Control of band 3 lateral and rotational mobility by band 4.2 in intact erythrocytes: release of band 3 oligomers from low-affinity binding sites.

Band 4.2 is a human erythrocyte membrane protein of incompletely characterized structure and function. Erythrocytes deficient in band 4.2 protein were used to examine the functional role of band 4.2 in intact erythrocyte membranes. Both the lateral and the rotational mobilities of band 3 were increased in band 4.2-deficient erythrocytes compared to control cells. In contrast, the lateral mobility of neither glycophorins nor a fluorescent phospholipid analog was altered in band 4.2-deficient cells. Compared to controls, band 4.2-deficient erythrocytes manifested a decreased ratio of band 3 to spectrin, and band 4.2-deficient membrane skeletons had decreased extractability of band 3 under low-salt conditions. Normal band 4.2 was found to bind to spectrin in solution and to promote the binding of spectrin to ankyrin-stripped inside-out vesicles. We conclude that band 4.2 provides low-affinity binding sites for both band 3 oligomers and spectrin dimers on the human erythrocyte membrane. Band 4.2 may serve as an accessory linking protein between the membrane skeleton and the overlying lipid bilayer.     

Rate of rupture and reattachment of the band 3-ankyrin bridge on the human erythrocyte membrane

The principal bridge connecting the erythrocyte membrane to the spectrin-based skeleton is established by band 3 and ankyrin; mutations leading to reduced bridge formation or increased bridge rupture result in morphological and mechanical abnormalities. Because membrane mechanical properties are determined in part by the protein interactions that stabilize the membrane, we have evaluated the rates of rupture and reattachment of band 3-ankyrin bridges under both resting and mechanically stressed conditions. To accomplish this, we have examined the rate of ankyrin displacement from inside-out vesicles by the hexahistidine-tagged cytoplasmic domain of band 3, cdb3-(His)6 and the rate of substitution of cdb3-(His)6 into endogenous band 3-ankyrin bridges in resealed erythrocytes in the presence and absence of shear stress. We demonstrate that 1) exogenous cdb3-(His)6 displaces endogenous ankyrin from IOVs with a half-time and first order rate constant of 42 +/- 14 min and 0.017 +/- 0.0058 min(-1), respectively; 2) exogenous cdb3-(His)6 substitutes endogenous band 3 in its linkage to ankyrin in resealed cells with a half-time and first order rate constant of 12 +/- 3.6 min and 0.060 +/- 0.019 min(-1), respectively; 3) cdb3-(His)6-mediated rupture of the band 3-ankyrin bridge in resealed cells results in decreased membrane mechanical stability, decreased deformability, abnormal morphology, and spontaneous vesiculation of the cells; and 4) the above on/off rates are not significantly accelerated by mechanical shear stress. We conclude that the off rates of the band 3-ankyrin interaction are sufficiently slow to allow sustained erythrocyte deformation without loss of elasticity.     

Analysis of the oligomeric state of Band 3, the anion transport protein of the human erythrocyte membrane, by size exclusion high performance liquid chromatography. Oligomeric stability and origin of heterogeneity

The oligomeric state of human Band 3 (Mr = 95,000), the erythrocyte membrane anion exchanger, was examined by size exclusion high performance liquid chromatography in solutions containing the nonionic detergent C12E8 (octaethylene glycol n-dodecyl monoether). Band 3 was heterogeneous with respect to oligomeric composition, the predominant (70%) species being a dimer that bound 0.57 mg of C12E8/mg of protein (Stokes radius = 78 A, s20,w = 6.9 S). Variable amounts of larger oligomers were also present; however, no evidence for equilibration between oligomeric species was observed in detergent solution. Analytical and large zone size exclusion chromatography showed that Band 3 could not be dissociated to monomers, other than by protein denaturation. The membrane domain of Band 3 (Mr = 52,000) was also dimeric, but without evidence for higher oligomeric forms, which implies that the interactions responsible for higher associations involve the cytoplasmic domain. Prelabeling of Band 3 with the anion exchange inhibitor 4,4'-diisothiocyanostilbene-2,2'-disulfonate had no effect upon the oligomeric state of either intact Band 3 or its 52-kDa membrane domain. Band 3 oligomeric state could be reversibly changed in the membrane by altering the pH of the solution. The fraction of Band 3 not associated with the cytoskeleton was almost entirely dimeric. Band 3 purified from erythrocytes separated by density gradient centrifugation revealed that older red cells contained a larger proportion of higher oligomers than did younger cells. We conclude that Band 3, in the membrane and in C12E8 solution, exists as a mixture of dimers and larger oligomers. The higher oligomers interact with the cytoskeleton, increase in amount with cell age, and are held together by interactions of the cytoplasmic domain.     

