March 20, 1933 [CONTRIBUTION KO.
HYDROLYSIS OF NICOTINYL-L-TRYPTOPHANAMIDE 1716 FROM THE GATESAND CRELLIN LABORATORIES OF CHEMISTRY,
1395
CALIFORNIA INSTITUTE OF
TECHNOLOGY]
The Inhibition of the a-Chymotrypsin-catalyzed Hydrolysis of Nicotinyl-L-tryptophanamide and of Methyl Hippurate by Indole1 BY H. T. HUANG AND CARLNIEMANN~ RECEIVED AUGUST18, 1952 It has been observed that while indole competitively inhibits the a-chymotrypsin-catalyzed hydrolysis of the trifunctional specific substrate, nicotinyl-L-tryptophanamide, it causes an entirely different type of inhibition in the hydrolysis of the bifunctional specific substrate, methyl hippurate. A consideration of the steric implications of the three center hypothesis has led to the conclusion that only with a bifunctional specific substrate and a monofunctional inhibitor will there be formed, in addition to the binary complexes arising from the separate interaction of the inhibitor and the specific substrate with the enzyme, a ternary complex resulting from the concurrent interaction of both the inhibitor and the specific substrate with the enzyme. Detailed analyses of the experimental data indicate that the kinetic behavior of the system a-chymotrypsinmethyl hippurate-indole is consistent with the above prediction and, if it is assumed that the affinity of a-chymotrypsin for indole is identical in the two reactions studied, that the ternary complex ESI is hydrolyzed a t a significantly lower rate than the binary complex ES. These results, therefore, provide support for the three center hypothesis as applied to a-chymotrypsin.
Our present knowledge3-j of the structural reIt is known that both types of bifunctional coinquirements of synthetic specific substrates of a- pounds in which a particularly susceptible RSgroup chymotrypsin is consistent with the hypothesis that is present, ;.e., R1CH2R3 as in methyl hippurate" a typical trifunctional specific substrate of the.gen- and R2CH2R3 as in methyl P-phenylpropionate,l2 eral formula R1CHR2R3,6 derived from an . ~ - a - can, when the second R group in the molecule posamino acid, combines with the catalytically active sesses a relatively high affinity for the enzyme, serve site of the enzyme a t three centers, pl, p2 and p3, as specific substrates for a-chymotrypsin. Thus which present a complementary aspect to the three the availability of bifunctional specific substrates characteristic structural features, R1, Rz and R3, and monofunctional inhibitors makes it possible to of the specific substrate.' Although the nature of devise a more stringent test of the steric requirethe forces involved in each of the three interactions, ments of the three-center hypothesis than has been Rl-pI, Rz-P~and R3-p~)is by no means well under- hitherto practicable. In a system containing enzyme and a bifuncstood, i t may be inferred from purely steric considerations, that if a close fit does exist between the R tional specific substrate the intermediate complex groups and the p centers, a blocking of any one, or ES, l 3 which is subsequently transformed into free two of the three centers will result in an impairment enzyme and reaction products, can be represented of the ability of the active site as a whole to combine by formulas I or 11. The three center hypothesis with a trifunctional specific substrate. Thus, it may be predicted that a compound which contains but two R groups separated from each other by the optimum distance, or one which may be considered to I I1 consist of only asingle K group, should be capable of functioning as a competitive inhibitor in the requires that in each complex one of the p centers a t a-chymotrypsin-catalyzed hydrolysis of a trifunc- the active site remains unoccupied. If the combintional specific substrate. A study of the effect of ing power of the vacant p center in I and I1 is revarious compounds on the kinetics of hydrolysis of tained, a t least in part, the introduction of a mononicotinyl-L-tryptophanamideand of acetyl-L-tyro- functional inhibitor, Rz or R1, into the system will sinamide has provided examples of competitive inhi- lead t o the formation of the ternary complex, I11 or bition of the a-chymotrypsin-catalyzed hydrolysis IV. The kinetic behavior of such a system will of a trifunctional specific substrate by all three be dependent upon the properties of the ternary possible types of bifunctional inhibitors, i.e., R1CH2R2,8RzCHzR39~10 and R1CH2R3,11and conipetitive inhibition of the a-chymotrypsin-catalyzed hydrolysis of a trifunctional specific substrate by 111 I \. a t least one monofunctional inhibitor, i.e., benzamcomplex. I t will, however, no longer assume the ide, has been observed.1° character of a classical competitive system as might (1) Supported in part by a grant from Eli Lilly and Company. be expected of one containing enzyme, a monofunc(2) T o whom inquiries regarding this article should be sent. tional inhibitor and a trifunctional specific substrate. (3) H. Neurath and G . TV. Schwert, Chem. Reus., 4 6 , 69 (1950). (4) H . J. Shine and C. Niemann, THIS JOURNAL, 74, 97 (1952). It thus appears possible, from an analysis of kinetic ( 5 ) H. T. Huang, R. J. Foster and C. Niemann, ibid., 74, 105 data relative to the enzymatic hydrolysis of a suit(1952). able bifunctional specific substrate in the presence (6) Where Ra is a functional derivative of the carboxyl group; Rz, the a-amino acid side chain; and RI, the remaining unspecified of an appropriate monofunctional inhibitor, to desubstituent of the a-carbon atom. duce the existence of a ternary complex of type I11 (7) H. T. Huang and C. Niemann, ibid.,73, 3223 (1951). and IV, which would in turn provide an indirect (8) H . T. Huang and C. Niemann, ibid., 74, 101 (1952). (9) H. Neurath and J. Gladner, J . Bid. Chevz., 188, 407 (1961). (IO) H. T. Huang and C. Niemann, THISJ O U R N A L , 74, 5863 (1952). (11) H. T. Huang and C. Niemann, ibid., 74, 4634 (1952).
