Critical test of bead–spring model to resolve the scaling laws of polymer melts: a molecular dynamics study

Abstract

To examine the intrinsic nature of the bead–spring Kremer–Grest (KG) model, long-time molecular dynamics simulations are performed. Certain scaling laws for representative polymer properties are compared with theoretical predictions. The results for static properties satisfy the expected static Gaussian nature, irrespective of the chain length. In contrast, the results for the dynamic properties of short chains show a clear discrepancy from theoretical predictions that assume ideal chain motion. This is clear evidence that the Gaussian nature of the dynamics of short chains is not necessarily established for the actual KG model, despite it being designed to have Gaussian characteristics by virtue of its stochastic equations of motion. This intrinsic nature of the KG model should be considered carefully when using this model for applications that involve relatively short chains.     

Lees–Edwards boundary condition for simulation of polymer suspension with dissipative particle dynamics method

The Lees–Edwards boundary condition (LEbc) is widely used in particle-based simulation for producing shear flow. Application of traditional LEbc in dissipative particle dynamics (DPD) method may encounter certain problems, e.g. it will destroy the momentum conservation law at the near boundary region, and the coordinate system gives an incorrect end-to-end vector for polymer beads. Special treatments of the implementation of LEbc in DPD method are introduced in this paper. A single side ghost layer is used to keep the momentum conservation, and the global coordinate system is employed to obtain a correct calculation of the spring force between polymer beads. The simulation results give a good prediction of velocity profile and system temperature, and the elastic dumbbell model for current method can well represent the Oldroyd-B fluid.     

Solution structure and dynamics of cartilage aggrecan

We studied the structure and dynamics of porcine laryngeal aggrecan in solution using a range of noninvasive techniques: dynamic light scattering (DLS), small-angle neutron scattering (SANS), video particle tracking (VPT) microrheology, and diffusing wave spectroscopy (DWS). The data are analyzed within the framework of a combined static and dynamic scaling model, and evidence is found for reptation of the comb backbones with unentangled side-chain dynamics. Small-angle neutron scattering indicated standard polyelectrolyte scaling of the mesh size (xi) with concentration (c) in semidilute solutions for the whole aggrecan aggregate, xi = Ac(-0.47+/-0.04), with the prefactor (A) implying there is on average 60 nm between the aggrecan subunits along the backbone. VPT demonstrated large exponents for the power law dependence of the intrinsic viscosity (eta) on the polymer concentration in the semidilute concentration regime, eta approximately c(alpha); with alpha equal to 2.04 +/- 0.06 and 1.95 +/- 0.08 for the assembled and disassembled aggrecan aggregates, respectively. DWS at high frequencies (10(4)-10(5) Hz) gave evidence for internal Rouse modes of the aggrecan monomers, independent of the degree of self-assembly of the molecules.     

Simulation of Polymer Solutions by Dissipative Particle Dynamics

Abstract

Dissipative Particle Dynamics (DPD) is employed to model the dynamics and rheology of polymer solutions, and suspensions of spherical particles with adsorbed polymers. Static and dynamic scaling relationships for the variation of radius of gyration and relaxation time with polymer chain length are reviewed, demonstrating that the DPD polymer solution model correctly represents the effects of hydrodynamic interaction and excluded volume. Rheological simulations for both polymer solutions and polymer-sphere suspensions predict Newtonian viscosities at low shear rate followed by shear-thinning behavior as a reduced shear rate of unity is approached. Both the Newtonian viscosity and the extent of shear-thinning are greatly enhanced in the case of good solvents, compared to the viscosity curves for polymers and polymer-spheres structures dissolved in theta solvents and poor solvents.     

