Search

Conventional simulations of complex systems in the canonical ensemble suffer from the quasi-ergodicity problem. A simulation in generalized ensemble overcomes this difficulty by performing a random walk in potential energy space and other parameter space. From only one simulation run, one can obtain canonical-ensemble averages of physical quantities as functions of temperature by the single-histogram and/or multiple-histogram reweighting techniques. In this article, we review the generalized-ensemble algorithms. Three well-known methods, namely multicanonical algorithm, simulated tempering, and replica-exchange method, are described first. Both Monte Carlo and molecular dynamics versions of the algorithms are given. We then present further extensions of the above three methods. [ABSTRACT FROM AUTHOR]

We describe a new Monte Carlo algorithm that produces results of high accuracy with reduced simulational effort. In the simplest application of the algorithm, a random walk is performed in energy space, and the resultant density of states is modified continuously to produce a "flat" histogram. This method permits us to directly access the entropy and free energy, is independent of temperature, and is efficient for the study of both first-order and second-order phase transitions as well as complex systems with a rough energy landscape. The method may be extended to random walks in more than one variable. [ABSTRACT FROM AUTHOR]

The successful deciphering of the human genome has highlighted an old challenge in protein science: For most of the resolved protein sequences, we do not know the corresponding structures and functions. Neither do we understand in detail the mechanism by which a protein folds into its biologically active form. Computer experiments offer one way to evaluate the sequence-structure relationship and the folding process but are extremely difficult for detailed protein models. Only over the last few years have algorithms been developed that allow an efficient sampling of relevant protein configurations. Important examples of these new techniques will be introduced in the context of all-atom simulations of small proteins. For these molecules, the folding mechanism and the relation between secondary structure formation and folding are explored. Limitations of current energy functions are discussed. [ABSTRACT FROM AUTHOR]

The computer revolution has been driven by a sustained increase of computational speed of approximately one order of magnitude (a factor of ten) every 5 years since about 1950. In natural sciences, this has led to a continuous increase of the importance of computer simulations. Major enabling techniques are Markov Chain Monte Carlo (MCMC) and molecular dynamics (MD) simulations. This article deals with the MCMC approach. First, basic simulation techniques as well as methods for their statistical analysis are reviewed. Afterwards, the focus is on generalized ensembles and biased updating. These are two advanced techniques, which are of relevance for simulations of biomolecules or are expected to become relevant in that respect. In particular, we consider the multicanonical ensemble and the replica exchange method (also known as parallel tempering or method of multiple Markov chains). [ABSTRACT FROM AUTHOR]

Folding and aggregation of proteins, the interaction between proteins and membranes, as well as the adsorption of organic soft matter to inorganic solid substrates belong to the most interesting challenges in understanding structure and function of complex macromolecules. This is reasoned by the interdisciplinary character of the associated questions ranging from the molecular origin of the loss of biological functionality as, for example, in Alzheimer's disease to the development of organic circuits for biosensory applications. In this lecture, we focus on the analysis of mesoscopic models for protein folding, aggregation, and hybrid systems of soft and solid condensed matter. The simplicity of the coarse-grained models allows for a more universal description of the notoriously difficult problem of protein folding. In this approach, classifications of structure formation processes with respect to the conformational pseudophases are possible. This is similar in aggregation and adsorption processes, where the individual folding propensity is influenced by external forces. The main problem in studies of conformational transitions is that the sequences of amino acids, which built up the proteins, are necessarily of finite length and, therefore, a thermodynamic limit does not exist. Thus, structural transitions are not phase transitions in the strict thermodynamic sense and the analysis of pseudouniversal aspects is intricate, as apparently small-system effects accompany all conformational transitions and cannot be neglected. [ABSTRACT FROM AUTHOR]

Finding a suitable transferable energy function for modeling of how different proteins fold into their respective native states is a major challenge in biophysics. Here, we discuss an all-atom protein model with implicit water and some studies based on this model. The model has a simplified and computationally convenient energy function. Despite its simplicity, the model has been found to quite successfully describe the structure and melting behavior of several peptides with about 20 amino acids. The same model, with unchanged parameters, has also been used to investigate the aggregation behavior of a fragment of Alzheimer's Aβ peptide and the mechanical properties of the 76-residue protein ubiquitin. [ABSTRACT FROM AUTHOR]

The understanding of the relation between the amino acid sequence and the spatial structure of the protein is an open task since many decades. Some tools for the prediction of protein structures from known ones were developed, but they let unanswered fundamental questions about properties of folded proteins and the folding process itself. Recently, coarse-grained models were developed, which are able to predict protein structures with an acceptable level of accuracy using probabilistic algorithms. In this paper, we introduce a new coarse-grained model, which neglects details on the amino acid level and uses structure elements of successive amino acids as building blocks instead. Within this approximation, we use a deterministic branch and bound algorithm, which is able to find the exact ground state and the complete low-energy landscape. The agreement of the calculated ground state with the native protein structure is shown. A possible application of the model to explain experiments with membrane proteins using dynamic force microscopy is sketched. [ABSTRACT FROM AUTHOR]

