Determination of dissociation constants of crystalline α-chymotrypsin complexes

J. Mol. Biol. (1974) 82, 27-33

Determination of Dissociation Constants of Crystalline a-Chymotrypsin Complexes LINDA

A. DAVIX$ AND GEORGE P. HESS$

Medical Research Council Laboratory of Molecular Biology, Hills Road, Cambridge, England (Received 22 January 1973) As a fist step in investigations of the properties of crystalline enzymes, the binding of indole, N-formyl-n-phenylalanine, and N-formyl-L-p-iodophenylalanine to or-chymotrypsin crystals, and the binding of indole to tosyl-or-chymotrypsin crystals, has been studied. The methods used were spectrophotometric measurements of the concentration of indole in the supernatant, or measurements of the concentration of radioactively labeled indole in both the supernatant and the crystal. The dissociation constants of the specific binding site of the crystalline enzyme have been determined for indole and N-formyl-L-phenylalanine. It was found that indole does not bind to tosyl-a-chymotrypsin crystals and that N-formyl-p-iodophenylalanine does not bind to the substrate binding site of the crystalline enzyme. The information obtained from these simple equilibrium measurements is in agreement with X-ray diffraction studies. The approach is, therefore, capable of determining whether or not compounds bind to the active site of a crystalline enzyme, and whether the occupancy of this site is sufficient for structure determinations using X-ray diffraction methods.

1. Introduction Investigations of enzymes and enzyme complexes using X-ray diffraction techniques have yielded detailed information about the static structure of these molecules (Blow & Steitz, 1970). The catalytic properties of crystalline enzymes, investigated in a few studies (Doscher & Richards, 1963; Quiocho & Richards, 1966; Sluyterman & de Graaf, 1969; Birktoft et al., 1970), are not as well known, since almost all investigations of enzyme-catalyzed reactions were done in solution. The crystallographic studies have given important insight into the catalytic mechanism. The conformation of the protein is, however, considerably more constrained in the crystalline enzyme than in the enzyme in solution. The importance of this conformational constraint on the efficiency of the catalytic reaction is not known. The efficiency of reactions catalyzed by crystalline enzymes is unknown, since it has not been possible previously to determine the concentration of active sites in the crystal that participates in a particular reaction during the time of measurements. t Present address: Department of Biological Chemistry, Washington University School of Medicine, St. Louis, MO. 63110, U.S.A. $ Present address: Section of Biochemistry, 270 Clark Hall, Cornell University, Ithaca, N.Y. 14850, U.S.A. 27

28

L. A. DAVIS

AND

G. P. HESS

The studies reported in this paper are pertinent to the determination of the concentration of active sites in enzyme crystals and to measurements of reaction efficiency. Two major problems arise in this regard in studies with crystalline enzymes. Unlike enzymes in solution, the diffusion of substrates and products in crystalline enzymes may be slow compared to the bond-breaking step. Due to crystal packing, substrates that bind well to the catalytic site of the enzyme in solution may not do so in the crystal, or may bind to non-specific sites. Both problems occur in cc-chymotrypsin (Steitz et al., 1969). In investigations of the binding of crystalline cr-chymotrypsin and proflavin, a chromophoric inhibitor of chymotrypsin (Wallace et al., 1963; Bernhard et al., 1966; Brandt et al., 1967), it was found (Rossi & Hess, unpublished observations) that equilibrium is reached in hours rather than in the milliseconds observed with the enzyme in solution. X-ray diffraction studies have indicated (Steitz et al., 1969) that some substrates which bind to the enzyme in solution, bind to non-specific sites and not to the catalytic site of the crystalline enzyme in sufficient concentration to be detected by X-ray diffraction. Because of these problems associated with crystalline enzymes, determination of the moles of active sites of the dissolved enzyme crystals may not be relevant to investigations of the enzymic properties of the crystal. The use of chromophoric inhibitors, which, as determined from X-ray diffraction studies, bind exclusively to the active site of the crystalline enzyme, can determine the substrates that bind to the catalytic site, the dissociation constant of these sites, and the occupancy of the sites during measurements of the catalytic reaction. Indole is a chromophoric inhibitor of a-chymotrypsin (Huang & Niemann, 1953) and is suitable for studies with the crystalline enzyme. The determination of the structure of the crystalline a-chymotrypsin-indole complex by X-ray diffraction (Steitz et al., 1969) has shown that indole occupies only the specific substrate binding site of the enzyme. As a first step in investigations of the enzymic properties of crystals, we have determined the dissociation constant of the crystalline a-chymotrypsin-indole complex. The displacement of this inhibitor from the crystal has been used to determine whether other compounds bind to the indole site in the crystal and their dissociation constants.

