An elastic network model based on the structure of the red blood cell membrane skeleton.

A finite element network model has been developed to predict the macroscopic elastic shear modulus and the area expansion modulus of the red blood cell (RBC) membrane skeleton on the basis of its microstructure. The topological organization of connections between spectrin molecules is represented by the edges of a random Delaunay triangulation, and the elasticity of an individual spectrin molecule is represented by the spring constant, K, for a linear spring element. The model network is subjected to deformations by prescribing nodal displacements on the boundary. The positions of internal nodes are computed by the finite element program. The average response of the network is used to compute the shear modulus (mu) and area expansion modulus (kappa) for the corresponding effective continuum. For networks with a moderate degree of randomness, this model predicts mu/K = 0.45 and kappa/K = 0.90 in small deformations. These results are consistent with previous computational models and experimental estimates of the ratio mu/kappa. This model also predicts that the elastic moduli vary by 20% or more in networks with varying degrees of randomness. In large deformations, mu increases as a cubic function of the extension ratio lambda 1, with mu/K = 0.62 when lambda 1 = 1.5.     

Mathematical analysis of human red blood cell volume regulation with regard to the elastic effect of the erythrocyte shell on metabolic processes

The mathematical model of the regulation of ion exchange and human erythrocyte volume is extended with a biomechanical model of the erythrocyte shell. This model was used to analyze the influence of elastic properties of the erythrocyte shell on erythrocyte volume in the experiments, where the volume of erythrocytes increased due to the formation of ion channels in the membrane after the treatment with amphotericin B and in case of placing red blood cells in a hypo-osmotic medium. During red blood cell deformation at a constant surface area up to sphericity, the influence of mechanical properties of the shell on volume regulation was shown to be negligible compared to the influence of ion exchange. Further osmotic swelling of red blood cells followed by the increase in their surface area is determined by tensile stiffness of the shell. The high value of tensile stiffness inherent to the erythrocyte shell is constraint for its volume change and also affects ion exchange.     

A multiscale model for red blood cell mechanics

The objective of this article is the derivation of a continuum model for mechanics of red blood cells via multiscale analysis. On the microscopic level, we consider realistic discrete models in terms of energy functionals defined on networks/lattices. Using concepts of Γ-convergence, convergence results as well as explicit homogenisation formulae are derived. Based on a characterisation via energy functionals, appropriate macroscopic stress–strain relationships (constitutive equations) can be determined. Further, mechanical moduli of the derived macroscopic continuum model are directly related to microscopic moduli. As a test case we consider optical tweezers experiments, one of the most common experiments to study mechanical properties of cells. Our simulations of the derived continuum model are based on finite element methods and account explicitly for membrane mechanics and its coupling with bulk mechanics. Since the discretisation of the continuum model can be chosen freely, rather than it is given by the topology of the microscopic cytoskeletal network, the approach allows a significant reduction of computational efforts. Our approach is highly flexible and can be generalised to many other cell models, also including biochemical control.     

A statistical model for red blood cell survival

A statistical model for the survival time of red blood cells (RBCs) with a continuous distribution of cell lifespans is presented. The underlying distribution of RBC lifespans is derived from a probability density function with a bathtub-shaped hazard curve, and accounts for death of RBCs due to senescence (age-dependent increasing hazard rate) and random destruction (constant hazard), as well as for death due to initial or delayed failures and neocytolysis (equivalent to early red cell mortality). The model yields survival times similar to those of previously published studies of RBC survival and is easily amenable to inclusion of drug effects and haemolytic disorders.     

Thermal fluctuations of red blood cell membrane via a constant-area particle-dynamics model

We describe a model of the mechanical properties of the cell plasma membrane using a finite-temperature particle-dynamics simulation of the whole cell, in which a two-dimensional network of virtual particles embedded in a three-dimensional closed surface represents the membrane. The particles interact via harmonic potential and dihedral angle potential and are subject to a constant area constraint. The evolution of the positions of the particles yields the equilibrium state of the membrane and allows determination of the membrane thermal fluctuations and the elastic moduli. We show that time-averaging of the cell-model configurations allows quantitative comparison with experimental data on membrane fluctuations and elastic moduli of the red blood cell.     

