Asymmetric Finite Size of Ions and Orientational Ordering of Water in Electric Double Layer Theory Within Lattice Model

In the present review, a brief historical survey of the mean-field theoretical description of Electric Double Layer (EDL) is presented. Special attention is devoted to asymmetric finite size of ions and orientational ordering of water dipoles. A model of Wicke and Eigen, who were first to explicitly derive the ion distribution functions for finite size of ions, is discussed. Arguments are given in favour of changing the recently adopted name of the mean-field EDL model for finite size of ions from Bikerman model to Bikerman-Wicke-Eigen model. Theoretically predicted asymmetric and symmetric camel-like shape of the voltage dependence of the differential capacitance is also discussed.

Morphological alterations of T24 cells on flat and nanotubular TiO2 surfaces

Aim

To investigate morphological alterations of malignant cancer cells (T24) of urothelial origin seeded on flat titanium (Ti) and nanotubular titanium dioxide (TiO₂) nanostructures.

Methods

Using anodization method, TiO₂ surfaces composed of vertically aligned nanotubes of 50-100 nm diameters were produced. The flat Ti surface was used as a reference. The alteration in the morphology of cancer cells was evaluated using scanning electron microscopy (SEM). A computational model, based on the theory of membrane elasticity, was constructed to shed light on the biophysical mechanisms responsible for the observed changes in the contact area of adhesion.

Results

Large diameter TiO₂ nanotubes exhibited a significantly smaller contact area of adhesion (P < 0.0001) and had more membrane protrusions (eg, microvilli and intercellular membrane nanotubes) than on flat Ti surface. Numerical membrane dynamics simulations revealed that the low adhesion energy per unit area would hinder the cell spreading on the large diameter TiO₂ nanotubular surface, thus explaining the small contact area.

Conclusion

The reduction in the cell contact area in the case of large diameter TiO₂ nanotube surface, which does not enable formation of the large enough number of the focal adhesion points, prevents spreading of urothelial cells.

Effects of counterion size on the attraction between similarly charged surfaces

Interaction between similarly charged surfaces can be attractive at high electrostatic coupling constants Ξ = l(B)Z(2)/μ(GC), where l(B) is the Bjerrum length, μ(GC) the Gouy-Chapman length, and Z the valency of counterions. While this effect has been studied previously in detail, as a function of surface charge density and valency of the pointlike counterions, much less is known about the effect of counterion size. We apply the Wang-Landau sampling Monte Carlo (MC) simulation method to compute the free energy F as a function of the scaled distance between the plates D̃=D/μ(GC) for a range of Ξ and scaled counterion radii R̃=R/μ(GC). We find that for large Ξ and small ion radius, there is a global equilibrium distance D̃=D̃(eq)=2(1+R̃), correctly giving the expected value at the point counterion limit. With increasing R̃ the global minimum in F(D̃) changes to a metastable state and finally this minimum vanishes when R̃ reaches a critical value, which depends on Ξ. We present a state diagram indicating approximate boundaries between these three regimes. The Wang-Landau MC method, as it is applied here, offers a possibility to study a wide spectrum of extended problems, which cannot be treated by the use of contact value theorem.

Protruding membrane nanotubes: attachment of tubular protrusions to adjacent cells by several anchoring junctions

Membrane nanotubes are a morphologically versatile group of membrane structures (some resembling filopodia), usually connecting two closely positioned cells. In this article, we set morphological criteria that distinguish the membrane nanotubes from filopodia, as there is no specific molecular marker known to date that unequivocally differentiates between filopodia and protruding nanotubes. Membrane nanotubes have been extensively studied from the morphological point of view and the transport that can be conducted through them, but little is known about the way they connect to the adjacent cell. Our results show that the nanotubes may connect to a neighboring cell by anchoring junctions. Among cell adhesion proteins, N-cadherin, β-catenin, nectin-2, afadin and the desmosomal protein desmoplakin-2 were immune-labeled. We found that N-cadherin and β-catenin are concentrated in nanotubes, while the concentrations of other junction-involved proteins are not increased in these structures. On the basis of data from transmission electron microscopy, we propose a model of the nanotube attachment where the connection of nanotubes is stabilized by several anchoring junctions, most likely adherens junctions that are formed when the nanotube is sliding along the target cell membrane.

Excluded volume effect and orientational ordering near charged surface in solution of ions and Langevin dipoles

The influence of a finite volume of ions and orientational ordering of water Langevin dipoles on the dielectric permittivity profile in the vicinity of charged surface is studied theoretically via a numerical solution of the modified Poisson-Boltzmann equation. It is shown that the dielectric permittivity profile close to the charged surface is mainly determined by two mechanisms; specifically, the depletion of dipoles at the charged surface due to accumulated counterions and the increased orientational ordering of the water dipoles.

