The adsorption of some proteins on hydroxylapatite and other absorbents used for chromatographic separations

Bioehimica et Biophysica Acta, 351 (1974) 57-76

© Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands BBA 36693

T H E A D S O R P T I O N OF SOME PROTEINS ON H Y D R O X Y L A P A T I T E A N D O T H E R ABSORBENTS USED FOR C H R O M A T O G R A P H I C SEPARATIONS

E. GLUECKAUF and L. PATTERSON Chemical Engineering Division, AERE Harwell, Didcot, Berks. (Great Britain)

(Received August 20th, 1973)

SUMMARY The absorption of bovine serum albumin and of y-globulin (y-G) has been studied, both with hydroxylapatite and for bovine serum albumin also with TiO2, all in the presence of potassium phosphate buffer (pH 6.8) of a wide range of concentrations (Cpi from 10 -3 to about 1 M). In all three cases the observed amounts of adsorbed protein can be represented over a wide range by empirical equations of the type qprot

Cprot

:

Q [ K1 +

Cprot

-[-

exp(--Ka" Cp,)]

(1)

where Q, K1 and K3 are constants for a given system. This suggests that a common mechanism underlies the process of protein adsorption and its elution by phosphate buffer, and that this mechanism must be much more complex than previously suspected. The phosphate ions themselves are also adsorbed, both on hydroxylapatite and TiO2, following simple Langmuir isotherms: qPl

~ Q'

Cpt Kz + Cpi

(2

The significance in physical terms of Eqn 1 is discussed in some detail. The first term represents a weak adsorption of proteins probably on negatively charged phosphate sites and independent of the phosphate buffer concentration, while the second term represents a very strong protein adsorption, invarient with protein concentration, but greatly influenced by phosphate adsorption on positively charged metal-ion sites.

58

INTRODUCTION Though chromatography on hydroxylapatite and other metal oxides is a powerful technique for the separation of macromolecules such as proteins and enzymes [1 ], the interactions between these substances and the absorbing column material are very poorly understood. Qualitatively, we know that elution from the column is facilitated by increasing the molarity of the eluting phosphate buffer, and, this has been suspected by Bernardi [2] to be due, not simply to the increase in ionic strength, but to the specific competition for adsorbing sites between the phosphate ions and the macromolecules. An interesting theoretical study on the nature of the adsorption isotherm was carried out by Kawasaki [3] who produced a modification of a Langmuir isotherm (see his Eqns 10, 11) in which phosphate and macromolecules mutually displace each other. He then deduced a number of facts which might logically follow from such a model. However, there was not attempt to correlate the "predicted" equations with the observable adsorption behaviour under the influence of buffer strength and adsorbent concentration. As we shall see subsequently, the idea of a mutual displacement of proteins and phosphate ions is not borne out by our experiments with bovine serum albumin and ),-G, and while phosphate ions displace proteins from positively charged sites, the converse was not observed. It is conceivable, though, that a mutual displacement mechanism might apply when polynucleotides with built-in phosphate groups compete with the ions of a phosphate buffer. Very recently Bernardi et al. [4] coneluded from the general chromatographic behaviour that hydroxylapatite-crystals have two different types of adsorption site on their surface, to be identified with phosphate and with calcium, and that these are responsible for the binding of basic and acidic side groups of proteins, respectively. Our physicochemical adsorption studies have led us to precisely the same conclusions, and these give us additional quantitative information on the actions and interactions of the components studied. In this paper we have studied experimentally the adsorption behaviour of phosphate buffer over a wide range of concentrations, both on hydroxylapatite and TiOz, and then the adsorption isotherms of bovine serum albumin and ~-G on hydroxylapatite, as well as of bovine serum albumin on TiO2, all over a wide range of both protein concentrations and phosphate buffer concentrations. As a second step, we then try to build up a model compatible with the results of these observations. LIST OF SYMBOLS USED q Q C V X f

Amount adsorbed on the adsorbent Adsorption capacity at saturation Concentration Elution volume (Vc elution volume at concentration c) Filled column volume Void space in column

K2,K1 Constant of the Langmuir isotherm in the form q

Q

--

K+c

59 K3 /u~

Constant of the exponential term in Eqn 1 Amount of solute remaining on the column when the eluate reaches the concentration c.

