Myron 1. Bender, Ferenc J. ~ & d ~ , and Fred C. Wedler
Northwestern University Evanston, lllinois 60201
a-Chymotrypsin: Enzyme Concentration and Kinetics
Alpha-chymotryysin is one of many crystalline enzymes whose properties can he investigated on a molecular basis. Its physiological role is the catalysis of the hydrolysis of protein; thus it is a catalyst for the cleavage of peptide or amide bonds. In addition to the cleavage of polymeric amides, it also catalyzes the cleavage of amides of individual amino acids (1). Furthermore, it catalyzes the hydrolysis of all other carboxylic acid derivatives, in addition to that of amides. For experimental reasons, the hydrolysis of esters is the most convenient reaction for the investigation of a-chymotrypsin catalyses. a-Chymotrypsin is a protein of molecular weight 24,800 (9)which has one "active site" per molecule, defined by the fact that it reacts stoichiometrically with the nerve gas, diisopropylphosphoroAuoridate,to give a monophosphorylated enzyme which is completely inactive (3). The phosphorus atom of diisopropylphosphorylchymotrypsin was found to be bonded to the hydroxyl group of a serine amino acid of the enzyme by hydrolysis of the phosphoryl derivative and identification of serine phosphate (4). This particular serine was later identified as amino acid 195 in the sequence of 246 amino acids1 (5). On the basis of this stoichiometric reaction, a-chymotrypsin has been called a serine proteinase (6). Other members of this family of enzymes include trypsin, elastase, thrombin, plasmin, and subtilisin. Of this family of related enzymes, a-chymotrypsin is the enzyme most carefully studied because of the ease of its isolation and purification and the straightforwardness of its study. In common with essentially all enzymes, the reactions catalyzed by a-chymotrypsin are characterized by a saturation phenomenon. That is, when a plot is made of reaction velocity versus substrate concentration, as shown in Figure 1, linear behavior is observed a t low substrate concentrations; but at very high substrate concentrations, the velocity eventually becomes independent of the substrate concentration. This phenomenon may be easily reconciled with a situation involving avery low concentration of enzyme (catalyst), a very high concentration of substrate, and the requirement that the enzyme bind the substrate before the catalytic reaction takes place. This situation is definedby eqn. (1), where:
E is enzyme, S is substrate, K , is the (dissociation)
'
The amino acid sequence was crtrried out on ehymotrypsinogen, the precursor of the enzyme.
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Journol of Chemical Education
constant. of binding, and k, is the catalytic rate constant. When [Slo is greater than [Elo it may be readily shown that:
where V is the velocity and Vm, the maximal velocity of the reaction graphed in Figure 1. Equation (2), usually described as Michaelis-Menten kinetics (7) based on some original observations of Henri, (8) adequately describes the behavior in Figure 1.
[SUBSTRATE] Figure 1. The effect of rubstrote concentrotion on tho rate of on enzyme. catalyzed reaction.
Spectrophotometric methods have played a large role in the elucidation of the kinetics of a-chymotrypsin catalyses. In particular, chromophoric substrates have been of great importance since they permit the observation of low concentrations of substrate, and thus permit the observation of corresponding low enzyme concentrations in stoichiometric reactions b e tween enzyme and substrate. One of the first such chromophoric substrates of or-chymotrypsin was pnitrophenyl acetate (9). a-Chymotrypsin was shown to catalyze the hydrolysis of this substrate, but the reaction proceeded in a very peculiar fashion (10). When the reaction was carried out using a much greater substrate than enzyme concentration, the reaction, as monitored by the appearance of p-nitrophenol, appeared to be biphasic. Initially a concentration of p-nitrophenol approximating the enzyme concentration was rapidly liberated, followed by a slow (zero-order) release of p-nitrophenol, PI, as shown schematically in Figure 2. This behavior implied two rate steps in the reaction, one of which was controlled by a stochiometric process between substrate and enzyme. Thus, two distinctly different rate
covalently to the serine of thc active site. This hypothesis was confirmed when radioactive p-nitrophenyl acetate was used. The enzyme-substrate compound isolated from this reaction was radioactive; furthermore, on degradation of this enzyme derivative, the radioactivity was found associated with the same serine 195 as in the reaction with diisopropylphosphorofluoridate (12). Thus, eqn. (3) may be described chemically as:
-11
-
n
En--OH
n
+ RCOR' = (EnOH .R h R ' ) Kn
0 ka
ks
e En0 R TIME Figure 2. Schematic drawing of the a-chymotryprin-catalyled hydrolyrir of p-nitmphenyl asetato with [SO] [Ed (after Honley ond Kilby (1011. The flrst absorbance reading war taken after m e minute (min time scale).
>>
TIME Figure 3. .%hematic drawing of the a-chymotryprin-cotoiyzed hydrolysis of some p-nitrophenyl & e n with [SO] [Ed: (1)p-nitraphenyl acetate (ohor Gutfrevnd and Sturtevant (1311; the fint absorbance reading war recorded after m. 5 mros (mrec time scale); 121 p-nitrophenyl trimethylacetate (after McDonald and Balls (14111 the first absorbance reading war recorded after thirty seconds lrec time scolel.