Structural analysis of telechelic polymer solution using dissipative particle dynamics simulations

A telechelic polymer is an amphiphilic polymer that can form micellar structures when dissolved in water. A telechelic polymer solution shows viscoelastic behaviour owing to the formation of characteristic networks, i.e. loops, bridges and dangling chains. For industrial purposes, telechelic polymers have many applications as thickening agents, such as in paints and cosmetics. Thus, it is desirable to predict and control the rheological properties of telechelic polymers. However, detailed studies at the molecular level have not yet been performed. In this study, I use the dissipative particle dynamics (DPD) method to investigate the relationship between the characteristic structural properties and the molecular structure in telechelic polymer solutions. I show that the morphology of telechelic polymer solutions depends on the concentration and chain length, the distribution of the end-to-end distance, the mean square end-to-end distance, the mean square radius of gyration and the time-averaged mean square displacement. Although an effect of entanglement is important for properties of polymer melts, the polymer chain composed of DPD particles cannot reproduce it. Therefore, I compare telechelic polymer solutions with and without the segmental repulsive potential (SRP), which can simulate the effect of entanglement in DPD simulations. The results indicate that it is necessary to include the SRP in DPD simulations to correctly analyse the behaviour of telechelic polymer solutions.     

Simulation of the conformation and dynamics of a double-helical model for DNA

We propose a partially flexible, double-helical model for describing the conformational and dynamic properties of DNA. In this model, each nucleotide is represented by one element (bead), and the known geometrical features of the double helix are incorporated in the equilibrium conformation. Each bead is connected to a few neighbor beads in both strands by means of stiff springs that maintain the connectivity but still allow for some extent of flexibility and internal motion. We have used Brownian dynamics simulation to sample the conformational space and monitor the overall and internal dynamics of short DNA pieces, with up to 20 basepairs. From Brownian trajectories, we calculate the dimensions of the helix and estimate its persistence length. We obtain translational diffusion coefficient and various rotational relaxation times, including both overall rotation and internal motion. Although we have not carried out a detailed parameterization of the model, the calculated properties agree rather well with experimental data available for those oligomers.     

Hydrodynamic properties of rigid particles: comparison of different modeling and computational procedures.

The hydrodynamic properties of rigid particles are calculated from models composed of spherical elements (beads) using theories developed by Kirkwood, Bloomfield, and their coworkers. Bead models have usually been built in such a way that the beads fill the volume occupied by the particles. Sometimes the beads are few and of varying sizes (bead models in the strict sense), and other times there are many small beads (filling models). Because hydrodynamic friction takes place at the molecular surface, another possibility is to use shell models, as originally proposed by Bloomfield. In this work, we have developed procedures to build models of the various kinds, and we describe the theory and methods for calculating their hydrodynamic properties, including approximate methods that may be needed to treat models with a very large number of elements. By combining the various possibilities of model building and hydrodynamic calculation, several strategies can be designed. We have made a quantitative comparison of the performance of the various strategies by applying them to some test cases, for which the properties are known a priori. We provide guidelines and computational tools for bead modeling.     

NIST/ISAC standardization study: Variability in assignment of intensity values to fluorescence standard beads and in cross calibration of standard beads to hard dyed beads

Results from a standardization study cosponsored by the International Society for Advancement of Cytometry (ISAC) and the US National Institute of Standards and Technology (NIST) are reported. The study evaluated the variability of assigning intensity values to fluorophore standard beads by bead manufacturers and the variability of cross calibrating the standard beads to stained polymer beads (hard-dyed beads) using different flow cytometers. Hard dyed beads are generally not spectrally matched to the fluorophores used to stain cells, and spectral response varies among flow cytometers. Thus if hard dyed beads are used as fluorescence calibrators, one expects calibration for specific fluorophores (e.g., FITC or PE) to vary among different instruments. Using standard beads surface-stained with specific fluorophores (FITC, PE, APC, and Pacific Blue?), the study compared the measured intensity of fluorophore standard beads to that of hard dyed beads through cross calibration on 133 different flow cytometers. Using robust CV as a measure of variability, the variation of cross calibrated values was typically 20% or more for a particular hard dyed bead in a specific detection channel. The variation across different instrument models was often greater than the variation within a particular instrument model. As a separate part of the study, NIST and four bead manufacturers used a NIST supplied protocol and calibrated fluorophore solution standards to assign intensity values to the fluorophore beads. Values assigned to the reference beads by different groups varied by orders of magnitude in most cases, reflecting differences in instrumentation used to perform the calibration. The study concluded that the use of any spectrally unmatched hard dyed bead as a general fluorescence calibrator must be verified and characterized for every particular instrument model. Close interaction between bead manufacturers and NIST is recommended to have reliable and uniformly assigned fluorescence standard beads. ? 2012 International Society for Advancement of Cytometry.     