The interaction of human erythrocyte band 3 with cytoskeletal components

Band 3 of the human erythrocyte is involved in anion transport and binding of the cytoskeleton to the membrane bilayer. Human erythrocytes were treated to incorporate varying concentrations of DIDS (4,4′-diisothiocyanostilbene-2,2′-disulfonic acid) a non-penetrating, irreversible inhibitor of anion transport, and both functions of Band 3 were analyzed. The rate of efflux of ³⁵SO₄. was measured and the binding of cytoskeletal components to the membrane was evaluated by extracting the membranes with 0.1 n NaOH and analyzing for the peptides remaining with the membrane. It was found that 0.1 n NaOH extracts all the extrinsic proteins from membranes of untreated cells, while, in the case of the membranes from cells treated with DIDS, a portion of the cytoskeletal components, spectrin (Bands 1 and 2) and Band 2.1 (ankyrin, syndein) remain with the membrane. The amount of these cytoskeletal components remaining with the membrane depends on the concentrations of DIDS incorporated. The effect of DIDS on the extractability of the spectrin-Band 2.1 complex correlates well with DIDS inhibition of anion transport (r = 0.91). At DIDS concentrations which completely inhibit anion transport, about 10% of total spectrin-Band 2.1 complex remains unextracted. Another anion-transport inhibitor, pyridoxal phosphate, has no effect on binding of the cytoskeleton to the membrane. On the other hand, digestion of DIDS-pretreated intact erythrocytes with Pronase, chymotrypsin, or trypsin releases the tight binding of Band 3 to cytoskeleton on the inside of the membrane. Since trypsin does not hydrolyze Band 3 the data suggest that a second membrane protein which is trypsin sensitive may be involved with Band 3 in cytoskeletal binding.     

Structure and organization of the murine band 3 gene

The Band 3 protein mediates the reversible exchange of chloride and bicarbonate anions across the plasma membrane of erythrocytes, and probably, certain epithelial cells. It also serves to anchor the spectrin cytoskeleton to the plasma membrane via its association with ankyrin. We have isolated and largely sequenced the 17-kilobase murine Band 3 gene. We show that this gene is present in a single copy in the mouse genome and have identified and mapped the 19 intervening sequences. The locations of the intron/exon junctions in the Band 3 mRNA correlate with predicted structural features of the erythrocyte Band 3 protein structure and membrane topology. One of the introns within this gene contains a single copy of a murine Alu-type high dispersed sequence, in addition to several unusual tandemly repeated sequences.     

Bilayer/cytoskeleton interactions in lipid-symmetric erythrocytes assessed by a photoactivable phospholipid analogue

Two mechanisms have been proposed for maintenance of transbilayer phospholipid asymmetry in the erythrocyte plasma membrane, one involving specific interactions between the aminophospholipids of the inner leaflet of the bilayer and the cytoskeleton, particularly spectrin, and the other involving the aminophospholipid translocase. If the former mechanism is correct, then erythrocytes which have lost their asymmetric distribution of phospholipids should display altered bilayer/cytoskeleton interactions. To test this possibility, normal erythrocytes, erythrocytes from patients with chronic myelogenous leukemia or sickle disease, and lipid-symmetric and -asymmetric erythrocyte ghosts were labeled with the radioactive photoactivable analogue of phosphatidylethanolamine, 2-(2-azido-4-nitrobenzoyl)-1-acyl-sn-glycero-3-phospho[14C]ethanolamine ([14C]AzPE), previously shown to label cytoskeletal proteins from the bilayer. The labeling pattern of cytoskeletal proteins in pathologic erythrocytes and lipid-asymmetric erythrocyte ghosts was indistinguishable from normal erythrocytes, indicating that the probe detects no differences in bilayer/cytoskeleton interactions in these cells. In contrast, in lipid-symmetric erythrocyte ghosts, labeling of bands 4.1 and 4.2 and actin, and to a lesser extent ankyrin, by [14C]AzPE was considerably reduced. Significantly, however, labeling of spectrin was unaltered in the lipid-symmetric ghosts, suggesting that its relationship with the bilayer is normal in these lipid-symmetric cells. These results do not support a model in which spectrin is involved in the maintenance of an asymmetric distribution of phospholipids in erythrocytes.     

