Relative affinity of antisera for myelin basic protein (MBP) and degree of affinity heterogeneity

0161-5R90i79i03014163 fOZ.OO/O

MolecularImmunology, Vol. 16.pp. 163-172. OPergamon PressLtd. 1979. Printedin Great Britain.

RELATIVE AFFINITY OF ANTISERA FOR MYELIN BASIC PROTEIN (MBP) AND DEGREE OF AFFINITY HETEROGENEITY* VINCENT A. VARITEK Department

of Microbiology-Immunology Durham,

and EUGENE

D. DAY

and Surgery, Duke University NC 27710, U.S.A.

(First received 18 April 1978; in revisedform

Medical

Center,

11 June 1978)

Abstract-A method based essentially on that of Steward and Petty (1972) was used to evaluate the relative binding affiinities of several syngeneic Lewis-rat antisera to myelin basic protein (MBP)t. The syngeneic immune reactions to this ‘self antigen were found to contain only populations of relatively high affinity antibodies, ranging from a K,, of 7 x 10’ to 2.6 x lOa M- * when measured at 100 nM MBP; and from 4 x lo8 to 9 x 109M- 1at 1 nM. The biphasic nature of the plots of antigen binding capacity (ABC) vs log MBP concentration suggested that MBP binding was usually distributed among two or more major discontinuous antibody populations. Advantage was taken of the dual-dilution phenomenon to obtain constants interpreted as degrees of relative affinity heterogeneity of syngeneic antisera. It was found that the dualdilution phenomenon (the decrease of ABC with increasing antigen P dilution) could be expressed mathematically in the form of a power curve

ABC = bP' -” with b (the intercept at 1 nM P) related to the total number of antibody molecules in the system and c(, the degree of affinity heterogeneity of antibodies against the multideterminant antigen. The more heterogeneous the system the higher the number of antibody molecules required to maintain a constant ABC at a given P and the more rapid the decrease of ABC with decreasing P. The degree of affinity heterogeneity of the syngeneic Lewis rat antisera ranged from pronounced (*. = 0.14) to moderately restricted (r = 0.8). The heterogeneity index of a rabbit anti-MBP serum was 0.821. An antiserum refractory to the dual-dilution effect was also found for which r was 0.98.

INTRODUCTION

Affinity is “a pivotal element in the biological activity of the antibody molecule” (Karush, 1970); thus, the capacity of antibody as a regulator of immune processes and its efficiency with respect to target localization is in large part dependent upon the strength (and intrinsic reversibility) of its interaction with a given antigenic determinant. It follows that affinity must play an important role in the immunopathology of reactions against self, and that knowledge of relative affinities and degrees of affinity heterogeneity would help in the understanding of these autoimmune processes. Unfortunately, the sophisticated approaches used to delineate affinity constants and degrees of affinity restriction by unambiguous unitary reactions between isolated *Work supported by Research Grant No. 833-D-4 from the National Multiple Sclerosis Society and U.S. Public Health Service Research Grant NS 10237 from the National Institutes of Health. t Abbreviations used: ABC, antigenic binding capacity; HSA, human serum albumin; MBP, myelin basic protein; MBP-(L,S)-rat, myelin basic protein of the rat containing both 18,000-dalton (L) and 14,000-dalton (S) forms; MBP-Lrat, 18,000-dalton form; MBP-S-Rat, 14,000-dalton form; MBP-SF, serum factor that inhibits the reaction of MBP with anti-MBP; ng, nanogram; nM, 10e9 molar or nanomolar; pg, picogram; PBS, phosphate-buffered saline, pH 7.4; EAE, experimental allergic encephalomyelitis.

and single determinants antibody populations (Reichlin, 1975) have not yet been successful in the case of MBP-anti-MBP systems (Wallace et al., 1978). Thus, we have turned to the method of Steward and Petty (1972) to gain some insight into the range of affinities that might be expected in syngeneic Lewis rat MBP-anti-MBP systems, and to the dual-dilution phenomenon to examine the extent of affinity heterogeneity. Relative afJinities

The method of Steward and Petty (1972) involves the measurement of the relative association constants of unselected and unpurified anti-protein antibodies in whole antisera, in essence “the summation of the reactions between a heterogeneous antigen and a heterogeneous antibody population”. The authors point out that although the affinity constants are not identical to determinations using purified heterogeneous antibody to single haptenic antigens they are, nevertheless, similar and can be used to make valid comparisons of K, among different antisera to the same protein antigen. The method has been successfully used in a number of their studies on the genetic control of affinity (Soothill & Steward, 1971; Petty et al., 1972; Petty & Steward, 1972; Katz & Steward, 1975; Steward et al., 1975; Steward & Petty, 1976), and has also formed the basis of affinity studies by Arend and Mannik (1974) and the computerelicited mathematical models of immune complex 163

VINCENT

164

A. VARITEK

interaction by Steensgaard et al. (1977). The concept has been applied to this study to determine affinity constants for whole syngeneic antisera to highly purified myelin basic protein that form in response to an EAE-inducing regimen. In essence, the Steward-Petty approach derives average affinity constants in terms of the concentrations of free antigen and immune complex such as might be distinguished in a Farr-type radioimmunoassay. In a fashion parallel to the usual unitary method, an experimental point is obtained in antigen excess where the number of bound antigen molecules, b, equals half that of the number of antibody binding sites, Ab,, added to the system. At this point the average affinity constant, K,, is taken as the reciprocal of the free antigen concentration, [Ag], i.e. when p=

b

and EUGENE

D. DAY

The approach taken by Stewart and Petty (1972) and also by Arend and Mannik (1974) was to hold antibody constant, to vary antigen concentrations and to obtain an effective Ab, by extrapolation of reciprocal plots of l/b vs l/c to l/c = 0 or of Sips plots of log (h/Ah,-h) vs log (’ to log c = 0. In the approach taken here antigen is held constant, antibody is varied, and Ab, is obtained in the form of a molar antigenic binding capacity (ABC) expressed in the manner of Farr (1958, 1971). (That the two approaches are equivalent is shown in Appendix B where the extensive binding data of Arend and Mannik (1974) are converted into the ABC form.) Letting b = qP, Ab, = ABC, q = 0.1, and P = c, one can then derive relative affinity constants from ABC* values: 0.1 ( ABC-O.1

