A possible mechanism determining the stability of spiculated red blood cells

Coupling of nematic in-plane orientational ordering and equilibrium shapes of closed flexible nematic shells

The impact of the intrinsic curvature of in-plane orientationally ordered curved flexible nematic molecules attached to closed 3D flexible shells was studied numerically. A Helfrich-Landau-de Gennes-type mesoscopic approach was adopted where the flexible shell's curvature field and in-plane nematic field are coupled and concomitantly determined in the process of free energy minimisation. We demonstrate that this coupling has the potential to generate a rich diversity of qualitatively new shapes of closed 3D nematic shells and the corresponding specific in-plane orientational ordering textures, which strongly depend on the shell's volume-to-surface area ratio, so far not predicted in mesoscopic-type numerical studies of 3D shapes of closed flexible nematic shells.

A new membrane formulation for modelling the flow of stomatocyte, discocyte, and echinocyte red blood cells

In this work, a numerical model that enables simulation of the deformation and flow behaviour of differently aged Red Blood Cells (RBCs) is developed. Such cells change shape and decrease in deformability as they age, thus impacting their ability to pass through the narrow capillaries in the body. While the body filters unviable cells from the blood naturally, cell aging poses key challenges for blood stored for transfusions. Therefore, understanding the influence RBC morphology and deformability have on their flow is vital. While several existing models represent young Discocyte RBC shapes well, a limited number of numerical models are developed to model aged RBC morphologies like Stomatocytes and Echinocytes. The existing models are also limited to shear and stretching simulations. Flow characteristics of these morphologies are yet to be investigated. This paper aims to develop a new membrane formulation for the numerical modelling of Stomatocyte, Discocytes and Echinocyte RBC morphologies to investigate their deformation and flow behaviour. The model used represents blood plasma using the Lattice Boltzmann Method (LBM) and the RBC membrane using the discrete element method (DEM). The membrane and the plasma are coupled by the Immersed Boundary Method (IBM). Previous LBM-IBM-DEM formulations represent RBC membrane response based on forces generated from changes in the local area, local length, local bending, and cell volume. In this new model, two new force terms are added: the local area difference force and the local curvature force, which are specially incorporated to model the flow and deformation behaviour of Stomatocytes and Echinocytes. To verify the developed model, the deformation behaviour of the three types of RBC morphologies are compared to well-characterised stretching and shear experiments. The flow modelling capabilities of the method are then demonstrated by modelling the flow of each cell through a narrow capillary. The developed model is found to be as accurate as benchmark Smoothed Particle Hydrodynamics (SPH) approaches while being significantly more computationally efficient.

Stability of Erythrocyte-Derived Nanovesicles Assessed by Light Scattering and Electron Microscopy

Extracellular vesicles (EVs) are gaining increasing amounts of attention due to their potential use in diagnostics and therapy, but the poor reproducibility of the studies that have been conducted on these structures hinders their breakthrough into routine practice. We believe that a better understanding of EVs stability and methods to control their integrity are the key to resolving this issue. In this work, erythrocyte EVs (hbEVs) were isolated by centrifugation from suspensions of human erythrocytes that had been aged in vitro. The isolate was characterised by scanning (SEM) and cryo-transmission electron microscopy (cryo-TEM), flow cytometry (FCM), dynamic/static light scattering (LS), protein electrophoresis, and UV-V spectrometry. The hbEVs were exposed to various conditions (pH (4–10), osmolarity (50–1000 mOsm/L), temperature (15–60 °C), and surfactant Triton X-100 (10–500 μM)). Their stability was evaluated by LS by considering the hydrodynamic radius (R_h), intensity of scattered light (I), and the shape parameter (ρ). The morphology of the hbEVs that had been stored in phosphate-buffered saline with citrate (PBS–citrate) at 4 °C remained consistent for more than 6 months. A change in the media properties (50–1000 mOsm/L, pH 4–10) had no significant effect on the R_h (=100–130 nm). At pH values below 6 and above 8, at temperatures above 45 °C, and in the presence of Triton X-100, hbEVs degradation was indicated by a decrease in I of more than 20%. Due to the simple preparation, homogeneous morphology, and stability of hbEVs under a wide range of conditions, they are considered to be a suitable option for EV reference material.

Mechanical and Electrical Interaction of Biological Membranes with Nanoparticles and Nanostructured Surfaces

In this review paper, we theoretically explain the origin of electrostatic interactions between lipid bilayers and charged solid surfaces using a statistical mechanics approach, where the orientational degree of freedom of lipid head groups and the orientational ordering of the water dipoles are considered. Within the modified Langevin Poisson–Boltzmann model of an electric double layer, we derived an analytical expression for the osmotic pressure between the planar zwitterionic lipid bilayer and charged solid planar surface. We also show that the electrostatic interaction between the zwitterionic lipid head groups of the proximal leaflet and the negatively charged solid surface is accompanied with a more perpendicular average orientation of the lipid head-groups. We further highlight the important role of the surfaces’ nanostructured topography in their interactions with biological material. As an example of nanostructured surfaces, we describe the synthesis of TiO₂ nanotubular and octahedral surfaces by using the electrochemical anodization method and hydrothermal method, respectively. The physical and chemical properties of these nanostructured surfaces are described in order to elucidate the influence of the surface topography and other physical properties on the behavior of human cells adhered to TiO₂ nanostructured surfaces. In the last part of the paper, we theoretically explain the interplay of elastic and adhesive contributions to the adsorption of lipid vesicles on the solid surfaces. We show the numerically predicted shapes of adhered lipid vesicles corresponding to the minimum of the membrane free energy to describe the influence of the vesicle size, bending modulus, and adhesion strength on the adhesion of lipid vesicles on solid charged surfaces.

