Sampling activated mechanisms in proteins with the activation-relaxation technique

The activated dynamics of proteins occur on time scales of milliseconds and longer. Standard all-atom molecular dynamics simulations are limited to much shorter times, of the order of tens of nanoseconds. Therefore, many activated mechanisms that are crucial for long-time dynamics will not be observed in such molecular dynamics simulation; different methods are required. Here, we describe in detail the activation-relaxation technique (ART) that generates directly activated mechanisms. The method is defined in the configurational energy landscape and defines moves in a two step fashion: (a) a configuration is first brought from a local minimum to a nearby first-order saddle point (the activation); and (b) the configuration is relaxed to a new metastable state (the relaxation). The method has already been applied to a wide range of problems in condensed matter, including metallic glasses, amorphous semiconductors and silica glass. We review the algorithm in detail, discuss some previously published results and present simulations of activated mechanisms for a two-helix bundle protein using an all-atom energy function.     

Simulating fermions on a quantum computer

The real-time probabilistic simulation of quantum systems in classical computers is known to be limited by the so-called dynamical sign problem, a problem leading to exponential complexity. In 1981 Richard Feynman raised some provocative questions in connection to the “exact imitation” of such systems using a special device named a “quantum computer”. Feynman hesitated about the possibility of imitating fermion systems using such a device. Here we address some of his concerns and, in particular, investigate the simulation of fermionic systems. We show how quantum computers avoid the sign problem in some cases by reducing the complexity from exponential to polynomial. Our demonstration is based upon the use of isomorphisms of algebras. We present specific quantum algorithms that illustrate the main points of our algebraic approach.     

Development and application of a simulation model for changes in land-use patterns under drought scenarios

In arid and semiarid areas of northern China, one of the most vulnerable regional environments, water resources are a key constraint on socioeconomic development. We constructed a simulation model for land-use patterns under a drought transition (i.e., the increased frequency and duration of drought since the late 1970s in the Yongding River Basin study area) to account for the complexity of both the driving factors behind land-use change and the micro-level changes in land-use patterns. This model was a combination of the “top-down” system dynamics model, the “bottom-up” cellular automaton model, and the artificial neural network model. In this model, we considered the socioeconomic development and water resource restrictions, as well as the balance between the land-use requirements and the land supply. We then verified the model through a case study. The results demonstrated the value of constructing a simulation model driven by water resource constraints under the influence of drought. The spatial distribution of land uses in future scenarios will help support decision-making for sustainable regional development.     

Molecular simulations of lactose-bound and unbound forms of the FaeG adhesin reveal critical amino acids involved in sugar binding

F4 fimbriae are protein filaments found in enterotoxigenic Escherichia coli cells and are implicated in the process of bacterial infection due to their function as bacterial adhesins. These filaments are comprised from several proteins, but the bacterial adhesin FaeG, which is a lactose-binding protein, is the major subunit comprising F4 fimbriae. Crystal structures for three variants of the FaeG protein were recently solved, including the ad variant of FaeG that was crystallized in complex with lactose. However, the dynamics of the FaeG protein bound to lactose have not been explored previously using molecular dynamics simulations. Therefore, in order to study the dynamical interactions between the FaeG ad variant and lactose, we have carried out the first all-atom molecular dynamics simulations of this system. We have also probed the role of crystallographic water molecules on the stability of lactose in the FaeG binding site, and have simulated seven FaeG mutants to probe the influence of amino acid substitutions on the ability of FaeG to bind lactose effectively. Our simulations agree well with experimental results for the influence of mutations on lactose binding, provide dynamical insights into the interactions of FaeG with lactose, and also suggest the possibility of additional regions of the FaeG protein that may act as secondary lactose binding sites.     

A domain decomposition molecular dynamics program for the simulation of flexible molecules of spherically-symmetrical and nonspherical sites. II. Extension to NVT and NPT ensembles

We describe the algorithms for NVT and NPT-ensemble simulations developed within the parallel molecular dynamics program GBMOLDD. This program uses the domain decomposition algorithm and is targeted at large-scale simulations of molecular systems (particularly polymers and liquid crystals) composed of both spherically-symmetric and nonspherical sites. The nonspherical sites can be described either by a Gay-Berne potential or by soft repulsive spherocylinders. The molecules can be of arbitrary topology and the intramolecular forces are described via standard force fields. We tested the stability of both leap-frog and velocity-Verlet integrators on two “real-life” systems—a nematic liquid crystal phase of 1944 one-site Gay-Berne molecules and on 512 flexible liquid-crystalline dimers. In both cases the algorithm demonstrates good stability over the typical simulation times required for new phase formation and/or molecular relaxation processes.     

