An analysis of lipid membrane morphology in the presence of coordinate-dependent non-uniformity

2020 ◽  
Vol 26 (1) ◽  
pp. 45-61
Author(s):  
Wenhao Yao ◽  
Chun IL Kim
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Linear Model ◽  
Energy Function ◽  
Lipid Membranes ◽  
Lipid Membrane ◽  
Membrane Interactions ◽  
Equilibrium Equations ◽  
Material Parameters ◽  
Membrane Morphology

A model for the mechanics of lipid membranes with non-uniform (coordinate-dependent) properties is discussed. The coordinate-dependent responses of the membranes are incorporated via the augmented non-uniform energy function and material parameters, which are dependent explicitly on the surface coordinates. We formulate the associated normal and tangential Euler equilibrium equations through which the coordinate-dependent responses of membranes are characterized. The admissible boundary conditions are taken from the existing non-linear model but reformulated and adopted to the present framework. Within the prescription of superposed incremental deformations, a compatible linear model is also formulated, from which a complete analytical solution describing the non-uniform responses of the membrane subjected to substrate–membrane interactions is obtained.

An Efficient Semi-Analytical Method to Compute Displacements and Stresses in an Elastic Half-Space with a Hemispherical Pit

2015 ◽  
Vol 7 (3) ◽  
pp. 295-322 ◽  
Author(s):  
Valeria Boccardo ◽  
Eduardo Godoy ◽  
Mario Durán
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Half Space ◽  
Plane Surface ◽  
Elastic Half Space ◽  
Numerical Results ◽  
Quadratic Functional ◽  
Infinite Plane ◽  
Equilibrium Equations ◽  
Finite Element Software

AbstractThis paper presents an efficient method to calculate the displacement and stress fields in an isotropic elastic half-space having a hemispherical pit and being subject to gravity. The method is semi-analytical and takes advantage of the axisymmetry of the problem. The Boussinesq potentials are used to obtain an analytical solution in series form, which satisfies the equilibrium equations of elastostatics, traction-free boundary conditions on the infinite plane surface and decaying conditions at infinity. The boundary conditions on the free surface of the pit are then imposed numerically, by minimising a quadratic functional of surface elastic energy. The minimisation yields a symmetric and positive definite linear system of equations for the coefficients of the series, whose particular block structure allows its solution in an efficient and robust way. The convergence of the series is verified and the obtained semi-analytical solution is then evaluated, providing numerical results. The method is validated by comparing the semi-analytical solution with the numerical results obtained using a commercial finite element software.

scholarly journals Notes on superposed incremental deformations in the mechanics of lipid membranes

2017 ◽  
Vol 24 (1) ◽  
pp. 181-194 ◽  
Author(s):  
Mahdi Zeidi ◽  
Chun IL Kim
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Lipid Membranes ◽  
Membrane System ◽  
Parametric Representation ◽  
Radius Of Convergence ◽  
Complete Analysis ◽  
Finite Domain ◽  
Morphological Transitions ◽  
Excellent Stability

We present an analysis of the superposed incremental deformations of lipid membranes in contact with a circular substrate. A complete analytical solution describing the morphological transitions of lipid membranes is obtained via Monge parametric representation and admissible linearization. The corresponding solution demonstrates smooth and bounded behavior within the finite domain of interest (annular) and, more importantly, shows excellent stability as it approaches the boundary of the circular substrate with the radius of convergence compatible with a few nanometers. Under the prescription of the superposed incremental deformations, a complete analysis of the necessary boundary conditions, the anchoring condition of the lipid molecules on an edge, and other geometrical quantities of the membrane is illustrated for the case of the circular substrate–membrane system.

scholarly journals Anionic nanoparticle-lipid membrane interactions: the protonation of anionic ligands at the membrane surface reduces membrane disruption

RSC Advances ◽  
2019 ◽  
Vol 9 (25) ◽  
pp. 13992-13997 ◽  
Author(s):  
Sebastian Salassi ◽  
Ester Canepa ◽  
Riccardo Ferrando ◽  
Giulia Rossi
Keyword(s):  
Lipid Membranes ◽  
Au Nanoparticles ◽  
Lipid Membrane ◽  
Membrane Surface ◽  
Membrane Disruption ◽  
Membrane Interactions ◽  
Carboxylate Groups ◽  
Model Lipid Membranes ◽  
Anionic Ligands

The interaction between anionic Au nanoparticles and model lipid membranes is facilitated by the spontaneous protonation of the NP ligand carboxylate groups, COO−˙ → COOH, in the lipid headgroup region.

scholarly journals Rapid evaluation of gold nanoparticle–lipid membrane interactions using a lipid/polydiacetylene vesicle sensor

The Analyst ◽  
2020 ◽  
Vol 145 (8) ◽  
pp. 3049-3055
Author(s):  
Congcong Gu ◽  
Yingying Geng ◽  
Feng Zheng ◽  
Vincent M. Rotello
Keyword(s):  
Gold Nanoparticles ◽  
Gold Nanoparticle ◽  
Lipid Membranes ◽  
Lipid Membrane ◽  
Rapid Evaluation ◽  
Membrane Interactions

Lipid/polydiacetylene vesicles serve as a sensor to rapidly measure the interactions between gold nanoparticles and lipid membranes. A colorimetric signal is generated upon membrane disturbance caused by gold nanoparticles.

scholarly journals Mechanics of Lipid Membranes under the Influence of Intramembrane Viscosity

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Chun Il Kim ◽  
Zhe Liu
Keyword(s):  
Boundary Conditions ◽  
Lipid Membranes ◽  
Deformation Energy ◽  
Second Fundamental Form ◽  
Viscous Effects ◽  
Equilibrium Equations ◽  
Admissible Sets ◽  
Elastic Boundary ◽  
Edge Conditions ◽  
Frame Work

