A review of Monte Carlo simulations of polymers with PERM

In this review, we describe applications of the pruned-enriched Rosenbluth method (PERM), a sequential Monte Carlo algorithm with resampling, to various problems in polymer physics. PERM produces samples according to any given prescribed weight distribution, by growing configurations step by step with controlled bias, and correcting "bad" configurations by "population control". The latter is implemented, in contrast to other population based algorithms like e.g. genetic algorithms, by depth-first recursion which avoids storing all members of the population at the same time in computer memory. The problems we discuss all concern single polymers (with one exception), but under various conditions: Homopolymers in good solvents and at the $\Theta$ point, semi-stiff polymers, polymers in confining geometries, stretched polymers undergoing a forced globule-linear transition, star polymers, bottle brushes, lattice animals as a model for randomly branched polymers, DNA melting, and finally -- as the only system at low temperatures, lattice heteropolymers as simple models for protein folding. PERM is for some of these problems the method of choice, but it can also fail. We discuss how to recognize when a result is reliable, and we discuss also some types of bias that can be crucial in guiding the growth into the right directions.Comment: 29 pages, 26 figures, to be published in J. Stat. Phys. (2011

Capturing the essence of folding and functions of biomolecules using Coarse-Grained Models

The distances over which biological molecules and their complexes can function range from a few nanometres, in the case of folded structures, to millimetres, for example during chromosome organization. Describing phenomena that cover such diverse length, and also time scales, requires models that capture the underlying physics for the particular length scale of interest. Theoretical ideas, in particular, concepts from polymer physics, have guided the development of coarse-grained models to study folding of DNA, RNA, and proteins. More recently, such models and their variants have been applied to the functions of biological nanomachines. Simulations using coarse-grained models are now poised to address a wide range of problems in biology.Comment: 37 pages, 8 figure

Single DNA conformations and biological function

From a nanoscience perspective, cellular processes and their reduced in vitro imitations provide extraordinary examples for highly robust few or single molecule reaction pathways. A prime example are biochemical reactions involving DNA molecules, and the coupling of these reactions to the physical conformations of DNA. In this review, we summarise recent results on the following phenomena: We investigate the biophysical properties of DNA-looping and the equilibrium configurations of DNA-knots, whose relevance to biological processes are increasingly appreciated. We discuss how random DNA-looping may be related to the efficiency of the target search process of proteins for their specific binding site on the DNA molecule. And we dwell on the spontaneous formation of intermittent DNA nanobubbles and their importance for biological processes, such as transcription initiation. The physical properties of DNA may indeed turn out to be particularly suitable for the use of DNA in nanosensing applications.Comment: 53 pages, 45 figures. Slightly revised version of a review article, that is going to appear in the J. Comput. Theoret. Nanoscience; some typos correcte

Backbone-free duplex-stacked monomer nucleic acids exhibiting Watson-Crick selectivity.

We demonstrate that nucleic acid (NA) mononucleotide triphosphates (dNTPs and rNTPs), at sufficiently high concentration and low temperature in aqueous solution, can exhibit a phase transition in which chromonic columnar liquid crystal ordering spontaneously appears. Remarkably, this polymer-free state exhibits, in a self-assembly of NA monomers, the key structural elements of biological nucleic acids, including: long-ranged duplex stacking of base pairs, complementarity-dependent partitioning of molecules, and Watson-Crick selectivity, such that, among all solutions of adenosine, cytosine, guanine, and thymine NTPs and their binary mixtures, duplex columnar ordering is most stable in the A-T and C-G combinations

Frustration in Biomolecules

Biomolecules are the prime information processing elements of living matter. Most of these inanimate systems are polymers that compute their structures and dynamics using as input seemingly random character strings of their sequence, following which they coalesce and perform integrated cellular functions. In large computational systems with a finite interaction-codes, the appearance of conflicting goals is inevitable. Simple conflicting forces can lead to quite complex structures and behaviors, leading to the concept of "frustration" in condensed matter. We present here some basic ideas about frustration in biomolecules and how the frustration concept leads to a better appreciation of many aspects of the architecture of biomolecules, and how structure connects to function. These ideas are simultaneously both seductively simple and perilously subtle to grasp completely. The energy landscape theory of protein folding provides a framework for quantifying frustration in large systems and has been implemented at many levels of description. We first review the notion of frustration from the areas of abstract logic and its uses in simple condensed matter systems. We discuss then how the frustration concept applies specifically to heteropolymers, testing folding landscape theory in computer simulations of protein models and in experimentally accessible systems. Studying the aspects of frustration averaged over many proteins provides ways to infer energy functions useful for reliable structure prediction. We discuss how frustration affects folding, how a large part of the biological functions of proteins are related to subtle local frustration effects and how frustration influences the appearance of metastable states, the nature of binding processes, catalysis and allosteric transitions. We hope to illustrate how Frustration is a fundamental concept in relating function to structural biology.Comment: 97 pages, 30 figure