Rotational diffusion of band 3 proteins in membranes from En(a—) and neuraminidase-treated normal human erythrocytes

Recent experiments have demonstrated an association between band 3 and glycophorin A in the human erythrocyte membrane (Nigg, E.A., Bron, C., Girardet, M. and Cherry, R.J. (1980) Biochemistry 19, 1887–1893). Here, the influence of sialoglycoproteins on the rotational diffusion of band 3 in the human erythrocyte membrane was investigated by studying membranes from En(a—) and neuraminidase-treated erythrocytes. Rotational diffusion was measured by observing flash-induced transient dichroism of eosin-labeled band 3. Although erythrocytes of the rare phenotype En(a—) lack the major sialoglycoprotein, glycophorin A, no significant difference in band 3 rotation at pH 7.4 and 37°C could be detected between En(a—) and normal erythrocyte membranes. Band 3 rotation at pH 7.4 was also insensitive to the enzymatic removal of sialic acid from the surface of normal erythrocytes. Moreover, the existence of an essentially similar temperature-dependent equilibrium between band 3 proteins with different mobilities was observed in normal, En(a—) and neuraminidase-treated erythrocytes. From these results it is concluded that glycophorin A contributes less than 15% to the cross-sectional diameter of the band 3-glycophorin A complex in the plane of the normal membrane. The rotation of the complex at pH 7.4 is not significantly influenced by either steric or electrostatic interactions involving the oligosaccharide moiety of glycophorin A.     

Mechanism of the change in erythrocyte osmotic resistance in rats exposed to valinomycin: the features seen in spontaneous hypertension

Introduction of valinomycin into erythrocyte incubation medium increased the cell stability to water-induced hemolysis. In these conditions the erythrocytes of spontaneously hypertensive and normotensive (control) rats release 63.2 +/- 1.5% and 80.9 +/- 1.6%, respectively, of the total hemoglobin content. Valinomycin effect is completely abolished with K+ substitution for Na+ and is independent of extracellular Ca2+ concentration. Valinomycin had no effect on human erythrocyte osmotic stability. It has been shown that valinomycin-induced kinetics of Na+ and K+ redistribution was different in human and rat erythrocytes. The distinctions are thought to be related to specific anion transport mediated by the third band protein--the main component of membrane cytoskeleton.     

Intermembrane protein transfer. Band 3, the erythrocyte anion transporter, transfers in native orientation from human red blood cells into the bilayer of phospholipid vesicles

Band 3, the erythrocyte anion transporter, has been shown to transfer between human erythrocytes and sonicated vesicles (Newton, A. C., Cook, S. L., and Huestis, W. H. (1983) Biochemistry 22, 6110-6117). Functional band 3 becomes associated with dimyristoylphosphatidylcholine vesicles incubated with human red blood cells. Proteolytic degradation patterns reveal that the transporter is transferred to the vesicles in native orientation. In erythrocytes, native band 3 is degraded on the exoplasmic membrane face by chymotrypsin and on the cytoplasmic surface by trypsin (Cabantchik, Z. I., and Rothstein, A. (1974) J. Membr. Biol. 15, 227-248; Jennings, M. L., Anderson, M. P., and Monaghan, R. (1986) J. Biol. Chem. 261, 9002-9010). Band 3 in intact protein-vesicle complexes is degraded by exogenous chymotrypsin but not by trypsin. In contrast, trypsin entrapped in the lumen of the vesicles proteolyses the vesicle-bound band 3 quantitatively. Band 3 remaining in the membranes of vesicle-treated cells and in cell fragments is not degraded detectably by vesicle-entrapped trypsin. These observations indicate that band 3 is unlikely to transfer between cell and vesicle membranes via a water-soluble form or to adhere nonspecifically to the vesicle surface; the aqueous contents of vesicles and cells (or membrane fragments) are not pooled during cell-vesicle incubations, hence no cell-vesicle fusion occurs; and the band 3 associated with the sonicated vesicle fraction is inserted in the vesicle bilayer in native orientation, with its cytoplasmic segment contacting the aqueous contents of the vesicle lumen.     