(12) J E Snoke and H. Neurath, Avch. Biochem., 21, 351 (1949). (13) F u r definition of the symbols used in this communication, 6.f. H. T. Huang and C. A-iemann, THISJ O U R N A L , 73, 1341 (1951).
H. T. HUANG AND CARLNIEMANN
1396
demonstration of the plausibility of the three center hypothesis. Preliminary Studies Methyl hippurate, R1CH2K3, where R1 = benzatnido and RB = carbomethoxy, was selected as the bifunctional specific substrate for the proposed study, because its kinetics of hydrolysis had been previously studied in aqueous media,“ and it had had been shown to react with the same catalytically active site as that involved in the a-chyniotrypsincatalyzed hydrolysis of a number of trifunctional specific substrates of the acylated a-amino acid amide type. l1 In order to find a suitable monofunctional inhibitor of structure KPthe inhibition of the a-chymotrypsin-catalyzed hydrolysis of nicotinylL-tryptophanamide by several monofunctional compounds was examined, and the results of these experiments are summari/,ed in Table I. It is apparent that of the compounds listed in Table I indole is the most useful inhibitor for the proposed study. I t not only possesses a high affinity for the enzyme but is also sufficiently soluble in aqueous media to permit its use over a wide range of inhibitor concentrations. The observed order of affinity, indole >> phenol, was anticipated from previous studies.l 4 - I 6
VOl. 75
Either V or VI can react with a second molecule of the inhibitor to form the ternary complex VII. As the formation of all three of the above complexes may prevent the active site from combining with a trifunctional specific substrate i t is, therefore, advisable that a detailed analysis be made of the effect that the formation of a ternary complex such as VI1 may have on the kinetics of hydrolysis of a trifunctional specific substrate in the presence of a monofunctional inhibitor such as indole. iVe have accordingly studied in detail the system a-chymotrypsin-nicotinyl-L-tryptophanamide-indole. The experimental conditions were identical with those employed in the preliminary investigation, with appropriate variations in the specific substrate and inhibitor concentrations. The reaction between the enzyme and the specific substrate rimy be formulated in terms of equation (l), where k’s = (k, k8)jkl. Since in all experi-
+
Ei
+ St
ki
k3
ES + Er
ki
+ PI, + Pz,
(1)
nients the extent of hydrolysis of the specific substrate was limited to within 30 %, the reaction of the enzyme with one of the hydrolysis products13 can be justifiably ignored. On the basis of the asTABLE I sumption that indole reacts with pz to give E1 (V), I\HIBITIOY OF THE CY-CHYMOTRYPSIN-CATALYZED HYDROLY- and that it also reacts with p1 to give EI’ (VI) we SIS OF SICOTINYL-L-TRYPTOPHANAMIDE BY SEVERAL MONO- may introduce equations (2) and (3) where K I = FUNCTIONAL COMPOUNDSa-C kj,/k4 and Inhibition,
Inhibitor
[I]*
G6
Approx K I e
Cyclohexanol 36 9 80 Pyridine 5il 20 50 Kicotinamide 20 8 50 Phenol 20 3s 7 0 Skatole ) 52 1 f) Indole I 6 (1 o 72 a In aqueous solutiolis a t 25” and pH 7.9, 0.02 Jf with respect t o the amine component of a tris-( hydroxymethy1)aminomethdne-hydrochloric acid buffer, with the rate determined by a formol titrati0t1.l~ * [SI = 10 X 10-3 Jf, KS = 2.7 X 10-3 W . l a c [E] equivalent to 0.208 mg. protein-nitrogen per 1x11. * [ I ] in units of 10-3 Af. * Calculated on the assumption that the inhibition is competitive, K I in units of 1 0 - 3 Bi.
Effect of Indole on the Hydrolysis of Nicotinyl-Ltryptophanamide Although i t is to be expected that indole will interact principally with the pz center, i t cannot be assumed that i t will do so exclusively. It should be realized that the exact mode of interaction of a monofunctional inhibitor of the type RJ, or Rz, with the active site of the enzyme as visualized in the three center hypothesis, is a matter of considerable uncertainty. For example, i t has been noted previouslyln that a compound such as benzamide, because of its structual relationship to a number of common Rz and R1 groups, may be capable of interacting not only with pz but also with pl, to form the binary complexes E1 (V) and EI’ (VI).
5‘ ~
1-I
VII
~
(14) H. T . Huangand C. Niemann, THISJ O U R N A L , I S , 1535 (1951). (15) D. W. Thomas, R. V. MacAllister and C. Niemann, i b i d . , 73, 1348 (1951).
