A reinvestigation of the kinetics of hydrolysis of N-benzoyl-n-argininamide by crystalline trypsin has led to the conclusion that the hydrolysis products enter into the over-all reaction as inhibitors

Harmon, Kent M.

Niemann, Carl

English

Caltech Authors - Main

THE HYDROLYSIS OF N-BENZOYL-L-ARGININAMIDE BY 
CRYSTALLINE TRYPSIN 
BY KENT M. HARMON* AND CARL NIEMANN 
(From the Gates and Crellin Laboratories of Chemislry,t California Institute 
of Technology, Pasadena) 
(Received for publication, November 26, 1948) 
Previous studies of the trypsin-catalyzed hydrolysis of N-benzoyl- 
L-argininamide to N-benzoyl-L-arginine and ammonia (1, 2) have led to 
the conclusion that the reaction is first order with respect to both en- 
zyme and substrate and that for any single experiment the rate of hydrol- 
ysis may be described by the equation 
ds 
-z 
= K’es 
where e = the total enzyme concentration, s = the substrate concentra- 
tion, t = the time, and K’ = the proteolytic coefficient (3) of the system. 
Reinvestigation of the above reaction over a greater range of initial 
substrate concentrations has now shown that the initial reaction veloc- 
ity at 25’ is essentially independent of the initial substrate concentration 
for concentrations varying from 0.01 to 0.05 M and that, for these and 
lesser substrate concentrations, the initial reaction rates obey the Michaelis- 
Menten (4) equation 
ds Vs 
=- 
-dt K,+s 
(II) 
within the limits of experimental error. At 25” and pH 7.7 K,,, was 
found to have an apparent value of approximately 0.002 M N-benzoyl- 
L-argininamide and was shown to be temperature-dependent (Table I). 
Further it has been observed that for any initial substrate concentration 
so the reaction rate decreases somewhat more rapidly with time than was 
expected for a reaction which is truly first order with respect to the sub- 
strate concentration and that the reaction products have a marked in- 
hibitory effect upon the reaction rate although ammonium ion alone is 
without effect. 
* Present address, General Electric Company, Richland, Washington. 
t Contribution No. 1251. 
743 
744 HYDROLYSIS OF BENZOYLARGININAMIDE 
Consider the equilibria 
E + BAA 4% 
k 
E,BAA --+ E + BA + A 
(e - P - 3 (4 (PI 
Ki 
E + BA t3 E.BA 
(e - p - 9) (SO - s + I) (!z) 
where BAA = N-bensoyl-L-argininamide, BA = N-benzoyl-L-arginine, 
A = ammonia, e = the total enzyme (E) concentration, s = the sub- 
strate concentration, SO = the initial substrate concentration, p = the 
concentration of the enzyme-substrate complex, q = the concentration 
of the enzyme-hydrolysate complex, I = the initial concentration of the 
hydrolysis products, and e-p-q = the free enzyme concentration. 
K, = ‘d!?-+ (III) 
Ki = 
(so-s+Z)(e- p-q) 
(IV) 
P 
From equation (IV) 
P ( 
SO-s+Z)(e-P) 
= Kc + (so - s + 1) 
Upon substitution into equation (III) 
esKt 
p=Km(Ki+so-S+Z)+sKi 
If K< = rK,,, (r = the ratio of the inhibitor constant to K,,,) and -ds/ 
at = kp, 
ds kes 
-ii=- K + (so+ n (1 - f-18 
m --- 
T  T  
(VI 
Integration gives 
ket = 2.3 Km -I- $ (so -I- Z) 1 (1 - T) log: - y-- (so - s) 
With I = 0, 
(VU 
ds kes 
--i= 
dt K,+2 (1 -1-18 
T  r 
(VII) 
K. M. HARMON AND C. NIEMANN 745 
With t = 0, 
With r = 1, 
ds kes 
-dt=K,+so+? 
(VIII) 
(IX) 
and the reaction would appear to be exactly first order with respect to 
substrate. 
An equation similar to equation (IX) can be obtained from Klotz’s 
linear equation (5, 6) for the binding of ions by a protein with n equiva- 
lent binding sites per molecule; i.e., 
e Kl 1 
-=--. 
A, n Ii+; 
(X) 
where e = the protein (enzyme) concentration, A = the ion concentra- 