On the Role of Curved Membrane Nanodomains, and Passive and Active Skeleton Forces in the Determination of Cell Shape and Membrane Budding

Biological membranes are composed of isotropic and anisotropic curved nanodomains. Anisotropic membrane components, such as Bin/Amphiphysin/Rvs (BAR) superfamily protein domains, could trigger/facilitate the growth of membrane tubular protrusions, while isotropic curved nanodomains may induce undulated (necklace-like) membrane protrusions. We review the role of isotropic and anisotropic membrane nanodomains in stability of tubular and undulated membrane structures generated or stabilized by cyto- or membrane-skeleton. We also describe the theory of spontaneous self-assembly of isotropic curved membrane nanodomains and derive the critical concentration above which the spontaneous necklace-like membrane protrusion growth is favorable. We show that the actin cytoskeleton growth inside the vesicle or cell can change its equilibrium shape, induce higher degree of segregation of membrane nanodomains or even alter the average orientation angle of anisotropic nanodomains such as BAR domains. These effects may indicate whether the actin cytoskeleton role is only to stabilize membrane protrusions or to generate them by stretching the vesicle membrane. Furthermore, we demonstrate that by taking into account the in-plane orientational ordering of anisotropic membrane nanodomains, direct interactions between them and the extrinsic (deviatoric) curvature elasticity, it is possible to explain the experimentally observed stability of oblate (discocyte) shapes of red blood cells in a broad interval of cell reduced volume. Finally, we present results of numerical calculations and Monte-Carlo simulations which indicate that the active forces of membrane skeleton and cytoskeleton applied to plasma membrane may considerably influence cell shape and membrane budding.

Non-uniform distribution of myosin-mediated forces governs red blood cell membrane curvature through tension modulation

The biconcave disk shape of the mammalian red blood cell (RBC) is unique to the RBC and is vital for its circulatory function. Due to the absence of a transcellular cytoskeleton, RBC shape is determined by the membrane skeleton, a network of actin filaments cross-linked by spectrin and attached to membrane proteins. While the physical properties of a uniformly distributed actin network interacting with the lipid bilayer membrane have been assumed to control RBC shape, recent experiments reveal that RBC biconcave shape also depends on the contractile activity of nonmuscle myosin IIA (NMIIA) motor proteins. Here, we use the classical Helfrich-Canham model for the RBC membrane to test the role of heterogeneous force distributions along the membrane and mimic the contractile activity of sparsely distributed NMIIA filaments. By incorporating this additional contribution to the Helfrich-Canham energy, we find that the RBC biconcave shape depends on the ratio of forces per unit volume in the dimple and rim regions of the RBC. Experimental measurements of NMIIA densities at the dimple and rim validate our prediction that (a) membrane forces must be non-uniform along the RBC membrane and (b) the force density must be larger in the dimple than the rim to produce the observed membrane curvatures. Furthermore, we predict that RBC membrane tension and the orientation of the applied forces play important roles in regulating this force-shape landscape. Our findings of heterogeneous force distributions on the plasma membrane for RBC shape maintenance may also have implications for shape maintenance in different cell types.

The spectrin-actin network of the membrane skeleton plays an important role in controlling specialized cell membrane morphology. In the paradigmatic red blood cell (RBC), where actin filaments are present exclusively in the membrane skeleton, recent experiments reveal that nonmuscle myosin IIA (NMIIA) motor contractility maintains the RBC biconcave disk shape. In this study, we have identified criteria for micron-scale distributions of NMIIA forces at the membrane required to maintain the biconcave disk shape of an RBC in the resting condition. Supported by experimental measurements of RBC NMIIA distribution, we showed that a heterogeneous force distribution with a larger force density at the dimple is able to capture the experimentally observed biconcave morphology of an RBC with better accuracy compared to previous models that did not consider the heterogeneity in the force distribution. Furthermore, we showed that the biconcave geometry of the RBC is closely regulated by the effective membrane tension and the direction of applied forces on the membrane. These findings can be generalized to any force-mediated membrane shape, providing insight into the role of actomyosin forces in prescribing and maintaining the morphology of different cell types.

Numerical Model for the Determination of Erythrocyte Mechanical Properties and Wall Shear Stress in vivo From Intravital Microscopy

The mechanical properties and deformability of Red Blood Cells (RBCs) are important determinants of blood rheology and microvascular hemodynamics. The objective of this study is to quantify the mechanical properties and wall shear stress experienced by the RBC membrane during capillary plug flow in vivo utilizing high speed video recording from intravital microscopy, biomechanical modeling, and computational methods. Capillaries were imaged in the rat cremaster muscle pre- and post-RBC transfusion of stored RBCs for 2-weeks. RBC membrane contours were extracted utilizing image processing and parametrized. RBC parameterizations were used to determine updated deformation gradient and Lagrangian Green strain tensors for each point along the parametrization and for each frame during plug flow. The updated Lagrangian Green strain and Displacement Gradient tensors were numerically fit to the Navier-Lame equations along the parameterized boundary to determined Lame's constants. Mechanical properties and wall shear stress were determined before and transfusion, were grouped in three populations of erythrocytes: native cells (NC) or circulating cells before transfusion, and two distinct population of cells after transfusion with stored cells (SC1 and SC2). The distinction, between the heterogeneous populations of cells present after the transfusion, SC1 and SC2, was obtained through principle component analysis (PCA) of the mechanical properties along the membrane. Cells with the first two principle components within 3 standard deviations of the mean, were labeled as SC1, and those with the first two principle components greater than 3 standard deviations from the mean were labeled as SC2. The calculated shear modulus average was 1.1±0.2, 0.90±0.15, and 12 ± 8 MPa for NC, SC1, and SC2, respectively. The calculated young's modulus average was 3.3±0.6, 2.6±0.4, and 32±20 MPa for NC, SC1, and SC2, respectively. o our knowledge, the methods presented here are the first estimation of the erythrocyte mechanical properties and shear stress in vivo during capillary plug flow. In summary, the methods introduced in this study may provide a new avenue of investigation of erythrocyte mechanics in the context of hematologic conditions that adversely affect erythrocyte mechanical properties.

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.

