The Effect of Ph and Ionic Strength on the Reaction Between Anti-D and Erythrocytes

Immunology, 1964, 7, 72. The Effect of pH and Ionic Strength on the Reaction between Anti-D and Erythrocytes

N. C. HUGHES-JONES, BRIGITTE GARDNER AND RACHEL TELFORD

Medical Research Council's Experimental Haematology Research Unit, Wright-Fleming Institute, St. Mary's Hospital, London, W.2

(Received 10th June 1963)

Summary. The effect of pH and ionic strength on the reaction between anti-D and erythrocytes was investigated using 131I-labelled antibody. The following observations were made. 1. The association constant of the reaction was influenced by the pH of the suspending medium. The highest values were obtained in the pH range 60-8&0. The association constant was considerably reduced above and below these values. 2. There was considerable heterogeneity of the rate of dissociation of the antigen-antibody complex at pH values below 6-0 3. The antibody was separated into fractions which, at neutral pH, had different rate constants for dissociation. 4. The rate ofassociation between anti-D and erythrocytes was greatly increased by a reduction in the ionic strength of the suspending medium.

INTRODUCTION The reaction between antibody and antigen can be interpreted in terms of the law of mass action (for review see Talmage and Cann, 1961). This not only applies to reactions between antibody and haptens or protein antigens, but also to antibodies against the blood group antigens, A, B, c and D (Mavrides, 1954; Wurmser and Filitti-Wurmser, 1957; Hughes-Jones, Gardner and Telford, 1962, 1963). Both hydrogen ion concentration and ionic strength of the medium influence the reaction. For instance, Singer and Camp- bell (1955) found that the binding constant for a rabbit anti-albumin antibody system diminished over the pH range 4*5-2-4, and concluded that one carboxyl group was involved in the reaction. Similarly, Epstein and Singer (1958) found a reduction in the binding constant for anti-benzenearsonic acid antibody over the pH range 8-2-10-6, and concluded that one amino group was involved in the reaction. The effect of salt concentration on the rate of association between antigen and antibody was first described byJerne and Skovsted (1953), who found that the rate ofneutralization of bacteriophage was increased 1000-fold when the salt concentration was reduced from 1-0 M to 0-001 M. Cann and Clark (1956) and Tsuji, Davis and Gindler (1962) also found that a reduction in salt concentration increased the rate of association of an anti-bacteriophage and anti-luciferase antibody respectively. Both groups have interpreted this effect as due to the interaction of oppositely charged ionic groups at the combining sites. 72 Reaction between Anti-D and Erythrocytes 73 We have recently described the production and purification of 131I-labelled anti-D (Hughes-Jones, Gardner and Telford, 1963). We have now studied the effect of hydrogen ion and salt concentration on the reaction between 131I-labelled anti-D and erythrocytes. METHODS Red Cells Rh-positive group 0 red cells of probable genotype CCDee (R1Rl) were used throughout. When necessary, Rh-negative control cells of the genotype ccddee were also used. Antibody The anti-D used was obtained from the same donor as that described as serum Av in a previous publication (Hughes-Jones et al., 1963). The labelling with 131I and the purification took place in three stages. Stage 1. Four ml. of serum (titre 1000) was added to 100 mg. of freeze-dried haemoglobin-free RR' red cell stroma at 370 for 30 minutes. The stroma was then washed three times with saline (0.17 M NaCi, 0 003 M NaH2PO4-Na2HPO4, pH 6.7) at 20 and the antibody dissociated at pH 3-5, into 5 ml. ofsaline containing 10 mg. of y-globulin at 200. This y-globulin solution was prepared by using 6-9-diamino-2-ethoxyacridine (Horiejsi and Smetana, 1956); this preparation also contains p,-globulin as impurity. Stage 2. The y-globulin solution containing the antibody was iodinated by the method of McFarlane (1958). Unbound l31J was removed by passage through an anion exchange column (Amberlite 401; Cl) followed by dialysis for 16 hours against saline. Stage 3. Purification was carried out in the sense that 131I-labelled antibody was freed from other l3lI-labelled compounds. This was achieved as follows. Two ml. ofconcentrated serum protein (30 per cent w/v) were added to the 131I-labelled y-globulin solution containing anti-D and mixed with 2 ml. ofR1R1 red cells for 30 minutes at 370. The cells were then washed eight times at 20, using for each wash 10 volumes of saline containing serum protein, 1 g. per 100 ml. Lysis of the cells was achieved by freezing at 790 and the haemoglobin removed from the stroma by washing with saline at 20 (usually two