ANALYTICAL

BIOCHEMISTRY

97, l- 10 (1979)

REVIEW Quantitative

Uses of Affinity IRWIN

Laboratory

of Chemical

Biology, National National Institutes

M.

CHAIKEN

Institute of Health,

Received

Chromatography

of Arthritis, Bethesda,

March

Metabolism, and Digestive Maryland 2020.5

Diseases,

12, 1979

finity chromatography case. The result has been development of a methodology for the use of affinity chromatography to measure binding constants and other quantitative features of protein-ligand interactions.

The intrinsic biospecificity of macromolecule-ligand interactions has been a keystone in the development of affinity chromatography for the fractionation of proteins. It is now well documented that biospecific interactions can be preserved in the immobilization of ligands, thus allowing the productive, differential binding of soluble proteins (l-6). As a result, there has been a wide ranging use of affinity chromatography for the purification of a variety of proteins. This success has stimulated the development of a significant chemistry for ligand immobilization, spacer group incorporation, and solid phase matrix adaptation, as well as of both theoretical and empirical guidelines for the design of purification systems. More recently, it has been recognized that retention of intrinsic biospecificity in affinity chromatography systems provides a basis for quantitative characterization of the macromolecular interactions themselves. For interactive liquid chromatography in general, relationships describing the dependence of elution behavior on matrix interaction properties are well established (7). Given the need for techniques to study macromolecule-ligand interactions-especially when other methods are precluded due to such factors as extremely tight or weak binding affinities and ligand size-efforts have been made to adapt general chromatographic relationships to the af-

MEASUREMENT OF MACROMOLECULE-LIGAND EQUILIBRIUM BINDING CONSTANTS

Competitive zonal elution quantitative afjinity chromatography. A basic methodology for the assessment of binding parameters has evolved from the approach of competitive zonal elution (8,9). The framework for this idea is given conceptually in Fig. 1, which shows a protein interacting with competing soluble and immobilized ligands in its elution through the typical affinity chromatographic milieu. This view indicates that the elution of proteins will depend on interaction with both immobilized and soluble ligands and that the extent of elution therein will vary as the concentrations and protein binding constants vary for these species. This evaluation in turn leads to the prediction that chromatographic elution behavior of proteins on immobilized ligand matrices will be a quantitative reflection of binding constants and related properties of protein-ligand interactions. Monovalent systems. When applied to a monovalent protein-ligand case, the view of Fig. 1 defines the simple set of competing equilibria, 1

0003-2697/79/l Copyright All rights

lOOOl-10$02.00/O

0 1979 by Academic Press. Inc. of reproductnon in any form reserved.

2

IRWIN M. CHAIKEN

P ? ”

protein 0

soluble

ligand

matrix-bound

ligand

b u

protein-tigand

complex

elutmn I

FIG. 1. Schematic drawing of competitive zonal elution of protein on an affinity chromatographic matrix. (Adapted from Ref. (9) with the permission of the American Chemical Society.)

ill PI where P is protein, L is soluble ligand, L is immobilized ligand, and PL and PL are complexes of protein with soluble and immobilized ligand, respectively. These equilibria, along with definitions of interactive liquid chromatography, have been used (8) to obtain the relationship,

+ K,(V, - V&C] ’ L31 where V, is the void volume and V,, is the unretarded volume. This expression relates the variation of V, the elution volume of a zone of protein, to the critical parameters implied in Fig. 1, namely the concentrations of immobilized and soluble ligand, [L] and [L], respectively, and the dissociation constants for these two respective species, Kc and K,. Use of Eq. [3] allows the constants IIt, and KC for a protein and its ligands to be