1,

-=l c

Ab,-b I(0=!=o_2Z (’ ABC

1 &=[Agl. As shown by the Otterness derivation of the Steward-Petty approximation (Appendix A) an svalent multivalent protein, P(G in the Otterness notation), can be related to the free antigen concentration c by c E (1 -q)i’“P,

(1 -q)“”

Z 1 -(q/s),

1 -(q/s)

z 1.

where the fraction of bound antigen in a multivalent system is kept reasonably small, e.g. at q = 0.1, the free antigen concentration c can be approximated by the total antigen concentration P. The approximation holds only in large antigen excess and depends on two assumptions: (a) the requirement that each determinant in a multivalent protein antigen is unique and present only once per antigen molecule and (b) Goldberg’s assumption (1952) that the probability that a given determinant remains unreacted with its antibody is the same as the probability for any other determinant. The first requirement would appear to be met in the case of MBP, a single small protein chain of known amino acid sequence without repeating segments (Dunkley & Carnegie, 1974). The Goldberg assumption, since it applies to multivalent antigen-antibody systems in general, would necessarily include the MBP-antiMBP system in particular. In a similar way, essentially the same assumptions were also needed by Berzofsky et al. (1976) to effect a probability analysis of antibody reactions with the /? chain of hemoglobin S. Thus,

*The ABC for affinity calculations should reflect the dilution brought about by the total volume of the antigen-antibody mixture in which it is evaluated, e.g. l/100 or 1% as in these experiments. ABC ~ 10, D,is used to indicate that the end-point-is 10% or l”/, as in ‘fhese experiments, ABC-lo., is used to indicate that the end-point is lo?/:, binding anzthat the affinity evaluation is made it the level of one part antiserum in a hundred of the total mixture.

Arend and Mannik (1974) studied a wide range of antigen excess (5-500 times) in an HSA-anti-HSA system in order to determine a suitable region from which to determine association constants by the method of Steward and Petty (1972) and found that since a plateau was reached beyond 60 times excess, the range 5-60 times was most useful for their affinity determinations. As shown in Appendix B this translates to an ABC evaluated between 4 and 40% binding, a very reproducible linear stretch with a high correlation coefficient. The dual-dilution

phenomenon

In their analyses Arend and Mannik (1974) encountered the ‘dual-dilution effect’ which had an influence upon their affinity determinations: “With a ten-fold increase in antibodies, the amounts of antigen in the binding studies were correspondingly increased IO-fold to maintain the same range of antigen excess. But the calculated association constant decreased by a factor of 10.” Thus. with 10 leg antibody K, = 2.2 x 10’ M-’ whereas with 105 pg antibody in the same range of antigen excess K, = 2.8 x lo6 JK’. A number of investigators had already observed and commented upon the increasing disparity that occurs between the dilution patterns of antigen and antibody with increasing antigen dilution when a fixed percentage of antigen binding is made the object (Farr, 1958, 1971; Brownstone et al., 1966; Hudson, 1968; Osler, 1971; Feldman et al., 1972). When they tried to maintain the same ratios of added ingredients in increasingly dilute systems (i.e. the dilution patterns of antigen and antibody were the same), the ABC of the antiserum diminished with increasing dilution. This ‘dual-dilution effect’ caused Farr (197 1) to qualify his ABC values not only by the end-point but also by the amount of antigen used in order to specify what degree of ‘avidity’ might be expected. According to Farr the higher the total antigen concentration the larger the ‘nonavid’ antibody in proportion of the antigen-antibody complexes. Indeed, Osler (1971) showed that in order to circumvent the dilution problem and to gain an accurate quantitative estimate “that would register all antibody molecules, regardless

Affinity

of Antibodies

for Myelin Basic Protein

of their aggregating capabilities” one should turn to the simple stratagem of keeping antibody and labeled antigen constant and increasing unlabeled antigen until, extremely far into the region of antigen excess, a constant ratio of bound antigen to bound antibody would be approached. Even though the dual-dilution phenomenon had been viewed as real, no attempt had been made to give it a mathematical expression. In these experiments use of the dilution effect was required to probe the degree of heterogeneity of affinity displayed by a particular antiserum; therefore, a general equation for the phenomenon was sought. It had already been determined in the case of one MBP-anti-MBP combination that a standard binding curve had the form of a power curve (Fig. 2 of Day et al., 1978~). At a constant level of 1% reagent syngeneic anti-MBP antiserum, the ng MBP bound (y) was related to the ng of MBP added (x) by: y = 4.785

X0.6”

with a correlation coefficient of 0.982. In terms of 1% n&f, ABC at 10% binding of different nM concentrations of added antigen (MBP) the power equation retained the same exponent while bearing a different coefficient: ABC- IO,._ = 3.82 MBP0.617.

