Dipolar interactions between domains in lipid monolayers at the air-water interface

Simulations and integral-equation theories for dipolar density interacting disks

Integral equation theories (IETs) based on the Ornstein-Zernike (OZ) relation can be used as an analytical tool to predict structural and thermodynamic properties and phase behavior of fluids with low numerical cost. However, there are no studies of the IETs for the dipolar density interaction potential in two-dimensional systems, a relevant interdomain interaction in lipid monolayers with phase coexistence. This repulsive interaction arises due to the excess dipole density of the domains, which are aligned perpendicular to the interface. This work studies the performance of three closures of the OZ equation for this novel system: Rogers-Young (RY), modified hypernetted chain (MHNC), and variational modified hypernetted chain (VMHNC). For the last two closures the bridge function of a reference system is required, with the hard disk being the most convenient reference system. Given that in two dimensions there is no analytical expressions for the hard disk correlation functions, two different approximations are proposed: one based on the Percus-Yevick (PY) approximation, and the other based on an extension of the hard spheres Verlet-Weis-Henderson-Grundke (LB) parametrization. The accuracy of the five approaches is evaluated by comparison of the pair correlation function and the structure factor with Monte Carlo simulation data. The results show that RY closure is satisfactory only for low-structured regimes. MHNC and VMHNC closures perform globally well, and there are no significant differences between them. However, the reference system in some cases affects their performance; when the pair correlation function serves as the measure, the LB-based closures quantitatively outperform the PY ones. From the point of view of its applicability, LB-based closures do not have a solution for all studied interaction strength parameters, and, in general, PY-based closures are numerically preferable.

Heterogeneous Nanostructures Cause Anomalous Diffusion in Lipid Monolayers

The diffusion and mobility in biomembranes are crucial for various cell functions; however, the mechanisms involved in such processes remain ambiguous due to the complex membrane structures. Herein, we investigate how the heterogeneous nanostructures cause anomalous diffusion in dipalmitoylphosphatidylcholine (DPPC) monolayers. By identifying the existence of condensed nanodomains and clarifying their impact, our findings renew the understanding of the hydrodynamic description and the statistical feature of the diffusion in the monolayers. We find a universal characteristic of the multistage mean square displacement (MSD) with an intermediate crossover, signifying two membrane viscosities at different scales: the short-time scale describes the local fluidity and is independent of the nominal DPPC density, and the long-time scale represents the global continuous phase taking into account nanodomains and increases with DPPC density. The constant short-time viscosity reflects a dynamic equilibrium between the continuous fluid phase and the condensed nanodomains in the molecular scale. Notably, we observe an "anomalous yet Brownian" phenomenon exhibiting an unusual double-peaked displacement probability distribution (DPD), which is attributed to the net dipolar repulsive force from the heterogeneous nanodomains around the microdomains. The findings provide physical insights into the transport of membrane inclusions that underpin various biological functions and drug deliveries.

Incorporation of Molecular Reorientation into Modeling Surface Pressure-Area Isotherms of Langmuir Monolayers

Langmuir monolayers can be assembled from molecules that change from a low-energy orientation occupying a large cross-sectional area to a high-energy orientation of small cross-sectional area as the lateral pressure grows. Examples include cyclosporin A, amphotericin B, nystatin, certain alpha-helical peptides, cholesterol oxydation products, dumbbell-shaped amphiphiles, organic-inorganic nanoparticles and hybrid molecular films. The transition between the two orientations leads to a shoulder in the surface pressure-area isotherm. We propose a theoretical model that describes the shoulder and can be used to extract the energy cost per molecule for the reorientation. Our two-state model is based on a lattice-sublattice approximation that hosts the two orientations and a corresponding free energy expression which we minimize with respect to the orientational distribution. Inter-molecular interactions other than steric repulsion are ignored. We provide an analysis of the model, including an analytic solution for one specific lateral pressure near a point of inflection in the surface pressure-area isotherm, and an approximate solution for the entire range of the lateral pressures. We also use our model to estimate energy costs associated with orientational transitions from previously reported experimental surface pressure-area isotherms.

A combined molecular/continuum-modeling approach to predict the small-angle neutron scattering of curved membranes

This paper develops a framework to compute the small-angle neutron scattering (SANS) from highly curved, dynamically fluctuating, and potentially inhomogeneous membranes. This method is needed to compute the scattering from nanometer-scale membrane domains that couple to curvature, as predicted by molecular modeling. The detailed neutron scattering length density of a small planar bilayer patch is readily available via molecular dynamics simulation. A mathematical, mechanical transformation of the planar scattering length density is developed to predict the scattering from curved bilayers. By simulating a fluctuating, curved, surface-continuum model, long time- and length-scales can be reached while, with the aid of the planar-to-curved transformation, the molecular features of the scattering length density can be retained. A test case for the method is developed by constructing a coarse-grained lipid vesicle following a protocol designed to relieve both the osmotic stress inside the vesicle and the lipid-number stress between the leaflets. A question was whether the hybrid model would be able to replicate the scattering from the highly deformed inner and outer leaflets of the small vesicle. Matching the scattering of the full (molecular vesicle) and hybrid (continuum vesicle) models indicated that the inner and outer leaflets of the full vesicle were expanded laterally, consistent with previous simulations of the Martini forcefield that showed thinning in small vesicles. The vesicle structure is inconsistent with a zero-tension leaflet deformed by a single set of elastic parameters, and the results show that this is evident in the scattering. The method can be applied to translate observations of any molecular model's neutron scattering length densities from small patches to large length and timescales.

