Effects of inner solution viscosity and membrane stiffness on erythrocyte deformability on passing through a microchannel: prediction by two-dimensional simulation

We studied erythrocyte deformability in an effort to develop diagnostic methods based on its measurement and thus aid in the development of therapies for circulatory diseases. In the reported work, we performed two-dimensional numerical simulations of blood flow through a microchannel (MC) to evaluate erythrocyte deformability, applying the immersed boundary method to simulate erythrocyte movement and deformation. To evaluate deformability, MC transit capacity and shape recoverability were considered, defined as the time required to pass through the MC and the time constant during the shape-recovery process after exiting the MC, respectively. The simulation results showed that the erythrocyte MC transit time increased when the viscosity of the inner solution or the stiffness of the membrane increased. The time constant for erythrocyte shape recovery increased as the inner solution viscosity increased. In contrast, the time constant decreased as the erythrocyte membrane stiffness increased. These time-constant trends were in agreement with a theoretical equation derived using the Kelvin model and with previous experimental results. This diagnostic method of measuring erythrocyte shape recoverability and MC transit capacity is anticipated to have clinical application.     

Red blood cell shape and deformability in the context of the functional evolution of its membrane structure

It is proposed that it is possible to identify some of the problems that had to be solved in the course of evolution for the red blood cell (RBC) to achieve its present day effectiveness, by studying the behavior of systems featuring different, partial characteristics of its membrane. The appropriateness of the RBC volume to membrane area ratio for its circulation in the blood is interpreted on the basis of an analysis of the shape behavior of phospholipid vesicles. The role of the membrane skeleton is associated with preventing an RBC from transforming into a budded shape, which could form in its absence due to curvature-dependent transmembrane protein-membrane interaction. It is shown that, by causing the formation of echinocytes, the skeleton also acts protectively when, in vesicles with a bilayer membrane, the budded shapes would form due to increasing difference between the areas of their outer and inner layers.     

Control of the erythrocyte membrane shape: recovery from the effect of crenating agents

Intact erythrocytes become immediately crenated upon addition of 2,4- dinitrophenol (DNP) or pyrenebutyric acid (PBA). However, when cells are incubated at 37 degrees C in the presence of the crenating agents with glucose, they gradually (4--8 h) recover the normal biconcave disc form. The recovery process does not reflect a gradual inactivation of DNP or PBA since fresh cells are equally crenated by the supernatant from the recovered cells. Further, after recovery and removal of the crenating agents, cells are found to be desensitized to the readdition of DNP as well as to the addition of PBA, but they are more sensitive to cupping by chlorpromazine. This alteration in the cell membrane responsiveness was reversible upon further incubation in the absence of DNP. Recovery is dependent upon cellular metabolic state since an energy source is needed and incubation with guanosine but not adenosine will accelerate conversion to the disc shape. It is suggested that the conversion of cells from crenated to disc shape in the presence of the crenators, represents an alteration or rearrangement of membrane components rather than a redistribution of the crenators within the membrane. This shape recovery process may be important for erythrocyte shape preservation as well as shape control in other cells.     

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     

Alteration of red cell membrane viscoelasticity by heat treatment: effect on cell deformability and suspension viscosity

The membrane shear elastic modulus (mu) and the time constant for extensional shape recovery (tc) were measured for normal, control human red blood cells (RBC) and for RBC heat treated (HT) at 48 degrees C. Three separate methods for the measurement of mu were compared (two used a micropipette and one employed a flow channel), and the membrane viscosity (n) was calculated from the relation n = mu. tc. The deformability of HT and control cells was evaluated using micropipette techniques, and the bulk viscosity of RBC suspensions at 40% hematocrit was measured. The shear elastic modulus, or "membrane rigidity", was more than doubled by heat treatment, although both the absolute value for mu and the estimate of the increase induced by heat treatment varied depending on the method of measurement. Heat treatment caused smaller increases in membrane viscosity and in membrane bending resistance, and only minimal changes in cell geometry. The deformability of HT cells was reduced: 1) the pressure required for cell entry (Pe) into 3 micrometers pipettes was increased, on average, by 170%; 2) at an aspiration pressure (Pa) exceeding Pe, longer times were required for cell entry into the same pipettes. However, when Pa was scaled relative to the mean entry pressure for a given sample (i.e, Pa/Pe), entry times were similar for control and HT cells. Bulk viscosity of HT RBC suspensions was elevated by approximately 12% on average (shear rates 75 to 1500 inverse seconds). These findings suggest that alteration of RBC membrane mechanical properties, similar to those induced by heat treatment, would most affect the in vivo circulation in regions where vessel dimensions are smaller than cellular diameters.     