165

(MBP)

by heterogeneity of antibody binding sites; and as Reichlin (1975) said in his review, “It has long been known that at least part of the heterogeneity of antiprotein sera reflected antibodies to a multiplicity of independent determinants.” In fact, since antibodies to distinct protein determinants “have thus far exhibited restriction in heterogeneity” (Reichlin, 1975), it would appear that a high degree of heterogeneity found for any given anti-MBP antiserum would most likely reflect a number of distinct MBP determinants involved, each with its own population of relatively restricted antibody, rather than an unrestricted population of antibodies against a single determinant. as

MATERIALS

AND

METHODS

Myelin basic protein (MOP) The larger 18,000-dalton myelin basic protein of Lewis rat central nervous system tissue (MBP-L-Rat) was prepared in highly purified form by methods previously described (Day et ef al., 1976a) for use in the a(., 1978a; Pitts radioimmunoassays. A highly purified natural mixture (MBP-LS-Rat) of both the 18,000-dalton and the smaller 14,000-dalton MBP was used for rat immunizations. MBP-SRat is identical to the larger chain except for a 40-aminoacid internal deletion (Dunkley & Carnegie, 1974). Anti-MBP antisera

Since an increased restriction in heterogeneity would lead to a diminished effect of dual-dilution upon ABC, the binding equation was written to give its exponent the same direction as a unitary heterogeneity constant. In other words, since ABC would be constant at PO(a point where the heterogeneity constant, a, of a unitary reaction would equal 1, the equation was transformed to read: ABC- lo,, = 3.82 MPB’1-0.3s3’. ” In the same way, the data for the heterogeneous HSA-anti-HSA system studied by Brownstone et al. (1966), (cf. Appendix C), was found to generate a similar binding equation: ABC - lo,, = 3.99 HSA” - o.542). 0 With P indicating the nM concentration of added antigen and LYindicating the degree of antibody heterogeneity to a multideterminant antigen, the general equation was recognized as: ABC,, = bl” -=

log ABC,,0 = log b+(l -a) log

P.

It must be emphasized that just as the affinity constant of Steward and Petty (1972) should not be misconstrued as identical to an affinity constant of a heterogeneous antibody for a homogeneous univalent ligand, neither should this heterogeneity constant be misconstrued as necessarily equivalent to heterogeneity affinity of antibody reactions to single determinants. As Brownstone et al. (1966) pointed out there may be as much contribution to heterogeneity by different degrees of exrjosure of protein determinants

The rabbit-anti-MBP-L-Rat immunoglobulin (E-24) has been described (Day et al., 1978a). It was a highly purified void volume IgG pseudoglobulin fraction that by quantitative precipitin analysis contained 93 pmoies antiMBP antibody per mg (based on an antibody mol. wt of 150,000 daltons). The syngeneic anti-MBP-LS-Rat antisera were raised in Lewis rats in the same manner as described previously (Pitts et al., 19766; Day et al., 1978a) by food-pad injections of 50 pg MBP and 500 pg Mycobacterium butyricum in Freund’s complete adjuvant and by simultaneous intraperitoneal injections of 6.4 x IO9 organism equivalents of B. pertussis. The pooled reagent antisera were collected at 28 days after immunization of 5 Lewis rats per pool. The individual antisera were collected as described in the text. Radioiodination of MBP MBP was labeled with lZsI and enough non-radioactive carrier iodide to obtain an average of 2.8 nCi/ng and 1.2 iodine atoms/18,000 daltons. The KI-nitrite iodination procedure (Day et al., 1967) as applied to MBP (Day & Pit&, 1974~; Day ef al., 1978a) was used. The experiments reported here utilized 3 different batches of lZSI-MBP-L-Rat prepared at about 4-month intervals. The labeled proteins were measured for protein content (E&,,, = 5.9) and specific radioactivity after exhaustive dialysis. and were then diluted with phosphate-buffered saline (pH 7.2) to the level of 10 ng/$ and stored frozen in 5CO-~clportions. Radioimmunoassays The sodium sulfate method of salting out (Day & Pitts, 1974a) was used to separate antibody-bound lz51-MBP complexes from unbound antigen. Volumes of the reaction mixture were maintained exactly at 100 ~1 and were made to contain uniform amounts of 50% normal rabbit serum. Dilutions of *Z51-MBP-L-Rat were made with ice-cold PBS; those of antibody, with ice-cold normal rabbit serum. Antigens at the desired dilutions were added in 50-p] vol to 5O+l vol of diluted antisera. Reaction mixtures were kept in covered tubes at 0°C for 18 hr (except when otherwise indicated); were then warmed to ambient room temperature

166

VINCENT

A. VARITEK

and EUGENE

D. DAY

+-2

4or

_;~L pl antlserum

added

before the addition of 2 vol (200 11) I .90M Na,SO, (kept at 37,-C): centrifuged at 3O’C for 30 min at 1500 g; and washed x 3 with 300-~1 portions of 1.27 M NA,SO,. The supernatant fluid and 3 washes of each individual assay were transferred directly to Beckman Biovials; the precipitate was dissolved in PBS ond quantitatively transferred to an additional Biovial. The sum of the count rates of supernatant fluid. washes, and precipitate was used to determine the percentage of L*SI-MBPprecipitated and the total amount of protein contained in the assay. Molarity of MBP in the reaction mixtures was calculated on the basis of 1 nM = 18 pg/pl. Each full assay of a given antiserum at a given dilution was made by keeping lz51-MBP constant in a 50-~1 volume while varying the antiserum from O-20 nl and balancing the latter to 50 ~1 with normal rabbit serum. The antigenic binding capacity (ABC) of the antiserum was determined in the manner of Day and Pitts (1974~) by linear regression analysis of multi-point B vs v plots (fraction rzSI-MBP bound vs nl antiserum added/ng ‘2SI-MBP added). An example of how that was done in these experiments is shown for E-24 at two different dual-dilutions of antibody and antigen (Fig. I). The slopes were then recalculated for use in these experiments in nanomolar terms (18. pmoles MBP bound/II whole serum = I nM). assa?;s

iZ’I-MBP solutions were used at up to 8 double-dilutions from an initial concentration of about 65-70 nM (in terms of the reaction mixture volume) and were matched with a similar double-dilution series of a given antiserum. (Two of these are shown for E-24 in Fig. I). Multipoint variable antibody assays of l/2-diluted antiserum were made against 112 *ZSI-MBP, 114 vs l/4. etc. Because of a slight loss due to glass adsorption in the izCI-MBP dilution series in PBS, the antigen dilutions were generally somewhat greater than double(e.g. 1:2.31; 1:5.12: l:ll.73; 1:24.91; l:54.60; 1:111.16; 1:215.44) but their exact composition was known from radioactivity assays, The antiserum double dilutions were very accurately executed, were made with normal rabbit serum to control non-specific effects, and had a very high degree of precision (as checked in the earlier experiments by full recovery of trace amounts of radioactive E-24 in the dilution series). RESULTS

