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Journal of Theoretical Biology 233 (2005) 127–135

www.elsevier.com/locate/yjtbi

A hypothesis of the disc–sphere transformation of the erythrocytesbetween glass surfaces and of related observations

Pierre Wong�

Department of Oncology, McGill University, 546 Pine Avenue West, Montreal, Quebec, Canada H2W 1S6

Received 31 May 2004; received in revised form 7 September 2004; accepted 22 September 2004

Available online 10 November 2004

Abstract

Erythrocytes suspended at a low hematocrit in a non-buffered isotonic saline change from biconcave discs to spheres between

glass surfaces of a slide and of a coverslip with the echinocyte as an intermediate. A pH increase is a major factor responsible for this

disc–sphere transformation or glass effect. It is also observed between surfaces made of various polymers and of mica provided that

the distance between them is controlled (0.1mm). The glass effect is antagonized by serum, plasma, serum albumin, ammonium salts

and CO2. It is not observed above a 1–2% hematocrit, but is enhanced by g-globulins. The sites of reappearance of the spicules arethe same and the order of their disappearance is the inverse of the order of their reappearance during the repetitive cycle of the

disc–sphere transformation and reversal when a small glass rod is alternatively approached near a site on the erythrocyte surface and

withdrawn. A mechanism of erythrocyte shape control has been previously hypothesized in which Band 3 (AE1), the anion exchange

protein, plays a central role. Specifically, decrease and increase of the ratio of its outward-facing conformation (Band 3o) and

inward-facing conformation (Band 3i) contract and relax the membrane skeleton, promoting the echinocytosis and stomatocytosis,

respectively. The Band 3o/Band 3i equilibrium ratio is determined by the Donnan equilibrium ratio of Cl�, HCO�3 and H+

(r ¼ Cl�i =Cl�o ¼ HCO�

3i=HCO�3o ¼ Hþ

o =Hþi ), increasing with it. The mechanism could explain by a change of the Donnan ratio the

above observations with the assumptions that polymers are permeable to CO2 and that an unstirred layer slows the propagation of

the change occurring at the site of approach of the glass rod to peripheral sites. The presence of HCO�3 in serum or plasma may be

the basis for the absence of the glass effect in these fluids.

r 2004 Elsevier Ltd. All rights reserved.

Keywords: Band 3; Donnan ratio; Erythrocyte; Glass effect; Spectrin

1. Introduction

More than 100 years ago, Hamburger observed thaterythrocytes at a low hematocrit in isotonic, hypertonicor hypotonic saline or sugar solutions, but not in serumor plasma, changed from biconcave discs to spheresbetween glass surfaces of a slide and of a coverslip of ahematocytometer, and that the addition of serum orplasma reversed the transformation (Ponder, 1948). Thisdisc–sphere transformation, which was referred as theglass effect as it was believed to be different from those

e front matter r 2004 Elsevier Ltd. All rights reserved.

i.2004.09.013

398 5940; fax: +1 514 398 5111.

ess: pierre.wong@mcgill.ca (P. Wong).

induced by surface-active substances, is the oldest oneknown and was attributed to a modification of thesurface tension in the absence of other explanations. Ithas been the object of investigations over the years(Gough, 1924; Furchgott, 1940; Furchgott and Ponder,1940; Ponder, 1948; Tompkins, 1954; Brown, 1956;Trotter, 1956; Ponder and Ponder, 1962; Bessis andPrenant, 1972; Mehta, 1983; Bifano et al., 1984;Eriksson, 1990; Deuticke, 2003). However, it remainsyet to be satisfactorily explained although significantprogress has been achieved. One difficulty is that fewsubstances can be eluted from the erythrocytes, as it hasbeen pointed out by Ponder and Ponder (1962). Asecond one, which has been early recognized, has been