2. Materials and Methods Thrice crystallized a-chymotrypsin was obtained from the Worthington Biochemical Corp., Freehold, N.J., U.S.A. Before recrystallization, the enzyme contained 0.8 mol of active site/m01 enzyme, as determined from its reaction with p-nitrophenylacetate (Hartley & Kilby, 1954). The a-chymotrypsin crystals were recrystallized according to a previously published procedure (Sigler et al., 1966), which gives crystals suitable for X-ray diffraction measurements. Before crystallization, each crystallization tube contained approximately 33 mg of the enzyme. For most experiments, crystallization was allowed to proceed for 4 to 5 days. Indole was obtained from the Fisher Scientific Co., Rochester, N.Y., U.S.A., and [14C]indole (4 mCi/mmol) was obtained from the New England Nuclear Co., Boston, Mass., U.S.A. All other chemicals were reagent grade. A 65% (NH&SO, solution was prepared by dilution of the supernatant of a saturated (NH&SO4 solution (at 20°C) with water. The concentrations of indole were determined spectrophotometrically at 275 nm, using a molar extinction coefficient of 5.14 X 10” ivr-l cm- l. Protein concentrations were determined spectrophotometrically at 280 nm using a value for i$$ of 50,000 M-I cm-l (Dixon & Neurath, 1957). All spectrophotometric measurements were made in a double-beam

CRYSTALLINE

a-CHYMOTRYPSIN

Gary model 14 recording spectrophotometer with a solvent blank Solvent blanks were obtained using the supernatant of 65% (v/v) cant aining a-chymotrypsin crystals (see below).

Determination of dissociation

29 in the reference cell. (NH&SO4 solutions

constants

At the beginning of the binding experiment the supernatant in the crystallization tube was removed with a Pasteur pipette. The crystals were then washed 3 times with 4 ml of 65% (v/v) (NH&SO, solution. Portions (3 ml) of 65% (v/v) (NH&SO4 solutions containing various concentrations of indole, or containing indole and various concentrations of substrate, were added. Control tubes contained only crystals and 3 ml of 65% (v/v) (NH&SO4 solution. All the tubes were allowed to equilibrate for about 12 h at 20°C. The supernatant was then withdrawn through a Pasteur pipette (solution A). The crystals were washed once by suspending them for 2 min in 3 ml of 65% (v/v) (NH,),SO, solution (solution B). The concentration of indole in both solutions was determined. The crystals were dissolved in 3 ml of 1 mm-HCl. Samples of this solution were used to determine the protein concentration. When [1*C]indole was used, the procedure was slightly different. The crystals were grown and then washed as described, but only 2.5 ml of 65% (v/v) (NH,),SO* solution were used. To measure the radioactivity of the supernatant indole solution, 100 pl of solution A and 100 pl of solution B were withdrawn and counted separately in 10 ml of Bray’s solution (Bray, 1960) in a scintillation counter. The concentration of indole in the supernatant was calculated from measurements of both solutions. Portions (100 ~1) of the solutions containing the dissolved crystals were also counted in 10 ml of Bray’s solution. An amount (50 ~1) of the [14C]indole solution, which contained 0.1 mCi/BOO ~1, was added to 25 ml of 65% (v/v) (NH&SO& solution. The stock solution was prepared by diluting 8 ml of this radioactive solution and appropriate amounts of cold indole or 8 ml of the radioactive solution containing both indole and substrate to 25 ml with 65% (v/v) (NH4),S04. When 100 ~1 of the stock solution was added to 10 ml of Bray’s solution it gave a count of approximately 36,000 otslmin. Stock solution and appropriate dilutions of the stock solution with 65% (v/v) (NH,),SO, solution were added to washed chymotrypsin crystals. With each experimental run a series of solutions containing [14C]indole (4 x 10m5 M to 8 x lo-* M) was prepared. These tubes were used to prepare standard curves, in which the molar concentration of [14C]indole was plotted wer.s’szc8radioactivity (cts/min). The oounts were directly proportional to the concentration of indole. The molar concentration of radioactively-labeled indole in the experimental solutions was determined tising the standard curves.

