centrifugation and it is therefore desirable to study mtigens which are readily resolvable from antibody 7-globulin by electrophoresis. It is necessary for .intigens to be well-defined homogeneous species of definite molecular weight in solution. On tlie other hand, since a specific >Ig-Ab precipitate is dissolved in d g excess, it is not necessary to isolate pure antibodies, which is a considerable advantage. (The enthalpy changes accompanying the reaction might be determined with greater precision by calorimetry, but the isolation of purified 'tntibodies u ould be recluired.) Fiiially, it iiiizlit be
~ C ~ J X I R l B U l I ONO. X FROM THE
notcd that although the Iirccisioii attaiiiablc by these methods leaves much to be desired when coinpared with that attainable for small molecule rcactions, the state of purity of most natural antigelis is probably a limiting factor a t the present tinie. The authors have profited greatly from discussions with Dr. Verner Schomaker. Grateful acknowledgment is made to Mrs. l l a r t n Shapiro for her excellent technical assistance in the course of this investigation. xE\V I I A V E N , COSS.
PASADENA, Car..
126%FKOhl '1'1111 s l l i R l , I X G C I l E M I S l R Y L A ~ O R A I Q KYY AL , E ~ ~ S I V l < R SY ,l lA S D C O S I K I H U ' I l t l h SO, I!tiiii GATESA N D CRELIJSCIICXISTRY LABORATORIES, CALIFORNIA I N s T r r w E OF T E ~ H N O L O G Y ]
Physical Chemical Studies of Soluble Antigen-Antibody Complexes. IV. The Effect of pH on the Reaction between Bovine Serum Albumin and its Rabbit Antibodies' BY S . J. SINGER AND D. H. CAMPBELL RECEIVEDFEBRUARY 14. 1055 Solutions of soluble complexes formed between boI-ine serum albumin (as antigen, Ag) arid its rabbit antibodies ( A b ) have been subjected t o electrophoresis and ultracentrifugation over a range of pH. \T'hile t h e distribution of species in these solutions is apparently not grossly altered between pH 7 . 5 and 4.5, between pH 4.5 and 3.0 very extensive dissociation of the complexes occurs. Equilibrium constants, K , for the reaction Ag Ab $ AgAb can be calculated as a function of pH. The variation of K with pH provides strong evidence that a single carboxyl group is involved in every Ag-Ab bond in this system,
+
Little is known about the molecular details of the bonding between natural protein antigens (Ag) and their antibodies (Ab). The sizes of the reactivc sites involved are thought t o be considerably smaller than the entire Ag or Ab molecules but their structure has not yet been elucidated. If a small number of ionizable groups were present in the reactive sites and were intimately involved in the reaction, then the strength of the Ag-Ab bonds should depend on the state of ionization of these groups, and hence upon the pH of the solution containing the -4g and Ab. With appropriate methods for measuring the Ag-Ab bond strength, and with a careful appraisal of auxiliary effects which changes in pH might have upon such a system, the presence of such ionizable groups might thus be detected, and their number determined. I n previous papers of this series,2-4 electrophoretic and ultracentrifugal studies have been carried out near neutral pH with the soluble Bg-Ab complexes formed by dissolving an Xg-iZb precipitate in an excess of Ag, in the system containing bovine serum albumin (BSA) as Ag and rabbit antibodies to BSX. These methods are well-suited to the determination of the influence of pH on rlg-.%b equilibria, and this application to the rabbit anti-BS-1 system is the major subject of this paper. Strong cvidence has been obtained in this manner that one (1) T h i s work was supported in p a r t by grants from t h e Rockefeller Voundation and t h e United S t a t e s Public H e a l t h Service. This paper was presented before t h e Meeting of t h e American Chemical Society a t New York City, September, 1954. A preliminary account of some of t h e results of this investigatiorl has appeared i n S. I. Sinser a n d 11. IT C,unpbrll, 'I'EIIS J O I : K N A I . , 76, 4 0 5 %( l Y , ? 4 ) i i ) S . J h i t g r r niid I). I f . Caiiipi,ell, i / , r f / , 7 G:) 5 . 1 Siiiger : i t i < I I) 11. C . ~ ~ n j r l ~ ith~i lcli ,, 76 i ~ h ldl ,77 ( 1 ) 5 . I S i i i r ~ r r. i i i t I I 1 11. C ~ i i i ~ , l ~
,ionized carboxyl g v o i ~ pis involved in every .Ig-AIb bond in this system. Other matters of interest also have been iiivcstigated and are reported. Additional evidence lias been obtained confirming our earlier conclusions2 concerning the rates of re-equilibration reactions, and the identities of the components appearing in the ultracentrifuge and electrophoresis diagrams of solutions of Ag-Ab complexes. In addition, we have developed an electrophoretic method for the determination of total BSA and total Ab in a solution, based on the observations that a t PH 2.4 the Xg-Ab bonds are essentially completely dissociated, and that ESA and Ab 7-globulin are electrophoretically resolvable under these conditions. (That the -4g and -1b in this system can be dissociated in sufficiently acid solution has been observed previous1y.j) This now enables us to use unaltered BS.1 whereas previously it was found desirable to label the BSA by iodination.2 It also has been possible in this study to makc a direct test of that part of the Goldberg theory for Ag-;lb reactions6 which deals with systems in hotnogeneous equilibrium. This theory has been used4 in the evaluation of thermodynamic parameters for the reactions in the rabbit anti-BSA system, and its l d i d i t y has not previously been confirmed. Materials and Methods T h e Ag-lb preparations, 111, I V , V aiid \.I, atid the methods employed t o study them have been described in detail in a previous paper.* Solutions t o be examined in different buffers werc t1i:ilyzed 4 8 hours at 4' against several ~~
L-,) 1 1 .
