Normal red blood cells' shape stabilized by membrane's in-plane ordering.

Red blood cells (RBCs) are present in almost all vertebrates and their main function is to transport oxygen to the body tissues. RBCs' shape plays a significant role in their functionality. In almost all mammals in normal conditions, RBCs adopt a disk-like (discocyte) shape, which optimizes their flow properties in vessels and capillaries. Experimentally measured values of the reduced volume (v) of stable discocyte shapes range in a relatively broad window between v ~ 0.58 and 0.8. However, these observations are not supported by existing theoretical membrane-shape models, which predict that discocytic RBC shape is stable only in a very narrow interval of v values, ranging between v ~ 0.59 and 0.65. In this study, we demonstrate that this interval is broadened if a membrane's in-plane ordering is taken into account. We model RBC structures by using a hybrid Helfrich-Landau mesoscopic approach. We show that an extrinsic (deviatoric) curvature free energy term stabilizes the RBC discocyte shapes. In particular, we show on symmetry grounds that the role of extrinsic curvature is anomalously increased just below the nematic in-plane order-disorder phase transition temperature.

Spatial variation of permittivity of an electrolyte solution in contact with a charged metal surface: a mini review.

Contact between a charged metal surface and an electrolyte implies a particular ion distribution near the charged surface, i.e. the electrical double layer. In this mini review, different mean-field models of relative (effective) permittivity are described within a simple lattice model, where the orientational ordering of water dipoles in the saturation regime is taken into account. The Langevin-Poisson-Boltzmann (LPB) model of spatial variation of the relative permittivity for point-like ions is described and compared to a more general Langevin-Bikerman (LB) model of spatial variation of permittivity for finite-sized ions. The Bikerman model and the Poisson-Boltzmann model are derived as limiting cases. It is shown that near the charged surface, the relative permittivity decreases due to depletion of water molecules (volume-excluded effect) and orientational ordering of water dipoles (saturation effect). At the end, the LPB and LB models are generalised by also taking into account the cavity field.

Mechanics and electrostatics of the interactions between osteoblasts and titanium surface.

Due to oxidation and adsorption of chloride and hydroxyl anions, the surface of titanium (Ti) implants is negatively charged. A possible mechanism of the attractive interaction between the negatively charged Ti surface and the negatively charged osteoblasts is described theoretically. It is shown that adhesion of positively charged proteins with internal charge distribution may give rise to attractive interaction between the Ti surface and the osteoblast membrane. A dynamic model of the osteoblast attachment is presented in order to study the impact of geometrically structured Ti surfaces on the osteoblasts attachment. It is indicated that membrane-bound protein complexes (PCs) may increase the membrane protrusion growth between the osteoblast and the grooves on titanium (Ti) surface and thereby facilitate the adhesion of osteoblasts to the Ti surface. On the other hand, strong local adhesion due to electrostatic forces may locally trap the osteoblast membrane and hinder the further spreading of osteointegration boundary. We suggest that the synergy between these two processes is responsible for successful osteointegration along the titanium surface implant.

Attachment of rod-like (BAR) proteins and membrane shape.

Previous studies have shown that cellular function depends on rod-like membrane proteins, among them Bin/Amphiphysin/Rvs (BAR) proteins may curve the membrane leading to physiologically important membrane invaginations and membrane protrusions. The membrane shaping induced by BAR proteins has a major role in various biological processes such as cell motility and cell growth. Different models of binding of BAR domains to the lipid bilayer are described. The binding includes hydrophobic insertion loops and electrostatic interactions between basic amino acids at the concave region of the BAR domain and negatively charged lipids. To shed light on the elusive binding dynamics, a novel experiment is proposed to expand the technique of single-molecule AFM for the traction of binding energy of a single BAR domain.

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.

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.

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.

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.

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.

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.

Mathematical estimation of stress distribution in normal and dysplastic human hips.

By using a mathematical model of the adult human hip in the static one-legged stance position of the body, the forces acting on the hip, peak stress in the hip joint and other relevant radiographic and biomechanical parameters were assessed. The aims were to examine if the peak stress in dysplastic hips is higher than in normal hips and to find out which biomechanical parameters contribute significantly to higher peak stress. The average normalized peak stress in dysplastic hips (7.1 kPa/N) was markedly higher (to approximately 100%) than the average normalized peak stress in normal hips (3.5 kPa/N). The characteristic parameters that contributed to higher peak stress in dysplastic hips included the smaller lateral coverage of the femoral head, the larger interhip distance, the wider pelvis, and the medial position of the greater trochanter. These results are consistent with the hypothesis that stress distribution over weight-bearing surface of the hip joint is the relevant parameter for assessment of the risk for developing coxarthrosis.

Hip stress reduction after Chiari osteotomy.

A mathematical model was developed to study the effect of the Chiari osteotomy on the distribution of contact hip stress over the weight-bearing area. It was shown that Chiari osteotomy can increase the weight-bearing area directly (on the lateral side), owing to the additional area formed by the ala ossis ilii segment, and indirectly (on the medial side), owing to the shift of the stress pole in the medial direction. As a consequence, the contact hip stress is reduced after Chiari osteotomy. The indirect effect is important and often larger than the direct one. Using the proposed mathematical model and standard anteroposterior roentgenographs from archives, the average peak stress on the weight-bearing area, normalised with respect to the body weight (pmax/ W(B)), was determined before and after Chiari osteotomy (8,310m(-2) and 4,480 m(-2), respectively) on a population of 29 dysplastic hips. The difference was statistically significant (p < 0.005). Based on the results presented, it can be concluded that the hip joint contact stress in dysplastic hips considerably decreases after Chiari osteotomy, indicating a favourable biomechanical effect of this operation.

