http://static.sif.it/SIF/resources/public/files/va2012/likos_0710.pdf

Effective interactions in soft condensed matter physics

Molecular dynamics (MD) is an invaluable tool with which to study protein folding in silico. Although just a few years ago the dynamic behavior of a protein molecule could be simulated only in the neighborhood of the experimental conformation (or protein unfolding could be simulated at high temperature), the advent of distributed computing, new techniques such as replica-exchange MD, new approaches (based on, e.g., the stochastic difference equation), and physics-based reduced models of proteins now make it possible to study proteinfolding pathways from completely unfolded structures. In this review, we present algorithms for MD and their extensions and applications to protein-folding studies, using all-atom models with explicit and implicit solvent as well as reduced models of polypeptide chains.

Protein-Folding Dynamics: Overview of Molecular Simulation Techniques

In complex systems with many degrees of freedom such as spin glass and biomolecular systems, conventional simulations in canonical ensemble suffer from the quasi-ergodicity problem. A simulation in generalized ensemble performs a random walk in potential energy space and overcomes this difficulty. 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 (MUCA), simulated tempering (ST), and replica-exchange method (REM), are described first. Both Monte Carlo (MC) and molecular dynamics (MD) versions of the algorithms are given. We then present five new generalized-ensemble algorithms which are extensions of the above methods.

Generalized-ensemble algorithms: enhanced sampling techniques for Monte Carlo and molecular dynamics simulations.

Motivated by experiments in which a polynucleotide is driven through a proteinaceous pore by an electric field, we study the diffusive motion of a polymer threaded through a narrow channel with which it may have strong interactions. We show that there is a range of polymer lengths in which the system is approximately translationally invariant, and we develop a coarse-grained description of this regime. From this description, general features of the distribution of times for the polymer to pass through the pore may be deduced. We also introduce a more microscopic model. This model provides a physically reasonable scenario in which, as in experiments, the polymer's speed depends sensitively on its chemical composition, and even on its orientation in the channel. Finally, we point out that the experimental distribution of times for the polymer to pass through the pore is much broader than expected from simple estimates, and speculate on why this might be.

Driven Polymer Translocation Through a Narrow Pore

Protein modeling could be done on various levels of structural details, from simplified lattice or continuous representations, through high resolution reduced models, employing the united atom representation, to all-atom models of the molecular mechanics. Here I describe a new high resolution reduced model, its force field and applications in the structural proteomics. The model uses a lattice representation with 800 possible orientations of the virtual alpha carbon-alpha carbon bonds. The sampling scheme of the conformational space employs the Replica Exchange Monte Carlo method. Knowledge-based potentials of the force field include: generic protein-like conformational biases, statistical potentials for the short-range conformational propensities, a model of the main chain hydrogen bonds and context-dependent statistical potentials describing the side group interactions. The model is more accurate than the previously designed lattice models and in many applications it is complementary and competitive in respect to the all-atom techniques. The test applications include: the ab initio structure prediction, multitemplate comparative modeling and structure prediction based on sparse experimental data. Especially, the new approach to comparative modeling could be a valuable tool of the structural proteomics. It is shown that the new approach goes beyond the range of applicability of the traditional methods of the protein comparative modeling.

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Protein modeling and structure prediction with a reduced representation.

The properties of simplified lattice models of confined branched polymers were studied by the Monte Carlo method. Model chains were located between two parallel impenetrable surfaces. The distance between surfaces, as well as the chain length, were varied. The model chains consisted of f=3 branches of equal length (star-branched polymers) and were based on a simple cubic lattice. The model was athermal and the excluded volume was introduced. Monte Carlo sampling algorithm using local chain micromodifications was applied. Both static and dynamic properties of the system were investigated. The differences between star-branched chains and linear ones which were trapped between walls were discussed. The behavior of static properties made it possible to construct a universal curve presenting the effect of surface-to-surface distance on chain dimensions. The possible explanation of the shape of this curve was given. The changes of dynamic properties were discussed in the context of possible chain’s mechanism of...

Monte Carlo simulations of star-branched polymers confined between two walls

We studied the properties of simple models of star-branched polymer chains confined in a slit. The chains were constructed of united atoms (segments) and were restricted to vertices of a simple cubic lattice. We modeled good solvent conditions and thus the chains interacted with the excluded volume only. The macromolecules were put between two parallel and impenetrable surfaces and the surfaces were attractive for polymer segments. The properties of the model chains were determined by means of Monte Carlo simulations with a sampling algorithm based on chain's local changes of conformation. The differences and similarities in the structure for different adsorption regimes and the size of the slit were shown and discussed. The dependence of the short- and long-time scale dynamic behavior of chains on these factors was determined.

Dynamics of polymer chains in confined space. A computer simulation study

In this study, we investigated the process of random sequential adsorption of stiff and flexible polymer chains on a two-dimensional square lattice. The polymer chains were represented by sequence of lattice points forming needles, T shapes, and crosses as well as flexible linear chains and star-branched chains consisted of three and four arms. The Monte Carlo method was employed to generate the model systems. The percolation threshold and the jamming threshold were determined for all systems under consideration. The influence of the chain length and the chain architecture on both thresholds was calculated and discussed. The changes in the ordering of the system were also studied.

A simple model of stiff and flexible polymer chain adsorption: The influence of the internal chain architecture

The lattice approximation of a heteropolymer chain as a model of a single polypeptide was used in the computer simulation. The residues of a model polypeptide were represented by the chain of alpha-carbons located on a very flexible [310] lattice. The force field that mimic the intramolecular interactions contained the long-range contact potential between the residues and the local preferences in forming helical structures. The chain consisted of two types of residues that had different hydrophobicity. The simulations were performed by means of the Replica Exchange Monte Carlo method combined with the Histogram method. The series of simulations were carried out to investigate the influence of both components of the force field on the transition temperature and the characteristics of the coil-to-globule transition. The properties of low-temperature ordered structures were determined. The thermodynamical description of the model chain was also given. The phase transition was found to be sharp and cooperative for longer chains and strong helical potential. The collapsed globule contained the strongly hydrophobic residues inside the globule while the remaining residues were mainly located close to the globule surface.

Thermodynamical properties of simple models of protein-like heteropolymers

A model of star-branched polymer chains confined in a slit formed by two parallel surfaces was studied. The chains were embedded to a simple cubic lattice and consisted of f=3 branches of equal length. The macromolecules had the excluded volume and the confining surfaces were impenetrable for polymer segments. No attractive interactions between polymer segments and then between polymer segments and the surfaces were assumed and therefore the system was a thermal. Monte Carlo simulations were carried out employing the sampling algorithm based on chain’s local changes of conformation. Lateral diffusion of star-branched chains was studied. Dynamic properties of star-branched chains between the walls with impenetrable rod-like obstacles were also studied and compared to the previous case. The density profiles of polymer segments on the slit were determined. The analysis of contacts between the polymer chain and the surfaces was also carried out.

Piotr Romiszowski

Papers

Monte Carlo simulations of star-branched polymers confined between two walls

Dynamics of polymer chains in confined space. A computer simulation study

A simple model of stiff and flexible polymer chain adsorption: The influence of the internal chain architecture

Thermodynamical properties of simple models of protein-like heteropolymers

Properties of branched confined polymers