Shallow shell theory of the buckling energy barrier: From the Pogorelov state to softening and imperfection sensitivity close to the buckling pressure

We study the axisymmetric response of a complete spherical shell under homogeneous compressive pressure p to an additional point force. For a pressure p below the classical critical buckling pressure p_{c}, indentation by a point force does not lead to spontaneous buckling but an energy barrier has to be overcome. The states at the maximum of the energy barrier represent a subcritical branch of unstable stationary points, which are the transition states to a snap-through buckled state. Starting from nonlinear shallow shell theory, we obtain a closed analytical expression for the energy barrier height, which facilitates its effective numerical evaluation as a function of pressure by continuation techniques. We find a clear crossover between two regimes: For p/p_{c}≪1 the postbuckling barrier state is a mirror-inverted Pogorelov dimple, and for (1-p/p_{c})≪1 the barrier state is a shallow dimple with indentations smaller than shell thickness and exhibits extended oscillations, which are well described by linear response. We find systematic expansions of the nonlinear shallow shell equations about the Pogorelov mirror-inverted dimple for p/p_{c}≪1 and the linear response state for (1-p/p_{c})≪1, which enable us to derive asymptotic analytical results for the energy barrier landscape in both regimes. Upon approaching the buckling bifurcation at p_{c} from below, we find a softening of an ideal spherical shell. The stiffness for the linear response to point forces vanishes ∝(1-p/p_{c})^{1/2}; the buckling energy barrier vanishes ∝(1-p/p_{c})^{3/2}; and the shell indentation in the barrier state vanishes ∝(1-p/p_{c})^{1/2}. This makes shells sensitive to imperfections which can strongly reduce p_{c} in an avoided buckling bifurcation. We find the same softening scaling in the vicinity of the reduced critical buckling pressure also in the presence of imperfections. We can also show that the effect of axisymmetric imperfections on the buckling instability is identical to the effect of a point force that is preindenting the shell. In the Pogorelov limit, the energy barrier maximum diverges ∝(p/p_{c})^{-3} and the corresponding indentation diverges ∝(p/p_{c})^{-2}. Numerical prefactors for proportionalities both in the softening and the Pogorelov regime are calculated analytically. This also enables us to obtain results for the critical unbuckling pressure and the Maxwell pressure.

Systems biology of cellular membranes: a convergence with biophysics

Systems biology and systems medicine have played an important role in the last two decades in shaping our understanding of biological processes. While systems biology is synonymous with network maps and '-omics' approaches, it is not often associated with mechanical processes. Here, we make the case for considering the mechanical and geometrical aspects of biological membranes as a key step in pushing the frontiers of systems biology of cellular membranes forward. We begin by introducing the basic components of cellular membranes, and highlight their dynamical aspects. We then survey the functions of the plasma membrane and the endomembrane system in signaling, and discuss the role and origin of membrane curvature in these diverse cellular processes. We further give an overview of the experimental and modeling approaches to study membrane phenomena. We close with a perspective on the converging futures of systems biology and membrane biophysics, invoking the need to include physical variables such as location and geometry in the study of cellular membranes. WIREs Syst Biol Med 2017, 9:e1386. doi: 10.1002/wsbm.1386 For further resources related to this article, please visit the WIREs website.

Changes observed in erythrocyte cells exposed to an alternating current

Background and aims

Appliance of electric pulses induces red blood cells (RBCs) membrane poration, membrane aminophospholipid perturbation and alteration of the normal flip-flop process, resulting in various shape changes of the RBCs. We studied morphological and water permeability changes of RBCs bombarded with electrons in an alternating current circuit.

Methods

We used three venous blood samples of 100 mL and an alternating current device. The harvested blood was divided into four experimental sets to be used for various exposure times: 0 hours (control RBCs), 0.5h, 3h and 6h (electric-stimulated RBCs).

Following the electric current each of the four sets were further divided into three samples: one for the assessment of the echinocytes/RBCs ratio, another for the electron microscopy study of ultrastructural changes induced by the alternating electrical current and a larger third one for determining water permeability of RCBs by ¹H-NMR spectroscopy and morphological measurements.

Results

There is a small but statistically significant effect of the RBC exposure to alternating electric current on cell diameters. Exposure to electric current is positively and strongly correlated with the percentage of echinocytes in a duration-dependent manner. There is a strong and statistically significant correlation between electric current exposure and permeability to water as measured by ¹H-NMR spectroscopy.

Conclusion

Following interactions between electric current and RBC membrane, certain modifications were observed in the erythrocyte structure. We attribute the increased cell size to a higher permeability to water and a decreased tonicity. This leads to the transformation of the RBCs into echinocytes.

Effect of shear stress in the flow through the sampling needle on concentration of nanovesicles isolated from blood

During harvesting of nanovesicles (NVs) from blood, blood cells and other particles in blood are exposed to mechanical forces which may cause activation of platelets, changes of membrane properties, cell deformation and shedding of membrane fragments. We report on the effect of shear forces imposed upon blood samples during the harvesting process, on the concentration of membrane nanovesicles in isolates from blood. Mathematical models of blood flow through the needle during sampling with vacuumtubes and with free flow were constructed, starting from the Navier-Stokes formalism. Blood was modeled as a Newtonian fluid. Work of the shear stress was calculated. In experiments, nanovesicles were isolated by repeated centrifugation (up to 17,570×g) and washing, and counted by flow cytometry. It was found that the concentration of nanovesicles in the isolates positively corresponded with the work by the shear forces in the flow of the sample through the needle. We have enhanced the effect of the shear forces by shaking the samples prior to isolation with glass beads. Imaging of isolates by scanning electron microscopy revealed closed globular structures of a similar size and shape as those obtained from unshaken plasma by repetitive centrifugation and washing. Furthermore, the sizes and shapes of NVs obtained by shaking erythrocytes corresponded to those isolated from shaken platelet-rich plasma and from unshaken platelet rich plasma, and not to those induced in erythrocytes by exogenously added amphiphiles. These results are in favor of the hypothesis that a significant pool of nanovesicles in blood isolates is created during their harvesting. The identity, shape, size and composition of NVs in isolates strongly depend on the technology of their harvesting.