tion, in this case the concentration of the substrate plus the hydrolysis 
products, and A, = the number of moles of ions bound to protein per 
unit volume of solution. 
If one takes the reciprocal, 
en A 
A. = - 
K+A 
and asswmes that only the substrate combines with the enzyme, 
ens 
Se=K+S 
If the rate of reaction is proportional to s,, the bound substrate concen- 
tration, 
ds Kens 
-dt=K+s 
(XI) 
Equation (XI) has the same form as the Michaelis-Menten equation, but 
with a different significance applied to the constants. 
If one assumes that the combining sites of the enzyme may be occupied 
equally well by either the substrate or the hydrolysis products, 
enA 
s. = $A+ s.- 
A KfA 
and 
ds kens 
--ii.=- K+A 
(XII) 
746 HYDROLYSIS OF BENZOYLARGININAMIDE 
If, in equation (VI), T is less than 1, the hydrolysis products must be 
more firmly bound to the enzyme than is the substrate. In such a case, 
as the reaction proceeds the rate should decrease more rapidly than would 
be predicted on the basis of a first order reaction. Such deviations have 
been observed in all experiments in which the initial substrate concentra- 
tions SO were relatively high, and at 25” an assumed value for r of 0.5 
appeared to fit such cases fairly well. However, with low initial substrate 
concentrations the deviation was not observed, most likely because of 
experimental difficulties. The rate constants k, calculated from equa- 
tion (VIII), are given for various initial substrate concentrations, en- 
zyme concentrations, and temperatures in Table I. 
TABLE I 
Rate Constants at pH 7.7 
k = mM minutes-1 (mg. of enzyme nitrogen)-‘. 
(1) 
0.050 
0.043 
0.030 
0.010 
0.0087 
0.0058 
0.0050 
0.0046 
0.0040 
0.0030 
0.0020 
- 
25"; K,,, = 0.0021 pr 
e = o.osst 
(2) 
I- 
0.0023 
0.0023 
0.0020 
0.0021 
0.0023 
- 
e = 0.034t 
(3) 
0.0022 
0.0024 
0.0018 
0.0021 
3O';K,,, = 0.0033 M 
e = 0.034t 
(4) 
0.0065 
0.0067 
0.0060 
0.0066 
0.0061 
0.0066 
- 
O";K,,, = 0.0082 M 
c = o.ol54t 
(5) 
0.0074 
0.0076 
0.0076 
0.0073 
0.0074 
* mM of N-benzoyl-L-argininamide per ml. 
t Mg. of protein nitrogen per ml. 
Experimental values for the extent of hydrolysis (SO - s) at 25” are 
compared in Table II with those calculated from equation (VI) with 
values of r = 0.5, 1, and a. In general the agreement is better for r 
= 0.5, although, as pointed out previously at very low initial substrate 
concentrations,? a better fit is obtained with r = 1. 
The effect of the reaction products upon the rate of hydrolysis of N- 
benzoyl-L-argininamide by trypsin is probably more clearly shown in 
Table III. It will be seen that 0.05 M ammonium ion causes no demon- 
strable effect. Because of the low solubility of N-benzoyl-L-arginine it 
was not possible to determine its effect upon the system directly and it is 
surprising that it was not precipitated from the reaction mixture. If it 
K. M. HARMON AND C. NIEMANN 747 
TABLE II 
Comparison of Experimental and Calculated Results at 26’ and pH Y.Y 
K, = 0.0021 M N-beneoyl-L-argininamide; k = 0.0022 mM minutes-l (mg. of 
enzyme nitrogen)-‘; e = 0.055 mg. of protein N per ml. 
so 
(1) 
9n.M per ml. 
0.010 
0.005 
0.004 
0.003 
0.002 
Time Hydrolysis 
(2) (3) 
min. per cent 
11.5 11.2 
20 17.0 
40 28.5 
10 16.2 
20 29.8 
30 37.0 
40 45.8 
50 51.0 
60 56.8 
10 16.7 
20 30.0 
30 41.8 
40 48.3 
50 59.0 
60 62.8 
10 20.0 
20 32.0 
30 44.7 
40 59.0 
50 65.3 
60 71.0 
10 26.5 
20 46.0 
30 61.5 
40 69.5 
50 70.5 
60 80.5 
so - s, mM per ml. x 106 
.- 
Observed 
(4) 
Calculated, Calculated, Calculated, 
I = 0.5 I = 1.0 r’=m 
(5) (6) (7) 
1.12 1.05 1.11 
1.70 1.73 1.83 
2.85 2.95 3.31 
0.81 0.78 0.80 
1.49 1.35 1.47 
1.85 1.83 2.02 
2.29 2.25 2.49 
2.55 2.57 2.88 
