Stability of sedimenting flexible loops

Waszkiewicz, Radost; Szymczak, Piotr; Lisicki, Maciej

doi:10.1017/jfm.2021.350

Cited by 7 publications

(10 citation statements)

References 52 publications

(108 reference statements)

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“…This finding provides an important input to future models of circularised polymers. Incorporating torsional interactions is more difficult than just bending interactions and is often neglected when constructing models of circularized molecules (68, 69, 70, 71). Since the torsional forces play a role even when Δ Lk is close to zero, additional care needs to be taken when generalising such models for the context of supercoiled DNA.…”

Section: Discussionmentioning

confidence: 99%

DNA supercoiling-induced shapes alter minicircle hydrodynamic properties

Waszkiewicz

Ranasinghe

Fogg

et al. 2023

Preprint

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DNA in cells is organized in negatively supercoiled loops. The resulting torsional and bending strain allows DNA to adopt a surprisingly wide variety of 3-D shapes. This interplay between negative supercoiling, looping, and shape influences how DNA is stored, replicated, transcribed, repaired, and likely every other aspect of DNA activity. To understand the consequences of negative supercoiling and curvature on the hydrodynamic properties of DNA, we submitted 336 bp and 672 bp DNA minicircles to analytical ultracentrifugation (AUC). We found that the diffusion coefficient, sedimentation coefficient, and the DNA hydrodynamic radius strongly depended on circularity, loop length, and degree of negative supercoiling. Because AUC cannot ascertain shape beyond degree of non-globularity, we applied linear elasticity theory to predict DNA shapes, and combined these with hydrodynamic calculations to interpret the AUC data, with reasonable agreement between theory and experiment. These complementary approaches, together with earlier electron cryotomography data, provide a framework for understanding and predicting the effects of supercoiling on the shape and hydrodynamic properties of DNA.

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Section: Discussionmentioning

confidence: 99%

DNA supercoiling-induced shapes alter minicircle hydrodynamic properties

Waszkiewicz

Ranasinghe

Fogg

et al. 2023

Preprint

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“…We focused on the flow far from the body and near the body surface as the SBT asymptotic representations are expected to be the most valid in these regions. We found that any line of regularized Stokeslets can approximate the flow far from the body provided that the regularization parameter, , is equal to the thickness of the body, aρ 0 , multiplied by a constant that depends on the regularization blob, (8π ∞ 0 u 4 f (u) du/3) −1/2 , Equation (23). This constant can be used for the unknown proportionality constant used in numerical simulations.…”

Section: Discussionmentioning

confidence: 99%

“…Broadly, SBTs have been divided into two types: those that expand the system in powers of 1/ ln(a) [1,3] and those that expand the system in powers of a [4][5][6][7]. The former is often called resistive force theory and provides useful analytical estimates [17][18][19][20][21][22][23][24], while the latter has been shown to provide highly accurate results in numerous situations [11][12][13][14][15][16].…”

Section: Classical Slender-body Theorymentioning

confidence: 99%

“…In the small a limit, asymptotic theories have been developed for the flow around slender bodies [1][2][3][4][5][6][7][8][9][10]. These theories are called slender-body theories (SBTs), and they expand the system in powers of a or 1/ ln a. Algebraically accurate SBTs have proven to be very accurate and provide exact results for prolate spheroids [3,5,7,[11][12][13][14][15][16], while logarithmically accurate SBTs are useful for analytical estimations [17][18][19][20][21][22][23][24]. Many of these theories place the singularity solutions of Stokes equations along the centreline of the body.…”

Section: Introductionmentioning

confidence: 99%

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Regularized Stokeslets Lines Suitable for Slender Bodies in Viscous Flow

Zhao

Koens

2021

Fluids

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Slender-body approximations have been successfully used to explain many phenomena in low-Reynolds number fluid mechanics. These approximations typically use a line of singularity solutions to represent flow. These singularities can be difficult to implement numerically because they diverge at their origin. Hence, people have regularized these singularities to overcome this issue. This regularization blurs the force over a small blob and thereby removing divergent behaviour. However, it is unclear how best to regularize the singularities to minimize errors. In this paper, we investigate if a line of regularized Stokeslets can describe the flow around a slender body. This is achieved by comparing the asymptotic behaviour of the flow from the line of regularized Stokeslets with the results from slender-body theory. We find that the flow far from the body can be captured if the regularization parameter is proportional to the radius of the slender body. This is consistent with what is assumed in numerical simulations and provides a choice for the proportionality constant. However, more stringent requirements must be placed on the regularization blob to capture the near field flow outside a slender body. This inability to replicate the local behaviour indicates that many regularizations cannot satisfy the no-slip boundary conditions on the body’s surface to leading order, with one of the most commonly used blobs showing an angular dependency of velocity along any cross section. This problem can be overcome with compactly supported blobs, and we construct one such example blob, which can be effectively used to simulate the flow around a slender body.

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“…The form of the integral operator in nonlocal slender body renders the dynamic problem for the curve evolution much more difficult. Using resistive force theory for the force-to-velocity map along the fiber simplifies the curve evolution problem while still remaining relevant from a current modeling perspective (see, for example, [1,4,5,6,30,43,46,52,60,63]).…”

Section: Introductionmentioning

confidence: 99%

Well-posedness and applications of classical elastohydrodynamics for a swimming filament

Mori¹,

Ohm²

2022

Preprint

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We consider a classical elastohydrodynamic model of an inextensible filament undergoing planar motion in R 3 . The hydrodynamics are described by resistive force theory, and the fiber elasticity is governed by Euler-Bernoulli beam theory. Our aim is twofold: (1) Serve as a starting point for developing the mathematical analysis of filament elastohydrodynamics, particularly the analytical treatment of an inextensibility constraint, and (2) As an application, prove conditions on internal fiber forcing that allow a free-ended filament to swim. Our analysis of fiber swimming speed is supplemented with a numerical optimization of the internal fiber forcing, as well as a novel numerical method for simulating an inextensible swimmer.

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Stability of sedimenting flexible loops

Abstract: Abstract

Cited by 7 publications

References 52 publications

DNA supercoiling-induced shapes alter minicircle hydrodynamic properties

DNA supercoiling-induced shapes alter minicircle hydrodynamic properties

Regularized Stokeslets Lines Suitable for Slender Bodies in Viscous Flow

Well-posedness and applications of classical elastohydrodynamics for a swimming filament

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