Computer simulation of a model network for the erythrocyte cytoskeleton.

The geometry and mechanical properties of the human erythrocyte membrane cytoskeleton are investigated by a computer simulation in which the cytoskeleton is represented by a network of polymer chains. Four elastic moduli as well as the area and thickness are predicted for the chain network as a function of temperature and the number of segments in each chain. Comparisons are made with mean field arguments to examine the importance of steric interactions in determining network properties. Applied to the red blood cell, the simulation predicts that in the bilayer plane the membrane cytoskeleton has a shear modulus of 10 +/- 2 x 10(-6) J/m2 and an areal compression modulus of 17 +/- 2 x 10(-6) J/m2. The volume compression modulus and the transverse Young's modulus of the cytoskeleton are predicted to be 1.2 +/- 0.1 x 10(3) J/m3 and 2.0 +/- 0.1 x 10(3) J/m3, respectively. Elements of the cytoskeleton are predicted to have a mean displacement from the bilayer plane of 15 nm. The simulation agrees with some, but not all, of the shear modulus measurements. The other predicted moduli have not been measured.     

Band 3 tyr-phosphorylation in human erythrocytes from non-pregnant and pregnant women

Pregnancy is associated with changes in circulating red blood cells, mainly involving band 3 protein and membrane lipid peroxidation. Membrane band 3 is a multifunctional protein containing four Tyr-phosphorylatable residues which modulate the physiological status of erythrocytes by regulating glycolysis, cell shape and membrane transport. Erythrocytes from nine pregnant and 12 age-matched non-pregnant healthy women were subjected to oxidative and hyperosmotic stress conditions and the extent of band 3 Tyr-phosphorylation and membrane Syk recruitment as a membrane marker were evaluated. Results indicated that, in pregnancy, red blood cells show a decrease in band 3 Tyr-phosphorylation and a clear-cut rearrangement of band 3 protein within the membrane. In fact, band 3 shows a decrease in high molecular weight aggregates (HMWA), with different subdivision between Triton-soluble and -insoluble compartments, and an increase in proteolytic fragments. In conclusion, it is demonstrated that pregnancy is associated with membrane adjustments which reduce the sensitivity of erythrocytes to both oxidative and osmotic stress. Band 3 Tyr-phosphorylation is proposed as a new parameter in the evaluation of erythrocyte membrane arrangement.     

Band 3 tyr-phosphorylation in human erythrocytes from non-pregnant and pregnant women

Pregnancy is associated with changes in circulating red blood cells, mainly involving band 3 protein and membrane lipid peroxidation. Membrane band 3 is a multifunctional protein containing four Tyr-phosphorylatable residues which modulate the physiological status of erythrocytes by regulating glycolysis, cell shape and membrane transport. Erythrocytes from nine pregnant and 12 age-matched non-pregnant healthy women were subjected to oxidative and hyperosmotic stress conditions and the extent of band 3 Tyr-phosphorylation and membrane Syk recruitment as a membrane marker were evaluated. Results indicated that, in pregnancy, red blood cells show a decrease in band 3 Tyr-phosphorylation and a clear-cut rearrangement of band 3 protein within the membrane. In fact, band 3 shows a decrease in high molecular weight aggregates (HMWA), with different subdivision between Triton-soluble and -insoluble compartments, and an increase in proteolytic fragments. In conclusion, it is demonstrated that pregnancy is associated with membrane adjustments which reduce the sensitivity of erythrocytes to both oxidative and osmotic stress. Band 3 Tyr-phosphorylation is proposed as a new parameter in the evaluation of erythrocyte membrane arrangement.     

Plasmodium falciparum: analysis of the interaction of antigen Pf155/RESA with the erythrocyte membrane

The location of the Plasmodium falciparum vaccine candidate antigen Pf155/RESA in the membrane of infected erythrocytes was analzyed by means of selective surface radioiodination and immunofluorescence of surface-modified cells. The lack of radiolabel in Pf155/RESA as well as its localization by immunofluorescence similar to that of the N-terminal region of erythrocyte band 3 suggests that the antigen is associated with the cytoplasmic phase of the erythrocyte membrane. In concordance with this, Pf155/RESA was detected by immunofluorescence on the surface of inside out membrane vesicles from P. falciparum-infected erythrocytes. Pf155/RESA from spent culture medium also bound to inside out membrane vesicles of normal erythrocytes as well as to cytoskeletal shells of such vesicles, but failed to bind to sealed right-side out membrane vesicles. Depletion of spectrin from the vesicles abolished antigen binding, suggesting that Pf155/RESA association with the erythrocyte cytoskeleton is mediated by spectrin.     

