The Membrane-Mediated Interaction of Liquid-Ordered Lipid Domains in the Presence of Amphipathic Peptides.

The lipid membranes of living cells are composed of a large number of lipid types and can undergo phase separation with the formation of nanometer-scale liquid-ordered lipid domains, also called rafts. Raft coalescence, i.e., the fusion of lipid domains, is involved in important cell processes, such as signaling and trafficking. In this work, within the framework of the theory of elasticity of lipid membranes, we explore how amphipathic peptides adsorbed on lipid membranes may affect the domain-domain fusion processes. We show that the elastic deformations of lipid membranes drive amphipathic peptides to the boundary of lipid domains, which leads to an increase in the average energy barrier of the domain-domain fusion, even if the surface concentration of amphipathic peptides is low and the domain boundaries are only partially occupied by the peptides. This inhibition of the fusion of lipid domains may lead to negative side effects of using amphipathic peptides as antimicrobial agents.

Determination of elastic parameters of lipid membranes from simulation under varied external pressure.

Many cellular processes such as endocytosis, exocytosis, and vesicle trafficking involve membrane deformations, which can be analyzed in the framework of the elastic theories of lipid membranes. These models operate with phenomenological elastic parameters. A connection between these parameters and the internal structure of lipid membranes can be provided by three-dimensional (3D) elastic theories. Considering a membrane as a 3D layer, Campelo et al. [F. Campelo et al., Adv. Colloid Interface Sci. 208, 25 (2014)10.1016/j.cis.2014.01.018] developed a theoretical basis for the calculation of elastic parameters. In this work we generalize and improve this approach by considering a more general condition of global incompressibility instead of local incompressibility. Crucially, we find an important correction to the theory of Campelo et al., which if not taken into account leads to a significant miscalculation of elastic parameters. With the total volume conservation taken into account, we derive an expression for the local Poisson's ratio, which determines how the local volume changes upon stretching and permits a more precise determination of elastic parameters. Also, we substantially simplify the procedure by calculating the derivatives of the moments of the local tension with respect to stretching instead of calculating the local stretching modulus. We obtain a relation between the Gaussian curvature modulus as a function of stretching and the bending modulus, showing that these two elastic parameters are not independent, as was previously assumed. The proposed algorithm is applied to membranes composed of pure dipalmitoylphosphatidylcholine (DPPC), dioleoylphosphatidylcholine (DOPC), and their mixture. The following elastic parameters of these systems are obtained: the monolayer bending and stretching moduli, spontaneous curvature, neutral surface position, and local Poisson's ratio. It is shown that the bending modulus of the DPPC/DOPC mixture follows a more complex trend than predicted by the classical Reuss averaging, which is often employed in theoretical frameworks.

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.

Characteristic lengths of transmembrane peptides controlling their tilt and lateral distribution between membrane domains.

Lipids and proteins of plasma membranes of eukaryotic cells are supposed to form protein-lipid domains, characterized by a different molecular order, bilayer thickness, and elastic parameters. Several mechanisms of preferable distribution of transmembrane proteins to the ordered or disordered membrane domains have been revealed. The mismatch between the length of the protein transmembrane domain and hydrophobic thickness of the lipid bilayer is considered to be an important driving force of protein lateral sorting. Utilizing the continuum theory of elasticity, we analyzed optimal configurations and preferable membrane domains for single-pass transmembrane peptides of various hydrophobic lengths and effective molecular shapes. We obtained that short transmembrane peptides stand perpendicularly to the membrane plane. The exceedance of a certain characteristic length leads to the tilt of the peptide. This length depends on the bilayer thickness. Thus, in the membrane with coexisting ordered (thicker) and disordered (thinner) phases tilting of the peptide in each phase is governed by its individual characteristic length. The lateral distribution of the peptides between ordered and disordered membrane domains is shown to be described by two additional characteristic lengths. The exceedance of the smaller one drives the peptide towards a more ordered and thicker membrane, while the exceedance of the larger characteristic length switches the preferable membrane domain from ordered and thicker to disordered and thinner. Thus, membrane proteins with long enough transmembrane domains are predicted to accumulate in the thinner disordered membrane as compared to the thicker ordered bilayer. For hourglass-like and barrel-like shaped transmembrane peptides the specific regime of sorting was obtained: the peptides distributed almost equally between the phases in a wide range of peptide lengths. This finding allowed explaining the experimental data on lateral distribution of transmembrane peptide tLAT.

Amphipathic Peptides Impede Lipid Domain Fusion in Phase-Separated Membranes.

Cell membranes are heterogeneous in lipid composition which leads to the phase separation with the formation of nanoscopic liquid-ordered domains, also called rafts. There are multiple cell processes whereby the clustering of these domains into a larger one might be involved, which is responsible for such important processes as signal transduction, polarized sorting, or immune response. Currently, antimicrobial amphipathic peptides are considered promising antimicrobial, antiviral, and anticancer therapeutic agents. Here, within the framework of the classical theory of elasticity adapted for lipid membranes, we investigate how the presence of the peptides in a phase-separated membrane influences the fusion of the domains. We show that the peptides tend to occupy the boundaries of liquid-ordered domains and significantly increase the energy barrier of the domain-domain fusion, which might lead to misregulation of raft clustering and adverse consequences for normal cell processes.

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

Lipid bilayer membranes under biologically relevant conditions are flexible thin laterally fluid films consisting of two unimolecular layers (monolayers) each about 2 nm thick. On spatial scales much larger than the bilayer thickness, the membrane elasticity is well determined by its shape. The classical Helfrich theory considers the membrane as an elastic two-dimensional (2D) film, which has no particular internal structure. 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)10.1007/s101890070003] derived the most general energy functional, taking into account the tilt and lipid monolayer curvature. Recently, Terzi and Deserno [J. Chem. Phys. 147, 084702 (2017)10.1063/1.4990404] 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 that require minimizations of the overall energy of deformations. 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 it should be considered small and 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.

Elastic deformations mediate interaction of the raft boundary with membrane inclusions leading to their effective lateral sorting.

Liquid-ordered lipid domains represent a lateral inhomogeneity in cellular membranes. These domains have elastic and physicochemical properties different from those of the surrounding membrane. In particular, their thickness exceeds that of the disordered membrane. Thus, elastic deformations arise at the domain boundary in order to compensate for the thickness mismatch. In equilibrium, the deformations lead to an incomplete register of monolayer ordered domains: the elastic energy is minimal if domains in opposing monolayers lie on the top of each other, and their boundaries are laterally shifted by about 3 nm. This configuration introduces a region, composed of one ordered and one disordered monolayers, with an intermediate bilayer thickness. Besides, a jump in a local monolayer curvature takes place in this intermediate region, concentrating here most of the elastic stress. This region can participate in a lateral sorting of membrane inclusions by offering them an optimal bilayer thickness and local curvature conditions. In the present study, we consider the sorting of deformable lipid inclusions, undeformable peripheral and deeply incorporated peptide inclusions, and undeformable transmembrane inclusions of different molecular geometry. With rare exceptions, all types of inclusions have an affinity to the ordered domain boundary as compared to the bulk phases. The optimal lateral distribution of inclusions allows relaxing the elastic stress at the boundary of domains.