ARTICLE IN PRESSP. Wong / Journal of Theoretical Biology 233 (2005) 127–135128

the inability of determining the manner by which theagents favoring and reversing the glass effect alter theerythrocyte shape, owing to the absence of knowledge ofthe basis of the biconcave disc shape. The view generallyheld on the erythrocyte shape is that it is determined bythe mechanical properties of the erythrocyte membraneenvelope since it is the only solid element resistingdeformations. The membrane envelope is a composite oftwo major layers: a fluid and asymmetric lipid bilayer inwhich integral proteins or transmembrane and amphi-philic proteins are diffusing or are immobilized by theirnon-covalent bindings to peripheral proteins, and aflexible membrane skeleton scaffold laminating thecytoplasmic surface of the lipid bilayer and constitutedby peripheral proteins. Attempts have been made formore than three decades to develop quantitativemechanical models of the erythrocyte shape based onthe bending, shearing and stretching elastic constantmoduli of the membrane envelope, of the lipid bilayerand of the membrane skeleton, as may be measured withsensitive microscopic tools such as the micropipette,flicker spectroscopy, atomic force microscopy andoptical tweezers (Berk et al., 1989; Lenormand et al.,2001; Scheffer et al., 2001). A recently proposed modelpostulates that the erythrocyte shape is determined bythe bending elasticity of the lipid bilayer and shearingand stretching elasticity of the membrane skeleton (Limet al., 2002; Mukhopadhyay et al., 2002). This model isable to reproduce remarkably the different stages of theechinocytosis and stomatocytosis by a simple variationof the relative areas of the inner and outer leaflets of thelipid bilayer, in accord with Sheetz and Singer’s (1974)lipid bilayer couple hypothesis. However, a difficultywith these models is their inability of explainingunequivocally by modifications of the structures of thelipid bilayer and of the membrane skeleton erythrocyteshape changes induced by alterations of pH and ioniccomposition of the medium (Hoffman, 1987; Bull andBrailsford, 1989, Gedde et al., 1995; Gimsa and Ried,1995). These models have also been developed based onthe premise that the erythrocyte membrane envelope is acontinuum, i.e. its components are distributed uniformlyalong the longitudinal plane. While this premise isreasonable, they are unable at present to explain thereappearance of the spicules at the same sites during therepetitive cycle disc–echinocyte transformation andreversal (Furchgott, 1940; Rand et al., 1965; Bessisand Prenant, 1972; Mukhopadhyay et al., 2002).Finally, there are data in disagreement with the Sheetzand Singer’s lipid bilayer couple hypothesis (Isomaaet al., 1987; Wong, 1999; Nakao, 2002). Based on thishypothesis, echinocytogenic amphiphilic compounds,generally anionic, intercalate preferentially into thecationic outer leaflet of the lipid bilayer and increaseits area, while stomatocytogenic compounds, generallycationic, intercalate preferentially into the anionic inner

leaflet and increase its area. However, we have suggestedthat most of these amphiphilic compounds, if not all,alter the shape by altering the conformation of Band 3(AE1 or anion exchanger 1) (Wong, 1999). Indeed, theyinhibit the Band 3 anion transport activity, and severalof them inhibit the Band 3 anion transport activity andalter the shape concomitantly. The slowly transportedBand 3 substrates arsenate, iodide, nitrate, oxalate andvanadate (Ponder, 1948; Vives-Corrons et al., 1981;Tajima, 1986; Eriksson, 1990; Winski and Carter, 1998),and the specific Band 3 anion transport inhibitorsdipyridamole, DIDS (4,40-diisothiocyanotostilbene-2,20-disulfonic acid) and DNDS (4,40-dinitrostilbene-2,20-disulfonic acid) are echinocytogenic (Bifano et al., 1984;Hoefner et al., 1994; Gimsa and Ried, 1995; Schwarz etal., 1999). Gimsa and Ried (1995) have also suggestedthat the erythrocyte shape transformations produced bypH change are caused by a Band 3 conformationalchange since they occur too rapidly to be explained by aredistribution of the phospholipids of the lipid bilayerand that the membrane skeleton is unable by itself tomaintain the shape, owing to its high flexibility. We havepreviously hypothesized a mechanism of erythrocyteshape control in which Band 3 plays a central role(Wong, 1999). It differs qualitatively from mechanicalmodels in that the membrane skeleton by its highconformational flexibility is used to generate differentshapes, and that Band 3 conformation determines themembrane skeleton conformation. This function of themembrane skeleton is consistent with proposals that itplays a more dominant role than the lipid bilayerasymmetry in determining the erythrocyte shape (Elgsa-eter et al., 1986; Nakao, 2002). A consequence of thismechanism is that the membrane skeleton has anegligible or no elasticity and that Band 3 conformationis altered directly or indirectly by mechanical andchemical stresses as they occur in the blood circulation,possibly coupled with the dissociation of spectrintetramer into dimer observed at modest shearing forces(An et al., 2002). The mechanism predicts shape changeswith changes of pH and ionic composition sincethe Band 3 conformation depends on the Donnanequilibrium ratio of Cl�, HCO3

