Internal configuration and electric potential in planar negatively charged lipid head group region in contact with ionic solution

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.

The Effect of the Osmotically Active Compound Concentration Difference on the Passive Water and Proton Fluxes across a Lipid Bilayer

The molecular details of the passive water flux across the hydrophobic membrane interior are still a matter of debate. One of the postulated mechanisms is the spontaneous, water-filled pore opening, which facilitates the hydrophilic connection between aqueous phases separated by the membrane. In the paper, we provide experimental evidence showing that the spontaneous lipid pore formation correlates with the membrane mechanics; hence, it depends on the composition of the lipid bilayer and the concentration of the osmotically active compound. Using liposomes as an experimental membrane model, osmotically induced water efflux was measured with the stopped-flow technique. Shapes of kinetic curves obtained at low osmotic pressure differences are interpreted in terms of two events: the lipid pore opening and water flow across the aqueous channel. The biological significance of the dependence of the lipid pore formation on the concentration difference of an osmotically active compound was illustrated by the demonstration that osmotically driven water flow can be accompanied by the dissipation of the pH gradient. The application of the Helfrich model to describe the probability of lipid pore opening was validated by demonstrating that the probability of pore opening correlates with the membrane bending rigidity. The correlation was determined by experimentally derived bending rigidity coefficients and probabilities of lipid pores opening.

Mechanical and Electrical Interaction of Biological Membranes with Nanoparticles and Nanostructured Surfaces

In this review paper, we theoretically explain the origin of electrostatic interactions between lipid bilayers and charged solid surfaces using a statistical mechanics approach, where the orientational degree of freedom of lipid head groups and the orientational ordering of the water dipoles are considered. Within the modified Langevin Poisson–Boltzmann model of an electric double layer, we derived an analytical expression for the osmotic pressure between the planar zwitterionic lipid bilayer and charged solid planar surface. We also show that the electrostatic interaction between the zwitterionic lipid head groups of the proximal leaflet and the negatively charged solid surface is accompanied with a more perpendicular average orientation of the lipid head-groups. We further highlight the important role of the surfaces’ nanostructured topography in their interactions with biological material. As an example of nanostructured surfaces, we describe the synthesis of TiO₂ nanotubular and octahedral surfaces by using the electrochemical anodization method and hydrothermal method, respectively. The physical and chemical properties of these nanostructured surfaces are described in order to elucidate the influence of the surface topography and other physical properties on the behavior of human cells adhered to TiO₂ nanostructured surfaces. In the last part of the paper, we theoretically explain the interplay of elastic and adhesive contributions to the adsorption of lipid vesicles on the solid surfaces. We show the numerically predicted shapes of adhered lipid vesicles corresponding to the minimum of the membrane free energy to describe the influence of the vesicle size, bending modulus, and adhesion strength on the adhesion of lipid vesicles on solid charged surfaces.

Water Pores in Planar Lipid Bilayers at Fast and Slow Rise of Transmembrane Voltage

Basic understanding of the barrier properties of biological membranes can be obtained by studying model systems, such as planar lipid bilayers. Here, we study water pores in planar lipid bilayers in the presence of transmembrane voltage. Planar lipid bilayers were exposed to fast and slow linearly increasing voltage and current signals. We measured the capacitance, breakdown voltage, and rupture time of planar lipid bilayers composed of 1-pamitoyl 2-oleoyl phosphatidylcholine (POPC), 1-pamitoyl 2-oleoyl phosphatidylserine (POPS), and a mixture of both lipids in a 1:1 ratio. Based on the measurements, we evaluated the change in the capacitance of the planar lipid bilayer corresponding to water pores, the radius of water pores at membrane rupture, and the fraction of the area of the planar lipid bilayer occupied by water pores.planar lipid bilayer capacitance, which corresponds to water pores, water pore radius at the membrane rupture, and a fraction of the planar lipid bilayer area occupied by water pores. The estimated pore radii determining the rupture of the planar lipid bilayer upon fast build-up of transmembrane voltage are 0.101 nm, 0.110 nm, and 0.106 nm for membranes composed of POPC, POPS, and POPC:POPS, respectively. The fraction of the surface occupied by water pores at the moment of rupture of the planar lipid bilayer The fraction of an area that is occupied by water pores at the moment of planar lipid bilayer rupture is in the range of 0.1–1.8%.

Ion size effect on electrostatic and electroosmotic properties in soft nanochannels with pH-dependent charge density

We report a theoretical study of the ion size effect on various properties in a soft nanochannel with pH-dependent charge density.

Structure of electric double layers in capacitive systems and to what extent (classical) density functional theory describes it

Ongoing scientific interest is aimed at the properties and structure of electric double layers (EDLs), which are crucial for capacitive energy storage, water treatment, and energy harvesting technologies like supercapacitors, desalination devices, blue engines, and thermocapacitive heat-to-current converters. A promising tool to describe their physics on a microscopic level is (classical) density functional theory (DFT), which can be applied in order to analyze pair correlations and charge ordering in the primitive model of charged hard spheres. This simple model captures the main properties of ionic liquids and solutions and it predicts many of the phenomena that occur in EDLs. The latter often lead to anomalous response in the differential capacitance of EDLs. This work constructively reviews the powerful theoretical framework of DFT and its recent developments regarding the description of EDLs. It explains to what extent current approaches in DFT describe structural ordering and in-plane transitions in EDLs, which occur when the corresponding electrodes are charged. Further, the review briefly summarizes the history of modeling EDLs, presents applications, and points out limitations and strengths in present theoretical approaches. It concludes that DFT as a sophisticated microscopic theory for ionic systems is expecting a challenging but promising future in both fundamental research and applications in supercapacitive technologies.

Pore formation in lipid membrane II: Energy landscape under external stress

Lipid membranes are extremely stable envelopes allowing cells to survive in various environments and to maintain desired internal composition. Membrane permeation through formation of transversal pores requires substantial external stress. Practically, pores are usually formed by application of lateral tension or transmembrane voltage. Using the same approach as was used for obtaining continuous trajectory of pore formation in the stress-less membrane in the previous article, we now consider the process of pore formation under the external stress. The waiting time to pore formation proved a non-monotonous function of the lateral tension, dropping from infinity at zero tension to a minimum at the tension of several millinewtons per meter. Transmembrane voltage, on the contrary, caused the waiting time to decrease monotonously. Analysis of pore formation trajectories for several lipid species with different spontaneous curvatures and elastic moduli under various external conditions provided instrumental insights into the mechanisms underlying some experimentally observed phenomena.