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1.
The transbilayer distribution of exogenous phospholipids incorporated into human erythrocytes is monitored through cell morphology changes and by the extraction of incorporated 14C-labeled lipids. Dilauroylphosphatidylserine (DLPS) and dilauroylphosphatidylcholine (DLPC) transfer spontaneously from sonicated unilamellar vesicles to erythrocytes, inducing a discocyte-to-echinocyte shape change within 5 min. DLPC-induced echinocytes revert slowly (t1/2 approximately 8 h) to discocytes, but DLPS-treated cells revert rapidly (10-20 min) to discocytes and then become invaginate stomatocytes. The second phase of the phosphatidylserine (PS)-induced shape change, conversion of echinocytes to stomatocytes, can be inhibited by blocking cell protein sulfhydryl groups or by depleting intracellular ATP or magnesium (Daleke, D. L., and W. H. Huestis. 1985. Biochemistry. 24:5406-5416). These cell shape changes are consistent with incorporation of phosphatidylcholine (PC) and PS into the membrane outer monolayer followed by selective and energy-dependent translocation of PS to the membrane inner monolayer. This hypothesis is explored by correlating cell shape with the fraction of the exogenous lipid accessible to extraction into phospholipid vesicles. Upon exposure to recipient vesicles, DLPC-induced echinocytes revert to discoid forms within 5 min, concomitant with the removal of most (88%) of the radiolabeled lipid. On further incubation, 97% of the foreign PC transfers to recipient vesicles. Treatment of DLPS-induced stomatocytes with acceptor vesicles extracts foreign PS only partially (22%) and does not affect cell shape significantly. Cell treated with inhibitors of aminophospholipid translocation (sulfhydryl blockers or intracellular magnesium depletion) and then incubated with either DLPS or DLPC become echinocytic and do not revert to discocytic or stomatocytic shape for many hours. On treatment with recipient vesicles, these echinocytes revert to discocytes in both cases, with concomitant extraction of 88-99% of radiolabeled PC and 86-97% of radiolabeled PS. The accessibility of exogenous lipids to extraction is uniformly consistent with the transbilayer lipid distribution inferred from cell shape changes, indicating that red cell morphology is an accurate and sensitive reporter of the transbilayer partitioning of incorporated exogenous phospholipids.  相似文献   

2.
L M Chi  W G Wu 《Biophysical journal》1990,57(6):1225-1232
When human erythrocytes are treated with exogenous monopalmitoyl phosphatidylcholine (MPPC), the normal biconcave disk shape red blood cells (RBC) become spiculate echinocytes. The present study examines the quantitative aspect of the relationship between effective bilayer expansion and erythrocyte shape change by a newly developed method. This method is based on the combination of direct surface area measurement of micropipette and relative bilayer expansion measurement of 13C crosspolarization/magic angle spinning nuclear magnetic resonance (NMR). Assuming that 13C NMR chemical shift of fatty acyl chain can be used as an indicator of lateral packing of membrane bilayers, it is possible for us to estimate the surface area expansion of red cell membrane induced by MPPC from that induced by ethanol. Partitions of lipid molecules into cell membrane were determined by studies of shape change potency as a function of MPPC and red cell concentration. It is found that 8(+/- 0.5) x 10(6) molecules of MPPC per cell will effectively induce stage three echinocytes and yield 3.2(+/- 0.2)% expansion of outer monolayer surface area. Surface area of normal cells determined by direct measurements from fixed geometry of red cells aspirated by micropipette was 118.7 +/- 8.5 microns2. The effective cross-sectional area of MPPC molecules in the cell membrane therefore was determined to be 48(+/- 4) A2, which is in agreement with those determined by x-ray from model membranes and crystals of lysophospholipids. We concluded that surface area expansion of RBC can be explained by a simple consideration of cross-sectional area of added molecules and that erythrocyte shape changes correspond quantitatively to the incorporated lipid molecules.  相似文献   