Ligand Distribution and Lipid Phase Behavior in Phospholipid-Coated Microbubbles and Monolayers

Phospholipid-coated targeted microbubbles are ultrasound contrast agents that can be used for molecular imaging and enhanced drug delivery. However, a better understanding is needed of their targeting capabilities and how they relate to microstructures in the microbubble coating. Here, we investigated the ligand distribution, lipid phase behavior, and their correlation in targeted microbubbles of clinically relevant sizes, coated with a ternary mixture of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) or 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC), with PEG40-stearate and DSPE-PEG2000. To investigate the effect of lipid handling prior to microbubble production in DSPC-based microbubbles, the components were either dispersed in aqueous medium (direct method) or first dissolved and mixed in an organic solvent (indirect method). To determine the lipid-phase behavior of all components, experiments were conducted on monolayers at the air/water interface. In comparison to pure DSPC and DPPC, the ternary mixtures had an additional transition plateau around 10-12 mN/m. As confirmed by infrared reflection absorption spectroscopy (IRRAS), this plateau was due to a transition in the conformation of the PEGylated components (mushroom to brush). While the condensed phase domains had a different morphology in the ternary DPPC and DSPC monolayers on the Langmuir trough, the domain morphology was similar in the coating of both ternary DPPC and DSPC microbubbles (1.5-8 μm diameter). The ternary DPPC microbubbles had a homogenous ligand distribution and significantly less liquid condensed (LC) phase area in their coating than the DSPC-based microbubbles. For ternary DSPC microbubbles, the ligand distribution and LC phase area in the coating depended on the lipid handling. The direct method resulted in a heterogeneous ligand distribution, less LC phase area than the indirect method, and the ligand colocalizing with the liquid expanded (LE) phase area. The indirect method resulted in a homogenous ligand distribution with the largest LC phase area. In conclusion, lipid handling prior to microbubble production is of importance for a ternary mixture of DSPC, PEG40-stearate, and DSPE-PEG2000.

Domain size polydispersity effects on the structural and dynamical properties in lipid monolayers with phase coexistence

In lipid monolayers with phase coexistence, domains of the liquid-condensed phase always present size polydispersity. However, very few theoretical works consider size distribution effects on the monolayer properties. Because of the difference in surface densities, domains have excess dipolar density with respect to the surrounding liquid expanded phase, originating a dipolar inter-domain interaction. This interaction depends on the domain area, and hence the presence of a domain size distribution is associated with interaction polydispersity. Inter-domain interactions are fundamental to understanding the structure and dynamics of the monolayer. For this reason, it is expected that polydispersity significantly alters monolayer properties. By means of Brownian dynamics simulations, we study the radial distribution function (RDF), the average mean square displacement and the average time-dependent self-diffusion coefficient, D(t), of lipid monolayers with normally distributed size domains. For this purpose, we vary the relevant system parameters, polydispersity and interaction strength, within a range of experimental interest. We also analyze the consequences of using a monodisperse model to determine the interaction strength from an experimental RDF. We find that polydispersity strongly affects the value of the interaction strength, which is greatly underestimated if polydispersity is not considered. However, within a certain range of parameters, the RDF obtained from a polydisperse model can be well approximated by that of a monodisperse model, by suitably fitting the interaction strength, even for 40% polydispersities. For small interaction strengths or small polydispersities, the polydisperse systems obtained from fitting the experimental RDF have an average mean square displacement and D(t) in good agreement with that of the monodisperse system.

Electrostatic interactions at the microscale modulate dynamics and distribution of lipids in bilayers

For decades, it has been assumed that electrostatic long-range (micron distances) repulsions in lipid bilayers are negligible due to screening from the aqueous milieu. This concept, mostly derived from theoretical calculations, is broadly accepted in the biophysical community. Here we present experimental evidence showing that domain-domain electrostatic repulsions in charged and also in neutral lipid bilayers regulate the diffusion, in-plane structuring and merging of lipid domains in the micron range. All the experiments were performed on both, lipid monolayers and bilayers, and the remarkable similarity in the results found in bilayers compared to monolayers led us to propose that inter-domain repulsions occur mainly within the plane of the membrane. Finally, our results indicate that electrostatic interactions between the species inserted in a cell membrane are not negligible, not only at nanometric but also at larger distances, suggesting another manner for regulating the membrane properties.