Coarse-grained Bead-spring Model Research Articles

Predicting scale-dependent chromatin polymer properties from systematic coarse-graining

Simulating chromatin is crucial for predicting genome organization and dynamics. Although coarse-grained bead-spring polymer models are commonly used to describe chromatin, the relevant bead dimensions, elastic properties, and the nature of inter-bead potentials are unknown. Using nucleosome-resolution contact probability (Micro-C) data, we systematically coarse-grain chromatin and predict quantities essential for polymer representation of chromatin. We compute size distributions of chromatin beads for different coarse-graining scales, quantify fluctuations and distributions of bond lengths between neighboring regions, and derive effective spring constant values. Unlike the prevalent notion, our findings argue that coarse-grained chromatin beads must be considered as soft particles that can overlap, and we derive an effective inter-bead soft potential and quantify an overlap parameter. We also compute angle distributions giving insights into intrinsic folding and local bendability of chromatin. While the nucleosome-linker DNA bond angle naturally emerges from our work, we show two populations of local structural states. The bead sizes, bond lengths, and bond angles show different mean behavior at Topologically Associating Domain (TAD) boundaries and TAD interiors. We integrate our findings into a coarse-grained polymer model and provide quantitative estimates of all model parameters, which can serve as a foundational basis for all future coarse-grained chromatin simulations.

Electrokinetic separation of cfDNA in insulator-based dielectrophoresis systems: a linear model of cfDNA and investigation of effective parameters

In this study, a comprehensive numerical simulation was done to investigate the electrokinetic translocation of cfDNA molecule as well as the possibility of its detection and separation in insulator based dielectrophoresis (iDEP) systems. Modeling was done for the first time by solving the Poisson equation for the electrical potential, Naiver–Stokes (NS) equation for the fluid flow and energy equation for the heat transfer in the system and considering a coarse-grained bead-spring model to describe the conformational and geometrical changes of cfDNA molecule. The effect of the geometrical parameters of the system, the initial orientation of the molecule, electrical conductivity of the solution and zeta potential of the wall was investigated on the translocation and the minimum voltage required for cfDNA trapping. When the ratio of the inlet height to the constriction zone height is large enough, cfDNA molecules cannot pass through the nanopore and trap in the constriction zone. Also, it was found that the electrical conductivity of the solution is a limiting parameter to directly isolate cfDNA from pure plasma without dilution due to significant increase in the temperature of the system. Our results demonstrate the enormous potential of iDEP systems for rapid detection of cfDNA from diluted plasma under special electrical potential and geometrical parameters of the iDEP systems.

Coarse-grained molecular dynamics study of elasticity of block copolymers with cubic symmetrical morphology

In the present study, we investigated the elasticity of block copolymers by coarse-grained molecular dynamics simulation. We focused on two typical cubic symmetry morphologies that mimic thermoplastic elastomers and soft plastics—i.e., body-centered cubic (BCC) and double gyroid (DG). The effects of morphology, bridge fraction, and deformation direction on the stress–strain curves were studied. The deformation of glassy networks with the DG morphology resulted in higher initial moduli than those with the BCC morphology. With the BCC morphology, the rubber elasticity was linearly dependent on the bridge fraction, whereas with the DG morphology the dependency was weak because the loop configuration in the DG networks also contributed to rubber elasticity. In both the BCC and DG morphologies, the effect of deformation direction was insignificant. This was inconsistent with the experimental results. The discrepancy demonstrates the peculiar nature of the coarse-grained bead-spring model in the glassy state.

Overlap Concentration in Salt-Free Polyelectrolyte Solutions

For strongly charged polyelectrolytes in salt-free solutions, we use molecular dynamics simulations of a coarse-grained bead-spring model to calculate overlap concentrations c* and chain structure ...

Conformational Properties of End-Grafted Bottlebrush Polymers

Scaling analysis combined with free-energy calculations and molecular dynamics simulations of a coarse-grained bead-spring model have been used to study the structural properties of planar brushes ...