Explicit design of FPGA-based coprocessors for short-range force computations in molecular dynamics simulations

FPGA-based acceleration of molecular dynamics simulations (MD) has been the subject of several recent studies. The short-range force computation, which dominates the execution time, is the primary focus. Here we combine: a high level of FPGA-specific design including cell-lists, systematically determined interpolation and precision, handling of exclusion, and support for MD simulations of up to 256 K particles. The target system consists of a standard PC with a 2004-era COTS FPGA board. There are several innovations: new microarchitectures for several major components, including the cell-list processor and the off-chip memory controller; and a novel arithmetic mode. Extensive experimentation was required to optimize precision, interpolation order, interpolation mode, table sizes, and simulation quality. We obtain a substantial speed-up over a highly tuned production MD code.     

Comparative structural studies of psychrophilic and mesophilic protein homologues by molecular dynamics simulation

Comparative molecular dynamics simulations of psychrophilic type III antifreeze protein from the North-Atlantic ocean-pout Macrozoarces americanus and its corresponding mesophilic counterpart, the antifreeze-like domain of human sialic acid synthase, have been performed for 10 ns each at five different temperatures. Analyses of trajectories in terms of secondary structure content, solvent accessibility, intramolecular hydrogen bonds and protein–solvent interactions indicate distinct differences in these two proteins. The two proteins also follow dissimilar unfolding pathways. The overall flexibility calculated by the trace of the diagonalized covariance matrix displays similar flexibility of both the proteins near their growth temperatures. However at higher temperatures psychrophilic protein shows increased overall flexibility than its mesophilic counterpart. Principal component analysis also indicates that the essential subspaces explored by the simulations of two proteins at different temperatures are non-overlapping and they show significantly different directions of motion. However, there are significant overlaps within the trajectories and similar directions of motion of each protein especially at 298 K, 310 K and 373 K. Overall, the psychrophilic protein leads to increased conformational sampling of the phase space than its mesophilic counterpart.Our study may help in elucidating the molecular basis of thermostability of homologous proteins from two organisms living at different temperature conditions. Such an understanding is required for designing efficient proteins with characteristics for a particular application at desired working temperatures.     

Simulation of pedestrian flow through a “T” intersection: A multi-floor field cellular automata approach

There are several ways to study pedestrian dynamics, such as the macroscopic hydrodynamics, molecular dynamics with social force, and cellular automata (CA) with mean field approach. In recent years, the cellular automata approach has received growing interest from researchers. Because this approach is not only to save the computing time but also to reduce the complexity of the problem. In this presentation, we report the study of the conformation of congestion in a “T” intersection by using a cellular automata procedure with multi-floor fields. By using the multi-floor fields, we can mimic the pedestrian flow from several entrances to different exits firstly, and we can simulate the different pedestrian speed by changing the controlling parameter. Our results show, there are some kinds of phase transition in this system.     

Stability tests on known and misfolded structures with discrete and all atom molecular dynamics simulations

The brevity of molecular dynamics simulations often limits their utility in developing and evaluating structural models of proteins. The duration of simulations can be increased greatly using discrete molecular dynamics (DMD). However, the trade off is that coarse graining, implicit solvent, and other time-saving procedures reduce the accuracy of DMD simulations. Here we address some of these issues by comparing results of DMD and conventional all atom MD simulations on proteins of known structure and misfolded proteins. DMD simulations were performed at a range of temperatures to identify a 'physiological' temperature for DMD that mimicked molecular motions of conventional MD simulations at 310K. We also compared results obtained with a new implicit solvent model developed here based on Miyazawa-Jernigan interaction pair potential to those obtained with a previously used model based on Kyte-Doolittle hydropathy scale. We compared DMD and all atom molecular dynamics with explicit water by simulating both correctly and incorrectly folded structures, and monomeric and dimeric α β-barrel structures to analyze the ability of these procedures to distinguish between good and bad models. Deviations from the correct structures were substantially greater with DMD, as would be expected from coarse-graining and longer simulation time. Deviations were smallest for β-strands and greatest for coiled loops. Structures of the incorrectly folded models were very poorly preserved during the DMD simulations; but both methods were able to distinguish between the correct and the incorrect structures based on differences in the magnitudes of the root mean squared deviation (RMSD) from the starting conformation.     