11. C J ~ I I ~ ~ , ~ .IC. II, r
. , , ~ w ~. it ~~l d~I , s peaks listed in Tahlc V arc corrcctetl for tlie Johiistoii -0gston ano~iinly.~'l'hc cquilibriuiii co;icciitratiotis of the free .kg a i i d Ah a t :I Kivcii PI-I are thus directly dctcriiiiiicd iroiii thr corrected ai-cas under their respective peaks. 111 addition, tlir corrected relative area under the acomplex peak is taken as the sum of the relative concentrations of the hgkb and (Xg)?lib species. The fvtrcfion of the a-complex area attributable to the rlgAb is evaluated, as a first approximation, on the assumption of the intrinsic equivalence of the bonds in the A\gAb and (Xg)zAb complexes. This assumption requires".'" that the concentrations of the two cciinplexcs in n given solutioii lie rclxteti :LS I:ig ,: I.ltracciitrifugc diagraini of iolution 1\' i i i lmffrr.: of c!iffcrciit PH aiiri ri3 0.1. Three patterlls at diffcrcllt t i i 1 i C l i n each rxprrimeiit are illustrated, from right to lcft chroriologically. Sediinentation proceeds t o thr lcft. The y j x a k reprcsciits f r w Ab, a and h, the ( I - arid h-roiiiplrxrs. i l l this serics of buffers are given ill Table 1'. I t is to be noted that the dissociation appears to be quantitatively independent of the chemical nature of the biiffer.
I < r ; ~ e cOP' r PI1
TABLE \. O N Ag A h
I l > l , t ~ l l Ihvd.i 'I 111' J ~ , K I ~ . ~ ~ , E ~ , ' ~ I I I ~ ~ I ~ ' ~ I . ! ~ ili(.rlts :It :I ralca sitiiilar riiougli to that of the ('4~)~.it1> l / K o ,and log (1/K - l / K o ) S -log K . In such circumstances, log K is a linear function of p H with slope unity. It is evident that the data of the first and last columns of Table V conform to this behavior. For a more quantitative test, the value 8, the posiof KOmust be determined. If a t pH tively and negatively charged groups in the reactive sites of the Ag and Ab molecules are fully ionized, then K = K Oat that pH. In a previous ~ a p e r , ~ . ' ~ for the reaction Ag Ab G AgAb a t pH 8.6, K was determined to be 1.0 X IOb. Using this value for KO,and the K values of Table V, we obtain the data plotted in Fig. 6. The relation between log (1/K - l/Ko) and PH is indeed linear with slope - 1.2. The difference from the theoretical slope -1.0 may be due to systematic errors in K , or to other effects discussed below. Furthermore, these data indicate that log (KHIKO) 0, and K H S' KO,from which it follows that the pK for the dissociation of the group in the reactive site is about 5 . This value is, within experimental error, equal to the pK of an isolated carboxyl group.