measured directly by chromatographic experiments. For any given affinity matrix of fixed EL], a series of elutions is carried out, each of a zone of specifically interacting protein with buffer containing a chosen concentration ([L]) of soluble competing ligand. The elution volumes of protein are measured at the various values of [L]. From a plot of the resulting data of f/(V - V,) against [L], both K, and E;z. can be calculated. The value K, is obtained from the ratio of slope/ordinate intercept, while Kt is calculated from the ordinate intercept. Alternatively, linear least-squares best tit of the variation of l/(V - V,) with [L] can be used to determine K, and Kc nongraphitally. The above calculations use [L] (usually determined as capacity for P), V, (determined as the volume of elution of noninteracting protein), and V, (determined as the volume of elution of a large molecule, such as dextran blue, which does not enter the pores of the matrix). Of note, the value #r can be determined independency of competitive elution simply from V measured in buffer without soluble ligand. In this condition, [L] = 0 and Eq. [3] simplifies to -= 1 v - v,

Ki;

(Vtl - Knm

*

c41

The above considerations are applicable in affinity chromatography mainly when the amount of eluting protein is small compared to Kc (9). This condition is analogous to that invoked for the steady-state assumption in enzyme kinetics (wherein initial velocities of enzymic reactions are measured with amounts of enzyme small by comparison to total substrate) (10). This limitation is of course acceptable, indeed preferable, for the chromatographic analysis of many if not most biological macromolecules, since it enables the use of only small amounts of such species. In practice, elution with relatively small amounts of protein is easily achievable, by optimizing postchromatographic detection. Perhaps the

QUANTITATIVE

USES

OF AFFINITY

CHROMATOGRAPHY

3

most universally convenient detection method the K, values obtained by the competitive is scintillation counting, which can be used elution approach of affinity chromatography in following elutions of radioisotopically adequately describe protein-ligand interaclabelled protein. Enzyme activity assay in tions as they normally occur in solution. the case of enzyme elution is also suitable, Higher order systems. The competitive as are immunoassay for essentially any zonal elution approach of quantitative afprotein for which specific antibodies are finity chromatography can be adapted for available and spectroscopic analysis when use in studying multivalent systems. The the protein contains a unique chromophore. bivalent case has been treated by conSeveral protein systems have been sidering the set of equilibria, analyzed successfully using the above quantitative considerations. For the wellPzL2 characterized monovalent systems of staphylococcal nuclease and thymidine-3’-(pi Kc Sepharose-aminophenylphosphate)-5’-phosphate (8,9), bovine pancreatic ribonuclease II and uridine-5’-(Sepharose-4-aminophenylphosphate)-2’(3’)-phosphate (11,12), and immunoglobulin A(TEPC 15) Fab fragment and phosphorylcholine-Sepharose (13a), competitive elutions have been accomplished with series of soluble ligands competitive with the immobilized species. The variations in l/(V - V,) with [L] have been found to be linear in all cases. This correlation of experimental behavior with that predicted from Eq. [3] has allowed dissociaPzL2 tion constants to be calculated. Where comparative data are available, the chromatBy assuming that all soluble ligand interographic values fit well with values ob- actions (described by KJ are equal, that tained by other procedures, including the the same is true for immobilized ligand (Kz, direct method of equilibrium dialysis and events), and that the species P2L, P&, and such less direct approaches as inhibition of P,LL actually each represent two distinct enzyme activity (see Table 1, A-C). The species of active site occupancy (P2L repredata in these cases support the view that sents -P-PL or LP-P-, etc.), the expression has been defined (13 a,b),

[61

This relationship allows both K, and Kc to be evaluated for a bivalent ligand-binding species, again by the measurement of V at varying [L]. Here, the data are fitted to Eq. [61 by nonlinear least-squares analysis.

