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The interaction between a charged metal implant surface and a surrounding body fluid (electrolyte solution) leads to ion redistribution and thus to formation of an electrical double layer (EDL). The physical properties of the EDL contribute essentially to the formation of the complex implant-biosystem interface. Study of the EDL began in 1879 by Hermann von Helmholtz and still today remains a scientific challenge. The present mini review is focused on introducing the generalized Stern theory of an EDL, which takes into account the orientational ordering of water molecules. To ascertain the plausibility of the generalized Stern models described, we follow the classical model of Stern and introduce two Langevin models for spatial variation of the relative permittivity for point-like and finite sized ions. We attempt to uncover the subtle interplay between water ordering and finite sized ions and their impact on the electric potential near the charged implant surface. Two complementary effects appear to account for the spatial dependency of the relative permittivity near the charged implant surface — the dipole moment vectors of water molecules are predominantly oriented towards the surface and water molecules are depleted due to the accumulation of counterions. At the end the expressions for relative permittivity in both Langevin models were generalized by also taking into account the cavity and reaction field.
Cylindrical microexovesicles were induced in human erythro-cytes by echinocytic amphiphile dodecyl maltoside. It is suggested that the effect of the curvature deviator is relevant for the stability of the observed cylindrical microexovesicle shapes.
A possible physical interpretation of a discontinuous transition between different red blood cell shapes is given. The red blood cell membrane is considered to consist of the bilayer part and the underlaying membrane skeleton. By taking into consideration that the stable cell shape corresponds to the minimum of the membrane energy, that consists of the bilayer and skeleton elastic energies and of the bilayer-skeleton interaction energy, it is shown that aggregation of the skeleton can cause the discontinuous cell shape transformation from a shape with the bilayer completely underlaid with the skeleton to the shape involving a spherical parent cell with completely underlaid bilayer and spherical daughter vesicles without the skeleton.
Radiographic and clinical studies, coupled with biomechanical assessment of the hip, are important tools for predicting the development of osteoarthitis of the hip. In order to better understand the treatment of hip dysplasia, it is necessary to determine the contact stress in the hip joint. In this study, a three-dimensional mathematical model was used to determine hip joint contact stress. Because of the discrepancy in the results of analyses of different radiographic indicators of hip dysplasia, the calculation of hip joint contact stress is proposed for a more accurate assessment of the severity of hip dysplasia.
Human erythrocytes were incubated at alkaline pH. In samples equilibrating within 60 min to pH 11 erythrocytes underwent prelytic vesiculation (fragmentation). Erythrocytes developed large (diameter often 1-2 µm) hemoglobin-filled blebs which could be released to the outer medium as hemoglobin containing vesicles. It is suggested that the described vesiculation at high pH occurs due to an uncoupling of the membrane skeleton from the lipid bilayer. Due to the uncoupling from the skeleton the erythrocyte lipid bilayer may behave similar to the membrane of a giant lipid vesicle.
The origin of characteristic torocyte-like shape of vesicles derived from transverse tubule in triad junction of skeletal muscles is studied theoretically. Two possible mechanisms are suggested. The first is the minimization of membrane bending energy where the special intermediate molecular structures in the central region of the vesicle is assumed to protect the opposing bilayers to come in the direct contact. The second mechanism is based on the assumption that the characteristic shape of the vesicles may be explained by non-homogenous lateral distribution of anisotropic membrane components.
The effect of counterion size on the electrical properties of an electrolyte solution in contact with charged planar, cylindrical and spherical surfaces is considered. Electrostatic interaction is considered by means of the mean electrostatic field, while the finite size of particles constituting the electrolyte solution is considered via the excluded volume effect within the lattice statistics. Different sizes of counterion are described by different values of the lattice constant. It is shown that the excluded volume effect considerably decreases the calculated number density of counterions near the charged surface. This effect is more pronounced in cylindrical geometry than in spherical geometry, and less pronounced than in planar geometry.
A view is presented on different roles which the bilayer part of the membrane and the skeleton play in establishing normal and some abnormal RBC shapes. The system is first studied at the level of elastic properties of red blood cell membrane where the latter is considered to be a trilayered structure. Then the contributions to the membrane energy are introduced which cause the membrane to become laterally inhomogeneous, in particular, the skeleton-bilayer interaction, the interaction between the membrane embedded molecules and the membrane curvature, and the distributional free energy of membrane embedded molecules. It is invoked that the role of skeleton in stabilizing red blood cell membrane is in keeping membrane integral proteins laterally distributed as homogeneously as possible.
The decrease in contact hip joint stress after Chiari osteotomy is studied using a mathematical model. In the model, additional coverage of the femoral head by the ala ossis ilei segment is taken into account. It is shown that this additional coverage significantly decreases stress, mostly by the indirect effect caused by the shift of the stress pole.
We studied the ability of di-cationic gemini surfactantsdi (amphiphiles), i.e. 1,4-butanediammonium-N,N-dialkyl-N,N,N',N'-tetramethyl bromides (Di-Cm-di-QAS (s = 4), where m = 8,11,13,16 and s = the number of alkyl groups in the spacer) to induce shape alteration, vesiculation, haemolysis and phosphatidylserine exposure in human erythrocytes, and to protect erythrocytes against hypotonic haemolysis. At high sublytic concentrations the Di-Cm-di-QAS (s = 4) amphiphiles rapidly induced echinocytic (spiculated) shapes and a release of exovesicles, mainly in the form of tubes, from the cell surface. Following 60 min incubation erythrocytes were sphero-echinocytic and a few cells with invaginations/endovesicles were observed. No phosphatidylserine exposure was detected. The haemolytic potency increased with an increase of the alkyl chain length. At sublytic concentrations the Di-Cm-di-QAS (s = 4) amphiphiles protected erythrocytes against hypotonic haemolysis. It is suggested that the Di-Cm-di-QAS (s = 4) amphiphiles perturb the membrane in a similar way as single-chain cationic amphiphiles, but that they do not easily translocate to the inner membrane leaflet.
We used a continuum model based on the Helfrich free energy to investigate the binding dynamics of a lipid bilayer to a BAR domain surface of a crescent-like shape of positive (e.g. I-BAR shape) or negative (e.g. F-BAR shape) intrinsic curvature. According to structural data, it has been suggested that negatively charged membrane lipids are bound to positively charged amino acids at the binding interface of BAR proteins, contributing a negative binding energy to the system free energy. In addition, the cone-like shape of negatively charged lipids on the inner side of a cell membrane might contribute a positive intrinsic curvature, facilitating the initial bending towards the crescent-like shape of the BAR domain. In the present study, we hypothesize that in the limit of a rigid BAR domain shape, the negative binding energy and the coupling between the intrinsic curvature of negatively charged lipids and the membrane curvature drive the bending of the membrane. To estimate the binding energy, the electric potential at the charged surface of a BAR domain was calculated using the Langevin-Bikerman equation. Results of numerical simulations reveal that the binding energy is important for the initial instability (i.e. bending of a membrane), while the coupling between the intrinsic shapes of lipids and membrane curvature could be crucial for the curvature-dependent aggregation of negatively charged lipids near the surface of the BAR domain. In the discussion, we suggest novel experiments using patch clamp techniques to analyze the binding dynamics of BAR proteins, as well as the possible role of BAR proteins in the fusion pore stability of exovesicles.
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