Electrophoresis of interacting proteins I. Complex formation of αs1- and β-casein

Biochimica et Biophy~'c~., ~iota, 336 (1974) 201-212 © Elsevier Scientific Publishing Compan~ ~, A m s t e r d a m - Printed in The Netherlands B B A 36634

ELECTROPHORESIS OF INTERACTING PROTEINS I. C O M P L E X F O R M A T I O N O F a~- A N D /~-CASEIN

T. A. J. P A Y E N S and H. N I J H U I S

Netherlands institute for Dairy Rresearch, Ede, and Department of Biochemistry, A~,ricultura! University, Wageningen (The Netherlands) (Received A u g u s t 22nd. 1973)

SUMMARY

The complex formation between ¢t~t- and fi-casein, two major proteins from milk, was studied by moving b o u n d a r y electrophoresis and uitracentrifugation. Complex formation was recognizable from the pronounced non-enantiography of the rising and descending electrophoretic patterns and from abnormal mobilities and relative areas. Application of the moving boundary theory leads to the conclusion that the constituent mobility of ~ts~-casein is fairly high, which indicates the presence of complexes of a high stoichiometric ratio ~ / p ' , The reaction boundaries were simulated by taking into account the selfpolymerization o f txs~-casein under the experimental conditions and the siraultaneous formation of various complexes. The results of such a simulation was found to be consistent with the conclusions ~,f the moving boundary theory.

1NTRODUCTION

The study of interacting biopolymers by such transport methods as sedimentation, electrophoresis and gel filtration has received considerable impetus over the last decades [I-4]. The relevancy of such studies is indicated by a number of biochemical p h e n o m e n a in which complex formation plays a central role. As early as 1942, Longsworth and Maclnnes [51 investigated the complex formation between a protein (ovomucoid) and nucleic acid (yeast RNA) by free electrophoresis and formulated the anomalies to be expected in the electrophoretic patterns. Further examples are the study of the enzyme-substrate complex between pepsin and bovine serum albumin by Cann and Klapper [6] and that of antigen-antibody interaction by Singer and C 'mpbell [7]. The complex formation between bovine plasma albumin and charged dextran derivatives was studied by T h o m p s o n and MacKernan [8]. In these studies the advantage of free electrophoresis over sedimentation lies in the fact that the non-enantiography of rising and descending patterns yields additional information which is lacking in the sedimentation experiment and which often facilitates diagnosis.

202 Rapid progress in our understanding o f the electrophoretic behaviour of interacting proteins is due to Gilbert and Jenkins [9], who solved the conservation-of-mass equation for the equilibrium system A + B ~-~ AB. The Gilbert theory accepts fast re.adjustment of the equilibrium upon changes in concentration brought a b o u t by transport and neglects the influence o f diffusion on the spreading of the boundaries. Another limitation o f the original theory is that the velocities are assumed to be constant, which is neither true in sedimentation [ I 0, I ! ] nor in electrophoresis [ I ]. Despite these restrictions, the Gilbert theory explains quite satisfactorily the anomalies observed during electrophoresis or sedimentation of complexing biopolymers. Notably Gilbert and Jenkins were able to account for the occurrence of a different number of moving peaks on both sides of the electrophoretic channel and for abnormal mobilities and percentages. The close resemblance of a n u m b e r of experimental electrophoretic patt~:rns [2, 5-8] to those computed by Gilbert and Jenkins suggests that rapid reequilibration is more c o m m o n than exceptional during etectrophoresis o f interacting biopolymer.,~. As regards the diffusion, its influence on the spreading o f the moving boundary may often be neglected in prolonged experiments, as shown by Baldwin [I 2] and by Gilbert and Jenkins [9]. However, there always remains the possibilily that small peaks or shoulders are obscured by the blurring effect of diffusion. This suspicion has prompted a number of authors [4. 13- ! 6] to solve the complete conservation, of-mass equation by various simulation methods. The simulation technique applied in the present study is described in the accompanying paper [17]. The present study deals especially with the complex formation between a~- and fl-casein, two major proteins from mitk, the self-association behaviour of which is Nell known [18-20]. Under the experimental conditions o f free etectrophoresis, i.e. 2 C, pH 6.5 and an ionic strength of 0. I, fl-casein is completely depolymerized [20], whereas ~ - c a s e i n undergoes a number of consecutive association steps, the association constants of which have been firmly established by Schmidt [19]. The study of ~t~-fl coml:,lex formation is of p a r a m o u n t importance to our understanding of the energe~.ics c f casein micelle formation in milk [21, 22]. The ~esLlts of the present investigation suggest that multiple association equilibria occur~ which can be represented by iA

