Previous Brownian Dynamics Simulations Research Articles

Topology-Dependent Dynamics of Single DNA Molecules

We present the data on the conformational dynamics of circular DNA molecules with defined levels of topological complexity, characterized by the knot type K and linking number Lk. Covalently closed DNAs covalently conjugated to specific fluorophores were investigated using fluorescence correlation spectroscopy (FCS) and fluorescence cross-correlation spectroscopy (FCCS) measurements. We investigate in detail the respective effects of supercoiling and DNA knotting using Lk-topoisomer pools and specific DNA-knot types that were respectively generated by topoisomerase-I relaxation and Cre site-specific recombination. Previous Brownian-dynamics simulations by Langowski et al. (1994) suggest that increasing superhelicity leads to progressively faster dynamics on long time scales, corresponding to translational diffusion, but also on short time scales, corresponding to segmental motions within supercoiled DNA. We investigate here whether DNA knotting similarly affects translational and internal motions. The acceleration of DNA dynamics with increased supercoiling may have implications for processes in cells, such as transcriptional regulation and DNA recombination, both of which are dependent on the dynamics of juxtaposition involving multiple DNA sites.

Dynamic Monte Carlo simulation of non-equilibrium Brownian diffusion of single-chain macromolecules

We performed dynamic Monte Carlo simulations of biased diffusion of 3D phantom single lattice polymer. We observed spontaneous deformation of polymer coil when the external driving forces exceed a critical strength. In addition, longer chains require lower critical strengths, at which their activated velocities deviate from Newtonian-fluid behaviours and merge into a master curve exhibiting shear-thinning followed with shear thickening. We attributed the cause of deformation to the random updating of monomers. The latter represents the dynamic heterogeneity along the real polymer chain, and raises a nonlinear asymmetric accumulation of local acceleration and then an internal tension between chain middle and chain end, as evidenced by our previous Brownian Dynamics simulations. Our results unravel a single-molecular-level source of nonlinear dynamics, which has been overlooked in current theoretical considerations on the basis of Rouse ideal-chain model.

Continuous‐time random walk models of DNA electrophoresis in a post array: Part I. Evaluation of existing models

Several continuous-time random walk (CTRW) models exist to predict the dynamics of DNA in micropost arrays, but none of them quantitatively describes the separation seen in experiments or simulations. In Part I of this series, we examine the assumptions underlying these models by observing single molecules of λ DNA during electrophoresis in a regular, hexagonal array of oxidized silicon posts. Our analysis takes advantage of a combination of single-molecule videomicroscopy and previous Brownian dynamics simulations. Using a custom-tracking program, we automatically identify DNA-post collisions and thus study a large ensemble of events. Our results show that the hold-up time and the distance between collisions for consecutive collisions are uncorrelated. The distance between collisions is a random variable, but it can be smaller than the minimum value predicted by existing models of DNA transport in post arrays. The current CTRW models correctly predict the exponential decay in the probability density of the collision hold-up times, but they fail to account for the influence of finite-sized posts on short hold-up times. The shortcomings of the existing models identified here motivate the development of a new CTRW approach, which is presented in Part II of this series.

Stochastic generation of particle structures with controlled degree of heterogeneity

The recently developed void expansion method (VEM) allows for an efficient generation of porous packings of spherical particles over a wide range of volume fractions. The method is based on a random placement of the structural particles under addition of much smaller "void-particles" whose radii are repeatedly increased during the void expansion. Thereby, they rearrange the structural particles until formation of a dense particle packing and introduce local heterogeneities in the structure. In this paper, microstructures with volume fractions between 0.4 and 0.6 produced by VEM are analyzed with respect to their degree of heterogeneity (DOH). In particular, the influence of the void- to structural particle number ratio, which constitutes a principal VEM-parameter, on the DOH is studied. The DOH is quantified using the pore size distribution, the Voronoi volume distribution and the density-fluctuation method in conjunction with fit functions or integral measures. This analysis has revealed that for volume fractions between 0.4 and 0.55 the void-particle number allows for a quasi-continuous adjustment of the DOH. Additionally, the DOH-range of VEM-generated microstructures with a volume fraction of 0.4 is compared to the range covered by microstructures generated using previous Brownian dynamics simulations, which represent the structure of coagulated colloidal suspensions. Both sets of microstructures cover similarly broad and overlapping DOH-ranges, which allows concluding that VEM is an efficient method to stochastically reproduce colloidal microstructures with varying DOH.

