Shape equations for axisymmetric vesicles: A clarification

Jülicher, Frank; Seifert, Udo

doi:10.1103/physreve.49.4728

Cited by 116 publications

(122 citation statements)

References 9 publications

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“…When we specialize our considerations to the Helfrich hamiltonian (40), this relation reduces to the well known first integral of the Helfrich shape equation for axially symmetric configurations (see e.g. [15,23,16]). …”

Section: Symmetriesmentioning

confidence: 99%

Stresses in lipid membranes

Capovilla

Guven

2002

J. Phys. A: Math. Gen.

169

298

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Abstract. The stresses in a closed lipid membrane described by the Helfrich hamiltonian, quadratic in the extrinsic curvature, are identified using Noether's theorem. Three equations describe the conservation of the stress tensor: the normal projection is identified as the shape equation describing equilibrium configurations; the tangential projections are consistency conditions on the stresses which capture the fluid character of such membranes. The corresponding torque tensor is also identified. The use of the stress tensor as a basis for perturbation theory is discussed. The conservation laws are cast in terms of the forces and torques on closed curves. As an application, the first integral of the shape equation for axially symmetric configurations is derived by examining the forces which are balanced along circles of constant latitude.

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Section: Symmetriesmentioning

confidence: 99%

Stresses in lipid membranes

Capovilla

Guven

2002

J. Phys. A: Math. Gen.

169

298

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“…For axisymmetric membranes, the derivation of the equations governing the shape has been standardized; see for example (Foret, 2014;Julicher and Seifert, 1994;Seifert et al, 1991). Computing the shape reduces to compute the 1D contour at a given revolution angle.…”

Section: Shape Equationsmentioning

confidence: 99%

ER Membrane Phospholipids and Surface Tension Control Cellular Lipid Droplet Formation

et al. 2017

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SUMMARYCells convert excess energy into neutral lipids that are made in the endoplasmic reticulum (ER) bilayer. The lipids are then packaged into spherical or budded lipid droplets (LDs) covered by a phospholipid monolayer containing proteins. LDs play a key role in cellular energy metabolism and homeostasis. A key unanswered question in the life of LDs is how they bud off from the ER. Here, we tackle this question by studying the budding of artificial LDs from model membranes. We find that the bilayer phospholipid composition and surface tension are key parameters of LD budding. Phospholipids have differential LD budding aptitudes, and those inducing budding decrease the bilayer tension. We observe that decreasing tension favors the egress of neutral lipids from the bilayer and LD budding. In cells, budding conditions favor the formation of small LDs. Our discovery reveals the importance of altering ER physical chemistry for controlled cellular LD formation.

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“…In equilibrated shapes such as our experimental vesicles, the force of the internal Laplace pressure is compensated by the surface tensions; consequently, both contributions drop out of the shape equations (162)(163)(164). For each phase, we integrate the mean (H) and Gaus-sian (K) curvature over the membrane patch S i occupied by that phase; the line tension contributes at the boundary ∂S of the two phases.…”

Section: (I)mentioning

confidence: 99%

“…The coordinates (r(s), z(s)) are fixed by the geometrical conditionsṙ = cos ψ(s) andż = − sin ψ(s), where dots denote derivatives with respect to the arclength. Variational calculus gives the basic shape equation (162)(163)(164):…”

Section: (I)mentioning

confidence: 99%