EstabIishment As shown

of equilibrium for rabbit-anti-MBP-rat

immunolglo-

~~~~;;

+

i9q nM

Fig, I. Rabbit E-24 anti-MBP reaction with “SI-MBP-LRat at 2 different dual-dilutions: (0) variable E-24 (600 ng IgC/~tl) with 68.5 nM MBP: (*) variable E-24 (75 ng IgG/pl) with 6.39 nM MBP. Linear regression equations of the plots: (0) la<>= 0.8882 /_II+ 11.99, Y = 0.97; (*) ‘<>= 0.4492 ~1 + 10.99. r = 0.95.

Dual-dilution

I ‘0

~1

+,

‘251~,MkP

Fig. 2. The dual-dilution effect at 30 mm (0) and at 4X hr (*) showing E-24 in its reaction with “II-MBP-L-Rat. Each point is a slope determmed by lmear regression analysis 01 variable antibody and fixed M BP at 9 separate dual-dilutions (as shown for 2 dual-dilutions in Fig. I). The initial concentration of E-24 was I.2 ng IgG:nl. The binding equation of the 48 hr data by linear regression analysis is log = 0.1789 log P- 0.307, with a correlation coefficient ABC , ,u<, of 0.971.

bulin E-24 equilibrium conditions are established in MBP-anti-MBP mixtures in the cold within the l-100 nM range in 48 hr (Fig. 2). For mixtures at the 100 nM level our radioimmunoassay (Day & Pitts, 1974~) calls for only a 30-min incubation at room temperature, a period which routinely gives reproducible results, and even at the 1 nM molar level the half-hour period can be used when very high affinity antibodies are sought (Day et al., 1978a); however, equilbrium conditions are not met in such assays except at levels above 100 nM (Fig. 2). It has been found subsequently that an 18hr period is sufficient to reach equilbrium in IOO-~1 mixtures containing as little as 0.5 nM MBP and that no detectable change in ABC occurs after that time. Stability qf MBP-anti-MBP

complexes at high dilution

It was determined that once MBP-anti-MBP complexes were formed extreme stability was obtained. Thus, complexes formed at 1.56 nM MBP and then diluted to 0.06 nM before salting-out with Table I. Lack of effect of dilution upon antigemc binding capacity (ABC) when made after complex formation nM concentration during complex formation

I .56 I .56 I .56 I .56 I .56 1.56

of antigen“

nM .4BC‘”

after dilution of complex 1.56 0.78 0.53 0.26 0.13 0.064 mean

I50 I58 171 I21 1x0 149 I55

“As determined by specihc activity of ‘z’I-MBP in radioimmunoassay. ’ Antigenic binding capacity of E-24 in terms of original concentration (5 mg/ml), as determined by the multipoint sodium sulfate method of radioimmunoassay.

Affinity

of Antibodies

for Myelin Basic Protein

161

(MBP)

- 1.2 -/ -1

+1 0 log nM MBP

+2

sodium sulfate, retained a constant ABC (Table 1). In a similar way several syngeneic Lewis rat MBP-anti-

MBPcomplexes exhibited the same degree of stability. Table 2. The nM binding

activity

Anti-MBP antiserum

equation”

constants h a

E-24d 4/75’ 5177’ 7/77’ 9177 19d 21aJ 296 33a’ 34aJ 19bg 33bg 34bg

0.493 0.369 0.133 0.136 0.398 0.374 0.771 0.395 0.122 0.022 0.180 0.047 0.267

0.821 0.711 0.419 0.624 0.367 0.627 0.799 0.720 0.361 0.138 0.512 0.234 0.679

I +2

Fig. 4. The dual-dilution effect for two different pools of syngeneic Lewis rat antiserum: (0) Pool 5/77 with a binding equation of log ABC?% 7 0.5806 log P- 0.8768, r = 0.986; (*) Pool 4!75 with a bmdmgequation of log ABC,, = 0.2893 log P-0.4325, r = 0.993. -

Fig. 3. The dual-dilution effect as shown by syngeneic Lewis rat antiserum 9/77 in its interaction with rZsI-MBP-L-Rat. Top, biphasic effect with ABC,,,, = 1.200 log P-0.311. r = 0.993 between 5.0 and 100 nA4; ABC,.” = 0.360 log Pf 0.424, r = 0.949, between 0.4 and 6.3 nM MBP. Bottom, binding equation by linear regression analysis is log ABC,. = 0.3671 log P -0.4001, T = 0.985.

Binding

I I 0 +l log nM MBP

It could be concluded, therefore, that once complex formation had taken place in the time allotted, subsequent treatment with sodium sulfate would not change the composition of the equilibrium mixture nor fail to precipitate all that had formed nor change the level of non-specific adsorption. The biphasic nature of anti-MBP dilution curves

As illustrated by syngeneic antiserum 9177, when the

of anti-MBP antisera antigen

correlation coefficient r

0.97 0.99 0.98 0.98 0.99 0.97 0.81 0.90 0.96 0.87 0.99 0.85 0.56

Strength at different

at different

0.74 0.72 0.51 0.32 0.93 0.88 1.22 0.75 0.53 0.16 0.55 0.27 0.56

concentrations

of MBP

and affinity of antiserum nM concentrations of MBP

nM ABC,. b nM MBP concentration 1 10 100 0.49 0.37 0.13 0.14 0.40 0.37 0.77 0.40 0.12 0.02 0.18 0.05 0.27

antiserum

1.12 1.40 1.92 0.77 2.16 2.08 1.94 1.44 2.32 1.18 1.70 1.60 1.17

lo9 K, (M-l) nM MBP concentration 1 10 100 0.41 0.54 1.51 1.47 0.50 0.54 0.26 0.51 1.63 9.00 1.14 4.26 0.75

0.27 0.28 0.40 0.62 0.22 0.23 0.16 0.26 0.38 1.24 0.36 0.73 0.36

0.18 0.14 0.10 0.26 0.09 0.10 0.10 0.14 0.07 0.17 0.12 0.12 0.17

“ABC = hP’-” in nM terms. h ABC of a 1% antiserum mixed with MBP. The antigenic binding capacity of whole antiserum is 100 times greater. cMeasured at 10% antigen binding as described in text. d IgG (1.200 mg/ml) from a rabbit immunized with purified 18,000-dalton MBP from Lewis rats. “Pools of reagent syngeneic antisera against Lewis rat MBP (containing both 18,000-dalton and 14,000-dalton chains) obtained 4 weeks after primary immunization, 2 weeks after recovery from EAE. 1 Individual antisera from Lewis rats 2 weeks after boosting, 6 weeks after recovery from EAE and 8 weeks after primary immunization. 4 Individual antisera from the same rats 2 weeks after a second boost and 6 weeks after the first boost.

168

VINCENT

A. VARITEK