The orientation of eosin-5-maleimide on human erythrocyte band 3 measured by fluorescence polarization microscopy.

The dominant motional mode for membrane proteins is uniaxial rotational diffusion about the membrane normal axis, and investigations of their rotational dynamics can yield insight into both the oligomeric state of the protein and its interactions with other proteins such as the cytoskeleton. However, results from the spectroscopic methods used to study these dynamics are dependent on the orientation of the probe relative to the axis of motion. We have employed polarized fluorescence confocal microscopy to measure the orientation of eosin-5-maleimide covalently reacted with Lys-430 of human erythrocyte band 3. Steady-state polarized fluorescence images showed distinct intensity patterns, which were fit to an orientation distribution of the eosin absorption and emission dipoles relative to the membrane normal axis. This orientation was found to be unchanged by trypsin treatment, which cleaves band 3 between the integral membrane domain and the cytoskeleton-attached domain. this result suggests that phosphorescence anisotropy changes observed after trypsin treatment are due to a rotational constraint change rather than a reorientation of eosin. By coupling time-resolved prompt fluorescence anisotropy with confocal microscopy, we calculated the expected amplitudes of the e-Dt and e-4Dt terms from the uniaxial rotational diffusion model and found that the e-4Dt term should dominate the anisotropy decay. Delayed fluorescence and phosphorescence anisotropy decays of control and trypsin-treated band 3 in ghosts, analyzed as multiple uniaxially rotating populations using the amplitudes predicted by confocal microscopy, were consistent with three motional species with uniaxial correlation times ranging from 7 microseconds to 1.4 ms.     

Erythrocyte signal transduction pathways, their oxygenation dependence and functional significance.

Erythrocytes play a key role in human and vertebrate metabolism. Tissue O2 supply is regulated by both hemoglobin (Hb)-O2 affinity and erythrocyte rheology, a key determinant of tissue perfusion. Oxygenation-deoxygenation transitions of Hb may lead to re-organization of the cytoskeleton and signalling pathways activation/deactivation in an O2-dependent manner. Deoxygenated Hb binds to the cytoplasmic domain of the anion exchanger band 3, which is anchored to the cytoskeleton, and is considered a major mechanism underlying the oxygenation-dependence of several erythrocyte functions. This work discusses the multiple modes of Hb-cytoskeleton interactions. In addition, it reviews the effects of Mg2+, 2,3-diphosphoglycerate, NO, shear stress and Ca2+, all factors accompanying the oxygenation-deoxygenation cycle in circulating red cells. Due to the extensive literature on the subject, the data discussed here, pertain mainly to human erythrocytes whose O2 affinity is modulated by 2,3-diphosphoglycerate, ectothermic vertebrate erythrocytes that use ATP, and to bird erythrocytes that use inositol pentaphosphate.     

Proteolytic degradation of human erythrocyte band 3 by membrane-associated protease activity

Summary Antisera directed against the cytoplasmic portion of human erythrocyte Band 3 were used to follow the degradation of the band 3 molecule. Small amounts of Band 3 were degraded when well-washed red cell membrane ghosts were incubated in the cold; this process was greatly accelerated by incubating ghosts at 37°C. Band 3 labeled with pyridoxal-phosphate was digested at comparable rates. Band 3 digestion also took place when alkali-extracted ghost membranes were incubated at 37° for prolonged periods. These results suggest that human erythrocytes contain tightly bound, membrane-associated proteolytic activity.     

