elec charge of blood

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T H E E L E C T R I C A L C H A R G E O F M A M M A L I A N R E D B L O O D

C E L L S

BY H A RO LD A . A BRA M SO N A~rD LA U REN CE S . M O Y ER*

(From The Biological Laboratory, Cold Spring Harbor, Long Island)

(Accepted for publication, Augus t 21, 1935)

I N TRO D U CTI O N

Although the e lectrophoretic mobi li ty of mam mal ian ery throcy tes

has been investigated to some extent, suitable est imation of their

surface electrical charge has not as yet been presented. Rec ent de-

velopments in the theories of electrokinetic phen ome na and in th e

theories of dilute solutions of electrolytes justify the calculation of

the dens ity of net surface charge from the available quan ti tat ive dat a

on the electric mobili ty of red cells. In add it ion, throu gh the work of

Ponder , measure ments of the surface areas of red cells perm it a calcu-

lation of the effective net c harge per red cell. The results of these

calculations now show tha t the differences in electrokinetic potentia l

(which is directly proportional to the electric mobili ty) calculated for

the blood cells of a series of mamm als bear no simple relat ionship to the

net cha rge for the cells of each mem ber of the series. These calcula-

t ions thus throw new light on the differences in the physicochemicalnatu re of the r ed cell under th e experim ental condit ions employed and

suggest further experimentation.

Theoretical

Since the electric mobili ty of r ed cells in salt solutions is indepen dent

of their orientation in the electric field (1) and since eryth rocy tes made

spherical by traces of saponin have electric mobili t ies, within the

limits of error, identical with the disc-shaped cells suspended in the

same buffer, the electric mobili ties of these m icroscopic part icles can

be treated by the theor y derived for large part icles (2). We can,

* Ste r l ing Fe l low, Ya le Un ive r s i ty , 1935-36 .

60 l

The Journal of General Physiology

Published March 20, 1936



602 ELECTRICAL CHARGE OF MAMMALIAN :RED BLO OD CELLS

with von Smoluchowski , ca lcula te the f -potent ia l f rom the e lec t r ic

mobi l i ty , %14zn

G = -~ - v, (~)

(a ll uni t s cent im ete r -gram-se cond and e lec t ros ta t ic uni t s of charge) ,

assuming tha t the viscos i ty , n , and die lec t r ic cons tant , D, in the

di f fuse double layer do not assume va lues which a re very di f fe rent

f r om those o f t he me d ium.2 I n a ny eve n t , t he me a sur e m e n t s o f

v w e r e c a rr i e d ou t i n t he s a me me d ium so t ha t a ny f u tu r e c o r r e c-

t i ons i n t he va lue s o f t he se c ons t a n t s w ou ld p r oba b ly on ly c ha nge

our resul t s by a propor t iona l i ty fac tor . Fro m ~e , the ne t charge

den sity, ~, on a surfac e ma y be calcu lated (2, 5, 6) in solutions con -

t a in ing a ny numb e r o f pos it i ve i ons o f t he t ype , i, and nega t ive ionsof t he t ype , j , by me a ns o f t he ge ne r a l i z e d t he or y o f G ouy , va l i d

for la rge par t ic les ,

o" ~q ¢+Z~kT_ l ,"V ~ :~ ' 1 + (2)

where l~ l i s Avogadro ' s number , k , the Bol tzmann constant , e , the

electronic charge, z , the valence, T, t he a bso lu t e t e mpe r a tu r e , a nd c,

the ionic concent ra t ions in tools per l i te r exis t ing in the body of the

solut ion. ~ has the same s ign as ~ ; al l uni t s a re in cent imete r -g ram-

second and e lec t ros ta t ic uni t s of charge.

Inspec t ion of th is eq ua t ion revea ls tha t ~ , unde r our condi t ions ,

1 In general , i t is desirable to calculate the ~--potential rath er than comb ine

equations (1) and (2) (vide infra) because of the possible dependence of the electric

mobi l i ty on the radius under othe r than the present condi tions.

2 "Th is assu mption is not altogeth er unjustified for the following reasons:

1. Substi tution of D an d ,1 of the solvent in the Onsager (3) condu ctance th eory

yields for concentrations up to about 0.05 ~r (simple salt solutions) satisfactory

values for the l imiting slopes and changes in mobili ty with conc entration.

2. If the electric mobili ty of microscopically visible quartz particles covered

with a fi lm of adsorbed protein is studied in different concentrations of alcohol

(4), i t is possible to correlate the surface potential and surface charge calculated

from these mobi l i t ies wi th the charge obtained by another ( thermodynamic)

metho d. As far as these results go, the characterization by the two parame ters,

viscosity and dielectric constant of the solvent, in the Helmholtz-Debye theory is

correct within 10 per cent" (2).