Comparison of neutral and charged poly electrolyte bottlebrush polymers in dilute salt-free conditions

ABSTRACTWe investigate the structure of neutral and charged bottlebrush polymers in salt-free solutions at different polymer concentrations. In particular, we use molecular dynamics simulations by utilizing a coarse-grained bead-spring model that includes an explicit solvent and complementary experiments made by small angle neutron scattering (SANS). We find that the charged groups along the side chains exert significant repulsive forces, resulting in polymer swelling and backbone stretching. In addition to the primary polyelectrolyte peak, we find that bottlebrush polymers exhibit an additional peak in the form and static structure factors, a feature that is absent in neutral polymers. We show that this additional peak describes the intra-molecular correlations between the charged side chains.

Computing 3D Chromatin Configurations from Contact Probability Maps by Inverse Brownian Dynamics

The three-dimensional (3D) organization of chromatin, on the length scale of a few genes, is crucial in determining the functional state—accessibility and amount of gene expression—of the chromatin. Recent advances in chromosome conformation capture experiments provide partial information on the chromatin organization in a cell population, namely the contact count between any segment pairs, but not on the interaction strength that leads to these contact counts. However, given the contact matrix, determining the complete 3D organization of the whole chromatin polymer is an inverse problem. In this work, a novel inverse Brownian dynamics method based on a coarse-grained bead-spring chain model has been proposed to compute the optimal interaction strengths between different segments of chromatin such that the experimentally measured contact count probability constraints are satisfied. Applying this method to the α-globin gene locus in two different cell types, we predict the 3D organizations corresponding to active and repressed states of chromatin at the locus. We show that the average distance between any two segments of the region has a broad distribution and cannot be computed as a simple inverse relation based on the contact probability alone. The results presented for multiple normalization methods suggest that all measurable quantities may crucially depend on the nature of normalization. We argue that by experimentally measuring predicted quantities, one may infer the appropriate form of normalization.

Semiflexible Polymers Interacting With Planar Surfaces: Weak versus Strong Adsorption.

Semiflexible polymers bound to planar substrates by a short-range surface potential are studied by Molecular Dynamics simulations to clarify the extent to which these chain molecules can be considered as strictly two-dimensional. Applying a coarse-grained bead-spring model, the chain length N and stiffness as well as the strength of the adsorption potential are varied over a wide range. The excluded-volume (EV) interactions inherent in this model can also be “switched off” to provide a discretized version of the Kratky–Porod wormlike chain model. We study both local order parameters (fraction f of monomers within the range of the potential, bond-orientational order parameter ) and the mean square gyration radius parallel, , and perpendicular, , to the wall. While for strongly adsorbed chains EV has negligible effect on f and , we find that is strongly affected when the chain contour length exceeds the persistence length. Monomer coordinates in perpendicular (⊥) direction are correlated over the scale of the deflection length which is estimated. It is found that , and converge to their asymptotic values with corrections. For both weakly and strongly adsorbed chains, the distribution functions of “loops”, “trains”, and “tails” are analyzed. Some consequences pertaining to the analysis of experiments on adsorbed semiflexible polymers are pointed out.

Bacterial chromosome organization. II. Few special cross-links, cell confinement, and molecular crowders play the pivotal roles.

Using a coarse-grained bead-spring model of bacterial chromosomes of Caulobacter crescentus and Escherichia coli, we show that just 33 and 38 effective cross-links in 4017 and 4642 monomer chains at special positions along the chain contour can lead to the large-scale organization of the DNA polymer, where confinement effects of the cell walls play a key role in the organization. The positions of the 33/38 cross-links along the chain contour are chosen from the Hi-C contact map of bacteria C. crescentus and E. coli. We represent 1000 base pairs as a coarse-grained monomer in our bead-spring flexible ring polymer model of the DNA polymer. Thus, 4017/4642 beads on a flexible ring polymer represent the C. crescentus/E. coli DNA polymer with 4017/4642 kilo-base pairs. Choosing suitable parameters from Paper I, we also incorporate the role of compaction of the polymer coil due to the presence of molecular crowders and the ability of the chain to release topological constraints. We validate our prediction of the organization of the bacterial chromosomes with available experimental data and also give a prediction of the approximate positions of different segments within the cell. In the absence of confinement, the minimal number of effective cross-links required to organize the DNA chains of 4017/4642 monomers was 60/82 [Agarwal et al., Europhys. Lett. 121, 18004 (2018) and Agarwal et al., J. Phys.: Condens. Matter 30, 034003 (2018)].

