Brownian dynamics simulations of flexible polymers with spring–spring repulsions

Kumar, Satish; Larson, Ronald G.

doi:10.1063/1.1358860

Cited by 114 publications

(104 citation statements)

References 24 publications

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“…The estimated entanglement length of DPD polymers is found to be consistent with the classical MD simulations [247,248]. These works build on studies by Goujon et al [249], who developed a repulsive potential between segments [250] in DPD simulation to avoid bond crossing. The blob model has been adopted to study the dynamic and rheological properties of PE and poly(ethylene-alt-propylene) (PEP) polymers [84,85,241].…”

Section: Blob Model and Uncrossability Of Coarse-grained Chainsmentioning

confidence: 70%

Challenges in Multiscale Modeling of Polymer Dynamics

et al. 2013

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The mechanical and physical properties of polymeric materials originate from the interplay of phenomena at different spatial and temporal scales. As such, it is necessary to adopt multiscale techniques when modeling polymeric materials in order to account for all important mechanisms. Over the past two decades, a number of different multiscale computational techniques have been developed that can be divided into three categories: (i) coarse-graining methods for generic polymers; (ii) systematic coarse-graining methods and (iii) multiple-scale-bridging methods. In this work, we discuss and compare eleven different multiscale computational techniques falling under these categories and assess them critically according to their ability to provide a rigorous link between polymer chemistry and rheological material properties. For each technique, the fundamental ideas and equations are introduced, and the most important results or predictions are shown and discussed. On the one hand, this review provides a comprehensive tutorial on multiscale computational techniques, which will be of interest to readers newly entering this field; on the other, it presents a critical discussion of the future opportunities and key challenges in the multiscale geometric mapping matrix between all-atomistic and coarse-grained models N number of monomers per chain N e entanglement length, which is the number of monomers between two entanglements n v number of polymer chains per unit volume n ij (n 0 (r ij )) entanglement number (at equilibrium) between particle pairs i and j p r , P R configurational probability distributions in all-atomistic and coarse-grained models, respectively R ee end-to-end distance of polymer chain R G radius of gyration of polymer chain s segment index/contour length variable along primitive chain S(q) single chain coherent dynamic scattering function Z number of entanglements per chain, defined as Z = N/N e α exponent in standard Mittag-Leffler function σ

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Section: Blob Model and Uncrossability Of Coarse-grained Chainsmentioning

confidence: 70%

Challenges in Multiscale Modeling of Polymer Dynamics

et al. 2013

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“…Torsional degrees of freedom can indeed be introduced in the model according to [83] and spring-spring repulsions according to [84], see equations (9) and (10) of the Appendix. This model predicts that the linking number decomposes approximately into 2/3 of writhe and 1/3 of twist, in fair agreement with experimental measurements [76].…”