3.
Smriti  Nemergut EC  Daleke DL 《Biochemistry》2007,46(8):2249-2259
The plasma membrane of most cells contains a number of lipid transporters that catalyze the ATP-dependent movement of phospholipids across the membrane and assist in the maintenance of lipid asymmetry. The most well-characterized of these transporters is the erythrocyte aminophospholipid flippase, which selectively transports phosphatidylserine (PS) from the outer to the inner monolayer. Previous work has demonstrated that PS and to a lesser extent phosphatidylethanolamine (PE) are substrates for the flippase and that other phospholipids move across the membrane only by passive flip-flop. The present study re-evaluates these results. The incorporation and transbilayer movement of a number of short-chain (dilauroyl) phospholipid analogues in human erythrocytes was measured by observing lipid-induced changes in cell morphology, and the effect of an ATPase inhibitor (vanadate) and a sulfyhdryl reagent (N-ethylmaleimide) was determined. Incubation of cells with these lipids causes the rapid formation of echinocytes, because of the accumulation of the lipid in the outer monolayer. While dilauroylphosphatidylcholine-treated cells retained this shape, cells treated with sn-1,2-DLP-l-S, sn-1,2-DLP-d-S, or N-methyl-DLPS rapidly changed morphology to stomatocytes, which is consistent with the transport and accumulation of the lipid in the inner monolayer. A similar, although slower, stomatocytic shape change was induced by sn-2,3-DLP-l-S. Other lipids that were tested (dilauroylphosphatidylhydroxypropionate, dilauroylphosphatidylhomoserine, DLPS-methyl ester, or sn-2,3-DLP-d-S) reverted to discocytes only. In all cases, pretreatment with vanadate or N-ethylmaleimide inhibited the conversion of echinocytes to discocytes or stomatocytes. This is the first report of a protein- and energy-dependent pathway for the inwardly directed transbilayer movement of lipids other than PS and PE in the erythrocyte membrane and suggests that the flippase has broader specificity for substrates or that other lipid transporters are present.  相似文献   

4.
12-O-Tetradecanoylphorbol-13-acetate (TPA) (100 nM) when incubated with human erythrocytes under conditions of ATP depletion, delayed the onset of the morphological transition from discocytes to echinocytes so that at 2 h, when control incubations were estimated to contain 65% echinocytes, those treated with TPA contained 23% echinocytes. TPA did not alter the subsequent rate of the transition which was complete by 3 h in control cells and 5 h in TPA-treated cells. Addition of 100 nM TPA to ATP-depleted erythrocytes at 2.5 h (greater than 80% echinocytes) for 0.5 h at 37 degrees C resulted in 17% reversal to a discocyte morphology, but as the time of incubation under conditions of ATP depletion was extended, the level of the reversal fell. TPA had no significant effect on the fall in ATP concentrations over the time course of the experiments (5 h). Preincubation of discocytes with TPA for 10 min also prevented, by approx. 50%, the echinocytosis induced by the calcium (0.2 mM) loading of discocytes using 5 microM A23187. TPA was unable to reverse the echinocyte morphology of calcium-loaded cells back to discocytes. The less potent tumour promotor 4-phorbol-12,13-didecanoate had no effect on this discocyte-echinocyte transition. Incubation of discocytes with the diacylglycerol 1-oleoyl-2-acetylglycerol (OAG) (1-10 microM) had complex effects on morphology, and the ATP-induced morphological transition, ranging from stomatocyte formation to echinocyte formation, depending upon the concentration of the agent and the time of incubation.  相似文献   

5.
The release of spectrin-free vesicles from ATP-depleted human red blood cells (Lutz et al. (1977) J. Cell. Biol. 73, 548) can be considered the final step of a shape change from discocytes to echinocytes. The study of physical and chemical properties of released vesicles suggests that vesicle release is not merely a consequence of charge alterations within either monolayer of the budding membrane. Fresh membranes and released vesicles have within experimental error the same sialic acid content per surface area and the same electrophoretic mobilities. Vesicle release cannot be stimulated by doubling the charge density on the outer monolayerby means of a phospholipase D-treatment, but correlates with a breakdown of polyphosphoinositides to diacylglycerol on the inner monolayer. This breakdown does not lead to a significant change in the negative charge density on the inner monolayer, because an increased phosphatidate content compensates for this alteration. Furthermore, polyphosphoinositide breakdown and diacylglycerol production are not the rate-limiting step in vesicle release from ATP-depleting red blood cells. This is evident from the fact that 10 mM EDTA inhibits vesicle release to 75% without affecting polyphosphoinositide breakdown and diacylglycerol production. Hence, diacylglycerol formation may be sufficient for membrane budding as suggested earlier (Allan et al.(1976) Nature 261, 58), but vesicle release requires a second, as yet unidentified process.  相似文献   

