Monte Carlo simulations of a polymer chain conformation. The effectiveness of local moves algorithms and estimation of entropy

Abstract

A linear chain on a simple cubic lattice was simulated by the Metropolis Monte Carlo method using a combination of local and non-local chain modifications. Kink-jump, crankshaft, reptation and end-segment moves were used for local changes of the chain conformation, while for non-local chain rearrangements the "cut-and-paste" algorithm was employed. The statistics of local micromodifications was examined. An approximate method for estimating the conformational entropy of a polymer chain, based on the efficiency of the kink-jump motion respecting chain continuity and excluded volume constraints, was proposed. The method was tested by calculating the conformational entropy of the undisturbed chain, the chain under tension and in different solvent conditions (athermal, theta and poor) and also of the chain confined in a slit. The results of these test calculations are qualitatively consistent with expectations. Moreover, the obtained values of the conformational entropy of self avoiding chain with ends fixed over different separations, agree very well with the available literature data.FigureVisualization of the neighborhood of two local chain microconformations containing a bead (indicated by the arrow) which a) can and b) cannot be moved by the kink-jump. In red there are marked the possible trajectories of chain fragment which can block the adjacent site

LASSI: A lattice model for simulating phase transitions of multivalent proteins

“…Acceptance of the move is predicated on the move not leading to an overlap with a site occupied by another monomer and the satisfaction of linker constraints. The choice for Δ r is made by uniformly sampling each component from the interval [–2,2] such that (shown in S2 Fig ) moves if the selected monomer is in the interior of a molecule [88], and they become analogous to end rotation moves if end monomers are selected [89].…”

Conformation and elasticity of a charged polymer chain bridging two nanoparticles

“…45). To this end, the simulations involved the calculation of probabilities of K-and C-type chain micromodifications that satisfied the chain continuity constraint (denoted as P S (K) and P S (C), respectively) and the excluded volume constraint (denoted as P E (K) and P E (C), respectively).…”

“…The conformational entropy of the chain was calculated by the combinatorial Monte Carlo method described in Ref. 45.…”

Generalizing Rosenbluth's Algorithm to Include Along‐the‐Chain Intramolecular Energies

“…Monte Carlo (MC) methods depend on generating a large subset of samples from an immensely larger population to properly describe a specific state . These methods have been used to study polymer chain behavior by sampling self‐avoiding walks (SAW) on cubic lattices in three dimensions (CL) with a coordination number of six or square lattices in two dimensions (SL) with a coordination number of four . Since the number of possible polymer configurations grows dramatically with the number of segments, it is challenging to sufficiently sample the space to obtain good results.…”