concentration from T, the “initial burst” of p-nitrophenol, as a function of the substrate concentration, Values of T were determined by graphical extrapolation, to f = 0, of the differencesbetween the steady-state extrapolated lines and the absorbances at time t (Table 1). By plotting l / d G as a function of 1 / S 0 we obtain a straight line (using the value of l/K,(app) from the steady-state kinetics as an additional point). The intercept of this plot on the ordinate gives6 r0 = Eo/(l (k3/k&2, and thus Eo = 6.45 X M , indicating a purity of the enzyme, by weight, of 50z. Since our system of equations is redundant, we can calculate Eo in an independent way: from kl and k3, we can calculate kcat, and then from the experimental value of kcatEo, EO = 7.40 X 1 0 - 6 M (57% purity by weight). The agreement of the two Eo values seems reasonable, considering the experimental difficulties and the complexity of the calculation^.^ The observation of “initial burst” of p-nitrophenol and of the kinetics of both the presteady-state and steady-state reactions are satisfactorily described by the three-step mechanism of eq. 1. These observations are consistent with the conclusion that, within experimental error, the totality of the tryptic hydrolysis of pnitrophenyl a-N-benzyloxycarbonyl-L-lysinate hydrochloride involves a single reaction pathway with the formation of an a-N-benzyloxycarbonyl-L-lysyl-trypsin intermediate. This substrate is the most specific substrate of trypsin, based on its kcat(lim) = 170 sec.-I, the fastest known trypsin catalysis. Studies of the pH dependence of this reaction show that kcatis dependent, as usual, on a single basic group of pK, 6.80 ( I = 0.05) from pH 2 to pH 7.4, indicating that the results obtained here at pH 2.66 may be reasonably extrapolated to neutral pH. Thus, the present observations must be pertinent to the pathway of trypsin catalysis.
+
L
I
I
,
0
50
100
Time (sed
J
Figure 1. The trypsin-catalyzed hydrolysis of p-nitrophenyl a-N-benzyloxycarbonyl-L-lysinateat pH 2.66, 0.05 M citrate buffer; Eo = 7.40 X 10-8 M; SO = 2.03 X lO-* M, 1.29z (v./v.) acetonitrile-water, 25“. Cary Mode1 14 spectrophotometer, 8 in./min. recording chart speed, noise level = 5 X l W 4 absorbance unit.
fied in this system. Therefore, for the calculation of the individual rate constants, we have used a combination of the presteady-state data together with data from the steady state, detei mined under identical conditions. Table I. The Presteady State of the Trypsin-Catalyzed Hydrolysis of pNitropheny1 a-N-Benzyloxycarbonyl-L-lysinateHydrochlorides
so x
a
bX
n X
10e,
106, M
seC.-’
106, M
56.5 38.5 20.3 13.7 9.78
18.2 13.4 9.44 7.88 5.71
5.36 4.74 4.57 4.03 3.62
Eo = 7.40 X
M . For other conditions, see Table 11.
From the Lineweaver-Burk plot for the steady state, kcatEoand K,/kzEowere determined from the intercept and the slope, respectively. Equation 2 may be rearranged to eq. 3. The quotient of Ks]kzEo divided by
the intercept of a plot of the left side of eq. 3 vs. So, Ks/kzk3Eo, yields ka. The product of the slope of this plot ( l / k p k ~ Eand ~ ) kcatE, (= kzk3Eo/(kz k3)) yields (k, k 3 ) and thus k,. Knowledge of the k2/k3 ratio (27.6) then permits the calculation of K, from K,(app) = KJ(1 (kz/k3)). The rate constants are summarized in Table 11.
+
+
+
Table 11. The Trypsin-Catalyzed Hydrolysis of pNitrophenyl a-N-Benzvloxvcarbonvl-L-lvsinate Hvdrochloride“ kz ka
KS
0.395 set.-' 1.43 X sec.-l 7.95 x 1 0 - 4 M
25.0”, 1.29% (v./v.) acetonitrile-water, pH 2.66, 0.05 M citrate. 2 X crystallized, lyophilized bovine trypsin (TRL 6256); age of solution: >20 min. and “nonactivated” methyl or ethyl esters and the amide; kBE = k M E )is in the expected nucleophilic order and and (3) the small spread of reactivities expected in the indicates that deacylation is not completely rate conseries of esters of argument 1 above casts doubt on the trolling; the Km(app) values are also in the expected validity of the argument. Therefore experiments were order (KmNPE