� and H+

(r ¼ Cl�i =Cl�o ¼ HCO�

3i=HCO�3o ¼ Hþ

o =Hþi ), which is

influenced by pH and ionic composition. We haveshown, based on its predictability, that it could explainseveral observations directly or indirectly related to theerythrocyte shape, suggesting its plausibility (Wong,1999, 2004). The mechanism is also supported byprevious studies showing that the shape of erythrocytesand resealed ghosts as a function of internal andexternal pH and ionic composition in the presence andabsence of ionophores correlated with the transmem-brane potential rather than with the pH and cell volume(Glaser, 1982; Muller et al., 1986). This parameter variesin parallel with the Donnan ratio (Dc ¼ RT=zF � ln r).

ARTICLE IN PRESS

H2O

H2CO3

H2O

H2CO3Hb

H-Hb

C.A.

Band 3Cl-

H+

HCO3- HCO3

-Cl-

+

H+

H2O

H2CO3

H2O

H2CO3Hb

H-Hb

C.A.

Band 3Cl-Cl-

H+H+

HCO3-HCO3- HCO3

-HCO3-

Cl-Cl-+

H+H+

P. Wong / Journal of Theoretical Biology 233 (2005) 127–135 129

We have indicated in a previous paper that themechanism would explain the disc–sphere transforma-tion between glass surfaces with the echinocyte as anintermediate since it is associated with a pH increase(Wong, 1999). A pH increase would ionize hemoglobinand 2,3-bisphosphoglycerate (2,3-BPG) and decrease theDonnan ratio, thus, promoting the echinocytosis.However, other related observations were unexplained.We show below that the mechanism could also explainthem by a change of the Donnan ratio.

CO2CO2

OI

CO2CO2

OI

Fig. 1. Illustration of the Jacobs–Stewart cycle. In the figure CO2 is

shown to diffuse across the lipid bilayer, but it may be transported by

Band 3, Aquaporin-1 or the Rh antigenic complex. The abbreviation

C.A. refers to carbonic anhydrase. See text for additional details.

2. Mechanism of erythrocyte shape control

The mechanism of the erythrocyte shape control hasbeen previously described in detail (Wong, 1999).Briefly, Band 3 mediates an obligatory one-to-one anionexchange of Cl� or HCO�

3 by alternating between anoutward-facing conformation (Band 3o) and an inward-facing conformation (Band 3i). Decrease and increase ofthe ratio of Band 3o/Band 3i contract and relax themembrane skeleton, thereby promoting the echinocyto-sis and stomatocytosis, respectively. The Band 3o/Band3i equilibrium ratio is determined by the Donnanequilibrium ratio of Cl�, HCO�

3 and H+, increasingwith it (Band 3o/Band 3i=kKo/k

0Ki� r; r ¼ Cl�i =Cl�o ¼

HCO�3i=HCO

�3o ¼ Hþ

o =Hþi ) (Knauf et al., 1996). The

Donnan ratio is mainly determined by hemoglobin, 2,3-BPG and the monovalent cations Na+ and K+.Hemoglobin is a weak electrolyte whose state ofionization is influenced by the pH and tensions of O2

and CO2. 2,3-BPG is a regulator of oxygen affinity ofhemoglobin and is present at a concentration equivalentto that of hemoglobin (5mM) and has an average ofthree to four negative charges at the erythrocyte pH.The Na+ and K+ can be viewed as impermeants sincethe membrane permeability to these ions is six orders ofmagnitude lower than those of Cl� and HCO�

3 : Theirdistribution across the membrane is determined by thenet activities of the Na+, K+-ATPase and cation leakpathways. While Cl� and HCO�

3 equilibrate rapidlyacross the membrane by the intermediary of the anionexchange protein Band 3, the non-penetrating protonsequilibrate by the Jacobs–Stewart cycle (Fig. 1). Thisreversible cycle depends on the presence of a catalyticamount of HCO�

3 ; which may be derived from air CO2

dissolved (the concentration of dissolved CO2 inequilibrium with air CO2 is 10–15 mM), and theinterconversion of CO2 and carbonic acid (H2CO3) inthe external medium is the rate limiting step of the cyclesince it is uncatalysed. It operates as follows. When theexternal pH increases, the equilibrium between CO2,H2CO3, H

