Coupled coarse graining and Markov Chain Monte Carlo for lattice systems

We propose an efficient Markov Chain Monte Carlo method for sampling equilibrium distributions for stochastic lattice models, capable of handling correctly long and short-range particle interactions. The proposed method is a Metropolis-type algorithm with the proposal probability transition matrix based on the coarse-grained approximating measures introduced in a series of works of M. Katsoulakis, A. Majda, D. Vlachos and P. Plechac, L. Rey-Bellet and D.Tsagkarogiannis,. We prove that the proposed algorithm reduces the computational cost due to energy differences and has comparable mixing properties with the classical microscopic Metropolis algorithm, controlled by the level of coarsening and reconstruction procedure. The properties and effectiveness of the algorithm are demonstrated with an exactly solvable example of a one dimensional Ising-type model, comparing efficiency of the single spin-flip Metropolis dynamics and the proposed coupled Metropolis algorithm.Comment: 20 pages, 4 figure

Introduction to Configuration Path Integral Monte Carlo

In low-temperature high-density plasmas quantum effects of the electrons are becoming increasingly important. This requires the development of new theoretical and computational tools. Quantum Monte Carlo methods are among the most successful approaches to first-principle simulations of many-body quantum systems. In this chapter we present a recently developed method---the configuration path integral Monte Carlo (CPIMC) method for moderately coupled, highly degenerate fermions at finite temperatures. It is based on the second quantization representation of the $N$-particle density operator in a basis of (anti-)symmetrized $N$-particle states (configurations of occupation numbers) and allows to tread arbitrary pair interactions in a continuous space. We give a detailed description of the method and discuss the application to electrons or, more generally, Coulomb-interacting fermions. As a test case we consider a few quantum particles in a one-dimensional harmonic trap. Depending on the coupling parameter (ratio of the interaction energy to kinetic energy), the method strongly reduces the sign problem as compared to direct path integral Monte Carlo (DPIMC) simulations in the regime of strong degeneracy which is of particular importance for dense matter in laser plasmas or compact stars. In order to provide a self-contained introduction, the chapter includes a short introduction to Metropolis Monte Carlo methods and the second quantization of quantum mechanics.Comment: chapter in book "Introduction to Complex Plasmas: Scientific Challenges and Technological Opportunities", Michael Bonitz, K. Becker, J. Lopez and H. Thomsen (Eds.) Springer Series "Atomic, Optical and Plasma Physics", vol. 82, Springer 2014, pp. 153-194 ISBN: 978-3-319-05436-0 (Print) 978-3-319-05437-7 (Online

An effective all-atom potential for proteins

We describe and test an implicit solvent all-atom potential for simulations of protein folding and aggregation. The potential is developed through studies of structural and thermodynamic properties of 17 peptides with diverse secondary structure. Results obtained using the final form of the potential are presented for all these peptides. The same model, with unchanged parameters, is furthermore applied to a heterodimeric coiled-coil system, a mixed alpha/beta protein and a three-helix-bundle protein, with very good results. The computational efficiency of the potential makes it possible to investigate the free-energy landscape of these 49--67-residue systems with high statistical accuracy, using only modest computational resources by today's standards

Ion association in concentrated NaCI brines from ambient to supercritical conditions: results from classical molecular dynamics simulations

Highly concentrated NaCl brines are important geothermal fluids; chloride complexation of metals in such brines increases the solubility of minerals and plays a fundamental role in the genesis of hydrothermal ore deposits. There is experimental evidence that the molecular nature of the NaCl–water system changes over the pressure–temperature range of the Earth's crust. A transition of concentrated NaCl–H(2)O brines to a "hydrous molten salt" at high P and T has been argued to stabilize an aqueous fluid phase in the deep crust. In this work, we have done molecular dynamic simulations using classical potentials to determine the nature of concentrated (0.5–16 m) NaCl–water mixtures under ambient (25°C, 1 bar), hydrothermal (325°C, 1 kbar) and deep crustal (625°C, 15 kbar) conditions. We used the well-established SPCE model for water together with the Smith and Dang Lennard-Jones potentials for the ions (J. Chem. Phys., 1994, 100, 3757). With increasing temperature at 1 kbar, the dielectric constant of water decreases to give extensive ion-association and the formation of polyatomic (Na(n)Cl(m))(n-m )clusters in addition to simple NaCl ion pairs. Large polyatomic (Na(n)Cl(m))(n-m )clusters resemble what would be expected in a hydrous NaCl melt in which water and NaCl were completely miscible. Although ion association decreases with pressure, temperatures of 625°C are not enough to overcome pressures of 15 kbar; consequently, there is still enhanced Na–Cl association in brines under deep crustal conditions

Unified Homogenization Theory for Magnetoinductive and Electromagnetic Waves in Split Ring Metamaterials

A unified homogenization procedure for split ring metamaterials taking into account time and spatial dispersion is introduced. The procedure is based on two coupled systems of equations. The first one comes from an approximation of the metamaterial as a cubic arrangement of coupled LC circuits, giving the relation between currents and local magnetic field. The second equation comes from macroscopic Maxwell equations, and gives the relation between the macroscopic magnetic field and the average magnetization of the metamaterial. It is shown that electromagnetic and magnetoinductive waves propagating in the metamaterial are obtained from this analysis. Therefore, the proposed time and spatially dispersive permeability accounts for the characterization of the complete spectrum of waves of the metamaterial. Finally, it is shown that the proposed theory is in good quantitative and qualitative agreement with full wave simulations.Comment: 4 pages, 3 figure