Er
+ Ir + If
Er
kr
E1
(2)
k.5 ks
EI’
ki
li, = k7/k6. The ternary complex EII’ (VII) may be formed from either EI’ or E1 according to equations (4) or ( 5 ) . EI’
+ If
E1
kr
I
k,
i
+ If If
EII’
(4)
ks i
EII’ k7
(5)
I
When all reactants possess unit activity coefficients it follows that
+ k7 iJEII’] - kB[EI] -
d[EI]ldt = kr[Er][If]
k6 i[EII[Irl (6) d[EI’]/dt = ks[Er][Ir] -/- k, i[EII’] - k7[EI’] k4 i[EI’I[Irl ( 7 ) d[EII’l/dt = k4 i[EI’lDfl ks 1[EI1[1tl (ks 1 k7 i)[EII’I ( 8 )
+
+
If it is assumed, as a first approximation, that k4>> kq1, k5 >> k51, kg >> ks.1 and k7 >> k71 then for the steady state condition, d [EI]/dt = d [EI’]/dt = d[EII’]/dt + 0, and with Ks = [Sf][Er]/[ES], KI = [Irl[ErI/’[EI] and K , = [Irl[Ef]/[EI‘l, equations ( 6 ) )(7) and (8) lead to the relations given in equations (9) and (10). lE11’1
[ I f ] * X Ks/[Srl X [ES]/Cr
~/C= I (kal’KL
+ ksl/Kr)(l/(ksi +
k71))
(9) (IO) = K,1
If by definition k6.1Ik41 = kr 1 and k71/k61 equation (10) may be transformed into equation
HYDROLYSIS OF NICOTINYL-L-TRYPTOPHANAMIDE
March 20, 1953
1397
(11). When [Sr]= [SIand [If] = [I], ;.e., when the system is in zone A with respect to both specific
The results of experiments a t four different inhibitor concentrations are summarized in Fig. 1 and in Table 11. These data indicate that the system is 1lC1 = I/KXI(Kxks.I/Kr.1 K~k7.1/K~.l)l/(ks.l +k7 1) essentially one of competitive inhibition because (11) within the range of the values of [I] studied, ;.e., substrate and competitive inhibitor,16*" [ E I ] , 0.70 to 5.0 X M , no apparent decrease in the [EI'] and [EII'] may be expressed in terms of [ES] KI' value was observed. as in equation (12). If by definition ZJ = lia[ES]
+
[ESI = [EI[Sl/(Kdl
+ [II/KI + [II/KL+ [112/CI) + [SI) (12)
I
9
IO
and I' = & [ E ] equation (12) can be transformed into equation (13). l / v = Ks/V(l
[I]: 5.0
+ [II/Kr + [II/Kc + [I12/C~)ll[SI+
9
1 / V (13)
Thus for a series of experiments a t a constant inhibitor concentration a plot of l/vo versus ~ / [ S ] would O be expected to give a straight line with the same intercept as for the case when [I] = 0. Comparing equation (13) with the Lineweaver and Burk equation for competitive inhibition, l8 Le., equation (14) i t is evident that the value of the I/v = Ks/V(l
+ [ I I / K I ' ) ~ I [ S I+ 1/J'
apparent enzyme-inhibitor
dissociation constant
suming simple competitive inhibition, will be given by equation (15).
+ + KIKI[I]/CI)
7 I/vo. 6
(14)
KI', determined from a l/vo versus l/[S]o plot asKI' = K I K L / ( K I Ki
8
(15)
It is seen from equation (15) that the value of KI' is not independent of [I] and will increase as [I]is increased. The actual contribution of the term containing [I] to the value of KI' will be dependent upon the magnitude of the relative affinity ratio KI/K,/CI which may be considered as an index relating the affinity of the binary complexes and that of the free enzyme for the inhibitor. The relation between K I K , and CI may be appreciated from an examination of equation (11) and by comparing the affinity of the inhibitor for the free enzyme Er, ;.e., the K I and K i values, with that for the binary complexes E1 and EI', Le., the K1.1 and K1,l values. Three possible conditions may exist, viz., (a) KIJ < KI and K1.l < K , with CI < KrKl; (b) K1.1 = KI and Kb.l = Kt with C = KIKL; and (c), KIJ > KI and K,.I > K , with CI > KIK,. For steric reasons it appears unlikely that an interaction between indole and p1 or p2 will facilitate the interaction of a second molecule of indole with one of the remaining p centers. Thus i t may be assumed that the first condition considered above can be ignored and that the term KIKJCI can be considered to be equal to or less than unity. TABLEI1 APPARENTENZYME-INHIBITOR DISSOCIATION CONSTANTS O F a-CHYMOTRYPSIN A N D INDOLE",^ [II" 0.70 1.60 2.40 5.0 KI" 0.71 0.68 0.68 0.72 At 25' and pH 7.9 in aqueous solutions 0.02 M with respect t o the amine component of a tris-( hydroxymethy1)aminomethane-hydrochloric acid buffer. * Specific subM. strate nicotinyl-&-tryptophanamide, & = 2.7 X c In units of 10-3 M . (16) 0.H.Straus and A. Goldstein, J . Gin. Physiol., S I , 559 (1943). (17) A. Goldstein, ibid., 37,52 (1944) (18) H. Lineweaver and D.Burk. T x i a J O U ~ N A L . I S . 658 (1934).