Influence of bonded interactions on structural phases of flexible polymers.

We introduce a novel coarse-grained bead-spring model for flexible polymers to systematically examine the effects of an adjusted bonded potential on the formation and stability of structural macrostates in a thermal environment. The density of states obtained in advanced replica-exchange Monte Carlo simulations is analyzed by employing the recently developed generalized microcanonical inflection-point analysis method, which enables the identification of diverse structural phases and the construction of a suitably parameterized hyperphase diagram. It reveals that icosahedral phases dominate for polymers with asymmetric and narrow bond potentials, whereas polymers with symmetric and more elastic bonds tend to form amorphous structures with non-icosahedral cores. We also observe a hierarchy in the freezing transition behavior associated with the formation of the surface layer after nucleation.

Effect of functional-group distribution on the structure of a polymer in non-aqueous solvent

ABSTRACTThe sizes and structures of isolated functionalised polymers in a hydrocarbon solvent are studied using atomistic molecular dynamics simulations and Monte Carlo simulations of coarse-grained chains. A specific functionalised polyethylene-polypropylene random copolymer in n-heptane is studied using atomistic simulations. The functional groups contain aromatic and polar groups, and eight of them are distributed on an polymer backbone in several different ways. It is shown that the radius of gyration and the end-to-end distance depend sensitively on the functional-group distribution. A random distribution of functional groups gives the most compact polymer structure, but other distributions give values up to larger; the largest values are when the functional groups are split evenly between both ends of the polymer. This is shown to be due to the association of the polar, and hence solvophobic, functional groups. A coarse-grained bead-spring model is then studied that includes solvophilic beads (representing unfunctionalised units) and solvophobic beads (representing functionalised units). Monte Carlo simulations are used to survey functional-group concentration and distribution. The results show that the collapse of a polymer with increasing solvophobicity depends sensitively on the distribution of different beads. Form factors are presented for both the atomistic and coarse-grained models and are analysed as if they were experimental scattering measurements. The apparent radii of gyration are in good agreement with those determined directly from the simulation.

Diffusion and Relaxation Dynamics of Supercooled Polymer Melts

The dynamic properties of polymer melts are investigated in the range of normal liquid regime to the supercooled liquid regime. The polymer is modeled as a coarse-grained bead-spring model with chain length ranging from 5 to 160. The mean squared displacement and non-Gaussian parameter are used to describe the self diffusion of polymer beads. We find slow dynamics with decreasing temperature and increasing chain length. The time evolution of non-Gaussian parameters shows two peaks (or one peak one shoulder) in the α-relaxation time, τα, regime and sub-diffusion time regime, respectively, where the first primary peak indicates the dynamic heterogeneity stemmed from the motion of beads, and the secondary peak is the result of correlated motion along a polymer chain. Moreover, the relaxation of polymer beads shows clear two-step decay in supercooled melts and the dynamics shows growing heterogeneity with decreasing temperature. As chain length is increased, a peak of the dynamic susceptibility occurs, and the peak height, χ*4, increases and then reaches a plateau. The curves of the height of the first peak of α2α*2, versus τα and the curves of χ*4 versus ταfollow two master curves for different chain lengths. Our results indicate the similarity of dynamic heterogeneity dominated by the motion of single bead even the chain length is different. It is interesting to find that the Stokes-Einstein (SE) relation between τα and diffusion coefficient D, D~τ −1 , is highly length-scale dependent. The SE relation breaks down in both normal melts regime and supercooled regime at large magnitude of wave vectors, attributed to the non-Brownian motion arising from the chain connectivity and growing heterogeneity due to supercooling. However, the SE relation is reconstructed when the probing length scale is large (at small magnitude of wave vectors). Our results show a hierarchical physical picture of the supercooled polymeric dynamics.

Toroidal Condensates by Semiflexible Polymer Chains: Insights into Nucleation, Growth and Packing Defects.

