Recent theoretical advances in elasticity of membranes following Helfrich's spontaneous curvature model

Tu, Z. C.; Ouyang, Zi

doi:10.1016/j.cis.2014.01.008

Cited by 42 publications

(37 citation statements)

References 122 publications

(236 reference statements)

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“…Furthermore, because they are codimension-1 branes, it means that the extrinsic curvature tensor only has one direction and hence a term proportional to K, where we have omitted the index i, can be added to (2) as well as terms proportional to worldvolume derivatives of K [5,18]. A recent review of different models for biophysical membranes and their usage can be found in [19]. Despite the fact that the black branes that we will consider are generically of codimension higher than one, the black ring configuration that we will analyse in detail is described by a two-dimensional membrane with only one extrinsic curvature component and hence effectively behaving like a fluid membrane of codimension-1.…”

Section: Arxiv:14026330v2 [Hep-th] 26 Nov 2014mentioning

confidence: 99%

Black holes and biophysical (mem)-branes

Armas

Harmark

2014

Phys. Rev. D

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We argue that the effective theory describing the long-wavelength dynamics of black branes is the same effective theory that describes the dynamics of biophysical membranes. We improve the phase structure of higher-dimensional black rings by considering finite thickness corrections in this effective theory, showing a striking agreement between our analytical results and recent numerical constructions while simultaneously drawing a parallel between gravity and the effective theory of biophysical membranes.Introduction. In the past three years many remarkable properties of higher-dimensional black holes were uncovered, leading to a new perspective on black holes as materials describable by effective theories of continuous media. In particular, in a long-wavelength regime, besides having fluid-like properties, they can behave as elastic (mem)-branes if bent and exhibit piezoelectric behaviour if charged and flexed. In this regime they are characterised by a set of transport coefficients such as shear and bulk viscosities [1,2], the Young modulus [3] and the piezoelectric moduli [4], which can be directly measured from gravity.Fluid and (mem)-brane elastic behaviour of a physical system can be described by a single unified framework of hydrodynamics on embedded surfaces [5,6]. When applied to black holes and black branes, this framework is commonly known as the blackfold approach [7,8], which has enabled a systematic scan of new horizon topologies in higher-dimensions [9] and the construction of new approximate solutions, such as black rings in arbitrary space-time dimensions [10].The blackfold approach, as originally developed in [7,8], consists in applying generic long wavelength perturbations of neutral asymptotically flat black p-brane metrics and describing its dynamics via an effective theory. In this case, to leading order in the perturbation, the black branes are described by a set of world volume fields composed of the induced metric γ ab , the local boost velocity u a and the brane thickness r 0 . Focusing on the stationary sector, the dynamics of these branes can be described by the free energy functional of a fluid living on an elastic brane. To next order in the perturbation, the black brane metric is corrected by terms proportional to derivatives of the fields γ ab , u a , r 0 which include, as we will explain shortly, terms proportional to the extrinsic curvature tensor K ab i , the Riemann curvature tensor of the world volume, or the vorticity of the fluid. [11] The dynamics of elastic membranes has also taken an important role in the context of biophysics, beginning with the early work of Helfrich [12] and Canham [13] in the 60's. They showed that the bending deformations of elastic membranes played a crucial role in the

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Section: Arxiv:14026330v2 [Hep-th] 26 Nov 2014mentioning

confidence: 99%

Black holes and biophysical (mem)-branes

Armas

Harmark

2014

Phys. Rev. D

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“…In this simplification, the variational principle can be interpreted as an analogue of Hamilton's principle of classical mechanics, with the free energy interpreted as an action describing the trajectory of a fictitious particle, and the parameter along the surface contour playing the role of a time parameter [4,27,28]. The problem is reduced to a finite number of degrees of freedom, but it is still highly non trivial, involving higher derivative non-linear ordinary differential equations [29]. In field theory, a different type of simplification is obtained by the use of the height, or Monge, representation, where the surface is represented by a height function, that depends on the two coordinates of a planar reference configuration [5].…”

Section: Introductionmentioning

confidence: 99%

Elastic Bending Energy: A Variational Approach

Capovilla¹

2017

JGSP

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Geometric continuum models for fluid lipid membranes are considered using classical field theory, within a covariant variational approach. The approach is cast as a higher-derivative Lagrangian formulation of continuum classical field theory, and it can be seen as a covariant version of the field theoretical variational approach that uses the height representation. This novel Lagrangian formulation is presented first for a generic reparametrization invariant geometric model, deriving its equilibrium condition equation, or shape equation, and its linear and angular stress tensors, using the classical Canham-Helfrich elastic bending energy for illustration. The robustness of the formulation is established by extending it to the presence of external forces, and to the case of heterogenous lipid membranes, breaking reparametrization invariance. In addition, a useful and compact general expression for the second variation of the free energy is obtained within the Lagrangian formulation, as a first step towards the study of the stability of membrane configurations. The simple structure of the expressions derived for the basic entities that appear in the mechanics of a lipid membrane is a direct consequence of the well established power of a Lagrangian variational approach. The paper is self-contained, and it is meant to provide, besides a new framework, also a convenient introduction to the mechanics of lipid membranes.

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“…The morphology of genus-0 vesicles has been intensively investigated, both experimentally and theoretically [14][15][16][17][18][19][20][21][22][23]. Discocyte, prolate, and stomatocyte, can be reproduced by the minimization of bending energy with area and volume constraints.…”

Section: Introductionmentioning

confidence: 99%

Construction of Nuclear Envelope Shape by a High-Genus Vesicle with Pore-Size Constraint

Noguchi

2016

Biophysical Journal

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Nuclear pores have an approximately uniform distribution in the nuclear envelope of most living cells. Hence, the morphology of the nuclear envelope is a spherical stomatocyte with a high genus. We have investigated the morphology of high-genus vesicles under pore-size constraint using dynamically triangulated membrane simulations. Bending-energy minimization without volume or other constraints produces a circular-cage stomatocyte, where the pores are aligned in a circular line on an oblate bud. As the pore radius is reduced, the circular-pore alignment is more stabilized than a random pore distribution on a spherical bud. However, we have clarified the conditions for the formation of a spherical stomatocyte: a small perinuclear volume, osmotic pressure within nucleoplasm, and repulsion between the pores. When area-difference elasticity is taken into account, the formation of cylindrical or budded tubules from the stomatocyte and discoidal stomatocyte is found.

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Recent theoretical advances in elasticity of membranes following Helfrich's spontaneous curvature model

Cited by 42 publications

References 122 publications

Black holes and biophysical (mem)-branes

Black holes and biophysical (mem)-branes

Elastic Bending Energy: A Variational Approach

Construction of Nuclear Envelope Shape by a High-Genus Vesicle with Pore-Size Constraint

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