The changing face of adaptive control: The use of multiple models

Adaptive systems that continuously monitor their own performance and adjust their control strategies to improve it, have been studied for over 50 years. The theory of such systems is now commonly referred to as classical adaptive control. Such control is now well established and is found to be satisfactory when the uncertainty in the system to be controlled (i.e. the plant) is small.During the past 15 years several attempts were made to extend this general methodology to systems with large uncertainties, by using multiple models to identify the plant. Among these, two general methods based on “switching” and “switching and tuning” have emerged as the leading contenders. Recently, a radically different approach was proposed by the authors (Han & Narendra, 2010b), in which the multiple models are used to play a significantly larger role in the decision making process, resulting in substantial improvement in performance.In this paper, which is tutorial in nature, the three methods based on multiple models are critically examined. At the same time, alternative methods using fixed and adaptive models are also proposed. In all cases, detailed simulation studies of adaptation in different environments are presented. Theoretical explanations are given, where available, for the wide spectrum of performances observed in the simulation studies.     

A hardware generator of multi-point distributed random numbers for Monte Carlo simulation

Monte Carlo simulation of weak approximations of stochastic differential equations constitutes an intensive computational task. In applications such as finance, for instance, to achieve “real time” execution, as often required, one needs highly efficient implementations of the multi-point distributed random number generator underlying the simulations. In this paper, a fast and flexible dedicated hardware solution on a field programmable gate array is presented. A comparative performance analysis between a software-only and the proposed hardware solution demonstrates that the hardware solution is bottleneck-free, retains the flexibility of the software solution and significantly increases the computational efficiency. Moreover, simulations in applications such as economics, insurance, physics, population dynamics, epidemiology, structural mechanics, chemistry and biotechnology can benefit from the obtained speedups.     

Exploiting hierarchy parallelism for molecular dynamics on a petascale heterogeneous system

Heterogeneous systems with nodes containing more than one type of computation units, e.g., central processing units (CPUs) and graphics processing units (GPUs), are becoming popular because of their low cost and high performance. In this paper, we have developed a Three-Level Parallelization Scheme (TLPS) for molecular dynamics (MD) simulation on heterogeneous systems. The scheme exploits multi-level parallelism combining (1) inter-node parallelism using spatial decomposition via message passing, (2) intra-node parallelism using spatial decomposition via dynamically scheduled multi-threading, and (3) intra-chip parallelism using multi-threading and short vector extension in CPUs, and employing multiple CUDA threads in GPUs. By using a hierarchy of parallelism with optimizations such as communication hiding intra-node, and memory optimizations in both CPUs and GPUs, we have implemented and evaluated a MD simulation on a petascale heterogeneous supercomputer TH-1A. The results show that MD simulations can be efficiently parallelized with our TLPS scheme and can benefit from the optimizations.     

Monte Carlo simulations of the 2d-Ising model in the geometry of a long stripe

The two-dimensional Ising model in the geometry of a long stripe can be regarded as a model system for the study of nanopores. As a quasi-one-dimensional system, it also exhibits a rather interesting “phase behavior”: At low temperatures the stripe is either filled with “liquid” or “gas” and “densities” are similar to those in the bulk. When we approach a “pseudo-critical point” (below the critical point of the bulk) at which the correlation length becomes comparable to the length of the stripe, several interfaces emerge and the systems contains multiple “liquid” and “gas” domains. The transition depends on the size of the stripe and occurs at lower temperatures for larger stripes. Our results are corroborated by simulations of the three-dimensional Asakura–Oosawa model in cylindrical geometry, which displays qualitatively similar behavior. Thus our simulations explain the physical basis for the occurrence of “hysteresis critical points” in corresponding experiments.     

