Self-Diffusion in Electrostatically Stabilized Colloidal Suspensions Using Brownian Dynamics

Abstract

Brownian dynamics is applied to suspended colloidal particles interacting through a screened Coulombic pair potential in the dilute region where the hydrodynamics is approximated by Stokes drag. Calculated properties include the osmotic pressure, the radial distribution function, and the self-diffusion coefficient. Verification is obtained by comparing the results to independently evaluated properties. Self-diffusion coefficicents are compared to approximate theories in the literature. The self-diffusion coefficient is observed to depend strongly on the local structure but only slightly on the longer range structure.     

Brownian Dynamics Simulations of Electro-Rheological Fluids,II

Electro-rheological fluids are technologically relevant colloidal dispersions that on application of an applied electric field manifest a yield stress and dramatic increase in viscosity. To assist optimisation of these fluids we have performed molecular simulations to understand the basic mechanisms operating in these fluids.

In this work a dispersion of field-aligned dipoles is simulated in shear flow by non-equilibrium Brownian dynamics. In agreement with experiment, a plot of the simultated relative, η _r , against a dimensionless characteristic ER parameter, the Mason Number, Mn, exhibits a plateau region (at low electric fields and/or high shear rates) prior to a steep increase in viscoisty for Mn smaller. Although, the simulations exhibit only an approximate data collapse according to the Mn. Following on from the first paper in this series we relate the origins of the ER effect in more detail to the temporal structural changes that take place in the fluid. We find for example, that the fluids reorganise microscopically into layers of strings of particles in the shearing plane at low Mn, a structure which is destroyed on entry onto the plateau in η _r at higher Mn. We suggest how the model could be made more realistic in future studies.     

Brownian Dynamics Computer Simulations of Quenched Lennard-Jones-like Fluids: I Morphology and Local Structural Evolution

Abstract

The structural characteristics during phase separation of a model colloidal system were investigated using Brownian dynamics simulation. The structures that formed were analysed using the radial distribution function and structure factor in separate time periods after the quench. The data were interpreted in terms of scale-invariancy and density inhomogeneities. The systems, which consisted of a gas-like phase and dense liquid or solid-like regions, developed with a highly interconnected morphology during the simulations. The aggregate morphology was sensitive to the range of the attractive part of the potential and the position in the phase diagram after the quench. The long-range 12:6 potential induced compact structures with thick filaments, whereas the systems generated using the shorter-ranged 24:12 and 36:18 potentials persisted in a more diffuse network and also evolved more slowly with time. The fractal dimensions were quite high, typically close to 3. The 24:12 and 36:18 potential systems developed regions of local crystalline order which formed contemporaneously with the more global morphological changes. In contrast, at low temperatures the particles of the longer-range 12:6 potential became trapped in glass-like states during the course of the morphological changes in the system. The value of the characteristic lengthscale with time exponent, α, was found to be dependent on the temperature, density and interaction potential and therefore cannot be described as ‘universal’.     

Configurational Temperature for Brownian Dynamics

Abstract

Expressions for the configurational temperature are evaluated in Brownian dynamics simulations of a Lennard-Jones fluid and compared with the input temperature which is used to generate the random displacements. It is found that the two temperatures agree in the limit of large numbers of particles, and even for moderate system sizes the configurational temperature is a useful check on the correctness of the simulation algorithm. Investigation of the autocorrelation functions shows that for Lennard-Jones and power-law fluids, the correlation time of the configurational temperature is shorter than other typical thermodynamic quantities, and it generally increases with the range of the potential.     

Brownian Dynamics Simulation of DNA Gel Electrophoresis

Abstract

Brownian dynamics computer simulation technique was applied to investigate DNA dynamics in gel electrophoresis. Under a constant electric field of moderate strength, large DNA chains take stretched and contracted conformations alternatively during the migration. The conformation change is quasi-periodic under certain conditions, and its frequency is closely related to the experimentally-found suitable frequency of pulse field gel electrophoresis.     

Proteins as micro viscosimeters: Brownian motion revisited

Translational and rotational diffusion coefficients of proteins in solution strongly deviate from the Stokes–Einstein laws when the ambient viscosity is induced by macromolecular co-solutes rather than by a solvent of negligible size as was assumed by A. Einstein one century ago for deriving the laws of Brownian motion and diffusion. Rotational and translational motions experience different micro viscosities and both become a function of the size ratio of protein and macromolecular co-solute. Possible consequences upon fluorescence spectroscopy observations of diffusing proteins within living cells are discussed.     

Self-assembly of two-patch particles in solution: a Brownian dynamics simulation study

We study the self-assembly behaviour of two-patch particles with D_∞h symmetry by using Brownian dynamics simulations. The self-assembly process of two-patch particles with diverse patch coverage in two selective solvent conditions is investigated. The patchy particles in a solvent that is bad for patches but good for matrix form linear thread-like structures with low patch coverage, whereas they form 3D network structures with relatively high patch coverage on surface. For patchy particles in a solvent which is good for patches but bad for body, monolayer structures are obtained at high patch coverage, and some cluster structures emerge when surface patch coverage is low.     