Interactions of nanoparticles with lipid vesicles: a population based computer aided image analysis approach

Novel properties of nanoparticles have numerous potential technological applications but at the same time they underlie new kinds of biological effects. Uniqueness of nanoparticles and nanomaterials requires a new experimental methodology. Much evidence suggests that nanoparticles affect cell membrane stability and subsequently exert toxic effects. For this kind of research, lipid vesicles are of high value due to controllability and repeatability of experimental conditions. The aim of work presented here was to develop a computer aided analysis of lipid vesicles shape transformations. We studied a population of palmitoyloleoylphosphatidylcholine (POPC) lipid vesicles after exposure to nanoparticles (C(60)) or a reference chemical (ZnCl(2)). With the use of computer image analysis methods, we detected differences in size distributions of vesicles in different exposure groups. Though, at the present state, we are not able to precisely identify effects of nanoparticles on shape transformations of vesicles, those incubated with nanoparticles were in average larger than those in other groups. This population based approach holds many promises for future investigation of nanoparticles-lipid vesicles, or even nanoparticles-biological membranes interactions. However, in order to get reliable results, numerous images have to be analyzed which requires improved and highly automated image segmentation and analyses methods.

Curvature-dependent lateral distribution of raft markers in the human erythrocyte membrane

The distribution of raft markers in curved membrane exvaginations and invaginations, induced in human erythrocytes by amphiphile-treatment or increased cytosolic calcium level, was studied by fluorescence microscopy. Cholera toxin subunit B and antibodies were used to detect raft components. Ganglioside GM1 was enriched in membrane exvaginations (spiculae) induced by cytosolic calcium and amphiphiles. Stomatin and the cytosolic proteins synexin and sorcin were enriched in spiculae when induced by cytosolic calcium, but not in spiculae induced by amphiphiles. No enrichment of flotillin-1 was detected in spiculae. Analyses of the relative protein content of released exovesicles were in line with the microscopic observations. In invaginations induced by amphiphiles, the enrichment of ganglioside GM1, but not of the integral membrane proteins flotillin-1 and stomatin, was observed. Based on the experimental results and theoretical considerations we suggest that membrane skeleton-detached, laterally mobile rafts may sort into curved or flat membrane regions dependent on their intrinsic molecular shape and/or direct interactions between the raft elements.

The role of obesity, biomechanical constitution of the pelvis and contact joint stress in progression of hip osteoarthritis

OBJECTIVE

The aim of our study was to explore whether earlier hip arthroplasty for idiopathic osteoarthritis (OA) might be explained by enlarged contact stress in the hip joint, and to what amount can that be attributed to obesity and biomechanical constitution of the pelvis.

METHOD

Fifty subjects were selected from a list of consecutive recipients of hip endoprosthesis due to idiopathic OA; standard pelvic radiographs made years prior to surgery were the main selection criteria. For 65 hips resultant hip force and peak contact hip stress normalized to the body weight (R/Wb and p(max)/Wb) were determined from the radiographs with the HIPSTRESS method. Body weight and body mass index (BMI) were obtained with an interview. Regression analysis was used to correlate parameters of obesity (body weight, BMI), biomechanical constitution of the pelvis (R/Wb, p(max)/Wb) and mechanical loading within the hip joint (R, p(max)) with age at hip arthroplasty.

RESULTS

Younger age at hip arthroplasty was associated with higher body weight (P=0.009), higher peak contact hip stress normalized to the body weight - p(max)/Wb (P=0.019), higher resultant hip force -R (P=0.027) and larger peak contact hip stress - p(max) (P<0.001), but not with BMI (P=0.121) or R/Wb (P=0.614).

CONCLUSION

Our results suggest that enlarged contact stress (p(max)) plays an important role in rapid progression of hip OA with both obesity (increased body weight) and unfavorable biomechanical constitution of the pelvis (greater p(max)/Wb) contributing.

Encapsulation of small spherical liposome into larger flaccid liposome induced by human plasma proteins

We show that human plasma can induce the encapsulation of small spherical liposomes into larger flaccid liposomes. To explain the observed phenomena, it is proposed that the orientational ordering of charged plasma proteins induces attractive interaction between two like-charged liposome surfaces in close contact. It is observed that the encapsulation of the spherical liposome is possible only if the membrane of the target liposome is flexible enough to adapt its shape to the shape of the spherical liposome. In the theoretical model, the shapes of the two agglutinated liposomes are determined by minimisation of the sum of the adhesion energy and the membrane elastic energy. In the simulations, the membrane of liposomes is considered as an elastic structure and discretised via the finite element method using spring elements. It is shown that the observed agglutination of liposomes and encapsulation of smaller spherical liposomes into larger flaccid liposomes may be explained as a competition between the membrane deformation energy and the membrane adhesion energy.

Role of phospholipid asymmetry in the stability of inverted hexagonal mesoscopic phases

The role of phospholipid asymmetry in the transition from the lamellar (L(alpha)) to the inverted hexagonal (H(II)) phase upon the temperature increase was considered. The equilibrium configuration of the system was determined by the minimum of the free energy including the contribution of the isotropic and deviatoric bending and the interstitial energy of phospholipid monolayers. The shape and local interactions of a single lipid molecule were taken into account. The minimization with respect to the configuration of the lipid layers was performed by a numerical solution of the system of the Euler-Lagrange differential equations and by the Monte Carlo simulated annealing method. At high enough temperature, the lipid molecules attain a shape exhibiting higher intrinsic mean and deviatoric curvatures, which fits better into the H(II) phase than into the L(alpha) phase. Furthermore, the orientational ordering of lipid molecules in the curvature field expressed as the deviatoric bending provides a considerable negative contribution to the free energy, which stabilizes the nonlamellar H(II) phase. The nucleation configuration for the L(alpha)-H(II) phase transition is tuned by the isotropic and deviatoric bending energies and the interstitial energy.