Theoretical study on the stability of insulin within poly-isobutyl cyanoacrylate (PIBCA) nanocapsule

To study the physical stability of insulin in drug delivery particles, we developed a coarse-grained (CG) model for insulin based on dissipative particle dynamics (DPD). Three insulin modelling schemes were considered: each amino acid as a bead (IM1), each amino acid being separated into one to three beads (IM2), and adding secondary structural information of insulin to IM2 (IM3). The best possible bead-bead interaction parameters were obtained from Hildebrand and Hansen solubility parameters by performing the constant-temperature DPD simulation with insulin models in 20% acetic acid solution. IM3 showed good results in terms of RMSF, RMSD and A1B30 distance compared to those of all-atom models from the literature. Then, the IM3 model was considered in an oil-filled poly (isobutyl cyanoacrylate) (PIBCA) nanocapsule. Two crucial factors were found that mainly influence the stability of insulin in oil: the PIBCA shell thickness and the amount of ethanol in the oil droplet. An appropriate PIBCA shell thickness is necessary to block the interaction between insulin and water outside, and ethanol could stabilise insulin with its good affinity for both insulin and oil.     

A bead and spring model for the stiffness of DNA.

The chain stiffness of linear native DNA is represented by a generalized bead and spring model recently proposed. It incorporates molecular rigidity by means of springs between beads, which are second neighbors along the contour of the chain. These springs are equivalent to elastic forces having longitudinal and transversal contributions. The model is compared with existing experimental data of sedimentation and low-angle light scattering to obtain the statistical parameters of DNA. The value of the statistical length obtained with this model is 1300 Å. The same value is obtained with the wormlike chain. Throughout this analysis, excluded volume is left out as a simplifying assumption.     

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.     

Molecular Dynamics Simulation of Linear Polymers in a Solvent

This paper reports a series of simulations of a single linear polymer chain in solution. Both the monomer units and the solvent particles are represented by “beads” which interact via a purely repulsive shifted Lennard-Jones potential; the chains themselves are constructed by linking beads with relatively stiff elastic bonds. The chain lenghts range from 8 to 48 beads, and the total system size is between 1000 and 14000 beads. The static and dynamic properties of the polymer chains obtained from long simulations of these systems (over 10⁶ timesteps) are discussed, and the size and density dependence of the chain behavior examined.     

Monte Carlo simulations of structure and entanglements in polymer melts

Atomistic models of short chain branched (SCB) polyethylene melts have been equilibrated at 450 K using a connectivity altering Monte Carlo method. Quantities related to the chain dimensions and entanglements have been determined. The simulated tube diameters, 〈a_pp〉, of SCB melts are found to scale with the backbone weight fraction, ?, as 〈a_pp〉～?^? 0.46, close to the scaling predicted by the binary contact model, 〈a_pp〉～?^? 0.5. Similar relationships are observed experimentally for polymer solutions, and reproduced by the present methods.     

