search (HTS) algorithm is presented for predicting the two-dimensional (2D) protein folding structure in AB off-lattice model which consists of hydrophobic (A) and hydrophilic (B) monomers. The tabu search minimization leads to the basins of local minima, near which a local search mechanism is then proposed to further search for lower-energy conformations. To test the performance of the proposed algorithm, experiments are performed on four Fibonacci sequences and two real protein sequences. The experimental results show that the proposed algorithm has found the lowest-energy conformations so far for three shorter Fibonacci sequences and renewed the results for the longest one, as well as two real protein sequences, demonstrating that the HTS algorithm is quite promising in finding the ground states for AB off-lattice model proteins.     

Monte Carlo optimization of signal-to-noise ratio for electrothermal atomizers

This work uses Monte Carlo simulation models for Cu and Ag to study the change in the signal-to-noise ratio (S/N) with variations on the electrothermal atomizer length and diameter. A 5 × 5 grid corresponding to different lengths (2.0–4.0 cm) and diameters (0.30–0.70 cm) is filled with S/N data from the simulations. It is assumed that the S/N is shot-noise limited. The dosing hole diameter is held at 1.5 mm in all cases. A double-desorption type mechanism for Ag atomization was tested against experimental profiles and good agreement was achieved. Spherical microdroplets release Ag(g) with a fractional order (2/3) and an activation energy of 238 kJ mol⁻¹. Ag(g) readsorbs as dispersed atoms on the wall upon collision. The secondary desorption is first order and has a lower activation barrier (117 kJ mol⁻¹). The S/N predicted by the Monte Carlo simulation does not strongly depend on the heating rate or the nature of the analyte being determined. The optimum with respect to geometry is broad. The optimum furnace diameter is near 0.50 cm, while the optimum furnace length is at the 4.0-cm limit used in these studies. Most commercial atomizers have diameters close to the optimum but shorter lengths, probably reflecting the pragmatic consideration that the longer tubes require larger power supplies and prolonged heating times which may substantially reduce the useful life of the furnace. Further increases in length may also accentuate atomizer nonisothermality which deters analytical improvement.     

Prediction of protein structure using a knowledge-based off-lattice united-residue force field and global optimization methods

A united-residue model of polypeptide chains developed in our laboratories with united side-chains and united peptide groups as interaction sites is presented. The model is designed to work in continuous space; hence efficient global-optimization methods can be applied. In this work, we adopted the distance-scaling method that is based on continuous deformation of the original rugged energy hypersurface to obtain a smoothed surface. The method has been applied successfully to predict the structures of simple motifs, such as the three-helix bundle structure of the 10-58 fragment of staphylococcal protein A in de novo folding simulations and more complicated motifs in inverse-folding simulations. Received: 24 April 1998 / Accepted: 4 August 1998 / Published online: 2 November 1998     

Fast protein structure prediction using Monte Carlo simulations with modal moves

Using normal modes to generate torsion space moves in Monte Carlo simulations of peptides and proteins is not a new idea; nevertheless, despite its power it has not received widespread application. We show that such a "Modal Monte Carlo" approach is an efficient tool for ab initio predictions of small-protein structures. We apply this method to the Trp cage, a 20-residue polypeptide designed to fold rapidly into a structure that includes tertiary contacts, despite its short length. We achieve a high-quality ab initio structure prediction in about 2 orders of magnitude less computation time than state of the art molecular dynamics techniques.     

Monte Carlo simulation algorithm for B‐DNA

Understanding the structure–function relationship of biomolecules containing DNA has motivated experiments aimed at determining molecular structure using methods such as small‐angle X‐ray and neutron scattering (SAXS and SANS). SAXS and SANS are useful for determining macromolecular shape in solution, a process which benefits by using atomistic models that reproduce the scattering data. The variety of algorithms available for creating and modifying model DNA structures lack the ability to rapidly modify all‐atom models to generate structure ensembles. This article describes a Monte Carlo algorithm for simulating DNA, not with the goal of predicting an equilibrium structure, but rather to generate an ensemble of plausible structures which can be filtered using experimental results to identify a sub‐ensemble of conformations that reproduce the solution scattering of DNA macromolecules. The algorithm generates an ensemble of atomic structures through an iterative cycle in which B‐DNA is represented using a wormlike bead–rod model, new configurations are generated by sampling bend and twist moves, then atomic detail is recovered by back mapping from the final coarse‐grained configuration. Using this algorithm on commodity computing hardware, one can rapidly generate an ensemble of atomic level models, each model representing a physically realistic configuration that could be further studied using molecular dynamics. © 2016 Wiley Periodicals, Inc.     