-
+
TABLE \'I
OH 4 22 3.90 3 88 3 .60 3.42 3.31 3.12
-
I n order to explain the effect of acid pH on Ag-Ab equilibria, let us consider a model system with the following properties: (a) in each of the two reactive sites of the Ab molecule there is one negatively charged group, and in all j sites of the Ag molecule one positively charged group, which must be ionized for reaction to occur. (Interchanging positive and negative charges would have no effcct on the argu~ n e n t . ) ; (b) the acid dissociation of the positive group occurs in the alkaline pH range; (c) the acid dissociation of the negative groups can be described by a single intrinsic equilibrium constant; (d) the effect on the reaction of the net charges on the entire Ag and Ab molecules is negligible. The equations governing the key equilibria in acid and neutral solutions may then be written
+ Ab-* Jr Ag+(f Ab-'; KO + H C HAb-'; ~ K H HAb-' + H + HZAb; K H / ~ "Ab-' + H + Agt[' "HAb; Ka
Ag+'
- ')
Ab-'
Ag+"
-
-
(1) (2) (3) (4)
The symbol for the equilibrium constant characterizing each reaction is written a t the right. The apparent equilibrium constant, K , determined exI:erimentdIv froin the sedimentation I'attcrns is given by
3.0
3.8
3.1
42
PH. Fig. 6.-- The variation of the apparent equilibriuni coilstunt with pH for solution I\-.
Our results are therefore consistent with the presence of one carboxyl group in each Ag-Ab bond which must be ionized in order for the bond to form. where [SIrepresents the molar concentration of spe- Whether this carboxyl group is exactly the same cies s, [ A b l t o t a i = [Ab-.'] [HAb-'1 [HzAb], from one site to the next, and whether it occurs in and [ A g A b I t o t a ~ = [Ag+(f-')Ab-'] [Ag+(f - I) every Ag site or every Ab site, it is not possible to judge from the present results. HAb]. From these relations it follows that Several alternative explanations of the influence of pH on this system might be advanced. The two most important ones are: (a) as the Ag-Ab soluIf two negative and two positive charges are involved tions become more acid and the Ag and Ab molein each bond, a similar but more complicated rela- cules acquire large net positive charges, non-specific tion is obtained which, for p H < pK, reduces to the intermolecular electrostatic repulsion of the Ag and form of equation 0 with, however, a coefficient of Ab molecules might cause dissociation of the bonds two for the p H term. between the twoi7; and (b) as the niolecules beT o test the applicability of this relationship to (17) An approximate theoretical calculation of the magnitude of this the data of Table V, let us first note that where ap- effect may be made by means of the theory of Verwey and O v t r l , t & , ~ ~ preciable dissociation of the cornplexes exists, 1/K brit the validity of the calculation is uncertain. l h e Ag and Ab (5)
+
(16) K fur t h e rractioii A y A, \I, actiuu Ay f .ab
.
+
','"
++
+ &&l b s ( A ~ ) ~ . a b
I & I,,'
of K for the re-
molecules are taken as spheres with a uniform surface charge density surrounded by ion atmospherrs. the spherrs beini: in contact with each other. With this model, a y u a i t i \ r clcctruat.dlc free tnLrdy is pie-
come highly positively charged, intrnmoleculnr repulsive forces may cause reversible configurational changes in either or both the Ag and Ab molecules, such t h a t the complementariness of the reactive sites is diminished and dissociation occurs. l9 That non-specific intermolecular electrostatic forces are not of primary significance under the conditions of our experiments is indicated by several facts. (a) There is no gross effect on the Ag-Ab reaction as the pH is lowered from 8.6 to values between the isoelectric points of Ag and Ab, where the molecules are now oppositely charged (Table I). (b) We expect the electrostatic forces to be proportional to the product of the surface charge densities of the Ag and Ab molecules, and in turn to the product of their electrophoretic mobilities under given conditions. Yet this mobility product has about the same value in this system a t pH -1.0 or pH 8.0 (Fig. 3). Therefore if the extensive dissociation a t
.
,
r
a
C
e
b
d
f
Fig. 7.--Ttie effTcct of ioiiic strength 011 the ulti-:icviitrifugc patterns of Ag-Ab solutions; solutioii V ill phosphate biiffers, (a) pH 7.50, r/2 O.l!); (b) p1-I 7.50, r/2 0.001; solu-
tion 11. in acetate buffers, (c) pH 5.38, r/2 1.0 (coiitainiiig 0.9JI SaS1); (d) pH 5.46, r/2 0.01; solution V iti lactate buffers; (e) pH 4.02, I’/2 0.10; ( f ) pH 4.03; r/2 0.001. Seditneiitatioii proceeds to the left in all patterns. ~
_._
dicted which is large enough t o cause dlssociation of t h e Ag-Ab bonds in t h e acid $13 range. This cannot be correct, however, since t h e theory would li!