Biological potential of nanomaterials strongly depends on the suspension media: experimental data on the effects of fullerene C₆₀ on membranes

Fullerenes (C60) are some of the most promising carbon nanomaterials to be used for medical applications as drug delivery agents. Computational and experimental studies have proposed their ability to enter cells by penetrating lipid bilayers. The aim of our study was to provide experimental evidence on whether pristine C60 in physiological media could penetrate cell membranes. The effect was tested on phospholipid vesicles (liposomes) composed of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine, and validated on isolated human red blood cells (RBCs). We incubated the liposomes in an aqueous suspension of C60 and dissolved the lipids and C60 together in chloroform and subsequently formatted the liposomes. By differential scanning calorimetry measurements, we assessed the effect of C60 on the phospholipid thermal profile. The latter was not affected after the incubation of liposomes in the C60 suspension; also, a shape transformation of RBCs did not occur. Differently, by dispersing both C60 and the phospholipids in chloroform, we confirmed the possible interaction of C60 with the bilayer. We provide experimental data suggesting that the suspension medium is an important factor in determining the C60-membrane interaction, which is not always included in computational studies. Since the primary particle size is not the only crucial parameter in C60-membrane interactions, it is important to determine the most relevant characteristics of their effects on membranes.

The plasma membrane as a capacitor for energy and metabolism

When considering which components of the cell are the most critical to function and physiology, we naturally focus on the nucleus, the mitochondria that regulate energy and apoptotic signaling, or other organelles such as the endoplasmic reticulum, Golgi, ribosomes, etc. Few people will suggest that the membrane is the most critical element of a cell in terms of function and physiology. Those that consider the membrane critical will point to its obvious barrier function regulated by the lipid bilayer and numerous ion channels that regulate homeostatic gradients. What becomes evident upon closer inspection is that not all membranes are created equal and that there are lipid-rich microdomains that serve as platforms of signaling and a means of communication with the intracellular environment. In this review, we explore the evolution of membranes, focus on lipid-rich microdomains, and advance the novel concept that membranes serve as "capacitors for energy and metabolism." Within this framework, the membrane then is the primary and critical regulator of stress and disease adaptation of the cell.

Vesiculation of healthy and defective red blood cells

Vesiculation of mature red blood cells (RBCs) contributes to removal of defective patches of the erythrocyte membrane. In blood disorders, which are related to defects in proteins of the RBC membrane, vesiculation of the plasma membrane is intensified. Several hypotheses have been proposed to explain RBC vesiculation but the exact underlying mechanisms and what determines the sizes of the vesicles are still not completely understood. In this work, we apply a two-component coarse-grained molecular dynamics RBC membrane model to study how RBC vesiculation is controlled by the membrane spontaneous curvature and by lateral compression of the membrane. Our simulation results show that the formation of small homogeneous vesicles with a diameter less than 40 nm can be attributed to a large spontaneous curvature of membrane domains. On the other hand, compression on the membrane can cause the formation of vesicles with heterogeneous composition and with sizes comparable with the size of the cytoskeleton corral. When spontaneous curvature and lateral compression are simultaneously considered, the compression on the membrane tends to facilitate formation of vesicles originating from curved membrane domains. We also simulate vesiculation of RBCs with membrane defects connected to hereditary elliptocytosis (HE) and to hereditary spherocytosis (HS). When the vertical connectivity between the lipid bilayer and the membrane skeleton is elevated, as in normal RBCs, multiple vesicles are shed from the compressed membrane with diameters similar to the cytoskeleton corral size. In HS RBCs, where the connectivity between the lipid bilayer and the cytoskeleton is reduced, larger-size vesicles are released under the same compression ratio as in normal RBCs. Lastly, we find that vesicles released from HE RBCs can contain cytoskeletal filaments due to fragmentation of the membrane skeleton while vesicles released from the HS RBCs are depleted of cytoskeletal filaments.

Effect of carbon black nanomaterial on biological membranes revealed by shape of human erythrocytes, platelets and phospholipid vesicles

BACKGROUND

We studied the effect of carbon black (CB) agglomerated nanomaterial on biological membranes as revealed by shapes of human erythrocytes, platelets and giant phospholipid vesicles. Diluted human blood was incubated with CB nanomaterial and observed by different microscopic techniques. Giant unilamellar phospholipid vesicles (GUVs) created by electroformation were incubated with CB nanomaterial and observed by optical microscopy. Populations of erythrocytes and GUVs were analyzed: the effect of CB nanomaterial was assessed by the average number and distribution of erythrocyte shape types (discocytes, echinocytes, stomatocytes) and of vesicles in test suspensions, with respect to control suspensions. Ensembles of representative images were created and analyzed using computer aided image processing and statistical methods. In a population study, blood of 14 healthy human donors was incubated with CB nanomaterial. Blood cell parameters (concentration of different cell types, their volumes and distributions) were assessed.

RESULTS

We found that CB nanomaterial formed micrometer-sized agglomerates in citrated and phosphate buffered saline, in diluted blood and in blood plasma. These agglomerates interacted with erythrocyte membranes but did not affect erythrocyte shape locally or globally. CB nanomaterial agglomerates were found to mediate attractive interaction between blood cells and to present seeds for formation of agglomerate - blood cells complexes. Distortion of disc shape of resting platelets due to incubation with CB nanomaterial was not observed. CB nanomaterial induced bursting of GUVs while the shape of the remaining vesicles was on the average more elongated than in control suspension, indicating indirect osmotic effects of CB nanomaterial.

CONCLUSIONS

CB nanomaterial interacts with membranes of blood cells but does not have a direct effect on local or global membrane shape in physiological in vitro conditions. Blood cells and GUVs are convenient and ethically acceptable methods for the study of effects of various substances on biological membranes and therefrom derived effects on organisms.

Effects of magnetic cobalt ferrite nanoparticles on biological and artificial lipid membranes

Background

The purpose of this work is to provide experimental evidence on the interactions of suspended nanoparticles with artificial or biological membranes and to assess the possibility of suspended nanoparticles interacting with the lipid component of biological membranes.