As in the monovalent case, a simplification of Eq. [6] for [L] = 0 can be obtained (Eq. [7]) which allows Kr to be determined, independent of competitive elution, by meas-

4

IRWIN

M. CHAIKEN TABLE

COMPARISON

OF DISSOCIATION CONSTANTS WITH THOSE OBTAINED

1

OBTAINED BY OTHER

Chromatogmphic

BY QUANTITATIVE AFFINITY CHROMATOGRAPHY METHODS-A SELECTED LIST

K,

Kd by other methods KiD

KL” Protein

Ligand

PdTp’

A. Staphylococcal nuclease

B. Bovine pancreatic ribonuclease C. Immunoglobulin (TEPC 15) monovalent

A

Value

CM)

2.5 x IO.6

pdTpaPhd NPpdTp’

2.3 x IO-b

2’.CMP’ aPhpUp”

1.6 x 10ms

I.1 x lo-be

I.1 x 10-5

9.3 x lo-“(

Phosphoryl choline

1.5-3.3

x 10-e

3.9-4.2

Phosphoryl choline

1.2-1.5

x 1O-6

2.7-4.8

x IO-"

2.5 5.9 2.5 6.3

Method

(M)

x IO-’

x 10-e x lo-@ x IO-’

Reference

Equilibrium dialysis Kinetics as enzymic inhibitor Kinetics as enzymic inhibitor Kineticsasenzymic substrate

(9)

9.7 x 10-e 1.7 x 10-5

Kinetics Kinetics

3.0 x 10-e

Equilibrium

dialysis

(13)

2.0 x 10-6

Equilibrium

dialysis

(13)

as enzymic as enzymic

inhibitor inhibitor

(II)

Fab

D. lmmunoglobulin A (TEPC 15) divalent “IOnOmer E. Beef lactate dehydrogenase H, (heart) M, (muscle)

x IO-B”’ I.2 x lo-“‘.* I.3 x lo-“.’

NADH NADH

3.8 x IO-’ 2.2 x 10-s

3.9 x lo-' 2.0 x 10-s

Fluorescence titration Quenching of protein Ruoresce”ce

(14)

F. Rabbit muscle lactate dehydrogenase

NADH

I.1 x 10-5

1.0 x 10-5

Frontal gel filtration chromatography

(15)

G. Trypsin

N”-AcetylGly-Gly-Arg

5.9 x lo-'

4.7 x 10-4”

Kinetics

1.3 x 10-4”

e K, for soluble l&and. as determined by competitive elution. b K, for immobilized ligand. c Thymidine-3’.5’-diphosphate. d Thymidine-3’-(p-aminophenylphosphatel-5’-phosphate. c For ligand immobilized to agarose through aminophenyl moiety. ’ Thymidine-3’-phosphate-5’-(p-nitrophenylphosphatel. s Cytidine-Z’amnophosphate. h Uridine-5’-(4-aminophenylphosphate)-2’(3’)-phosphate. ’ For ligand immobilized to agarose through a glycyl(azophenyl)tyrosyl arm on the phosphate ’ Microscopic Kc, determined using Eq. 161. x Functional Ki, determined at [i] = 9 X 1O-6 M using Eq. [31. ’ Functional KE, determined at [i] = 5 X 10ms M using Eq. [3]. D For ligand immobilized to agarose through a-amino of Gly-Gly-Arg. ” Determined at pH 6.0, versus pH 6.2 and 6.0 for corresponding K, and Ki. respectively.

thing V for zones of protein in buffer without soluble ligand. v-V,=(V,-v+g+

($)‘I

[7]

The above relationships have been used to evaluate the microscopic dissociation constants for the binding of phosphorylcholine to the bivalent immunoglobulin A (TEPC 15) monomer (13 a,b). As exhibited by this system (see Table 1, D), not only can the microscopic constant be calculated

as enzymic

inhibitor

(16.17)

moiety.

for each equal binding site of the bivalent species (Kc using Eqs. [6] and [7]), but the functional affinity (overall avidity) of the bivalent protein to multivalent ligand on the affinity matrix also can be determined (as KL using Eqs. [3] and [4]). As expected, it is observed that while the microscopic affinity remains constant with increasing ligand density ([L]), the functional affinity increases. Of note, if the multivalent protein system is converted to one that is monovalent (as in the conversion of bivalent im-