Red cell extensional recovery and the determination of membrane viscosity.

A theory of membrane viscoelasticity developed by Evans and Hochmuth in 1976 is used to analyze the time-dependent recovery of an elongated cell. Before release, the elongated cell is the static equilibrium where external forces are balanced by membrane elastic force resultants. Upon release, the cell recovers its initial shape with a time-dependent exponential behavior characteristic of the viscoelastic solid model. It is shown that the model describes the time-dependent recovery process very well for a time constant in the range of 0.1-0.13 s. The time constant is the ratio membrane surface viscosity eta:membrane surface elasticity mu. Measurements for the shear modulus mu of 0.006 dyne/cm give a value for the surface viscosity of red cell membrane as a viscoelastic solid material of eta = mu tc = (6-8) X 10(-4) poise . cm.     

The elliptocyte: a study of the relationship between cell shape and membrane structure using the camelid erythrocyte as a model

1. The elliptocytic shape of the camelid erythrocyte is very stable and has a high resistance to modification by drugs and treatment which alter the shape of the discocytic erythrocytes of scimitar-horned oryx and man. 2. Differences in the erythrocyte membrane proteins have been found which indicate that proteins play an important role in stabilisation of the camelid elliptocyte. 3. The organisation of the cytoskeletal network in camelid elliptocytes differs from that established for human discocytes.     

Influence of cholesterol-enrichment under in vivo and in vitro conditions on the erythrocyte membrane lipids and its deformability

The cholesterol feeding in rabbits leads to an increase in the levels of cholesterol and phospholipids in plasma and erythrocytes. The increases in cholesterol (C) level is more than that of phospholipids (P) thereby resulting in increase of C/P ratio. The levels of phosphatidylcholine and sphingomyelin are increased in plasma and that of phosphatidylcholine in erythrocytes. Under in vitro conditions the incubation of normal human erythrocytes in cholesterol-enriched plasma (CEP) leads to increase in the cholesterol level, whereas there is no change in phospholipid composition. The deformability of cholesterol-enriched erythrocytes, as measured by their passage time through micropore membranes, under in vivo and in vitro conditions, is significantly decreased.     

Study of the bovine erythrocyte. Enzymatic activities of the cell and its membrane

In bovine red cells, haemolysed and extensively washed, ten different enzyme activities were found to be present. The cells easily release glucose 6-phosphate dehydrogenase, glucose phosphate isomerase, fructose bisphosphate aldolase, and aspartate aminotransferase into the haemolysis medium. An important part of the last two enzymes and all the isocitrate dehydrogenase (NADP linked) are retained in the membrane. The levels of these enzymes in the membrane are strongly dependent on the age of the preparation. The optimal assay conditions have been defined for some of these enzymes. These findings are discussed in relation to red cell and membrane structure.     

Human erythrocyte spectrin dimer intrinsic viscosity: temperature dependence and implications for the molecular basis of the erythrocyte membrane free energy

We have determined experimentally the temperature dependence of human erythrocyte spectrin dimer intrinsic viscosity at shear rates 8-12 s-1 using a Cartesian diver viscometer. We find that the intrinsic viscosity decreases from 43 +/- 3 ml/g at 4 degrees C to 34 +/- 3 ml/g when the temperature is increased to 38 degrees C. Our results show that spectrin dimers are flexible worm-like macromolecules with persistence length about 20 nm and that the mean square end-to-end distance for this worm-like macromolecules decreases when the temperature is increased. This implies that the spectrin dimer internal energy decreases when the end-to-end distance is increased and that the free energy increase associated with making the end-to-end distance longer than the equilibrium value for the free molecules is of entropic origin. The temperature dependence of the erythrocyte membrane shear modulus reported previously in the literature therefore appears mainly to be due to temperature dependent alterations in the membrane skeleton topology.     