Rabbit red blood cell hexokinase

Summary Rabbit hexokinase (EC 2.7.1.1) has been shown to exist in reticulocytes as two distinct molecular forms, designated hexokinase Ia and Ib, but only one of these was consistently present in mature red cells. In vivo, hexokinase la and Ib show a decay rate of 3 and 8% a day, respectively, while in vitro they show a similar stability.The possibility that the proteolytic activities of the reticulocyte could be responsible for the fast decay of hexokinase was investigated. No differences were found in the decay rates of hexokinase la and Ib during in vitro reticulocyte maturation in presence or absence of proteolytic inhibitors. Contrariwise, many findings indicate the ATP-dependent proteolytic system of the reticulocyte as a possible mechanism. In fact, the decay of hexokinase and the degradation of 3H-globins are both stimulated by ATP and ubiquitin; they show similar kinetic properties and both disappear during reticulocyte maturation.The cellular localization of hexokinase la and Ib was shown to be responsible for the differences found between their decay rates.Abbreviations PMSF phenylmethylsulfonyl fluoride - TPCK 1-1-tosylamide-2-phenylethyl-chloromethyl ketone - TLCK N -p-tosyl-L-lysine chloromethyl ketone     

Elasticity of the human red blood cell skeleton

We have measured by optical tweezers micromanipulations the area expansion and the shear moduli of spectrin skeletons freshly extracted from human red blood cells, in different controlled salinity conditions. At medium osmolarity (150 mOsm/kg), we measure KC=9.7+/-3.4 microN/m, muC=5.7+/-2.3 microN/m, KC/muC=2.1+/-0.7. When decreasing the osmolarity, both KC and muC decrease, while KC/muC is nearly constant and equal to about 2. This result is consistent with the predictions made when modeling the spectrin skeleton by a two-dimensional triangular lattice of springs. From the measured elastic moduli we estimate the persistence length of a spectrin filament: xi approximately 2.5 nm at 150 mOsm/kg.     

Membrane rafts of the human red blood cell

The cell type of election for the study of cell membranes, the mammalian non-nucleated erythrocyte, has been scarcely considered in the research of membrane rafts of the plasma membrane. However, detergent-resistant-membranes (DRM) were actually first described in human erythrocytes, as a fraction resisting solubilization by the nonionic detergent Triton X-100. These DRMs were insoluble entities of high density, easily pelleted by centrifugation, as opposed to the now accepted concept of lipid raft-like membrane fractions as material floating in low-density regions of sucrose gradients. The present article reviews the available literature on membrane rafts/DRMs in human erythrocytes from an historical point of view, describing the experiments that provided the solution to the above described discrepancy and suggesting possible avenue of research in the field of membrane rafts that, moving from the most studied model of living cell membrane, the erythrocyte’s, could be relevant also for other cell types.     

Permeability of the human red blood cell tomeso-erythritol

Summary Using¹⁴C-erythritol, we measured net as well as unidirectional erythritol fluxes. Up to near saturation, net and unidirectional fluxes were virtually identical and linearly related to the erythritol concentration in the medium (isotonic saline). No saturation of the transfer system was observed. At 20°C, a maximum of 60 to 70% of the erythritol flux could be inhibited by glucose, phlorizin, or a combination of both substances. Dinitrofluorobenzene and HgCl₂ also reduce erythritol permeability. These findings confirm the earlier conclusion of F. Bowyer and W. F. Widdas that the glucose transport system is involved in erythritol permeation. Glycerol partially inhibits the glucose-phlorizin-sensitive component of erythritol flux, but not the glucose-phlorizin-insensitive component. Apparently glycerol has a slight affinity to that portion of the glucose transport system which is involved in erythritol transfer, whereas the glucosephlorizin-insensitive fraction of erythritol movements is not identical with the glycerol system. This latter inference is supported by the observation that, in contrast to glycerol permeability, erythritol permeability is insensitive to variations of pH or to the addition of copper. The apparent activation energy of the glucose-phlorizin-sensitive and-insensitive fractions of erythritol permeation are 22.2 and 20.7 kcal/mole, respectively. These values are not significantly different from one another.     