6.
The effect of lysophosphatidic acid (LPA) on the shape and aggregation of human erythrocytes in autologous plasma was studied. The morphology of erythrocytes and their aggregates were studied by light microscopy. It is shown that the addition of plasma with a high LPA content to erythrocytes leads to a change of their shape: discocytes are transformed into echinocytes. There is practically no aggregation of erythrocytes in the form of rouleaux. At the same time, there is observed a strong aggregation of echinocytes. This is accompanied by the formation of microvesicles. The addition of normal blood plasma to echinocytes restores their shape and aggregation of red blood cells in the form of rouleaux. A possible mechanism of action of lysophosphatidic acid on erythrocytes is discussed.  相似文献   

7.
Membrane potential and human erythrocyte shape.   总被引:1,自引:0,他引:1  
Altered external pH transforms human erythrocytes from discocytes to stomatocytes (low pH) or echinocytes (high pH). The process is fast and reversible at room temperature, so it seems to involve shifts in weak inter- or intramolecular bonds. This shape change has been reported to depend on changes in membrane potential, but control experiments excluding roles for other simultaneously varying cell properties (cell pH, cell water, and cell chloride concentration) were not reported. The present study examined the effect of independent variation of membrane potential on red cell shape. Red cells were equilibrated in a set of solutions with graduated chloride concentrations, producing in them a wide range of membrane potentials at normal cell pH and cell water. By using assays that were rapid and accurate, cell pH, cell water, cell chloride, and membrane potential were measured in each sample. Cells remained discoid over the entire range of membrane potentials examined (-45 to +45 mV). It was concluded that membrane potential has no independent effect on red cell shape and does not mediate the membrane curvature changes known to occur in red cells equilibrated at altered pH.  相似文献   

8.
Intact human erythrocytes, initially depleted of Mg2+ by EDTA incubation in the presence of A23187, exhibit Mg(2+)-dependent phosphate production of around 1.5 mmol per liter cells.h, half-maximally activated at around 0.4 mM added free Mg2+. This appears to correspond to Mg(2+)-stimulated adenosine triphosphatase (Mg(2+)-ATPase) activity found in isolated membranes, which is known to have a similar activity and affinity for Mg2+. Vanadate (up to 100 microM) inhibited Mg(2+)-dependent phosphate production and ATP breakdown in intact cells. Over a similar concentration range vanadate (3-100 microM) transformed intact cells from normal discocytes to echinocytes within 4-8 h at 37 degrees C, and more rapidly in Mg(2+)-depleted cells. The rate of Ca(2+)-induced echinocytosis was also enhanced in Mg(2+)-depleted cells. These results support previous studies in erythrocyte ghosts suggesting that vanadate-induced shape change is associated with inhibition of Mg(2+)-ATPase activity localized in the plasma membrane of the red blood cell.  相似文献   

9.
This study was concerned with the quantitative evaluation of dark field light scattering by sedimented erythrocytes of banked human blood samples. Due to considerable variability of both appearance and amount of scattered light the discocyte group had to be subdivided into discocyte I and discocyte II. The mean intensity of scattered light increased about three fold from discocyte II to echinocytes I, II, III, sphaeroechinocyte, and sphaerocyte. On the other hand the average light scattering intensity of discocytes I exceeded that of discocytes II about 2.5 times, with individual data varying over a wide range. There was a rapid disappearing of discocytes I correlated with time of storage. Therefore it is concluded that discocytes I represent the initial stage of erythrocytes transforming under banking conditions.  相似文献   

10.
The mechanism whereby lithium carbonate controls manic episodes and possibly influences affective disorders is not yet known. There is evidence, however, that lithium alters sodium transport and may interfere with ion exchange mechanisms and nerve conduction. For these reasons it was thought of interest to study its perturbing effects upon membrane structures. The effects of lithium carbonate (Li+) on the human erythrocyte membrane and molecular models have been investigated. The molecular models consisted in bilayers of dimyristoylphosphatidylcholine (DMPC) and dimyristoylphosphatidylethanolamine (DMPE), representing classes of phospholipids located in the outer and inner monolayers of the erythrocyte membrane, respectively. This report presents the following evidence that Li+ interacts with cell membranes: a) X-ray diffraction indicated that Li+ induced structural perturbation of the polar head group and of the hydrophobic acyl regions of DMPC and DMPE; b) experiments performed on DMPC large unilamellar vesicles (LUV) by fluorescence spectroscopy also showed that Li+ interacted with the lipid polar groups and hydrophobic acyl chains, and c) in scanning electron microscopy (SEM) studies on intact human erythrocytes the formation of echinocytes was observed, effect that might be due to the insertion of Li+ in the outer monolayer of the red cell membrane.  相似文献   