Erythropoietin control of terminal erythroid differentiation: maintenance of cell viability, production of hemoglobin, and development of the erythrocyte membrane

Using the spleen cells of mice infected with the anemia-inducing strain of Friend leukemia virus, an in vitro model system of erythropoiesis has been developed in which a homogeneous population of murine proerythroblasts terminally differentiates in response to erythropoietin (EP). The biochemical events involved in EP's capacity to maintain viability, induce hemoglobin production, and promote the development of the specialized erythrocyte membrane were studied during the 48-72 hour period required for proerythroblasts to differentiate into reticulocytes. The results show that EP increases glucose uptake and the syntheses of RNA and protein in the first few hours after exposure of the erythroblasts to the hormone. A coordinated production of heme, alpha and beta globin occurs later and peaks at about 48 hours. This peak corresponds to the time at which the majority of cells are undergoing enucleation and becoming reticulocytes. The syntheses of the erythrocyte membrane and membrane skeletal proteins are not coordinated, and multiple patterns of synthesis are found with respect to the time of EP exposure. A number of proteins are lost from the membrane fraction while the characteristic proteins of the mature erythrocyte become prominent in the membrane fraction of erythroid cells as they develop from reticulocytes into erythrocytes.     

Investigation of erythrocyte shape, plasma membrane fluidity and conformation of haemoglobin haemoporphyrin under the influence of long-term space flight

The investigation of long-term space flight (SF) effect on the blood cells function is of great importance for modern space biology and medicine. We established that the number of discocytes decreased in the period of early rehabilitation after long-term SF. After SF plasma membrane fluidity and phospholipid content decreased and cholesterol content increased. After SF the amount of haemoglobin decreased and the parameters characterizing haemoglobin haemoporyphyrin (HH) conformation changed. We suppose that erythrocyte shape, membrane fluidity and HH conformation are among factors affecting oxygen transfer during and after space flight.     

Allosteric properties of hemoglobin and the plasma membrane of the erythrocyte: new insights in gas transport and metabolic modulation

Within the red blood cell the hemoglobin molecule is subjected to modulation mechanisms, namely homo- and heterotropic interactions, which optimize its functional behavior to the specific physiological requirements. At the cellular level, these modulation mechanisms are utilized to perform a number of other functions that are not minor with respect to the basic function of oxygen transport. Here we report some key examples concerning: (i) the interaction of hemoglobin with band 3 and its influence on glucose metabolism; (ii) the role of the ligand-linked quaternary transition of hemoglobin in the control of "NO bioactivity" and of gas diffusion; (iii) the interaction of plasma membrane with the various oxidative derivatives of the hemoglobin molecule.     

Performance of bench-scale membrane bioreactor under real work conditions using pure oxygen: viscosity and oxygen transfer analysis

Pure oxygen to supply the aerobic condition was used in the performance of a bench-scale submerged membrane bioreactor (MBR). The pilot plant was located in the wastewater treatment plant of the city of Granada (Spain) and the experimental work was divided into two stages (Unsteady state and steady state conditions). Operation parameters (MLSS, MLVSS and dissolved oxygen concentration) and physical characteristics (temperature, conductivity, pH, COD and BOD₅) were daily monitored. The results showed the capacity of the MBR systems to remove organic material under a hydraulic retention time of 18.46 h and sludge retention time of 18.6 days. Therefore, Viscosity of the sludge and αkLa-factor of the aeration, were determinate in the steady stage condition to understand the behavior of the system when pure oxygen has been used to supply the aerobic conditions of the MBR system showed an alpha-factor of 0.238 when the viscosity of the system was 4.04 Cp.     

Contribution of each membrane binding domain of the CTP:phosphocholine cytidylyltransferase-alpha dimer to its activation, membrane binding, and membrane cross-bridging

CTP:phosphocholine cytidylyltransferase (CCT), a rate-limiting enzyme in phosphatidylcholine synthesis, is regulated by reversible membrane interactions mediated by an amphipathic helical domain (M) that binds selectively to anionic lipids. CCT is a dimer; thus the functional unit has two M domains. To probe the functional contribution of each domain M we prepared a CCT heterodimer composed of one full-length subunit paired with a CCT subunit truncated before domain M that was also catalytically dead. We compared this heterodimer to the full-length homodimer with respect to activation by anionic vesicles, vesicle binding affinities, and promotion of vesicle aggregation. Surprisingly for all three functions the dimer with just one domain M behaved similarly to the dimer with two M domains. Full activation of the wild-type subunit was not impaired by loss of one domain M in its partner. Membrane binding affinities were the same for dimers with one versus two M domains, suggesting that the two M domains of the dimer do not engage a single bilayer simultaneously. Vesicle cross-bridging was also unhindered by loss of one domain M, suggesting that another motif couples with domain M for cross-bridging anionic membranes. Mutagenesis revealed that the positively charged nuclear localization signal sequence constitutes that second motif for membrane cross-bridging. We propose that the two M domains of the CCT dimer engage a single bilayer via an alternating binding mechanism. The tethering function involves the cooperation of domain M and the nuclear localization signal sequence, each engaging separate membranes. Membrane binding of a single M domain is sufficient to fully activate the enzymatic activity of the CCT dimer while sustaining the low affinity, reversible membrane interaction required for regulation of CCT activity.     