:-,~

{i

Aj : B : ~ A : B ( . ]

2.3 . , . 6 ) ]

J

1,2 . . . 6) ,

(i)

in ~hich A and B stand for ¢~,~-and/l-casein, respectively. Preliminary reports of this investigatio~ were published earlier [23, 24]. The pertinency of this study is by no means restricted to the field of casein chemistry. It could well stand as a model for all those complex formations in which one of the components is su .~jected to self-association. The inleraction between virus coat protein and RNA is ar outstanding example of such a system [25]. MATERIALS AND METHODS as:Casein was isolated from bulk milk by the method of Schmidt and Payens [26], whereas /~-casein was prepared in the manner described by Payens and Van Markw~jk [20],

203 For electrophoresis the protein solutions were dialysed exhaustively against the appropriate buffer. The buffer of the last dialysis step was also used for the electrophoretic experiment. In those experiments in which the salt a n o m a l y had to be suppressed, the solution was enriched with protein and diluted after completion of dialysis [27]. Sedimentation runs were m a d e in the Phywe air-driven ultracentrifuge under conditions comparable to those applied during electrophoresis. Sedimentation coefficients, electrophoretic mobilities and peak areas were determined from enlarged tracings by routine measurements [!, 28]. The computations simulating the electrophoretic transport were performed with the university CDC-3200 digital computer. The source program was written in Algol-60. Details concerning the simulation procedure are given in the accompanying paper [17]. RESULTS

Typical electrophoretic patterns of mixed solutions of as1- and/~-casein in two types of buffer are shown in Fig. !. Peak mobilities and percentages from these and other experiments have been collected in Table I. The fast formation of complexes between a,~- and/~-casein is clearly indicated by the different number of moving peaks on the ascending and descending sides [9]. The mobilities of the trailing ascending and leading descending peaks, which are intermediate between those of pure a~- and ~-casein and the a b n o r m a l distribution of the protein over the different peaks also afford convincing evidence of complex formation [I, 9]. As is shown by comparison of the patterns of Figs I a and I c or 1b and I d and the data in Table I, buffer composition does not influence the general appearance of the electrophoretic patterns. Protein-buffer interactions seem therefore to be of no importance to the explanation of the anomalies observed [4]. Table | actually suggests that the mobilities of the complexes formed are intermediate between those of pure ~sl- and (]-casein [9]'. The fast re-equilibration of the complex formation during the electrophoretic transport was further checked by comparing experiments at different field strengths. Figs la and 2 and the data in Table | demonstrate that indeed variation of the field does not affect the mobilities and percentages of the electrophoretic patterns, confirming rapid re-equilibration. The electrophoretic patterns in Figs I and 2 show welldeveloped h- and c-boundaries, As is well known [I], these boundaries are due to the constancy of the Kohlrausch regulating function, as a result of which considerable conductivity changes may occur along the electrophoretic channel. A related consequence is (as was already pointed out by Svensson {29]) that the fastest peaks are always enlarged at the cost of the slower ones. The dilution factor, ~), occuring at the ~-boundaries in Figs I and 2, ~vas ~,stimated in two independent ways. First, according to Longsworth [30] o -

(~'O~ - - O~)/(A~Oj -

O~),

(2)

" The relatively high mobilities observed with (he 70/30 mixture in phosphate buffer probably ~houid be explained by leakage during the electrophoretic experiment.

