Variable tilt on lipid membranes

Rangamani, Padmini; Steigmann, David J.

doi:10.1098/rspa.2014.0463

Cited by 17 publications

(14 citation statements)

References 31 publications

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“…Further, our model accounts for the elastic free-energy of the edge of open lipid bilayers in which the lipid molecules are tilted only at the edge, forming a semicylindrical rim along it. Another generalization of the present work would include tilt fields of smaller gradient, such as those considered by Hamm and Kozlov [45], Rangamani and Steigmann [46], and Rangamani et al [47]. In such an approach, the gradual tilt at the vicinity of the edge changes the thickness of the lipid bilayer and, thus, leads to the deviation of the conformation of the edge from a semicylindrical shape.…”

Section: Discussion and Summarymentioning

confidence: 89%

“…It was demonstrated in the previous section that when the spheroidal interaction potential [27] is employed in the microphysical model, the spontaneous curvatures κ g• and κ n• , and the coefficient k 5 vanish, while the bending moduli k 1 and k 2 find the same value. Using those results in (46) yields…”

Section: Illustrative Example: Dependence Of Freeenergy On the Pore Sizementioning

confidence: 97%

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Free energy of the edge of an open lipid bilayer based on the interactions of its constituent molecules

Asgari

Biria

2015

International Journal of Non-Linear Mechanics

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Lipid-bilayers are the fundamental constituents of the walls of most living cells and lipid vesicles, giving them shape and compartment. The formation and growing of pores in a lipid bilayer have attracted considerable attention from an energetic point of view in recent years. Such pores permit targeted delivery of drugs and genes to the cell, and regulate the concentration of various molecules within the cell. The formation of such pores is caused by various reasons such as changes in cell environment, mechanical stress or thermal fluctuations. Understanding the energy and elastic behaviour of a lipid-bilayer edge is crucial for controlling the formation and growth of such pores. In the present work, the interactions in the molecular level are used to obtain the free energy of the edge of an open lipid bilayer. The resulted free-energy density includes terms associated with flexural and torsional energies of the edge, in addition to a line-tension contribution. The line tension, elastic moduli, and spontaneous normal and geodesic curvatures of the edge are obtained as functions of molecular distribution, molecular dimensions, cutoff distance, and the interaction strength. These parameters are further analyzed by implementing a soft-core interaction potential in the microphysical model. The dependence of the elastic free-energy of the edge to the size of the pore is reinvestigated through an illustrative example, and the results are found to be in agreement with the previous observations.

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Section: Discussion and Summarymentioning

confidence: 89%

Section: Illustrative Example: Dependence Of Freeenergy On the Pore Sizementioning

confidence: 97%

Free energy of the edge of an open lipid bilayer based on the interactions of its constituent molecules

Asgari

Biria

2015

International Journal of Non-Linear Mechanics

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“…Cell surface receptors, linkers, enzymatic proteins, and proteins responsible for cell adhesion [66] are all classes of integral membrane proteins and hormone receptors, Band3, rhodopsin, histocompatibility antigens, glycophorin, and Na + and K + channels are some examples of integral proteins in a cell membrane. Recent studies have shown that activity of these proteins depends on the lipid composition and membrane-protein interactions more so than previously thought [79,80], highlight the role of lipids in the activity of these molecules fundamental for biological information transfer [81][82][83].…”

Section: Integral Proteinsmentioning

confidence: 94%

Modeling Membrane-Protein Interactions

Alimohamadi¹,

Rangamani²

2018

Preprint

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In order to alter and adjust the shape of the membrane, cells harness various mechanisms of curvature generation. Many of these curvature generation mechanisms rely on the interactions between peripheral membrane proteins, integral membrane proteins, and lipids in the bilayer membrane. One of the challenges in modeling these processes is identifying the suitable constitutive relationships that describe the membrane free energy that includes protein distribution and curvature generation capability. Here, we review some of the commonly used continuum elastic membrane models that have been developed for this purpose and discuss their applications. Finally, we address some fundamental challenges that future theoretical methods need to overcome in order to push the boundaries of current model applications.