Extended nonlinear waves in multidimensional dynamical lattices

We explore spatially extended dynamical states in the discrete nonlinear Schrödinger lattice in two- and three-dimensions, starting from the anti-continuum limit. We first consider the “core” of the relevant states (either a two-dimensional “tile” or a three-dimensional “stone”), and examine its stability analytically. The predictions are corroborated by numerical results. When the core is stable, we propose a method allowing the extension of the structure to as many sites as may be desired. In this way, various patterns of excited sites can be formed. The stability of the full extended nonlinear structures is studied numerically, which yields instability thresholds for such structures, which are attained with the increase of the lattice coupling constant. Finally, in cases of instability, direct numerical simulations are used to elucidate the evolution of the pattern; it is found that, typically, the unstable extended nonlinear pattern breaks up in an oscillatory way, leading to “lattice turbulence”.     

Monte Carlo simulations of the HP model (the "Ising model" of protein folding)

Using Wang–Landau sampling with suitable Monte Carlo trial moves (pull moves and bond-rebridging moves combined) we have determined the density of states and thermodynamic properties for a short sequence of the HP protein model. For free chains these proteins are known to first undergo a collapse “transition” to a globule state followed by a second “transition” into a native state. When placed in the proximity of an attractive surface, there is a competition between surface adsorption and folding that leads to an intriguing sequence of “transitions”. These transitions depend upon the relative interaction strengths and are largely inaccessible to “standard” Monte Carlo methods.     

Investigation of multiscale fluid flow characteristics based on a hybrid atomistic–continuum method

A computer program based on a molecular dynamics–continuum hybrid method has been developed in which the Navier–Stokes equations are solved in the continuum region and the molecular dynamics in the atomistic region. The coupling between the atomistic and continuum is constructed through constrained dynamics within an overlap region where both molecular and continuum equations are solved simultaneously. The simulation geometries are solved in three dimensions and an overlap region is introduced in two directions to improve the choice of using the molecular region in smaller areas. The proposed method is used to simulate steady and start-up Couette flow showing quantitative agreement with results from analytical solutions and full molecular dynamics simulations. The prepared algorithm and the computer code are capable of modeling fluid flows in micro and nano-scale geometries.     

计算生物学中的高性能计算（Ⅰ）-分子动力学

分子动力学是高性能计算应用的重要领域,大量的高性能计算资源或机时被用于分子动力学模拟。描述了分子动力学的计算方法和特点,包括常用并行算法、性能改进方式等,介绍了常用的分子动力学大规模并行计算软件及其功能特性,最后展望了分子动力学模拟的发展与挑战。     

An investigation of mating and population maintenance strategies in hybrid genetic heuristics for product line designs

This research builds on prior work on developing near optimal solutions to the product line design problems within the conjoint analysis framework. In this research, we investigate and compare different genetic algorithm operators; in particular, we examine systematically the impact of employing alternative population maintenance strategies and mutation techniques within our problem context. Two alternative population maintenance methods, that we term “Emigration” and “Malthusian” strategies, are deployed to govern how individual product lines in one generation are carried over to the next generation. We also allow for two different types of reproduction methods termed “Equal Opportunity” in which the parents to be paired for mating are selected with equal opportunity and a second based on always choosing the best string in the current generation as one of the parents which is referred to as the “Queen bee”, while the other parent is randomly selected from the set of parent strings. We also look at the impact of integrating the artificial intelligence approach with a traditional optimization approach by seeding the GA with solutions obtained from a Dynamic Programming heuristic proposed by others. A detailed statistical analysis is also carried out to determine the impact of various problem and technique aspects on multiple measures of performance through means of a Monte Carlo simulation study. Our results indicate that such proposed procedures are able to provide multiple “good” solutions. This provides more flexibility for the decision makers as they now have the opportunity to select from a number of very good product lines. The results obtained using our approaches are encouraging, with statistically significant improvements averaging 5% or more, when compared to the traditional benchmark of the heuristic dynamic programming technique.     

Hardware accelerator for molecular dynamics: MDGRAPE-2

We developed MDGRAPE-2, a hardware accelerator that calculates forces at high speed in molecular dynamics (MD) simulations. MDGRAPE-2 is connected to a PC or a workstation as an extension board. The sustained performance of one MDGRAPE-2 board is 15 Gflops, roughly equivalent to the peak performance of the fastest supercomputer processing element. One board is able to calculate all forces between 10 000 particles in 0.28 s (i.e. 310000 time steps per day). If 16 boards are connected to one computer and operated in parallel, this calculation speed becomes ∼10 times faster. In addition to MD, MDGRAPE-2 can be applied to gravitational N-body simulations, the vortex method and smoothed particle hydrodynamics in computational fluid dynamics.