Human spectrin. I. A classical light scattering study

Human spectrin. I. A classical light scattering study

235 Biochimica et Biophysica Acta, 536 (1978) 235--244 © Elsevier/North-Holland Biomedical Press BBA 37977 HUMAN SPECTRIN I. A CLASSICAL LIGHT SCAT...

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235

Biochimica et Biophysica Acta, 536 (1978) 235--244 © Elsevier/North-Holland Biomedical Press

BBA 37977

HUMAN SPECTRIN I. A CLASSICAL LIGHT SCATTERING STUDY

ARNLJOT ELGSAETER Institute of Biophysics, The Norwegian Institue of Technology, N-7034 Trondheim-NTH (Norway) (Received March 17th, 1978)

Summary Human spectrin heterodimers were analyzed in solutions containing different amounts of salt employing the classical light scattering technique. 1. At 22°C the radius of gyration of isolated human spectrin heterodimers in 0.1 M NaC1 aqueous solution (pH 7.3) was found to be about 22 nm. 2. The radius of gyration of isolated human spectrin heterodimers was found to increase to a b o u t 40 nm as the ionic strength of the spectrin solution (pH 7.3) was reduced to about 1 mM. 3. The light scattering study indicates that the isolated human spectrin heterodimers were highly expanded and flexible molecules with a contour length exceeding a b o u t 140 nm.

Introduction Human spectrin was first isolated by Marchesi and Steers [1]. Spectrin isolated from human and bovine erythrocytes has since been subjected to an intensive study by a large number of investigators. A short review of these studies was given by Kirkpatrick [ 2]. A recent light scattering study by Kam et al. [3] concludes that the human spectrin heterodimer radius of gyration is less than 8 nm. This implies that (a) if the spectrin heterodimers have spherical symmetry and homogeneous density, the diameter is less than 20 nm and (b) if the spectrin heterodimers are rodshaped, the length is less than 28 nm. Our data indicate that the human spectrin heterodimers prepared by us have a radius of gyration which is three to five times the value reported by Kam et al. [3].

236 Materials and Methods

Preparation of human erythrocyte ghosts Ghosts were prepared from 250--300 ml blood drawn from healthy, adult, male volunteers. The blood was collected in Fenwal (Travenol Laboratories S.A., Belgium) JF-15 bags containing 63 ml citrate/phosphate/dextrose solution. This solution contains 327 mg citric acid monohydrate, 2.63 g sodium citrate dihydrate, 251 mg monosodium phosphate dihydrate and 2.55 g dextrose m o n o h y d r a t e per 100 ml. The preparation of ghosts was started less than half an hour after the blood had been drawn. The erythrocytes in one bag of blood were washed twice with 1200--1300 ml of phosphate buffered saline (145 mM NaC1 in 20 mosM phosphate buffer, pH 7.6) at 0--4°C and stored overnight at 4°C. The erythrocytes were then washed once in 1200--1300 ml of 310 mosM sodium phosphate buffer (pH 7.6) at 0 - 4 ° C . One bag of blood yielded 80--100 ml of washed erythrocytes, one sixth of which were lyzed at a time in 300 ml of 20 mosM sodium phosphate buffer (pH 7.6) while stirring on ice for 15 min. The ghosts were harvested by centrifugation at 30 000 X g (18 000 rev./min in a Beckman JA-20 rotor) for 10 min at 0--4°C. After aspiration of the supernatant, special care was taken to assure removal of the sticky pellet which was formed beneath the loose ghost pellet. The ghosts were resuspended in 300 ml of 9 mM NaC1 in 2 mosM sodium phosphate buffer (pH 7.6) at 0--4°C and centrifuged at 30 000 X g (18 000 rev./min in a Beckman JA-20 rotor) for 10 min at 0--4°C. After removal of the sticky pellet the ghosts were stored on ice until ghosts also had been prepared from the remaining washed erythrocytes. The ghosts were then pooled and resuspended in 300 ml of 9 mM NaC1 in 2 mosM sodium phosphate buffer (pH 7.6) at 0--4°C and centrifuged at 30 000 < g (18 000 rev./min in a Beckman JA-20 rotor} for 60 min. The ghost pellets, but not the red sticky 'buttons' of lymphocytes and other cell debris (found under the ghost pellets) were pooled and diluted with distilled water at 0--4°C to a final volume of 60 ml. The colour of the ghost suspension was pink to light red.