3. Results In the treatment of the data it is assumed that an equilibrium is established between the specific substrate binding site of the crystalline enzyme and substrates or inhibitors in the solution that contains the enzyme crystals. The dissociation constant for the binding of an inhibitor (or substrate) to the crystalline enzyme, is given the following operational definition : (%E, - L,)L K = (n& - EL)L EL = L, ’ The molar concentration of the crystalline enzyme EC was calculated assuming the enzyme was dissolved in the same volume of solution as that in which the experiments were performed. EL represents the molar concentration of enzyme-inhibitor complex, and n the number of binding sites. L and L, are the experimentally determined quantities, the molar concentration of free ligand and bound ligand respectively, in the solution containing the enzyme crystals.

30

L. A. DAVIS

AND

G. P. HESS

Equation (1) can be rearranged and the experimental (L)-1 = n.E,(L,K)-1

data plotted:

- (K)-1.

(2)

Figure 1 shows the data for the binding of indole to crystalline a-chymotrypsin plotted according to equation (2). The negative intercept of the ordinate (--I/K,), gives a dissociation constant for the crystalline a-chymotrypsin-indole complex of 2.4~ 10e4 M. The intercept of the abscissa (I/n) gives a value of 1 for n, indicating a single site for indole binding to a-chymotrypsin crystals.

TABLE 1 Determination of dissociation constants (K,) of crystalline cc-chymotrypsin complexes in 65% (v/v) ammo&m sulfate solution at 20°C Enzyme

E, x lo4

Tosyl-achymotrypsin

2.9 2.5

a-ohymotrypsin

3.5 3.5

Compound added

M

X

10’

Indole I, x 106 I x 10s 10.3 18-9

N-formylq-iodon-phenylalanine

3.0

KS x 10s

10.2 18.5

11.0 Il.0

5*0t 4*6#

1.2

0.6s

ti-chymotrypsin

3.0

cr-chymotrypsin

2.4

N-formyl-Lphenylalanine

4.0

1.2

0.85

34lI

cc-chymotrypsin

2.6

N-formyl-nphenylalanine

5.0

1.2

0.85

33rj

E,, the molar concentration of crystalline enzyme. The concentretion of the crystalline enzyme was calculated assuming the enzyme was dissolved in the same volume of solution BS that in which the experiments were performed. I,,, the initial molar concentration of indole in the solution containing the enzyme crystals. I, the molar concentration of free indole in the solution containing the enzyme crystals. t Kr value for indole of 2.5 x 1O-4 M is calculated. $ KI value for indole of 2.1 x 10V4 M is calculated. 8 Kr value for indole of 2.4 x 10 -4 M is calculated. 7 Based on a Kr value for indole of 2.4 x lo-* M.

Table 1 gives the results obtained when indole is equilibrated with tosyl-a-chymotrypsin crystals, and when N-formyl-L-p-iodophenylalanine or N-formyl-n-phenylalanine is added to equilibrium mixtures of indole and a-chymotrypsin crystals. It can be seen from the Table that tosyl-cc-chymotrypsin crystals do not bind indole. All the indole added to the supernatant of the tosyl-cc-chymotrypsin crystals was found in the supernatant after the 12-hour equilibration period. The data also indicate that when N-formyl-L-p-iodophenylalanine was added to a-chymotrypsin crystals in equilibrium with 0.11 m,M-indole, indole was not displaced from the crystals and has the same K, value as in the absence of this compound (Table 1). These results were checked by X-ray diffraction experiments, in which crystals were equilibrated