washes). The antibody was then dissociated at pH 3-5 at 200 into 5 ml. ofa 1 in 5 dilution ofhuman serum in saline. Specific Activity of 131I-Labelled Antibody It was assumed that the specific activity of the antibody was the same as that of the 7S y-globulin fraction. The method used was the same as that previously described (Hughes-Jones et al., 1962) except that y-globulin was obtained by fractionation of the impure l3ll-labelled y-globulin on a diethylaminoethyl cellulose column, using the method described by Adinolfi, Polley, Hunter and Mollison (1962). Calculations The concentrations ofreactants, equilibrium constants and rate constants for association and dissociation were calculated as previously described (Hughes-Jones et al., 1962, 1963). The Effect ofpH on the Equilibrium Constant The concentration of the l3lI-labelled anti-D and the volume of red cells were adjusted so that approximately half the antibody was bound at equilibrium. The required pH was 74 4N. C. Hughes-Jones, Brigitte Gardner and Rachel Telford obtained by addition of0-1 N HC1 or 0-1 N NaOH and the system brought into equilibrium by incubation at 370 for 2 hours. Initial experiments had shown that equilibrium was reached during this time. When lysis occurred, stroma was separated from the supernatant by centrifuging at 10,000 g. The Effect ofpH on the Rate of Dissociation of Antigen-Antibody Complex Measurement of the rate of dissociation of antigen-antibody complex (approximately 4-0 PmM.) was carried out at 370 at various pH values, using serum protein (2 g. per 100 ml.) as a buffer. Red cell stroma was used for experiments at pH values below 7 0 and dissociation was stopped by rapid freezing; the suspensions were allowed to thaw while centrifuging at 10,000 g. Whole red cells were used at pH values above 7 0, the reaction being stopped by centrifuging at 3000 g. The pH of suspension did not fall by more than 0-2 units during the experiments. The Dissociation of Antibody from a Stroma-Celite Column at Acid pH Values Three ml. of red cells which had taken up 2-5 x 10-10 moles of antibody were lysed by freezing at -79° and the stroma washed twice at 20 with saline. The stroma was then added to 0-8 g. of diatomaceous earth (celite, 512) and packed in a column 1 cm. in diameter. Dissociation of the complex was carried out at 40 using a solution of serum protein (2 g. per 100 ml.) as eluant. The pH value ofeach succeeding 9 ml. ofeluant was decreased by 0-2 pH units. The rate offlow was 3 ml./min. The eluate was collected in 3 ml. aliquots and the 1311 content and the pH value of each was estimated. The pH of the eluate was then adjusted to 6-7 and the antibody from selected eluates was recombined with 20 mg. of dry red cell stroma (95 per cent uptake was obtained in each case). The antibody-stroma complex was then used for further dissociation at acid pH values under similar conditions. Other antibody-containing fractions obtained in a similar manner by dissociation at acid pH values were also recombined with red cells and the rate of dissociation then determined at 370, pH 6-7, in the manner previously described (Hughes-Jones et al., 1963). Excess unlabelled antibody was added to prevent reassociation of the 131I-labelled antibody. The Relationship between Ionic Strength and the Rates of Association and Dissociation 131I-labelled anti-D solutions at pH 6-7 were diluted with a solution of glucose (7 g. per 100 ml.) to give final ionic strengths ranging from 0 037 to 0 17 L Ionic strengths below 0*037 I were obtained by gel filtration (Sephadex G 25). The solutions were then left for 1 hour at 4°. Precipitated protein was removed by centrifuging at 10,000 g. The final concentration of antibody in each solution was approximately 1-3 jimM. Each solution was then added to red cells at 4°. The volume of red cells used was predetermined to give a rate of formation of antigen-antibody complex that could conveniently be estimated. The amount of antibody combined with red cells at 5, 10, 20, 40 and 60 minutes was determined, the cells being separated by centrifuging. Correction was made for non- specific uptake of 131I, using Rh-negative control cells. The ionic strength of the 5 minute samples was estimated using a conductivity meter, and this value used in presenting the results. The amount of antigen-antibody complex formed was plotted against time, and the rate constant for association calculated from the initial slope of the curve. Reaction between Anti-D and Erythrocytes 75 The rate of dissociation of the antigen-antibody complex was estimated by allowing the complex to dissociate at 370 in solutions of ionic strength ranging from 003 to 017 I in the presence of excess unlabelled antibody. The osmolarity of the solutions was main- tained with glucose.