Monte Carlo structure simulations for aqueous 1,4-dioxane solutions

Monte Carlo simulations in the NpT ensembles have been performed for the structure exploration of aqueous 1,4-dioxane solutions. Three different systems with all-atom dioxane:TIP4P water molar compositions of 2:500 (code:D2), 8:465 (D8), and 17:425 (D17) modeled solutions of 0.22, 0.88, and 1.86 mol/dm3 concentrations, respectively, at T = 298 K and p = 1 atm. The calculated solution densities increase from 0.992 to 1.002 g/cm3 with increasing dioxane concentration and approach the experimentally determined densities within 1%. This close agreement was achieved by utilizing RESP charges fitted to the in-solution IEF-PCM/B3LYP/6-31G* electrostatic potential of dioxane taken in its chair conformation and recently developed C, H steric parameters for ethers for calculations with a 12-6-1 all-atom potential. Solution structure analyses pointed out that the dioxane molecules arrange in the solutions with favorable distances of 4-8 angstroms for the ring symmetry centers. Within this range not only pairs of rings but triangular triads and tetrads have also been observed with center-center distances <8 angstroms. For the D8 system, about 25% of the sampled configurations included such a triad. In the case of the D17 model, two simulations starting from different solution configuration predicted different degrees for the dioxane aggregation in aqueous solution. In the more aggregated structure 3-21 triads are consistently maintained and 1-2 tetrads are formed in 58% of the configurations. Each dioxane oxygen forms about one hydrogen bond, on average, to a water molecule in the 0.22-1.86 molar range. The most likely O(dioxane)...H(water) hydrogen bond distance is 1.75-1.80 angstroms compared to the optimal distance of 1.72 angstroms in the isolated dimer. The optimal dioxane-water interaction energy of -5.65 kcal/mol indicates a remarkable hydrogen-bond acceptor character for dioxane.     

Path integral hybrid Monte Carlo algorithm for correlated Bose fluids

Path integral hybrid Monte Carlo (PIHMC) algorithm for strongly correlated Bose fluids has been developed. This is an extended version of our previous method [S. Miura and S. Okazaki, Chem. Phys. Lett. 308, 115 (1999)] applied to a model system consisting of noninteracting bosons. Our PIHMC method for the correlated Bose fluids is constituted of two trial moves to sample path-variables describing system coordinates along imaginary time and a permutation of particle labels giving a boundary condition with respect to imaginary time. The path-variables for a given permutation are generated by a hybrid Monte Carlo method based on path integral molecular dynamics techniques. Equations of motion for the path-variables are formulated on the basis of a collective coordinate representation of the path, staging variables, to enhance the sampling efficiency. The permutation sampling to satisfy Bose-Einstein statistics is performed using the multilevel Metropolis method developed by Ceperley and Pollock [Phys. Rev. Lett. 56, 351 (1986)]. Our PIHMC method has successfully been applied to liquid helium-4 at a state point where the system is in a superfluid phase. Parameters determining the sampling efficiency are optimized in such a way that correlation among successive PIHMC steps is minimized.     

Parallelization strategies for molecular simulation using the Monte Carlo algorithm

We describe the development of Metropolis Monte Carlo algorithms for a general network of multiple instruction multiple data (MIMD) parallel processors. The implementation of farm, event, and systolic parallel algorithms on transputer-based computers is detailed and their relative performance discussed. Although the emphasis is on methodology, the application of such parallel algorithms will be important for addressing computational problems such as the determination of free energy differences in complex biologically important molecular systems. © 1993 John Wiley & Sons, Inc.     

A new algorithm for the fixed-node quantum Monte Carlo method

A novel algorithm is proposed for the fixed-node quantum Monte Carlo (FNQMC) method.In contrast to previous procedures,its "guiding function" is not optimized prior to diffusion quantum Monte Carlo (DMC) computation but synchronistically in the diffusion process The new algorithm can not only save CPU time,but also make both of the optimization and diffusion carried out according to the same sampling fashion,reaching the goal to improve each other This new optimizing procedure converges super-linearly,and thus can accelerate the particle diffusion During the diffusion process,the node of the "guiding function" changes incessantly,which is conducible to reducing the "fixed-node error" The new algorithm has been used to calculate the total energies of states X3B1 and a1A1 of CH2 as well as π-X2B1 and λ-2A1 of NH2 The singlet-triplet energy splitting (λEsT) in CH2 and π energy splitting in NH2 obtained with this present method are (45 542±1.840) and (141.644±1.589) kJ/mol,respectively The calculated     

PHAISTOS: A framework for Markov chain Monte Carlo simulation and inference of protein structure

We present a new software framework for Markov chain Monte Carlo sampling for simulation, prediction, and inference of protein structure. The software package contains implementations of recent advances in Monte Carlo methodology, such as efficient local updates and sampling from probabilistic models of local protein structure. These models form a probabilistic alternative to the widely used fragment and rotamer libraries. Combined with an easily extendible software architecture, this makes PHAISTOS well suited for Bayesian inference of protein structure from sequence and/or experimental data. Currently, two force‐fields are available within the framework: PROFASI and OPLS‐AA/L, the latter including the generalized Born surface area solvent model. A flexible command‐line and configuration‐file interface allows users quickly to set up simulations with the desired configuration. PHAISTOS is released under the GNU General Public License v3.0. Source code and documentation are freely available from http://phaistos.sourceforge.net . The software is implemented in C++ and has been tested on Linux and OSX platforms. © 2013 Wiley Periodicals, Inc.