11.
M E Blank  D F Diedrich 《Biorheology》1990,27(3-4):345-355
Light scattering measurements and scanning electron microscopy show that p-azidobenzylphlorizin (p-AzBPhz) causes changes in the shape and volume of human erythrocytes by at least two, dose-dependent mechanisms: At nominal concentrations above 5 microM, the azide induces cell swelling by either enlarging a pre-existent channel or by creating pores between phase boundaries of the membrane through which salt and water enter, but sucrose remains excluded. However, over the range 0.03 to 0.3 microM, in either isosmotic NaCl or KCl media, when fewer than 1 million molecules of azide are bound per cell, the ligand causes membrane deformations that convert discocytes into cells resembling stage 2 echinocytes. Whereas a cell volume increase of about 10% accompanies these shape changes, (microhematocrit and electronic cell sizing measurements), no net influx of either Na+ or K+ during this stage of swelling was detectable. These cell alterations take place at p-AzBPhz concentrations which concurrently inhibit both chloride and 3-methoxyglucose equilibrium exchange transport. The results may indicate that when the membrane impermeable p-AzBPhz interacts with the anion and/or sugar transporter, some trans-membrane perturbation occurs which alters the cytoskeleton.  相似文献   

12.
The relationship between shape and spontaneous and fibrinogen-induced aggregation change in human erythrocytes was studied. Spontaneous and fibrinogen-induced erythrocyte aggregation was investigated using a rheoscope designed according to the method of H. Schmid-Schonbein et al. (1973). The erythrocyte shape was studied by means of light microscopy. It was shown that plasma enriched with lysophosphatidic acid and ATP depletion of erythrocytes led to the change of erythrocyte shape: discocytes transformed into echinocytes. It was found that spontaneous aggregation of such cells was considerably decreased. Aggregation of erythrocytes, treated with lysophosphatidic acid, was diminished more markedly. Fibrinogen-induced aggregation of echinocytes, obtained after treatment with lysophosphatidic acid and produced by ATP depletion, was also greatly reduced.  相似文献   

13.
Echinocytosis and release of microvesicles from human erythrocytes treated with the impermeant fluorescent dye merocyanine 540 (MC540) has been correlated with the extent of dye binding to intact cells and ghosts. At 20 degrees C binding appeared to saturate at about 9.3.10(6) molecules per cell (3.6 mol/100 mol phospholipid), equivalent to an expansion of the outer leaflet lipid area of about 2.7%. Stage 3 echinocytes were formed upon binding of (3-4).10(6) molecules of MC540/cell (about 1.3 mol/100 mol phospholipid), equivalent to an expansion of the outer leaflet lipid area of about 1.0%. Negligible release of microvesicles was observed with MC540 at 20 degrees C. Binding of MC540 to permeable ghosts was approximately twice that to cells suggesting that there was no selective binding to the unsaturated (more fluid) phospholipids which are concentrated in the inner lipid leaflet of the membrane. At 37 degrees C apparent maximal binding of MC540 was about 3.2 mol/100 mol phospholipid and correlated with the maximal release of microvesicles from the cells as measured by release of phospholipid and acetylcholinesterase. These results are discussed in relation to the bilayer couple hypothesis of Sheetz and Singer (Proc. Natl. Acad. Sci. USA 71 (1974) 4457-4461).  相似文献   