RESULTS THE EFFECT OF pH ON THE EQUILIBRIUM CONSTANT The relationship between the logarithm of the apparent equilibrium constant and the pH value of the solution is given in Fig. 1.

64 6 8 10 pH FIG. 1. The relationship between the apparent equilibrium constant, Ka, and the pH of the suspension for the reaction between anti-D and erythrocytes. Each point represents the result of a single deter- mination of the equilibrium constant.

THE EFFECT OF pH ON THE RATE OF DISSOCIATION OF ANTIGEN-ANTIBODY COMPLEX AT 370 The effect ofpH on the rate ofdissociation ofthe antibody was investigated by suspending erythrocytes or stroma combined with l3KI-labelled anti-D in solutions at pH values ranging from 4-5 to 10-6 and measuring the amount of antibody remaining bound after 5, 10, 60 and 150 minutes. The results are shown in Fig. 2. It can be seen that the rate of dissociation progressively increases as the pH departs further from neutrality. The concentration of antigen-antibody complex plotted against time would be expected to be curvilinear as reassociation of free antibody takes place until eventually equilibrium conditions are reached. If the assumption is made that the antibody is homogeneous with respect to the rate of dissociation at acid and alkaline pH values, then the expected shape of these dissociation curves can be calculated, using various values for the rate constant for dissociation (Hughes-Jones et al., 1962). It was found that the shape of the observed curves differed considerably from the shape of the theoretical curves. This difference indicates that the basic assumption of homogeneity was incorrect, and that there was considerable heterogeneity of the rate constant for dissociation under these conditions. 76 6N. C. Hughes-Jones, Brigitte Gardner and Rachel Telford 100 pH 6.0 pH 8.5 pH 517 50 pH 9-1 pH 5'3 x Go DISSOCIATIONpH 9.7 0 U .0 pH 10 9.9 pH50

pH 4*5 pHi 10*6

4 p _ _ _ _ _ 0 150 015 Time (minutes) FIG. 2. The rate of dissociation of the antigen-antibody complex at 370 over the pH range 4-5-10-6. The first observations were made at 5 minutes.

DISSOCIATION OF ANTIBODY FROM A STROMA-CELITE COLUMN AT ACID pH VALUES A further investigation was carried out to determine whether the heterogeneity in the rate of dissociation of the complex at acid pH values could be explained at least in part by heterogeneity of the antibody molecules, in that some antibody molecules form antigen-antibody complexes which dissociate more rapidly than others at any given pH. Antibody bound to red cell stroma was mixed with diatomaceous earth (celite) and placed in a column. Antibody was dissociated from this column by a progressive stepwise increase in the hydrogen ion concentration of the eluant. Four of the eluted antibody fractions were then recombined with red cell stroma and redissociated at acid pH values in an identical manner. The results are shown in Fig. 3. As antigen-antibody complexes dissociate at neutral pH, it is clearly not possible to obtain discreet antibody fractions which only dissociate at one particular pH value. Thus fraction 1 (obtained initially at pH 4.9-5.4) was found to be composed of two separate antibody populations: 20 per cent ofthe total antibody in this fraction dissociated a second time over the same pH range as on the original occasion (population A); the remaining 80 per cent dissociated over the pH range 30-4 5 (population B). This division of fraction 1 into two populations was confirmed in further experiments. It is probable that population A consisted of those antibody molecules which dissociated rapidly in the region of pH 5.0, and population B was composed of antibody whose rate of dissociation was not specifically affected at this pH value. Similarly, the antibody in fractions 2, 3 and 4 was not sharply delineated on the second fractionation. Nevertheless, the antibody in fractions 3 and 4, which was obtained initially at average pH values of 3f3 and 3 0, showed peaks at these same values on the second fractionation. It can be seen that there is a difference of 2 pH units between the Reaction between Anti-D and Erythrocytes 77 peak of population A in fraction 1 and the peak of the antibody in fraction 4. The differences are sufficiently marked to show that antigen-antibody complexes are heterogeneous with respect to the rate of dissociation with increasing hydrogen ion concentration, and that this heterogeneity is at least in part determined by differences between antibody molecules. 0.25[ Al . Fraction 4

