Geometry and dynamics of lipid membranes: The Scriven-Love number

Sahu, Amaresh; Glisman, Alec; Tchoufag, Joël; Mandadapu, Kranthi K.

doi:10.1103/physreve.101.052401

Cited by 14 publications

(12 citation statements)

References 77 publications

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“…In this section, the accuracy of the (2 + δ)-dimensional theory is tested on flat geometries, cylinders, and spheres, which are common lipid membrane geometries encountered in both theory and experiments [7,[47][48][49][50]. Section 5.1 considers examples with analytical solutions while Sec.…”

Section: Comparison To Three-dimensional Gauss Lawmentioning

confidence: 99%

The $(2 + δ)$-dimensional theory of the electromechanics of lipid membranes: I. Electrostatics

Omar¹,

G.²,

Mandadapu³

2023

Preprint

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The coupling of electric fields to the mechanics of lipid membranes gives rise to intriguing electromechanical behavior, as, for example, evidenced by the deformation of lipid vesicles in external electric fields. Electromechanical effects are relevant for many biological processes, such as the propagation of action potentials in axons and the activation of mechanically-gated ion channels. Currently, a theoretical framework describing the electromechanical behavior of arbitrarily curved and deforming lipid membranes does not exist. Purely mechanical models commonly treat lipid membranes as two-dimensional surfaces, ignoring their finite thickness. While holding analytical and numerical merit, this approach cannot describe the coupling of lipid membranes to electric fields and is thus unsuitable for electromechanical models. In a sequence of articles, we derive an effective surface theory of the electromechanics of lipid membranes, named a (2 + δ)-dimensional theory, which has the advantages of surface descriptions while accounting for finite thickness effects. The present article proposes a new, generic dimensionreduction procedure relying on low-order spectral expansions. This procedure is applied to the electrostatics of lipid membranes to obtain a (2 + δ)-dimensional theory that captures potential differences across and electric fields within lipid membranes. This new model is tested on different geometries relevant for lipid membranes, showing good agreement with the corresponding three-dimensional electrostatics theory.

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Section: Comparison To Three-dimensional Gauss Lawmentioning

confidence: 99%

The $(2 + δ)$-dimensional theory of the electromechanics of lipid membranes: I. Electrostatics

Omar¹,

G.²,

Mandadapu³

2023

Preprint

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“…This means that tangential flows can generate motion in the normal di-rection on curved surfaces [94,95]. The dimensionless number associated with these out-of-plane forces is often called the Scriven-Love number [96,97].…”

Section: A Passive Surfacesmentioning

confidence: 99%

Active Flows and Deformable Surfaces in Development

Al-Izzi¹,

Morris²

2021

Preprint

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We review progress in active hydrodynamic descriptions of flowing media on curved and deformable manifolds: the state-of-the-art in continuum descriptions of single-layers of epithelial and/or other tissues during development. First, after a brief overview of activity, flows and hydrodynamic descriptions, we highlight the generic challenge of identifying the dependence on dynamical variables of so-called active kinetic coefficients-active counterparts to dissipative Onsager coefficients. We go on to describe some of the subtleties concerning how curvature and active flows interact, and the issues that arise when surfaces are deformable. We finish with a broad discussion around the utility of such theories in developmental biology. This includes limitations to analytical techniques, challenges associated with numerical integration, fitting-to-data and inference, and potential tools for the future, such as discrete differential geometry.

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“…Mathematically, the development of theory that couples hydrodynamics to surface geometry has led to many interesting predictions on the role of viscous forces in the ordering and shaping of membranes in both isotropic (Steigmann 1999;Hu, Zhang & Weinan 2007;Arroyo & DeSimone 2009;Rangamani et al 2013;Sahu et al 2020a;Tchoufag, Sahu & Mandadapu 2022) and ordered (Napoli & Vergori 2016;Nestler & Voigt 2022) fluids. Of particular note has been the inclusion of activity, leading to a variety of interesting morphodynamical phenomena and instabilities (Salbreux & Jülicher 2017;Bächer et al 2021;Khoromskaia & Salbreux 2023;Rank & Voigt 2021;Alert 2022;Bell et al 2022;Hoffmann et al 2022;Nestler & Voigt 2022;Salbreux et al 2022;Vafa & Mahadevan 2022) and even some attempts to construct rigorous shell theories of active materials (da Rocha, Bleyer & Turlier 2022).…”

Section: Introductionmentioning

confidence: 99%

Morphodynamics of active nematic fluid surfaces

Al-Izzi

Morris

2023

J. Fluid Mech.

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Morphodynamic equations governing the behaviour of active nematic fluids on deformable curved surfaces are constructed in the large deformation limit. Emphasis is placed on the formulation of objective rates that account for normal deformations whilst ensuring that tangential flows are Eulerian, and the use of the surface derivative (rather than the covariant derivative) in the nematic free energy, which elastically couples local order to out-of-plane bending of the surface. Focusing on surface geometry and its dynamical interplay with the hydrodynamics, several illustrative instabilities are then characterised. These include cases where the role of the Scriven–Love number and its nematic analogue are non-negligible, and where the active nematic forcing can be characterised by an analogue of the Föppl–von Kármán number. For the former, flows and changes to the nematic texture are coupled to surface geometry by viscous dissipation. This is shown to result in non-trivial relaxation dynamics for a nematic tube. For the latter, the nematic active forcing couples to the surface bending terms of the nematic free energy, resulting in extensile (active ruffling) and contractile (active pearling) instabilities in the tube shape, as well as active bend instabilities in the nematic texture. In comparison to the flat case, such bend instabilities now have a threshold set by the extrinsic curvature of the tube. Finally, we examine a topological defect located on an almost flat surface, and show that there exists a steady state where a combination of defect elasticity, activity and non-negligible spin connection drive a shape change in the surface.

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Geometry and dynamics of lipid membranes: The Scriven-Love number

Cited by 14 publications

References 77 publications

The $(2 + δ)$-dimensional theory of the electromechanics of lipid membranes: I. Electrostatics

The $(2 + δ)$-dimensional theory of the electromechanics of lipid membranes: I. Electrostatics

Active Flows and Deformable Surfaces in Development

Morphodynamics of active nematic fluid surfaces

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