Theoretical model of reticulocyte to erythrocyte shape transformation

A theoretical model describing the kinetics of reticulocyte shape transformation was developed. The model considers the evolution of a simple cellular shape under transmembrane pressure difference, and proposes a four-parameter axisymmetric approximation of the cell surface. The mathematical analysis considers plasma membrane tension in the plane of bilayer leaflets, membrane spontaneous curvature and transmembrane transport of water. Cytoskeleton dilatational and shear rigidity, and the energetic barrier preventing the decrease of cell volume below a certain minimum are also incorporated. The set of adequate physical assumptions allowed for formulation of the equation for free energy of the investigated system. Computer simulations of cell shape changes, down to the state of free energy minimum, together with estimation of the time needed for the resulting transport of water, revealed a complex, three-phase picture of temporal alterations in cellular geometry with a wide spectrum of final results, and led to propose a standard model of reticulocyte-erythrocyte transformation. According to the model, both cell volume and surface undergo changes, and the work of the pressure, initially accumulated in the cytoskeleton, is consumed for local bending of the cell membrane. Further simulations with modified initial shape or parameters of the standard model show the trajectories of system evolution and help in better understanding the conditions for the erythro-, sphero-, ovalo-, stomato-, and leptoidal metamorphosis of maturing red blood cells. The stability of the final biconcave shape was also verified. Spherogenic modifications were discussed in the context of spherocytosis. Future development of the model was proposed.     

Passive transmembrane redistributions of phospholipids as a determinant of erythrocyte shape change. Studies on electroporated cells

Echinocytes formed from discocytic erythrocytes by electric field pulses at 0 degrees C return to the discoytic shape upon incubation at 37 degrees C and subsequently turn into stomatocytes. Active and passive components of phospholipid translocation are involved in this shape recovery. Following low-field-strength pulses (5 kV cm-1), shape recovery is fully suppressed by ATPase inhibitors, such as vanadate. When vanadate is only added after stomatocyte formation has been completed, the cells return to the stage of echinocytosis prevailing before recovery. At higher field strength (7 kV cm-1) and in particular after repetitive field pulses, the subsequent incubation at 37 degrees C results in partial shape recovery even in the presence of vanadate. On the basis of the enhanced passive transmembrane mobilities of phospholipid probes observed previously following electroporation, the shape changes in the presence of vanadate are proposed to be due to a passive net movement of phospholipids from the outer to the inner membrane leaflet, as a consequence of the different mobilities of the various membrane phospholipids. Repetitive pulses at higher field strengths lead to a progressively more discocytic stationary shape during subsequent resealing. This phenomenon is explained by the progressively increased transbilayer mobility of the normally almost immobile phospholipid sphingomyelin and a consecutive progressive symmetrization of all membrane phospholipds.     

Influence of erythrocyte shape on the rate of Ca2+-induced scrambling of phosphatidylserine

Membrane-perturbing agents that cause transformation of biconcave erythrocytes into echinocytes or stomatocytes were used to investigate the influence of erythrocyte shape on the rate of Ca²⁺-induced scrambling of phospholipids. Erythrocytes were treated with a variety of lipid-soluble compounds to induce these shape changes, followed by incubation with calcium and ionomycin to activate lipid scramblase. Prothrombinase activity of the cells was used to monitor the rate of surface exposure of phosphatidylserine, which is taken as a measure of scramblase activity. Echinocytes show an enhanced rate of scrambling, whereas stomatocytes show a reduced rate, relative to normocytes. This phenomenon appears to correlate with enhanced and diminished micro-exovesicle shedding from echinocytes and stomatocytes, respectively. It is concluded that the rate of calcium-induced phosphatidylserine exposure (rate of lipid scrambling) in erythrocytes depends for a considerable part on the cells' ability to form microvesicles.     

Fluorescence assay of non-transferrin-bound iron in thalassemic sera using bacterial siderophore

Transfusional iron overload associated with thalassemia leads to the appearance of non-transferrin-bound iron (NTBI) in blood that is toxic and causes morbidity and mortality via tissue damage. Hence, a highly sensitive and accurate assay of NTBI, with broad clinical application in both diagnosis and validation of treatment regimens for iron overload, is important. An assay based on iron chelation by a high-affinity siderophore, azotobactin, has been developed. The steps consist of blocking of native apotransferrin iron binding sites, mobilization of NTBI, ultrafiltration of all serum proteins, and finally the addition of the probe, which has a chromophore that fluoresces at 490 nm. Binding of Fe³⁺ to azotobactin quenches the fluorescence in a concentration-dependent manner. Measured NTBI levels in 63 sera ranged from 0.07 to 3.24 μM (0.375 ± 0.028 μM [means ± SEM]). It correlated well with serum iron and percentage transferrin saturation but not with serum ferritin. Pearson’s correlation coefficients were found to be 0.6074 (P < 0.0001) and 0.6102 (P < 0.0001) for percentage transferrin saturation and total serum iron, respectively. The low values are due to the patients being under regular chelation therapy even prior to sampling, indicating that the method is sensitive to very low levels of NTBI, allowing a much lower detection limit than the available methods.     