Section: -Compaction Mechanisms Specific To Dnamentioning

confidence: 99%

Compaction of bacterial genomic DNA: clarifying the concepts

Joyeux

2015

J. Phys.: Condens. Matter

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: The unconstrained genomic DNA of bacteria forms a coil, which volume exceeds 1000 times the volume of the cell. Since prokaryotes lack a membrane-bound nucleus, in sharp contrast with eukaryotes, the DNA may consequently be expected to occupy the whole available volume when constrained to fit in the cell. Still, it has been known for more than half a century that the DNA is localized in a well defined region of the cell, called the nucleoid, which occupies only 15% to 25% of the total volume. Although this problem has focused the attention of many scientists for the past decades, there is still no certainty concerning the mechanism that enables such a dramatic compaction. The goal of this Topical Review is to take stock of our knowledge on this question by listing all possible compaction mechanisms with the proclaimed desire to clarify the physical principles they are based upon and discuss them in the light of experimental results and the results of simulations based on coarse-grained models. In particular, the fundamental differences between ψ-condensation and segregative phase separation and between the condensation by small and long polycations are highlighted. This review suggests that the importance of certain mechanisms, like supercoiling and the architectural properties of DNA-bridging and DNA-bending nucleoid proteins, may have been overestimated, whereas other mechanisms, like segregative phase separation and the self-association of nucleoid proteins, as well as the possible role of the synergy of two or more mechanisms, may conversely deserve more attention.Keywords : bacteria, genomic DNA, nucleoid, compaction, coarse-grained model 2 -IntroductionIllustrations of the hierarchical compaction of genomic DNA in the nuclei of eukaryotic cells can be found in any textbook, from the initial wrapping of DNA around histone proteins to the final X-shaped chromosomes, through the various levels of fiber condensation. While seemingly simpler, the compaction of bacterial genomic DNA is nevertheless more poorly understood. One of the main reasons is that typical cell dimensions and DNA size of prokaryotes are significantly smaller than those of eukaryotes, with cell radii of the order of 1 µm against 10 to 100 µm and DNA size of the order of millions of base pairs against billions of base pairs. As a consequence, optical microscopy experiments are able to show that DNA occupies only a small part of the cell (from 15% to 25%) but fail to provide more detail because of resolution issues [1]. In contrast, electronic microscopy is able to provide information on the ultra-structure of the nucleoid (the region where the DNA is localized) but results depend dramatically on the experimental procedure that is used to prepare the cells [1,2]. Finally, the more recent techniques that consist in labeling specific genes with fluorescent dyes or proteins [3] usually provide information on the dynamics close to the loci of these genes but not on the global organization of the nucleoid. Owing to these difficulties, ev...

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“…We make two comments regarding this point. First, Kumar and Larson 28 have recently addressed the issue of chain-crossing with a model that, rather than imposing bead-bead repulsions, imposes ''spring-spring'' repulsions acting along the shortest line segment between nearby connector vectors. Nevertheless, with a soft potential, they find results essentially identical to those with bead-bead repulsions, while with a singular (r Ϫ12 ) potential the time step required becomes prohibitive.…”

Section: Modelmentioning

confidence: 99%

Stochastic simulations of DNA in flow: Dynamics and the effects of hydrodynamic interactions

Jendrejack

Pablo

Graham

2002

The Journal of Chemical Physics

269

364

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We present a fully parametrized bead-spring chain model for stained -phage DNA. The model accounts for the finite extensibility of the molecule, excluded volume effects, and fluctuating hydrodynamic interactions ͑HI͒. Parameters are determined from equilibrium experimental data for 21 m stained -phage DNA, and are shown to quantitatively predict the non-equilibrium behavior of the molecule. The model is then used to predict the equilibrium and nonequilibrium behavior of DNA molecules up to 126 m. In particular, the HI model gives results that are in quantitative agreement with experimental diffusivity data over a wide range of molecular weights. When the bead friction coefficient is fit to the experimental relaxation time at a particular molecular weight, the stretch in shear and extensional flows is adequately predicted by either a free-draining or HI model at that molecular weight, although the fitted bead friction coefficients for the two models differ significantly. In shear flow, we find two regimes at high shear rate (␥ ) that follow different scaling behavior. In the first, the viscosity and first normal stress coefficient scale roughly as ␥ Ϫ6/11 and ␥ Ϫ14/11 , respectively. At higher shear rates, these become ␥ Ϫ2/3 and ␥ Ϫ4/3 . These regimes are found for both free-draining and HI models and can be understood based on scaling arguments for the diffusion of chain ends.

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Brownian dynamics simulations of flexible polymers with spring–spring repulsions

Cited by 114 publications

References 24 publications

Challenges in Multiscale Modeling of Polymer Dynamics

Challenges in Multiscale Modeling of Polymer Dynamics

Compaction of bacterial genomic DNA: clarifying the concepts

Stochastic simulations of DNA in flow: Dynamics and the effects of hydrodynamic interactions

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