Spectrin isolation The ghost suspension was dialyzed at 0--4°C for 40--42 h against 2 Y 1000 ml of 0.1 mM ethylenediaminetetraacetic acid (EDTA) and 0.05 mM dithiothreitol titrated to pH 9.5 with 1 M NH4OH. Subsequent to this dialysis step the following spectrin isolation procedure (Procedure A) was used unless otherwise specified: The ghost suspension was centrifuged at 200 000 X g (50 000 rev./min in a Beckman 50Ti rotor) for 60 min at 0--4°C, the pellet discarded, and the supernatant centrifuged at 200 000 X g for 60 min at 0--4°C to ensure complete removal of small vesicles. This yielded 35--37 ml of coarse aqueous protein containing extract. This extract was then applied to a column (45 × 2.6 cm) of Sepharose CL-4B beads equilibrated with 0.1 mM EDTA, 0.05 mM dithiothreitol and 1 mM Tris • HC1 (pH 8.0) at 0--4°C. The column was eluted at a flow of 15 ml/h and the protein elution profile determined by measuring the absorbance at 280 nm of the different fractions off the column. The protein composition of the different fractions were analyzed using sodium dodecyl sulfate-polyacrylamide gel electrophoresis. The void volume peak off

237 this column was found to contain mainly spectrin and only minor amounts of actin and other proteins. From the spectrin containing fractions were taken a total of 27--30 ml which was then incubated at 37°C for 30 min. To this spectrin containing solution was subsequently added under gentle stirring 2.7-3.0 ml 1.1 M NaC1, 0.1 mM EDTA and 0.05 mM dithiothreitol (pH 7.3) at 0--4°C. The resulting spectrin solution was applied to a column (90 X 2.6 cm) of Sepharose CL-4B beads equilibrated with 0.1 M NaC1, 0.1 mM EDTA and 0.05 mM dithiothreitol (pH 7.3) at 0--4°C. The column was eluted at a flow rate of 15 ml/h and the fractions off the column analyzed as described above. From the spectrin-containing peak off this column 26--27 ml were taken which were then dialyzed for 18--42 h at 0--4°C against 2 X 1000 ml of the desired salt solution. A dialysis time of 18 h was used when spectrin was dialyzed against solutions containing 100 mM or 10 mM NaC1. A dialysis time of 42 h was employed when spectrin was dialyzed against solutions containing 5 mM or 1 mM NaC1. Finally all the different spectrin solutions were dialyzed for 3 h at 22°C against 1000 ml of the appropriate salt solutions. The yield of purified spectrin from one bag of blood was 8--10 mg. At the early stage of this study (before the work by Ralston et al. [4] had been published) the following spectrin isolation procedure (Procedure B) was used subsequent to the 40--42 h dialysis at 0--4°C: the ghost suspension was centrifuged at 200 000 × g (500 000 rev./min in a Beckman 50Ti rotor) for 120 min at 0--4°C, the pellet discarded, and the supernatant centrifuged at 200 000 X g for 120 min at 0--4°C to ensure complete removal of vesicles. This yielded 35--37 ml of protein containing extract which was applied to a column (90 X 2.6 cm) of Sepharose CL-4B beads equilibrated with 0.1 mM EDTA, 0.05 mM dithiothreitol and 1 mM Tris • HC1 (pH 8.0) at 0--4°C. The protein elution profile and the protein composition of the different fractions off the column were analyzed as described above. The spectrin yield from one bag of blood was 13--16 mg. Sodium dodecyl sulfate-polyacrylamide gel electrophoresis Sodium dodecyl sulfate-polyacrylamide gel electrophoresis was performed in 0.2% sodium dodecyl sulfate according to Falrbanks et al. [5] and Steck and Yu [6]. The gels were scanned using a Zeiss PMQ3 spectrophotometer equipped with a Zeiss ZK5 gelscanner. Spectrin concen tra tion measuremen ts From the amino acid composition of human spectrin given by Fuller et al. [7] the spectrin nitrogen content was calculated to be 16.1%. The nitrogen content of 1000 pl of spectrin solution of known absorbances at 280 nm and of 1000 pl of buffer was determined using a Carlo Erba Elemental Analyzer model 1104 equipped with a Hewlett Packard 3372B integrator. The instrument was calibrated using acetanelide standards *. From these data human spectrin specific absorbance at 280 nm, Alcm -~1~ (280 nm), was calculated. Spectrin concentrations were subsequently determined by measuring the absorbance at 280 nm and using the obtained value of Alcm~cal%( 2 8 0 nm). * T h e n i t r o g e n d e t e r m i n a t i o n w a s p e r f o r m e d b y Mr. Paal B r e k k e .