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“…∇ → z 0) as approaching the boundary. In particular, the unknown potential ξ η H q ( , , ) can be expressed as 40 The detailed procedures which can be found in [29][30][31] where μ λ = k 2 / is the natural length scale which is commonly adopted in the membrane studies (see, for example 11,14,25 ). Details regarding the dimensionless variables adopted in the present work will be discussed in later section.…”

Section: Solutions To the Linearized Systemsmentioning

confidence: 99%

“…In the present study, we assimilate data under the normalized setting using the aforementioned values. The dimensionless parameters used in the simulations are adopted from the works 11,14,25 as;…”

Section: Solutions To the Linearized Systemsmentioning

confidence: 99%

Deformation analysis of lipid membranes subjected to general forms of intra-membrane viscous flow and interactions with an elliptical-cross-section substrate

Liu

Kim

2020

Sci Rep

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We study the morphology of lipid membranes subjected to intra-membrane viscous flows and interactions with elliptical cylinder substrates. From the non-linear theory of elastic surfaces, a linearized shape equation and admissible boundary conditions are formulated in elliptical coordinates via the Monge representation of a surface. In particular, the intra-membrane viscosity terms are linearized and mapped into elliptic coordinates in order to accommodate more general forms of viscous flow. The assimilated viscous flow is characterized by potential functions which satisfies the continuity condition. A complete solution in terms of Mathieu function is then obtained within the prescription of incremental deformations superposed on large. The results describe smooth morphological transitions over the domain of interest and, more importantly, predicts wrinkle formations in the presence of intramembrane viscous flow in the surface. Lastly, the obtained solution accommodates the results from the circular cases in the limit of vanishing eccentricity and intra-membrane viscous flow.The mechanics of lipid membranes has consistently been the subject of intense research for its importance in the understanding of a wide variety of essential cellular processes 1-5 . Traditionally, it was believed that cells are surrounded by a thin oil-based barrier, yet the structure of this membrane was not well understood. In 1920s, E. Gorter and F. Grendel. 6 found that the cell membrane is composed of lipid molecules (phospholipids) which are generally divided into two important groups: the hydrophilic head parts and hydrophobic tail groups. When dispersed into aqueous solutions, lipid molecules are driven by hydrophobic effects to form a unique bilayer structure (a lipid bilayer) with opposing orientations, that maintain symmetry about a mid-surface. In fact, with the advances in electron microscopy, the bilayer structure was identified as a characteristic of all biological membranes (biomembranes) 7 . Since they are negligibly thin (typically 5-10 nm), and fragile, the study of various aspects of lipid bilayers is often achieved by employing mathematical models in order to overcome the formidable difficulties of experimental studies. Also, from a mechanical perspective, the responses of a lipid membrane can be idealized as a thin elastic film. Within this context, the development of theoretical models describing the behavior of lipid bilayers has greatly benefited from the differential geometry of a surface and the theory of an elastic surface such that the deformation of energy of a thin membrane can be expressed by the mean and Gaussian curvatures of a surface 8,9 . In particular, Helfrich proposed a well-known Helfrich energy potential 1 which addresses the symmetry of lipid bilayers and further ensures the resulting equilibrium state to be energy minimizing 10 . This, together with the use of variational principle, and the virtual-work statement, furnish the Euler-Lagrange equations also known as "membrane shape equations", which h...

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Variable tilt on lipid membranes

Cited by 17 publications

References 31 publications

Free energy of the edge of an open lipid bilayer based on the interactions of its constituent molecules

Free energy of the edge of an open lipid bilayer based on the interactions of its constituent molecules

Modeling Membrane-Protein Interactions

Deformation analysis of lipid membranes subjected to general forms of intra-membrane viscous flow and interactions with an elliptical-cross-section substrate

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