0i3 . Fraction 3

0l Al Fraction 2

Fraction 1 c 0r3 * ~ ~ ~~~~B

8 0 8~~0r 1 ~ ~2 1 O3riginal4 antibody CL m11 '"1 1ii1111llE,lk 6-- - 3 2 pH of eluate FIG. 3. Dissociation of anti-D from a stroma-celite column at acid pH values, 40. Dissociation of the antigen-antibody complex was brought about by a progressive lowering of the pH value of the eluant. Fractions 1-4 from the original dissociation were then recombined with fresh stroma and again dissociated under identical conditions. For explanation of populations A and B in fraction 1, see text. Ordinate: percentage oftotal antibody combined with the stroma for the original dissociation. Volume of each eluate: 3 ml. Rate of flow: 3 ml./min.

THE RATE OF DISSOCIATION OF ANTIBODY OBTAINED BY FRACTIONATION AT ACID pH VALUES The complex formed by anti-D and Rh positive red cells has been shown previously to be heterogeneous in its rate of dissociation at pH 6-7 (Hughes-Jones et al., 1963). It was possible that the fraction of the antibody which dissociated at a relatively low hydrogen ion concentration (i.e. pH 5.0) was that which also dissociated rapidly at pH 6-7. This was investigated as follows. Estimates were made ofthe rate ofdissociation ofthree ofthe antibody fractions obtained by acid elution from the stroma-celite column. The antibodies fractions chosen were those eluting at pH 5 0, 3-8 and 2-4. The results are shown in Fig. 4. It has already been shown (Fig. 3) that the fraction obtained by elution at pH 5.0 was composed of at least two different populations of antibody. Further separation of these two populations was 78 7N. C. Hughes-Jones, Brigitte Gardner and Rachel Telford achieved by combining the whole fraction again with red cell stroma and then eluting the antibody a second time at pH 5*0. The rate of dissociation at pH 6-7 of the fraction obtained a second time at pH 5 0 is shown in Fig. 4 as curve B.

100

~280

IV E24 1100 60 .0 C

C <40

0 300 600 Time (minutes) FIG. 4. The rate of dissociation at pH 6X7, 370, of four fractions of antibody obtained by dissociation from the stroma-celite column at pH 5-0, 3-8 and 2 4. The fraction labelled 'pH 5-0 B' was dissociated twice from the stroma-celite column and thus was a more homogeneous preparation than fraction 'pH 5 0 A', which was only dissociated once. Excess unlabelled anti-D was added to prevent reassociation of 131I-labelled anti-D. It can be seen that the antibody which is the first to dissociate as the hydrogen ion concentration is increased also has the highest rate ofdissociation at pH 6*7. Each antibody fraction is, however, still heterogeneous with respect to the rate ofdissociation, as is shown by the non-linearity of the curves. The minimum range of the rate constants calculated from the slope of the curves was 12 x 10-5 to 50 x 10-5 sec.-1. The evidence does not allow one to decide whether the serum was composed of a mixture of several populations of antibody, each population possessing a different rate constant for dissociation, or whether there was a continuous distribution of rate constants throughout the antibody population.