5
4
3
0 Fig. 1.-Competitive inhibition of the a-chymotrypsincatalyzed hydrolysis of nicotinyl-L-tryptophanamide by indole in aqueous solutions at 25' and pH 7.9; vo in units of Mlmin.; [SIand [I] in units of M ; [E]equivalent t o 0.208 mg. protein nitrogen/ml.; 0.02 M tris-(hydroxymethyl)-aminomethane-hydrochloric acid buffer.
Two sets of conditions will cause the term containing [I] in equation (15) to become negligible, Viz., (a) when the affinity of the inhibitor for one of the two reactive p centers is much greater than that for the other, e.g., when K , >> K I then KI' + K I ; and (b) when CI >> KIK, then K I + K I K J (KI K,). It may be argued that if the condition CI >> K I K , is true, then KIJ >> K I and K,.I >> K,, and the concentration of EII' in the system will be experimentally unimportant. In other words, this condition implies that the combination of either p1 or p2 with indole will effectively hinder the vacant p centers from interacting with another indole molecule. While the structure and properties of the active site may be such that this condition can be accommodated, such a limitation makes it extremely improbable that any significant amount of a ternary complex of type 111 could be formed and the system a-chymotrypsin-methyl hippurateindole would also be expected to behave as one involving only classical competitive inhibition. Since the results of studies on the latter system, which
+
are presented later, do show marked deviations
Vol. 75
H. T. HUANG AND CARLNIEMANN
1398
from the kinetics of classical competitive inhibition, it appears reasonable t o assume that the first condition postulated above is true, and that the interaction between indole and the active site principally involves the center p z . It may, of course, be contended that in the system under consideration both of the above conditions are only partially operative, i.e., K, > K I but not >> K I and CI > but not >> KIK,. While K I , A-L and Cr all have significant values relative to each other, the two factors are jointly effective in reducing the actual degree of dependence of the KI’ value on the value of [I]. I t is of interest to define the limiting values for K I / K , and KIK,/’CI. For an error of *5% in the mean K I ’ value it may be assumed that Kr’ a t [I] = 0.70 X l o w 3-I[, is 0.70, and KI’ a t [I] = 3.0 X Jf is 0.655. CI is then 50.6. Thus, if K I / K , > 0.10 then &K,/ CI must be > K I is, for all practical purposes, a valid approximation for the system under consideration. Effect of Indole on the Hydrolysis of Methyl Hippurate The system or-chymotrypsin-methyl hippurateindole was studied under the same conditions and within the same limitations as those employed in the previous investigation of the cr-chymotrypsincatalyzed hydrolysis of methyl hippurate itself .I1 In the following discussion of various modes of interaction of the inhibitor, the specific substrate and the enzyme it is assumed that of the possible reactions between indole and achymotrypsin, as depicted by equations (a),(3) and (4), only (2) need be considered as significant, ;.e., KI‘ = K I . As has been pointed out previously,ll methyl hippurate (R1CHnR3,R1 = benzamido and R3 = carbomethoxy) may react with the active site of the enzyme in two ways to give: the susceptible complex ES (R1interacts with p1 and R3 with p3), as in I, and the inert complex ES’ (R1 interacts with p2 and R3 is free). Thus, in addition to equations (1) and ( 2 ) i t is necessary to consider equation (16) where Ko = ks’ks. Ef
+ Sf
ks
ES’
(16)
ku
The ternary complex ESI (111) if i t is formed in the system, may then be derived from both E1 and ES according to equations (17) and (18) where k3.1 is E1
+ Pzt
(17)
+ If Jr ESI + E1 + Pit + Pq
(18)
ki.1 + Sf J r ESI
+ E1 + Pit k3.1
kz.1
ES
k4.2
ka.1
ka.2
assumed to be the specific rate constant for the transformation of ESI into E I and reaction products. With unit activity coefficients assumed for all reactants i t is evident from equations (17) and (18) that d[ESI]/dt is given by equation (19). d[ESII/dt = ki.i[EIILSrl
+ ~ J S [ E S I / I-I J i+ ka,~)[ES11 (19) (k2.1
kb,*
For the simplifying assumptions that kl >> k1.1, k2 >> ke.l, k4 >> k4.2 and k5 >> k5.2, i.e., KS = [Ef] [Sf]/[ES]and K I = [Ef] [Ir]./[EI], and that [Sf] = [SI and [If] = [I], ;.e., the system is in zone A with respect to both the specific substrate and the inhibitor, we have, when d[ESI]/dt = 0, equations (20), (21) and (22). If Ks.1 is defined as IESI 1 = [II(Ks[ESIICu)
I :Ce [ESI
=
(20)
+ kr r/Ks)(l/(k?.l + + k5.s)) (21) [EI[SI/(Ks(l + IIl/Kr) -I- [Sl(1 + K s / K , 4-
(ki.i/Kr
k3.1
~s[II/CuKd)( 2 2 )
+ k3.l)/kl.l and KIAas k w equation (20) may be rearranged to give equation(23). For the same jk2.1
k4.2
reasons advanced to interpret the significance of I / & = 1/KaKr [ ( & . I
+ k3.1)Ka/Ks.i + k5.2K1IK1.21 [l/(kz.i + ks.1 + k d l (23)
CI, it is probable that Ks I Ks.1 and K I I K I .so ~ that the affinity ratio K~KI/C,,may be considered as being equal to or less than unity. If by definition u = ks [ES] k3.1 [ESI],;.e., u = k3 ([ES] 47 [ESI]), where r = k3.l/k3, we arrive a t equation (23)where V = k3[E].