+ and HCO�3 is shifted toward the formation

of HCO�3 (pKa ¼ 6:3), which exchanges with cell Cl� by

the intermediary of Band 3. Within the cell, HCO�3

combines with a proton bound to hemoglobin to yield

H2CO3, which is dehydrated by carbonic anhydraseto yield CO2. The CO2 diffuses across the membranelipid bilayer or may be transported by Band 3,Aquaporin-1 or the Rh antigenic complex in theexternal medium where it is reconverted to HCO�

3

(Blank and Ehmke, 2003; Bruce et al., 2003; Soupene etal., 2002, 2004). The net effect of a pH increase is adecrease in the Donnan ratio, which would favor theechinocytosis. When the external pH decreases, the cycleoperates in the opposite direction with the net effect ofan increase of the Donnan ratio, which would favor thestomatocytosis.

3. Rationalization of observations

The mechanism could be the basis of the glass effectas it can rationalize self-consistently the followingobservations:

(a)

The occurrence of the disc–sphere and disc–echino-cyte transformations of the erythrocytes in non-buffered and buffered isotonic saline (Furchgott,1940): In the two transformations the pH isincreased, which ionizes hemoglobin and 2,3-BPG,and decreases the Donnan ratio. The extent of pHincrease or of the Donnan ratio decrease is thatexpected based on the fact that the echinocyte is anintermediate in the sphere formation. Indeed, in thefirst and second transformations, the pH is increasedto values of 9.20–9.31 and 7.87–8.05, respectively.

(b)

The absence of the disc–echinocyte transformationabove a hematocrit of 1–2% in a buffered isotonicsaline (Eriksson, 1990): This result would beexpected based on the fact that the amount ofequivalent HCO�

3 in the solution is limiting and that

ARTICLE IN PRESSP. Wong / Journal of Theoretical Biology 233 (2005) 127–135130

the equilibration of Cl�, HCO�3 and H+ across the

membrane is dependent on the H+ binding tohemoglobin (Fig. 1). Thus, the proportion of cellstransformed would be a function of the ratio of thelimiting equivalent amount of HCO�

3 in the solutionper erythrocyte or per equivalent amount ofhemoglobin, increasing with an increase of the ratio.

(c)

The reversal of the disc–sphere transformation bythe adjunction of CO2 (Furchgott, 1940): Themechanism would explain this reversal as follows.The adjunction of CO2 acidifies and promotes theoperation of the Jacobs–Stewart cycle in the direc-tion increasing the Donnan ratio, thereby favoringthe stomatocytosis and opposing the echinocytosis.In agreement with this explanation is the observa-tion that the local anesthetic lidocaine induced astomatocytosis by decreasing the cell pH and thatthe inhibition of carbonic anhydrase by acetazola-mide, thus the inhibition of the Jacobs–Stewartcycle, prevented the stomatocytosis (Nishiguchiet al., 1995).

(d)

The disc–sphere transformation of erythrocytes in afree suspension did not occur until the suspensionwas titrated to pH 11.3–11.4 with a NaOH solution(Furchgott, 1940): Since the pH between glasssurfaces increased only to 9.2, this observation hasbeen interpreted to indicate that the pH increase isnot alone responsible for the glass effect: anantispheric factor present in the suspension boundto the erythrocyte surface and adsorbed by the glasshas been hypothesized; serum albumin has beensuggested as the antispheric factor since it preventedthe disc–sphere transformation. However, the disc–-sphere transformation occurred at the same pH asbetween glass surfaces when the erythrocyte suspen-sion was titrated with a NaHCO3 solution (Brown,1956). Based on the high permeability of theerythrocyte membrane to HCO�

3 ; due to its trans-port by Band 3, and based on evidence that serumalbumin did not bind to the erythrocyte surface (seealso below), it has been suggested that the instanta-neous disc–sphere transformation between glasssurfaces was due to a dissolution of the baseNa2CO3 embedded in the glass and equilibrationof CO3

2� with HCO�3 (pKa, 10.4) and alkalinization

of the cell by the diffusion of HCO�3 (Brown, 1956).

The mechanism would be in accord with this viewsince the Donnan equilibrium of anions and protonswould be reached more rapidly in the presence ofHCO�

3 and that the amount of HCO�3 or base

available for titrating hemoglobin and 2,3-BPG totheir unprotonated forms would be significantlyhigher.