Subscript 1: protein. Subscript 2: phosphate. EXPERIMENTAL PROCEDURE The proteins used were: Bovine serium albumin, crystallised and lyophilised, and y-globulin (99 70 7) Cohn fraction II, both from "Sigma" Chem. Co., St. Louis, U.S.A. The adsorbents, hydroxylapatite and TiO2 were supplied by Dr A. R. Thompson (A.E.R.E) in the form of highly porous spheroidal particles [5]. Particle sizes were hydroxylapatite: 100 # diameter, and TiO2:500 # diameter. Because of the physical stability of the particles, the same batches of hydroxylapatite and TiO2 were used for all the experiments, and columns were used many times, before re-pouring of the beds became necessary. The protein concentrations in the eluted solutions were measured continuously with a LKB-Uvicord II instrument. Electrical conductivities were measured with a Wayne-Kerr conductance bridge with auto-balance and were recorded together with time and drop number. Measurement of the adsorption isotherms Bovine albumin serum and ~-G. Our problem was that of measuring the adsorption of proteins as a function both of their concentration and of that of phosphate buffer over a wide range of concentrations. Such a binary system requires of necessity the determination of a very large number of equilibrium relationships. One of the most convenient ways to obtain this mass of data is provided by chromatographic elution data, provided that elution is carried out sufficiently slowly for solution and adsorbent to approach equilibrium locally. The fundamental connection between elution data from the chromatographic column and the adsorption isotherm is given by the relation [6]

V --f X

dq dc

(3)

where V is the elution volume at which the concentration c is reached (ml), X is the filled column volume (ml), f i s the void space in the column ( + the volume between column outlet and analyser) (ml), q is the amount of solute adsorbed on the adsorbent contained in 1 ml of column and C is the amount of solute contained in 1 ml of solution in equilibrium with q. Eqn 3 can also be used in integrated form [7] q = [#~ -t- (V~ - - f ) C ] X -~

(4)

where/~c is the amount of solute which remains on the column, when the eluate reaches the concentration C, and which may be eluted subsequently (if necessary with

60 a displacing agent) and Vc is the elution volume when the eluate reaches the concentration C. Eqns 3 and 4 are based on the assumption that the theoretical plate height in the eluted column is infinitely small. If that is not the case, one should add on the righthand side Of Eqn 4 the term 0.75

Vc2 dC NX dV

where N is the number of theoretical plates in the column. In our case the number N was about 100 and the correction term could therefore be neglected. (For bovine serum albumin, it was generally of the magnitude --½ ~/C when C and q are in #g/ml.). Eqn 4 can be used for the step by step determination of the adsorption isotherm, if a large number of points are obtainable from the elution curve of a single adsorbate, and if the amount left on the column at the end of the elution has been ascertained by a second elution step with a more strongly eluting solution. Rear boundary I0

0

oi' Elution

curves ( V - l ) m l 20

30

2000

600 400

ioo ,

60

~ "~

O.

'( 20

U

o

\

,o 4 2 !

IO Follow-up

20 with

O'SM

30 K p h o $ : V (IM)

Fig. ]. E l u t i o n curves o f bovine serum a l b u m i n f r o m h y d r o × y l a p a t i t e c o l u m n (a) 0.1 m potassium

phosphate; (b) 0.05 m potassium phosphate; (c) 0.035m potassium phosphate; (d) 0.0125 m potassium phosphate; (e) (...... ) calculated elution curve for Eqn 8. Inset: follow-up elution with 0.5 m potassium phosphate for run (c) and (d).

6i Let us assume that the rear boundary of our elution diagram had the shape shown in Fig. 1. In this case, the amount left on the column after the first elution is given by the value

/~=o = J'C d V corresponding to the area under the second peak produced by a high buffer strength. Step by step integration then gives successive values of:

/zl = #c=o q- (Vc=o -- Va)Cl/2

(5a)

/'Z2 = //1 + (V1 - - 1'/'2) (Cl -~ c2)/2

(5b)

tza = #2 + (1/2 -- V3) (c2 + c3)/2 etc.

(5c)

and from this the amount of material adsorbed per ml of column volume is then calculated according to Eqn 4.

ql = [Zl "q- (V1 -- f ) c l / X

(6a)

q2 = ,u2 + (1"2 - - f ) c 2 / X

(6b)

As an example we show a few typical elution curves of bovine serum albumin with 0, 1, 0.05, 0.035 and 0.0125 M potassium phosphate buffer from an hydroxylapatite column (Fig. 1). The experiments were done in the following way. A volume of 18 ml of spherical porous hydroxylapatite of mean diameter of 0.01 cm was contained in a column of 1.0 cm diameter. The total dead space was determined by the breakthrough of CaCI2 solution. The column was first equilibrated with the buffer, then 20 mg of bovine serum albumin in 3 ml of that buffer solution was added, and then elution was started with the same buffer solution at room temperature. Stability of bovine serum albumin was adequate at this temperature. The eluted bovine serum albumin concentration was measured continuously with a LKB-Uvicord II. After the bovine serum albumin concentration had fallen to zero or near zero, the remainder of the bovine serum albumin, if any, was eluted with a stronger buffer (0.5 m) and the area under this follow-up elution curve was determined (#c=o -- f C dV) (See Fig. 1 Inset). In the case of the 0.1 M buffer solution the q -- c relation can be fairly represented by a Langmuir isotherm:

ql - -

Qc1 g l _~_ C1

with Q = 900/~g/ml adsorbent and/(1 -----800/zg/ml solution

(7)

62 a n d this affords a test of the E q n 3, by calculating backwards the elution v o l u m e V.

