On the variational theory of cell-membrane equilibria

Steigmann, David J.; Baesu, Eveline; Rudd, Robert E.; Belak, J.; McElfresh, M.

doi:10.4171/ifb/83

Cited by 85 publications

(113 citation statements)

References 14 publications

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“…• The membrane is impermeable (no osmosis), the number of molecules remains fixed in each layer, and the energetic cost of stretching or compressing the membrane is much larger than the cost of bending deformations [33,23,35]. As a consequence, the membrane γ minimizes its bending energy under global area A(γ) = γ 1 and volume V(γ) = 1 3 γ x · ν constraints.…”

Section: The Canham-helfrich Energymentioning

confidence: 99%

Dynamics of Biomembranes: Effect of the Bulk Fluid

Bonito

Nochetto

Pauletti

2011

Math. Model. Nat. Phenom.

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Abstract. We derive a biomembrane model consisting of a fluid enclosed by a lipid membrane. The membrane is characterized by its Canham-Helfrich energy (Willmore energy with area constraint) and acts as a boundary force on the Navier-Stokes system modeling an incompressible fluid. We give a concise description of the model and of the associated numerical scheme. We provide numerical simulations with emphasis on the comparisons between different types of flow: the geometric model which does not take into account the bulk fluid and the biomembrane model for two different regimes of parameters.

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Section: The Canham-helfrich Energymentioning

confidence: 99%

Dynamics of Biomembranes: Effect of the Bulk Fluid

Bonito

Nochetto

Pauletti

2011

Math. Model. Nat. Phenom.

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“…In contrast, in the procedure adopted universally in the literature, the shape equation is derived as the Euler equation associated with the variational problem of minimizing the energy of a uniform film under appropriate side conditions (Ou-Yang et al 1999). A recent derivation of this kind, extending the argument from a commonly imposed global area constraint to the local version assumed here, has been presented in Steigmann et al (2003). This too is restricted to films with properties that are uniform in the sense that the energy density W on ω does not depend explicitly on the coordinates.…”

Section: Variational Approachmentioning

confidence: 99%

“…In Steigmann et al (2003) the pressure p appearing in (12) is a (constant) Lagrange multiplier enforcing a global constraint on the volume enclosed by the film, considered there to be a closed surface. However, typically the concern is with circumstances in which the volume-to-area ratio adjusts in response to changes in temperature or osmotic pressure.…”

Section: Variational Approachmentioning

confidence: 99%

Modeling protein-mediated morphology in biomembranes

Agrawal

Steigmann

2008

Biomech Model Mechanobiol

114

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The equilibrium theory for lipid membranes is used to describe the structure of nuclear pores and the membrane shapes accompanying endocytosis. The commonly used variant of the theory contains a fixed parameter called the spontaneous curvature which accounts for asymmetry in the bending response of the membrane. This is replaced here by a variable distribution of spontaneous curvature representing the influence of attached proteins. The required adjustments to the standard theory are described and the resulting model is applied to the study of membrane morphology at the cites of protein-assisted nuclear pore formation and endocytosis.

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“…In Steigmann et al (2003) a similar model to ours here is studied. First, we must repeat that both λ and p should be considered as functions, rather than constants, and here we have treated them as such only for simplicity.…”

Section: For Example) It Is Reported Inmentioning

confidence: 99%

Rigidity and stability of spheres in the Helfrich model

Bernard

Wheeler

2018

Interfaces Free Bound.

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The Helfrich functional, denoted by Hc0, is a mathematical expression proposed by Helfrich (1973) for the natural free energy carried by an elastic phospholipid bilayer. Helfrich theorises that idealised elastic phospholipid bilayers minimise Hc0 among all possible configurations. The functional integrates a spontaneous curvature parameter c0 together with the mean curvature of the bilayer and constraints on area and volume, either through an inclusion of osmotic pressure difference and tensile stress or otherwise. Using the mathematical concept of embedded orientable surface to represent the configuration of the bilayer, one might expect to be able to adapt methods from differential geometry and the calculus of variations to perform a fine analysis of bilayer configurations in terms of the parameters that it depends upon. In this article we focus upon the case of spherical red blood cells with a view to better understanding spherocytes and spherocytosis. We provide a complete classification of spherical solutions in terms of the parameters in the Helfrich model. We additionally present some further analysis on the rigidity and stability of spherocytes. Helfrich (1973) for the natural free energy carried by an elastic phospholipid bilayer. Helfrich theorises that idealised elastic phospholipid bilayers minimise H c 0 among all possible configurations. The functional integrates a spontaneous curvature parameter c 0 together with the mean curvature of the bilayer and constraints on area and volume, either through an inclusion of osmotic pressure difference and tensile stress or otherwise. Using the mathematical concept of embedded orientable surface to represent the configuration of the bilayer, one might expect to be able to adapt methods from differential geometry and the calculus of variations to perform a fine analysis of bilayer configurations in terms of the parameters that it depends upon. In this article we focus upon the case of spherical red blood cells with a view to better understanding spherocytes and spherocytosis. We provide a complete classification of spherical solutions in terms of the parameters in the Helfrich model. We additionally present some further analysis on the rigidity and stability of spherocytes. Disciplines Engineering | Science and Technology Studies

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On the variational theory of cell-membrane equilibria

Cited by 85 publications

References 14 publications

Dynamics of Biomembranes: Effect of the Bulk Fluid

Dynamics of Biomembranes: Effect of the Bulk Fluid

Modeling protein-mediated morphology in biomembranes

Rigidity and stability of spheres in the Helfrich model

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