Dynamics of membrane structure of frog erythrocyte ghosts measured with a nanosecond fluorometer

The dynamics of membrane microstructure was studied as molecular motions of phospholipids for bullfrog erythrocyte ghosts by the DPH fluorescence depolarization technique with a nanosecond fluorometer. The bullfrog erythrocyte ghosts were obtained by hypotonic lysis and collagenase treatment. The constituents of membrane proteins were confirmed by the disk gel electrophoresis. The viscosity of erythrocyte membrane ghosts was estimated to be 3.3 +/- 1.0 at 10 degrees C, and 2.1 +/- 0.1 at 20 degrees C and 1.3 +/- 0.2 at 30 degrees C in the unit of poise and the wobbling angle of lipid molecule was 35 +/- 1, 41 +/- 1 and 43 +/- 1 degree at the respective temperatures on an average and +/- S.D. The viscosity is lower than that of human erythrocytes. The relatively low viscous phospholipid bilayer may be one of the factors for the deformability of bullfrog erythrocytes.     

Characterization of immunoglobulin binding to isolated human erythrocyte membranes: evidence for selective, temperature-induced binding of naturally occurring autoantibodies to the cytoskeleton

Human plasma contains naturally occurring autoantibodies to the predominant components of the erythrocyte membrane: band 3 and spectrin bands 1 and 2 of the cytoskeleton. The titer of cytoskeletal plasma autoantibodies increases in various hemolytic conditions, suggesting that opsonization of the cytoskeleton may play an important role in the clearance of hemolyzed (not senescent) erythrocytes from the circulation. In this study, we use Alexa Fluor 488 goat anti-human IgG conjugate (Molecular Probes, Eugene, OR, USA), to characterize plasma immunoglobulin binding to erythrocyte membranes from osmotically hemolyzed cells ('ghosts'). The results show that exposure of ghosts to plasma results in 4-fold more immunoglobulin binding to the cytoskeleton than is bound to the proteins contained within the lipid bilayer. Preincubation of the ghosts at 37 degrees C causes 8-fold more immunoglobulin binding to the cytoskeleton compared to bilayer proteins. This temperature-induced change resulted from selective immunoglobulin binding to the cytoskeleton, with no change in immunoglobulin binding to bilayer proteins. However, the rate of increase in cytoskeletal antigenicity at 37 degrees C did correlate with the rate of a conformational change in band 3, a transmembrane protein which serves as a major membrane attachment site for the cytoskeleton. The results of this study suggest that the cytoskeleton is the primary target in the opsonization of hemolyzed erythrocyte membranes by naturally occurring plasma autoantibodies. The conformational changes which occur in ghosts at 37 degrees C are associated with selective exposure of new immunoglobulin binding sites on the cytoskeleton, and with a change in the structure of band 3. We propose a model suggesting that opsonization of the cytoskeleton occurs prior to the decomposition of hemolyzed erythrocytes at 37 degrees C.     

Reconstitution of band 3, the erythrocyte anion exchange protein

Band 3, the erythrocyte membrane protein thought to be responsible for anion transport, was purified to near homogeneity using a Concanavalin A affinity column. Band 3 was then combined with egg lecithin, erythrocyte lipid, cholesterol, and glycophorin, the major erythrocyte sialoglycoprotein, to form vesicles capable of rapid sulfate transport. The transport activity was sensitive to prior treatment of the erythrocytes with pyridoxal phosphate-NaBH₄, a potent inhibitor of anion transport in these cells.     

Plasmodium falciparum histidine-rich protein 1 associates with the band 3 binding domain of ankyrin in the infected red cell membrane

Infection of erythrocytes by the malaria parasite Plasmodium falciparum results in the export of several parasite proteins into the erythrocyte cytoplasm. Changes occur in the infected erythrocyte due to altered phosphorylation of proteins and to novel interactions between host and parasite proteins, particularly at the membrane skeleton. In erythrocytes, the spectrin based red cell membrane skeleton is linked to the erythrocyte plasma membrane through interactions of ankyrin with spectrin and band 3. Here we report an association between the P. falciparum histidine-rich protein (PfHRP1) and phosphorylated proteolytic fragments of red cell ankyrin. Immunochemical, biochemical and biophysical studies indicate that the 89 kDa band 3 binding domain and the 62 kDa spectrin-binding domain of ankyrin are co-precipitated by mAb 89 against PfHRP1, and that native and recombinant ankyrin fragments bind to the 5' repeat region of PfHRP1. PfHRP1 is responsible for anchoring the parasite cytoadherence ligand to the erythrocyte membrane skeleton, and this additional interaction with ankyrin would strengthen the ability of PfEMP1 to resist shear stress.