Designing generalized statistical ensembles for numerical simulations of biopolymers (original) (raw)
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A constrained maximum entropy method in polymer statistics
The Journal of Chemical Physics, 2003
A modified version of the maximum entropy principle, called ''constrained maximum entropy'' method ͑MEC͒, is revisited to combine the information obtained in computer simulations of polymers with external information in the form of configurational averages. A random-temperature molecular dynamics trajectory is being proposed as a biased random walk in configurational space to be reweighted by using the given average information. This random walk, generating a ''meta'' configurational probability, has been found to contain relevant information on the system. The method is compared with other computational techniques, like the generalized-ensemble and configurational-biased Monte Carlo, for simple models in the field of polymers and biopolymers. The main features of polymer configurational distribution functions of interest in polymer physics are consistent among the different methods in a wide range of temperatures and especially at room conditions. The advantage of the MEC approach is in taking into account all the degrees of freedom in the model, thus allowing applications in complicated biopolymers in the explicit solvent.
The main assumptions of the statistical counting (SC) method [D. Zhao et al., J. Chem. Phys. 104, 1672 (1996)] for the calculation of the conformational entropy of a chain modeled on the lattice are presented. The method is discussed in terms of its applicability to different physical systems and the integrity of results. Also, an extension of the SC method for the analysis of the statistics of some Verdier-Stockmayer algorithms in the Metropolis Monte Carlo simulation is proposed. The results of the application of this new method, named here as the micomodification probabilities (MMP) method, for the study of the effect of different solvent conditions, different types of geometrical constraints and deforming external forces on the free energy of a polymer chain, are presented. The use of the MMP method for the investigation of a charged polymer in the presence of other charged objects (ions, nanoparticles) is also reported.
The Journal of Chemical Physics, 2000
Entropy sampling Monte Carlo, the replica method, and the classical Metropolis scheme were applied in numerical studies of the collapse transition in a simple face-centered cubic lattice polymer. The force field of the model consists of pairwise, contact-type, long-range interactions and a short-range potential based on the -sheet definition assumed in the model. The ability to find the lowest energy conformation by various Monte Carlo methods and the computational cost associated with each was examined. It is shown that all of the methods generally provide the same picture of the collapse transition. However, the most complete thermodynamic description of the transition derives from the results of entropy sampling Monte Carlo simulations, but this is the most time-consuming method. The replica method is shown to be the most effective and efficient in searching for the lowest energy conformation. The possible consequences of these findings for the development of simulation strategies for the folding of model proteins are discussed briefly.
General Statistical Approach to the Description of Polymers with Arbitrary Chemical Structure
A field-theory approach using a replica method is proposed for calculating the thermodynamic and correlation characteristics of polymer solutions and melts containing macromolecules of various chemical compositions and various structures. The distribution of components among phases and the conditions for thermodynamic equilibrium are derived for arbitrary sets of macromolecules by a mean-field theory. In the case of solutions of linear heteropolymers in which the alternation of monomer units in the macromolecules obeys Markovian statistics, a phase diagram is constructed, and the conditions for the appearance of periodic spatial superstructures are derived. Over a wide range of the composition of such heteropolymers, there can be a thirdorder phase transition to a superstructure with a rhombohedra1 symmetry and a period which depends strongly on the parameters of the bulk interactions. The possibilities of this new general approach are demonstrated in the particular case of a calculation of the correlation function for density fluctuations in solutions of branched statistical heteropolymers of fairly arbitrary chemical structure. + , determine the conditional probability that unit n + 1 of the chain is of type in + , in the case in which unit n is of type in. The quantities ij,, and ?lo are the probabilities for finding initial and final units of types i, and i,, respectively. Their normalization conditions are 368 Sov. Phys. JETP 72 (2),
Macromolecular Theory and Simulations, 1997
We have explored the performance of a simulation model for Gaussian chains at different concentrations in a good solvent. The Gaussian statistics for the distances between contiguous beads in the model is directly implemented in the individual moves of a Monte Carlo algorithm. When the results of conformational properties for the Gaussian model are compared with those provided by a freely jointed model in the same conditions, significant differences arise at finite concentrations. The modeled Gaussian chain yields incorrect results for the quadratic average dimensions (R2) and (S') at high concentrations, but correctly reproduces the results for the scaled end-to-end distance distribution function at any concentration, showing the effects of the screening of excluded volume when concentration increases. The reason for the wrong behavior of the simulated Gaussian model comes from a strong distortion of the "bond distance" distribution as a result of the concentration increase. We conclude that this model can only be safely applied to infinitely dilute solutions.
Physical Review Letters, 2002
Two novel connectivity-altering atomistic Monte Carlo moves are presented for the fast equilibration of condensed phases of long-chain systems with a variety of chain architectures. With the new moves, isotropic or oriented melts of linear or long-chain branched polymers, dense brushes of terminally grafted macromolecules, and cyclic peptides can be simulated. Results concerning the structural, conformational, and volumetric properties of linear, monodisperse polyethylene melts, simulated with a new united-atom molecular model, are in excellent agreement with experimental data.
2018
In this thesis, the Expanded Ensemble Density-of-States (EXEDOS) method a combination of the Wang-Landau and Expanded Ensemble Monte Carlo algorithms is employed to investigate spatial conformations of a polymer chain under spherical confinement. The study focuses on flexible chains up to 600 monomers and semi-flexible chains with various stiffnesses up to 300 monomers in length. Spatial conformations of the polymer are studied, using a simple pearl-necklace chain model of varied diameter and stiffness, as well as the model of fused-sphere chain. To test the applicability of the EXEDOS method, the confinement free energy was calculated for ideal and non-ideal flexible chains inside spheres of sizes smaller than their unconfined size. For ideal chains, the power-law dependence of the free energy on a confining radius is in excellent agreement with previous theoretical predictions. For self-avoiding chains at intermediate concentrations, the dependence of free energy on concentration ...
The Journal of Chemical Physics, 1997
We develop here a highly efficient variant of the Monte Carlo method for direct evaluation of the partition function, free energy, and other configurational dependent physical properties for long polymer chains. This method ͑CC-BB͒ combines continuous configurational biased sampling with Boltzmann factor biased enrichment. To illustrate the efficiency and to validate the bias correction for weighting the torsion and chain enrichments, we applied this model to isolated single chains using a united atom force field. For a 50 monomer polymer chain CC-BB with 400 chains leads to an accuracy of 0.1% in the free energy whereas simple sampling direct Monte Carlo requires about 10 9 chains for this accuracy. This leads to cost savings by a factor of about 350 000. CC-BB is easily extended to multichain systems, to the condensed state, to more realistic force fields, and to evaluating the mixing free energy for polymer blends.
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.