XQK1 Vc,,¢ = f + X--~c = f + (K 1 _L_ C1)2

(8)

The values of V - - f calculated in this way are shown in Fig. 1, d o t t e d line (X = 18 ml). One can see that at the low concentrations there is a divergence from the " L a n g m u i r " shape, obviously due to a small n o n - u n i f o r m i t y of the surface which results in a n increased " t a i l i n g " effect.

Adsorption of phosphate on hydroxylapatite The absorption of phosphate was measured by determining the break-through volume of an advancing front of phosphate fed into the c o l u m n at constant concentration C after c o n d i t i o n i n g at the lower c o n c e n t r a t i o n C'. More precisely it was the mass centre of this front which was used for the b r e a k - t h r o u g h volume (V). F r o m this follows the e q u i l i b r i u m adsorption as

q - - q' = ( C - - C')

(V--f)

(9)

X

The difficulty in this case was that V a n d f were of very similar value, due the high internal porosity of the hydroxylapatite adsorbent, a n d considerable pre-

TABLE IA X = 18.5 ml of adsorbent. Break-through volumes of non-adsorbed electrolyte (CaCI2). C

I7

0.1M 0.1M 0.2M

14.93 14.95 14.91

mean value 14.93 ml = f for Table Ib

TABLE IB Break-through volumes of potassium phosphate buffer (pH 6.8). C'

C

ff

10-4 10-4 10-4 10-4 10-4 10-4 10-4 0.25

10-a 2.5" 10-3 10-2 0.025 0.1 0.25 0.25 0.50

1.10 1.12 0.85 0.72 0.54 0.27 0.29 0.04

f(ml)

q/C

q × 104

qca,o x 104 (Eqn 10)

0.0595 0.0605 0.0460 0.039 0.029 0.0146 0.0156 0.0022

0.595 1.51 4.60 9.7 29 37~ 38j 44.5

0.591 1.45 5.36 11.6 27.8 38.6 44.3

63 cision had to be attained in order to obtain meaningful results. These are shown in Table I. The results of Table IB column 5 can be represented as a Langmuir type isotherm

C2 qz = Q Kz + C2

(10)

with a saturation value solution (see column 6).

0.0052 moles/l adsorbent and K2 = 0.087moles/l

Qsat =

10--2 6

Ti 0 2

i0

-3 6

~

L

Q.

2

m

wlO

w4

o

6

I

4

IP

2

I0

J ~

-S

10--4

•

4

6 i0- $ C

I 2

m-moles

I 4

A

I e 10-

per

ml

I a

2 of

I 4

I 6 I0-

/ I

~

I 6

solution

Fig. 2. Adsorption of phosphate ions on hydroxylapatite and on TiO~. The continuous curves are Langmuir isotherms with the constants given in the text.

Adsorption of phosphate on porous Ti02 spheres TiO2 adsorbs phosphate much more strongly than does hydroxylapatite and consequently the measurement of adsorption values represented very few difficulties. Measurements were done both by the elution technique employing Eqn 4, and by the break-through technique using Eqn 9, with concordant results which are shown

64 in Fig. 2. The points show the values of the experimental work while the drawn curve represents a Langmuir isotherm (Eqn 10) with the constants Qs.t

0.0125 M adsorbent

-

and /£2 = 0.0047 M solution The adsorption o f bovine serum albumin on a spherical hydroxylapatite The adsorption of bovine serum albumin was measured over a concentration range from about 2-10/~g/ml to 1000-2000 #g/ml at a pH of 6.8 and at phosphate buffer concentrations ranging from 1.10 -3 M to 0.5 M. Fig. 3 shows the adsorption isotherms (ql against el) on log-log paper for the different phosphate buffer concentrations. While at phosphate buffer concentrations ~0.05 the isotherms were very nearly of the Langmuir type, those at lower buffer strength were characterised by the log-log plot being convex against the c-axis at low protein concentrations. Generally, this last behaviour can only be expected when

moo00 4000 4000

O.O01S

2000

IOO0

0"001__

¢.,,-

0"003

600 400

200

IOO

Z

80 40

•w

u ,a

m 'u

Io

0 " I ~ -0.!

"~

4

o 2

m

I

I

I

2

4

s

I°

I0

2

I

I

4 0 so CB$

A

I

I

I

I

I00 aoo 4oo6ooi0002ooo (P9/ml)

Fig. 3. Adsorption of bovine serum albumin on hydroxylapatite in the presence of potassium phosphate buffer (pH 6.8) of concentrations varying from 10-3 to 0.5 M.

