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.     

Coarse-grained Modeling and Simulation of Actin Filament Behavior Based on Brownian Dynamics Method

The actin filament, which is the most abundant component of the cytoskeleton, plays important roles in fundamental cellular activities such as shape determination, cell motility, and mechanosensing. In each activity, the actin filament dynamically changes its structure by polymerization, depolymerization, and severing. These phenomena occur on the scales ranging from the dynamics of actin molecules to filament structural changes with its deformation due to the various forces, for example, by the membrane and solvent. To better understand the actin filament dynamics, it is important to focus on these scales and develop its mathematical model. Thus, the objectives of this study were to model and simulate actin filament polymerization, depolymerization, and severing based on the Brownian dynamics method. In the model, the actin monomers and the solvent were considered as globular particles and a continuum, respectively. The motion of the actin molecules was assumed to follow the Langevin equation. The polymerization, which increases the filament length, was determined by the distance between the center of the actin particle at the barbed end and actin particles in the solvent. The depolymerization, which decreases the filament length, was modeled such that the number of dissociation particles from the filament end per unit time was constant. In addition, the filament severing, in which one filament divides into two, was modeled to occur at an equal rate along the filament. Then, we simulated the actin filament dynamics using the developed model, and analyzed the filament elongation rate, its turnover, and the effects of filament severing on the polymerization and depolymerization. Results indicated that the model reproduced the linear dependence of the filament elongation on time, filament turnover process by polymerization and depolymerization, and acceleration of the polymerization and depolymerization by severing, which qualitatively agreed with those observed in experiments.     

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.     

Brownian dynamics study of the association between the 70S ribosome and elongation factor G

Protein synthesis on the ribosome involves a number of external protein factors that bind at its functional sites. One key factor is the elongation factor G (EF-G) that facilitates the translocation of transfer RNAs between their binding sites, as well as advancement of the messenger RNA by one codon. The details of the EF-G/ribosome diffusional encounter and EF-G association pathway still remain unanswered. Here, we applied Brownian dynamics methodology to study bimolecular association in the bacterial EF-G/70S ribosome system. We estimated the EF-G association rate constants at 150 and 300 mM monovalent ionic strengths and obtained reasonable agreement with kinetic experiments. We have also elucidated the details of EF-G/ribosome association paths and found that positioning of the L11 protein of the large ribosomal subunit is likely crucial for EF-G entry to its binding site.     

The Role of Molecular Dynamics Simulations for the Study of Slow Dynamics

Abstract

A two step strategy is proposed to study dynamical properties of a physical system much slower than the time scales accessible by molecular dynamics simulations. The strategy is applied to investigate the slow dynamics of supercooled liquids.     

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.     

Brownian dynamic study of an enzyme metabolon in the TCA cycle: Substrate kinetics and channeling

Malate dehydrogenase (MDH) and citrate synthase (CS) are two pacemaking enzymes involved in the tricarboxylic acid (TCA) cycle. Oxaloacetate (OAA) molecules are the intermediate substrates that are transferred from the MDH to CS to carry out sequential catalysis. It is known that, to achieve a high flux of intermediate transport and reduce the probability of substrate leaking, a MDH‐CS metabolon forms to enhance the OAA substrate channeling. In this study, we aim to understand the OAA channeling within possible MDH‐CS metabolons that have different structural orientations in their complexes. Three MDH‐CS metabolons from native bovine, wild‐type porcine, and recombinant sources, published in recent work, were selected to calculate OAA transfer efficiency by Brownian dynamics (BD) simulations and to study, through electrostatic potential calculations, a possible role of charges that drive the substrate channeling. Our results show that an electrostatic channel is formed in the metabolons of native bovine and recombinant porcine enzymes, which guides the oppositely charged OAA molecules passing through the channel and enhances the transfer efficiency. However, the channeling probability in a suggested wild‐type porcine metabolon conformation is reduced due to an extended diffusion length between the MDH and CS active sites, implying that the corresponding arrangements of MDH and CS result in the decrease of electrostatic steering between substrates and protein surface and then reduce the substrate transfer efficiency from one active site to another.     

Brownian dynamics simulation of helix-capping motifs

Helix-capping motifs are believed to play an important role in stabilizing alpha-helices and defining helix start and stop signals. We performed microsecond scale Brownian dynamics simulations to study ten XAAD sequences, with X = (A,E,I,L,N,Q,S,T,V,Y), to examine their propensity to form helix capping motifs and correlate these results with those obtained from analyzing a structural database of proteins. For the widely studied capping box motif S**D, where the asterisk can be any amino acid residue, the simulations suggested that one of the two hydrogen bonds proposed earlier as a stabilizing factor might not be as important. On the other hand, side-chain interactions between the capping residue and the third residue downstream on the polypeptide chain might also play a role in stabilizing this motif. These results are consistent with explicit-solvent molecular dynamics simulations of two capping box motifs found in the proteins BPTI and alpha-dendrotoxin. Principal component analysis of the SAAD trajectory showed that the first three principal components, after those corresponding to translational-rotational motion were removed, accounted for more than half of the conformational fluctuations. The first component separated the conformational space into two parts with the all-helical conformation and the capping box motif lying largely in one part. The second component, on the other hand, could be used to describe conformational transitions between the all-helical form and the capping box motif.     

Perceived and Physiological Indicators of Relaxation: As Different as Mozart and Alice in Chains

The effects of listening to different types of music on perceived and physiological indicators of relaxation were evaluated. Fifty-six undergraduate students, 24 males and 32 females, mean age of 21, were randomly assigned to listen to classical, hard rock, self-selected relaxing music, or no music. Participants' relaxation level, skin temperature, muscle tension and heart rate were evaluated before and after exposure to a music condition. Analyses of variance using baseline measures as covariates indicated that skin temperature decreased for all conditions (p = 0.001) and the classical, self-selected relaxing music and no music groups reported significant increases in feelings of relaxation (p = 0.004). These results partially support the hypothesis that classical and self-selected relaxing music can increase perceptions of relaxation to a greater degree than listening to hard rock music. However, no differences were found between different types of music on physiological indicators of arousal. Implications for using music to reduce stress were discussed.     

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.