QUANTITATIVE

USES

OF AFFINITY

munoglobulin A monomer to monovalent Fab (13 a)), the microscopic binding constant of the monovalent species can be calculated from elution data using Eqs. [31 and 141. This constant can be used for comparison with microscopic constants obtained with the multivalent species. An alternate if less classical approach for measuring affinities of multivalent proteins is through limitation of the extent of multivalent matrix interaction by restricting immobilized ligand density. At a sufficiently low density, a value which will vary with the geometry of the particular protein system, a steric limit will be reached at which no two binding sites on a single protein will be able to interact simultaneously with immobilized ligand. Under these conditions, the behavior of the multivalent protein in competitive elution affinity chromatography reverts to that of one that is monovalent, so that Eqs. [3] and [4] can be used. This device has been used to evaluate the microscopic dissociation constants for psychotropic drug binding to the multimerit bovine glutamate dehydrogenase (18). Similarly, in the case of bivalent immunoglobulin A monomer cited above, the density of immobilized antigen can be decreased to a degree such that multivalent interaction becomes minimal (Table 1, D). Although formulations have not yet been derived and tested for many types of multivalent systems (higher order than bivalent, cooperative, etc.), it is expected that at least some of these cases can be handled by quantitative affinity chromatography. For example, the interaction of ligands with protease subsites has been treated by Danner and Dunn (19). In this case, both positive and negative effects of soluble ligand have been noted and evaluated for the interaction of porcine carboxypeptidase B to immobilized D-phenylalanine. Also, Andrews et al. (20) have observed enhancement effects of soluble monosaccharide on the retardation of zones of lactose synthetase eluted from cY-lactalbumin-

CHROMATOGRAPHY

5

Sepharose and have devised equations for quantitatively defining this interactive system between the a-lactalbumin, lactose synthetase, and monosaccharide species. Other methods. Several variations of the competitive zonal elution approach have been developed which offer quantitative alternatives for measuring K, and Kt for certain systems. Equations have been defined for determining the binding constant, analogous to Kc above, for lactate dehydrogenase to immobilized adenosine-5’monophosphate (21). Manipulation of this same chromatographic system has led to a graphical device for approximating K, by gradient elution (14). In the latter, single competitive zonal elutions are carried out for protein with buffers, each containing a gradient of competitive soluble ligand. A stanciard curve is constructed of dissoclation constant against concentration of ligand in the gradient at which the protein elutes; K, values for unknowns can then be defined by measuring the corresponding eluting ligand concentrations in gradient elution and interpolating on the standard plot (see Table 1, E). In addition, methods for determining dissociation constants have been described which entail affinity chromatographic manipulations other than those of competitive zonal elution. One widely used alternatlve approach is that of continuous elution (IS17,22,23). Here, elutions are performed in which solutions of fixed concentrations of protein are applied continuously to the affinity matrix until elution fronts are defined, with the nature of these fronts used to calculate binding constants (see Table 1, F-G). For example, an expression analogous to Eq. [33, namely Eq. [8] (notation of present paper, with [PI being the total eluting protein concentration, [L] the concentration of free soluble ligand, and f the fraction of immobilized phase accessible to protein), has been derived (23) for the continuous elution case for a soluble protein interacting

6

with soluble ligands .