14.
The effect of benzyl alcohol on the transverse mobility and repartition of phospholipids in the human erythrocyte membrane was investigated using electron spin resonance and morphological modification of red blood cells. Transmembrane internalization rates and equilibrium distribution in red blood cells of short-chain spin-labeled phosphatidylcholine, phosphatidylethanolamine and phosphatidylserine were strongly modified by treatment with 10-70 mM benzyl alcohol. A dual effect was observed: (a) at 4 degrees C and 37 degrees C there was an N-ethylmaleimide-sensitive, long lasting and fully reversible increase in the spin-labeled phosphatidylserine and phosphatidylethanolamine internalization rate; (b) at 37 degrees C, an enhancement of N-ethylmaleimide-insensitive fluxes of all the labeled phospholipids through the membrane occurred. Both effects were dose-dependent. Erythrocytes submitted to benzyl alcohol incubation also showed dose-dependent shape changes: an immediate one from discocytes to echinocytes, followed by a slower N-ethylmaleimide- and ATP-dependent change to stomatocytes. Moreover, benzyl alcohol treatment was shown to lead to enhanced hydrolysis of intracellular ATP. All the effects of benzyl alcohol can be described as an accumulation of labeled phosphatidylethanolamine (and labeled phosphatidylcholine at 37 degrees C) in the inner leaflet. This can be interpreted as a perturbation of the erythrocyte membrane, leading to an energy-consuming specific increase in aminophospholipid translocase activity, in addition to a slow and passive bidirectional flux of all phospholipids at 37 degrees C.  相似文献   

15.
Mechanism of red blood cell acanthocytosis and echinocytosis in vivo   总被引:1,自引:0,他引:1  
Patients with abetalipoproteinemia have an inborn absence of the major apoprotein of low density plasma lipoproteins, an abnormal serum and red cell lipid profile, and spiny erythrocytes, called acanthocytes. We now show that these deformed cells are reversibly converted to a normal shape, that of a biconcave disk, by incubation with 3 to 10 X 10(-5) M chlorpromazine. We suppose that chlorpromazine acts by expanding the cytoplasmic leaflet of the bilayer, thus promoting inward curvature. Ghosts isolated from the acanthocytes are themselves spiny but are also converted to normal, concave disks by chlorpromazine or merely by a brief incubation at 37 degrees C in low ionic strength buffer. We attribute the latter to a redistribution of lipids between the two leaflets of the membrane bilayer. Similar observations were made with red cells and ghosts from a patient with benign echinocytosis. These observations suggest that the morphological abnormality in acanthocytes and echinocytes can be ascribed to the same mechanism as crenation in vitro; that is, a bilayer couple effect in which an excess of surface area in the outer leaflet over the inner leaflet of the membrane bilayer drives outward curvature. It is striking that cells which were chronically abnormal in shape in vivo contain the information to become biconcave disks immediately upon simple chemical treatment in vitro.  相似文献   

16.
Various structural components of biological membranes are asymmetrically localized in the two surfaces of the membrane bilayer. This asymmetry is absolute for membrane (glyco) proteins, but only a partial asymmetry has been observed for membrane phospholipids. In the red cell membrane, choline-phospholipids are localized mainly in the outer monolayer whereas aminophospholipids are distributed almost exclusively in the inner monolayer. Several evidences are now available to suggest that this distribution of membrane phospholipids in red cells is directly or indirectly maintained by the membrane-associated cytoskeleton (membrane skeleton). This belief is well supported by the previous as well as recent studies carried out in the authors laboratory. Previously, it has been shown that lipid-lipid interactions play no major role in maintaining the transmembrane phospholipid asymmetry in erythrocytes, and that the asymmetry is lost upon covalent crosslinking of the major membrane skeletal protein, spectrin. The recent data presented here further shows that degradation or denaturation of spectrin indices rapid transbilayer movement of membrane phospholipids in the cells which, in turn, leads to more random phospholipid distributions across the membrane. These studies taken together strongly suggest that the skeleton-membrane associations are the major determinants of the transmembrane phospholipid asymmetry in erythrocytes, and that the dissociation of the skeleton from the membrane bilayer probably results in generation of new reorientation sites for phospholipids in the membrane. Communication No 3648 from C.D.R.I., Lucknow.  相似文献   