65 there is more than one mode of adsorption, of which one type is much more intense that the other. The picture is complicated by the fact that the ratio of the quantities involved in these different modes seems to change as a function of buffer strength. Another complication which can be seen qualitatively from Fig. 3 is that while the curves at higher buffer strength tend towards a saturation value of about 900/~g bovine serum albumin per ml of adsorbed column, those at lower buffer strength (<5" l0 -3) tend towards a considerably higher value. Another feature becomes very obvious if we plot the amounts of bovine serum albumin adsorbed at constant aqueous bovine serum albumin concentration against a changing phosphate buffer strength (see Fig. 4). There is a relatively sudden change to 4

I0

6 4

~

2

E

~C B0S~ I 0

=~. 10 3 'u

m,. o m

2

U

I0 A

2

4

2

I0 10--4

I0

~

i I I 4 6 1 0 -- 3 2

I I 4 6 10-2

C (pho s.l

2

4 61

0 I- I

,

2

i I 4 6

molarlty

Fig. 4. Adsorption of bovine serum albumin on hydroxylapatite at constant bovine serum albumin concentrations, abscissa: potassium phosphate-buffer concentration. ( + , ×, O = 10, 100, 1000 #g of bovine serum albumin/ml, respectively).

a constant adsorption value for a buffer strength of ~0.05 M, a change which is particularly pronounced at moderate to low protein concentration. The same effect was also observed when studying the adsorption of 7-globulin of hydroxylapatite. Though generally the results with 7-globulin were not as reproducible as those with bovine serum albumin, the general picture was much the same (see Fig. 5). We note again the convex curvature of the isotherms towards the c-axis at lower buffer strength, the Langmuir type of adsorption behaviour at high buffer strength, and small changes only of the adsorption curves between 0.1 M and 0.5 M buffer strength (see also Fig. 6). The change in the maximum adsorption capacity is even more marked than in the case of bovine serum albumin, and it appears to change from about 900 #g of 7-G/ml at high buffer strength to at least 3 times that value at very low buffer strength.

66 I0000 6000 4000

2000

0 0

• 002 • 005

I000

~ "

,oo

400

.

200

~

~

60 I

40

"

: io

S

)o

,r

II I

5

r

4

I i ,I ,o ,oI 4'o~',oo,o~4oo'~,ooo,ooo

¢~-G (pe/.I} Fig. 5. Adsorption of ~-globulin on hydroxylapatite in the presence of potassium phosphate buffer (pH 6.8) of concentrations varying from 10-3 to 0.5 M. We wondered whether these features were characteristic only for hydroxylapatite adsorbent, and therefore studied also:

The adsorption of bovine serum albumin on Ti02 The results are shown in Fig. 7: q-C isotherms at constant buffer strength, and in Fig. 8: qbovi. . . . . . . . ]bumi, with varying CpI. The general features of the isotherms are again the same. This peculiar behaviour is specially marked in Fig. 8, where there is a sharp break in the adsorption values around CpI = 0.25. One must conclude i'rom this, that what we observe is of general relevance to the adsorption of proteins iaa the presence of phosphate buffer on all sorts of surfaces, and consequently, we must postulate an adsorption mechanism which is compatible with a variety of surfaces.

Representation of the protein adsorption curves In spite of the obvious complexity of the adsorption behaviour, all three systems investigated can, with a reasonable accuracy, be represented by empirical equations of the type C1

ql : Q [ K j q- CI + expl° (--K3C2)] i.e. with only three constants, as can be seen in Tables IIA, B, C.

(11)

67

t

-:'F

c _o

u

~

I00

Io

1

ll~i 4

i

i

6 10-3

10- 2

C (phos.)

I

I

a

4

q I

6 i0 -I

molarlty

Fig. 6. Adsorption of ~-G on hydroxylapatite at constant ~-G-concentrations, abscissa: potassium phosphate-buffer concentration ( ÷ , ×, O = 10, 100, 1000/~g ~-G/ml, respectively). I0000 6000 4000

2000

0"0001 ~ .

I000

I

600

0.001

0.01

~oo

0.000.5

~

. :::::::::I=~ ~

i,°!

2' I

Ii

~

•

s

IO

2o

I

I

I

I

, o 61o I O 0 200 ,oo 6 o o l o 0 0 2 o o o

CBS A (pg

roll

Fig. 7. Adsorption of bovine serum albumin on TiO2 in the presence of potassium phosphate-buffer of concentrations from lO -4 to 1 M.