Attraction between negatively charged surfaces mediated by spherical counterions with quadrupolar charge distribution

We observed monoclonal antibody mediated coalescence of negatively charged giant unilamellar phospholipid vesicles upon close approach of the vesicles. This feature is described, using a mean field density functional theory and Monte Carlo simulations, as that of two interacting flat electrical double layers. Antibodies are considered as spherical counterions of finite dimensions with two equal effective charges spatially separated by a fixed distance l inside it. We calculate the equilibrium configuration of the system by minimizing the free energy. The results obtained by solving the integrodifferential equation and by performing the Monte Carlo simulation are in excellent agreement. For high enough charge densities of the interacting surfaces and large enough l, we obtain within a mean field approach an attractive interaction between like-charged surfaces originating from orientational ordering of quadrupolar counterions. As expected, the interaction between surfaces turns repulsive as the distance between charges is reduced.

Different types of cell-to-cell connections mediated by nanotubular structures

Communication between cells is crucial for proper functioning of multicellular organisms. The recently discovered membranous tubes, named tunneling nanotubes, that directly bridge neighboring cells may offer a very specific and effective way of intercellular communication. Our experiments on RT4 and T24 urothelial cell lines show that nanotubes that bridge neighboring cells can be divided into two types. The nanotubes of type I are shorter and more dynamic than those of type II, and they contain actin filaments. They are formed when cells explore their surroundings to make contact with another cell. The nanotubes of type II are longer and more stable than type I, and they have cytokeratin filaments. They are formed when two already connected cells start to move apart. On the nanotubes of both types, small vesicles were found as an integral part of the nanotubes (that is, dilatations of the nanotubes). The dilatations of type II nanotubes do not move along the nanotubes, whereas the nanotubes of type I frequently have dilatations (gondolas) that move along the nanotubes in both directions. A possible model of formation and mechanical stability of nanotubes that bridge two neighboring cells is discussed.

Bridging like-charged macroions through long divalent rodlike ions

Like-charged macroions in aqueous electrolyte solution can attract each other because of the presence of inter- and/or intramolecular correlations. Poisson-Boltzmann theory is able to predict attractive interactions if the spatially extended structure (which reflects the presence of intramolecular correlations) of the mobile ions in the electrolyte is accounted for. We demonstrate this for the case of divalent, mobile ions where each ion consists of two individual charges separated by a fixed distance. Variational theory applied to this symmetric 2:2 electrolyte of rodlike ions leads to an integro-differential equation, valid for arbitrary rod length. Numerical solutions reveal the existence of a critical rod length above which electrostatic attraction starts to emerge. This electrostatic attraction is distinct from nonelectrostatic depletion forces. Analysis of the orientational distribution functions suggests a bridging mechanism of the rodlike ions to hold the two macroions together. For sufficiently large rod length, we also observe "overcharging", that is, an over-compensation of the macroion charges by the diffuse layer of mobile rodlike ions. Our results emphasize the importance of the often rodlike internal structure that condensing agents such as polyamines, peptides, or polymer segments exhibit. The results were compared with Monte Carlo simulations.

Actin is not required for nanotubular protrusions of primary astrocytes grown on metal nano-lawn

We used sub-micron metal rod decorated surfaces, 'nano-lawn' structures, as a substrate to study cell-to-cell and cell-to-surface interactions of primary murine astrocytes. These cells form thin membranous tubes with diameters of less than 100 nm and a length of several microns, which make contact to neighboring cells and the substrate during differentiation. While membrane protrusions grow on top of the nano-lawn pillars, nuclei sink to the bottom of the substrate. We observed gondola-like structures along those tubes, suggestive of their function as transport vehicles. Elements of the cytoskeleton such as actin fibers are commonly believed to be essential for triggering the onset and growth of tubular membrane protrusions. A rope-pulling mechanism along actin fibers has recently been proposed to account for the transport or exchange of cellular material between cells. We present evidence for a complementary mechanism that promotes growth and stabilization of the observed tubular protrusions of cell membranes. This mechanism does not require active involvement of actin fibers as the formation of membrane protrusions could not be prevented by suppressing polymerization of actin by latrunculin B. Also theoretically, actin fibers are not essential for the growing and stability of nanotubes since curvature-driven self-assembly of interacting anisotropic raft elements is sufficient for the spontaneous formation of thin nano-tubular membrane protrusions.

Higher peak contact hip stress predetermines the side of hip involved in idiopathic osteoarthritis

BACKGROUND

Biomechanical parameters of the hip have been suggested to have an important influence on the development of osteoarthritis. We aimed to find out whether higher stress is generated in a hip that subsequently results in earlier hip arthroplasty compared to the contralateral hip in the same subject.