IRWIN

and immobilized

competing

M. CHAIKEN

factors more restricted for use of equilibrium dialysis. With respect to size, the only major limitation is the geometry of the solid phase matrix. For example, in the case of the commonly available agarose, the matrix exhibits porosities large enough to accommodate ligands and proteins alike of up to at least lo6 M, (25). Even when exL clusion limits are approached or exceeded, + KLi,"t' ) or when nonporous insoluble carriers are 0 m m used, the outside of the matrix should prof vide ample ligand capacity for analytical A variant of the continuous elution method purposes. has been described in which the amount of Limits on the range of dissociation conbound protein, and not the elution volume, stants which can be measured by the is measured at variable soluble competing chromatographic method also are not too ligand concentrations (24). A major benefit severe. This derives from the fact that one of continuous elution, as indicated by Eq. often can choose either a weak or strong [8], is that the amount of protein being binder as immobilized ligand. Constants as eluted is treated directly in the applicable high as 10e2 M have been measured for mathematical formulations and thus that soluble ligands in the case of a ribonuclease dissociation constants can be evaluated active site analog by using more strongly when the ratio of eluted protein to Kc interacting immobilized ligand (12). It is to is significantly greater than zero. However, be expected that immobilized ligand binding an important weakness to note is that any processes will become difficult to assess method of continuous elution involves the when they are sufficiently strong that the use of relatively large amounts of eluting small dissociation rate constants will proprotein, which in many cases are not avail- hibit effective exchange of protein for able for biochemical systems. The zonal soluble and immobilized ligands during the elution approach does not suffer this dynamic process of elution. A practical restriction. lower limit to measurable Kr. values has been estimated to be about 10mgM (9). HowUSES IN FUNCTIONAL ever, when such high affinity is encountered, CHARACTERIZATION the immobilized ligand can be changed to Active sites. Quantitative affinity chro- one of weaker binding to the same protein site. This manipulation should have little if matography offers a general, relatively simple methodology for characterizing sev- any effect on assessment of K, values for eral features of protein active sites. The competing soluble ligands. In the special case of enzymes, results technique provides a rapid means to survey nuclease and bovine many compounds for quantitative recogni- with staphylococcal pancreatic ribonuclease (8,9,11,12) indicate tion by a protein or set of related proteins, e.g., antibodies. Thus, it can be used as an that the specificity of ligand recognition can alternative to equilibrium dialysis for be ascertained readily for both competitive direct measurement of active-site ligand inhibitors and substrates when these are competing with immobilized ligand. For binding. In its favor, the chromatographic substrates, the action of the enzyme during method exhibits a versatility in allowing assessment of binding for species with a elution apparently has no important effect on the K, values determined (9), probably wide range of size and strength of binding,

QUANTITATIVE

USES

OF AFFINITY

due both to the very low amounts of eluting protein relative to the amount of substrate in eluting buffer and to the relative rapidity of competitive elutions (often within an hour or two). Both of these factors serve to limit the extent of substrate depletion. To be sure, enzyme specificity can be evaluated by kinetic analysis. Yet, affinity chromatography does offer the advantage of giving a direct measure of binding. In contrast, in kinetic analysis, the presumed result of interaction, e.g., inhibition of action on substrate, and not the interaction itself, is observed. Beyond specificity, active site availability itself can be assessed for chemically modified proteins using the affinity chromatographic method. The case of [4fluoro-L-histidine 12lsemisynthetic ribonuclease-S (26) represents a graphic example. The enzymatic analog was found to be catalytically inactive, so that active site ligand binding could not be assessed by kinetic analysis. Nonetheless, the competitive elution chromatographic method allowed the direct detection of recognition of both substrate and competitive nucleotide inhibitor by this protein species (12), thereby allowing the demonstration of intactness of the site of substrate recognition in the absence of catalysis. Binding surfaces and subunit interactions. Since the affinity chromatographic approach measures interactions directly, without regard to size or functional implication, the technique can be used to characterize binding processes between relatively complex partners and at loci other than active sites. The use of immobilized oxy-hemoglobin has been suggested for defining aspects of subunit interaction for this multimeric hemoprotein (27). Similarly, the chromatographic procedure would seem to offer a useful means to characterize the nature of interaction between hemoglobin (and its subunits) and haptoglobin by using haptoglobin-agarose (28). And as previously mentioned, analysis of the monosaccharide-