68 I0 3 6 4

c.iA

=. i 0 2 6 U 8t

4

0

2

IB U

IO I 6

a

4

2

I0 10- 4 2

I

I

4

6

10- 3

f

I

a

4

C ( p h o s.I

t

610- 3

I

I

a

4

I

610- I

I 2

I 4

I 6

molarlty

Fig. 8. A d s o r p t i o n o f bovine s e r u m a l b u m i n on TiOz at c o n s t a n t bovine s e r u m a l b u m i n concentrations. Abscissa: p o t a s s i u m phosphate-buffer concentration. ( + , × , © = 10, 100, 1000/~g bovine s e r u m a l b u m i n / m l respectively).

At the very lowest buffer concentrations Eqn 11 breaks down and to make it fit would require further and higher exponential terms of Cz. Even so the fit is pretty good over a phosphate concentration range by a factor of 20 and a protein concentration range by a factor of 100. A possible interpretation of the need for further exponential terms might be that at these very low buffer concentrations, the strongly adsorbing areas might adsorb the proteins in a manner which requires less surface area per molecule. This could mean a manner of adsorption where the long axis of the protein stands vertical or almost vertical to the surfaces, with simultaneous proteinprotein interaction. DISCUSSION

The most characteristic feature is the dependence of the amount of protein adsorbed at varying buffer strength. Taking the case of bovine serum albumin on hydroxylapatite, especially at low protein concentrations: after an increase of phosphate concentration from 10 .3 M to 0.05 M has produced a more than 100-fold decrease in the amounts of bovine serum albumin adsorbed, there is almost no further change in bovine serum albumin adsorption when the phosphate concentration is increased further by another factor of 10. If any change is observed it is in the direction of a slight increase in bovine serum albumin adsorption (more noticeable in the case of bovine serum albumin on TiO2). It is of interest to note that at a phosphate concentration of 0.05 M, the hydroxylapatite surface is by no means saturated with phosphate ions, but according to Fig. 2,

69 TABLE IIA Bovine serum albumin on hydroxylapatite: Q = 900/~g/ml adsorbent, K, = 800#g/ml solution, K3 = 57.5 ml/mmole buffer. C2 (molarity)

0.5 0.1 0.05 0.035 0.025 0.0125 0.005 0.004 0.002 0.001

qbovln©se. . . . lbumln(in ~g/mlhydroxylapatitO (qx) C ~ = 10~g/ml

C ~ = 100~g/ml

C1:

1000#g/ml

obs

Eqn 11

Eqn 17

obs

Eqn 11

Eqn 17

obs

Eqn 11

Eqn 17

14 14 13 27 45 150 390 600 1100 1200

11 11 12 20 44 180 480 550 (700) (800)

11 11 14 22 30 170 450 510 (676) (785)

110 110 100 120 145 250 480 720 1170 1300

100 100 101 109 133 268 566 630 (790) (890)

100 100 102 111 119 258 540 600 (767) (875)

510 500 480 520 520 580 750 950 1350 1500

500 500 501 508 533 668 966 1030 (1190) (1290)

500 500 502 510 518 658 938 1000 (1170) (1274)

TABLE IIB Bovine serum albumin on TiO2: Q - 475/~g/ml absorbent, K~ = 360/~g/ml solution, K3 -- 5 l/moles buffer. C2 (molarity)

qbovine serum

C~ =

1.0 0.5 0.25 0.2 0.1 0.05 0.01 0.002

albumill (ql)

10/~g/ml

C~ =

100~g/ml

6"1 =

1000/~g/ml

obs

Eqn 11

obs

Eqn 11

obs

Eqn 11

34 28 28 82 190 300 450 500

25 26 51 72 176 291 447 490

125 115 105 180 300 390 550 580

105 106 131 152 257 371 527 570

370 360 350 390 580 620 750 760

350 351 376 397 502 616 772 815

TABLE IIC ~-G on hydroxylapatite; Q = 900/~g/ml absorbent, K1 = 890/~g/ml solution, K3 -- 23 1/moles buffer.

c~

0.5 0.1 0.05 0.025 0.01 0.005 0.001

C1 = 10 g/ml

C1 = 100 g/ml

C1 = 1000 g/ml

Obs

Eqn 11

Eqn 18

Obs

Eqn 11

Eqn 18

Obs

Eqn 11

Eqn 18

10 13 72 290 480 1020 2100

10 14 73 253 540 (710) (870)

10 13 71 190 630 870 (900)

85 100 187 450 670 1220 2400

91 95 164 335 621 (790) (960)

91 94 152 271 711 960 (991)

440 480 580 900 1020 1400 3000

476 480 540 720 1006 (1180) (1330)

476 479 537 656 1100 1350 (1380)

70 only about 36 ~ of the saturation value has been reached. (In the case of ?,-G this occurs at about 0.1 M phosphate, corresponding to about 53 % saturation). One must concluse from this that when a certain phosphate saturation has been achieved on the hydroxylapatite or TiO2 surfaces, the proteins are no longer able to make "contact" with the positively charged adsorption sites of the adsorbent, which cause strong adsorption, and what we observe then must be the weak adsorption of the proteins on the negatively charged phosphate ions (see schematic representation of Fig. 9). Presumably this interaction will take place between the adsorbed phosphate

