Membrane deformations induced by attached BAR superfamily domains could trigger or facilitate the growth of plasma membrane protrusions. The BAR domain family consists of BAR, F-BAR and I-BAR domains, each enforcing a different local curvature when attached to the membrane surface. Our theoretical study mainly focuses on the role of I-BAR in the membrane tubular deformations generated or stabilised by actin filaments. The influence of the area density of membrane attached BAR domains and their intrinsic curvature on the closed membrane shapes (vesicles) was investigated numerically. We derived an analytical approximative expression for the critical relative area density of BARs at which the membrane tubular protrusions on vesicles are most prominent. We have shown that the BARs with a higher intrinsic curvature induce thinner and longer cylindrical protrusions. The average orientation of the membrane attached BARs is altered when the vesicle shape is subjected to external force of growing actin rod-like structure inside a vesicle. The average orientation angle of membrane attached BARs may indicate whether the actin filaments are just stabilising the protrusion or generating it by stretching the vesicle.

Long-lasting over-elevated stress on the hip joint articular surface can damage the articular cartilage and is connected with arthrosis development. Periacetabular pelvic osteotomy is performed in order to prevent arthrosis development in different cases of residual hip dysplasia where the stress on the hip joint articular surface is increased because of inadequate femoral head coverage, i.e., too small hip joint weight bearing area. The aim of this work is to estimate a decrease of the stress on the hip joint articular surface after the periacetabular osteotomy. For this purpose, a three-dimensional mathematical model is constructed taking into account the spherical shape of the femoral head and of the acetabulum inner surface before and after the operation. On the basis of the presented results it is concluded that while performing the periactabular osteotomy the proximal part of the acetabulum should be rotated over the femoral head in lateral direction with the simultaneous medial displacement of the whole joint. In this way postoperative stress on the hip joint articular surface is reduced to the greatest extent.

Manufactured nanoparticles are potentially capable of inducing defects in lipid membranes. The effects of nanoparticles on cell membranes are one of the key issues in nanomedicine, nanotoxicology, food and pharmaceutical application of products of nanomaterials and others. Our aim is to demonstrate the nanoparticle-lipid vesicle interactions and to develop a controllable experimental setup for data acquisition. We studied interactions between nanoparticles (C 60) and lipid vesicles (POPC), using ZnCl 2 as a positive control. Light microscopy computer aided image segmentation was developed and population differences among vesicles incubated in different media were assessed. Data obtained by statistical image analysis methods revealed that nanoparticles (C 60) caused changes in vesicle size distribution in the population of lipid vesicles as well as a burst of vesicles in time and in a concentration gradient. No significant changes in shape of vesicles were recorded. The advantage of the experimental set up presented here is that it employs statistical image analysis methods and direct microscopy observation of large populations of lipid vesicles. We discuss the applicability of this in vitro approach in analysing the effects of nanoparticles on simplified biological membranes.

We studied biological membranes of spherical topology within the framework of the spontaneous curvature model. Both Monte Carlo simulations and the numerical minimization of the curvature energy were used to obtain the shapes of the vesicles. The shapes of the vesicles and their energy were calculated for different values of the reduced volume. The vesicles which exhibit in-plane ordering were also studied. Minimal models have been developed in order to study the orientational ordering in colloids coated with a thin sheet of nematic liquid crystal (nematic shells). The topological defects are always present on the surfaces with the topology of a sphere. The location of the topological defects depends strongly on the curvature of the surface. We studied the nematic ordering and the formation of topological defects on vesicles obtained by the minimization of the spontaneous curvature energy.

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