238

Spectrin specific refractive index increment measurements The spectrin refractive index increment at 436 nm (25°C), (~n/~c), was determined using a Winopal spectrodifferential refractometer. The instrument was calibrated using NaC1 standard solutions [ 8]. Spectrin optical clarification After dialysis for 3 h at 22°C the spectrin heterodimer solutions prepared according to the procedure A and containing 100 mM or 10 mM NaCl were centrifuged at 100 000 × g (35 000 rev./min a Beckman 50Ti rotor) for 60 min at 22°C. The spectrin heterodimer solutions containing 5 mM or 1 mM NaC1 were centrifuged at 200 000 × g (50 000 rev./min in a Beckman 50Ti rotor) for 60 min at 22°C. The spectrin solutions were further clarified by passing the solutions through two Millipore filters type AA 0.80 pm, 35 mm diameter. A b o u t 3 liters of distilled water and a b o u t 200 ml of the appropriate salt solution were passed through these filters before use. The spectrin solutions were then passed slowly {1--2 ml/min) through the filters by suction {pressure difference 0--0.01 atm) and directly into the cell used for the light scattering measurements. After the light scattering measurement an alequot was removed for determination of spectrin concentration. The rest of the spectrin solution was then diluted with the salt solution against which the spectrin preparation had been dialyzed for 3 h at 22°C. The diluted solution was filtered again as described above and following the light scattering measurements an alequot was removed for determination of the spectrin concentration. The light scattering measurements were normally done at three different spectrin concentrations. Spectrin prepared according to procedure B was clarified by centrifugation at 200 000 × g (50 000 rev./min in a Beckman 50Ti rotor) for 120 min at 22°C followed by filtration as described above except that the dilutions were done employing the salt solution used for equilibrating the Sepharose CL-4B gelfiltration column. Light scattering measurements The light scattering measurements were made at 436 nm employing a BricePhoenix Light Scattering Photometer {Model 2000). A cylindrial cell (type C101) with flat entrance and exit window was used. The light scattering p h o t o m e t e r was first calibrated according to the directions given by Phoenix Precision Instrument Company, U.S.A. The calibration was then checked by measuring the light scattering from benzene at 20°C. The obtained Rayleigh ratio at 436 nm agreed within 5% with the value reported by Kratokvil et al. [9]. The calibration was further checked by measuring the light scattering from bovine serum albumin {bovine serum alumin, Sigma, fraction V) in 0.15 M KC1, 8 mM phosphate buffer, pH 7.6. The bovine serum albumin solution was optically clarified by centrifugation at 200 000 X g (50 000 rev./ min in a Beckman 50Ti rotor) for 4 h at 22°C and then filtered (1--2 ml/min) through two washed, Millipore filters type AA 0.80 pm. The bovine serum albumin concentrations were determined by measuring the absorbance at 280 Alcm nm and employing the specific absorbance ~ 1 ~ (280) = 6.66 [10]. Using ~n/~c = 0.197 ml/g [10] this gave bovine serum albumin molecular weight of 69 000 Dalton. The angular distribution of light from the light scattering cell

239

was checked using a dilute fluorescein solution and a Leitz S 525 interference filter in front of the light detector. At all scattering angles from 30 ° to 135 ° the angular dependence of the light intensity was found to be within -+1% of the angular dependence expected theoretically. The light scattering from all the spectrin solutions was measured at 20 different angles between 30 ° and 135 ° . The customary reflection corrections were applied to the data before making the Zimm plot [11,12]. The measured light scattering at 30 ° , 35 ° and 40 ° was corrected using the measured light scattering intensity at 135 ° . Results