CRYSTALLINE

E-CHYMOTRYPSIN

31

with both indole and N-formyl-p-iodo-n-phenylalanine. X-ray diffraction data from these crystals were collected using precession photographs of the h0Z projections. Appropriate reflexions in these photographs were then compared, using a microdensitometer, to the equivalent reflexions of identical photographs of crystals to which either N-formyl-p-iodo-L-phenylalanine or indole was bound. N-formyl-L-phenylalanine displaces indole from the crystals (Table 1). The CCchymotrypsin crystals used in the experiments, when equilibrated with 1.2 x low5 M-indole, are expected to bind half the indole and give a free indole concentration of 0.6 X 10F5 M when K, for indole is 2+4X lo-* M (see equation (1)). As can be seen from the data presented in Table 1, the free indole concentration is 0%5X 10e5 M in the presence of 4X 10V2 M-N-formyl-L-phenylalanine; that is to say, the latter compound has displaced indole from its binding site in the a-chymotrypsin crystals. From these data the dissociation constant, K,, of N-formyl-L-phenylalanine or any other compound (8,) and u-chymotrypsin crystals can be evaluated by the following relation :

Y is the ratio of moles of indole bound per mole of crystalline enzyme in the absence and presence of various amounts of substrate. IO represents the initial molar concentration of indole, S,, the initial concentration of substrate, KI the constant for dissociation of indole from the active site of the crystalline enzyme, and K, the constant for dissociation of the substrate from this site. When the initial concentration of indole and the concentration of indole sites in the crystalline enzyme are held constant from experiment to experiment but S, is varied, K, can be evaluated from the slope of a plot of the data according to a rearranged version of equation (3) :

y = (1 - Y) K KI + IO I, “K,’ A value for K, of 33 mM for the binding of N-formyl-L-phenylalanine trypsin crystals was determined (Table 1).

(4) to a-chymo-

4. Discussion The results of the experiments described are in agreement with structural and chemical information obtained by other methods (Wallace et al., 1963; Bernhard et al., 1966; Brandt et al., 1967; Steitz et al., 1969; Huang & Niemann, 1953; Henderson, 1970; Foster & Niemanu, 1955; Himoe et al., 1967; Matthews et al., 1967; Sigler et al., 1968). The data in Figure 1 indicate only one binding site for indole in u-chymotrypsin crystals, when the indole concentration is less than 0.5 mM, in agreement with crystallographic data (Steitz et al., 1969). Indole does not bind to tosyl-a-chymotrypsin crystals (Table 1) in agreement with X-ray diffraction experiments, which indicate that the tosyl group occupies the specific binding site. The dissociation constant of the crystalline enzyme-indole complex of 2.4 x lo-* M is similar to the known indole-a-chymotrypsin dissociation constant of 3 x lo-* M in solution (Huang & Niemann, 1953).

32

L.

A. DAVIS

AND

G. I’.

HESS

FIN. 1. The binding of indole to a-chymotrypsin crystals in 65% (v/v) (NH&SO4 solution at 20°C. The inverse of the free indole concentrations is plotted versus the quotient, initial chymotrypsin concentration divided by the concentration of enzyme-indole complex. (0) Experiments in which the concentration of indole was determined spectrophotometrically; (0) experiments in which [Wlindole was used. The concentration of crystalline enzyme varied from 2.2 to 4.1 x lo-4 M and the initial indole concentration was varied from 1.6 to O-4 x 10m4 M. The reciprocal of the intercept of the abscissa gives the number of indole binding sites n. (?z = 1) and the negative of intercept of the ordinate is equal to -l/K, (K, = 2.4~ lo-* M). The molar concentration a-ohymotrypsin is obtained by considering the crystals to be dissolved in the volume of solution in which the crystals are suspended.

The data in Table 1 show that N-formyl-L-phenylalanine displaces indole from the specific binding site of a-chymotrypsin crystals. The K, value determined in these studies (Table 1) is similar to the known constant for this compound binding to the enzyme in solution (Poster 8.rNiemann, 1955). Prom the K, value and the solubility of N-formyl-L-phenylalanine, it can be calculated that this compound can occupy the specific binding site in the crystal sufficiently to determine the structure of the complex by X-ray diffraction methods. The crystal structure of this complex has been determined (Henderson, 1970). The indole displacement experiments (Table 1) indicate that N-formyl-p-iodoL-phenylalanine does not displace indole from the specific substrate binding site of the crystalline enzyme. These results are consistent with X-ray diffraction experiments, which indicate that this substrate analogue does not bind to the specific substrate binding site in the crystal (Henderson, 1970). Unlike the inhibitor displacement experiments described, direct binding measurements with a substrate and a-chymotrypsin crystals would not differentiate between specific and non-specific substrate binding sites. The data indicate that once the structure of a specific complex between a crystalline protein and an indicator compound have been determined by X-ray diffraction, the displacement of the indicator from its specific site by other compounds can be used to determine binding parameters of a compound by the technique described. Compounds that do not bind to the specific site of the enzyme correctly, or that bind to regulatory sites in allosteric enzymes, may also displace this indicator compound. Compounds that bind to non-specific sites are eliminated from further studies. The method is simple, rapid and, therefore, capable of screening many compounds as to their suitability for X-ray diffraction experiments. The displacement of a chromophoric inhibitor from its specific site in the crystal by substrate can be measured as part of kinetic investigations. This information, together with a knowledge of the diffusion constants of the chromophoric inhibitors, allows one to determine the