ABC,, is plotted against log MBP a biphasic curve is produc”ed which usually can be divided conveniently into two linear segments. Each segment, when analyzed by linear regression, ordinarily displays a high correlation coefficient (Fig. 3). One interpretation would hold that at least two populations of antibodies are in evidence which are distinguished by different affinities separated by a gap. Most of the whole antisera we have analyzed show a similar biphasic nature when plotted in semilog form. Schmid et al. (1974) have also noted and commented upon the biphasic nature of anti-MBP binding in the case of some of their rabbit antisera to human myelin basic protein. The generation of binding equationsfrom

dilution curves

When most pools of reagent syngeneic antisera are analyzed for the dilution effect, and the data are plotted as log ABC vs log MBP, the correlation coefficients of linearity are high (Fig. 4). the equations for the plots have the form ABC = bP’-“, where h is the ABC,, intercept at 1 nM MBP and (1 -a) is the slope (Tible 2). Some of the plots for individual antisera are relatively flat, showing ABCs that are relatively unresponsive to antigen dilution (‘antiserum No. 21a, Table 2). Others are quite steep, indicative of considerable heterogeneity (antiserum No. 34a, Table 2). Still others tend to be biphasic even in the log-log plots (antiserum No. 34b, Table 2), i.e. steep at high antigen concentrations and flat at high antigen dilutions with low linear correlation coefficients, suggesting a higher proportion of high affinity antibodies than are ordinarily encountered. The remaining antisera fit the intermediate patterns characteristic of rats No. 19 and No. 33. As shown by comparative values of ABC and K, at three different concentrations of ‘251-MBP (1, 10 and 100 nM), the lower the heterogeneity constant a (and the higher 1 -z), the greater the gain of ABC with increasing antigen concentration and the greater the decrease in average binding affinity. DISCUSSION

Relative affinities and degrees of’ affinity heterogeneity Syngeneic antibodies to Lewis rat myelin basic protein (MBP) have been found in the present study to display a range of affinity constants characteristic of antibodies to many other protein determinants (Reichlin, 1975). Although the average affinities reported in Table 2 cannot and must not be taken as identical to or typical of the K, of purified heterogeneous antibodies to any given single haptenic antigen. as derived by a unitary binding equation, the values do represent a summation and average of the many individual reactions between heterogeneous antibody and multivalent antigen, and help to establish the magnitude of affinities to be expected if and when unitary binding measurments become possible in the MBP-anti-MBP system. Measured at * The antiserum reagents used in the MBP-SF studies cited above included the first 3 antisera described in Table 2 of this study.

and EUGENE

D. DAY

the 100 nM level of MBP, the antibody affinity constants in this study ranged from a K, of 4 x 10’ to 3 x 1ORMm I; at the 1 nM level, from I x IOx to 9 x IO” Mm I. The antibodies also were frequently found to possess a fairly high degree of heterogeneity with a heterogeneity index (a) of about 0.3-0.7. On one occasion, extreme heterogeneity was found with the index as low as 0.14; on another, moderate restriction was observed (X = 0.82). In no case of a whole antiserum was any evidence found to suggest that this reaction against ‘self was restricted to a narrow range of association constants. It would appear that a considerable part of the observed affinity heterogeneity in the syngeneic antisera was due to reactions against multideterminants of the MBP molecule, a concept that receives support from the biphasic nature of many ABC vs log P plots encountered here and from the biphasic binding curves described by Schmid et al. (1974). Although xenogeneic antisera had been known to be directed against at least 3 or 4 MBP determinants (Wallace et al., 1978), it was not known whether syngeneic would have similar properties. The antisera absorption studies of Pitts et ul. (1976c), although demonstrating that inter-species cross-reactions of syngeneic antisera were confined for the most part to sequences of the MBP molecule shared in common by the different species, did not settle the question of unitary vs multiple determinant binding. The present studies, taken in the context of what has been found in other systems (Reichlin, 1975), would seem to suggest that multideterminancy is also characteristic of the syngeneic immune response to MBP The import of the results with respect to MBP-SF MBP-SF (Day et al., 1978a, b). a serum factor candidate for an endogenous autoneurotolerogen. appears to be highly cross-reactive with syngeneic antisera. If the antibody in those studies had been directed to only one MBP determinant the MBP-SF inhibitor could have conceivably consisted of only a small single fragment perhaps not even synthesized by nervous system tissue. Since from the current study multiple determinants appear to be involved*, then MBP-SF must represent either a number of small fragments or a relatively large piece, and the likelihood of nervous system derivation is increased, perhaps by the enzymatic procees advanced by Prescovitz ef ul.. (in press). Apparently, the rabbit immune response to human serum albumin raises antibodies with affinities one or two orders of magnitude lower than the responses to MBP. The same method of calculation as used for the MBP-anti-MBP system give a K, = 5 x 10’ Mm 1 at nM HSA for the data of Brownstone et al. (1966) and a K, = 2 x lo6 Mm Lat 1 PM; and gives K, = 2 x 10’ M- ’ for the data of Arend and Mannik (1972) whether arrived at by their use of the specific method of Steward and Petty (1972) or by the alternate one used in this study. For MBP-SF to compete with MBP in an additive type of reaction with relatively high affinity anti-MBP antibodies indicates in yet another way its probable origin within the nervous system. We are now using the present dual-dilution technique, in collaboration with Dr. P. Y. Paterson, to examine the inhibitory power of MBP-SF at various