The spectrin elution profile off the Sepharose CL-4B column and the result of polyacrylamide gel electrophoresis on isolated spectrin are shown respectively in Fig. 1 and Fig. 2. The specific absorbance of human spectrin at 280 lcm (280) the Alcm (280), was found to be 10.1. Using this value of A1% nm, --,1% specific refractive index increment, ~n/bc, of human spectrin at 25°C and 436 nm was found to be 0.195 ml/g. The spectrin light scattering data were plotted in Zimm diagrams as shown in Figs. 3--6 where K = 2~2n~)(On/ac)2/(hrh~) and Re = r2Io/(Io(1 + cos20)). In these equations no is the refractive index of the spectrin solution, (an/~c) is the spectrin specific refractive index increment, N is the Avogadro number, X0 is the vacuum wavelength of the incident light, r is the spectrin scattering volume-light detector distance, Io is the intensity of light scattered per unit

O~ A I I e4 O=

i

, I

c

/ ~ B

~ o4 D

II \\

O~

01 u

,J,

200

~\

/

300 Elut,on volume (rnl)

'-, 400

500

F i g . I . E l u t i o n profile at 0 - - 4 ° 0 o f w a t e r - s o l u b l e h u m a n e r y t h r o c y t e m e m b r a n e proteins o f f a Sepharose C L - 4 B c o l u m n ( 9 0 X 2 . 6 c m ) u s i n g a buffer consisting o f 0 . 1 M N a C I , 0 . 1 m M E D T A a n d 0 . 0 5 m M d i t h i o t h r e i t o l ( p H 7 . 3 ) . S p e c t r i n prepared according to procedure A ( ). H u m a n e r y t h r o c y t e m e m b r a n e proteins e x t r a c t e d i n 0 . 1 m M E D T A ( p H 7 . 5 ) a t 2 - - 4 ° C ( . . . . . . ). ( A ) S p e c t r i n agg~cegates, ( B ) spectrin h e t e r o t e t r a m e r e s , ( C ) s p e c t r i n h e t e r o d i m e r s , and ( D ) a c t i n .

240

Q 1.C

O.E

"I

o.e

g o4

1

02

0

b

i!jl

Fig. 2.

D e n s i t o m e t e r s c a n (a) a n d p h o t o g r a p h ( b ) o f C o o m a s s i e brilliant b l u e - s t a i n e d s o d i u m d o d e c y l s u l f a t e o p o l y a c r y l a m i d e gel o f h u m a n s p e c t r i n h e t c r o d i m e r s prepared according to procedure A. The s a m p l e is f r o m a s p e c t r i n s o l u t i o n w h i c h h a d b e e n s u b j e c t e d t o t h e full s e q u e n c e o f d i l u t i o n s a n d light scattering measurements.

(6 pg)

volume from the spectrin solution at an angle 0 away from the incident light beam and I0 is the intensity of the incident light. The value of o~ = ~ ( g c / R o )/~

(sin20/2) equals (16~2n~/(3~t/w)) • R~

26

25

1

---3

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'j

22

21

/

/~/"

20 19

0

,

h

,

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Sin2(O/2) + 104c (ml/g) Fig. 3. Z i m m p l o t f o r h u m a n s p e c t r i n h e t e r o d i m e r s in 1 0 0 m M NaC1. 0 . 1 m M E D T A a n d 0 . 0 5 m M d i t h i o t h r e i t o l ( p H 7 . 3 ) at 2 2 ° C p r e p a r e d a c c o r d i n g t o p r o c e d u r e A . T h e s o l u t i o n c o n t a i n i n g 3 . 8 • 1 0 -4 g/rnl ( e ) s p e c t r i n h e t e r o d i m e r s w a s clarified o n l y b y c e n t x i f u g a t i o n at 1 0 0 0 0 0 X g f o r 6 0 rain. T h e o t h e r s p e c t r i n h e t e r o d i m e r s o l u t i o n s w e r e g i v e n t h e n o r m a l c l a r i f i c a t i o n p r o c e d u r e w h i c h in a d d i t i o n t o t h e c e n t r i f u g a t i o n i n c l u d e s s l o w f i l t r a t i o n t h r o u g h t w o M i l l i p o r e filters t y p e A A 0 . 8 0 / ~ m .