We review a class of 3D lattice spin models in which planar Peierls boundaries between + and - spins can be created at zero energy cost. These so-called Gonihedric Ising models have (in general) specially tuned nearest neighbour, next-to-nearest neighbour and plaquette interactions, which endow the models with some novel properties both in and out of equilibrium. After reviewing the genesis of the models in string theory, we discuss investigations of both their equilibrium and non-equilibrium behaviours by various analytical and numerical means. The purely plaquette variant of the model displays all the standard indications of glassy behaviour without any recourse to quenched disorder, whilst still possessing a crystalline low-temperature phase in equilibrium. [ABSTRACT FROM AUTHOR]

Molecular dynamics (MD) simulations of various sodium silicate melts, (Na2O)x(SiO2) with x=2, 3, 20, are presented. In these systems, the mobility of sodium ions is much higher, often by orders of magnitude, than that of the silicon and oxygen atoms forming a tetrahedral network structure. We show that the high mobility of sodium is intimately related to the chemical ordering in sodium silicates. A network of percolating sodium-rich channels is formed in the static structure that serve as diffusion channels for the sodium ions. This channel network is revealed in static structure factors by a prepeak at the wavenumber q=0.95 Å-1. Inelastic neutron scattering experiments of sodium silicate melts, done at temperatures as high as 1600 K, confirm the existence of the latter prepeak. The channel diffusion of sodium ions yields a peculiar behavior of time-dependent density-density correlation functions, the so-called intermediate scattering functions. Whereas the incoherent scattering function for sodium, FsNa(q,t), detects the fast sodium ion diffusion, the coherent scattering function for Na-Na correlations, F NaNa(q,t), decays on the slow time-scale of the Si-O matrix. This reflects the hopping motion of sodium ions between sodium sites, thereby FNaNa(q,t) describing site-site correlations. Numerical calculations in the framework of mode-coupling theory (MCT) are presented which use the partial static structure factors from the MD simulations as an input. The MCT results are in qualitative agreement with those from MD simulations. [ABSTRACT FROM AUTHOR]

Dynamical scaling and ageing in disordered systems far from equilibrium is reviewed. Particular attention is devoted to the question to what extent a recently introduced generalization of dynamical scaling to local scale-invariance can describe data for either non-glassy systems quenched to below Tc or for spin glasses at criticality. The dependence of the scaling behaviour on the distribution of the random couplings is discussed. It is shown that finite-time corrections to scaling can become quite sizable in these systems. Numerically determined ageing quantities are confronted with available experimental results. [ABSTRACT FROM AUTHOR]

This chapter is devoted to spin glasses, a vast class of disordered magnetic materials [1, 2, 3, 4, 5]. Spin glasses are prototypical systems widely studied in condensed matter physics and statistical mechanics. A lot of research has been devoted to such systems, more than 10 000 scientific publications about spin glasses exist. The reason for this strong interest is that spin glasses exhibit a very puzzling behavior at low temperatures, which is still not completely understood. Furthermore, the theoretical treatment of these systems has led to many advances, with considerable impact on other cross-disciplinary applications such as neural networks [6], error-correcting codes [7], or optimization problems [8]. Here, we start with a general introduction, mentioning some fundamental experiments. Then we describe the standard model for spin glasses, the Edwards-Anderson Ising model, and mention some results of theoretical treatments, in particular the opposing mean-field and droplet pictures. The main part of this contribution is devoted to the numerical treatment of two-dimensional spin glasses with short-range interactions. These systems are special because they do not exhibit an ordered phase at low temperature. This means that the behavior for finite-size systems and small temperatures can be probably very well described by the droplet picture. Here, two-dimensional spin glasses are studied via ground-state (GS) calculations. In the main algorithmic part, it is shown that the ground-state problem for planar spin glasses can be mapped on the minimum-weight perfect-matching problem, a classical graph-theoretic problem from computer science. For this problem, efficient algorithms are available. In the next section, it is shown that using this approach not only true (classical) ground states but also different types of excitations can be calculated. It is shown that by comparing the results for different types of excitations, important assumptions made by the droplet picture can be verified. In the last section, the presented approach is extended, such that also dynamical properties of two-dimensional spin glasses can be probed, namely the scaling of energy barriers with the system size. [ABSTRACT FROM AUTHOR]

The question whether there is a static phase transition underlying the freezing of a supercooled fluid into a glass, or a purely dynamical transition (such as described by the mode-coupling theory of the glass transition) is briefly reviewed. The mean-field Potts glass with р > 4 states provides a model where both a static and a dynamic transition occur. We describe Monte Carlo simulations which provide insight into the behavior of this model and discuss how these transitions show up in systems of finite size. By studying a 10-state Potts glass with nearest-neighbor interactions on the simple cubic lattice, evidence is obtained that even at very low temperatures only short range order due to small clusters of strongly correlated Potts spins is possible. No trace of the static and dynamic glass transition found in the mean-field limit is left. Possibilities to construct models which better describe the phenomena at the glass transition of real materials are briefly discussed. [ABSTRACT FROM AUTHOR]