169

Affinity of Antibodies for Myelin Basic Protein (MBP) affinities of reagent anti-MBP antisera and have already encountered sera with different properties: (a) high affinity inhibitor alone; (b) low affinity inhibitor alone; (c) high and low affinity inhibitor; (d) high affinity inhibitor plus low affinity antibody; (e) low affinity inhibitor plus high affinity antibody. These preliminary findings are consistent with the view advanced in this study that the high degree of heterogeneity found in an anti-MBP antiserum most likely reflects a number of distinct MBP determinants involved, each with its own population of relatively widely rather than a restricted antibody, heterogeneous population of antibodies against each determinant. An inhibitor would not be able to neutralize antibody selectively within a given range of affinity in the latter case. The data also reinforce the view that syngeneic antisera in the Lewis rat represent antibodies against a number of determinants, not just one. The comparison of ABCs from different laboratories Whitaker and McFarlin (1977) in comparing their radioimmunoassays at 10 nM MBP with our original method at 148 nM MBP (Day & Pitts, 1974a, b) stated that the “higher concentration of antigen. would facilitate detecting antibodies of lower affinity but would theoretically enhance binding to nonimmunoglobulin proteins.” They were, of course, describing one of the problems associated with this Osler approach “to register all antibody molecules”. As a result of the present studies, however, we do not believe non-specific binding was a problem in our earlier studies since the association constants of syngeneic and xenogeneic low affinity anti-MBP measured at high antigen antibodies, as concentrations, appear to be two or three orders of magnitude higher ($ lo6 M ‘) than those expected for non-specific binding (<
MBP-anti-MBP elsewhere.

systems either in their laboratory

or

How the “extent of the reaction” affects the dual-dilution phenomenon

It would appear that the natural biological systems involving immune reactions to MBP (and, perhaps, to other self proteins) ordinarily involve antibodies with relatively high affinities and relatively low concentrations (the higher the affinity, the lower the amount needed) thus illustrating the “extent of reaction” as expressed by Karush (1970) for a unitary reaction. According to that biological principle a given immunological effect is sustained in viva according to the product of an affinity and a concentration in reciprocal relation to each other. It seems reasonable, therefore, that even in a non-unitary heterogeneous multideterminant protein-anti-protein system, one should also find that the higher the affinity the lower the quantity of antibody needed, thus making the lower affinity antibody the dominant immunoglobulin with respect to quantity, and making ABC decrease with increasing antigen dilution. In such a system, the Karush effect has its influence on the parameters of the general binding equation of the dual-dilution effect, ABC = bP’-*, as the product of a concentration and multideterminant heterogeneity. Consequently, any given binding capacity will consist of two kinds of values: a quantitative one, b, related to the total number of antibody molecules in the system, and a distributive one, a, related to heterogeneity. The result is a product (ratio), bP/P”. The more heterogeneous the system the higher the number of antibody molecules required to maintain a constant ABC at a given P and the more rapid the decrease of ABC with decreasing P. A third kind of value-a statistical one not contained in a particular binding equation but associated with it-is the correlation coefficient, r, which, as it drops from 1.00, measures an increasing discontinuity in distribution of binding affinities, or, as it approaches 0.00, indicates a preponderance of affinities about a restricted value. The creation of an antiserum r@actory the dual-dilution effect

to

An experiment to be described at a later date had been designed to test whether the ABC of passively transferred anti-MBP antisera into adult rats would be influenced by MBP-SF found in the adult (Day et al., 19786). In a set of tests preliminary to the main experiment it was found that passively transferred anti-MBP antisera were indeed affected by the sojourn in vivo and that the changes were reflected in a change in the dual-dilution pattern. Many types of changes were observed, one of which deserves mention here. A group of six normal adult Lewis rats with no previous anti-MBP activity, one day after having passively received a syngeneic reagent antiserum, 2/78, showed the following binding activity: ABC,.,> = 1.032 P’ m”.h34. r = 0.97. At the end of 7 days the binding activity had shifted to ABC,,,,, = 1.903 P’-“~98”. r = 0.09,

I70

VINCENT

A. VARITEK