CRYSTALLINE

a-CHYMOTRYPSIN

33

concentration of enzymic sites that participate in the enzymic reaction, and, therefore, determine the efficiency of catalysis in the crystal. Initial investigations of oompounds suitable for structure determinations by preliminary X-ray diffraction studies have been markedly improved by the method and techniques developed by Richards and co-workers (Wyckoff et al., 1967). Nevertheless, the X-ray measurements are slow compared to the chemical measurements described in this paper and are not suitable at present for monitoring kinetic experiments with crystalline proteins. One of us (L. A. D.) is grateful for support received from the National Institutes of Health grant no. GM0082410 awarded to the Section of Biochemistry and Molecular Biology, Cornell University, Ithaca, N.Y. 14850, U.S.A. One of us (G. P. H.) was a United States Public Health Service Fellow (1969-70) when the work reported here was done. We wish to thank Drs Christine Wright, Richard Henderson and David Blow for their patient tutelage in X-ray diffraction methods, and Drs Max Perutz and David Blow for their hospitality. REFERENCES Bernhard, S. A., Lee, B. F. & Tashjian, Z. H. (1966). J. Mol. Biol. 18, 405-430. Birktoft, J. J., Blow, D. M., Henderson, R. & Steitz, T. A. (1970). Phil. Trans. Roy. Sot. London (Xer. B), 257, 67-76. Blow, D. M. & Steitz, T. A. (1970). Annu. Rev. Biochem. 39, 63-100. Brandt, K. G., Himoe, A. & Hess, G. P. (1967). J. Biol. Chem. 242, 3973-3982. Bray, G. A. (1960). ArzaE. Biochem. 1, 279-295. Dixon, G. H. & Neurath, H. (1957). J. Biol. Chem. 225, 1049-1059. Doscher, M. & Richards, F. M. (1963). J. Bill. Chem. 238, 2399-2406. Foster, R. C. & Niemann, C. (1955). J. Amer. Chem. Sot. 77, 1886-1892. Hartley, B. S. & Kilby, B. A. (1954). Biochem. J. 56, 288-297. Henderson, R. (1970). Ph.D. Thesis, University of Cambridge, England. Himoe, A., Brandt, K. G. t Hess, G. P. (1967). J. BioZ. Chem. 242, 3963-3972. Huang, H. T. & Niemann, C. (1953). J. Amer. Chem. Sot. 75, 1395-1401. Matthews, B. W., Sigler, P. B., Henderson, R. & Blow, D. M. (1967). Nature (London), 214, 652-656. Quiocho, F. A. Bt Richards, F. M. (1966). Biochemistry, 5, 4062-4076. Sigler, P. B., Jeffery, B. A., Matthews, B. W. t Blow, D. M. (1966). J. Mol. Biol. 15, 175-192. Sigler, P. B., Blow, D. M., Matthews, B. W. & Henderson, R. (1968). J. Mol. BioZ. 35, 143164. Sluyterman, L. A. AE. & de Graaf, M. J. M. (1969). Biochim. Biophys. Acta, 171,277-287. Steitz, T. A., Henderson, R. & Blow, D. M. (1969). J. Mol. Biol. 46, 337-348. Wallace, R. A., Ku&z, A. N. & Niemann, C. (1963). Biochemistry, 2, 824-836. Wyckoff, H. W., Doscher, M., Tsernoglou, D., Inagami, T., Johnson, L. N., Hardman, K. D., Allewell, N. M., Kelly, D. M. & Richards, F. M. (1967). J. Mol. Biol. 27, 563578.