(e)

The addition of a NaOH solution to a stirredsuspension of washed erythrocytes at pH 6.45 so asto increase the equilibrium pH to about 8 caused an

immediate disc–sphere transformation, but subse-quently the erythrocyte reverted to the disc shapeover a period of 15–20min. The disc–spheretransformation was accelerated by the addition ofa small amount of NaHCO3 (0.5mM; equilibriumpH 8.3), but was prevented by the addition of alarger amount of NaHCO3 (Hoffman, 1972, 1987).According to the mechanism, the disc–spheretransformation after the addition of the NaOHsolution would be caused by a decrease of theDonnan ratio, which can occur relatively rapidly inthe presence of trace amounts of HCO�

3 : Thereversion to the disc shape over time at moderatealkaline pH would be explained by the dissolution ofair CO2 facilitated by the continuous stirring of theerythrocyte suspension and the shift of the equili-brium between CO2 and HCO�

3 toward the forma-tion of HCO�

3 at alkaline pH (pKa, 6.3). Thisdissolved CO2 would increase the Donnan ratio andreverse the disc–sphere transformation in the man-ner described above. Moreover, the use of a lowhematocrit (0.11%) would also favor this reversionsince the extent of reversion increases with theincrease of the amount of moles of CO2 pererythrocyte or the molar ratio of CO2 to hemoglobinand that the concentration of hemoglobin at thehematocrit used (5.5 mM) is comparable to that ofdissolved CO2 in equilibrium with air CO2

(10–15 mM). The acceleration of the disc–spheretransformation by the addition of a small amount ofHCO�

3 can be understood since its presence in-creases the rate at which the Donnan ratioequilibrium is reached, as indicated above. Theprevention of the disc–sphere transformation byincreasing the NaHCO3 concentration would beexplained since at a higher HCO�

3 concentration therate at which the Donnan ratio equilibrium isreached would increase and that the addition ofHCO�

3 at a moderate alkaline pH would result in anew equilibrium at which the Donnan ratio wouldbe increased since a fraction of the HCO�

3 would beconverted to CO2.

(f)

The reversal of the disc–sphere transformation byammonium oxalate (1%, 81mM; (COONH4)2) and1% ammonium chloride (1%, 187mM; NH4Cl) salts(Gough, 1924): Ammonium (NH4

+) may be trans-ported by the Rh antigenic complex or can diffuseacross the membrane under the form of NH3 gas(pKa, 9.26) (Labotka et al., 1995; Marini et al., 2000;Westhoff et al., 2002, 2004; Hemker et al., 2003):studies on the function of the Rhesus protein Rh1protein of the green alga Chlamydomonas reinhardtii

suggest that the Rh antigenic complex may transportCO2 rather than NH4

+ (Soupene et al., 2002, 2004).The increase of NH4

+ level in the cell would increasethe Donnan ratio, thereby favoring the stomatocy-

ARTICLE IN PRESS

Tab

Effe

Hct.

0.45

0.45

0.1

0.1

0.1

0.45

3

10

10

10

0.2

0.2

0.2

aPbPc1

addidAeEfEgE

P. Wong / Journal of Theoretical Biology 233 (2005) 127–135 131

tosis and thus opposing the echinocytosis. Support-ing this explanation are these two observations. (i)There is a stomatocytosis in individuals with theRhnull phenotype or expressing a 40–70-fold excessof a normal adenosine deaminase (Kanno et al.,1988). The stomatocytosis in individuals with theRhnull phenotype would be predicted by the mechan-ism whether the Rh antigenic complex transportsNH4

+ or CO2 since these end products of themetabolism increase the Donnan ratio: the possibi-lity may also not be excluded that the stomatocytosisis due to the binding of the Rh antigenic complex toBand 3 or to the membrane skeleton by theintermediary of ankyrin (Bruce et al., 2003; Nicolaset al., 2003; Soupene et al., 2004). (ii) Erythrocytessuspended in a hypotonic saline swell toward aspherical shape. However, many stomatocytes wereobserved when the erythrocytes were suspended in ahypotonic saline buffered to pH 7.4 with Tris-HCl(Canham, 1970). Tris, a primary amine base (pKa,8.1), increases the Donnan ratio since its unproto-nated form can diffuse across the membrane (Luthraet al., 1975; Bodemann and Karsch, 1984).