UB

UA

~

UB

UA

Fig. l. Free ¢lectrophorcsis of mixtures of et,~- and fl-casein at a total protein concentration of 1.20 g dl. Experimental conditions: pH 6.6. 0.1 ionic strength and 2 :C. Field strength 3.05 V cm. Picturer~ taken after 4800 s. Mixing ratio: (a) ~,~ fi --~-50 50, barbiturate buffer: (b~ <~,~;; 70 30. barbiturate buffer; ~c) ",L fl ~ 50 50, phosphate buffer: (d) ~.~ /; 70 30. phosphate buffer.

x~here ~ O , is the total d i a g r a m area a n d O0 and O~ that o f the a- and ~*-boundaries. The axerage xalue o f , , t\~und in tbis s~ay f r o m the p a t t e r n s in Fig. I ~sas 0.84. Secondly. ~ e gradually suppressed the ,'J- and ~-boundaries by d i l u t i n g the protein solu;ion x~ith respect to the electrophoresis buffer [27]. An e x a m p l e is g i i e n in Fig. 3. Extrapolation of the decreasing ,'~-areas to zero then also xields '2 0.84. Sedimentation patterns o f a I :1 m i x t u r e o f ,_'.~- and ;-casein u n d e r the same experinaental conditions as those used ~ i t h electrt~ph~re~i,, arc presented in Fig. 4. Rapid re-equilibration is suggested b~ the fact that b e t ~ e e n the peaks the .~chtiercn p~ttern does not come back to the base line [9]. The sedimentation coefficient s....,, o f the leading peak x~as f o u n d to bc 4.5 S. ~ h e r e a s that of the trailing b o u n d a r ) is !.5 S.

205

TABLE l ELECTROPHORESIS OF ¢~,- AND q-CASEIN AT pH6.6 AND0.1 IONIC STRENGTH Field strength 3.05 V/cm. Mixing ratio

Protein concentration

~t/~

(g/dl)

Buffer

Ascending

Descending

Mobilities cm2/V's)

~,~ 0~,,* Mobilities {I0 -~ cm*,V.s)

8.4 8.4 8.9 8.2 8.3 8.0

52 54 31 32 35

(I0 -~

Pure cg, 7q/30 70/30 50/50 50/50 50'50" ° Pure/3

0.77 1.20 1.20 1.20 1.20 1.20 0,80

barbiturate barbiturate phosphate barbiturate phosphate barbiturate barbiturate

o~

,,

86 86 74 71) 67

14 14 26 30 33

6.8 6.0 6.3 5.5 5.5 5.2

4~4 4.7 4.1 4.2 4.1 3.2

48 46 69 68 65

6.3 7.2 5.8 6.5 6.1

2.5 3.4 2.3 2.7 2.5 2.7

* Total area under bimodal peak. "" Field strength I.O0 V/cm.

I

-- descending

tt •

ue

......... -

ascending

t

t t

t

u^

,~

uA

ue

Fig. 2. Free eleetrophoresis of a I :I mixture of ~r,,- and fi-casein at a total protein concentration of 1.20g/dl. Experimental conditions: pH 6.6. 0.1 ionic strength and 2 C. Field strength 1.0OV s: picture taken after 14400 s.

DISCUSSION T h e n o n - e n a n t i o g r a p h i c p a t t e r n s p r e s e n t e d in Figs I-3 a n d the mobilities :ind percentages recorded in Table I afford good evidence, that . ~ : ar~,d/#casein interact t o f o r m c o m p l e x e s o f i n t e r m e d i a t e m o b i l i t y . T h e o v e r l a p o f the p a t t e r n s at different field s t r e n g t h ( c f Figs. I a a n d 2) is c o n s i s t e n t ~s ith the idea o f rapid r e - e q u i l i b r a t i o n du ring e l e c t r o p h o r e t i c t r a n s p o r t [2, 91. It is s~orthy o f note. t h a t a l r e a d y Krejci et al. [3 !, 32] s u s p e c t e d t h a t the a n o m a l o u s e l e c t r o p h o r e t i c b c h a v i o u r of t o t a l casein is due to the i n t e r a c t i o n o f its c o m p o n e n t s . it is i n s t r u c t i v e to a n a l y s e t h e velocities a n d a r e a s o f the v a r i o u s peaks by the m o v i n g b o u n d a r y t h e o r y d e v e l o p e d by Longs~vorth for e l e c t r o p h o r e s i s [I ] a n d applied by o t h e r s to s i m i l a r sitt, a t i o n s in s e d i m e n t a t i o n a n d gel t i l t r a t i o n [33, 34]. In the n o t a t i o n i n t r o d u c e d by Longsxvorth [i] the rt,~-casein c o n c c n t r a l i o n C~ (w/v) u n d e r the l e a d i n g a s c e n d i n g p e a k is given by ¢