METHODS

Standard anterior-posterior pelvic radiographs with no or subtle radiological signs of hip osteoarthritis, of 59 female patients, who underwent hip arthroplasty for primary osteoarthritis years later, were selected from the archives. For each subject peak contact hip stress of the hip with earlier arthroplasty and of the contralateral hip (pair of hips), was calculated from the radiographically obtained geometrical parameters with the HIPSTRESS program, which is based on a three-dimensional biomechanical model of the resultant hip force in the one-legged stance and a three-dimensional mathematical model of the contact hip stress distribution. Differences in peak contact hip stress within pairs of hips were determined for subjects with unilateral (22 pairs of hips) and bilateral disease (37 pairs of hips) by using paired-samples T-test.

FINDINGS

In the population of subjects with unilateral osteoarthritis, average peak contact hip stress was significantly higher (P = 0.007) in hips with arthroplasty (2.44 kPa/N) than in contralateral hips (2.32 kPa/N). In the population of subjects with bilateral osteoarthritis, average peak contact hip stress was significantly higher (P<0.001) in hips with earlier arthroplasty (2.54 kPa/N) than in contralateral hips (2.35 kPa/N).

INTERPRETATION

Results are consistent with the hypothesis that higher peak contact hip stress results in earlier hip arthroplasty due to faster development of idiopathic osteoarthritis.

Membrane skeleton detachment in spherical and cylindrical microexovesicles

We observed that amphiphile-induced microexovesicles may be spherical or cylindrical, depending on the species of the added amphiphile. The spherical microexovesicle corresponds to an extreme local difference between the two monolayer areas of the membrane segment with a fixed area, while the cylindrical microexovesicle corresponds to an extreme local area difference if the area of the budding segment is increased due to lateral influx of anisotropic membrane constituents. Protein analysis showed that both types of vesicles are highly depleted in the membrane skeleton. It is suggested that a partial detachment of the skeleton in the budding region is favoured due to accumulated skeleton shear deformations in this region.

Coalescence of phospholipid membranes as a possible origin of anticoagulant effect of serum proteins

Interactions between phospholipid membranes (made of palmitoyloleoylphosphatidylcholine, cardiolipin and cholesterol) after addition of beta2 glycoprotein I (beta2GPI) or anti-beta2GPI antibodies or a mixture of both were studied by observing giant phospholipid vesicles under the phase contrast microscope. Both, negatively charged and neutral vesicles coalesced into complexes and adhered to the bottom of the observation chamber in the presence of beta2GPI in solution. Anti-beta2GPIs alone or previously mixed with beta2GPI caused coalescence of charged but not neutral vesicles, i.e. for neutral membranes the effect of beta2GPI was abolished by the presence of anti-beta2GPIs. Since the presence of the above adhesion mediators can prevent fragmentation of the membrane we propose a (new) possible anticoagulant mechanism for some serum proteins by preventing the release of prothrombogenic microexovesicles into circulation.

Hip joint contact stress as an additional parameter for determining hip dysplasia in adults: comparison with Severin's classification

BACKGROUND

The hip's biomechanical state affects its future development. Therefore, a relevant biomechanical evaluation would be of use in assessing hip dysplasia. Recently, a noninvasive method was developed to determine stress on the weight-bearing area of the hip. The biomechanical assessment was compared with Severin's radiographic classification.

MATERIAL/METHODS

Standard anteroposterior radiographs, taken prior to surgery, of 35 adult patients who were treated for hip dysplasia were analyzed. The AP radiographs of 59 hips were classified into groups 1-3 according to Severin's classification. The geometrical and biomechanical parameters of the hips within each of Severin's groups were compared.

RESULTS

The differences between the mean peak stress on the weight-bearing area of the hip and the peak stress normalized to body weight of both the first and second groups compared with the third group were highly statistically significant. All three of Severin's groups had stress readings ranging from 2 to 4 MPa.

CONCLUSIONS

This study shows that, in general, the biomechanical results corresponded to the results obtained by Severin's evaluation; however, when assessing an individual hip, important differences may be present. Since all of Severin's groups had a stress reading ranging from 2 to 4 MPa, it would be useful to determine the hip's stress distribution when determining treatment.

Possible role of flexible red blood cell membrane nanodomains in the growth and stability of membrane nanotubes

Tubular budding of the erythrocyte membrane may be induced by exogenously added substances. It is shown that tubular budding may be explained by self-assembly of anisotropic membrane nanodomains into larger domains forming nanotubular membrane protrusions. In contrast to some previously reported theories, no direct external mechanical force is needed to explain the observed tubular budding of the bilayer membrane. The mechanism that explains tubular budding may also be responsible for stabilization of the thin tubes that connect cells or cell organelles and which might be important for the transport of matter and information in cellular systems. It is shown that small carrier vesicles (gondolas), transporting enclosed material or the molecules composing their membrane, may travel over long distances along the nanotubes connecting two cells.

Elastic properties of biological membranes influenced by attached proteins

Positively charged proteins can attach themselves to the negatively charged outer surface of biological cell membranes and liposomes. In this work, the influence of the intrinsic shape of the membrane-attached proteins on the elastic properties of the membrane is considered theoretically. It is shown that attachment of anisotropic proteins to the outer surface of biological membranes may induce tubulation of the membrane. The attachment of semi-flexible rod-like proteins increases the local bending constant, while the attachment of semi-flexible plate-like anisotropic proteins may also reduce the local bending constant of the membrane. The role of the hydrophobic protrusion of the attached protein which is embedded in the outer membrane layer is also discussed.