241

4C

28 27 26

~

25 ~ x

2f

2 ~. 2" 2c

1

2C O

2 3 Sin2(e/2) + 104c (ml/g)

,

,

J

Sin2(e/2) + 104c (ml/g)

Fig. 4. Z i m m p l o t f o r h u m a n sPectrin h e t e r o d i m e r s in 5 m M NaCI, 0.1 m M E D T A a n d 0 . 0 5 m M d i t h i o tbxeitol ( p H 7.3) a t 2 2 ° C p r e p a r e d a c c o r d i n g to p r o c e d u r e A. Fig. 5. Z i m m p l o t f o r h u m a n spect~in h e t e r o d i m e r s in 1 m M NaC1, 0.1 m M E D T A a n d 0 . 0 5 m M d i t h i o t h r e i t o l ( p H 7.3) a t 2 2 ° C p r e p a r e d a c c o r d i n g to p r o c e d u r e A.

upon extrapolation to spectrin concentration c = 0 g/ml, where Mw is the spectrin weight average molecular weight and R6 is the light scattering radius of gyration. The spectin light scattering data are summarized, in Figs. 7a and 7b.

% v-

-0

2

4

6

8

10

Sin2(8/2) + 2 • 104c (ml/g) Fig. 6. Z i m m p l o t f o r spectxin h e t e r o d i m e r s in 1 m M Tris • HCI, 0.1 m M E D T A a n d 0 . 0 5 m M d i t h i o o t h r e i t o l ( p H 7.4) a t 2 2 C p r e p a r e d a c c o r d i n g to p r o c e d u r e B.

242

50

Ionic strer~gtth (mivl) 10 5 2

100

Ionic s t r e n g t h (miVl) 10 5 2

100 i

i

b

E E 40

o

3c O~ >

0

rY 2C 0

V3 I

I

I

I

2 4 6 8 10 Debye shielding distance (rim)

-1 0

I

I

I

I

2 4 6 8 10 Debye slqteldtng distance (nm)

Fig. 7. H u m a n s p e c t r i n h e t e r o d i m e r r a d i u s of g y r a t i o n (a) a n d s e c o n d viral c o e f f i c i e n t (b) as f u n c t i o n of t h e D e b y e s h i e l d i n g d i s t a n c e . S p e c t r i n h e t e r o d i m e r s p r e p a r e d a c c o r d i n g t o p r o c e d u r e A (o) a n d a c c o r d i n g t o p r o c e d u r e B (A).

Discussion

Judged by polyacrylamide gel electrophoresis incubation at 37°C for 30 rain of a spectrin containing coarse aqueous extract invariably gave rise to partial proteolytic breakdown of spectrin. This proteolytic breakdown was found to be prevented if the coarse aqueous extract was purified by Sepharose CL-4B gelfiltration prior to incubation at 37°C for 30 min. Procedure A gave mainly spectrin heterodimers (Fig. 1). When spectrin heterodimers were prepared according to procedure A, barely any proteolytic spectrin breakdown could be detected at the end of the light scattering measurements (Fig. 2). Spectrin obtained after the Sepharose CL-4B gelfiltration according to procedure B was found to contain a mixture of spectrin aggregates and spectrin heterotetramers. However, after the optical clarification procedure at 22°C, spectrin prepared according to procedure B was found to comprise spectrin dimers only and no spectrin aggregates when analyzed by the gelfiltration system of Ralston et al. [4]. Judged by polyacrylamide gel electrophoresis spectrin prepared according to procedure B contained only trace amounts of actin. Measurements of spectrin specific absorbance have been reported by a number of different authors [3,13--16]. The reported values of ~l~Alcm(280) vary from 8.8 to 11.5. The value reported here, 10.1, is in the middle of this range and coincides with the value reported by Clarke [13] for bovine spectrin. Our value of the spectrin refractive index increment of 0.195 ml/g at 436 nm is 4--5% higher than the value at 514.5 nm reported by Kam et al. [3]. Both values fall within the normal range of (an/~c) for proteins [17]. The light scattering theory developed for binary systems [12] can not be used without amendment for polyelectrolyte-simple salt-water systems. However, it has been shown [18--20] that the equations developed for binary sys-