-=

c

o ~),(u,,

-

C~).

f3)

206 in this equation Ca* represents the constituent c o n c e n t r a t i o n o f as~-casein in the b -

solution, defined ct

2:+ c.', +

as

jMA j,

jMa

+ kMn

b

+ C~jB~

(4)

s

+her¢ Ma a n d Mn are the m o n o m e r molecular weights o f as~- a n d fl- casein, which lmv¢ been ~ t a b l i s h e d aq 23 000 [19] and 24 0O0 [35], respectively. Further, U+~ is the v¢locity of pure a,,-casein in the c solution and U~ is the constituent velocity o f that ¢~mmlmn¢nt in the b s o l u t i o n a n d defined as

t*',

. .

.h

I"c*,t*' •

i

+

iMA

jli

iMA 4 kM "

Cb

irb

I/r-h

(5)

4 ¢orrc+ponding definition holds for the constituent velocity Ug, and it can b e s h o w n l l ) t~t

t'~

J

(6)

+'

~hcre I 'b'' is the volume sw:pt through by the be-boundary per unit time. Similarly. for the concentration of pure fl-casein under the trailing descending peak v.e have:

~ith

r *'+.

(8)

1"he velocities occurring in Eqns 3 and 7 are a p p r o x i m a t e d as follows" U~ +s calculated from the m a x i m u m gradient velocity o f the leading descending peak by U A,++~• b'~ is averaged over the m a x i m u m gradient velocities of the ascending bimodal peak and ~

L.

it found from"

U. +j

;

the pure c o m p o n e n t velocities U~ and UnSafe the average values from Table !. We are well aware that in principle nobilities and especially Ug should be measured by the median of the oc-boundary. In the present case this is n o t feasible, however+ since also the concentration change of dissociating ~tsl-casein is measured refractometrically across that boundary. In any case the difference between the present average and the median nobilities is found to be less than a few percent a n d therefore can be neglected in view of other uncertainties. W e are now able to compare the experimental areas o f the leading ascending " It can readily be calculated that changes in the constituent nobilities due to shifts of the association equilibria ir the ,4-boundary are negligible.

207 TABLE II C O M P A R I N G OBSERVED A N D C O M P U T E D PURE C O M P O N E N T PEAK AREAS IN THE E L E C T R O P H O R E S I S O F I N T E R A C T I N G ~ - ,,,ND/~-CASEIN

Mixing ratio

Velocities (10 -s cm/s)

50/50 70/30

% leading ascending

A

A

IBI

B

A

18.5 20.3

22.1 24.3

14.4 16.1

I2.1 13.4

24.8 25.9

% trailing descending

Obsd

Catcd

Obsd

Calcd

32 53

37 58

28 14

29 18

B

7.5 8.9

and trailing descending peaks with the computed C~ and Ca from Eqns 3 and 7. The results are given in Table II, from which it is seen that the calculated areas compare fairly well with the observed ones. It should also be noticed from this table that the leading ascending peaks cover as much as 70~, of the A component, whereas on the descending side the trailing peaks contain about 50/,, o, o f t h e B component. It is evident from Eqns 3 and 7 that these abnormally high percentages are due to a relatively high constituent velocity 0.~, which in turn suggests that complexes of a high stoichiometric ratio A/B dominate a m o n g the complexes (el. Eqn 5). The presence of higher complexes was already indicated by preliminary Gilbert-type computations in an earlier attempt to reproduce the b/modal reaction boundary [24]. descending

t t ,

uB

• ascendin9

t uA

t ,~

uB

u^

Fig. 3. Free electrophoresis of a ! :i mixture of ,,~- and fi'-casein at a total protein cor'centration of i,20g/dl. Experimental conditions: pH 6.6, 0.1 ionic strength (electrophoresis baff(.'r) and 2 C. Pictures taken after 4800 s. Ratio ionic strength of electrophoresis to dialysis buffer: 1.15.