Influence of rigid inclusions on the bending elasticity of a lipid membrane

We model the influence of rigid inclusions on the curvature elasticity of a lipid membrane. Our focus is on conelike transmembrane inclusions that are able to induce long-range deformations in the host bilayer membrane. The elastic properties of the membrane are described in terms of curvature and tilt elasticity. The latter adds an additional degree of freedom that allows the membrane to accommodate an inclusion not only through a curvature deformation but also via changes in lipid tilt. Using a (mean-field level) cell model for homogeneously distributed inclusions in a small membrane segment of prescribed (mesoscopic-scale) spherical shape, we calculate the optimal microscopic-scale deviation of the membrane shape around the intercalated inclusions and the corresponding free energy, analytically. We show that the lipid tilt degree of freedom can lead to local softening of the inclusion-containing lipid bilayer segment. The predicted softening requires a sufficiently small value of the tilt modulus; its origin lies in the reduction of the excess membrane-inclusion interaction energy. We compare our results to the case of suppressed microscopic shape relaxation. Here, too, local softening of the membrane is possible.

The influence of anisotropic membrane inclusions on curvature elastic properties of lipid membranes

A membrane inclusion can be defined as a complex of protein or peptide and the surrounding significantly distorted lipids. We suggest a theoretical model that allows for the estimation of the influence of membrane inclusions on the curvature elastic properties of lipid membranes. Our treatment includes anisotropic inclusions whose energetics depends on their in-plane orientation within the membrane. On the basis of continuum elasticity theory, we calculate the inclusion-membrane interaction energy that reflects the protein or peptide-induced short-ranged elastic deformation of a bent lipid layer. A numerical estimate of the corresponding interaction constants indicates the ability of inclusions to sense membrane bending and to accumulate at regions of favorable curvature, matching the effective shape of the inclusions. Strongly anisotropic inclusions interact favorably with lipid layers that adopt saddlelike curvature; such structures may be stabilized energetically. We explore this possibility for the case of vesicle budding where we consider a shape sequence of closed, axisymmetric vesicles that form a (saddle-curvature adopting) membrane neck. It appears that not only isotropic but also strongly anisotropic inclusions can significantly contribute to the budding energetics, a finding that we discuss in terms of recent experiments.

Shape and size of giant unilamellar phospholipid vesicles containing cardiolipin

The effect of cardiolipin content on the shape and size of giant palmitoyloleylphosphatidylcholine/cardiolipin vesicles was studied. Unilamellar vesicles were prepared in sugar solution by the method of electroformation, from mixtures containing up to 50% weight ratio of cardiolipin. At room temperature the vesicles containing cardiolipin exhibited abrupt changes in the curvature of the vesicle contour indicating regions of phase separation. The deviations from the spherical shape were larger if vesicles were made from mixtures with a higher content of cardiolipin. Numerous vesicles with soft fluctuating walls were observed. The estimated size of the vesicles containing cardiolipin was found to be smaller than the size of pure palmitoyloleylphosphatidylcholine vesicles.

Contact stress in hips with osteonecrosis of the femoral head

Contact stress distribution in the articular surface of the hip is considered a factor in the development of osteoarthritis, a common complication in hips with aseptic necrosis of the femoral head. We present evidence supporting the hypothesis that osteoarthritis in hips with aseptic necrosis of the femoral head can be caused by elevated contact stress related to the reduced load-bearing ability of the necrotic bone. By using a previously validated mathematical model, we observed that hip contact stress may increase considerably if the load-bearing capacity of the necrotic lesion is decreased, if the size of the necrotic segment is increased, and if the necrotic segment is located more laterally. These effects are affected by the intrinsic shape of the hip. As the estimated values of stress in hips with osteonecrosis are in the range obtained by the same method in dysplastic hips, osteoarthritis in hips with osteonecrosis can be caused by elevated contact stress.

Interaction of giant phospholipid vesicles containing cardiolipin and cholesterol with beta2-glycoprotein-I and anti-beta2-glycoprotein-I antibodies

Antiphospholipid syndrome is characterized with thrombotic events and/or pregnancy morbidity and antiphospholipid antibodies (aPL). The most common antigen for aPL is beta2-glycoprotein-I (beta(2)GPI), a plasma protein binding to negatively charged phospholipids. The influence of aPL on coagulation is not well understood. Giant phospholipid vesicles (GPVs) are a convenient in vitro system for studying interactions between phospholipid membranes and proteins resulting in the change of the vesicles' configuration. We aimed to set up an in vitro model and to study changes in the morphology of GPVs with high content of cardiolipin upon addition of beta(2)GPI and/or IgG fraction of a patient with antiphospholipid syndrome (APS). Addition of the IgG fraction of the APS patient caused lateral segregation of the membrane inclusions and adhesion of GPVs. Addition of beta(2)GPI caused adhesion of GPVs. Addition of both, the patient IgG fraction and beta(2)GPI caused adhesion of vesicles to the glass slides and to each other, formation of pores and burst of vesicles. Our results indicate that adhesion of the cardiolipin-containing vesicles does not seem specific for added proteins, rather, it indicates electrostatic and curvature-mediated interactions between the membrane constituents.