THE RELATIONSHIP BETWEEN IONIC STRENGTH AND THE RATES OF ASSOCIATION AND DISSOCIATION The relationship between the logarithm of the rate constant for association and the square root of the ionic strength of the medium is shown in Fig. 5. The results have been plotted in this manner on the assumption that there is an interaction between ionized groups on antibody and antigen and thus that they can be analysed in terms of the Bronsted theory of the influence of an ionic environment on the rate of association of electrically charged solutes (Moelwyn-Hughes, 1947). According to this derivation, the relationship between the rate constant for association, k1 and the ionic strength I, is given by logioki = logioko+ZgbAb1Ag1Il Reaction between Anti-D and Erythrocytes 79 where ko is the rate constant for association at zero ionic strength, and ZAb and ZAg represents the charge on the reacting molecules. The value of ZAbZAg is given by the slope of the curve, namely -14, suggesting that there may be between three and four pairs of ionic groups concerned in the reaction. The negative sign indicates that the ionic groups concerned are oppositely charged. The effect of a reduction of ionic strength was thus pronounced; there was a 1000-fold increase in the rate of association for a reduction in ionic strength from 0- 17 I to 0-03 I. The rate of association reached a maximum at an ionic strength of 0*03 L

-5

0 01 0-2 0-3 0*4 0-5 A(ionic strength) FIG. 5. The relationship between the logarithm of the rate constant for association at 40, ki, and the square root of the ionic strength of the suspending medium.

The effect of the ionic strength on the initial rate of dissociation was also investigated. It was found that a reduction of the ionic strength brought about a slowing of the rate of dissociation, but the effect was only small. Thus the rate constant for dissociation fell from 8 x 10-5 to 2-5 x 10-5 sec.-1 when the ionic strength was reduced from 0 17 I to 0 03 L DISCUSSION The results of the experiments on the rate of dissociation of the antigen-antibody complex at acid and alkaline pH values (Figs. 2 and 3) have shown that there is considerable heterogeneity in the response of the complex under these conditions. Heterogeneity of the rate of dissociation implies heterogeneity of the equilibrium constant; hence the calculation of the apparent equilibrium constant at various pH values (Fig. 1) is a simpli- fication, and the calculated values give only an order of magnitude. Because of this heterogeneity it is not possible to analyse the results shown in Fig. 1 by the method advocated by Singer and Campbell (1955) and Epstein and Singer (1958); their analysis was based on the supposition that the reactions between hydrogen ions, antigen and antibody could be represented by single values of the equilibrium constants. Hughes-Jones et al. (1963) have shown that there was heterogeniety of the rate of dissociation at pH 6-7 of three samples of anti-D; the heterogeneity of the rate of dissociation could have been the result of heterogeneity of either the antibody or antigen or of both. The separation of antibody at acid pH values into fractions which form complexes 80 N. C. Hughes-Jones, Brigitte Gardner and Rachel Telford with differing rates of dissociation at pH 6-7 show that one of the factors concerned is heterogeneity of the antibody. The initial rate of association of antibody and red cells was found to increase approximately 1000-fold on reducing the ionic strength of the medium from 0417 I to 0 03 L Cann and Clark (1956) found heterogeneity of an anti-bacteriophage antibody in its response to a reduction of ionic strength. Only the initial rate of association was determined in the experiments described here, and the question of heterogeneity was not investigated. These observations presented here appear to conform to the requirements of Bronsted's theory ofthe effect ofionic strength on the rate of reaction between electrically charged molecules (Fig. 5). This theory states that the logarithm of the rate constant for association is a linear function ofthe square root ofthe ionic strength ofthe medium. This conformity to Bronsted's theory could be used in support of the postulate that oppositely charged ionic groups are involved in the reaction. We have insufficient data concerning the isoelectric point ofthe antibody to be able to make any further deductions concerning the question as to whether it is the net charge on the reactants which determines the rate of reaction or whether the ionized groups concerned are at, or close to, the combining sites. An alternative explanation ofthe effect ofionic strength is that under normal conditions access to the combining sites on either one or both reactants is difficult owing to the spatial configuration of the surrounding surface and that lowering of the ionic strength alters this configuration, making the combining sites easier of access. Below an ionic strength of0 03 I, there was no further increase ofthe rate ofassociation, the maximum value of ki being approximately 1 x 107 1. mole -1 . sec. -1 at 4°. It is probable that this is the maximum rate that is obtainable. The maximum rate of reaction will occur when each collision between the combining sites results in union, the rate-controlling process being that of diffusion of the reactants. Using the gas collision formula, it has been previously calculated that the maximum theoretical rate of association is of the order of 1 x 108 1. mole-1 . sec. -1 (Hughes-Jones et al., 1963). This value makes no allowance for the correct spatial orientation between colliding combining sites and is probably an overestimate; the maximum observed rate thus approaches within a factor of 10 of the theoretical maximum. Lowering of the ionic strength caused only a small reduction in the rate of dissociation of the complex. It is possible that this result is at least in part due to an artefact, namely that some of the dissociated antibody molecules may have become insoluble at the low ionic strengths and thus have been centrifuged down with the red cells.

