The curvature elasticity of fluid membranes : A catalogue of vesicle shapes

Deuling, H.J.; Helfrich, W.

doi:10.1051/jphys:0197600370110133500

Cited by 414 publications

(291 citation statements)

References 8 publications

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“…The formation occurs either spontaneously [1,9] or under slight and probably immaterial agitation [11,12], Also, the complete mathematical analysis [13,14] of photographed shapes of axi-symmetric, oblate vesicles of egg lecithin whose membrane was in contact with itself over a certain area did not provide any evidence of mutual attraction. The membranes of these vesicles were judged from experience to consist of only a few bilayers.…”

Section: Discussionmentioning

confidence: 97%

“…The membranes of these vesicles were judged from experience to consist of only a few bilayers. Accordingly, the total curvatureelastic energy residing in a membrane was probably of the order of a few 10 -10 erg [13,14]. For the approximate area of contact of 100 fjt 2 and a membrane spacing of 27.5 A, one computes from (70) a cohesion energy of 185 • 10~1 0 erg.…”

Section: Discussionmentioning

confidence: 99%

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Steric Interaction of Fluid Membranes in Multilayer Systems

Helfrich

1978

Zeitschrift Für Naturforschung A

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1,058

435

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The out-of-plane fluctuations of fluid membranes are sterically hindered in multilayer systems. The repulsive interaction associated with the steric or excluded-volume effect is studied theoretically by two methods. The interaction energy per unit area of membrane is derived as a function of temperature, membrane curvature elasticity and mean membrane spacing; it is inversely proportional to the square of the latter. Steric repulsion is estimated for lecithin bilayers in water. There and in other cases, it may compete with van der Waals attraction.

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Section: Discussionmentioning

confidence: 97%

Section: Discussionmentioning

confidence: 99%

Steric Interaction of Fluid Membranes in Multilayer Systems

Helfrich

1978

Zeitschrift Für Naturforschung A

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1,058

435

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“…Such shapes can be predicted by a mathematical procedure (Deuling and Helfrich, 1976) in which the shape with the minimum energy is found essentially by scanning theoretically over all possible shapes. In the minimization procedure, the only role is played by the first term in Eq.…”

Section: Spontaneous Curvature Model Of Vesicle Shapesmentioning

confidence: 99%

Shape behavior of lipid vesicles as the basis of some cellular processes

Svetina

Žekš

2002

Anat. Rec.

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The basic principles that govern the shape behavior of phospholipid vesicle shapes are discussed. The important membrane parameters of the system are defined by presenting the expressions for the relevant contributions to the system's mechanical energy. In the description of the rather unique shape behavior of lipid vesicles, the emphasis is on providing a qualitative understanding of the dependence of vesicle shape on the parameters of the system. The vesicle shape behavior is then related to biologically important phenomena. Some examples are given of how the results of the shape behavior of lipid vesicles can be applied to the analysis of cellular systems. Red blood cell shape and shape transformations, vesicle fission and fusion processes, and the phenomenon of cellular polarity are considered. It is reasoned that the current biological processes that involve changes of membrane conformation may have their origin in the general shape behavior of closed lamellar membranes. Anat Rec 268: 215-225, 2002.

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“…Their shape is determined by the minimum of the bending energy of the membrane subject to constraints on the total area and the enclosed volume (for reviews, see [1 -3]). In the so-called spontaneous curvature model, the bending energy is given by [4,5] This paper is organized as follows. In Sec.…”

Section: Introductionmentioning

confidence: 99%

Shape equations for axisymmetric vesicles: A clarification

1994

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We derive the shape equations for axisymmetric vesicles and show that they are identical to the general shape equation [Ou-Yang Zhong-Can and W. Helfrich, Phys. Rev. A 39, 5280 (1989)] specialized to axisymmetry.We consider three difFerent topologies (an axisymmetric membrane segment suspended between two circular rings and closed vesicles of spherical and toroidal topology). We point out that the shape equations are independent of the variational method used.

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The curvature elasticity of fluid membranes : A catalogue of vesicle shapes

Cited by 414 publications

References 8 publications

Steric Interaction of Fluid Membranes in Multilayer Systems

Steric Interaction of Fluid Membranes in Multilayer Systems

Shape behavior of lipid vesicles as the basis of some cellular processes

Shape equations for axisymmetric vesicles: A clarification

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