On the role of anisotropy of membrane constituents in formation of a membrane neck during budding of a multicomponent membrane

The expression for the isotropic membrane bending energy was generalized for the case of a multicomponent membrane where the membrane constituents (single molecules or small complexes of molecules-membrane inclusions) were assumed to be anisotropic. Using this generalized expression for the membrane energy it was shown that the change of intrinsic shape of membrane components may induce first-order-like shape transitions leading to the formation of a membrane neck. The predicted discontinuous membrane shape transition and the concomitant lateral segregation of membrane components were applied to study membrane budding. Based on the results presented we conclude that the budding process might be driven by accumulation of anisotropic membrane components in the necks connecting the bud and the parent membrane, and by accumulation of isotropic (conical) membrane components on the bud. Both processes may strongly depend on the intrinsic shape of membrane components and on the direct interactions between them.

The Bernese periacetabular osteotomy: clinical, radiographic and mechanical 7-15-year follow-up of 26 hips

BACKGROUND

The Bernese periacetabular osteotomy is used in dysplastic hips to increase the load-bearing area of the hip and to prevent osteoarthritis. The aim of our work was to determine the contact hip stress before and after the osteotomy and to compare the relief of stress with the long-term radiographic and clinical outcome.

PATIENTS AND METHODS

We followed 26 dysplastic hips (26 patients) for 7-15 years after the index operation. Clinical evaluation was based on the WOMAC score, osteoarthrosis was evaluated with the Tönnis classification, the angles of lateral (CE) and anterior (VCA) femoral coverage were measured, and biomechanical parameters were studied.

RESULTS

Periacetabular osteotomy increased the mean CE from 15 degrees to 37 degrees , and the mean VCA from 22 degrees to 38 degrees . The mean normalized peak contact stress was reduced from 5.2 to 3.0 kPa/N. Four hips required total hip arthroplasty after an average of 4.5 years, 8 hips showed considerable arthrosis progression, and 14 hips had no or mild arthrosis at follow-up. Preoperative WOMAC score, preoperative Tönnis grade and postoperative normalized peak contact stress were the most important predictors of outcome.

INTERPRETATION

The Bernese periacetabular osteotomy improves the mechanical status of the hip. Long-term success depends on the grade of arthrosis preoperatively and on the magnitude of operative correction of the contact hip stress.

The shape of acetabular cartilage optimizes hip contact stress distribution

The biomechanical role of the horseshoe geometry of the acetabular cartilage is described using a three-dimensional mathematical model. It is shown that the acetabular fossa contributes to a more uniform articular contact stress distribution and a consequent decrease in the peak contact stress. Based on the results it is suggested that the characteristic horseshoe shape of the articular cartilage in the human acetabulum optimizes the contact stress distribution in the hip joint.

Curvature-induced accumulation of anisotropic membrane components and raft formation in cylindrical membrane protrusions

Coupling between the area density of anisotropic membrane inclusions and local membrane curvature is considered theoretically for a simple case of nearly flat bilayer membrane with thin tubular membrane protrusions. Lateral phase separation, i.e. accumulation of membrane inclusions in tubular membrane protrusions was obtained for strongly anisotropic inclusions if the radius of tubular protrusions is small enough. In accordance with these theoretical predictions we observed persistence of long tubular membrane protrusions devoid of internal rod-like microtubular structure in cells. We suggest that the stability of the tubular membrane protrusions without the inner supporting rod-like cytoskeleton is a consequence of the accumulation of anisotropic membrane components in the bilayer membrane of these protrusions. Based on the presented theoretical and experimental results it is suggested that previously reported concentration of prominin rafts in thin tubular membrane protrusions may be caused by a curvature-induced accumulation of small prominin-lipid complexes (inclusions) in protrusions and their coalescence into larger rafts.

Unsteady 3D simulation of intra stent flow

The computer system for quantitative determination of musculoskeletal geometry from computer tomography (CT) images has been developed. The computer system processes series of CT images to obtain three-dimensional (3D) model of bony structures where the effective muscle fibres can be interactively defined. Presented computer system has flexible modular structure and is suitable also for educational purposes.

Excluded volume driven counterion condensation inside nanotubes in a concave electrical double layer model

The physical properties of organic nanotubes attract increasing attention due to their potential benefit in technology, biology and medicine. We study the effect of ion size on the electrical properties of cylindrical nanotubes filled with electrolyte solution within a modified Poisson-Boltzmann (PB) approach. For comparison purposes, small hollow nanospheres filled with electrolyte solution are considered. The finite size of the particles in the inner electrolyte solution is described by the excluded volume effect within a lattice statistics approach. We found that an increased ion size reduces the number of counterions near the charged inner surface of the nanotube, leading to an enlarged electrostatic surface potential. The concentration of counterions close to the inner surface saturates for higher surface charge densities and larger ions. In the case of saturation, the closest counterion packing is achieved, all lattice sites near the surface are occupied and an actual counterion condensation is observed. By contrast, the counterion concentration at the axis of the nanotube steadily increases with increasing surface charge density. This growth is more pronounced for smaller nanotube radii and larger ions. At larger nanotube radii for small ion size counterion condensation may also be observed according to the Tsao criterion, i.e. the counterion concentration at the centre is independent of the number of counterions in the system. With decreasing radius the Tsao condensation effect is shifted towards physiologically unrealistic surface charge densities.