BSA~ Fig. 9. Schematic view of bovine serum albumin molecule adsorbed on a phosphate-covered surface (Langmuir adsorption).

ions and the amino groups of the protein. This model would explain why bovine serum albumin adsorption can increase slightly, when the phosphate buffer concentration is increased from 0.05-0.5 M, as the increase of adsorbed phosphate ions then permits a somewhat closer packing of protein molecules on the phosphated surface. It is useful to compare the observed saturation densities of phosphate, bovine serum albumin and 7-G e.g. on hydroxylapatite. The extrapolation of the Langmuir isotherms give complete coverage: for phosphate at QPt = 0.0052 moles/1 of hydroxylapatite, for bovine serum albumin at Q = 900 #g/ml = mole/1 of hydroxylapatite for ?,-G at Q apatite

900 #g/ml =

0.9 × g/1 hydroxylapatite _ 1.3.10 .5 69 000 g/mole

0.9 g/l hydroxylapatite = 0.55.10 .5 moles/lhydroxyl165 000 g/mole

| f we were to assume that all phosphate sites are also accessible to the protein molecules, we would have to conclude that bovine serum albumin covers an area of 5.2" 10 -a 5.2.10 -3 1.3" 10 -s -- 400 sites while 7-G covers an area of -0.55.10 -5 - 940 sites. In the case of TiO2 the numbers are even larger: for phosphate: QPl = 0.0125 mole/1 of TiO2 0.475 g/1 TiO2 for bovine serum albumin: Q = 475 #g/ml = 69 000 g/mole bovine serum albumin = 0.69.10 -s moles bovine serum albumin/l TiO2 0.0125 so that bovine serum albumin covers -- 1810 sites. 0.69.10 -5 These values appear to be rather larger than one would conclude from a comparison of molecular dimensions. Phosphate ions (and similar MO4-ions) may be

71 assumed to be fairly spherical with a volume of about 100 A 3 (see ref. 8), leading to an estimated area of 26 A 2. The dimensions of serum albumin (man) Mr = 69 000 (see ref. 9) major axis: 150 A, minor axis: 38 A, estimated area ~

× 150 × 38 =- 4350 A 2.

The dimensions of y-G (man) Mr = 165 000 are major axis: 235 A, minor axis: 44 A, estimated area ~- × 235 × 44 = 8200 A 2. Thus we obtain for the area ratios: (assuming the same sizes for human and bovine materials) Bovine serum albumin

Pi 1810 for TiOz)

--

4350 2 ~ -- 167 ( = 4 2 ~ of 400 for hydroxylapatite) (9.2 ~ of 7-G 8200 P ~ -- 2 ~ -- 315 ( = 33 ~ of 940 for hydroxylapatite)

It appears from this that even in the case of hydroxylapatite not all the sites accessible to phosphate are available for protein adsorption, only about 42 ~o in the case of bovine serum albumin and about 33 ~ in the case of the larger y-globulin, and this may account for the relatively low protein adsorption capacities [2] of our adsorbents*. We shall come back to these figures at a later stage.

Discussion of the adsorption isotherms for bovine serum albumin and ~,-G Without experimentation one would have tended to think [3] that the adsorption isotherms would be based on the mutual competition of protein (Subscript 1) and phosphate (Subscript 2) for the strongly adsorbing metal ion sites of the surfaces, which would have led to a function: ql = ~(C1,C2) in which these two concentrations are intricately mixed up, so that the elution curve V -- f

X

dql -- ~ (C1,CD, dc~

is also an intricately mixed up function of both concentrations. Even in the simplest Langmuir case, we would have had ql Q

al C1 1 + alC1 + a2C2

and (_~_~)

Q al (1 -r a2C2) c2 const. ---- (l + a~C~ + a2C2)"

* One of the reviewers of this paper has kindly pointed out that some of the observed adsorption of potassium phosphate on hydroxylapatite may be due primarily to interaction of the positive potassium ion with negative adsorption sites on the hydroxylapatite. This factor would somewhat reduce the calculated ratios of the positively charged phosphate-ion adsorption sites to protein adsorption sites, but this would not affect the subsequent discussion.