Deciphering the principles of DNA condensation is important to understand problems such as genome packing and DNA compaction for delivery in gene therapy. DNA molecules condense into toroids and spindles upon the addition of multivalent ions. Nucleation of a loop in the semiflexible DNA chain is critical for both the toroid and spindle formation. To understand the structural differences in the nucleated loop, which cause bifurcation in the condensation pathways leading to toroid or spindle formation, we performed molecular dynamics simulations using a coarse-grained bead-spring polymer model. We find that the formation of a toroid or a spindle is correlated with the orientation of the chain segments close to the loop closure in the nucleated loop. Simulations show that toroids grow in size when spindles in solution interact with a pre-existing toroid and merge into it by spooling around the circumference of the toroid, forming multimolecular toroidal condensates. The merging of spindles with toroids is facile, indicating that this should be the dominant pathway through which the toroids grow in size. The Steinhardt bond order parameter analysis of the toroid cross section shows that the chains pack in a hexagonal fashion. In agreement with the experiments there are regions in the toroid with good hexagonal packing and also with considerable disorder. The disorder in packing is due to the defects, which are propagated during the growth of toroids. In addition to the well-known crossover defect, we have identified three other forms of defects, which perturb hexagonal packing. The new defects identified in the simulations are amenable to experimental verification.

Ordered quasi-two-dimensional structure of nanoparticles in semiflexible ring polymer brushes under compression

Molecular dynamics simulations of a coarse-grained bead-spring model of ring polymer brushes under compression are presented. Flexible polymer brushes are always disordered during compression, whereas semiflexible polymer brushes tend to be ordered under sufficiently strong compression. Further, the polymer monomer density of the semiflexible polymer brush is very high near the brush surface, inducing a peak value of the free energy near the surface. Therefore, when nanoparticles are compressed in semiflexible ring polymer brushes, they tend to exhibit a closely packed single-layer structure between the brush surface and the impenetrable wall, and a quasi-two-dimensional ordered structure near the brush surface is formed under strong compression. These findings provide a new approach to designing responsive applications.

Effects of Polymer Length and Salt Concentration on the Transport of ssDNA in Nanofluidic Channels

Electrokinetic phenomena in micro/nanofluidic channels have attracted considerable attention because precise control of molecular transport in liquids is required to optically and electrically capture the behavior of single molecules. However, the detailed mechanisms of polymer transport influenced by electroosmotic flows and electric fields in micro/nanofluidic channels have not yet been elucidated. In this study, a Langevin dynamics simulation was used to investigate the electrokinetic transport of single-stranded DNA (ssDNA) in a cylindrical nanochannel, employing a coarse-grained bead-spring model that quantitatively reproduced the radius of gyration, diffusion coefficient, and electrophoretic mobility of the polymer. Using this practical scale model, transport regimes of ssDNA with respect to the ζ-potential of the channel wall, the ion concentration, and the polymer length were successfully characterized. It was found that the relationship between the radius of gyration of ssDNA and the channel radius is critical to the formation of deformation regimes in a narrow channel. We conclude that a combination of electroosmotic flow velocity gradients and electric fields due to electrically polarized channel surfaces affects the alignment of molecular conformations, such that the ssDNA is stretched/compressed at negative/positive ζ-potentials in comparatively low-concentration solutions. Furthermore, this work suggests the possibility of controlling the center-of-mass position by tuning the salt concentration. These results should be applicable to the design of molecular manipulation techniques based on liquid flows in micro/nanofluidic devices.

Parameter-free prediction of DNA dynamics in planar extensional flow of semidilute solutions

The dynamics of individual Deoxyribonucleic acid (DNA) molecules in semidilute solutions undergoing planar extensional flow is simulated using a multiparticle Brownian dynamics algorithm, which incorporates hydrodynamic and excluded volume interactions in the context of a coarse-grained bead-spring chain model for DNA. The successive fine-graining protocol [P. Sunthar and J. R. Prakash, Macromolecules 38, 617–640 (2005); R. Prabhakar et al., J. Rheol. 48, 1251–1278 (2004)], in which simulation data acquired for bead-spring chains with increasing values of the number of beads Nb, is extrapolated to the number of Kuhn steps NK in DNA (while keeping key physical parameters invariant), is used to obtain parameter-free predictions for a range of Weissenberg numbers and Hencky strain units. A systematic comparison of simulation predictions is carried out with the experimental observations of Hsiao et al. [J. Rheol. (in press)], who have recently used single molecule techniques to investigate the dynamics of dilute and semidilute solutions of λ-phage DNA in planar extensional flow. In particular, they examine the response of individual chains to step-strain deformation followed by cessation of flow, thereby capturing both chain stretch and relaxation in a single experiment. The successive fine-graining technique is shown to lead to quantitatively accurate predictions of the experimental observations in the stretching and relaxation phases. Additionally, the transient chain stretch following a step strain deformation is shown to be much smaller in semidilute solutions than in dilute solutions, in agreement with experimental observations.