Amphiphile-induced tubular budding of the bilayer membrane

Amphiphile-induced tubular budding of the erythrocyte membrane was studied using transmission electron microscopy. No chiral patterns of the intramembraneous particles were found, either on the cylindrical buds, or on the tubular nanoexovesicles. In agreement with these observations, the tubular budding may be explained by in-plane ordering of anisotropic membrane inclusions in the buds where the difference between the principal membrane curvatures is very large. In contrast to previously reported theories, no direct external mechanical force is needed to explain tubular budding of the bilayer membrane.

Spherocyte shape transformation and release of tubular nanovesicles in human erythrocytes

We have studied dodecylmaltoside-induced echinocyte-spheroechincyte-spherocyte shape transformation and membrane vesiculation using transmission electron microscopy (TEM) on freeze-fracture replicas. It is indicated that spherical erythrocyte shape at higher dodecylmaltoside concentration is formed due to loss of membrane in the process where small, mostly tubular nanovesicles are released predominantly from the top of echinocyte and spheroechinocyte spicules.

Shape transformation of giant phospholipid vesicles at high concentrations of C12E8

Giant unilamellar phospholipid vesicles were prepared by the method of electroformation from 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine (POPC). We studied the influence of different concentrations of the surfactant octaethyleneglycol dodecylether (C(12)E(8)) on the spontaneous shape transformations of POPC vesicles at room temperature. In accordance with previous results, we observed that low concentration of C(12)E(8) increased the speed of the characteristic vesicle shape transformation, starting from the initial shape with thin tubular protrusion, through beaded protrusion where the number of beads gradually decreased, to final spherical shapes with invagination, whereby the average mean curvature of the vesicle membrane monotonously decreased. In contrast, higher concentration of C(12)E(8) initially induced the shape transformation in the "opposite direction": in the protrusion, the number of beads gradually increased and eventually a tube was formed whereby the average mean curvature of the vesicle membrane gradually increased. However, at a certain point, an abrupt shape change took place to yield the vesicle with invagination. In this transition, the average mean curvature of the vesicle membrane discontinuously decreased. After this transition, the vesicle began to shrink and finally disappeared. We discuss possible mechanisms involved in the observed transformations.

High contact hip stress is related to the development of hip pathology with increasing age

BACKGROUND

High contact hip stress is believed to be one of the key biomechanical factors involved in the hip cartilage degeneration and osteoarthritis. Accordingly, with increasing age high contact hip stress is expected to cause elimination of subjects from the population of healthy hips, but its predictive value has not been evaluated so far. The objective of the paper is to investigate whether the exposure of healthy hips to estimated high contact hip stress is related to the development of hip pathology with increasing age.

METHODS

A cross-sectional age- and gender-matched analysis of the peak contact hip stress calculated from pelvic geometry was made in 103 adult subjects with healthy hips. The peak contact hip stress was calculated from anterior-posterior pelvic radiographs of healthy hips by using a mathematical model of the human hip in the static one-legged stance.

FINDINGS

In both female and male population, the average values of the peak contact hip stress normalized to the body weight are significantly higher and the values are also more dispersed in younger subjects when compared to older subjects.

INTERPRETATION

The hip joints which remain healthy in the old age have lower average estimated peak contact hip stress. These results are consistent with the explanation that subjects with high estimated peak contact hip stress are more likely to develop hip disease in the course of life.

Endovesicle formation and membrane perturbation induced by polyoxyethyleneglycolalkylethers in human erythrocytes

Polyoxyethyleneglycolalkylether (CmEn, m=12, n=8) can induce a large torocyte-like endovesicle in human erythrocytes. The present study aimed to examine how variations in the molecular structure of CmEn (m=10,12,14,16,18; n=1-10,23) affect the occurrence of torocyte endovesicles. Our results show that torocytes occur most frequently when m=12,14 and n=8,9. At this molecular configuration the detergents induce inward membrane bending (stomatocytic S1-S2 shapes) resulting in the formation of a large membrane invagination. These detergents have a strong membrane perturbing, i.e., haemolytic, effect. Theoretical calculations indicate that a torocyte-shaped inside-out membrane vesicle can be created from a large membrane invagination due to the impact of laterally mobile anisotropic membrane inclusions. Such inclusions may be detergent-membrane component complexes or unanchored integral membrane proteins. It is shown that a nonhomogeneous lateral distribution of anisotropic membrane inclusions may stabilise the torocyte endovesicle shape, characterised by having opposite membranes in the thin central region of the vesicles separated by a certain distance. Tubular, conical or inverted conical isotropic inclusions cannot do so.

Coupling between vesicle shape and the non-homogeneous lateral distribution of membrane constituents in Golgi bodies

In this work, a hypothesis is presented that could explain the non-homogeneous lateral distribution of membrane components in Golgi vesicles. It is shown that the non-homogeneous lateral distribution of membrane components and the specific flattened shape of Golgi vesicles are strongly coupled. In agreement with experimental evidence, it is indicated that some of the membrane components may be concentrated mainly on the curved bulbous rims of the Golgi vesicles, while the other components are distributed predominantly in their flat central part.