Methods

1-Palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) lipid vesicles and human red blood cells were incubated in suspensions of magnetic bare cobalt ferrite (CoFe₂O₄) or citric acid (CA)-adsorbed CoFe₂O₄ nanoparticles dispersed in phosphate-buffered saline and glucose solution. The stability of POPC giant unilamellar vesicles after incubation in the tested nanoparticle suspensions was assessed by phase-contrast light microscopy and analyzed with computer-aided imaging. Structural changes in the POPC multilamellar vesicles were assessed by small angle X-ray scattering, and the shape transformation of red blood cells after incubation in tested suspensions of nanoparticles was observed using scanning electron microscopy and sedimentation, agglutination, and hemolysis assays.

Results

Artificial lipid membranes were disturbed more by CA-adsorbed CoFe₂O₄ nanoparticle suspensions than by bare CoFe₂O₄ nanoparticle suspensions. CA-adsorbed CoFe₂O₄-CA nanoparticles caused more significant shape transformation in red blood cells than bare CoFe₂O₄ nanoparticles.

Conclusion

Consistent with their smaller sized agglomerates, CA-adsorbed CoFe₂O₄ nanoparticles demonstrate more pronounced effects on artificial and biological membranes. Larger agglomerates of nanoparticles were confirmed to be reactive against lipid membranes and thus not acceptable for use with red blood cells. This finding is significant with respect to the efficient and safe application of nanoparticles as medicinal agents.

Anti-plasmodial activity of aroylhydrazone and thiosemicarbazone iron chelators: effect on erythrocyte membrane integrity, parasite development and the intracellular labile iron pool

Iron chelators inhibit the growth of the malaria parasite, Plasmodium falciparum, in culture and in animal and human studies. We previously reported the anti-plasmodial activity of the chelators, 2-hydroxy-1-naphthylaldehyde isonicotinoyl hydrazone (311), 2-hydroxy-1-naphthylaldehyde 4-methyl-3-thiosemicarbazone (N4mT), and 2-hydroxy-1-naphthylaldehyde 4-phenyl-3-thiosemicarbazone (N4pT). In fact, these ligands showed greater growth inhibition of chloroquine-sensitive (3D7) and chloroquine-resistant (7G8) strains of P. falciparum in culture compared to desferrioxamine (DFO). The present study examined the effects of 311, N4mT and N4pT on erythrocyte membrane integrity and asexual parasite development. While the characteristic biconcave disk shape of the erythrocytes was unaffected, the chelators caused very slight hemolysis at IC50 values that inhibited parasite growth. The chelators 311, N4mT and N4pT affected all stages of the intra-erythrocytic development cycle (IDC) of P. falciparum in culture. However, while these ligands primarily affected the ring-stage, DFO inhibited primarily trophozoite and schizont-stages. Ring, trophozoite and schizont-stages of the IDC were inhibited by significantly lower concentrations of 311, N4mT, and N4pT (IC50=4.45±1.70, 10.30±4.40, and 3.64±2.00μM, respectively) than DFO (IC50=23.43±3.40μM). Complexation of 311, N4mT and N4pT with iron reduced their anti-plasmodial activity. Estimation of the intracellular labile iron pool (LIP) in erythrocytes showed that the chelation efficacy of 311, N4mT and N4pT corresponded to their anti-plasmodial activities, suggesting that the LIP may be a potential source of non-heme iron for parasite metabolism within the erythrocyte. This study has implications for malaria chemotherapy that specifically disrupts parasite iron utilization.

Small scale membrane mechanics

Large scale changes to lipid bilayer shapes are well represented by the Helfrich model. However, there are membrane processes that take place at smaller length scales that this model cannot address. In this work, we present a one-dimensional continuum model that captures the mechanics of the lipid bilayer membrane at the length scale of the lipids themselves. The model is developed using the Cosserat theory of surfaces with lipid orientation, or 'tilt', as the fundamental degree of freedom. The Helfrich model can be recovered as a special case when the curvatures are small and the lipid tilt is everywhere zero. We use the tilt model to study local membrane deformations in response to a protein inclusion. Parameter estimates and boundary conditions are obtained from a coarse-grained molecular model using dissipative particle dynamics (DPD) to capture the same phenomenon. The continuum model is able to reproduce the membrane bending, stretch and lipid tilt as seen in the DPD model. The lipid tilt angle relaxes to the bulk tilt angle within 5-6 nm from the protein inclusion. Importantly, for large tilt gradients induced by the proteins, the tilt energy contribution is larger than the bending energy contribution. Thus, the continuum model of tilt accurately captures behaviors at length scales shorter than the membrane thickness.

Equilibrium shape equation and geometrically permissible condition for two-component lipid bilayer vesicles

Equilibrium shapes of vesicles composed of a mixture of partially miscible amphiphiles are investigated. To take into account the influences of the composition, a simple phenomenological coupling between the co mposition and the curvatures, including the mean curvature and the Gauss curvature of the membrane surface, is suggested. By minimizing the potential functional, the general shape equation is obtained and solved analytically for vesicles with simple shapes. Besides, the geometrical constraint equation and geometrically permissible condition for the two-component lipid vesicles are put forward. The influences of physical parameters on the geometrically permissible phase diagrams are predicted. The close relations between the predictions and existing experimental phenomena published recently are shown.

DISEASED RED BLOOD CELLS STUDIED BY ATOMIC FORCE MICROSCOPY

In recent years, many mammalian cells, especially erythrocytes because of simpleness of their membrane surfaces, were widely studied by atomic force microscopy. In our study, diseased erythrocytes were taken from patients of lung cancer, myelodisplastic syndrome (MDS), and so on. We obtained many clear topographical images of numerous erythrocytes, single erythrocyte, and ultramicrostructure of erythrocyte membrane surfaces from normal persons and patients. By studying the red cells of lung cancer patients, we found that many erythrocytes of lung cancer patient have changed into echinocytes. One erythrocyte has 10–20 short projections, most of which, with a mean width of 589.0 nm and a length of 646.7 nm, are on the edge of cell. The projections in the center of echinocytes are lodged and embedded, but in conventional model of echinocytes, the projections in the center stretch outside cell membrane, so a novel model of erythrocytes was designed in our paper. After observation of microstructure of MDS patient's erythrocyte membrane surface, we found that many apertures with different diameters of tens to hundreds nanometers appeared on the surface of cell membrane. It can be concluded that AFM may be widely applied in clinic pathological inspection.