Bending undulations and elasticity of the erythrocyte membrane: effects of cell shape and membrane organization

The undulatory excitations (flickering) of human and camel erythrocytes were evaluated by employing the previously used flicker spectroscopy and by local measurements of the autocorrelation function K (t) of the cell thickness fluctuations using a dynamic image processing technique. By fitting theoretical and experimental flicker spectra relative values of the bending elastic modulus K _c of the membrane and of the cytoplasmic viscosity were obtained. The effects of shape changes were monitored by simultaneous measurement of the average light intensity I ₀ passing the cells and by phase contrast microscopic observation of the cells. Evaluation of the cellular excitations in terms of the quasi-spherical model yielded values of K _c /R _inf0 ^sup3 and · R ₀ (R ₀=equivalent sphere radius) and allowed us to account (1) for volume changes, (2) for effects of surface tension and spontaneous curvature and (3) for the non-exponential decay of K (t). From the long time decay of K (t) we obtained an upper limit of the bending elastic modulus of normal cells of K _c = 2–3 · 10^–19 Nm which is an order of magnitude larger than the value found by reflection interference contrast microscopy (RICT, K _c , = 3.4 · 10^–20 Nm, Zilker et al. 1987) but considerably lower than expected for a bilayer containing 50% cholesterol (K _c = 5 · 10^–19 Nm, Duwe et al. 1989). The major part of the paper deals with long time measurements (order of hours) of variations of the apparent K _c and values of single cells (and their reversibility) caused (1) by osmotic volume changes, (2) by discocytestomatocyte transitions induced by albumin and triflouperazine, (3) by discocyte-echinocyte transitions induced by expansion of the lipid/protein bilayer (by incubation with lipid vesicles) and by ATP-depletion in physiological NaCI solution, (4), by coupling or decoupling of bilayer and cytoskeleton using wheat germ agglutinin or erythrocytes with elliptocytosis and (5) by cross-linking the cytoskeleton using diamide. These experiments showed: (1) K _c and are minimal at physiological osmolarity and temperature and well controlled over a large range of these parameters. (2) Echinocyte formation does not markedly alter the apparent membrane bending stiffness. (3) During swelling the cell may undergo a transient discocyte-stomatocyte transition. (4) Strong increases of the apparent K _c and after cup-formation or strong swelling and deflation are due to the effect of shear elasticity and surface tension. Our major conclusions are: (1) The erythrocyte membrane exhibits a shear free deformation regime which requires ATP for its maintenance. (2) Shape transitions may be caused by relative area changes either of the two monolayers of the lipid/protein bilayer (corresponding to the bilayer coupling hypothesis) or of the bilayer and the cytoskeleton where the latter mechanism appears to be more frequent. (3) The low bending stiffness and the shear free deformation regime are explained in terms of a slight excess area of the lipid bilayer leading to a pre-undulated surface profile. Freeze fracture electron microscopy studies provide direct evidence for a pre-undulated bilayer with an undulation wavelength of approximately 100 nm. Offprint requests to: E. Sackmann     

Nature of non-transferrin-bound iron: studies on iron citrate complexes and thalassemic sera

Despite its importance in iron-overload diseases, little is known about the composition of plasma non-transferrin-bound iron (NTBI). Using 30-kDa ultrafiltration, plasma from thalassemic patients consisted of both filterable and non-filterable NTBI, the filterable fraction representing less than 10% NTBI. Low filterability could result from protein binding or NTBI species exceeding 30 kDa. The properties of iron citrate and its interaction with albumin were therefore investigated, as these represent likely NTBI species. Iron permeated 5- or 12-kDa ultrafiltration units completely when complexes were freshly prepared and citrate exceeded iron by tenfold, whereas with 30-kDa ultrafiltration units, permeation approached 100% at all molar ratios. A g = 4.3 electron paramagnetic resonance signal, characteristic of mononuclear iron, was detectable only with iron-to-citrate ratios above 1:100. The ability of both desferrioxamine and 1,2-dimethyl-3-hydroxypyridin-4-one to chelate iron in iron citrate complexes also increased with increasing ratios of citrate to iron. Incremental molar excesses of citrate thus favour the progressive appearance of chelatable lower molecular weight iron oligomers, dimers and ultimately monomers. Filtration of iron citrate in the presence of albumin showed substantial binding to albumin across a wide range of iron-to-citrate ratios and also increased accessibility of iron to chelators, reflecting a shift towards smaller oligomeric species. However, in vitro experiments using immunodepletion or absorption of albumin to Cibacron blue–Sepharose indicate that iron is only loosely bound in iron citrate–albumin complexes and that NTBI is unlikely to be albumin-bound to any significant extent in thalassemic sera.     