A possible origin of the torocyte-like shape of vesicles derived from the transverse tubule in the triad junction of skeletal muscle

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.

Influence of contact hip stress on the outcome of surgical treatment of hips affected by avascular necrosis

INTRODUCTION

Biomechanical analysis is an important tool that could improve the treatment of a diseased hip. However, it is still unclear how the biomechanical status affects the clinical outcome of a certain disease. In this work we studied the long-term effect of contact hip stress on the clinical outcome of hips that were operated on by various intertrochanteric osteotomies due to avascular necrosis of the femoral head. The hypothesis being tested is that the hips with a more favourable postoperative distribution of contact hip stress have a better clinical outcome.

MATERIALS AND METHODS

The study was performed on a population of 30 hips. For each hip, we determined the peak contact hip stress before the operation and immediately after the operation by using a recently developed method based on a three-dimensional mathematical model and the data from standard anteroposterior roentgenographs of both hips and pelvis. The hips were evaluated clinically 9-26 years after the operation and divided into a successful and an unsuccessful group. The average change of the peak stress due to the operation was calculated for each group, and the values were compared by t-test.

RESULTS

In the successful group the operation caused an average decrease of the peak hip stress of about 10%, while in the unsuccessful group the operation caused an average increase of the peak hip stress of about 4%, the difference between the respective changes of the peak stress due to the operation being statistically significant ( p=0.001).

CONCLUSION

Our results support the hypothesis that the hips with a more favourable postoperative distribution of contact hip stress have a better clinical outcome.

Polyethylene wear in total hip prostheses: the influence of direction of linear wear on volumetric wear determined from radiographic data

PURPOSE

To develop a new mathematical model for calculating the volumetric wear of polyethylene cups from known values of the radius of the prosthesis head, the extent of linear wear and the direction of linear wear determined from standard antero-posterior radiographs.

METHOD

A new mathematical model was developed. The results of this new mathematical model were compared with the results obtained using the standard, frequently used mathematical model, which takes into consideration only the radius of the prosthesis head and the extent of linear wear of the polyethylene cups. The results of both mathematical models were further compared with the results obtained by direct measurement of volumetric wear using the fluid displacement method.

RESULTS

Comparison of the mathematical models shows that the average volumetric wear calculated using the new mathematical model is 8.5% smaller than the average volumetric wear determined by the fluid displacement method, while the average volumetric wear calculated by standard mathematical model is 17.5% higher. The results of the new mathematical model are, thus, notably less biased than those of the standard one.

CONCLUSION

In calculating the volumetric wear from antero-posterior radiographs, not only the radius of the prosthesis head and the extent of the linear wear but also the direction of the latter has to be considered.

Shape transformation and burst of giant POPC unilamellar liposomes modulated by non-ionic detergent C12E8

We studied spontaneous shape transformations and burst of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine (POPC) vesicles with exogeneously added non-ionic detergent octaethylene-glycol dodecylether C(12)E(8). The addition of C(12)E(8) increased the speed of the vesicle shape transformation, so that we were able to study for the first time the complete sequence of POPC vesicle shapes starting from initial spherical vesicle with long thin tubular protrusion to final shape with invagination(s). The average mean curvature of the vesicle membrane continuously decreases during this process. The shape of the invaginations is usually spherical, however also non-spherical shapes of invaginations were observed. C(12)E(8) increases amplitudes of the fluctuations of the vesicle membrane. At higher concentrations in the membrane, C(12)E(8) induces the membrane leakage and burst of the vesicles.

Gradient of contact stress in normal and dysplastic human hips

The stress gradient index (G(p)) is introduced for the assessment of dysplasia in human hip joint. The absolute value of G(p) is equal to the magnitude of the gradient of the contact stress at the lateral acetabular rim. The parameter G(p) normalized with respect to the body weight (W(B)) is determined from the standard anteroposterior radiographs of adult human hips and pelvises using the mathematical model. The average value of G(p)/W(B) was determined for the group of dysplastic hips and for the group of normal hips. In the group of normal hips the average value of G(p)/W(B) is smaller (-0.445x10(5) m(-3)) than in the group of dysplastic hips (+1.481x10(5) m(-3)). The difference is statistically significant P<0.001. The average value of G(p)/W(B) changes its sign at the value of the centre-edge angle theta(CE) approximately 20( composite function ) which is usually considered as the boundary value of theta(CE) (lower limit) for the normal hips. Accordingly we suggest a new definition for the hip dysplasia with respect to the size and sign of the normalized stress gradient index G(p)/W(B). The hips with positive G(p)/W(B) are considered to be dysplastic while the hips with negative G(p)/W(B) are considered to be normal. The statistically significant correlation between the value of the Harris hip score, used in the clinical assessment of the hip dysplasia, and the normalized stress gradient index was found.

Hypothesis of regulation of hip joint cartilage activity by mechanical loading

Hypothesis of regulation of proteosynthetic activity of chondrocytes is suggested. A deformation of the cartilage caused by contact hip joint stress and consequent deformation of the chondrocytes are considered as main factors that could influence the metabolism of the cartilage.

Planar, cylindrical and spherical electrical double layers in biological systems. The effect of counterion size

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.