Thermodynamics and structure of macromolecules from flat-histogram Monte Carlo simulations

Abstract

Over the last decade flat-histogram Monte Carlo simulations, especially multi-canonical and Wang-Landau simulations, have emerged as a strong tool to study the statistical mechanics of polymer chains. These investigations have focused on coarse-grained models of polymers on the lattice and in the continuum. Phase diagrams of chains in bulk as well as chains attached to surfaces were studied, for homopolymers as well as for protein-like models. Also, aggregation behavior in solution of these models has been investigated. We will present here the theoretical background for these simulations, explain the algorithms used and discuss their performance and give an overview over the systems studied with these methods in the literature, where we will limit ourselves to studies of coarse-grained model systems. Implementations of these algorithms on parallel computers will be also briefly described. In parallel to the development of these simulation methods, the power of a micro-canonical analysis of such simulations has been recognized, and we present the current state of the art in applying the micro-canonical analysis to phase transitions in nanoscopic polymer systems.

Equilibrium properties of 3-arm star-shaped polyions: an entropic sampling Monte Carlo study

“…The method that we used here is the entropic sampling (ES) method [23,24] within Wang-Landau (WL) algorithm [25] initially applied to polymers in our simulation group [26] and successfully used later by us [27-29, 34, 37, 40, 41] and by other researchs [30,33,[42][43][44][45] for studying different polymer systems. In the ES-WL computer experiment the density of states g(E) is calculated just as it was done in [27] (see [27] for details).…”

Efficient implementation of the Wang-Landau algorithm for systems with length-scalable potential energy functions

“…Owing to several refinements and improvements , it has been gradually implemented to study complicated systems with continuous energy spectra as well. Examples include complex fluids [3][4][5], atomic clusters [6,7], liquid crystals [8], biomolecules [9][10][11], polymers [12][13][14][15], logarithmic gas in the context of random matrix theory [29], etc.…”

Multicanonical Monte Carlo ensemble growth algorithm

“…PACS numbers: 05. 10.Ln, 02.70.Tt, 87.15.A-Over the past two decades, chain-growth algorithms proved to be among the most powerful methods for sampling the equilibrium configuration of polymer systems, in different environments and with various interactions [1][2][3][4]. Such methods are superior to classic move-sets based random-walk Monte Carlo (MC) sampling, both in the configuration space and in the energy space [5][6][7][8][9].…”

“…As the name indicates, a chaingrowth algorithm grows the polymer chain one monomer at a time, while avoiding occupied locations (in case of selfavoiding random walks), and by correcting the corresponding sampling bias with suitable weight factors. Nowadays, several efficient chain-growth algorithms are available, and many of them show impressive performances, such as PERM [2], or FlatPERM [3], including a large family of variations and refinements (for reviews see, e.g., [10,11]).…”