Further evidence for a membrane potential-dependent shape transformation of the human erythrocyte membrane

The influence of various factors (pH, temperature, sodium gluconate) on the ionic strength-dependent stomatocyte-discocyte-echinocyte transformation of the human erythrocyte membrane was investigated. The results give further evidence for a correlation between shape of erythrocyte membrane and the transmembrane potential of the cells.     

Alterations in human erythrocyte shape and the state of spectrin and phospholipid phosphorylation induced by cholesterol depletion

Cholesterol depletion of erythrocytes, obtained after incubation with phosphatidylcholine vesicles, induces in most of the experiments: (1) a discocytestomatocyte transformation as observed by scanning electron microscopy; (2) a specific decrease in spectrin phosphorylation of intact erythrocytes; (3) an increase in lipid phosphorylation. It is concluded that the effect of cholesterol on erythrocyte shape is probably mediated through its action on the activity o of membrane-bound enzymes, proteases or kinases.     

Ultrastructural localization of glycogen in erythrocytes and developing erythrocytic cells in normal human bone marrow

Summary The periodic acid-thiosemicarbazide-silver proteinate (PA-TSC-SP) reaction was employed for the ultrastructural cytochemical localization of saliva-labile glycogen in the erythrocytic cells in normal human blood and bone marrow. Particulate glycogen was demonstrated in the cytoplasm of all developmental forms of erythrocytic cells from the proerythroblast through the reticulocyte; a few particles of glycogen also were present in mature erythrocytes even in the peripheral blood. Statistical evaluation of the number of glycogen particles in mid-plane cell sections at each morphological stage of development indicated a significant and stepwise decrease during cellular maturation. This change in glycogen content may reflect both cellular utilization and mitosis during the maturational sequence.Supported by Grant No. SR01AM 12084-15 from the National Institutes of Health, Bethesda, Maryland.Appreciation is expressed to Anita Topson, Barbara Speakmon and Marjorie Griffith for their technical assistance and to Dr. Gerald King for performing the bone marrow aspirations.     

The human erythrocyte membrane skeleton may be an ionic gel

Biochemical and biophysical observations indicate that the erythrocyte membrane skeleton is composed of a swollen network of long, flexible and ionizable macromolecules located at the cytoplasmic surface of the fluid membrane lipid bilayer. We have analyzed the mechanochemical properties of the erythrocyte membrane assuming that the membrane skeleton constitutes an ionic gel (swollen ionic elastomer). Using recently established statistical thermodynamic theory for such gels, our analysis yields mathematical expressions for the mechanochemical properties of erythrocyte membranes that incorporate membrane molecular parameters to an extent not achieved previously. The erythrocyte membrane elastic shear modulus and maximum elastic extension ratio predicted by our membrane model are in quantitative agreement with reported values for these parameters. The gel theory predicts further that the membrane skeleton modulus of area compression, K _G, may be small as well as large relative to the membrane elastic shear modulus, G, depending on the environmental conditions. Our analysis shows that the ratio between these two parameters affects both the geometry and the stability of the favoured cell shapes.     

Theoretical model of interactions between ligand-binding sites in a dimeric protein and its application for the analysis of thiamine diphosphate binding to yeast transketolase

The binding of thiamin diphosphate (ThDP) to yeast dimeric apotransketolase (apoTK) is accompanied by the appearance of a band in the absorption spectrum with maximum at 320 nm. The saturation function has been analyzed using a scheme that involves binding of ThDP to each subunit followed by the conformational transition of this subunit. It is assumed that the binding of ThDP to one subunit may affect the conformational transition of the other subunit. Rigorous mathematical expressions describing the dependence of the optical absorption on the total concentration of ThDP are first developed. Equilibrium constants and corresponding rate constants for the binding of ThDP to apoTK have been estimated. The negative cooperativity in the ThDP binding has been characterized by the function reflecting the dependence of the conformational change on the saturation of apoTK by ThDP.     

Aging of the erythrocyte

In contrast to situation found in other cell types, no linear dependence of product fluorescence vs time is observed when fluoresceine diacetate (FDA) is hydrolysed by erythrocytes and hemolysates. The rate of hydrolysis is increased by high concentrations of sucrose suggesting a positive effect of viscosity on the rate of the reaction. These peculiarities can be explained by assumption of a two-step hydrolysis of FDA. The FDA-hydrolytic activity decreases with increasing cell density (age).     