Brownian dynamics mean first passage time of two hard disks diffusing in a channel

We use Brownian dynamics simulations of two hard disks in a channel to study the mean first passage time to pass each other. The disks have a diameter sigma and are confined in a channel with hard reflective walls. The mean first passage time diverges with an exponent eta as the channel width (2R(p)) approaches that of the nonpassing limit (2sigma). There are two different theoretical predictions for the exponent eta of the two disk hopping time divergences. Transition state theory and a Fick-Jacobs type of dimensional reduction approach predict exponents of 2 and 32, respectively. Previous Brownian dynamics simulations results have a range of effective exponents and are inconclusive. Here, we present extensive Brownian dynamics simulations results which are consistent with the predictions of transition state theory. The new data show that one must be close to the nonpassing limit to observe the asymptotic scaling exponent. The scaling dependence crosses over from the bulk limit to the nonpassing limit as the width of the channel narrows, corresponding to a range of effective exponents between 0 and 2. This crossover provides an explanation of the inconclusive results reported in previous Brownian dynamics simulations.

Structure of a tethered polymer under flow using molecular dynamics and hybrid molecular-continuum simulations

We analyse the structure of a single polymer tethered to a solid surface undergoing a Couette flow. We study the problem using molecular dynamics (MD) and hybrid MD-continuum simulations, wherein the polymer and the surrounding solvent are treated via standard MD, and the solvent flow farther away from the polymer is solved by continuum fluid dynamics (CFD). The polymer represents a freely jointed chain (FJC) and is modelled by Lennard-Jones (LJ) beads interacting through the FENE potential. The solvent (modelled as a LJ fluid) and a weakly attractive wall are treated at the molecular level. At large shear rates the polymer becomes more elongated than predicted by existing theoretical scaling laws. Also, along the normal-to-wall direction the structure observed for the FJC is, surprisingly, very similar to that predicted for a semiflexible chain. Comparison with previous Brownian dynamics simulations (which exclude both solvent and wall potential) indicates that these effects are due to the polymer–solvent and polymer–wall interactions. The hybrid simulations are in perfect agreement with the MD simulations, showing no trace of finite size effects. Importantly, the extra cost required to couple the MD and CFD domains is negligible.

Ion Diffusion within Charged Porous Network as Probed by Nuclear Quadrupolar Relaxation

23Na and 7Li relaxation measurements were used over a broad range of frequencies to determine ion diffusion in aqueous dispersions of Montmorillonite and Laponite clays. In agreement with our previous Brownian dynamics simulations of ion diffusion and relaxation in such heterogeneous system, the spectral densities of these 3/2 spin nuclei exhibit a transition between two dynamical regimes characterized by a plateau and a power-law decrease. The frequency crossover is determined by the spatial extent of microdomains composed of partially oriented clay particles. This result illustrates the potentiality of nuclear quadrupolar relaxation as a sensitive probe of the spatial propagation of orientational order within heterogeneous systems limited by charged interfaces.

Extended rotational isomeric model for describing the long time dynamics of polymers

An extended rotational isomeric states (RIS) model is used in conjunction with the matrix expansion method for describing the long time dynamics of flexible polymers in solution. The extended RIS model is derived directly from the potential functions that contain hindered torsional potentials, nonbonded interactions, etc. The matrix expansion method for describing the long time dynamics contains equilibrium conformational averages which are evaluated here from the extended RIS model. The theory effectively assumes that the torsional barriers provide the dominant mechanism for the decay of orientational correlations in the polymer chains. The theory is applied to united atom alkane chain dynamics where previous Brownian dynamics simulations with the same potentials are available for an unambiguous, no-parameter test of the theory. The present computation of equilibrium averages with the extended RIS model represents a significant advancement over the prior treatments that evaluate the equilibrium averages using Brownian dynamics simulations. The comparison with the previous approach indicates the degree to which bond angle fluctuations affect the orientational time correlation functions.

Molecular Dynamics Computer Simulation of Polyisoprene Local Dynamics in Dilute Toluene Solution

Fully atomistic molecular dynamics computer simulations have been performed on a polyisoprene chain of 35 repeat units in a solution of 207 toluene molecules. Simulated orientation correlation functions of polymer C-H vectors compare favorably with 13 C NMR experiments. In particular, the ordering of the different correlation times is as expected, and their absolute values agree with experiment within a factor of 2. Also in good agreement with experiment, backbone C-H correlation functions were found to be nearly exponential after a very fast small-amplitude decay. The simulation trajectories have been analyzed to examine the changes in atomic positions and torsional coordinates which accompany conformational transitions. Adjustments in these degrees of freedom are found to be localized to 1-2 repeat units in polyisoprene, in good agreement with the results of previous Brownian dynamics simulations. Cooperative pairs of conformational transitions account for less than half of all transitions if coupling up to second neighbors is considered. About two-thirds of all transitions occur in cooperative pairs if coupling up to ninth neighbors is considered.

Application of the pivot algorithm for investigating the shapes of two- and three-dimensional lattice polymers

A pivot algorithm is used to numerically investigate the shape properties of linear polymers, with and without excluded volume, in two and three dimensions. The high computational efficiency of the pivot algorithm has allowed us to obtain data which is four to eight times more accurate than our previous Brownian dynamics simulations, while employing considerably less computational resources. The accurate data for long polymer chains highlight the inadequacy of the d expansion of polymer shapes to first order only.