Discretization parameters in fine-grained lattice simulations of linear and branched polymers

Abstract

Monte Carlo simulations of polymer chains on a discretized lattice, where each atom occupies multiple lattice sites, have been shown to provide accuracies comparable with off-lattice simulations in one-tenth the computation time. For polyatomic molecules, the main requirement for the level of discretization required is set by the intramolecular geometry of the molecule. The current work provides a method to determine this level of discretization without running full off lattice simulations for comparison of results. Chains are generated off-lattice, placed on lattices of various discretizations, and the resulting errors are analyzed. We apply the method to three cases, united atom polyethylene, united atom polypropylene, and atomistic polyethylene. The atomic diameter to lattice size ratios required are 12 for the united atom cases, and 17 for atomistic polyethylene.

Simulation of an Ensemble of Conformational Transitions in a United-Residue Model of Calmodulin

“…Thus the approach substitutes rapid “look-ups” for typically quite expensive calculations of forces and/or energies. The general grid/lattice strategy has been in use for decades in protein systems. ,,,− Our implementation for proteins is strongly motivated by high-coordination lattice models of proteins, notably those of Kolinski and Skolnick; , see also the work of Olson and co-workers. , The approach we follow directly was developed by Panagiotopoulos and Kumar for liquids simulation 124,125 and has also been applied to polymers. , …”

“…The fine spacing permits calculations that essentially mimic continuum approaches with minimal artifacts. Indeed, recent work suggests that, for polymer systems, a particle-to-grid size ratio of 17 or 18 is sufficient to prevent artifacts with atomically detailed potentials, whereas 12 suffices for united-atom models. , In the present work, a conservative ratio exceeding 30 is employed, primarily to implement dynamic Monte Carlo dynamics (see below) with a sufficiently large acceptance ratio. The grid spacing is 0.13 Å.…”

“…Grid-based simulation is also used as a technical device to speed up the simulations, following many precedents, ,,,− particularly the general approach of high coordination lattice studies by Kolinski, Skolnick, and co-workers. Most directly, we employ the simple approach of Panagiotopoulos and Kumar, , which involves the use of a fine grid (with lattice spacing much less than the particle or atom size) to mimic continuum calculations.…”

Thermodynamic properties of lattice hard-sphere models

“…Finely discretized models have also been used to study simple atomic fluids, 13 biomolecules, 14 and polymers. 15 The main attractive feature of such models is that the thermodynamic properties of continuum systems are closely reproduced at relatively low values of , often with significant computational savings. Such savings result because of the reduction of the dimensionality of configuration space and the existence of specialized algorithms for evaluating intermolecular interactions for the lattice models.…”

Finely discretized lattice simulations of SPC/E water

“…The required degree of discretization in each case was entirely due to intramolecular bond lengths and angles. It was found that the deviation of bond lengths and angles in each model discussed above uniformly decreased with increasing ζ [4].…”