arXiv subjects

Konstantin V. Pinigin

Publications and source records attributed to Konstantin V. Pinigin.

6 recordsLinked to original sources

arXiv2026

Molecular Decomposition of the Area Compressibility Modulus of Lipid Membranes

The area compressibility modulus is a key descriptor of lipid membrane mechanics, but the molecular interactions that determine this elasticity are not evident from the total modulus alone. Here, molecular dynamics simulations of a POPC bilayer described by the coarse-grained Martini 3 force field were combined with virial stress analysis to decompose the area compressibility modulus into contributions from molecular groups and their interactions. Partial lateral tensions were evaluated as functions of membrane area strain, and their derivatives at the equilibrium state were used to obtain the corresponding contributions to the area compressibility modulus. Hydrocarbon chains provided the dominant positive contribution, accounting for approximately 70% of the total modulus, whereas water-lipid interactions contributed approximately 30%, predominantly through water-headgroup interactions. Within the bilayer, the headgroup and headgroup-chain contributions were of similar magnitude but opposite in sign and nearly canceled. Direct intermonolayer interactions contributed only about 3% of the bilayer-only modulus, indicating an almost additive elastic response of the two monolayers. The hierarchy of elastic contributions differed markedly from that of equilibrium partial tensions, showing that interactions responsible for static stress balance are not necessarily those governing membrane stiffness. This decomposition provides a microscopic interpretation of lipid bilayer area elasticity.

cond-mat.soft↗

arXiv2025

Local Mechanical Response of Lipid Membranes to Tilt Deformation

Using molecular dynamics, this study investigates the local elastic properties of transverse shear deformation of lipid membranes. The analysis demonstrates that transverse shear deformation induces anisotropy in the local stress profile of the lipid bilayer, a phenomenon attributed to the Poynting effect. By analyzing the relationship between transverse shear stress and the induced anisotropy, the local transverse shear modulus is determined. From the local transverse shear modulus, several integral elastic parameters can be derived, including the monolayer tilt modulus, tilt-curvature coupling modulus, and curvature-gradient modulus. The calculated tilt modulus values show good agreement with results from an independent analysis of lipid director fluctuations.

cond-mat.soft↗

arXiv2024

Local stress in cylindrically curved lipid membrane: insights into local versus global lateral fluidity models

Lipid membranes, fundamental to cellular function, undergo various mechanical deformations. Accurate modeling of these processes necessitates a thorough understanding of membrane elasticity. The lateral shear modulus, a critical parameter describing membrane resistance to lateral stresses, remains elusive due to the membrane's fluid nature. Two contrasting hypotheses, local fluidity and global fluidity, have been proposed. While the former suggests a zero local lateral shear modulus anywhere within lipid monolayers, the latter posits that only the integral of this modulus over the monolayer thickness vanishes. These differing models lead to distinct estimations of other elastic moduli and affect the modeling of biological processes, such as membrane fusion/fission and membrane-mediated interactions. Notably, they predict distinct local stress distributions in cylindrically curved membranes. The local fluidity model proposes isotropic local lateral stress, whereas the global fluidity model predicts anisotropy due to anisotropic local lateral stretching of lipid monolayers. Using molecular dynamics simulations, this study directly investigates these models by analyzing local stress in a cylindrically curved membrane. The results conclusively demonstrate the existence of a static local lateral shear stress and anisotropy in local lateral stress within the monolayers of the cylindrical membrane, strongly supporting the global fluidity model. These findings have significant implications for the calculation of surface elastic moduli and offer novel insights into the fundamental principles governing lipid membrane elasticity.

cond-mat.soft↗

arXiv2022

Determination of Elastic Parameters of Lipid Membranes with Molecular Dynamics: A Review of Approaches and Theoretical Aspects

Lipid membranes are abundant in living organisms, where they constitute a surrounding shell for cells and their organelles. There are many circumstances in which the deformations of lipid membranes are involved in living cells: fusion and fission, membrane-mediated interaction between membrane inclusions, lipid-protein interaction, formation of pores, etc. In all of these cases, elastic parameters of lipid membranes are important for the description of membrane deformations, as these parameters determine energy barriers and characteristic times of membrane-involved phenomena. Since the development of molecular dynamics (MD), a variety of in silico methods have been proposed for the determination of elastic parameters of simulated lipid membranes. These MD methods allow for the consideration of details unattainable in experimental techniques and represent a distinct scientific field, which is rapidly developing. This work provides a review of these MD approaches with a focus on theoretical aspects. Two main challenges are identified: (i) the ambiguity in the transition from the continuum description of elastic theories to the discrete representation of MD simulations, and (ii) the determination of intrinsic elastic parameters of lipid mixtures, which is complicated due to the composition-curvature coupling effect.

cond-mat.soft↗

arXiv2022

Local stress and elastic properties of lipid membranes obtained from elastic energy variation

A theory and computational method are provided for the calculation of lipid membranes elastic parameters, which overcomes the difficulties of the existing approaches and can be applied not only to single-component but also to multi-component membranes. It is shown that the major elastic parameters can be determined as the derivatives of the stress-profile moments with respect to stretching. The more general assumption of the global incompressibility, instead of the local one, is employed, which allows the measurement of the local Poisson's ratio from the response of the stress profile to the isotropic ambient pressure. In the case of the local incompressibility and quadratic energy law, a direct relation between the bending modulus and Gaussian curvature modulus is established.

cond-mat.soft↗

arXiv2020

Additional contributions to elastic energy of lipid membranes: Tilt-curvature coupling and curvature gradient

Lipid bilayer membranes are flexible thin laterally fluid films consisting of two unimolecular layers of lipids. On spatial scales much larger than the bilayer thickness, the membrane elasticity is well determined by its shape and adequately described by the classical Helfrich Hamiltonian. However, various local membrane heterogeneities can result in a lipids tilt relative to the membrane surface normal. On the basis of the classical elasticity theory of 3D bodies, Hamm and Kozlov [Eur. Phys. J. E 3, 323 (2000)] derived the most general energy functional, taking into account the tilt and bending. Recently, Terzi and Deserno [J. Chem. Phys. 147, 084702 (2017)] showed that Hamm and Kozlov's derivation was incomplete because the tilt-curvature coupling term had been missed. However, the energy functional derived by Terzi and Deserno appeared to be unstable, thereby being invalid for applications. Here, we derive a stable elastic energy functional, showing that the squared gradient of the curvature was missed in both of these works. This change in the energy functional arises from a more accurate consideration of the transverse shear deformation terms and their influence on the membrane stability. We also consider the influence of the prestress terms on the stability of the energy functional, and we show that the effective Gaussian curvature should be neglected because of the stability requirements. We further generalize the theory, including the stretching-compressing deformation modes, and we provide the geometrical interpretation of the terms that were previously missed by Hamm and Kozlov. The physical consequences of the new terms are analyzed in the case of a membrane-mediated interaction of two amphipathic peptides located in the same monolayer. We also provide the expression for director fluctuations, comparing it with that obtained by Terzi and Deserno.

physics.bio-ph↗