Curvature factor and membrane solubilization, with particular reference to membrane rafts

The composition of membrane rafts (cholesterol/sphingolipid-rich domains) cannot be fully deduced from the analysis of a detergent-resistant membrane fraction after solubilization in Triton X-100 at 4°C. It is hypothesized that the membrane curvature-dependent lateral distribution of membrane components affects their solubilization. The stomatocytogenic, Triton X-100, cannot effectively solubilize membrane components, especially with regard to the outward membrane curvature.

The role of counterions in the membrane-disruptive properties of pH-sensitive lysine-based surfactants

Surfactants are among the most versatile and widely used excipients in pharmaceuticals. This versatility, together with their pH-responsive membrane-disruptive activity and low toxicity, could also enable their potential application in drug delivery systems. Five anionic lysine-based surfactants which differ in the nature of their counterion were studied. Their capacity to disrupt the cell membrane was examined under a range of pH values, concentrations and incubation times, using a standard hemolysis assay as a model for endosomal membranes. The surfactants showed pH-sensitive hemolytic activity and improved kinetics at the endosomal pH range. Low concentrations resulted in negligible hemolysis at physiological pH and high membrane lytic activity at pH 5.4, which is in the range characteristic of late endosomes. With increasing concentration, the surfactants showed an enhanced capacity to lyse cell membranes, and also caused significant membrane disruption at physiological pH. This observation indicates that, at high concentrations, surfactant behavior is independent of pH. The mechanism of surfactant-mediated membrane destabilization was addressed, and scanning electron microscopy studies were also performed to evaluate the effects of the compounds on erythrocyte morphology as a function of pH. The in vitro cytotoxicity of the surfactants was assessed by MTT and NRU assays with the 3T3 cell line. The influence of different types of counterion on hemolytic activity and the potential applications of these surfactants in drug delivery are discussed. The possibility of using pH-sensitive surfactants for endosome disruption could hold great promise for intracellular drug delivery systems in future therapeutic applications.

Hemolytic activity of a bacterial trehalose lipid biosurfactant produced by Rhodococcus sp.: evidence for a colloid-osmotic mechanism

A succinoyl trehalose lipid produced by Rhodococcus sp. behaves as a biological surfactant and also displays various interesting biological activities. Trehalose lipid has been shown to have a great tendency to partition into phospholipid membranes; therefore, the characterization of its interaction with biological membranes is of central importance. In this work, human red blood cells have been used as an experimental model. Trehalose lipid causes the swelling of human erythrocytes followed by hemolysis at concentrations well below its critical micellar concentration. Kinetic measurements show that, upon addition of trehalose lipid, K(+) release precedes that of hemoglobin. Osmotic protectants of the appropriate size added to the external medium make it possible to avoid hemolysis. The results indicate that trehalose lipid causes the hemolysis of human erythrocytes by a colloid-osmotic mechanism, most likely by formation of enhanced permeability domains, or "pores" enriched in the biosurfactant, within the erythrocyte membrane. Scanning electron microscopy shows trehalose lipid-induced spherocytosis and echinocytosis of red blood cells, which fits well within the framework of the bilayer-couple hypothesis. The presented results contribute to establishing a molecular basis for the biological properties of this trehalose lipid biosurfactant.

Mathematical models of naturally "morphed" human erythrocytes: stomatocytes and echinocytes

We present two mathematical models that describe human red blood cells (RBCs) with morphologies that are attained naturally under certain patho-physiological conditions, namely stomatocytes and echinocytes. Muñoz San Martín et al. (Bioelectromagnetics 27:521-527, 2006) recently presented models of these shapes based on our previous set of parametric equations (Kuchel and Fackerell, Bull. Math. Biol. 61:209-220, 1999) that involve Jacobi elliptic functions and integrals. Thus, both discocytes and stomatocytes are described. Here, we derived the Cartesian forms of these new equations; and, in addition, present a realistic model of a Type III echinocyte, using prolate spheroids 'decorating' a central sphere at the vertices of an internal dodecahedron. The RBC models based on Cartesian equations have been used for representing the shape changes (morphological transformations or "morphing") that occur in RBCs under various experimental conditions; specifically, when the shape changes have been monitored by nuclear magnetic resonance (NMR) micro-imaging.

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.

Shapes of Red Blood Cells: Comparison of 3D Confocal Images with the Bilayer-Couple Model

Cells and organelles are shaped by the chemical and physical forces that bend cell membranes. The human red blood cell (RBC) is a model system for studying how such forces determine cell morphology. It is thought that RBCs, which are typically biconcave discoids, take the shape that minimizes their membrane-bending energies, subject to the constraints of fixed area and volume. However, recently it has been hypothesized that shear elasticity arising from the membrane-associated cytoskeleton (MS) is necessary to account for shapes of real RBCs, especially ones with highly curved features such as echinocytes. In this work we tested this hypothesis by following RBC shape changes using spherical harmonic series expansions of theoretical cell surfaces and those estimated from 3D confocal microscopy images of live cells. We found (i) quantitative agreement between shapes obtained from the theoretical model including the MS and real cells, (ii) that weakening the MS, by using urea (which denatures spectrin), leads to the theoretically predicted gradual decrease in spicule number of echinocytes, (iii) that the theory predicts that the MS is essential for stabilizing the discocyte morphology against changes in lipid composition, and that without it, the shape would default to the elliptocyte (a biconcave ellipsoid), (iv) that we were able to induce RBCs to adopt the predicted elliptocyte morphology by treating healthy discocytes with urea. The latter observation is consistent with the known connection between the blood disease hereditary elliptocytosis and spectrin mutations that weaken the cell cortex. We conclude that while the discocyte, in absence of shear, is indeed a minimum energy shape, its stabilization in healthy RBCs requires the MS, and that elliptocytosis can be explained based on purely mechanical considerations.

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.