72 It was therefore surprising to find that the adsorption isotherms in all three cases had the approximate form (12)

ql = Oi(G) -F Oz(Cz)

While this has been demonstrated in Tables IIA, B, C the most stringent test lies in a comparison of the elution curves themselves, because the differentiation of Eqn 12 leads to

V -- f X

dql dCx

- -

-

o~(G)

(13)

or in plain language, the elution curves of e.g. bovine serum albumin from an hydroxylapatite column, should all follow much the same C-V curve, independent of buffer concentration, and the only difference in the elution behaviour should be the quantity which is not eluted, and which is only released in the follow-up elution at high buffer strength. The example of the elution curves in Fig. 1 shows that for the case of bovine serum albumin on hydroxylapatite this is, in fact, so, though the elution with very low buffer strength did show moderate shifts. The elution curves for 6"2 = 0.0125, 0.025, 0.035 and 0.1 are almost identical and differ only by the amounts remaining adsorbed when the protein concentration of the eluted solution has become unmeasurably low (5 #g/ml). (The dispersion of the curves of Fig. 1 at low concentration may or may not be real, as the readings in that region are greatly affected by small changes of the zero of the Uvicord instrument). It remains for us to discuss the exponential part of Eqn 1 (or 11). A function of this type is most likely connected with the probability that a certain surface coverage by phosphate occurs at a certain concentration Cz which affects the ability of positively charged sites to adsorb proteins. We propose the following model: If a given adsorption site suitable for a bovine serum albumin molecule (comprising n sites suitable for phosphate adsorption) contains m or more free sites, then protein is strongly adsorbed (presumably on positively charged sites). If it contains less than m free sites, i.e. n-m phosphate covered sites, then no strong adsorption takes place at all and we find only a weak (Langmuir) adsorption taking place on the phosphate groups of that site (or perhaps no adsorption at all). The probability e of finding m out of n sites free of phosphate, when the mean adsorption ratio for phosphate is q2/Q2 is given by

n!

.( qz ~.-m, ( 1 -

e,,,= rn!(n-- m)!

\~-2 !

qz ~'~ Q2 ?

(14)

The probability that m or more sites are free is then given by m=n

e(~m)=

S tn=

em m

(15)

73 The experimental bovine serum albumin data at C = 10 #g/ml indicate that this then gives for the protein adsorption curves the function

Cx m=n ] q~ = Q K~ + CI + m=m X e,,

(16)

The question is now: can one find one number m and one number n which when used with Eqns 14 and 16 will satisfy all the adsorption curves for a given protein? In fact, both in the case of bovine serum albumin and of T-G on hydroxylapatite there is only one solution: for bovine serum albumin: n = 13 and m = 13, (though n = 14 and m = 14 will also give a reasonable fit); for ~-G we get n -- 14, m = 12. In view of the very small value of (n-m) in both cases the summation functions take on very simple forms: (replacing qz/Q by Eqn 10) C1 for bovine albumin serum: q~ = Q K1 + C1

K2

13

]

with K2 = 0.087, K1 = 800 and Q = 900,

f o r T - G : q l = Q { K l + C~---~-4-(K2+C2)1411 4-14

1-J-~"-"~'-lljj

(18)

/{2 =- 0.087, K1 = 890 and Q = 900. The degree of agreement between Eqns 17 and 18 and the experimental adsorption data is shown in Tables I I A and IIC. It is clear from this that a very small number of phosphate ions can stop the adsorption of a protein: a single one in the case of bovine serum albumin, and three in the case of )J-G, and that on a patch of 13 to 14 adsorption sites. The numbers n = 13 and 14 observed for bovine serum albumin and 7-G with hydroxylapatite are very much smaller than what one would have expected from the ratio of areas covered by the proteins to the area covered by a phosphate ion or a hydroxylapatite unit, which was about 167 (for serum albumin) and about 315 (for ~,-G). It would appear from this that the actual contact area of the proteins is only about 8 to 4 ~ of the area covered, which would be understandable if the proteins have a considerable curvature and so can make contact with a flat adsorbing surface only over a small area (see Fig. 10). One cannot quite exclude the possibility that the contact area is larger, but that the interaction is limited to 13 or 14 specially placed sites, the selection of which is governed by the position of the interacting groups of the protein. But the conclusion that the bovine serum albumin cannot be strongly adsorbed if a single one of the 14 sites is covered with phosphate makes it likely that the interaction area is physically small and compact, say about 2 sites by 7 sites. Only then can the occupation of a single site have such a drastic influence. If it was a matter of separating the two proteins bovine serum albumin and

74

13 s i t e s contoct

Is-GI°b" 14 s l t c s CohtLQct

Fig. 10. Schematic view of proposed "strong" adsorption of bovine serum albumin and 7-globulin on a partially phosphate-covered surface.

