Dynamics of a semiflexible polymer or polymer ring in shear flow

Lang, Philipp; Obermayer, Benedikt; Frey, Erwin

doi:10.1103/physreve.89.022606

Cited by 44 publications

(51 citation statements)

References 83 publications

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“…Using this relation between our model and the inextensible WLC, we demonstrate that the maximal allowable time step t max for the inextensible WLC model of a dsDNA chain of 63 base pairs is ≈0.02 fs, in good agreement with Ref. [28] (that has recently implemented Morse's algorithm for the inextensible WLC). In other words, as shown in Table I, to simulate dsDNA our model achieves a maximal allowable time step that is five to six orders of magnitude larger than that of the inextensible WLC.…”

Section: Introductionsupporting

confidence: 65%

Efficient simulation of semiflexible polymers

2015

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Using a recently developed bead-spring model for semiflexible polymers that takes into account their natural extensibility, we report an efficient algorithm to simulate the dynamics for polymers like double-stranded DNA (dsDNA) in the absence of hydrodynamic interactions. The dsDNA is modeled with one bead-spring element per base pair, and the polymer dynamics is described by the Langevin equation. The key to efficiency is that we describe the equations of motion for the polymer in terms of the amplitudes of the polymer's fluctuation modes, as opposed to the use of the physical positions of the beads. We show that, within an accuracy tolerance level of 5% of several key observables, the model allows for single Langevin time steps of ≈1.6, 8, 16, and 16 ps for a dsDNA model chain consisting of 64, 128, 256, and 512 base pairs (i.e., chains of 0.55, 1.11, 2.24, and 4.48 persistence lengths), respectively. Correspondingly, in 1 h, a standard desktop computer can simulate 0.23, 0.56, 0.56, and 0.26 ms of these dsDNA chains, respectively. We compare our results to those obtained from other methods, in particular, the (inextensible discretized) wormlike chain (WLC) model. Importantly, we demonstrate that at the same level of discretization, i.e., when each discretization element is one base pair long, our algorithm gains about five to six orders of magnitude in the size of time steps over the inextensible WLC model. Further, we show that our model can be mapped one on one to a discretized version of the extensible WLC model, implying that the speed-up we achieve in our model must hold equally well for the latter. We also demonstrate the use of the method by simulating efficiently the tumbling behavior of a dsDNA segment in a shear flow.

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Section: Introductionsupporting

confidence: 65%

Efficient simulation of semiflexible polymers

2015

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“…For standard circumstances c 52 ps. This time scaling differs from the scaling that we used for extensible chains [15] and it corresponds to the scaling used in simulations of the IWLC [16,17]. The scaled Hamiltonian contains instead of λ and κ the dimensionless parameters…”

Section: Hamiltonian Contextmentioning

confidence: 99%

“…(12). As the literature has few estimates [16] for the appropriate time steps in a reliable simulation, we specifically address this issue. A simulation is correct if it produces the correct time-dependent correlation functions.…”

Section: Hamiltonian Contextmentioning

confidence: 99%

Efficient simulation of semiflexible polymers with stiff bonds

Barkema

Leeuwen

2017

Phys. Rev. E

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We investigate the simulation of stiff (extensible) and rigid (inextensible) semiflexible polymers in solution.In particular, we focus on polymers represented as chains of beads, interconnected by bonds with a low to zero extensibility, and significant persistence in the bond orientations along the chain, whose dynamical behavior is described by the Langevin equation. We review the derivation of the pseudopotential needed for rigid bonds. The efficiency of a number of routines for such simulations is determined. We propose a routine for handling rigid bonds which is, for longer chains, substantially more efficient than the existing ones. We also show that for extensible polymers, the Rouse modes can be exploited to achieve highly efficient simulations. At realistic values for the extensibility, e.g., that of double-stranded DNA, the simulations are orders of magnitude faster than those for rigid bonds. With increasing stiffness, however, the allowable time step and hence the efficiency decreases, until a crossover point is reached below which the routines with rigid bonds are more efficient; we present a numerical estimate of this crossover point.

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“…These issues of buckling and the tumbling frequency were taken up by Lang et al [12] by an extensive modeling study, using the inextensible wormlike chain as Hamiltonian. They discussed the tumbling frequency for the whole range spanning the two extremes, i.e., from flexible to semiflexible polymer segments, and reported, in the intermediate regime, the dependence f ∝ Wi 3/4 .…”

Section: Introductionmentioning

confidence: 99%

“…Although irregular at short time scales, a tumbling frequency could be defined based on the long-time statistics of the chain's orientation. The tumbling behavior soon started to receive further attention from researchers: Over the last decade and a half, a number of models have been constructed [10][11][12] and further experiments have been performed [13][14][15][16] to characterize and quantify the tumbling behavior, in particular, the dependence of the tumbling frequency on the shear strength. The subject of this paper, too, is tumbling behavior in a shear flow, specifically for a dsDNA chain that is smaller than its persistence length.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a double-stranded DNA segment in a shear flow

2016

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We study the dynamics of a double-stranded DNA (dsDNA) segment, as a semiflexible polymer, in a shear flow, the strength of which is customarily expressed in terms of the dimensionless Weissenberg number Wi. Polymer chains in shear flows are well known to undergo tumbling motion. When the chain lengths are much smaller than the persistence length, one expects a (semiflexible) chain to tumble as a rigid rod. At low Wi, a polymer segment shorter than the persistence length does indeed tumble as a rigid rod. However, for higher Wi the chain does not tumble as a rigid rod, even if the polymer segment is shorter than the persistence length. In particular, from time to time the polymer segment may assume a buckled form, a phenomenon commonly known as Euler buckling. Using a bead-spring Hamiltonian model for extensible dsDNA fragments, we first analyze Euler buckling in terms of the oriented deterministic state (ODS), which is obtained as the steady-state solution of the dynamical equations by turning off the stochastic (thermal) forces at a fixed orientation of the chain. The ODS exhibits symmetry breaking at a critical Weissenberg number Wi c , analogous to a pitchfork bifurcation in dynamical systems. We then follow up the analysis with simulations and demonstrate symmetry breaking in computer experiments, characterized by a unimodal to bimodal transformation of the probability distribution of the second Rouse mode with increasing Wi. Our simulations reveal that shear can cause strong deformation for a chain that is shorter than its persistence length, similar to recent experimental observations.

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Dynamics of a semiflexible polymer or polymer ring in shear flow

Cited by 44 publications

References 83 publications

Efficient simulation of semiflexible polymers

Efficient simulation of semiflexible polymers

Efficient simulation of semiflexible polymers with stiff bonds

Dynamics of a double-stranded DNA segment in a shear flow

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