>>
steps must be added to the primary adsorption step, leading to a description of the a-chymotrypsin catalysis as a three step reaction, as shown in eqn. (3) :
where E is enzyme, S is substrate, E .S is the (adsorptive) enzyme-substrate complex, ES' is the product of the stoichiometric reaction of the substrate with the enzyme, liberating one mole of p-nitrophenol (PI)per mole of enzyme, and Pa is acetate ion. If one defines ES' as an acetylenzyme and further specifies that kz >> k8,then the experimental observation of Figure 2 may be explained. When the p-nitrophenylacetate-a-chymotrypsin reaction was carried out in acid solution (pH 5), the initial "burst" of pnitrophenol was still observed, hut the subsequent zero-order reaction was so slow as to be nearly negligible. This observation suggested the possibility of the isolation of the intermediate compound, ES' (11). This was, in fact, accomplished. The compound ES' proved to be completely inactive enzymatically when isolated a t pH 5; but when the pH was changed to 8, and especially when the nucleophile hydroxylamine was added, complete enzymatic activity was restored. These observations were rationalized on the basis that the compound ES' was acetyla-chymotrypsin, in which the acetyl group was bound
-t
EnOH
+R
+R' OH
Using a stopped-flow spectrophotometric technique that permitted observations on a millisecond time scale, it was found that the reaction in Figure 2 could more accurately be described as shown in Figure 3 (IS). That is, the initial "burst" of p-nitrophenol was not infinitely fast but was, in fact, measurable on a faster time scale. The a-chymotrypsin-catalyzed hydrolysis of p-nitrophenyl trimethylacetate was shown to exhibit the same characteristics as the hydrolysis of p-nitrophenyl acetate. However, since the former ester is sterically hindered by the bulky trimethylacetate group, all of its reactions are slowed down, and the behavior shown in Figure 3 is seen on a "seconds" time scale (14). In fact, the rate constants of its reaction are so small that it was possible by careful technique to crystallize the compound trimethylacetyl-a-chymotrypsin at low pH (15). Thus, the a-chymotrypsincatalyzed hydrolysis of p-nitrophenyl trimethylacetate is a particularly convenient reaction to use to investigate chymotrypsin reactions. Theory of Kinetics:
The observations from Figure 3 allow the calculation of the following quantities: (1)the absolute concentration of enzyme in the solution; (2) the binding constant Ks; (3) the rate constant of acylation of the enzyme, kz, and (4) the rate constant of deacylation of the acyl-enzyme, ka. It is the object of this experiment to determine some of these quantities in the a-chymotrypsin-catalyzed hydrolysis of p-nitrophenyl trimethylacetate. A complete kinetic description of reactions following eqns. 3 and 4 has been given (IS, 16, 17). The following derivation is based on the work of R6zdy and Bender (17). The following conservation equation and differential equations follow from eqn. (3), assuming [Slo >> [Elo.
+
+ [ES'I
[El, = [El [ESI d[P,]/dt = b[ESl d[Pn]/dt = kdES'1 dWS']/dt
=
b[ESl
(5) (6) (7)
- ka[ES']
(8)
Since we have five unknowns and only four equations, we need one further equation. The simplest fifth equation is produced if we assume that the primary adsorptive step, E S ES, is a fast pre-equilibrium:
+
Ks
=
[El [SI
[ES]
Volume 44, Number 2, February 1967
(9)
/
85
Since [S]
[SIo,eqn. (9) may be transformed to: (El = [ESlKsl[Slo
(10)
Usingeqn. (lo), eqn. ( 5 ) may be transformed to: [ES]
=
[El, - IES'I Ks l+m
Then eqn. (8) may be transformed to:
For a given experiment, t,he first term and the coefficient of the second term are constants, and thus eqn. (12) may be transformed t,o eqn. (13) where
and k* = kr + 1 (Ksl[Slo) d[ES'l/dt = a - b[ES'l
obtain b is to subtract the experimental [PI] curve from the extrapolated straight line and plot the differences according to a first-order equation. Thus, we have as primary experimental observahles the slope and intercept of the straight line portion of Figure 3-A and B respectively-and the first-order rate constant, b, of the initial exponential part of the curve. What can we do with thesevalues? Let us consider A first. Substituting values of a and b (eqns. (12) and (13)) into the value of A (eqn. (19)) gives
Equation (21) has the form of an expression for the rate of a reaction conforming to eqn. (2)-that is, Michaelis-Alenten kinetics. This expression can be transformed to
+
by using the transformations kc., = k2k3/(kz ka) and K, (apparent) = KSk3/(k2 k3) which follow directly from the relationship between eqns. (21) and (22). The reciprocal of eqn. (22) gives:
+
+
(13)
Equation (13) is integrable, as shown in eqn. (14). -l/b
In (a - b [ES'I) = t
+c
(14)
When t = 0 and [ES'] = 0, c = (l/b) In a. Suhstitution of thisvalue of c into eqn. (14) gives:
[ES'] =
b
Thus by determiningA at several [Slis, and by plotting 1/A versus 1/[SIa, k, [Elo and K, (apparent) can be determined from the intercept and slope/intercept ratio respectively. Alternatively from eqn. (22), if [Slo>> K, (apparent), then A = kc,, [Elo. The value of B gives a direct measure of [Elo. From eqns. (19) and (12) :
(1 - e"')
Snhstitntingeqn. (16) into eqn. (11) gives:
Then snbstitutingeqn. (17) into eqn. (6) gives:
Equation (18) may be integrated to yield an equation which predicts the observable curve in Figure 3, [PI] versus t:
Equation (19) has the form of: [P,]
=
At
+ B(l - e - 9
(20)
which is seen to be the form of the curve in Figure 3. From eqn. (20), the following relations may be seen. At t approaching infinity, [PI] = At B, a straight line relationship. On the other hand, at very low t, [PI] = At B - Bed'. Thus the extrapolated straight line from large t, [PI] = At B, minus the value of [PI] at very small t, [PI] = At B - Bed', will yield Be&'. In practice all that need be done to
+
+
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Journal of Chemicol Education
+ +
Thus if ks kP, this determination will also lead to [Elo. According to eqn. (12), the constant b is given as follows:
I n the or-chymotrypsin-catalyzed hydrolysis of pnitrophenyl trimethylacetate, k3 K g > [Ela reasonably well. Became of the very high kdkp rat,ia even vdoes below 10 deviate only slightly (see Fig. 4).