+
+
+
+
l/v = KdV(1 PI/K1)(1/(1 r&l[Il/Cu))I/[Sl I/V(1/(1 rKsJII/Cn))(1 KslKu Ks[II/Cu) (24)
+
+
+
+
I t will be recalledll that l/V’ = 1/ P ( l Ks/ = Ks’/V’ and V’ = k3’[E]. Hence equation (24) can be rearranged to give the more useful equation (25). Thus, for the present system, a plot of l/uo versus l/[S]o will also give a straight
K,),&/I/
+
+
+
l / v = K s / / V / ( l [II/KI)(l/(l rK8[Il/Cu))l/[Sl (1/(1 ~ K S [ I I / C ~ ) X ~ / ’ V(Ks’/T.”)( ’ [Il/Cu)) (25)
+
+
line, but now both the slope and the intercept are functions of the inhibitor concentration. When equation (25) is compared with the equivalent equation for the case where [I] = 0, i t will be appreciated that the value of the ratio r has a profound effect on the value of the slope and of the intercept. If 7 = 0, ;.e., k3.1 = 0, then the slope will be identical with that calculated on the basis of simple competitive inhibition, but the intercept will be raised by the amount Ks’[I]/~”C,. This situation is analogous to the case of so-called non-competitive inhibition so familiar in enzyme kinetics.’*-?O However, if r is finite, the value of (1 f rKs [I]/C,) is greater than unity, and the slope should be less than that calculated on the basis of simple competitive inhibition. However, the slope may be less than, equal to, or greater than the quantity Ks‘/ V’, L e . , the slope for the case where [I] = 0, depending upon whether the quantity C,/rKs is greater than, equal to, or less than Kr. Similarly, the position of the intercept will be determined by the relative values of 7Ks and Ks‘, ;.e., the intercept will be less than, equal to, or greater than 1/V’ when rKs is greater than, equal to or less than Ks‘. The experimental results obtained at two inhibitor concentrations are summarized in Fig. 2. It is evident that the observed plots indicate a direct proportionality between 1/v0 and 1/ [S]O. (19) P. W. Wilson in H. A. I.ardy “Respiratory Enzymes,” Burgess, Afinneapolis. Minn., 1948. (20) L. Marsart in J. B. Sumner and K. Myrbhck “The Enzymes,” Academic Press, I n c , N-ew York, N. Y., 1U51.
HYDROLYSIS OF NICOTINYL-L-TRYPTOPHANAMIDE
March 20, 1953
However, the character of the intercepts clearly excludes any possibility of reconciling the data with the kinetics of a simple competitive system. I n order to test the validity of the concepts which led to the formulation of equation (25)) values for C, and rKs/C, a t each given [I] value have been calculated from the data given in Fig. 2 with the aid of equation (25) and the known values of Ks', ;.e., 8.5 X M , and ks', i.e., 2.2 X M/min./mg. protein-nitrogen/ml. l1 These calculations lead to the values given in Table 111. The slope and intercept which should have been obtained if the system had been one of simple competitive inhibition are included to facilitate comparison with the observed values. TABLEI11 ANALYSIS OF THE KINETICDATA FOR THE SYSTEMcyCHYMOTRYPSIN-METHYL HIPPURATE-INDOLE ACCORDING TO EQUATION (25)" [I]
Observed value in Fig. 2 Intercept
Slope
Found for Cu
rKs/Cs
Calcd. for comp. inhib.b Slope Intercept
49.6 2.15 0.59 10.0 29.0 2.55 9.5 70.6 2.15 3.00 0.51 35.0 [I], [SIin units of 10-3 iM, V' = 0.465 X 10-3 M/min., K I = 0.70 X 10-3 M , Kn' = 8.5 X 10-8 M , C,, in units of (10-3 M)z. Slope = &'(l [I]/&)/V', intercept = 1/ V'. 1.2 2.0
T
(21) All values used in the discussion which follows are based upon units of 10-a M for K 8 and Rr.