(g)

The protection by a low concentration of serumalbumin against the disc–echinocyte transformation(0.2% hematocrit; 0.13mg/ml, 1.91 mM) (Eriksson,1990) and the stomatocytosis induced by a relativelyhigh concentration of this protein (0.1–10% hema-tocrit; 3–40mg/ml; 44.11–588.23 mM) in a bufferedisotonic saline between glass surfaces and in a freesuspension (Jay, 1975; Scheven et al., 1980; Mehta,1983; Reinhart and Chien, 1987) (Table 1): It is

le 1

cts of serum albumin and g-globulins on the shape of the erythrocytes betwe

(%) Buffer pH Protein [Pro

Locke’s solution 6.35 — —

Locke’s solution 6.35 Serum albumin 220

Na2HPO4/KH2PO4 7.3 — —

Na2HPO4/KH2PO4 7.3 Serum albumin 294

Na2HPO4/KH2PO4 7.3 g-Globulins 31.2

Tris-HCl 7.4 Serum albumin 44.1

Tris-HCl 7.4 Serum albumin 588

Tris-HCl 7.4 — —

Tris-HCl 7.4 Serum albumin 73.5

Tris-HCl 7.4 g-Globulins 12.5

HEPES 7.4 — —

HEPES 7.4 Serum albumin 1.91

HEPES 7.4 g-Globulins 1.06

rotein concentrations were calculated by assuming molecular weights of 68 0

rotein/Hb molar ratios were calculated based on the hematocrit value and a

, Tompkins (1954); 2, Scheven et al. (1980); 3, Jay (1975); 4, Mehta (1983)

tional details.

sphere was observed after washing the erythrocytes.

rythrocyte shape was examined between glass surfaces by light microscopy.

rythrocyte shape was examined with the erythrocytes hanging from the glass

rythrocyte shape was examined with the erythrocytes free in suspension by

generally presumed that the effect of serum albuminon the erythrocyte shape is due to its binding to theerythrocyte surface. However, observations indicatean absence of binding of this protein to theerythrocyte surface (Furchgott and Ponder, 1940;Brown, 1956; Lahiri et al., 1970). This absence ofbinding could be rationalized by the fact that theerythrocyte surface and serum albumin are stronglynegatively charged since the former is delimited by aglycocalyx layer formed by glycophorin A having ahigh content in sialic acid residues while the latter isan acid protein with an isolectric point (pI) of 4.9. Itseems also unlikely that the antispheric action byserum albumin is caused by its binding to HCO�

3

derived from the base Na2CO3, presumably em-bedded in the glass, as previously suggested (Brown,1956). The anion Cl�, which also binds to serumalbumin, would compete effectively for the bindingof HCO�

3 ; owing to its high concentration. It may besuggested that the epsilon amino groups (e NH2) oflysine residues of serum albumin react with theCO3

2� present to form a carbamino adduct, therebypreventing the disc–sphere transformation. How-ever, this possibility also appears unlikely since theepsilon amino groups (eNH2) of lysine residues of g-globulins (IgGs) would also be expected to reactwith CO3

2� and prevent the disc–sphere transforma-tion. The mechanism could explain the antisphericaction and stomatocytosis by serum albumin. Serumalbumin is an acid protein with a pI of 4.9, whichwould increase the Donnan ratio, thereby favoringthe stomatocytosis and thus opposing the echinocy-

en glass surfaces and free in suspension

tein]a (mM) Protein/Hbb Shape Ref.c

— Sphered,e 1

.59 9.80 Stomatocyted,e 1

— Echinocytee 2

.11 58.82 Stomatocytee 2

6.24 Echinocytee 2

1 1.96 Stomatocytef 3

.23 3.81 Stomatocytee 4

— Discocyteg 5

3 0.13 Stomatocyteg 5

-156.2 0.02-0.28 Echinocyteg 5

— Echinocytee 6

0.19 Discocytee 6

-93.75 0.11-9.37 Echinocytee 6

00 and 160 000 for serum albumin and g-globulins, respectively.hemoglobin concentration of 5mM.

; 5, Reinhart and Chien (1987); 6, Eriksson (1990). See text for

slide by light microscopy.

electron microscopy.