Cytoplasmic viscosity near the cell plasma membrane: translational diffusion of a small fluorescent solute measured by total internal reflection-fluorescence photobleaching recovery.

Total internal reflection-fluorescence recovery after photobleaching (TIR-FRAP) was applied to measure solute translational diffusion in the aqueous phase of membrane-adjacent cytoplasm. TIR fluorescence excitation in aqueous solutions and fluorescently labeled cells was produced by laser illumination at a subcritical angle utilizing a quartz prism; microsecond-resolution FRAP was accomplished by acousto-optic modulators and electronic photomultiplier gating. A mathematical model was developed to determine solute diffusion coefficient from the time course of photobleaching recovery, bleach time, bleach intensity, and evanescent field penetration depth; the model included irreversible and reversible photobleaching processes, with triplet state diffusion. The validity and accuracy of TIR-FRAP measurements were first examined in aqueous fluorophore solutions. Diffusion coefficients for fluorescein isothiocyanate-dextrans (10-2000 kDa) determined by TIR-FRAP (recovery t1/2 0.5-2.2 ms) agreed with values measured by conventional spot photobleaching. Model predictions for the dependence of recovery curve shape on solution viscosity, bleach time, and bleach depth were validated experimentally using aqueous fluorescein solutions. To study solute diffusion in cytosol, MDCK epithelial cells were fluorescently labeled with the small solute 2',7'-bis-2-carboxyethyl-5-carboxyfluorescein-acetoxymethyl-ester (BCECF). A reversible photobleaching process (t1/2 approximately 0.5 ms) was identified that involved triplet-state relaxation and could be eliminated by triplet-state quenching with 100% oxygen. TIR-FRAP t1/2 values for irreversible BCECF bleaching, representing BCECF translational diffusion in the evanescent field, were in the range 2.2-4.8 ms (0.2-1 ms bleach times), yielding a BCECF diffusion coefficient 6-10-fold less than that in water. These results establish the theory and the first experimental application of TIR-FRAP to measure aqueous-phase solute diffusion, and indicate slowed translational diffusion of a small solute in membrane-adjacent cytosol.     

Microwaves and the cell membrane. IV. Protein shedding in the human erythrocyte: quantitative analysis by high-performance liquid chromatography

The erythrocyte responds to microwave fields by shedding at least 11 low-molecular-weight proteins of less than or equal to 31,000 Da, with components of 28,000-31,000 Da released during the destabilization of divalent calcium-protein bridges [R.P. Liburdy and P.F. Vanek, Radiat. Res. 109, 382-395 (1987)]. Significantly, protein shedding was shown to be restricted to exposure temperatures coinciding with the cell membrane phase/structural transition temperature, Tc, of 17-25 degrees C. We report here a further characterization of protein shedding at Tc using high-performance liquid chromatography and membrane-associated blood group antigen testing. Proteins shed from human erythrocytes in microwave fields (2450 MHz, CW) compared to sham-heating displayed a twofold increase in total protein mass released concomitant with the appearance of unique protein species during reverse-phase, hydrophobic interaction, and anion-exchange HPLC. These HPLC analyses indicate that microwaves result in the shedding of proteins which are relatively nonpolar and hydrophobic and which carry a net positive electrostatic charge compared to those released during sham-heat treatment. Assessment of 23 blood group antigens that represent integral protein markers on the erythrocyte cell surface indicates that microwave fields do not result in the exhaustive loss of these proteins. The class of proteins that is shed in response to microwave fields most likely is the loosely bound "peripheral" or extrinsic proteins associated with the exterior of the cell surface. Such proteins play a major role in the transduction of signals to integral membrane proteins which span the bilayer. That this class of proteins is susceptible to release by microwave fields is discussed in relation to microwave absorption at the cell surface by membrane-associated bound water, field interaction with dipolar side groups, and the disruption of divalent cation bridges known to stabilize peripheral membrane proteins.