A new bead-spring model for simulation of semi-flexible macromolecules.

A bead-spring model for semi-flexible macromolecules is developed to overcome the deficiencies of the current coarse-grained bead-spring models. Specifically, model improvements are achieved through incorporation of a bending potential. The new model is designed to accurately describe the correlation along the backbone of the chain, segmental length, and force-extension behavior of the macromolecule even at the limit of 1 Kuhn step per spring. The relaxation time of different Rouse modes is used to demonstrate the capabilities of the new model in predicting chain dynamics.

Dynamics of DNA Squeezed Inside a Nanochannel via a Sliding Gasket.

We use Brownian dynamics (BD) simulation of a coarse-grained (CG) bead-spring model of DNA to study the nonequilibrim dynamics of a single DNA molecule confined inside a rectangular nanochannel being squeezed with a sliding gasket piston or “nanodozer”. From our simulations we extract the nonequilibrim density profile of the squeezed molecule along the channel axis (x-coordinate) and then analyze the non-equilibrium profile using a recently introduced phenomenological Nonlinear Partial Differential Equation (NPDE) model. Since the NPDE approach also fits the experimental results well and is numerically efficient to implement, the combined BD + NPDE methods can be a powerful approach to analyze details of the confined molecular dynamics. In particular, the overall excellent agreement between the two complementary sets of data provides a strategy for carrying out large scale simulation on semi-flexible biopolymers in confinement at biologically relevant length scales.

Semiflexible polymers under good solvent conditions interacting with repulsive walls.

Solutions of semiflexible polymers confined by repulsive planar walls are studied by density functional theory and molecular dynamics simulations, to clarify the competition between the chain alignment favored by the wall and the depletion caused by the monomer-wall repulsion. A coarse-grained bead-spring model with a bond bending potential is studied, varying both the contour length and the persistence length of the polymers, as well as the monomer concentration in the solution (good solvent conditions are assumed throughout, and solvent molecules are not included explicitly). The profiles of monomer density and pressure tensor components near the wall are studied, and the surface tension of the solution is obtained. While the surface tension slightly decreases with chain length for flexible polymers, it clearly increases with chain length for stiff polymers. Thus, at fixed density and fixed chain length, the surface tension also increases with increasing persistence length. Chain ends always are enriched near the wall, but this effect is much larger for stiff polymers than for flexible ones. Also the profiles of the mean square gyration radius components near the wall and the nematic order parameter are studied to clarify the conditions where wall-induced nematic order occurs.

Complex formation between polyelectrolytes and oppositely charged oligoelectrolytes.

We study the complex formation between one long polyanion chain and many short oligocation chains by computer simulations. We employ a coarse-grained bead-spring model for the polyelectrolyte chains and model explicitly the small salt ions. We systematically vary the concentration and the length of the oligocation and examine how the oligocations affects the chain conformation, the static structure factor, the radial and axial distribution of various charged species, and the number of bound ions in the complex. At low oligocation concentration, the polyanion has an extended structure. Upon increasing the oligocation concentration, the polyanion chain collapses and forms a compact globule, but the complex still carries a net negative charge. Once the total charge of the oligocations is equal to that of the polyanion, the collapse stops and is replaced by a slow expansion. In this regime, the net charge on the complexes is positive or neutral, depending on the microion concentration in solution. The expansion can be explained by the reduction of the oligocation bridging. We find that the behavior and the structure of the complex are largely independent of the length of oligocations, and very similar to that observed when replacing the oligocations by multivalent salt cations, and conclude that the main driving force keeping the complex together is the release of monovalent counterions and coions. We speculate on the implications of this finding for the problem of controlled oligolyte release and oligolyte substitution.