Stretching a self-interacting semiflexible polymer

Abstract

PACS. 82.35.Lr -Physical properties of polymers. PACS. 87.15.-v -Biomolecules: structure and physical properties.Abstract. -We present results from three-dimensional off-lattice Monte-Carlo simulations to investigate the stretching response of a semi-flexible polymer subjected to self-attractive interactions. We employ the quasi-static approximation and consider both the fixed elongation and the fixed force ensemble, which can equally well be reproduced in experiments nowadays. The force versus elongation curves are in general non-monotonic, and the quantity and height of peaks increase with decreasing temperature, and with increasing stiffness. We finally compute the variation of unfolding force with temperature. Our results should be relevant for stretching experimental studies, and for more refined theoretical modeling, taking non-equilibrium and kinetic effects into account.Introduction. -In recent years, the elastic properties of bio-polymers like proteins and DNA have been thoroughly investigated experimentally, thanks to the rapid development of single-molecule techniques, e.g. soft micro-needles [1], atomic force microscopes (AFMs) [2] and optical tweezers [3]. A major motivation for these studies comes from the possibility to enhance our quantitative understanding of the physical and biochemical properties of biomolecules. For instance, monitoring the applied tension at the ends of a macromolecule offers an insight into the molecular forces acting among its constituents. The detailed scenario emerging from the experimental force-elongation curves has called for the validating of a number of theoretical models previously introduced in polymer physics. The Freely Jointed Chain (FJC) [4] and the Worm-like Chain (WLC) models [5] are arguably the simplest and most widely known ones. These models predict markebly different shapes for the force versus elongation curves for a polymer, notably for intermediate to large forces [4,[6][7][8]. Briefly, evidence has shown that the FJC model is appropriate for flexible polymers like polyethylene, while using the WLC model is crucial when fitting elasticity data for double-stranded (ds) DNA and other semi-flexible polymers and proteins.However, neither of these models take into account of the excluded volume, and their validity is further limited to cases in which self-interactions between distinct polymer segments are negligible. This is appropriate in the strong-force regime, or far from the θ point (or folding temperature) for a self-attractive chain, such as a DNA molecule with multivalent counterions

Analysis of DNA Elasticity

“…The measured steady-state fluctuation of this position was negligible. The simulated extension responses of FJC by both forcing schemes in a poor solvent and at a low temperature (k B T= 0:2, where is the strength of V LJ ) differed markedly by showing peaks in the constantextension scheme in agreement with [16] [see Fig. 1(a)], which validates our computational implementation of the constant-extension pulling.…”

Dissecting Entropic Coiling and Poor Solvent Effects in Protein Collapse

“…The force plateau directly passes into the entropic chain behavior, since nonlocal contact formation is not hampered by bending rigidity even for large chain extensions. A plateau 15,16 for flexible chains and a hump-like shape for comparably stiff chains have been predicted theoretically 22 and have been found in force spectroscopy measurements of single hydrophobic polymer chains in water. 17 Proteins are stiff polymers (p gs ) 1.2 nm) in poor solvents, yet their experimental force-extension behavior does not exhibit a hump but instead approximately follows an apparent worm-like chain behavior.…”

Simulating the collapse transition of a two-dimensional semiflexible lattice polymer

“…For a flexible self-attractive polymer, mean-field theories predicted a second-order continuous globule-coil phase-transition as the ambient temperature is elevated. This prediction was confirmed by more recent analytical calculations 20,21,22 in 2D; however, there are still some controversies in the literature concerning Monte Carlo simulations in 3D (for example, Refs. [23,24] believed that the 3D globule-coil transition is a first-order phase-transition in the thermodynamic limit).…”

“…The force-induced collapse-transition have also been studied in recent years. For 3D polymers, the transition is shown to be first-order no matter whether the polymer is flexible or semiflexible 21,25 . For 2D flexible polymer, this transition is believed to be second-order 20,25,30 ; while the results of an exactly solvable model 22 suggest that the order will change to be first-order when the polymer is semiflexible.…”