Interpretation of NMR relaxation properties of Pin1, a two-domain protein, based on Brownian dynamic simulations

Many important proteins contain multiple domains connected by flexible linkers. Inter-domain motion is suggested to play a key role in many processes involving molecular recognition. Heteronuclear NMR relaxation is sensitive to motions in the relevant time scales and could provide valuable information on the dynamics of multi-domain proteins. However, the standard analysis based on the separation of global tumbling and fast local motions is no longer valid for multi-domain proteins undergoing internal motions involving complete domains and that take place on the same time scale than the overall motion.The complexity of the motions experienced even for the simplest two-domain proteins are difficult to capture with simple extensions of the classical Lipari-Szabo approach. Hydrodynamic effects are expected to dominate the motion of the individual globular domains, as well as that of the complete protein. Using Pin1 as a test case, we have simulated its motion at the microsecond time scale, at a reasonable computational expense, using Brownian Dynamic simulations on simplified models. The resulting trajectories provide insight on the interplay between global and inter-domain motion and can be analyzed using the recently published method of isotropic Reorientational Mode Dynamics which offer a way of calculating their contribution to heteronuclear relaxation rates. The analysis of trajectories computed with Pin1 models of different flexibility provides a general framework to understand the dynamics of multi-domain proteins and explains some of the observed features in the relaxation rate profile of free Pin1.     

Brownian dynamics simulations of intramolecular energy transfer

A novel technique for modelling intramolecular energy transfer is presented. Brownian dynamics calculations are used to compute the trajectories of donor and acceptor species, and the instantaneous orientation factor is calculated during each temporal iteration. In this work, several model systems are considered. Trajectories were computed for energy transfer between a flexible donor and a rigidly fixed acceptor. We have considered configurations where the donor is, (1) tethered to a fixed point in space, but free to diffuse rotationally, and (2) constrained to wobble in a cone. The luminescence decay of the donor is ‘measured’, and a non-single-exponential decay is observed for configurations of efficient energy transfer. Luminescence anisotropy measurements of constrained and unconstrained donors reflect the contribution of both energy transfer and rotational diffusion to the shape of the anisotropy decay curve.     

Multiple Time Step Brownian Dynamics for Long Time Simulation of Biomolecules

We report a multiple time step algorithm applied to an atomistic Brownian dynamics simulation for simulating the long time scale dynamics of biomolecules. The algorithm was based on the original multiple time step method; a short time step was used to keep faster motions in local equilibrium. When applied to a 28-mer # # ! folded peptide, the simulation gave stable trajectories and the computation time was reduced by a factor of 160 compared to a conventional molecular dynamics simulation using explicit water molecules. We applied it for the folding simulation of a 13-mer ! -helical peptide, giving a successful folding simulation. These results indicate that the Brownian dynamics with the multiple time step algorithm is useful for studies of biomolecular motions by long time simulation.     

Brownian dynamics simulation of the unsaturated lipidic molecules oleic and docosahexaenoic acid confined in a cellular membrane

A Brownian dynamics (BD) simulation of two unsaturated molecules, oleic and docosahexaenoic acid, in an environment that reproduces a cellular membrane, is presented. The results of the simulations, performed using mean-field potentials, were calibrated with experimental results obtained for oleic acid in a cellular membrane. The agreement between simulation and experimental results is excellent which validates subsequent simulation outcome for docosahexaenoic acid. This molecule is a major component of several cellular membranes thought to be involved in specific biological functions that require conformational changes of membrane components. The results for docosahexaenoic acid indicate that it is minimally influenced by temperature changes and that it presents great conformational variability.     

The histone octamer influences the wrapping direction of DNA on it: Brownian dynamics simulation of the nucleosome chirality

In eukaryote nucleosome, DNA wraps around a histone octamer in a left-handed way. We study the process of chirality formation of nucleosome with Brownian dynamics simulation. We model the histone octamer with a quantitatively adjustable chirality: left-handed, right-handed or non-chiral, and simulate the dynamical wrapping process of a DNA molecule on it. We find that the chirality of a nucleosome formed is strongly dependent on that of the histone octamer, and different chiralities of the histone octamer induce its different rotation directions in the wrapping process of DNA. In addition, a very weak chirality of the histone octamer is quite enough for sustaining the correct chirality of the nucleosome formed. We also show that the chirality of a nucleosome may be broken at elevated temperature.     

A First-Passage Time Approach to Diffusion in Liquids and Superionic Conductors

Abstract

As a new tool to investigate single-particle motion in condensed matter, a first-passage time (FPT) approach to diffusion is developed and applied to the molecular dynamics simulations of simple liquids and superionic conductor CaF₂. It is shown that a continuous diffusion model reproduces the observed FPT distribution quite well for both liquids and CaF₂, which enables us to evaluate diffusion constants with good accuracy by our method. On a length scale as small as a lattice constant, however, the effect of hopping appears in the FPT distribution of F^? ions, which can not be described by a continuous diffusion model. A simple hopping diffusion model is proposed and examined from the FPT viewpoint.     