CHROMATOGRAPHY

7

dependent interaction of lactose synthetase with immobilized a-lactalbumin has been accomplished (20,23). To be sure, the overall applicability of the chromatographic method for measuring quantitative parameters for subunits, interacting proteins, and more complex species has not yet been explored adequately. This is especially true with respect to examination of possible limiting factors, such as the complex nature of interactions possible among large molecules and the increased potential for nonbiospecific interactions with the matrix. Nonetheless, since there are no a priori limits to studying such complex systems, it is reasonable to expect useful applications. USES IN PURIFICATION

Evaluation of biospecijicity . A corrolary of the validity of relationships such as Eqs. [3] and [6] is that adherence of protein affinity chromatographic elution behavior to such expressions connotes maintenance of biospecificity in the protein-immobilized ligand interaction. This is particularly useful in developing affinity chromatographic systems for purification. By definition, the latter demands an immobilized ligand which interacts as specifically as possible with only the protein to be isolated. However, it is an empirical fact of life that nonspecific interactions often occur. These may be between protein and either the matrix backbone or spacer arm (which anchors ligand to matrix and often must be of significant size to make the ligand accessible to protein) or between the ligand and some nonspecific surface of the protein. Whatever the source, these interactions will interfere in affinity chromatographic purification of macromolecules. Given nonspecificity as anathema for purification, the analytical zonal elution method offers an elegant and direct means for assessing such effects for a particular affinity matrix. For example, agreement of chromatographic KL (determined by zonal elution in the absence of

8

IRWIN

M. CHAIKEN

competing ligand (Eq. [4])) with expected dissociation constants can be used as a strong argument for retention of biospecificity. The same can be concluded from adherence to such relationships as Eqs. [3] and [6] (or others for more complex cases) of the variation of elution volume in competitive elutions with selected soluble ligands. Noncorrelation in the above aspects is a reasonable indication that alternative conditions of affinity chromatographic elution should be sought. This tactic has allowed the detection of nonspecific interactions at low ionic strength for bovine pancreatic ribonuclease with uridine-5’(Sepharose-4-aminophenylphosphate)-2’(3’)phosphate and the eventual definition of more biospecific high-ionic-strength conditions for the affinity chromatographic fractionation of the enzyme (11). System design. The analysis of affinity chromatographic purification systems also is useful in achieving optimal geometry and chemical design. The choice of such system components as matrix, spacer arms, and ligand density normally needs to be made in designing immobilized ligands for purification. Variation of such components can lead to significant effects on the overall specificity and material demands for separation. Zonal elution analysis can aid in the systematic testing of particular options, since it provides data describing the extent to which both biospecificity and differential protein retardation are achieved. For example, oversubstitution with immobilized ligand for the fractionation of a multivalent protein can reduce the chances for facile elution of the specifically retarded protein by leading to high functional binding affinities. Observation of such a problem, often seen as the virtual inability to elute a bound protein from an affinity matrix, was noted in competitive elution analyses with glutamate dehydrogenase in its elution from high-density immobilized ligands (18). Such a phenomenon is a strong indication that ligand density needs to be decreased. Competitive ligands as elutants. Beyond

analytical usages, competitive elution offers a convenient preparative tool, for the specific removal of proteins from affinity matrices. Schemes of protein elution normally have been of a two-step nature, first a wash with buffer under conditions promoting the retention of the desired protein on the matrix, then elution with a chaotropic agent (l-5). Although this approach has been effective, the use of chaotropic agents can lead to difficulties, such as irreversible protein denaturation. Even limited unfolding of protein during chaotropic elution can cause aggregation and resultant “sticking” to the matrix (a phenomenon observed for both .bovine pancreatic ribonuclease and staphylococcal nuclease (29)). There also may be instances in which unwanted proteins are nonspecifically retarded in the wash step, and then eluted along with specifically bound protein, without discrimination, during chaotropic elution. A means of eliminating all of the above problems is through elution of protein with soluble ligands that are competitive with the immobilized species. This can be accomplished using high concentrations of soluble ligand directly in place of chaotropic agent. Alternatively, continuous competitive elution can proceed from the outset of protein sample application, much as in an analytical competitive zonal elution but with preparative amounts of protein. In the latter case, the concentration of soluble ligand would be ascertained by analytical elutions, in order to optimize the separation of retarded protein from contaminants. DETERMINATION