243 terns can be applied to polyelectrolyte solutions provided that (I) the simple salt concentration is above a certain minimum, (II) the polyelectrolyte solution is equilibrated against the supporting electrolyte solution, (III) the dilution of the polyelectrolyte solution is made using the supporting electrolyte solution against which it has been equilibrated and (IV) the polyelectrolyte (an/bc) is determined between the polyelectrolyte solution and the supporting electrolyte solution against which it has been equilibrated. Light scattering studies of polyelectrolytes are complicated by the strong, long range electrostatic interaction among the polyelectrolytes as the ionic strength of the supporting solution is reduced. Firstly, such interactions result in a nonlinear concentration dependence of the polyelectrolyte apparent molecular weight making the extrapolation to zero polyelectrolyte concentration very difficult and inaccurate [21]. Secondly, strong electrostatic interactions among the polyelectrolytes tend to create order in the polyelectrolyte solution. This gives rise to dimunition of light scattering per molecule and reduction of the scattering envelope dissymmetry at high polyelectrolyte concentrations [22]. Normally these effects of electrostatic interactions are minor when the ionic strength of the supporting electrolyte solution is 1 mM or more [18,19]. Thus, the highly charged linear polyelectrolyte polystyrene-p-sulfonate with molecular weights ranging from 4 • l 0 s to 2.3 • 106 has been successfully studied in the concentration range 5--30 • 10 -4 g/ml, in the presence of only 5 mM NaC1, employing the light scattering technique [21]. It is important to notice that a polystyrene-p-sulfonate molecule with molecular weight of 5 • l 0 s has a net electrostatic charge which is a b o u t 1 0 t i m e s that of a spectrin heterodimer at pH 7.3 [23,24]. The light scattering technique should therefore be applicable to aqueous spectrin heterodimer solutions containing 1--4 • 10 -4 g/ml spectrin and substantially less than 5 mM NaCl. Data from gelfiltration analysis indicate that spectrin prepared according to procedure A or B comprises spectrin heterodimers. This is moreover born out by the results from the light scattering investigations (Figs. 3--6). The latter data give a spectrin molecular weight of (4.8 _+0.5) • l 0 s, which is close to the value expected from polyacrylamide gel electrophoresis analysis of spectrin [5]. Down to an ionic strength of 5 mM there is no sign of strong interaction among the spectrin heterodimers (Fig. 4). In the presence of 1 mM NaC1 (Fig. 5) there is a significant reduction in a with increasing spectrin heterodimer concentration as described by Doty and Steiner [22]. In the presence of 1 mM Tris • HC1 this effect is augmented and at spectrin heterodimer concentrations exceeding about 5 • 10 -4 g/ml, a even became negative. The radius of gyration obtained from the data presented in Fig. 6 therefore is rather uncertain. The spectrin heterodimer radius of gyration and second virial coefficient values as function of the Debye shielding, ~D, presented in Figs. 7a and 7b are calculated assuming that the standard theory of Zimm [12] is valid. The obtained values of R G are independent of the numerical values used for spectrin specific absorbance and spectrin specific refractive index increment. The results summarized in Fig. 7a indicate that if the spectrin heterodimers prepared by us maintain spherical symmetry and homogeneous density, the spectrin heterodimer diameter varies from about 57 nm to a b o u t 110 nm [25] as the ionic strength is reduced from 0.1 M to 0.001 M. If the spectrin hetero-

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dimers maintain rodshape the light scattering results (Fig. 7a) suggest that the rod length varies from about 76 nm to about 140 nm [25] as the ionic strength is reduced from 0.1 M to 0.001 M. However, it is unlikely that a stiff rod-like molecular would increase in length as the ionic strength is reduced. If the spectrin heterodimers were compact unsolvated spheres of density 1.37 g/ml, the spectrin heterodimer diameter would be about 10.3 nm. The light scattering results presented therefore indicate that the spectrin heterodimers are highly expanded and flexible coil-like or worm-like molecules. The contour length of a coil-like or worm-like molecule is longer than that of a stiff rod with the same radius of gyration. The light scattering data of spectrin heterodimers obtained thus tend to show that the spectrin heterodimer contour length exceeds about 140 nm and that it is possible for spectrin to form a molecular network on the cytoplasmic side of the erythrocyte membrane as discussed previously [23,24,26]. Acknowledgements The author thanks Professor O. Smidsr~d, Institute of Marine Biology, University of Trondheim, Norway, for use of equipment for light scattering and elemental analysis. The author is greatly indebted to those who volunteered to donate blood to this project. The technical assistance of Ms. I.K. Almaas and Mr. Paal Brekke is greatfully acknowledged. The author thanks Professor K.B. Eik-Nes for all his generous help. References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

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