producing an antiserum whose ABC remained nearly constant over a lOtSfold dilution of antigen, whose average affinity constant changed only from 0.96 x 1Os to 1.05 x IOR M-l, and whose heterogeneity constant at 0.98 was very nearly that expected for homogeneous binding. It is not known, of course. whether the anti-MBP antibody remaining free at 7 days was actually restricted in its affinity for MBP, since multiple criteria are required to establish true restriction; however, the assay does demonstrate that the dilution effect is not an inherent property upon which measurements of antigenic binding capacity necessarily depend, but rather comprises just one more parameter than can be used to characterize particular antisera. Acknowledgements -The authors wish to thank Vicki Ashley, Shirley Day, Lewis Rigsbee. Edith Tatum and Gordon Quin for their technical assistance and Pam Daniel for her secretarial assistance. REFERENCES

Arend W. P. & Mannik M. (1974) Determination of soluble immune complex molar composition and antibody association constants by ammonium sulfate. J. Immun. 112, 451-461. Berzofsky J. A., Curd J. G. & Schechter A. N. (1976) Probability of the interaction of antibodies with multideterminant antigens in radioimrrmnoassay: application to the amino terminus of the p chain of hemoglobulin S. Eochemistry 15, 2113-2123. Brownstone A., Mitchison N. A. & Pitt-Rivers R. (1966) Chemical and serological studies with an iodine containing synthetic immunoiogi~l determinant 4-dydroxy-3-iodo-5nitrophenylacetic acid (NIP) and related compounds. Immunology 10, 465-479. Cohen S. R., McKhann G. M. & Guarnieri M. (1975) A radioimmunoassay for myelin basic protein and its use for quantitative measurements. J. Neurochem. 25, 371-385. Day E. D., Lassiter S. & Fritz R. (1967) Radioiodination of antibodies absorbed to insoluble antigens. J. Immun. 98, 67-7 1. Day E. D. & Pitts 0. M. (1974a) Radioimmunoassay of myelin basic protein in sodium sulfate. Irnrn~noche~z~str,~, 11, 651-659. Day E. D. & Pitts 0. M. (1974h) The antibody response to myelin basic protein (BP) in Lewis rats: the effect of time, dosage of BP, and dosage of .~~~cobucterium butyricum. .I. immun. 113, 1958-1967. Day E. D., Varitek V. A., Fujinami R. S. & Paterson P. Y. (19780) MBP-SF, a prominent serum factor in suckling Lewis rats that additively inhibits the primary binding of myelin basic protein (MBP) to syngeneic anti-MBP antibodies. Im~~no~hemi~try 15, l-9. Dav E. D.. Varitek V. A. & Paterson P. Y. (197863 Mvelin basic protein serum factor (MBP-SF) in adult Lewis rats: a method for detection and evidence that MBP-SF influences the appearance of antibody to MBP in animals developing experimental allergic enc~phalomyelitis. Imm&o&emi&y 15, 437-442. Dunkley P. R. & Carnegie P. R. (1974) Sequence of a rat myelin basic protein. Biochem. J 141, 243-255. Far;R. S. (1958) A quantitative immunochemical measure of the primary interaction between I*BSA and antibody. .I. infect. Diseases 103, 239-269. Farr R. S. (1971) Ammonium sulfate precipitation of soluble antigen-antibody complexes. Meth. Immunol. Immunothem. 3, 6673. Feldman H., Rodbard D. & Levine D. (1972) Mathematical theory of cross-reaction radioimmunoassay and ligand

and EUGENE

D. DAY

binding system at equilibrium. Attu/yr Bio&cnr 45. 53&556. Goldberg R. J. (1952) A theory of antibody-alltiger reactions. I. Theory for reactions of multtvalcnt antigen with bivalent and univalent antibody, J ilnr c,ht,trr Sort 74. 5715-5725. Hudson B. W. (1968) An investigation of theeffect ofantigen concentration on protein antigen-antiprotein association constants. Immunochrmistr~ 5, 87-105. Karush F. (1970) Affinity and the immune response. .-inn .y. Y Atad Sci. 169, 56-64. Katz F. E. & Steward M. W. (1975) The genetic control of antibody affinity in mice. Immunologl~ 29, 543-548. Lennon V. A.. Whittingham S.. Carnegie P. R.. McPherson T. A. & Mackay 1. R. (1971 f Detection of antibodies to the basic protein of human myelin by radioimmunoassa~ and immunofluorescence. J 1nmn~1 107, 5662. McFarlin D. E., Hsu S. C-L., Slemenda F.. Chou C-H. & Kibler R. F. (1975) The tmmune response against myelin basic protein in two strains of rat with different genetic capacity to develop expertmentaI allergic encephalomyehtis. J. esp hfed 141, 72-8 1. Osler A. G. (1971) Weight esttmates of antibody based on antigen binding capacity. Meth Immwwl Immunochem 3, 73-85. Pescovitz M. D., Paterson P. Y.. Kelly J. & Lorand I.. Serum degradation of myeiin basic protein with loss of encephalitogenic activity: evidence for an enzymatic process. Cell. Immun., in press. Petty R. E., Steward M. W. R: Soothill J. F. (1972) The heterogeneity of antibody affinity in inbred mice and its possible tmmunopathologtc significance. f‘iirr (JV,I. Immunol. 12, 231-241. Petty R. E. & Steward M. W. (1972) Relative affintty of antiprotein antibodtes in New Zealand mice. C’lirr ‘-I-P InI~zu~ol. 12, 343-350. Pitts 0. M.. Barrows A. A. & Day E. D. (19760) An evaluation of a procedure for the isolation of myelin basic protein (BP). Prep Biochem 6, 239-264. Pitts 0. M.. Varitek V. A. 8r Day E. D. (19766) The antibody response to myelin baste protein (BP) in Lewis rats: the effects of ~ordeteI/u pertussis .I fmmzn~ 115, I I i 4-l 116. Pitts 0. M., Varitek V. A. & Day E. D. (1976~) The extensive cross-reaction of several syngeneic rat-anti-BP antiserums with myelin basic protein (BP) of other species. Irn~7z~~~eI~e~?~.