Bending elastic modulus of red blood cell membrane derived from buckling instability in micropipet aspiration tests.

Observation of cell membrane buckling and cell folding in micropipette aspiration experiments was used to evaluate the bending rigidity of the red blood cell membrane. The suction pressure required to buckle the membrane surface initially was found to be about one-half to two-thirds of the pressure that caused the cell to fold and move up the pipet. A simple analytical model for buckling of a membrane disk supported at inner and outer radii correlates well with the observed buckling pressures vs. pipet radii. The buckling pressure is predicted to increase in inverse proportion to the cube of the pipet radius; also, the buckling pressure depends inversely on the radial distance to the toroidal rim of the cell, normalized by the pipet radius. As such, the pressure required to buckle the membrane with 1 X 10(-4) cm diam pipet would be about four times greater than with a 2 X 10(-4) cm pipet. This is the behavior observed experimentally. Based on analysis of the observed buckling data, the membrane bending or curvature elastic modulus is calculated to be 1.8 X 10(-12) dyn-cm.     

Mathematical model of red cell sickling

A mathematical model of red cell sickling without crisis was established in vitro as a function of the parameters on which it depends: the oxygen partial pressure, the abnormal hemoglobin S concentration, the temperature and the pH. This model was verified both for the homozygotic sickling SS and heterozygotic sickling SC. Such a model allows systematic investigation of patients. Moreover, it opens up the way for rational comparison in the testing of drugs which are effective in the treatment of red cell sickling.     

Thromboxane induced red blood cell lysis

The two thromboxane A₂ mimetics, carbocyclic thromboxane A₂ (CTA₂) and U-46619 (9,11-methanoepoxy PGH₂) at concentrations of 400 ng/ml significantly enhanced the release of hemoglobin from both feline and human erythrocyte suspensions. This effect was significantly attenuated by the thromboxane receptor antagonist BM-13,505 indicating that the membrane leakiness is in some way receptor mediated. The effects also appear to be concentration-dependent over the range of 100–400 ng/ml. The membrane labilizing effect of thromboxane analogs is not due to a non-specific eicosanoid effect since iloprost, the stable prostacyclin analog, actually stabilized erythrocyte membranes. Moreover, synthetic thromboxane A₂ exerted similar effects to that of the two TxA₂-mimetics. This membrane labilizing action of thromboxanes may be important in propagating the other pathophysiologic effects of thromboxane A₂ in cardiovascular disease states.     

Thromboxane induced red blood cell lysis

The two thromboxane A2 mimetics, carbocyclic thromboxane A2 (CTA2) and U-46619 (9,11-methanoepoxy PGH2) at concentrations of 400 ng/ml significantly enhanced the release of hemoglobin from both feline and human erythrocyte suspensions. This effect was significantly attenuated by the thromboxane receptor antagonist BM-13,505 indicating that the membrane leakiness is in some way receptor mediated. The effects also appear to be concentration-dependent over the range of 100-400 ng/ml. The membrane labilizing effect of thromboxane analogs is not due to a non-specific eicosanoid effect since iloprost, the stable prostacyclin analog, actually stabilized erythrocyte membranes. Moreover, synthetic thromboxane A2 exerted similar effects to that of the two TxA2-mimetics. This membrane labilizing action of thromboxanes may be important in propagating the other pathophysiologic effects of thromboxane A2 in cardiovascular disease states.     

Invertebrate red blood cell carbonic anhydrase

This is the first report documenting the presence of carbonic anhydrase (CA) for any invertebrate red cells. CA activity was measured in plasma, hemolysates of blood cells, and in hemolymph of selected species of invertebrates. Annelid red blood cells (RBC) and sipunculid pink blood cells both possessed significant levels of CA activity. Molluscan RBC, on the other hand, lacked CA activity. The distribution appears to have fallen along phylogenetic lines, with CA being present only in blood cells of the two more closely related groups. However, the presence of extracellular CA was confirmed in oyster hemolymph. Oyster hemolymph CA showed a similar affinity (Ki) for the sulfonamide inhibitors acetazolamide and ethoxzolamide, as did the vertebrate RBC CA II isozyme, supporting the idea that this isozyme could be the ancestral form of the enzyme.