In vivo production of scFv-displaying biopolymer beads using a self-assembly-promoting fusion partner

Recombinant production and, in particular, immobilization of antibody fragments onto carrier materials are of high interest with regard to diagnostic and therapeutic applications. In this study, the recombinant production of scFv-displaying biopolymer beads intracellularly in Escherichia coli was investigated. An anti-beta-galactosidase scFv (single chain variable fragment of an antibody) was C-terminally tagged with the polymer-synthesizing enzyme PhaC from Cupriavidus necator by generating the respective hybrid gene. The functionality of the anti-beta-galactosidase scFv-PhaC fusion protein was assessed by producing the respective soluble fusion protein in an Escherichia coli AMEF mutant strain. AMEF (antibody-mediated enzyme formation) strains contain an inactive mutant beta-galactosidase, which can be activated by binding of an anti-beta-galactosidase antibody. In vivo activation of AMEF beta-galactosidase indicated that the scFv is functional with the C-terminal fusion partner PhaC. It was further demonstrated that polymer biosynthesis and bead formation were mediated by the scFv-PhaC fusion protein in the cytoplasm of recombinant E. coli when the polymer precursor was metabolically provided. This suggested that the C-terminal fusion partner PhaC acts as a functional insolubility partner, providing a natural cross-link to the bead and leading to in vivo immobilization of the scFv. Overproduction of the fusion protein at the polymer bead surface was confirmed by SDS-PAGE and MALDI-TOF/MS analysis of purified beads. Antigen binding functionality and specificity of the beads was assessed by analyzing the binding of beta-galactosidase to scFv-displaying beads and subsequently eluting the bound protein at pH 2.7. A strong enrichment of beta-galactosidase suggested the functional display of scFv at the bead surface as well as the applicability of these beads for antigen purification. Binding of beta-galactosidase to the scFv-displaying beads was quantitatively analyzed by enzyme-linked assays measuring beta-galactosidase activity. These indicated that the anti-beta-galactosidase scFv-displaying beads bound a maximum of 38 ng of beta-galactosidase per 1 microg of bead protein, showing an apparent equilibrium dissociation constant ( KD) of 12 x 10 (-7) M. This study clearly demonstrated that anti-beta-galactosidase scFv-displaying polymer beads can be produced in engineered E. coli in a one-step process by using PhaC as a self-assembly-promoting fusion partner.     

Physical Modeling of Chromosome Segregation in Escherichia coli Reveals Impact of Force and DNA Relaxation

The physical mechanism by which Escherichia coli segregates copies of its chromosome for partitioning into daughter cells is unknown, partly due to the difficulty in interpreting the complex dynamic behavior during segregation. Analysis of previous chromosome segregation measurements in E. coli demonstrates that the origin of replication exhibits processive motion with a mean displacement that scales as t^0.32. In this work, we develop a model for segregation of chromosomal DNA as a Rouse polymer in a viscoelastic medium with a force applied to a single monomer. Our model demonstrates that the observed power-law scaling of the mean displacement and the behavior of the velocity autocorrelation function is captured by accounting for the relaxation of the polymer chain and the viscoelastic environment. We show that the ratio of the mean displacement to the variance of the displacement during segregation events is a critical metric that eliminates the compounding effects of polymer and medium dynamics and provides the segregation force. We calculate the force of oriC segregation in E. coli to be ∼0.49 pN.     

Combining particle tracking microrheology and viscometry for the study of DNA aqueous solutions

We use video particle tracking microrheology (VPTMR) in order to investigate the viscoelasticity of salmon DNA and correlate it to its steady-flow shear-thinning viscosity. Aqueous solutions of DNA are tested in a wide concentration range from the dilute to the semidilute unentangled concentration regime. The observed mean squared displacement shows power-law scaling with lag-time which is equivalent to power-law behavior of the complex modulus as a function of frequency that is, |G^*(ω)| = S ∙ ω ^α . The relaxation exponent α changes abruptly with concentration in the semidilute regime from about 1 to about 0.5 which is the exponent predicted by the Rouse model. The quasi-property S follows the scaling of viscosity for uncharged polymers near θ-conditions in the semidilute regime that is, with ν_eff = 0.50 − 0.51 . The shear-thinning exponent observed by viscometry increases gradually towards the value of 0.5 which has been predicted for Rouse chains under flow. Our findings are in agreement with recent studies of DNA solutions where DNA is treated as a model polymer and addresses the low-molar mass regime of DNA viscoelasticity. This work demonstrates that the combination of passive particle tracking with viscometry can provide a complete picture on the viscoelasticity of DNA-based biopolymer materials.     