1-
9
8
7 6
I /v,. 5
4
3
2
-
The agreement in the two sets of values for rKs/ C, and C, obtained from the observed slopes and intercepts of the plots given in Fig. 2 may be regarded as satisfactory in view of the experimental limitations encountered in this investigation. The kinetic data are, therefore, consistent with the expectation that in addition to the binary complexes ES, ES' and EI, a ternary complex ESI, resulting from the interaction of both inhibitor and specific substrate with the enzyme, is also formed i n , t h e system. The existence of such a ternary complex was predicted from a consideration of the steric requirements of the three center hypothesis and the structure of the compounds capable of interacting with the active site of the enzyme. The above results therefore provide indirect experimental support for the basic concepts of the three center hypothesis. It is, moreover, possible to extend the present analysis to include an estimate of the probable limiting values of r and Ks. The mean value for the quantity rKs/C, is 0.55,21and that for Cu is 9.75 from which i t follows that rKs = 5.36. Since, KS must be greater than Ks', Le., KS > 8.5, the , 1, and KI = 0.70, it may affinity ratio K ~ K I C < be inferred that the following relationships will bevalid: KsKI/C, > 0.61 but < 1.0, Ks > 8.5 but < 13.9, and r < 0.64 but > 0.39. The significance of these limiting values in terms of the three-center hypothesis will be briefly discussed. The ratio KsKI/C, is a measure of the over-all affinity of the three p centers in ES and E1 for the complementary R groups relative to that of the same three centers in the free enzyme. It will be recalled from equation (23) that K . s K I / C ~= 1 when K S . ~ = KS and K I . ~ = KI. The calculated lower limit of about 0.6 for the quantity KsKI/C, may then be interpreted to mean that the over-all
1399
I
0
I
0.2
Fig. 2.-Effect of indole on the a-chymotrypsin-catalyzed hydrolysis of methyl hippurate in aqueous solutions a t 25" and fiH 7.9; YO in units of 10-3 Mlmin.; [SIand [I] in units of 10-8 M; [E] equivalent to 0.208 mg. protein nitrogen/ml. ; 0.02 M tris-(hydroxymethy1)-aminomethane-hydrochloric acid buffer.
combining ability of the binary complexes must compare favorably with that of the free enzyme. Two situations are conceivable wherein the formation of a binary complex of the type ES or E1 may adversely affect the affinity of the vacant p center or centers for a second reacting molecule; (a) where the reaction with S or I materially distorts the unoccupied center or centers; and (b) where the presence of S or I a t the active site hinders the approach of a second reacting molecule. In view of the probable proximity of the p centers to each other i t is perhaps inevitable that the second situation must be operative to some extent. However, it does appear that the inherent combining power and the integral structure of a p center remains relatively unimpaired by the interaction of R groups with adjacent p centers. It should be emphasized that in the system under consideration both the inhibitor, Le., indole and the specific substrate, i.e., methyl hippurate, possess structural features which can be considered to be entirely complementary to the p centers a t the active site. Neither possess non-interacting structural features which may, by virtue of their mass effectively screen the neighboring p centers from the approach of other molecules containing one or more complementary R groups. Such an effect could, for example, be operative in the complex ES' where the benzamido group interacts with p ~ and , the carbomethoxy group is free, and hence is in a position to screen both p3 and p i . The exterit to whieh the unoccupied p centers are
H. T. HUAKG AND CARLNIEMANN
1400
I T o l . 7.5
+
Ks.1 = (kz i k3 i ) / k i I [ESI!SI/lESIl (26) thus masked may be of another order of magnitude 1/21 = KR'/V'(l [II/Kr)(l/(l rKs[Il/SsIKl)jl/!SI+ greater than that indicated above. (1/(1 rKs!II/KsIKI>)(l/V' From the limiting values for Ks, i.e., lis > RCjbut ( K y ' / V ' ) ([I]/KH X I ) ) ( 2 7 ) < 13.9, and from the relation, Ks' = K s K , ( K s K g ) I 1 it is estimated that the value of h-g, In case 111 the assumption is made that an inthe enzyme-substrate dissociation constant for the dole--pz interaction will effectively prevent p1 and non-susceptible complex ES', must be greater than p3 from interacting with the bifunctional specific 22. These values indicate that of the reactions be- substrate, ;.e., ESI is exclusively formed from ES tween a-chymotrypsin and methyl hippurate which and I. By omitting equation (17) from case I and lead to the formation of intermediate complexes, from the relation given in equation (28) the initial the formation of the susceptible complex ES is the KI 3 = ( k s z k 3 . 1 ) / k l ? = [ESl[II/[ESII (28) more important reaction. For the system a-chyKs/ rate expression for case TI1 is that given by equamotrypsin-methyl hippurate V = V'(1 K,)." Substituting the appropriate limiting val- tion (29). ues for Ks and K,, it is evident that ?'must have a l l = ~ Ks'/V'(1 [ ~ 1 / ~ 1 ) ( 1 / ( 1 r[II/Kr 3))1/[Sl value between V' and 1.63 V'. Therefore k3 lies (1/(1 r[II/Ki 3))(1/V' (Ks'/V')([II/KsKr 3 ) ) (29) between k3' and 1.63 kg', i.e., between 2.2 and 3 . G X The interpretation of the experimental data given I 0-3 M/min.,/nig. protein nitrogen,/ml. The limits for r indicate the k3 1 has a value of cn. 0.4 k3 to in Fig. 2 in terms of equations (25), (27) and (29) 0.f.i k3. The rate of hydrolysis of ESI is thus ap- is summarized in Table IV. Although all three proximately one-half that of ES. From a previous equations lead to the same limiting values for r , analysis of the factors which appear to be itnpor- ;.e., 0.39, and for Ks, ;.e., 8..5, it is seen that the values 