Stresses in lipid membranes

Capovilla, Riccardo; Guven, Jemal

doi:10.1088/0305-4470/35/30/302

Cited by 169 publications

(317 citation statements)

References 25 publications

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“…This result raised the interest of studying the shape equation and boundary conditions of lipid bilayer vesicles with free exposed edges. Capovilla and Guven [22] and Capovilla et al [23] studied this problem and gave the equilibrium equation and boundary conditions for open lipid bilayer vesicles. In recent papers, Yin et al [24] studied heterogeneous biomembranes with arbitrary deformation modes through differential operators and integral theorems.…”

Section: Introductionmentioning

confidence: 99%

Equilibrium Theory and Geometrical Constraint Equation for Two-Component Lipid Bilayer Vesicles

Yin

2008

J Biol Phys

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This paper aims at the general mathematical framework for the equilibrium theory of two-component lipid bilayer vesicles. To take into account the influences of the local compositions together with the mean curvature and Gaussian curvature of the membrane surface, a general potential functional is constructed. We introduce two kinds of virtual displacement modes: the normal one and the tangential one. By minimizing the potential functional, the equilibrium differential equations and the boundary conditions of two-component lipid vesicles are derived. Additionally, the geometrical constraint equation and geometrically permissible condition for the two-component lipid vesicles are presented. The physical, mathematical, and biological meanings of the equilibrium differential equations and the geometrical constraint equations are discussed. The influences of physical parameters on the geometrically permissible phase diagrams are predicted. Numerical results can be used to explain recent experiments.

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Section: Introductionmentioning

confidence: 99%

Equilibrium Theory and Geometrical Constraint Equation for Two-Component Lipid Bilayer Vesicles

Yin

2008

J Biol Phys

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“…Although institutions like the Instituto de Fisiología Celular [30][31][32] at UNAM and the Center for Research and Advanced Studies (Cinvestav) offer graduate programs in biophysics, their emphasis is more in the biological side of the subject [32,33]. With regards to BP, Cinvestav's physics department is already developing a research core [34][35][36][37][38][39], which other departments at Cinvestav are also doing research in biological physics and related issues [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57]. We also should account for the work at the biophysics group in the Instituto de Física y Matemáticas of the Universidad Michoacana San Nicolás Hidalgo [58], as well as the Instituto de Ciencias Físicas [59][60][61][62][63][64][65][66][67][68][69][70][71][72], Instituto de Física [73]…”

Section: Some Historical Remarks On Biological Physics Méxicomentioning

confidence: 99%

Biological physics in México

Hernández‐Lemus

2011

J Biol Phys

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Biological and physical sciences possess a long-standing tradition of cooperativity as separate but related subfields of science. For some time, this cooperativity has been limited by their obvious differences in methods and views. Biological physics has recently experienced a kind of revival (or better a rebirth) due to the growth of molecular research on animate matter. New avenues for research have been opened for both theoretical and experimental physicists. Nevertheless, in order to better travel for such paths, the contemporary biological physicist should be armed with a set of specialized tools and methods but also with a new attitude toward multidisciplinarity. In this review article, we intend to somehow summarize what has been done in the past (in particular, as an example we will take a closer look at the Mexican case), to show some examples of fruitful investigations in the biological physics area and also to set a proposal of new curricula for physics students and professionals interested in applying their science to get a better understanding of the physical basis of biological function.

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“…This was done in [16] by decomposing the deformation in its normal and tangential parts. Here, we provide an alternative derivation, which has the advantage of being more direct.…”

Section: Stresses and Torquesmentioning

confidence: 99%

“…In Sect. 7, we derive general expressions for the stresses and torques associated with the Hamiltonian, providing an alternative derivation of the results of [16]. The second order variation of the Hamiltonian is derived in Sect.…”

Section: Introductionmentioning

confidence: 99%

Second variation of the Helfrich–Canham Hamiltonian and reparametrization invariance

Capovilla¹,

Guven²

2004

J. Phys. A: Math. Gen.

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Abstract.A covariant approach towards a theory of deformations is developed to examine both the first and second variation of the Helfrich-Canham Hamiltonian -quadratic in extrinsic curvature -which describes fluid vesicles at mesoscopic scales. Deformations are decomposed into tangential and normal components; At first order, tangential deformations may always be identified with a reparametrization; at second order, they differ. The relationship between tangential deformations and reparametrizations, as well as the coupling between tangential and normal deformations, is examined at this order for both the metric and the extrinsic curvature tensors. Expressions for the expansion to second order in deformations of geometrical invariants constructed with these tensors are obtained; in particular, the expansion of the Hamiltonian to this order about an equilibrium is considered. Our approach applies as well to any geometrical model for membranes.

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Stresses in lipid membranes

Cited by 169 publications

References 25 publications

Equilibrium Theory and Geometrical Constraint Equation for Two-Component Lipid Bilayer Vesicles

Equilibrium Theory and Geometrical Constraint Equation for Two-Component Lipid Bilayer Vesicles

Biological physics in México

Second variation of the Helfrich–Canham Hamiltonian and reparametrization invariance

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