Flexible histone tails in a new mesoscopic oligonucleosome model

We describe a new mesoscopic model of oligonucleosomes that incorporates flexible histone tails. The nucleosome cores are modeled using the discrete surface-charge optimization model, which treats the nucleosome as an electrostatic surface represented by hundreds of point charges; the linker DNAs are treated using a discrete elastic chain model; and the histone tails are modeled using a bead/chain hydrodynamic approach as chains of connected beads where each bead represents five protein residues. Appropriate charges and force fields are assigned to each histone chain so as to reproduce the electrostatic potential, structure, and dynamics of the corresponding atomistic histone tails at different salt conditions. The dynamics of resulting oligonucleosomes at different sizes and varying salt concentrations are simulated by Brownian dynamics with complete hydrodynamic interactions. The analyses demonstrate that the new mesoscopic model reproduces experimental results better than its predecessors, which modeled histone tails as rigid entities. In particular, our model with flexible histone tails: correctly accounts for salt-dependent conformational changes in the histone tails; yields the experimentally obtained values of histone-tail mediated core/core attraction energies; and considers the partial shielding of electrostatic repulsion between DNA linkers as a result of the spatial distribution of histone tails. These effects are crucial for regulating chromatin structure but are absent or improperly treated in models with rigid histone tails. The development of this model of oligonucleosomes thus opens new avenues for studying the role of histone tails and their variants in mediating gene expression through modulation of chromatin structure.     

Dissipative particle dynamics simulation of a gold nanoparticle system

Dissipative particle dynamics (DPD) was carried out to study systems containing gold atoms, organic ether (oligohydroquinonyl ether terminated with a thiol group) and organic solvents. The components in the simulated system are very different in size and chemical nature. Our simulation showed that the reproduction of the macroscopic experimental phase separation, properly dividing the polymeric molecule into beads, selecting the size of gold bead, and choosing the appropriate interaction parameters between beads are crucial. In addition, the solvent effect was the dominant factor for the formation of spherical aggregates of Au atoms and organic ether molecules. We report the interaction strengths between the solvent and gold clusters. Our work has demonstrated that DPD methods can be applied to the study of complex meso-scale systems.     

Viscometric flow for a many-body dissipative particle dynamics (MDPD) fluid with Lees–Edwards boundary condition

Viscometric properties of polymer are explored by the many-body dissipative particle dynamics (MDPD) using Lees–Edwards boundary conditions. The equation of state for the MDPD system is modified by fitting the density correction to different values of the cut-off radius. Due to the many-body interactions in MDPD, the viscosity contributed from the conservative force increases considerably with increasing repulsive coefficient, density and cut-off radius, and cannot be ignored compared to the ‘standard’ DPD case. The influence of these parameters on the MDPD viscosity is investigated, and we propose an equation to predict the viscosity in MDPD model. Additionally, the dumbbell polymer suspension model is investigated in the MDPD fluid, and the relations concerning first normal stress difference and shear rate, the relaxation time and spring constant, are consistent to theoretical works. We conclude that the MDPD model can be used to investigate the dynamics of non-Newtonian droplets.     

Tribology of polymer brush: microscale modelling and simulation

In order to examine the tribological behaviour of the polymer brush, we constructed a mesoscale particle model of a polymer brush system, based on a Brownian dynamics scheme. The polymer model consists of coarse-grained beads connected with harmonic springs. The Lennard-Jones type interaction is assumed between beads. The flow velocity is affected by the local packing fraction of beads. With this model, we executed a series of molecular dynamics simulation to investigate the mechanical responses of brush to shear flow.