9.75, mean of 10.0 of the a-chymotrypsin-specific substrate com- and 9.5, and 0.55, mean of 0.59 and 0.51, have a difplexesl' it appears that two effects may be responsi- ferent significance in each of the three equations. ble for the lesser susceptibility to hydrolysis of ESI As it is clearly beyond the scope of the experimental relative to that of ES, z.e., a diminution of the data summarized in Fig. 2 to distinguish between strain centered in the R3-p3 interaction, and a re- cases I, I1 and 111 it should be realized that the seduction in the accessibility of the R3-p3 locus to lection of case I, ;.e., the general case, for the subsequent attack by other reactants.' Since it treatment of the system a-chymotrypsin-methyl appears, a t least for the case under consideration, hippurate-indole is based upon accessory arguments that the interaction of a given R group with a par- which deny the validity of the limitations inherent ticular p center has relatively little effect upon the in cases I1 and 111 for the particular example being structural integrity of the adjacent p centers there considered. From considerations similar to those above it is little reason to postulate a lesser strain in the R3will be appreciated that in the so-called non-competp3 interaction of EST than in the K3-p3 interaction itive systems the assumption that the enzyme-subof ES. Therefore, the principal reason for the destrate-inhibitor complex is formed exclusively from creased susceptibility to hydrolysis of ESI may be the enzyme-substrate complex and the free inhibascribed to the effectiveness of the indole-pz inno means sustained by the experiitor18-20 is by teraction in limiting the accessibility of the R3-p3 locus in ESI to subsequent attack. This inter- mental data ordinarily available, even though the pretation suggests that a bimolecular mechanism rate equation formulated on this basis is consistent may be the rate-determining step in the transforina- with the experimental data expressed in terms of a tion of ES and ESI to free enzyme, reaction prod- 1 'yo uersus l/[S]o plot. Unless there is good reason ucts and, in the latter instance, inhibitor or enzyme- for imposing limitations of the kind illustrated in cases I1 and 111the rate equations for the formation inhibitor complex. The treatment used in the preceding discussion, of ternary complexes should be based upon the hereafter referred to as case I, is based upon the general case. TABLE IV proposition that the ternary complex ESI can be COMPARISON OF EQUATIONS ( 2 5 ) , (27) AND (29)" formed from both ES and EI. I n view of the fact Values from data that in most discussions of the mode of formation of Ternary complex Affinity ternary complexes in so-called non-competitive sys- Case Ea. 9.7.5b in Fig.02. X c constant ratiod terns 18 -20 it is tacitly assumed that the ternary comI 25 C, rKsIC, C, = 9.75 KsKI/C,, I1 27 K s . l K 1 Y K ~ / K s . I KKs.1 I = 13.9 K s / K s .I plex can be formed from only one of the binary 111 29 KsiY1.3 r / K I . a K1.8 > 0.70 < 1.15 KI/KI.3 complexes, it is of interest to compare the initial ,K1,etc., in units of 10-3 M . * Mean of 10.0 and rate equations for the special cases where ESI can 9.5.a K BMean Affinity ratio in all cases of 0.59 and 0.51. only be formed from either E1 or ES with that for 0.6. case I. Experimental2 In Case I1 the assumption is made that an Rrp1, Specific Substrates and Inhibitors.-The preparation of R g p 3 interaction will effectively prevent an indolenicotinyl-~-tryptophanamide'~ and methyl hippyrate" has been described previously. Indole, m.p. 52-53 , skatole, p2 interaction. ESI is then exclusively formed m.p. 95-96', and nicotinamide, m.p. 133-134', were Eastfrom E1 and S. Of the reactions considered in man Kodak Co. reagent grade products and were recrystalcase I the one represented by equation (18) can, lized a t least twice from appropriate solvents. Cyclohextherefore, be omitted. From the relation given in anol, pyridine and phenol were reagent grade products and equation (26) it follows that the initial rate equa- were redistilled prior to use. (221 .\!l r n c l t i n q >int. iire c e r r c c t e i l . tion far case TI is equation ( 2 7 )
+
+
+
+
+
+
+
+
+
11
+
+
+
March 20, 1953
DECARBOXYLATION O F 2,4,6-TRIHYDROXYBENZOIC ACID
Enzyme Experiments.-All experiments were conducted 0.1 in aqueous solution 0.02 M with respect to the amine component of a tris-(hydroxymethyl)aminomethane-hydrochloric acid buffer. The methods employed for the experiments with nicotinyl-L-tryptophanamide, Ks = 2.7 X 10-3 M,l3 and with methyl hippurate, M , l l were identical with those described KB' = 8.5 X
at 25" and fiH 7.9
*
[CONTRIBUTION FROM
THE
1401
previously for other experiments with these specific substrates. The enzyme preparation was an Armour product, lot no. 90402, and it will be noted that the specific enzyme concentrations Est and E*' for all experiments were such as to satisfy A conditions.i3,~~,~7 PASADENA 4, CALIFORNIA
DEPARTMENT OF CHEMISTRY ASD CHEMICAL ENGINEERING OF THE UNIVERSITY OF WASHINGTON J
The Kinetics of the Decarboxylation of 2,4,6-Trihydroxybenzoic Acid in Perchloric Acid Solution BY W. M. SCHUBERT AND J. D. GARDNER RECEIVED AUGUST18, 1952 Both the rate of decarboxylation of 2,4,6-trihydroxybenzoic acid and the ratio [RCOz-]/ [RC??H] were determined by an ultraviolet spectroscopic method in several concentrations of perchloric acid. The value of kz in the equation k1' = kob.d. ( [RCOz-] [RCOZH])/[RCOZH] was found constant in the region of 0.135 t o 38.2% perchloric acid. This is consistent with the rate-controllmg step being a first order decomposition of RCOZH(or something proportional t o RCOzH), or the reaction of RCO2- with a proton released from the solution to give the products directly. The reaction is solvent dependent.