C h u n [36] has analysed the ultracentrifugal pattern of a mixture of -~t- and /~-casein, assuming the formation o f a I :! complex ofdepolymerized ~ l - and/;-casein with the aid of the Gilbert '.heory [9]. Several objections can be made to his treatment however. First, the sedimentation method is much less sensitive in discriminating interaction than free electrophoresis, since only a descending boundary is available. More serious, however, is the fact that under the experimental conditions (t~-casein is highly polymerized [19] and consequently the interaction between the ,.~,-casein polymers and the fl-casein m o n o m e r should also be considered, The sedimentation pattern presented in Fig. 4 is also indicative of the presence of higher complexes. The slower sedimentation coefficient (I.5 S) corresponds to the

208

¢

FiS. 4. Sedirr~ntation patterns o f a 1:1 mixture of ~ , - and/'/-casein at a total protein concentration of 1.208/dl. l=xperimental conditions: barbiturate bulTer p H b . 6 and 0.1 ionic strength, 3 - C ; 50000 rev./min. Pictures taken after: a, 107 rain: b, 122 rain; e, 152 rain; d, 183 rain.

m o n o m e r of fl-casein and the m o n o m e r o f a~t-casein which have c o m p a r a b l e sedimentation coefficients [20,37]. F r o m these values it is readily calculated that the I:1 complex of m o n o m e r s , if it were spherical could have a sedimentation coefficient o f at the most 2.4 S. This is far below the experimental value o f 4.5 S f o u n d lbr the rapid peak in Fig. 4. it should further be realized that in re-equilibrating systems the sedim e n t a t i o n of this faster peak is always slower than that o f the complex itself [9], which iridicates that the complexes present m u s t consist o f at least four subunits. We are now able to roughly qualify the association equilibria which occur under the experimental conditions o f electrophoresis. fl-Casein, on account of the low temperature, will be completely depolymerized [20]. On the other hand, it can be obtained from Schmidl's work [19] that a~t-casein, under the experimental conditions will be polymerized conscc'.:zively at least up to the hexamer. A m o n g the complexes f o r m e d between (t~. and /-/-casein those of stoichiometry AjB ( j ~ I) will p r e d o m i n a t e . This conclusion was confirmed by c o m p u t e r simulation o f the be- and , ~ reaction boundaries. A preliminary account of the simulation m e t h o d was given earlier [231 and a m o r e detailed a c c o u n t v, ill be presented in the a c c o m p a n y i n g paper [17]. The parameters introduced in the c o m p u t a t i o n s were obtained as follows: (I) The polymerization constants and electrophoretic mobilities o f (:~-casein were taken from Schmidt's and this work: notably Schmidt observed that ,c~-monomers and -polymers have equal n lobilities: (2) the A~B-complex mobilities were calculated by linear interpolation between the pure c o m p o n e n t mobilities: it is a f o r t u n a t e coincidence that the c o m p u t a t i o n s are rather insensitive to the actual values accepted for the complex mobilities; (3) the equilibrium constants for the complex f o r m a t i o n were defined as J

J

and, since the caseins interact t h r o u g h h y d r o p h o b i c b o n d i n g [19, 20, 38], initial K:

209 values are chosen so as to c o m p a r e with the polymerization constants given by Schmidt for pure as~-casein polymerization [! 9]. in accordance with previous experience [24], the c o m p u t a t i o n s d e m o n s t r a t e clearly that bimodality o f the b e - b o u n d a r y could be p r o d u c e d only if complexes A~B with j > ! were taken into account. Moreover, it was observed that the agreement between the experimental and c o m p u t e d mobilities a n d percentages improved if more weight was given to the higher A~B-complexes. This led us to introduce six parameters for the interactions between all kinds o f a ~ - p o l y m e r s a n d the fl-monomer. It is realized that the i n t r o d u c t i o n o f so m a n y p a r a m e t e r s in the c o m p u t a t i o n s certainly will n o t provide a unique solution. T h e point of interest is, however, that only tl~.e consideration o f these multiple equilibria yield the observed bimodai be-boundaries and mobilities and percentages in agreement with the large constituent velocity /.?~ arrived at before. S o m e typical simulation results are collected in Table Iil and in Figs 5 and 6. TABLE Ill COMPARING SIMULATED AND EXPERIMENTAL REACTION BOUNDARIES C O M P L E X F O R M I N G ¢q~- A N D fl-CASEIN D U R I N G E L E C T R O P H O R E S I S