;~-G from each other, then one might choose a buffer strength which does not permit bovine serum albumin to be strongly adsorbed in any great quantity while interfering as little as possible with the adsorption of y-G. The best condition for this purpose would arise at a phosphate buffer strength around 0.025 M where the chances for a strong adsorption of bovine serum albumin are only 0.036 while those for y-G are almost 10 times greater. A comparison of the adsorption curves of bovine serum albumin and v-G, by means of Figs 3 and 5, would in fact also lead to this phosphate buffer concentration as the most discrimination condition. Adsorption of bovine serum albumin on Ti02 We have not discussed in detail the adsorption of bovine serum albumin on TiO2 on the basis of Eqn 15, because the observed adsorption of phosphate on TiO2 is so strong, that at C2 = 0.1 the probability of finding a single free adsorption site is only about 0.02, and that of groups of free sites would be nearly zero. It would appear from this that the strong adsorption of bovine serum albumin (that is bovine serum albumin which is adsorbed on sites other than those covered with phosphate) takes place on other crystal faces than those responsible for the observable bulk adsorption of phosphate. Under these circumstances the sites responsible for strong bovine serum albumin adsorption would have a lesser phosphate adsorption (with unknown constants K a n d Q). With four constants to choose (m, n, K a n d Q) a detailed interpretation would not be convincing. But there can be little doubt that the general pattern for bovine serum albumin adsorption on TiO2 must be very similar to that on hydroxylapatite otherwise it would not be represented by the same empirical Eqn 1. (See Table liB). CONCLUSIONS

The general conclusion which may be drawn from this study is that both hydroxylapatite and TiO2 adsorb proteins on two types of surfaces. One of these adsorbs weakly and produces a Langmuir type of adsorption isotherm which is not affected by the concentration of the buffer phosphate. It is suspected that, in fact, this adsorption takes place on a phosphate covered surface, or, in the case of hydroxylapatite, on a natural phosphate surface.

75 There is a second type of surface presumably associated with Ca or Ti sites which adsorbs proteins very strongly, so much so that when it is available it saturates fully with proteins and the amount adsorbed is thus effectively independent of the protein concentration of the solution. Adsorption on this surface is, however, very greatly dependent on the phosphate buffer concentration, which governs the fraction of surface available for protein adsorption and which itself is not displaced by protein. When the Ca-sites of hydroxylapatite are nearly or fully saturated with the phosphate ions of the buffer, they resemble the natural phosphate sites of the hydroxylapatite crystals. This follows most clearly from the similarity of the adsorption isotherm of bovine serum albumin on phosphate saturated TiO2 (which has no natural phosphate sites) with the adsorption isotherms of bovine serum albumin on hydroxylapatite (which has). It also follows from the observable increase of bovine serum albumin adsorption on hydroxylapatite at very high phosphate buffer strength, when the phosphated Ca-surface adds its weak adsorption to that of the natural phosphate surface of the hydroxylapatite. This adsorption behaviour on the strongly adsorbing Ca and Ti surfaces can be explained by a statistical model, which is particularly simple in the case of bovine serum albumin on hydroxylapatite. To be strongly adsorbed on this surface the bovine serum albumin molecule requries a contact area of about 13 adsorption sites, and it will only be adsorbed, if this contact area is completely free of adsorbed phosphate ions. The probability of that happening is a function of the phosphate concentration of the solution, and the model leads to the simple Eqn 17. In the case of y-globulin on hydroxylapatite, the pattern is similar, except that y-G requires a 14-Site contact area, and can tolerate the adsorption of up to two phosphate ions on these 14 sites. This then leads to a slightly different statistical result, and the final adsorption function is then given by Eqn 18. While these functions are derived with a definite model in mind, it is also possible to describe the adsorption process by a simple empirical equation which can be applied to all the cases studied (see Eqn 1). The dual nature of these isotherms, containing separate functions of the protein and of the phosphate concentration, rather than a mixed function q)(CIC2) means that the shapes of the elution curves are almost independent of the buffer concentration, and elution differs essentially only by the amount of strongly adsorbed protein which is not eluted at all except at a buffer strength which is high enough to ensure the invasion of all the contact areas by phosphate ions. ACKNOWLEDGEMENT We wish to thank Dr A. R. Thomson (AERE) for helpful discussions. REFERENCES 1 Tiselius, A., Hjerten, A. and Levin, O. (1956) Arch. Biochem. Biophys. 65, 132-155 2 Bernardi, G. (1965) Nature 206, 779-783 3 Tawasaki, T. (1970) Biopolymers 9, 277-289 4 Bernardi, G., Giro, M.-G. and Gaillard, C. (1972)Biochim. Biophys. Acta 278,409-420

76 5 Thomson, A. R. and Miles, B. J. (1973) Methodological Developments in Biochemistry (Reid, E., ed.), Vol. 2, Phys. Techniques, p. 95, Longman, London 6 DeVault, D. (1943) J. Am. Chem. Soc. 65, 532-540 7 Glueckauf, E. (1949) J. Chem. Soc. 3280-3285 8 Glueckauf, E. (1965) Trans. Faraday Soc. 61,914-921 9 Florkin, M. and Stotz, E. H. (1963) Comprehensive Biochemistry, Vol. 7, Table 9, Elsevier, Amsterdam