Global minimizers for axisymmetric multiphase membranes

Choksi, Rustum; Morandotti, Marco; Veneroni, Marco

doi:10.1051/cocv/2012042

Cited by 30 publications

(23 citation statements)

References 22 publications

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“…It can also be shown that lipid bilayers present a high level of incompressibility due to the energy penalty associated with areal stretching being significantly higher compared to membrane deformations due to bending (28). This is similar to the approach taken by Choksi et al (29) and Sarasij et al (30).…”

Section: Methodssupporting

confidence: 80%

A Biophysical Model for Plant Cell Plate Development

Jawaid

Drakakaki

Sinclair

et al. 2020

Preprint

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Plant cell division involves de novo formation of a 'cell plate' that partitions the cytoplasm of the dividing cell. Cell plate formation is directed by orchestrated delivery of cytokinetic vesicles via the phragmoplast, vesicle fusion, and membrane maturation to the nascent cell wall by the timely deposition of polysaccharides such as callose, cellulose, and crosslinking glycans. In contrast to the role of endomembrane protein regulators the role of polysaccharides, particularly callose, in cell plate development is poorly understood. It has been suggested that the transient accumulation of callose provides an anisotropic spreading force which helps the transition of earlier, membrane-network cell plate stages into a more mature fenestrated sheet stage. Here we present a biophysical model based on the Helfrich free energy for membranes that models this spreading force. We show that proper cell plate development in the model is possible, depending upon the selection of the bending modulus, with a twodimensional spreading force parameter of between 2 − 6 / , an osmotic pressure difference of 2 − 10 , and a range of spontaneous curvature between 0 − 0.04 −1 . With these conditions, we can achieve stable membrane conformations in agreement with observed sizes and morphologies corresponding to intermediate stages of cell plate development. Altogether, our mathematical model predicts that a spreading force generated by callose and/or other polysaccharides, coupled with a concurrent decrease in spontaneous curvature, is vital for the transition of a membrane network to a nearly mature cell plate. Significance StatementPlant cell division features the development of a unique membrane network called the cell plate that matures to a cell wall which separates the two daughter cells. During cell plate development, callose, a β-1-3 glucan polymer, is transiently synthesized at the cell plate only to be replaced by cellulose in mature stages. The role for this transient callose accumulation at the cell plate is unknown. It has been suggested that callose provides mechanical stability, as well as a spreading force that widens and expands tubular and fenestrated cell plate structures to aid the maturation of the cell plate. Chemical inhibition of callose deposition results in the failure of cell plate development supporting this hypothesis. This publication establishes the need for a spreading force in cell plate development using a biophysical model that predicts cell plate development in the presence and the absence of this force. Such models can potentially be used to decipher for the transition/maturation of membrane networks upon the deposition of polysaccharide polymers. Main Text

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Section: Methodssupporting

confidence: 80%

A Biophysical Model for Plant Cell Plate Development

Jawaid

Drakakaki

Sinclair

et al. 2020

Preprint

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“…After this work was completed, we became aware of the preprint [19], which studies the Γ-limit of a diffuse-interface approximation of Helfrich's functional for two-phase axisymmetric surfaces, and where many of the same technical difficulties that we encounter are addressed. We are independently treating the sharp-interface case of two-phase axisymmetric surfaces in [11].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Global minimizers for the doubly-constrained Helfrich energy: the axisymmetric case

Choksi

Veneroni

2012

Calc. Var.

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Since the pioneering work of Canham and Helfrich, variational formulations involving curvature-dependent functionals, like the classical Willmore functional, have proven useful for shape analysis of biomembranes. We address minimizers of the Canham-Helfrich functional defined over closed surfaces enclosing a fixed volume and having fixed surface area. By restricting attention to axisymmetric surfaces, we prove the existence of global minimizers.

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“…(41),T L has an obvious analogous definition and ∆T c,M are defined by Eqs. (42). By plugging these expressions into (37) and expanding for small differences we get the equation…”

Section: Appendix A: Geodesic Normal Coordinatesmentioning

confidence: 99%

“…in Refs. [37][38][39][40][41][42][43][44], and also by us in Ref. [18]) and appears to be the most popular choice within the mathematics-oriented literature.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic equilibrium of binary mixtures on curved surfaces

et al. 2019

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We study the global influence of curvature on the free energy landscape of two-dimensional binary mixtures confined on closed surfaces. Starting from a generic effective free energy, constructed on the basis of symmetry considerations and conservation laws, we identify several model-independent phenomena, such as a curvature-dependent line tension and local shifts in the binodal concentrations. To shed light on the origin of the phenomenological parameters appearing in the effective free energy, we further construct a lattice-gas model of binary mixtures on non-trivial substrates, based on the curved-space generalization of the two-dimensional Ising model. This allows us to decompose the interaction between the local concentration of the mixture and the substrate curvature into four distinct contributions, as a result of which the phase diagram splits into critical sub-diagrams. The resulting free energy landscape can admit, as stable equilibria, strongly inhomogeneous mixed phases, which we refer to as "antimixed" states below the critical temperature. We corroborate our semi-analytical findings with phase-field numerical simulations on realistic curved lattices. Despite this work being primarily motivated by recent experimental observations of multi-component lipid vesicles supported by colloidal scaffolds, our results are applicable to any binary mixture confined on closed surface of arbitrary geometry.

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Global minimizers for axisymmetric multiphase membranes

Cited by 30 publications

References 22 publications

A Biophysical Model for Plant Cell Plate Development

A Biophysical Model for Plant Cell Plate Development

Global minimizers for the doubly-constrained Helfrich energy: the axisymmetric case

Thermodynamic equilibrium of binary mixtures on curved surfaces

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