ARTICLE IN PRESSP. Wong / Journal of Theoretical Biology 233 (2005) 127–135132

tosis. Consistent with this explanation is the increaseof the fraction of stomatocytes with the increase ofthe molar ratio of serum albumin to hemoglobin.The ratios were, in three observations A, B and C,0.13, 1.96 and 3.81, respectively, with the corre-sponding relative fraction of stomatocytes A5BoC(Jay, 1975; Mehta, 1983; Reinhart and Chien, 1987)(Table 1).

(h)

The echinocytosis of erythrocytes induced by g-globulins (IgGs) between glass surfaces (0.1–0.2%hematocrit; 0.17–15mg/ml; 1.06–93.75 mM) or in afree suspension (10% hematocrit; 2–25mg/ml;12.5–156.25 mM) (Scheven et al., 1980; Reinhartand Chien, 1987; Eriksson, 1990) (Table 1): It maybe proposed that the echinocytosis is caused by theirbindings to the erythrocyte surface since they are inaverage basic proteins, but this possibility seemsunlikely since no more than 400 IgG molecules arebound per cell when erythrocytes are suspended inthe whole plasma (Turrini et al., 1991; Prin et al.,1995). However, it would be explained by themechanism since these basic proteins would decreasethe Donnan ratio.

(i)

The maintenance of the disc shape in serum orplasma between glass surfaces: Two explanationscompatible with the hypothesized mechanism can beproposed for this observation. (i) The disc shape isthe result of antagonistic action of serum albuminand g-globulins on the erythrocyte shape, aspreviously suggested (Mehta, 1983; Reinhart andChien, 1987). However, their antagonistic actionwould unlikely be the basis for the maintenance ofthe disc shape in the blood circulation. Indeed, themolar ratio of serum albumin to hemoglobin inblood based on a hematocrit of 45% is 0.144, whichis comparable to that preventing the glass effect inan isotonic saline (0.191), but is significantly lowerthan that inducing a strong stomatocytosis(1.96–3.81) (Table 1). On the other hand, the molarratio of g-globulins to hemoglobin in blood and thatobserved to enhance the glass effect are 0.015 and0.106, respectively (Table 1). (ii) The disc shape isdue to the presence of a relatively high concentrationof HCO�

3 (25mM) in the serum or plasma. Asmentioned earlier, the presence of HCO�

3 wouldproduce an equilibrium resulting in an increase ofthe Donnan ratio since a fraction of the HCO�

3

would be transformed into CO2, which in turnwould be transformed into HCO�

3 and H+ bycarbonic anhydrase after its diffusion or transport inthe erythrocyte. Moreover, if we assumed that thepH between the glass slide and coverslip is between9.2 and 10 (pH measured was 9.2; Furchgott, 1940),a solution of 25mM HCO�

3 would result in a pHincrease between 7 and 8 based on a pKa of 10.4 forthe ionization of HCO�

3 to H+ and CO32�. It may

also be possible that the high concentration ofHCO�

3 itself contributes to the maintenance of thedisc shape between glass surfaces and also in theblood circulation by interacting with Band 3.Indeed, recent kinetic studies on the transport ofCl� and HCO�

3 by Band 3 suggest that Cl� andHCO�

3 decrease and increase the Band 3o/Band 3i

ratio, respectively (Knauf et al., 2002). This wouldimply, with respect to the mechanism of erythrocyteshape control, that Cl� and HCO�

3 are echinocyto-genic and stomatocytogenic, respectively.

(j)

The cycle of the disc–echinocyte transformation andreversal can be repeated numerous times when asmall diameter glass rod is alternatively broughtclose to a given site on the erythrocyte surface andwithdrawn, which presumably involves a local pHincrease and decrease (Bessis and Prenant, 1972).However, the sites of reappearance of the spicules onthe membrane were the same and the order of theirdisappearance was the inverse of their order ofreappearance. This observation may be interpretedas a strong evidence for some sort of fixed cellularstructure, which would be at variance with theerythrocyte having a homogeneous structure(Furchgott, 1940; Ponder, 1948). However, it wouldbe compatible with the mechanism on the assump-tion of the existence of an unstirred layer at themembrane surface. Such a layer would create adecreasing or an increasing pH gradient from thesite where the increase or decrease pH initiallyoccurs to the peripheral sites. On the other hand, itmay be that this observation is a consequence of thefact that the two-dimensional membrane skeletonreticulum is not constructed uniquely of hexagonalunits and of spectrin tetramers: the reticulum has3% and 8% pentagonal and heptagonal units,respectively, with 11% of spectrin hexamer (Liu etal., 1987). This absence of homogeneity is alsoindicated by the detection of the presence, in a minoramount, of bI spectrin S2 with a monoclonalantibody against this spectrin isoform (Pradhan etal., 2004). The reason for this feature of thereticulum is not understood, but it has previouslybeen stated several years ago that a surface of a rigidreticulum enclosing a space, as exemplified by thesilica skeleton of some radiolarian species, cannot beconstructed solely with hexagonal units, whether thehexagons be equal or unequal, regular or irregular; aclosed rigid reticulum was observed to contain alsosome pentagonal and heptagonal units (ThompsonD’Arcy, 1966).