OF RATE CONSTANTS

Using classical chromatographic considerations as a basis, Denizot and Delaage (30) have proposed the interesting use of affinity chromatography to evaluate the association and dissociation rate constants of binding of macromolecules to immobilized ligands. Experimentally, two critical analytical zonal elutions, similar to those described above for K, and KI; determination,

QUANTITATIVE

USES OF AFFINITY

would be performed. One is of the soluble interacting macromolecule through the affinity matrix with no competing ligand. The second is for a noninteracting species (or the interacting species with saturating soluble competitive ligand) through the same column. The time required for peak elution and the distribution characteristics of the peak, measured for both retardation and nonretardation elutions, can be incorporated into algebraic expressions related directly to the rate constants (30). However, it has been shown for various trypsin ligands immobilized on the porous-support Sepharose that the rate-limiting steps in the association and dissociation of trypsin are mass transfer within the matrix particle and mass transfer through the external liquid film (31). This conclusion suggests that rate constant determination with porous-support affinity chromatography systems will yield a measure mainly of the rate constants for the mass transfer processes and not for the primary microscopic binding events of macromolecule to ligand. An analysis according to the Denizot-Delaage formulation has been carried out for the elution of ribonuclease on uridine-5’-(Sepharose-4-aminophenylphosphate)-2’(3’)-phosphate (32). While the ratio of dissociation to association rate constants obtained for protein to the ligand matrix corresponded to the Kr determined by competitive elution (Eq. (3)), the absolute values of these rate constants were several orders of magnitude lower than the rate constants for the ligandprotein interaction in solution. If biologically meaningful association and dissociation rate constants are to be obtained by affinity chromatographic manipulations, these results suggest that ligands immobilized onto low-porosity supports will be required. GENERALITY OF QUANTITATIVE APPLICATIONS

The experimental observations that are available indicate that affinity chromatography can be used with significant flexi-

CHROMATOGRAPHY

9

bility to measure quantitative parameters of macromolecule-ligand interactions. The general findings that biospecificity can be retained upon ligand immobilization, and that there are no intrinsic limitations on the types of molecules incorporated as either immobilized or soluble interactants, indicate that the technique is applicable to biological systems over a wide range of component type-from small molecules to macromolecules to macromolecular assemblies to cells. Equilibrium binding constants and characteristics reflected by these constants are the most dependable parameters attainable by present quantitative chromatographic methods. Furthermore, these chromatographic parameters seem to be accurate indicators of the biospecific processes of the interactants as they take place in solution. The methodology for determining association and dissociation rate constants also appears available but as yet untested for a range of systems. There is clearly fertile ground remaining for development and application in quantitative usage. Nonetheless, it seems that affinity chromatography is firmly established as a convenient tool for the characterization of macromolecular interactions. REFERENCES 1. Cuatrecasas, P., and Anfinsen, C. B. (1971) in Methods in Enzymology (Jakoby, W. B., ed.), Vol. 22, pp. 345-378, Academic Press, New York. 2. Jakoby, W. B., and Wilchek, M., eds. (1974) Methods in Enzymology, Vol. 34. Academic Press, New York. 3. Lowe, C. R.. and Dean, P. D. G. (1974) Affinity Chromamgruphy, Wiley, New York. 4. Porath, J., and Kristiansen, T. (1975) in The Proteins (Neurath, H., and Hill, R. L., eds.), 3rd ed., Vol. 1, pp. 95-178, Academic Press, New York. 5. Wilchek, M., and Hexter, C. S. (1976) in Methods of Biochemical Analysis (Glick, D., ed.), Vol. 23, pp. 347-385, Wiley. New York. 6. Nishikawa, A. H., Bailon, P., and Ramal, A. H. (1976) J. Mucromol. Sri. Chem. AlO, 149- 190. 7. Giddings, J. C. (1965) Dynamics of Chromatography Part I-Principles and Theory, Dekker, New York.