17.
The structural effects of cadmium on cell membranes were studied through the interaction of Cd(2+) ions with human erythrocytes and their isolated unsealed membranes (IUM). Studies were carried out by scanning electron microscopy and fluorescence spectroscopy, respectively. Cd(2+) induced shape changes in erythrocytes, which took the form of echinocytes. According to the bilayer couple hypothesis, this result meant that Cd(2+) ions located in the outer monolayer of the erythrocyte membrane. Fluorescence spectroscopy measurements in IUM indicated a disordering effect at both the polar headgroup and the acyl chain packing arrangements of the membrane phospholipid bilayer. Cd(2+) ions also interacted with molecular models of the erythrocyte membrane consisting in bilayers of dimyristoylphosphatidylcholine (DMPC) and dimyristoylphosphatidylethanolamine (DMPE), representing classes of phospholipids located in the outer and inner monolayers the erythrocyte membrane, respectively. X-ray diffraction indicated that Cd(2+) ions induced structural perturbation of the polar headgroup and of the hydrophobic acyl regions of DMPC, while the effects of cadmium on DMPE bilayers were much milder. This conclusion is supported by fluorescence spectroscopy measurements on DMPC large unilamellar vesicles (LUV). All these findings point to the important role of phospholipid bilayers in the interaction of cadmium on cell membranes.  相似文献   

18.
Cytoplasmic pH and human erythrocyte shape.   总被引:1,自引:0,他引:1  
Altered external pH transforms human erythrocytes from discocytes to stomatocytes (low pH) or echinocytes (high pH). The mechanism of this transformation is unknown. The preceding companion study (Gedde and Huestis) demonstrated that these shape changes are not mediated by changes in membrane potential, as has been reported. The aim of this study was to identify the physiological properties that mediate this shape change. Red cells were placed in a wide range of physiological states by manipulation of buffer pH, chloride concentration, and osmolality. Morphology and four potential predictor properties (cell pH, membrane potential, cell water, and cell chloride concentration) were assayed. Analysis of the data set by stratification and nonlinear multivariate modeling showed that change in neither cell water nor cell chloride altered the morphology of normal pH cells. In contrast, change in cell pH caused shape change in normal-range membrane potential and cell water cells. The results show that change in cytoplasmic pH is both necessary and sufficient for the shape changes of human erythrocytes equilibrated in altered pH environments.  相似文献   

19.
Refinement of a method described previously (Cryobiology12, 110–118, April, 1975) made possible routine freezing of full units of packed erythrocytes after separation of platelet rich plasma, and buffy coats. The volume frozen was 405 ml which included packed red cells (190–220 ml), plasma (43–73 ml), and cryo-HES (142 ml, final concentration 14% wv). The units could be frozen with or without shaking by direct immersion in liquid nitrogen. Thawing was accomplished by transferring units quickly from liquid nitrogen storage to a shaking water bath at 54 °C. The average yield from units of red cells was 98.4%. The stability to a 50-fold dilution in 0.15 m NaCl was 87.8%. Thawing rate was the critical variable in producing the most stable thawed cells. Plasma expander HES was usable but the thawed units were more viscous and about 7% less stable. Red cells prewashed with 0.15 m NaCl and frozen without plasma showed no significant changes in cellular yield or stability. The optimum resuspension medium was 3% glucose. A morphologic study of cells fixed in 1% glutaraldehyde revealed that before freezing red cells were partially dehydrated in 14% HES. These were smooth, flat discs. Cells fixed on thawing were extensively dehydrated and seen as large, thin, smooth, flat discs with approximately 10% echinocytes. On dilution with 6% glucose (1:1) these swelled and reverted to biconcave discocytes except for approximately 5% echinocytes. Storage in liquid nitrogen measured in groups of three units of 15 units for 0, 3, 6, 9, and 12 weeks revealed normal postthawed oxygen delivery (P-50). The greatest measurable effect of freezing red cells in HES was a loss of cellular K+ compensated by a corresponding increase in Na+.  相似文献   

20.
We have developed what we believe is an efficient method to determine the electric parameters (the specific membrane capacitance C(m) and the cytoplasm conductivity kappa(i)) of cells from their dielectric dispersion. First, a limited number of dispersion curves are numerically calculated for a three-dimensional cell model by changing C(m) and kappa(i), and their amplitudes Deltaepsilon and relaxation times tau are determined by assuming a Cole-Cole function. Second, regression formulas are obtained from the values of Deltaepsilon and tau and then used for the determination of C(m) and kappa(i) from the experimental Deltaepsilon and tau. This method was applied to the dielectric dispersion measured for rabbit erythrocytes (discocytes and echinocytes) and human erythrocytes (normocytes), and provided reasonable C(m) and kappa(i) of the erythrocytes and excellent agreement between the theoretical and experimental dispersion curves.  相似文献   

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