+
A study of the decarboxylation of hydroxy aromatic acids was undertaken with the view of determining (1) whether the reactions are acidcatalyzed, and ( 2 ) if they are acid-catalyzed, what is the rate controlling step; ;.e., is it represented by equation (l), (2) or (3). The acid-catalyzed
+ H30+ + R H + COz + Hz0 RCOzH (+HgO) +R H + COz (+HzO)
RCOz-
k3
(4)
k4
kr [RCOzHI Evaluation of k2 and kq from the observed rate constants required a knowledge of the degree of R ~ O -+ ~ H RH ~ + C&H, or R C O ~ H+ H + , - - + ionization of RC02H to RC02-, which was calcuRH COZH (1) lated from a value for the ionization constant, K , On this basis k2 was determined to of 2 X RCOz'Hz Hz0 +R H COS + H30' (2) be about five times as large as kq a t 40". decarboxylation of hindered alkyl benzoic acids is Since mechanisms (1) and ( 2 ) [or (3)] are kineticcomplicated by the occurrence of a side ionizdtion ally indistinguishable in dilute mineral acids, the + to the acyl ion, RCO, in a t least the higher ranges reaction was studied in these laboratories over a of sulfuric acid solutions in which i t has been wide range of acid concentrations, from 0 to 58.5% studied.' It appeared that the decarboxylation perchloric acid. Perchloric acid was chosen beof hydroxy aromatic acids could be examined over cause i t is a strong acid for which values of HOare a range of acid concentration in which ionization known, i t is monobasic and is a non-sulfonating medium. It was found that an ultraviolet specto acyl ion does not occur. I n the meantime, Hammick, Brown and Elliot2a troscopic method could very readily be adapted to reported on the kinetics of the decarboxylation of following the rate of disappearance of the carboxylic 2,4,6-trihydroxybenzoic acid in 0 to 0.18 N HCI. acid, which has limited solubility in aqueous minThe reaction rate was followed by a titration eral acids. Furthermore, the spectroscopic method method. Earlier the kinetics of decarboxylation could a t the same time be used to determine diof this and other hydroxy aromatic acids had been rectly the actual concentrations of RCOOH and studied in resorcinol as a solvent a t higher tempera- RCOO- in the reaction media. ture.2b It was concluded that two simultaneous Experimental mechanisms applied. The first of these, reaction Materials.-2,4,6-Trihydroxybenzoic acid prepared by (3), was pictured as proceeding via attack of a solv- carbonation of phloroglucinol3 was recrystallized from acetoPerchloric acid solutions of desired ated proton on the a-carbon of the undissociated nitrile, m.p. 205-206'. strength were made by dilution of Baker C.P. 20% acid and acid Mallinckrodt C.P. 60% acid. The strength of each acid
+
RCOzH
+
+
= k3 [HaO+] [RCOz-] =
I
kz + HtO+ + R H + COz + H30+
- dc/dt
- dc/dt
(3)
= kz[H,Of] [RCOzH]
The second reaction (4) was pictured as the attack of a solvated proton on the carboxylic acid anion, or the decomposition of the undissociated acid with or without the intervention of a molecule of water (1) W.M. Schubert, THISJOWNAL, 71, 2639 (1949). (2) (a) B. R. Brown, W. W. Elliot aud D. Ll. Hammick, J . Chcm. Soc., 1884 (1961); (b) B. R.Brown, D. L1.Hammick and J. B.Scholefield, i b i d . , 778 (1950).
solution was determined by titration of a suitable aliquot against standard alkali. Apparatus and Kinetic Method.-A stock solution was prepared by dissolving about 20 mg. of 2,4,6-trihydroxybenzoic acid in 100 ml. of water kept at constant temperature. For each kinetic run, 5 ml. of the stock solution was diluted quickly to 50 ml. with perchloric acid of appropriate strength and at constant temperature. A portion of this solution was transferred quickly to a quartz stoppered Beckman cell. This cell and the cell containing the blank solution, made by diluting 5 ml. of water to 60 ml. with the same strength perchloric acid, were placed in a small constant temperature water-bath that had been inserted between the (3) P.Holmes, D.E. W h i t e and I. H.Wilaon, i b i d . , 28 (1Q50).