HAROLD A. ABRAMSON AND LAURENCE S. MOYER 603

wi ll depen d only on ~ , for a ll of the oth er te rm s a re co nstants in a given

solution of electroly te. Simplifying equ ation (2) by collecting con-s tants ( except those here given by the concent ra t ion and va lence)

there i s obta ined:

/ / - " ~ ) [ + ~ )o------a'~/ ~¢ ,t, a --1 + ~,c, e ' --1 ,

(3)

whe re a = 17,600 and ~ = 0.0256 vol t at 25°C. I f ~ in volts is intro -

duced into this equa t ion wi th proper regard to i t s s ign, the resul tant

va lue for ~ wi ll be in e lec t ros ta t ic uni t s of charge . S ince ¢ i s the n e t

charge per square cent ime ter , the e f fec tive ne t charge per ce ll ma y be

ca lcula ted i f the sur face a rea of the ce ll is known.

RESULTS

The va lues of the charge were ca lcula ted by eq ua t ion (3) f rom da ta

obta ined wi th var ious mammal ian red ce l l s (1) in i sotonic (5/15)

phos pha te buf fe r s a t pH 7.4 . In this case , the problem is comp l ica ted

by the presence of three ionic types :3 a s ingle pos i t ive uni va len t ty pe ,

i , and two nega t ive types , j (H~PO~) and j j (HPO~/~), of different

va lences. The m etho d of ca lcula t ion i s i l lus t ra ted as follows:

Let v = -1 .00 /~/se c . /vo l t /cm . , the n ~- = -0 .0 128 vol t , z~ = 1 ,

~i = zii = $, and c~ = 0.1 20, ci = 0.0133, cii = 0.0533 , so th at ,

/ / --L~(--o.om) \ / +2×(-o.o~28) / +~×(--o.om)° -')+ °°53 3L" k' o0, _,) .

T hr ough the k indne ss o f Ponde r , w e ha ve be e n f u r n i she d w i th

va lues for the sur face a reas ( found by methods descr ibed in de ta i l in

his monograph (7) ) of the var ious red ce l l s inves t iga ted, wi th the

except ion of those for the s loth , where no da ta were ava i lable . I t

wi ll be note d (Table I ) th a t the n e t charge of the red ce l l does not var y

in the same order , f rom spec ies to spec ies , as a , the charge per uni t a rea .

Nor does there seem to be any c lear r e la t ionship be tween ne t charge

per cell and zoological classif ication.

By dividing the n e t charge by the e lec t ronic charge (4 .77 X 10 -~°

e .s .u . ) , the n um ber of e f fect ive e lec t rons a t t he sur face has been ca lcu-

The concentrations of the H + and P O 4- -- ions are here neglected.




604 ELECTRICAL CHARGE O~ MAMMALIAN RED BLOOD CELLS

lated (Table I , Column 7). For example, in the case of man, the re

are f if teen million electrons on each red cell , the highest value amon gthese mamm als. One migh t say that this corresponds to the "va-

lence" of each cell . A similar comp utation of the net charge has been

mad e for the typh oid bacillus (8) . By assuming that each effective

electronic charge occu pies an ionic area of, say, 1 × 10 -1~ cm3, the

percentage of the surface occupied by these charges may be roughly

estimated (Table I , Column 8). The values never r ise far above 1 per

cent , which agrees in magni tude wi th data obtained on other sur -

faces (2).

T A B L E I

Animal

R a bb it . . . . . . . . . . . . . . . . . . . . . . . . . .S lo th . . . . . . . . . . . . . . . . . . . . . . . . .

P i g . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Op oss um .......................

G ui ne a p ig . . . . . . . . . . . . . . . . . . . .

Ma n . . . . . . . . . . . . . . . . . . . . . . . . . . .R h e s u s m o n k e y . . . . . . . . . . . . . . . .

C at . . . . . . . . . . . . . . . . . . . . . . . . . . . .M ou se . . . . . . . . . . . . . . . . . . . . . . . . .

R a t . . . . . . . . . . . . . . . . . . . . . . . . . . . .D o g . . . . . . . . . . . . . . . . . . . . . . . . . .

Mobil.ity

~lsec.

0.55

0.97

0.98

1.07

1.11

1.311.33

1.39

1.40

1.45

1.65

~ol~

O. 0070~

0.0124

0.0125

0.01370.0142

0.0168

0.0170

0.0178

0.0179

0.0186

0.0211

u

~.$.U.

1890

3330

3 3 ~

3680

37804 5 ~

45704780

4800

49805660

A r ea

1.10

0.95

1.561.15

1.631.37

0.80

0.96

1.02

1.22

Net

charge

e.s.l~ >

2.08

3.19

5.744.35

7.34

6.263.82

4.61

5.086.90

'umber Area

,felec- occu-trons pied

< 10-6 per cenl

4.37 0.40

6.70 0.70

12.0 0.779.14 0.80

15.4 0.94

13.2 0 . 9 6

8.03 L 1.00

9.701 1.0110.7 1.05

14.5 1.19

DISCUSSION

In general , for small values of v, the Deb ye ap proximation,

D= 4~ ~ ' (4 )

m a y b e e m p l o y e d . I t w a s n o t c l e ar t o th e w r i t e r s w h e t h e r t h i s e q u a -

t i o n w o u l d g i v e v a l u e s i n x ~ /1 5 p h o s p h a t e b u f f e r d i f f e r e n t f r o m t h o s e

o b t a i n e d w i t h e q u a t i o n ( 3 ). I n F i g . 1 a r e p l o t t e d ¢ - v c u r v e s fo r t h i s

p h o s p h a t e b u ff e r, c a l c u l a t e d b o t h b y m e a n s o f t h e e x a c t f o r m u l a

( E q u a t i o n 2 ) a n d b y t h e a p p r o x i m a t e f o r m u l a g i v e n b y e q u a t i o n ( 4) .