Effects of 5-fluorouracil on erythrocytes in relation to its cardiotoxicity: membrane structure and functioning

In the present study, we showed that the antineoplastic drug 5-fluorouracil (5-FU) induces in vitro exposure-time/dose-dependent changes on the level of an erythrocyte's morphology, ionic balance, and membrane fluidity. These changes are partially or fully irreversible, and we suggest that they are provoked by an irreversible depletion of ATP. Because of these changes that could also occur in vivo during 5-FU infusion, a certain amount of erythrocytes with echinocytic shape and diminished ability to deliver oxygen is present in blood for longer periods of time. This renders oxygen transport and delivery more difficult, leaving the heart with an insufficient supply of oxygen, thus leading to cardiotoxicity.

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.

Indentation and adhesive probing of a cell membrane with AFM: theoretical model and experiments

In probing adhesion and cell mechanics by atomic force microscopy (AFM), the mechanical properties of the membrane have an important if neglected role. Here we theoretically model the contact of an AFM tip with a cell membrane, where direct motivation and data are derived from a prototypical ligand-receptor adhesion experiment. An AFM tip is functionalized with a prototypical ligand, SIRPalpha, and then used to probe its native receptor on red cells, CD47. The interactions prove specific and typical in force, and also show in detachment, a sawtooth-shaped disruption process that can extend over hundreds of nm. The theoretical model here that accounts for both membrane indentation as well as membrane extension in tip retraction incorporates membrane tension and elasticity as well as AFM tip geometry and stochastic disruption. Importantly, indentation depth proves initially proportional to membrane tension and does not follow the standard Hertz model. Computations of detachment confirm nonperiodic disruption with membrane extensions of hundreds of nm set by membrane tension. Membrane mechanical properties thus clearly influence AFM probing of cells, including single molecule adhesion experiments.

Shape equations and curvature bifurcations induced by inhomogeneous rigidities in cell membranes

This article aims at two objectives: one is the shape equation for the equilibrium configurations of biomembranes with heterogeneous rigidities; another is the possible mechanism for curvature bifurcations in various biomembranes such as human red blood cells (RBC). The shape equation is established by treating the inhomogeneous biomembrane as a lipid bilayer vesicle containing inclusions or impurities. After careful investigation of the equation, the rigidity gradient is found to be an initial "driving force" that may destabilize the biomembrane and stimulate shape transitions, and the concept (or mechanism) termed "curvature bifurcations induced by rigidity gradients" is suggested. Various post-bifurcation modes recording the new equilibrium configurations are disclosed. A few post-bifurcation modes are found to coincide well with some practical shape transitions in cells such as the cup-like shape (stomatocyte) transition and spiculated shape (echinocyte) transition in RBC.

General Mathematical Frame for Open or Closed Biomembranes (Part I): Equilibrium Theory and Geometrically Constraint Equation

This paper aims at constructing a general mathematical frame for the equilibrium theory of open or closed biomembranes. Based on the generalized potential functional, the equilibrium differential equation for open biomembrane (with free edge) or closed one (without boundary) is derived. The boundary conditions for open biomembranes are obtained. Besides, the geometrically constraint equation for the existence, formation and disintegration of open or closed biomembranes is revealed. The physical and biological meanings of the equilibrium differential equation and the geometrically constraint equation are discussed. Numerical simulation results for axisymmetric open biomembranes show the effectiveness and convenience of the present theory.

Giant lipid vesicles filled with a gel: shape instability induced by osmotic shrinkage

We report the properties of giant lipid vesicles enclosing an agarose gel. In this system, the lipid bilayer retains some basic properties of biological membranes and the internal fluid exhibits viscoelastic properties, thus permitting us to address the question of the deformation of a cell membrane in relation to the mechanical properties of its cytoskeleton. The agarose gel (concentration c0gel = 0.07%, 0.18%, 0.36%, and 1% w/w), likely not anchored to the membrane, confers to the internal volume elastic moduli in the range of 10-10(4) Pa. Shapes and kinetics of de-swelling of gel-filled and aqueous solution-filled vesicles are compared upon either a progressive or a fast osmotic shrinkage. Both systems exhibit similar kinetics. Shapes of solution-filled vesicles are well described using the area difference elasticity model, whereas gel-filled vesicles present original patterns: facets, bumps, spikes (c0gel < 0.36%), or wrinkles (c0gel > or = 0.36%). These shapes partially vanish upon re-swelling, and some of them are reminiscent of echinocytic shapes of erythrocytes. Their characteristic size (microns) decreases upon increasing c0gel. A possible origin of these patterns, relying on the formation of a dense impermeable gel layer at the vesicle surface and associated with a transition toward a collapsed gel phase, is advanced.

Mechanics of Curved Plasma Membrane Vesicles: Resting Shapes, Membrane Curvature, and In-Plane Shear Elasticity

Highly curved cell membrane structures, such as plasmalemmal vesicles (caveolae) and clathrin-coated pits, facilitate many cell functions, including the clustering of membrane receptors and transport of specific extracellular macromolecules by endothelial cells. These structures are subject to large mechanical deformations when the plasma membrane is stretched and subject to a change of its curvature. To enhance our understanding of plasmalemmal vesicles we need to improve the understanding of the mechanics in regions of high membrane curvatures. We examine here, theoretically, the shapes of plasmalemmal vesicles assuming that they consist of three membrane domains: an inner domain with high curvature, an outer domain with moderate curvature, and an outermost flat domain, all in the unstressed state. We assume the membrane properties are the same in these domains with membrane bending elasticity as well as in-plane shear elasticity. Special emphasis is placed on the effects of membrane curvature and in-plane shear elasticity on the mechanics of vesicle during unfolding by application of membrane tension. The vesicle shapes were computed by minimization of bending and in-plane shear strain energy. Mechanically stable vesicles were identified with characteristic membrane necks. Upon stretch of the membrane, the vesicle necks disappeared relatively abruptly leading to membrane shapes that consist of curved indentations. While the resting shape of vesicles is predominantly affected by the membrane spontaneous curvatures, the membrane shear elasticity (for a range of values recorded in the red cell membrane) makes a significant contribution as the vesicle is subject to stretch and unfolding. The membrane tension required to unfold the vesicle is sensitive with respect to its shape, especially as the vesicle becomes fully unfolded and approaches a relative flat shape.