REFERENCES ADINOLFI, M., POLLEY, M. J., HUNTER, D. A. and HokEjsI, J. and SMETANA, R. (1956). 'Isolation of MOLLISON, P. L. (1962). 'Classification of blood- gamma globulin from blood-serum by rivanol.' group antibodies as P2M or gamma globulin.' Acta med. scand., 155, 65. Immunology, 5, 566. HUGHES-JONES, N. C., GARDNER, B. and TELFORD, R. CANN, J. R. and CLARK, E. W. (1956). 'Kinetics of (1962). 'The kinetics of the reaction between the the antigen-antibody reaction. Effect of salt con- blood-group antibody anti-c and erythrocytes.' centration and pH on the rate of neutralization of Biochem. j., 85, 466. bacteriophage by purified fractions of specific HUGHES-JONES, N. C., GARDNER, B. and TELFORD, R. antiserum.'J. Amer. chem. Soc., 78, 3627. (1963). 'Studies on the reaction between the blood EPSTEIN, S. I. and SINGER, S. J. (1958). 'Physical- group antibody anti-D and erythrocytes.' Biochem. chemical studies of soluble antigen-antibody com- j., 88, 435. plexes. IX. The influence of pH on the association JERNE, N. K. and SKOVSTED, L. (1953) .'The rate ofinacti- of a divalent hapten and antibody.' J. Amer. chem. vation of bacteriophage T4R in specific anti-serum. Soc., 80, 1274. I. Salt effect. II. Cofactor.' Ann. Inst. Pasteur, 84, 73. Reaction between Anti-D and Erythrocytes 81 MAVRIDES, S. (1954). 'Etude quantitative de l'iso- bovine serum albumin and its rabbit antibodies.' hemagglutination des hematies du groupe A.' J. J. Amer. chem. Soc., 77, 3499. Chim. Phys., 51, 600. TALMAGE, D. W. and CANN,J. R. (1961). The Chemistry McFARLANE, A. S. (1958). 'Efficient trace-labelling of ofImmunity in Health and Disease. Thomas, Springfield. proteins with iodine.' Nature (Lond.), 182, 53. Tsuji, F. I., DAVIS, D. L. and GINDLER, E. M. (1962). MOELWYN-HUGHES, E. A. (1947). The Kinetics of 'Effect of sodium chloride and pH on the rate of Reactions in Solutions, 2nd edn., p. 96. Clarendon neutralization of cypridina luciferase by specific Press, Oxford. antibody.'3. Immunol., 88, 83. SINGER, S. J. and CAMPBELL, D. H. (1955). 'Physical- WURMSER, R. and FILrrIT-WURMSER, S. (1957). chemical studies of soluble antigen-antibody com- 'Thermodynamic study of the isohaemagglutinins.' plexes. III. Thermodynamics ofthe reaction between Progr. Biophys., 7, 87.