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Journal of Chemical Education
Literature Cited (1) BERGMANN, M., AND FRUTON,J. S., Advon. Enzymol., 1, 63
b =
of tallis solution (to detect any impurity) and the spontaneous hydrolysis of the substrate are then measured spectrophotometrically, over the length of time expected for the reaction course. Although the (linear) spontaneous hydrolysis is small, it must be subtracted from the observed [PI a t a given time, before any calculations are made. Then 1G50 pl of the enzyme stock solution is introduced, with stirring for about 5 sec (20 pl should give [Elo = 1 X M). Then spectrophotometric readings are again taken up to 2000 see. Optimal concentrations that conform to the requirement* of [SIo>> [Eloand also to the requirement that [Elo is large enough so that the "initial burst" of pnitrophenolate may he seen are [SIo = 1 X 10W4 M and [Elo= 1 X M, as described above. Data obtained from an experiment conducted with a Beckman DU spectrophotometer under conditions approximately these are shown in Figure 4. From the slope, intercept, and exponential of a plot such as Figure 4, A, B, and b, defined above, may be obtained. The value of B gives the enzyme concentration directly.
88
From the pseudo first-order rate constant b, the value of k2[SIo/Ksmay be obtained directly. Using both the slope A and the intercept B, the value of k,, = ka may be calculated. Both kp[SIo/Ksand ka depend on a basic catalytic group on the enzyme of pK. approximately 7. Thus, if the above reaction is conducted a t pH 7, these rate constants will be only 50% as large as at pH 8.5. Doubling the enzyme concentration at constant [SIoshould double both the intercept B and the slope A but should not affect the rate constant b. Doubling the substrate concentration a t constant [Elo should not affect either the intercept B or the slope A but should double the rate constant b.
,
,
(4) SCHAFFER, N. K., MAY,S. C., JR., AND SUMMERSON, W. El., J . B i d . Chem., 206, 201 (1954). (5) HARTLEY, B. S., Nature, 201, 1284 (1964). B. S., Ann. Revs. Bwehem., 29, 45 (1960). (6) HARTLEY, (7) MICHLELIS, L. AND MENTEN,M., Bioehem. Z., 49, 353 (1913). HENRI,V., C. R. Acad. Sci., Paris, 135, 916 (1902). HIRTLEY,B. S., AND KILRY,B. A., Biochem. J., 50, 672 (1952). HARTLEY,B. S., AND KILBY,B. A,, Bioehem. J . , 56, 288 (1954).
BILLLS,A. K., AND ALDRICA, F. L., PTOC. Natl. Aead. Sci, U S . , 41, 190 (1955); BALLS,A. K., AND WOOD,H. N., J . Bid. Chm., 219, 245 (1956). OO~TERBAAN, R. A,, AND VAN ADREHEM,M. E., Biochem. Biophys. Acla, 27, 423 (1958). GUTFREUND, H., AND STURTEVANT, J. M., Bioehem. J., 63, 656 (1956); GUTFREUND, H., AND STURTEVANT, J. M., Proc. Natl. Acad. Sci., U S . , 42, 719 (1956). MCDONALD, C. E., AND BALLS,A. K., J. Biol. Chem., 227, 727 (1957).
BALLS,A. K., MCDONALD, C. E., AND BRECEER,A. S., Proc. Int. Symp. Enzyme Chem., Tokyo, Maruaen, 392 (1958).
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. OWLLET.L.. AND STEWART.J. A,. Can. J . Chem... 37.. 737
(1959): (17) KBZDY,F. J.,
AND
BENDER,M. L., Biochemistry, 1 , 1097
(1962). \----,-
(18) BENDER,M. L., AND HAMILTON, G. A,, J . Am. Chem. S O ~ . , 84, 2570 (1962).