Biomechanical evaluation of hip joint after Salter innominate osteotomy: a long-term follow-up study.

The biomechanical state of the hip after a Salter innominate osteotomy was investigated by using the radiographic data of 38 operated and 21 contralateral nonoperated hips from our archives. The centre-edge angle of Wiberg was determined from the radiographs taken shortly after the operation. From the radiographs of the latest follow-up (7-13 years after the operation), we also determined the peak value of contact hip joint stress normalized by the body weight, and the functional angle of the weight-bearing area. A mathematical model was used. We show that the geometrical parameters aside from the centre-edge angle may considerably influence the contact hip stress distribution. We also show that the functional angle of the weight-bearing area is a more relevant parameter than the normalized peak stress if the exact magnification of the images is not known and if there is considerable variation of the image size within the sample. The development of the centre-edge angle of the operated hips and of the contralateral hips was also studied. We found that the centre-edge angle increases on average during the follow-up time in the operated hips as well as in the contralateral nonoperated hips, but the average increase is smaller in the former. It is shown that an unfavorable stress distribution is connected to the decrease of the centre-edge angle over time. Finally, we found a weak positive correlation between the centre-edge angle shortly after the operation and the functional angle of the weight-bearing area at the of the latest follow-up.

Amphiphile-induced vesiculation in aged hereditary spherocytosis erythrocytes indicates normal membrane stability properties under non-starving conditions.

Aged HS erythrocytes with a defined primary defect in band 3 protein or ankyrin were incubated with amphiphiles (detergents) at sublytic concentrations (37 C, 60 min) or glucose-starved (37 C, 24 h). In line with previous studies, the release of AChE (exovesicles) from HS erythrocytes during glucose-starvation was significantly higher (11%) compared to that from control erythrocytes (1%). Control and HS cells responded, however, similarly to amphiphile-treatment (non-starving conditions). Amphiphiles induced similar types of shape alterations and a similar amount of AChE release (14-15%). Furthermore, the size and shape of amphiphile-induced exo- and endovesicles released from control and HS erythrocytes were similar. The results suggest that the stability properties of the membrane are not seriously disturbed in aged HS erythrocytes under non-starving conditions.

Oxyethylene chain-cation complexation: nonionic polyoxyethylene detergents attain a positive charge and demonstrate electrostatic head group interactions.

We report literature data indicating that the polyoxyethylene chain of polyoxyethylene detergents attracts cations via dipole-ion interactions thereby attaining a positive charge character. This implies that nonionic polyoxyethylene detergents like Triton X-100 and C12E8 may interact electrostatically with phospholipid head groups. We describe how a positive charge character of Triton X-100 and C12E8 can explain their hitherto mysterious stomatocytogenic shape altering effect in human erythrocytes.

On stability of circular hole in membrane bilayer.

It was observed recently that nonionic surfactant octaethyleneglycol dodecylether (Cl2E8) decreases threshold for irreversible electroporation in membrane bilayers. In accordance, it is shown theoretically in this work that anisotropic C12E8 membrane inclusions may stabilize circular hole in a flat membrane segment.

Determination of contact hip stress from nomograms based on mathematical model.

Nomograms are presented that enable determination of maximal stress on the hip joint weight bearing area if certain geometrical parameters of the hip and pelvis and the body weight are known. The nomograms are calculated by using previously developed mathematical models. It is demonstrated how the maximal stress on the hip joint weight bearing area is determined from the presented nomograms for a hip for which the geometrical parameters were obtained from a standard anteroposterior rentgenograph. This simple and noninvasive method may give insight into the biomechanical status of the hip which should be considered in routine surgical planning and as a part of the routine examination of the patient without the use of any additional tools.

Theoretical analysis of shape transformation of V-79 cells after treatment with cytochalasin B.

We observed that after treatment of V-79 fibroblasts with cytochalasin B the area of cell contact with the substrate is essentially reduced, the microtubules are organized into rodlike structures and the actin filaments are disintegrated. Remnants of the actin cortex become concentrated in the form of discrete patches under the plasma membrane. The described changes in the organization of the cytoskeleton and of the cortical shell are accompanied by the formation of a cell shape resembling the Greek letter phi. We calculated that the phi shape corresponds to the minimum of the stretching energy of the cortical shell at relevant geometrical constraints. In line with this result, if cytochalasin B treatment was followed by colchicine application which disrupted the microtubular rod, the characteristic phi shape completely disappeared. This study suggests that the effect of the microtubular rod on the cell shape can be theoretically well described by taking into account some basic conditions for the mechanical equilibrium of the cell cortical shell and the appropriate geometrical constraints.

The assessment of contact stress in the hip joint after operative treatment for severe slipped capital femoral epiphysis.

We determined contact stress on the articular surface of the hip joint in a group of patients who underwent operative treatment for severe slipped capital femoral epiphysis. Two different procedures were considered: the modified osteotomy of Dunn-Fish and the osteotomy of Imhäuser. In order to determine the stress distribution, a three-dimensional mathematical model was used taking into account the geometrical parameters of the pelvis and hip, which were measured from standard antero-posterior radiographs. We found that the Dunn-Fish procedure produced lower peak stress than the Imhäuser procedure.