We discuss a continuum-based model describing the deformations of lipid membranes subjected to intramembrane viscosity. Within the frame work of the theory of an elastic surface, the membrane equilibrium equations and the expressions of viscous stress are obtained. The corresponding deformation energy of the membrane is computed via the first and second fundamental form of surface. A compatible linear model is also formulated within the prescription of superposed incremental deformations through which the deformation profiles of the membrane is obtained. It is shown that the intramembrane viscous flow gives rise to straining effects on the membranes. Further, the corresponding dynamic edge conditions reduce to purely elastic boundary conditions in the limit of vanishing viscous effects. Lastly, admissible sets of velocity fields are also examined and are used to formulate membrane shape equations and the associated dynamic boundary conditions.

scholarly journals Superposed Incremental Deformations of an Elastic Solid Reinforced with Fibers Resistant to Extension and Flexure

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Chun IL Kim
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Linear Model ◽  
Analytical Solutions ◽  
Elastic Solid ◽  
Fiber Reinforced Composites ◽  
Reinforced Composites ◽  
Equilibrium Equations ◽  
Systems Of Differential Equations ◽  
Plane Deformations

A comprehensive linear model for an elastic solid reinforced with fibers resistant to extension and flexure is presented. This includes the analysis of both unidirectional and bidirectional fiber-reinforced composites subjected to in-plane deformations. Within the prescription of the superposed incremental deformations, the fiber kinematics are approximated and used to determine the Euler equilibrium equations. The constraints of bulk incompressibility and admissible boundary conditions are also discussed for completeness. In particular, the complete systems of differential equations are obtained for the cases of Neo-Hookean and Mooney–Rivlin types of materials from which analytical solutions can be obtained.

scholarly journals Electrochemical Properties of Lipid Membranes Self-Assembled from Bicelles

Membranes ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 11
Author(s):  
Damian Dziubak ◽  
Kamil Strzelak ◽  
Slawomir Sek
Keyword(s):  
Electrochemical Properties ◽  
Self Assembly ◽  
Lipid Membranes ◽  
Lipid Membrane ◽  
Membrane Resistance ◽  
Electrochemical Characteristics ◽  
Freeze Thaw ◽  
Lipid Films ◽  
Supported Lipid Membranes

Supported lipid membranes are widely used platforms which serve as simplified models of cell membranes. Among numerous methods used for preparation of planar lipid films, self-assembly of bicelles appears to be promising strategy. Therefore, in this paper we have examined the mechanism of formation and the electrochemical properties of lipid films deposited onto thioglucose-modified gold electrodes from bicellar mixtures. It was found that adsorption of the bicelles occurs by replacement of interfacial water and it leads to formation of a double bilayer structure on the electrode surface. The resulting lipid assembly contains numerous defects and pinholes which affect the permeability of the membrane for ions and water. Significant improvement in morphology and electrochemical characteristics is achieved upon freeze–thaw treatment of the deposited membrane. The lipid assembly is rearranged to single bilayer configuration with locally occurring patches of the second bilayer, and the number of pinholes is substantially decreased. Electrochemical characterization of the lipid membrane after freeze–thaw treatment demonstrated that its permeability for ions and water is significantly reduced, which was manifested by the relatively high value of the membrane resistance.

scholarly journals Interactions of Linear Analogues of Battacin with Negatively Charged Lipid Membranes

Membranes ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 192
Author(s):  
Kinga Burdach ◽  
Dagmara Tymecka ◽  
Aneta Urban ◽  
Robert Lasek ◽  
Dariusz Bartosik ◽  
...  
Keyword(s):  
Lipid Membranes ◽  
Liquid Crystalline ◽  
Lipid Membrane ◽  
Attenuated Total Reflection ◽  
Gram Positive ◽  
Insertion Depth ◽  
Force Microscopy ◽  
Acyl Chains ◽  
Hydrophobic Portion ◽  
Membrane Fluidization

The increasing resistance of bacteria to available antibiotics has stimulated the search for new antimicrobial compounds with less specific mechanisms of action. These include the ability to disrupt the structure of the cell membrane, which in turn leads to its damage. In this context, amphiphilic lipopeptides belong to the class of the compounds which may fulfill this requirement. In this paper, we describe two linear analogues of battacin with modified acyl chains to tune the balance between the hydrophilic and hydrophobic portion of lipopeptides. We demonstrate that both compounds display antimicrobial activity with the lowest values of minimum inhibitory concentrations found for Gram-positive pathogens. Therefore, their mechanism of action was evaluated on a molecular level using model lipid films mimicking the membrane of Gram-positive bacteria. The surface pressure measurements revealed that both lipopeptides show ability to bind and incorporate into the lipid monolayers, resulting in decreased ordering of lipids and membrane fluidization. Atomic force microscopy (AFM) imaging demonstrated that the exposure of the model bilayers to lipopeptides leads to a transition from the ordered gel phase to disordered liquid crystalline phase. This observation was confirmed by attenuated total reflection Fourier-transform infrared spectroscopy (ATR-FTIR) results, which revealed that lipopeptide action causes a substantial increase in the average tilt angle of lipid acyl chains with respect to the surface normal to compensate for lipopeptide insertion into the membrane. Moreover, the peptide moieties in both molecules do not adopt any well-defined secondary structure upon binding with the lipid membrane. It was also observed that a small difference in the structure of a lipophilic chain, altering the balance between hydrophobic and hydrophilic portion of the molecules, results in different insertion depth of the active compounds.

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