10

IRWIN M. CHAIKEN

8. Dunn, B. M., and Chaiken, I. M. (1974) Proc. Nut. Acad. Sci. U.S.A. 71, 2382-2385. 9. Dunn, B. M., and Chaiken, I. M. (1975)Biochemis-

try

14, 2343-2349.

10. Bender, M. L., and Brubacher, L. J. (1973) Catalysis and Enzyme Action, p. 25, McGrawHill, New York. 11. Chaiken, I. M., and Taylor, H. C. (1976) J. Biol. Chem.

251, 2044-2048.

12. Taylor, H. C., and Chaiken, I. M. (1977) J. Biol. Chem. 252, 6991-6994. 13. a.1 Eilat, D., and Chaiken, I. M. (1979) Biochemistry 18, 790-794. b. Chaiken, I. M., Eilat, D., and McCormick, W. M. (1979) Biochemistry 18, 794-795. 14. Brodelius, P., and Mosbach, K. (1976) Anal. Biochem. 72, 629-636. 15. Brinkworth, R. I., Masters, C. J., and Winzor, D. J. (1975) Biochem. J. 151, 631-636. 16. Kasai, K., and Ishii, S. (1975) J. Biochem. 77, 261-264. 17. Nishikata, M., Kasai, K., and Ishii, S. (1977) J. Biochem. 82, 1475-1484. 18. Veronese, F. M., Bevilacqua, R., and Chaiken, I. M. (1979) Mol. Pharmacol 15, 313-321. 19. Danner, J., and Dunn, B. M. (1978) Fed. Proc. 37, (No. 20.

21. Lowe, C. R., Harvey, M. J., and Dean, P. D. G. (1974) Eur. J. Biochem. 42, I-6. 22. Lowe, C. R.. Harvey, M. J., Craven, D. B., and Dean, P. D. G. (1973) Biochem. J. 133,499-506. 23. Nichol, L. W., Ogston, A. Cl., Winzor, D. J., and Sawyer, W.H. (1974)Biochem.J. 143,435-443. 24. Bottomly, R. C., Storer, A. C.. and Trayer, I. P. (1976) Biochem. .I. 159, 667-676. 25. Beaded Sepharose 2B-4B-6B, publication of Pharmacia Fine Chemicals AB, Uppsala, Sweden. 26. Dunn, B. M., DiBello, C., Kirk, K. L., Cohen, L. A., and Chaiken, I. M. (1974) /. Biol. Chem. 249, 6295-6301. 27.

28. 29. 30. 31.

267-280.

6), 1436.

Andres, P., Kitchen, B. J., and Winzor, (1973) Biochem. J. 135, 897-900.

Antonini, E., and Rossi Fanelli, M. R. (1976) Methods in Enzymology (Mosbach, K., ed.), Vol. 44, pp. 538-546, Academic Press, New York. Tsapis, A., Rogard, M., Alfsen, A., and Mihaesco, C. (1976) Eur. J. Biochem. 64, 369-472. Taylor, H. C., and Dunn, B. M., and Chaiken, I. M., unpublished results. Denizot, F. C., and Delaage, M. A. (1975) Proc. Nat. Acad. Sci. U.S.A. 72, 4840-4843. Katoh, S., Kambayashi, T., Deguchi, R., and Yoshida, F. (1978) Biotechnol. Bioengin. 20,

D. J.

32.

Long, R. H., and Chaiken, I. M., unpublished results.