~tr~ 13, 307-3 12. Reichlin M. (1975) Amino acid substitution and the antigenicity of globular proteins. .4dr Imtmurrol 20, 71-123. Schmid G., Thomas G.. Hempel K. & Gruniger W. (1974) Radioimmunologi~di determination of myelin basic protein (MBP) and MBP-antibodies. Eur ~Veurol 12, 173-185. Soothill J. F. & Steward M. W. (1971) The immunopathological significance of the heterogeneity of antibody affinity. c’fin. erp lmmunol 9, 193-199. Steensgaard J.. Liu B. M., Cline G. B. & Moller N. P. H. (1977) The properties of immune complex-forming systems. Intmunolog~ 32. 445-456. Steward M. W. & Petty R. E. (1972) The use of ammonium sulfate globulin precipitation for determination ofaffinity of antiprotein antibodies in mouse serum. ~~7~?7~~~~~~~,~122, 747-756. Steward M. W., Katz F. E. & West N. J. (1975) The role of low affinity antibody in immune complex disease. c‘lr~ e.vp. ImmunoI. 21, 121-130. Steward M. W. & Petty R. E. ( 1976) Evidence for the genetic control of antibody affinity from breeding studies with inbred mouse strains producing high and low affinity antibody. Immunology j0, 789-797. _ Waliace A. D.. Shapira R. & Fritz R. B. (1978) Isolation and characterization of rabbit antibodies to bovine myelin basic protein. ImmunochemLur~ 15, 47-X

171

Affinity of Antibodies for Myelin Basic Protein (MBP) 5Or

Whitaker J. N. & McFarlin D. E. (1977) A comparison of immunochemical methods for the detection of antibodies to myelin encephalitogenic protein. Bruin Res. 129, 121-128.

APPENDIX A* Derivation of the Stewar&Petty

approximation

u

r 20 Y t

The

binding equation for antibodies to multivalent proteins must be written in terms of binding at a single epitope. It is assumed that binding at each epitope is independent, and that each epitope is unique and present only once per antigen molecule. Consider, for example, a pentavalent antigen with epitopes 1.2, 5: G = antigen concentration,

(1.b)

A = antibody concentration,

(1.c)

A = Ai.

(1.4

Since Gi reacts with Ai but not Aj where j # i, Ki defines the reaction of Gi with Ai,

(1.e)

q = fraction of antigen combined with

at least one antobody,

0.20 0.40 0.60 0.80 1.00 1.20 pg IgG added fpg HSA added

Fig. 5. Binding data for an HSA-anti-HSA system from Table 1of Arend & Mannik (1974) recalculated and plotted in manner of Day and Pitts (19740). Linear regression equation is y = 39.31x + 0.664, r = 0.998, where y is % HSA precipitated and x is pg anti-HSA added/pg HSA added. The point at 41.33% is identical to the authors’ 4.78 degrees of antigen excess; at 4.27%, 57.9 degrees of antigen excess.

(1.D

Pi = the probability the ith epitope is unreacted with antibody of type Ai.

(1 -Pi)Gi [2,Ai-(1 -Pi)Gi]PiGi

(7) Now we are in a position to derive the Steward-Petty equation. Substitution of equations (l.b), (3). (6) and (7) into equation (2) gives:

(2)

We are obviously forced to admit that we can obtain only a crude approximation to the true Ki since we cannot define Ai and Pi independently but must use an average. Recognizing this let us then evaluate the terms. As a crude estimate of the antibody against a single epitope we use the mean Ai z A/S

(3)

(q/W

(8)

But this just reduces to qG ---=KKic

(8.a)

2A-qG 01

~

r

=K,c

(8.b)

2-r

(4)

where ll means the product of all Pi, i = 1, 2, . _ 5. This formula is correct as long as all epitopes react independently. Thus the experimentally measurable variable qG is: qG = G-nPiG

= Ki[l - (q/5]G.

2(4/5)- (q/5)G

where 5 = valence of the antigen. Evaluation is best carried out by the definition: = IlPiG

l-(4/5).

P=(l-q)‘f5z

(W

Using these symbols, the association constant is:

free antigen

J

Y

L’“L

(La)

Gi = G = concentration of the ith epitope,

Ki =

2

where, instead of the normal definition for the free antigen concentration,

c = G( 1 -

q), we find that

c = G[ 1 -(q/5)].

(9)

(5)

or q = 1 -llPi.

(5.4

Since we do not know the individual Pi,we use the assumption that ail Pis are equal P = Pi.

(6)

Then (I = l-P5

(6.a)

P = (1 -q)“S.

(6.b)

or

Substitution of equations (l.b), (3), (6) and (6.b) into equation (2) will allow, in principle, an approximate evaluation in any region of the Farr curve. In antigen excess as G-+co, 2 A/G+q, and q is small compared to 1. Thus, we can use the Taylor series expansion: * Work done by Ivan Otterness at Central Research, Pfizer, Inc., Groton, CT 06340 (26 January 1978).

I

I

I

1

2

3

log nM HSA Fig. 6. The data of Brownstone et al. (1966) for an HSA-antiHSA system recalculated and presented in the form of log ABC so%vs log HSA added. Linear regression analysis of the binding data calculates to be log ABC,. = (I -0.542) log HSA + log 3.99 with a correlation coefficient of r = 0.99.

VINCENT

A. VARITEK

we are working

in the range

172 However. since by definition where y is small,

c r G.

(9.a)

Thus, in far antigen excess, the Steward-Petty equation is a reasonable assumption. Moreover, it estimates the K, rather than a global K, something that was not apparent in the original formulation of Steward and Petty.

APPENDIX B The data of Arend and Mannik (1974. Table I) for an HSA-anti-HSA system have been recalculated in terms of ?;

and EUGENE

D. DAY

lZSI-HSA bound vs pg antibody added/pg HSA added and plotted according to the method of Day and Pitts (1974~~) to show the high degree of linearity of the segment up to 40”, binding (Fig. 5).

APPENDIX C The dual-dilution data of Brownstone et al. (1966) have been extracted from their binding curves for an HSA-antiHSA system, recalculated in terms needed to formulate a binding equation, and plotted as log ABC vs log P (Fig. 6) to illustrate the tightness of fit and high correlation of the linear regression analysis.