N o t e t h a t i n t h e r a n g e o f v ( u p t o 1 . 65 # p e r s e c. ) e n c o u n t e r e d i n t h i s




HAROLD A. ABRAMSON AND LAURENC E S. MOYER 605

2O

1 2 3 4 5

FIo. 1. T he straig ht line has been calculated according to the D ebye approxi-

mation a nd the c urved one by m eans of equation (2) for ~r/15 phosphate buffer.

15

5

0

i n v es t i g a t i o n , v a l u es o f ~ ca l cu l a t ed b y t h e t w o m e t h o d s ag r ee w i t h i n

t h e l i m i t s o f e r r o r. I m p o r t an t d i v e r g en ces o ccu r ab o v e 2 # p e r s ec.




6 06 ELECTRICAL CHARGE O F MAMMALIAN RED BLOOD CELLS

The changes in the sur face chem is t ry of the red ce l l due to a l te ra t ion

of t he suspe nd ing me d iu m ma y be i nve s ti ga t ed w i th p r o f i t by m e a nsof the metho d ut il i zed to calcula te the charge . Thus , mamm al ian red

cells increase their electr ic mobil i t ies in isotonic glucose buffered

s l ight ly by phosp ha te (1) . Adva ntage could be taken of th is ef fec t

to d eterm ine if the net charge is affected or if i t is only the F-potential

which var ies. Specif ic ion or molecular effects could be more closely

followed. Th e same procedu re is , of course, applicable to other types

of cells.

In a short ser ies of experiments on the electrophoretic mobil i t ies of

red cells in twelve cases of varying types of anemia (1) , i t was found

tha t both the macrocytes and microcytes when suspended in the same

phospha te buf fe r have mobi l i t ies , wi th few except ions , which a re

ident ica l , wi thin the l imi ts of e r ror , wi th the mobi l i ty of e rythrocy tesf rom a normal individua l. Theo ry demand s tha t la rge par t ic les

which exhibit identical mobil i t ies in solutions of the same ionic con-

cent ra t ion must in each case have an equa l number of charges per

uni t area (2). Obviou sly if ~ is near ly the same for bot h norma l cells

and the ce l l s of abnormal s i ze found in the anemias , the ne t charge

per ce l l must be markedly di f fe rent , for the two types of ce l l s have

very different surface areas. Hence some mec han ism seems to exist ,

capable of stabil iz ing the charge per unit area, within l imits, while the

sur face undergoes compara t ive ly marked changes in a rea and shape .

The condi t ions which mu st be sa t i s fied to es tabl ish the ident i ty of two

surfaces have been discussed before (9) .

S U M V , A R Y

Fro m da ta on the sur face a rea and e lec t rica l mobi l i t ies of ma mm a-

l ian red blood ce l l s in ~ /15 phospha te buf fe r a t pH 7 .4 , i t has been

poss ible , wi th the he lp of the Gouy and von Smoluchowski theor ies,

to calculate the net surface charge per cell as well as the charge per

uni t a rea . I t was found tha t a s ingle mam mal i an red cel l has a ne t

surface charge rangin g from four to f if teen mill ion electrons, depe ndin g

on the species. No clear relat ionship between zoological classif ication

and sur face charge i s apparent . I t i s sugges ted tha t a mechan ism

exists which is capable of keeping the surface density of net charge

constant when compara t ive ly la rge changes in sur face a rea occur in

the anemias .




HAROL D A. ABRAM SON AND LAURE NCE S. MOYE R 607

BIBLIOGRAPHY

1. Abramson, H. A., J. Gen. Physiol., 1929, 12, 711.2. Abramson, H. A., Electrokinetic phenomena, New York, The Chemical Catalog

Co., Inc., 1934.

3. Onsager, L., Tr. Faraday Soc., 1927, 23, 241.

4. Daniel, J., I. Gen. Physiol., 1933, 16, 457.

5. Moyer, L. S., and Bull, H. B., Y. Gen. Physiol., 1935, 19, 239.

6. Moyer, L. S., Biockem. Z., Berlin, 1934, 273p 122; Y. Gen. Physiol., 1935, 18,

749; 1935, 19, 87.7, Ponder, E., Th e mamm alian red cell and the properties of haem olytic systems,

Protoplasma-Monographien, Berlin, Gebriider Bomtraeger, 1934.

8. Abramson, H. A., Tr. Electrochem. Soc., 1934, 66, 153.

9. Abramson, H. A., Y. Gen. Physiol., 1932, 15, 575.


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