A mathematical model of iron metabolism

A mathematical model of iron metabolism is presented. It comprises the following iron pools within the body: transferrin-bound iron in the plasma, iron in circulating red cells and their bone marrow precursors, iron in mucosal, parenchymal and reticuloendothelial cells. The control exerted by a hormone, called erythropoietin, on bone marrow utilization of iron for hemoglobin synthesis is taken into account. The model so obtained consists of a system of functional differential equations of retarded type. Most model parameters can be estimated from radiotracer experiments, others can be measured and numerical values can be assigned to the remaining ones making few reasonable assumptions according to the available physiological knowledge. Iron metabolism behavior under different therapeutical treatments was simulated. Model predictions were compared to experimental data collected in clinical routine.This work has been partially supported by C.N.R. (Italy) through grants N. 80.01227.07 and N. 81.00888.07     

蛋白质折叠机理的理论研究

简要综述了近年来蛋白质折叠机理的理论研究。首先回顾了蛋白质折叠理论的发展历程,然后对折叠中间体的研究现状作了较详细的介绍。同时,对折叠机理理论研究中的几种理论模型和模拟算法作了细致评述,分析了其现状和存在的问题。最后,总结和讨论了折叠机理理论研究的现存问题及研究热点,并展望了该领域研究的发展趋势。     

A combination of an iron chelator with an antioxidant exerts greater efficacy on cardioprotection than monotherapy in iron-overload thalassemic mice

Many recent studies have shown that antioxidant compounds decrease cardiac oxidative stress, decrease cardiac iron deposition, and improve cardiac dysfunction in iron-overload induced cardiomyopathy in animal models. Interestingly, a therapy including the combination of the iron chelator deferiprone (DFP) plus the antioxidant N-acetylcysteine (NAC) has been shown to significantly decrease oxidative stress and restore heart and brain function in iron-overloaded rats. However, the cardioprotective effects of this combined DFP and NAC treatment in thalassemic mice have not been investigated. We hypothesised that the combination of DFP and NAC exerts better cardioprotection than monotherapy via decreasing cardiac iron accumulation, oxidative stress, and apoptosis in thalassemic mice. The iron-overload condition was induced in heterozygous β^KO HT and wild-type mice by instigating high iron diet consumption (FE) for three months. Then, iron chelator DFP (75?mg/kg/day twice a day), antioxidant NAC (100?mg/kg/day once a day), and combined DFP plus NAC were fed via oral gavage for one month with continuous iron feeding. Left ventricular (LV) function, heart rate variability (HRV), apoptosis, and cardiac iron accumulation were determined. Chronic iron-overload in mice led to increased cardiac iron deposition, oxidative stress, apoptosis, and impaired LV function and HRV. Although DFP and NAC showed similar cardioprotective efficacy, combined DFP plus NAC exerted greater efficacy in reducing both cardiac iron deposition and cellular apoptosis than monotherapy. In conclusion, combined iron chelator and NAC treatment exert the greatest cardioprotective efficacy when compared with either of the monotherapies in iron-overload thalassemic mice.     

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.     

Asymptotic solution of the model of the erythrocyte shape as an autowave process

An asymptotic solution was plotted for a model of erythrocyte forms assuming that the biomembrane is anisotropic and of "small" thickness. This leads to small non-linearity and low diffusion, therefore the solution is unrelaxational. The model was investigated qualitatively assuming that the liquid current directed inside the spheric membrane induces its "distension", while that directed outside-its "crumpling". In the spherical system of coordinates the lines of solution level at theta = const are circumferences, while at phi-const-trochoids (Pascal coil, for example). Trochoids rotation areas show stomacyte and discocyte forms. Several hypotheses based on the analysis performed are advanced.     

Permeability of human erythrocyte membrane vesicles to alkali cations

The permeability of inside-out and right-side-out vesicles from erythrocyte membranes to inorganic cations was determined quantitatively. Using ⁸⁶Rb as a K analog, we have measured the rate constant of ⁸⁶Rb efflux from vesicles under equilibrium exchange conditions, using a dialysis procedure. The permeability coefficients of the vesicles to Rb are only about an order of magnitude greater than that of whole erythrocytes. Furthermore, we have measured many of the specialized transport systems known to exist in erythrocytes and have shown that glucose, sulfate, ATP-dependent Ca and ATP-dependent Na transport activities are retained by the vesicle membranes. These results suggest that inside-out and right-side-out vesicles can be used effectively to study transport properties of erythrocyte membranes.