(k)

The disc–echinocyte transformation can also occurbetween surfaces made of various polymers and ofmica provided that the distance between them iscontrolled (0.1mm) (Eriksson, 1990): It is likely thatthis transformation is unrelated to that occurring

ARTICLE IN PRESSP. Wong / Journal of Theoretical Biology 233 (2005) 127–135 133

between glass surfaces since the pH between plasticsurfaces made of vinyl was near neutral (Trotter,1956). Plastic may contain a plasticizer that mayleak into the solution and interact with theerythrocytes. A disc–echinocyte transformation wasinduced between the glass slide and coverglasssurfaces coated with polystyrene using the DPXTM

mountant, which has dibutyl phthalate as a plasti-cizer. However, it is unlikely that the plasticizer wasresponsible for this transformation since its struc-tural analogue di (2-ethylhexyl) phthalate, which isused as a plasticizer in manufacturing polyvinylchor-ide (PVC) bags for storing blood, preserves thebiconcave disc shape (Greenwalt et al., 1991).However, polymeric materials are permeable toCO2 and a plasticizer such as di (2-ethylhexyl)phthalate increases the CO2 permeability (Beutler,1973; Lim et al., 1999). This would suggest thefollowing explanation for the disc–echinocyte trans-formation between surfaces made of various poly-mers. The HCO�

3 in the suspending solutionexchanges with the cell Cl� by the intermediary ofBand 3. Within the cell, HCO�

3 combines with aproton bound to hemoglobin to yield H2CO3, whichis dehydrated by carbonic anhydrase to yield CO2.The latter diffuses or is transported across the cellmembrane and partitions into the slide and cover-slip. The net effect of this process would be adecrease of the Donnan ratio.

In conclusion, a previously hypothesized mechanismof erythrocyte shape control in which Band 3, the anionexchange protein, plays a critical role, could explain thedisc–sphere transformation of the erythrocytes betweenglass surfaces and of related observations. The followingobservations would be expected if the hypothesizedmechanism was the basis of the glass effect and ofrelated observations. Acid proteins other than serumalbumin would also prevent the glass effect. Basicproteins other than g-globulins would also enhance theglass effect. Washing the erythrocytes with an isotonicsolution containing the same proportion of Cl� andHCO�

3 as that in serum or plasma would prevent theinduced echinocytosis or the enhancement of the glasseffect when the erythrocytes are washed with an isotonicsaline (Bessis and Prenant, 1972; Eriksson, 1990).Washing the erythrocytes with an isotonic HCO�

3

solution would transform them into stomatocytes sincethis anion increases the ratio Band 3o/Band 3i. Finally, amutation of Band 3 may prevent the glass effect. Thelast prediction appears fulfilled since there is an absenceof glass effect in Southeast Asian ovalocytosis (Saul etal., 1984). This phenotype is the result of a mutation ofBand 3, which deletes a segment of 9 amino acidresidues at the flexible boundary of its cytoplasmic andmembrane domains, and which abolishes the anion

transport. The mechanism would explain the absence ofglass effect in this phenotype since the flexibility betweenthe two Band 3 domains and anion transport activity arerequired for deformations and shape alterations of theerythrocyte. This feature of the mechanism would alsoexplain that the erythrocytes in Southeast Asianovalocytosis have an increased rigidity, an absence ofa significant echinocytosis after metabolic depletion, areduction of endocytosis by stomatocytogenic amphi-philic compounds and a greater thermal stability(Kidson et al., 1981; Saul et al., 1984; Mohandaset al., 1992; Schofield et al., 1992; Bjork et al., 1997).

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