Ascending

Mixing ratio

FOR

Descending

Velocities (10 -5 c m ' s )

Relative area

(10 -scms)

Velgcities

Relative area

50:50

Fig. 5 Fig. 6 Exptl*

iO,8 10.8 12,7

20.0 21.2 16.9

63.6 64.2 68

17.7 17.6 18,5

64.2 64.8 72

7O 3O

Fig. 5 Fig. 6 Exptl"

13,8 13.1 13.9

20.9 21.7 18.9

51.9 54.6 47

18.1 18.O 20,2

86.2 87.4 86

" Average values from Table I.

it is seen t h a t the c o m p u t e d mobilities and percentages c o m p a r e satisfactorily with the experimental values. We do not consider further refinements of these calculations ~ a r r a n t a b l e for the following reasons. Firstly, as m a y be noted from a c o m p a r i s o n of Fig. 5 with Fig. 6. variations in the interaction parameters d o not signilicantly influence the results of the computations once the existence of the higher complexes has been accepted. Of course this implies that such c o m p u t a t i o n s will never yield unique values for the equilibrium constants. Secondly, as a c o n s e q u e n c e of the Kohlrausch Svensson effect the faster peaks are always enlarged at the cost of the slower ones [1, 29]. This effect has not been accounted for in the present calculations, since its m a g n i t u d e is difficult to evaluate in systems c o n t a i n i n g m o r e than three ionic species. Thirdly, on close inspection the electrophoretic patterns of Figs ! to 3 show a non-zero gradient in the b-phase, and sometimes a m i n o r shoulder ahead of the -t/-boundaries. It is suspected that these abnormalities are due to the presence of m i n o r quantities o f complexes which have a mobility a p p r o a c h i n g that of pure ¢~casein, and which were not a c c o u n t e d for in the present calculations.

210

a

~h

b

=¢ ...

~

i~]iHi

iiiiiiilh

"",-,

$~g:llg

.

¢gl::~i

=glll~l=l=

iih~iiliiiii~i,

Fig. 5. Simulated Ix:- and ./~Lreaction boundaries for complex forming ~,- and /~-casein during electropho~'~is. Parameters: Kt : 10, K~ = 15, Ks : 50, K, =: 100, Ks = 150, K~ : 100 (g/dl). Average diffusion cocEcients varying from I • 1 0 - 7 - 5 , ! 0 -~ cmZ/$ (see ref. I 7). M i x i n g nltio: a, ,~,//~ 50/50; b, ~,/~ 70/30. -

------"'

-

~

}iii}~

........

--

~

~scendrng

~h~a~

~

iH,cendln(j

...... ~

d~¢e~dlc
~

. . . . m,* a~ce~dlr,g

Fig. 6. Simulated Ix:- and e~-reaction boundaries for complex forming ~,~- and ~-¢ascin during elcctrophoresis. P a n l n ~ t e - . : Kt = 10, K~ ~ 25, K3 ~ 100, K4 ~ 200, Ks - 300, /(6 ~,~200 (g/dr). Average diffusion coefficients varying from !. ! 0 - 7 - 5 . 1 0 -7 cm2/s (see ref. 17). M i x i n g ratio: a, ~t,=/# ---50/50; b, ~ 1 / ~ = 70/30.

211 In conclusion we state that the interaction between c~ 1. and/%casein gives riseto an intricate assembly of complexes in which eat-casein dominates. This is in line with the well-known tendency of these proteins to form colloidal micelles in milk [22] ACKNOWLEDGEMENTS

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