Chromatin and epigenetics: current biophysical views

Recent advances in high-throughput sequencing experiments and their theoretical descriptions have determined fast dynamics of the "chromatin and epigenetics" field, with new concepts appearing at high rate. This field includes but is not limited to the study of DNA-protein-RNA interactions, chromatin packing properties at different scales, regulation of gene expression and protein trafficking in the cell nucleus, binding site search in the crowded chromatin environment and modulation of physical interactions by covalent chemical modifications of the binding partners. The current special issue does not pretend for the full coverage of the field, but it rather aims to capture its development and provide a snapshot of the most recent concepts and approaches. Eighteen open-access articles comprising this issue provide a delicate balance between current theoretical and experimental biophysical approaches to uncover chromatin structure and understand epigenetic regulation, allowing free flow of new ideas and preliminary results

Binding Free Energy Landscape of Domain-Peptide Interactions

Peptide recognition domains (PRDs) are ubiquitous protein domains which mediate large numbers of protein interactions in the cell. How these PRDs are able to recognize peptide sequences in a rapid and specific manner is incompletely understood. We explore the peptide binding process of PDZ domains, a large PRD family, from an equilibrium perspective using an all-atom Monte Carlo (MC) approach. Our focus is two different PDZ domains representing two major PDZ classes, I and II. For both domains, a binding free energy surface with a strong bias toward the native bound state is found. Moreover, both domains exhibit a binding process in which the peptides are mostly either bound at the PDZ binding pocket or else interact little with the domain surface. Consistent with this, various binding observables show a temperature dependence well described by a simple two-state model. We also find important differences in the details between the two domains. While both domains exhibit well-defined binding free energy barriers, the class I barrier is significantly weaker than the one for class II. To probe this issue further, we apply our method to a PDZ domain with dual specificity for class I and II peptides, and find an analogous difference in their binding free energy barriers. Lastly, we perform a large number of fixed-temperature MC kinetics trajectories under binding conditions. These trajectories reveal significantly slower binding dynamics for the class II domain relative to class I. Our combined results are consistent with a binding mechanism in which the peptide C terminal residue binds in an initial, rate-limiting step

Polarizable Water Model for the Coarse-Grained MARTINI Force Field

Coarse-grained (CG) simulations have become an essential tool to study a large variety of biomolecular processes, exploring temporal and spatial scales inaccessible to traditional models of atomistic resolution. One of the major simplifications of CG models is the representation of the solvent, which is either implicit or modeled explicitly as a van der Waals particle. The effect of polarization, and thus a proper screening of interactions depending on the local environment, is absent. Given the important role of water as a ubiquitous solvent in biological systems, its treatment is crucial to the properties derived from simulation studies. Here, we parameterize a polarizable coarse-grained water model to be used in combination with the CG MARTINI force field. Using a three-bead model to represent four water molecules, we show that the orientational polarizability of real water can be effectively accounted for. This has the consequence that the dielectric screening of bulk water is reproduced. At the same time, we parameterized our new water model such that bulk water density and oil/water partitioning data remain at the same level of accuracy as for the standard MARTINI force field. We apply the new model to two cases for which current CG force fields are inadequate. First, we address the transport of ions across a lipid membrane. The computed potential of mean force shows that the ions now naturally feel the change in dielectric medium when moving from the high dielectric aqueous phase toward the low dielectric membrane interior. In the second application we consider the electroporation process of both an oil slab and a lipid bilayer. The electrostatic field drives the formation of water filled pores in both cases, following a similar mechanism as seen with atomistically detailed models

The ELBA Force Field for Coarse-Grain Modeling of Lipid Membranes

A new coarse-grain model for molecular dynamics simulation of lipid membranes is presented. Following a simple and conventional approach, lipid molecules are modeled by spherical sites, each representing a group of several atoms. In contrast to common coarse-grain methods, two original (interdependent) features are here adopted. First, the main electrostatics are modeled explicitly by charges and dipoles, which interact realistically through a relative dielectric constant of unity (). Second, water molecules are represented individually through a new parametrization of the simple Stockmayer potential for polar fluids; each water molecule is therefore described by a single spherical site embedded with a point dipole. The force field is shown to accurately reproduce the main physical properties of single-species phospholipid bilayers comprising dioleoylphosphatidylcholine (DOPC) and dioleoylphosphatidylethanolamine (DOPE) in the liquid crystal phase, as well as distearoylphosphatidylcholine (DSPC) in the liquid crystal and gel phases. Insights are presented into fundamental properties and phenomena that can be difficult or impossible to study with alternative computational or experimental methods. For example, we investigate the internal pressure distribution, dipole potential, lipid diffusion, and spontaneous self-assembly. Simulations lasting up to 1.5 microseconds were conducted for systems of different sizes (128, 512 and 1058 lipids); this also allowed us to identify size-dependent artifacts that are expected to affect membrane simulations in general. Future extensions and applications are discussed, particularly in relation to the methodology's inherent multiscale capabilities

Molecular dynamics simulation of humic substances

© 2014, Orsi. Humic substances (HS) are complex mixtures of natural organic material which are found almost everywhere in the environment, and particularly in soils, sediments, and natural water. HS play key roles in many processes of paramount importance, such as plant growth, carbon storage, and the fate of contaminants in the environment. While most of the research on HS has been traditionally carried out by conventional experimental approaches, over the past 20 years complementary investigations have emerged from the application of computer modeling and simulation techniques. This paper reviews the literature regarding computational studies of HS, with a specific focus on molecular dynamics simulations. Significant achievements, outstanding issues, and future prospects are summarized and discussed