The cooperative role of membrane skeleton and bilayer in the mechanical behaviour of red blood cells

Red blood cell (RBC) shape, behaviour and deformability can be consistently accounted for by a model for the elastic properties of the RBC membrane that includes the elasticity of the membrane skeleton in dilation and shear, and the local and nonlocal resistance of the bilayer to bending. The role of the corresponding energy terms in different RBC shape and deformation situations is analyzed. RBC shape transformations are compared to the shape transformations of phospholipid vesicles that are driven by the difference between the equilibrium areas of the bilayer leaflets (DeltaA0). It is deduced that the skeleton energy contributions play a crucial role in the formation of an echinocyte. The effect of a transformation of the natural biconcave RBC shape into an echinocyte on its resistance to entry into capillary-sized cylindrical tubes is analyzed. It is shown that, during the aspiration of an echinocyte into a pipette, there are two competing skeleton deformation effects, which arise due to skeleton density changes, one due to spicule formation and the other due to deformation induced by micropipette aspiration. Furthermore, the shift of the observed dependence of the projection length on the aspiration pressure of more crenated cells towards higher aspiration pressures can be accounted for by an increase of the equilibrium area difference DeltaA0 and consequent modification of the nonlocal contribution to the cell elastic energy.

Elastic properties of the red blood cell membrane that determine echinocyte deformability

The natural biconcave shape of red blood cells (RBC) may be altered by injury or environmental conditions into a spiculated form (echinocyte). An analysis is presented of the effect of such a transformation on the resistance of RBC to entry into capillary sized cylindrical tubes. The analysis accounts for the elasticity of the membrane skeleton in dilation and shear, and the local and nonlocal resistance of the bilayer to bending, the latter corresponding to different area strains in the two leaflets of the bilayer. The shape transformation is assumed to be driven by the equilibrium area difference (delta A(0), the difference between the equilibrium areas of the bilayer leaflets), which also affects the energy of deformation. The cell shape is approximated by a parametric model. Shape parameters, skeleton shear deformation, and the skeleton density of deformed membrane relative to the skeleton density of undeformed membrane are obtained by minimization of the corresponding thermodynamic potential. Experimentally, delta A(0) is modified and the corresponding discocyte-echinocyte shape transition obtained by high-pressure aspiration into a narrow pipette, and the deformability of the resulting echinocyte is examined by whole cell aspiration into a larger pipette. We conclude that the deformability of the echinocyte can be accounted for by the mechanical behavior of the normal RBC membrane, where the equilibrium area difference delta A(0) is modified.

Stomatocyte-discocyte-echinocyte sequence of the human red blood cell: evidence for the bilayer- couple hypothesis from membrane mechanics

Red-cell shape is encoded in the mechanical properties of the membrane. The plasma membrane contributes bending rigidity; the protein-based membrane skeleton contributes stretch and shear elasticity. When both effects are included, membrane mechanics can reproduce in detail the full stomatocyte-discocyte-echinocyte sequence by variation of a single parameter related to the bilayer couple originally introduced by Sheetz and Singer [Sheetz, M. P. & Singer, S. J. (1974) Proc. Natl. Acad. Sci. USA 71, 4457-4461].

In vitro Plasmodium falciparum drug sensitivity assay: inhibition of parasite growth by incorporation of stomatocytogenic amphiphiles into the erythrocyte membrane

Lupeol, which shows in vitro inhibitory activity against Plasmodium falciparum 3D7 strain with a 50% inhibitory concentration (IC50) of 27.7 +/- 0.5 microM, was shown to cause a transformation of the human erythrocyte shape toward that of stomatocytes. Good correlation between the IC50 value and the membrane curvature changes caused by lupeol was observed. Preincubation of erythrocytes with lupeol, followed by extensive washing, made the cells unsuitable for parasite growth, suggesting that the compound incorporates into erythrocyte membrane irreversibly. On the other hand, lupeol-treated parasite culture continued to grow well in untreated erythrocytes. Thus, the antiplasmodial activity of lupeol appears to be indirect, being due to stomatocytic transformation of the host cell membrane and not to toxic effects via action on a drug target within the parasite. A number of amphiphiles that cause stomatocyte formation, but not those causing echinocyte formation, were shown to inhibit growth of the parasites, apparently via a mechanism similar to that of lupeol. Since antiplasmodial agents that inhibit parasite growth through erythrocyte membrane modifications must be regarded as unsuitable as leads for development of new antimalarial drugs, care must be exercised in the interpretation of results of screening of plant extracts and natural product libraries by an in vitro Plasmodium toxicity assay.

Echinocyte shapes: bending, stretching, and shear determine spicule shape and spacing

We study the shapes of human red blood cells using continuum mechanics. In particular, we model the crenated, echinocytic shapes and show how they may arise from a competition between the bending energy of the plasma membrane and the stretching/shear elastic energies of the membrane skeleton. In contrast to earlier work, we calculate spicule shapes exactly by solving the equations of continuum mechanics subject to appropriate boundary conditions. A simple scaling analysis of this competition reveals an elastic length Lambda(el), which sets the length scale for the spicules and is, thus, related to the number of spicules experimentally observed on the fully developed echinocyte.

Theoretical predictions of electromechanical deformation of cells subjected to high voltages for membrane electroporation

An electromechanical analysis based on thin-shell theory is presented to analyze cell shape changes in response to external electric fields. This approach can be extended to include osmotic-pressure changes. Our calculations demonstrate that at large fields, the spherical cell geometry can be significantly modified, and even ellipsoidal forms would be inappropriate to account for the deformation. Values of the surface forces obtained from our calculations are in very good agreement with the 1--10 mN/m range for membrane rupture reported in the literature. The results, in keeping with reports in the literature, demonstrate that the final shape depends on membrane thickness. This has direct implications for tissues in which significant molecular restructuring can occur. It is also shown that, at least for the smaller electric fields, both the cellular surface area and volume change roughly in a quadratic manner with the electric field. Finally, it is shown that the bending moments are generally quite small and can be neglected for a simpler analysis.

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.

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.