Effect of Cation Concentration on Molecular Dynamics Simulations of UDP-Glucose

Abstract

Glycosyl esters of nucleoside di or mono-phosphates, generally referred to as “sugar nucleotides”, serve as a sugar donors during the biosynthesis of oligo- and polysaccharides; they are therefore of a primary importance in carbohydrate metabolism in the living world. Molecular dynamics simulations were used to explore the conformational flexibility of one nucleotide sugar, UDP-glucose (UDP-Glc). The AMBER program package was used with some new parameters especially developed for nucleotide sugars. Several simulations on this molecule in aqueous solution, each of 2 ns duration, were carried out for increasing concentrations of monovalent K⁺ and divalent Mg²⁺ ions. For the monovalent ion, it is revealed that its presence and concentration is crucial for the conformational behavior, resulting in the stabilization of the extended conformation. The preferred location of K⁺ is in close proximity to the negatively charged phosphate oxygens, but the ion moves freely and can occupy other sites. Since the size of this cation is close that of the water molecules, the hydration scheme is not perturbed. Completely different results are obtained when the divalent Mg²⁺ cation is introduced in the simulation. A very strong interaction is established between the phosphate group and the cation; as a result the UDP-Glc molecule is locked in a rigid extended geometry. The analyses of the trajectories provide new insight on the role of the metal ion in the catalytic mechanism of glycosyltransferases.     

Brownian dynamics study of flux ratios in sodium channels

Measurements of unidirectional fluxes in ion channels provide one of the experimental methods for studying the steps involved in ion permeation in biological pores. Conventionally, the number of ions in the pore is inferred by fitting the ratio of inward and outward currents to an exponential function with an adjustable parameter known as the flux ratio exponent. Here we investigate the relationship between the number of ions in the pore and the flux ratio exponent in a model sodium channel under a range of conditions. Brownian dynamics simulations enable us to count the precise number of ions in the channel and at the same time measure the currents flowing across the pore in both directions. We show here that the values of the flux ratio exponent n′ ranges between 1 and 3 and is highly dependent on the ionic concentrations in which measurements are made. This is a consequence of the fact that both inward and outward currents are susceptible to saturation with increasing concentration. These results indicate that measurements of the flux ratio exponent cannot be directly related to the number of ions in the pore and that interpretation of such experimental measurements requires careful consideration of the conditions in which the study is made.     

Molecular Dynamics Simulations of a Nucleosome and Free DNA

Abstract

All atom molecular dynamics simulations (10ns) of a nucleosome and of its 146 basepairs of DNA free in solution have been conducted. DNA helical parameters (Roll, Tilt, Twist, Shift, Slide, Rise) were extracted from each trajectory to compare the conformation, effective force constants, persistence length measures, and fluctuations of nucleosomal DNA to free DNA. The conformation of DNA in the nucleosome, as determined by helical parameters, is found to be largely within the range of thermally accessible values obtained for free DNA. DNA is found to be less flexible on the nucleosome than when free in solution, however such measures are length scale dependent. A method for disassembling and reconstructing the conformation and dynamics of the nucleosome using Fourier analysis is presented. Long length variations in the conformation of nucleosomal DNA are identified other than those associated with helix repeat. These variations are required to create a proposed tetrasome conformation or to qualitatively reconstruct the 1.75 turns of the nucleosome's superhelix. Reconstruction of free DNA using selected long wavelength variations in conformation can produce either a left-handed or a right-handed superhelix. The long wavelength variations suggest 146 basepairs is a natural length of DNA to wrap around the histone core.     

Estimation of Solvent Diffusion Coefficients Using Molecular Dynamics Simulations

Abstract

Molecular dynamics simulations have been used to investigate diffusion in two commonly used industrial solvents, toluene and tetrahydrofuran. Several different models for the solvents are compared (flexible vs. rigid, all-atom vs. united atom), and it is found that united atom and all-atom models of the solvents produce very different diffusion coefficients at the experimental density. This disagreement can be explained by the pressure dependence of the diffusion coefficient, which is found to vary in accord with the Chapman-Enskog result for hard spheres. It is recommended that force fields be parametrized carefully to produce reasonable pressures at the experimental densities, or that simulations be carried out at constant pressure, if they are to be used for the purposes of calculating transport coefficients.     

On the Bond-angle Distributions in Liquids and Liquid Solutions

Bond-angle distributions are used for the study of local orientational order in liquid systems. Bond-angles between a central particle and particles in both the first and second coordination shells are considered. Molecular dynamics calculations are carried out for determining the bond-angle distributions in a Lennard Jones liquid. The resulting distributions are compared with those obtained from stochastic simulations of a subset of atoms (solute) of the same system (solution). Although the radial distribution functions from the two simulations are in agreement, the bond-angle distributions show noticeable difference. Computer simulation findings are compared with results obtained by using both the superposition and convolution approximations. The reliability of the generalized Langevin dynamics simulation method is discussed.