In the eye lens, the oxygen partial pressure is very low and the cholesterol (Chol) content in cell membranes is very high. Disturbance of these quantities results in cataract development. In human lens membranes, both bulk phospholipid-Chol domains and the pure Chol bilayer domains (CBDs) were experimentally detected. It is hypothesized that the CBD constitutes a significant barrier to oxygen transport into the lens. Transmembrane profiles of the oxygen diffusion-concentration product, obtained with electron paramagnetic resonance spin-labeling methods, allow evaluation of the oxygen permeability (P) of phospholipid membranes but not the CBD. Molecular dynamics simulation can independently provide components of the product across any bilayer domain, thus allowing evaluation of the P across the CBD. Therefore, to test the hypothesis, MD simulation was used. Three bilayers containing palmitoyl-oleoyl-phosphorylcholine (POPC) and Chol were built. The pure Chol bilayer modeled the CBD, the 1:1 POPC-Chol bilayer modeled the bulk membrane in which the CBD is embedded, and the POPC bilayer was a reference. To each model, 200 oxygen molecules were added. After equilibration, the oxygen concentration and diffusion profiles were calculated for each model and multiplied by each other. From the respective product profiles, the P of each bilayer was calculated. Favorable comparison with experimental data available only for the POPC and POPC-Chol bilayers validated these bilayer models and allowed the conclusion that oxygen permeation across the CBD is ~10 smaller than across the bulk membrane, supporting the hypothesis that the CBD is a barrier to oxygen transport into the eye lens.

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We consider a family of 2-dimensional ODEs of the form Δ ξ (z)z = f ξ (z) depending on a real parameter ξ which was investigated by Vladimirov [Rep. Math. Phys., 61 (2008), pp. 381-400]. In this system, there exist stationary points p ξ which belong to the set of zeros of Δ ξ. We prove, using rigorous numerics, the existence of a homoclinic orbit to p ξ for some parameter value ξ = ξ h. Due to the singularity of the system it takes a finite time to travel along this orbit, and this property gives rise to a compacton-like traveling wave in some hydrodynamic system describing relaxing media. Our approach could be used to prove similar results in other singular systems as well.

We present an algorithm for the rigorous integration of delay differential equations (DDEs) of the formAs an application, we give a computer-assisted proof of the existence of two attracting periodic orbits (before and after the first period-doubling bifurcation) in the Mackey-Glass equation.

In this study, carried out using computational methods, the organisation of the lipid/water interface of bilayers composed of galactolipids with both α-linolenoyl acyl chains is analysed and compared in three different lyotropic liquid-crystalline phases. These systems include the monogalactosyldiglyceride (MGDG) and digalactosyldiglyceride (DGDG) bilayers in the lamellar phase, the MGDG double bilayer during stalk phase formation and the inverse hexagonal MGDG phase. For each system, lipid-water and direct and water-mediated lipid-lipid interactions between the lipids of one bilayer leaflet and those of two apposing leaflets at the onset of new phase (stalk) formation, are identified. A network of interactions between DGDG molecules and its topological properties are derived and compared to those for the MGDG bilayer.