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.