2.84 2.85 3.20 
0.67 0.67 0.73 
1.20 1.22 1.31 
1.67 1.65 1.79 
1.93 1.98 2.18 
2.36 2.26 2.51 
2.51 2.49 2.77 
0.60 0.60 0.57 
0.96 1.05 1.14 
1.34 1.43 1.53 
1.77 1.72 1.84 
1.96 1.92 2.08 
2.13 2.06 2.27 
0.53 0.48 0.52 
0.92 0.83 0.90 
1.23 1.08 1.18 
1.39 1.27 1.39 
1.41 1.42 1.54 
1.71 1.53 1.68 
- 
1.13 
1.98 
3.88 
0.83 
1.65 
2.37 
2.97 
0.78 
1.47 
2.08 
2.55 
0.67 
1.25 
1.78 
2.16 
0.57 
1.00 
1.33 
1.57 
1.76 
had, upon reaching the concentration u, the rate from that time on would 
be expressed by the equation 
ds 
-z= 
kes 
(XIII) 
Consequently, the plot of log s (as ordinate) against time would give a 
curve which would be concave upward from zero time to the time when 
the copcentration of N-benzoyl-L-arginine became equal to u and coa- 
748 HYDROLYSIS OF BENZOYLARGININAMIDE 
cave downward from that time to the end of the reaction. Such an ef- 
fect was not observed in any of the experiments. In order to circumvent 
the di%culty occasioned by the low solubility of N-benzoyl-n-arginine, a 
solution 0.05 M in N-benzoyl-n-argininamide was completely hydrolyzed, 
the enzyme destroyed by heating, and fresh substrate and enzyme added. 
The rate observed in this solution which was initially 0.042 M in benzoyl- 
L-arginine and ammonium ion was markedly less than that noted in the 
absence of added hydrolysis products and agreement between observed 
and calculated values was good (Table III). While these data offer 
support for the postulate that the hydrolysis products function in an in- 
hibitory manner, it should be pointed out that Schwert et al. found no evi- 
TABLE III 
Effect of Reaction Products on Rate of Hydrolysis at 16” and pH 7.7 
K, = 0.0021 M N-benzoyl-L-argininamide; k = 0.0022 InM minutes-r (mg. of en- 
zyme nitrogen)-‘; e = 0.077 mg. of protein nitrogen .P 
Reaction products added Time Hydrolysis 
(1) (2) ____- 
min. 
60 
120 
270 
60 
120 
60 
120 
240 
(3) 
None 
0.05 M NHd+ 
0.042 M N-beneoyl-n- 
arginine, 0.042 M NH,+ 
- - 
)W cent 
16.8 
29.0 
50.0 
16.9 
29.4 
8.3 
15.5 
27.3 
t 
erml.;s~ = 0.050mMperml. 
- 
so - s, lnM per ml. x 108 
Observed 
(4) 
Calculated, Calculated, 
I = 0.5 , = 1.0 
(5) 16) 
8.4 8.3 9.0 
14.5 14.3 16.2 
25.0 25.0 29.3 
8.5 8.3* 9.0* 
14.7 14.3* 16.2* 
4.1 3.7t 5.2t 
7.8 6.71 9.8t 
13.6 12.51 17.5t 
- 
* Assuming no inhibition by ammonium ion. 
t Assuming inhibition by N-benzoyl-L-arginine. 
dence of inhibitory action by the hydrolysis products in the trypsin- 
catalyzed hydrolysis of N-benzoyl-L-arginine methyl ester (7) and it may 
be that both ammonium ion and N-benzoyl-L-arginine are necessary for 
inhibitory action. 
EXPERIMENTAL 
Reagents-The data presented were obtained with a preparation of 
crystalline trypsin procured from Armour. Similar results were ob- 
tained with a Lehn and Fink preparation. Benzoyl-L-argininamide hy- 
drochloride was prepared according to the procedure of Bergmann, Fruton, 
and Pollok (8). The 0.1 M phosphate buffer (pH 7.9) was prepared from 
K. M. HARMON AND C. NIEMANN 749 
potassium dihydrogen phosphate and disodium hydrogen phosphate. 
Reagent grade formaldehyde, 40 per cent by volume, was shaken with 
basic magnesium carbonate, filtered, and the filtrate (pH 8) used for the 
form01 titrations (9-11). All solutions were prepared with water redis- 
tilled from an all-glass apparatus. 
Procedure-Generally 5.0 ml. of substrate solution and 1.0 ml. of buf- 
fer solution were pipetted into a 1 X 6 inch test-tube, the tube placed in 
a thermostat, 1.0 ml. of enzyme solution added, the solution shaken, 
and a 1.0 ml. aliquot immediately withdrawn for a blank determination. 
After suitable time intervals, additional 1.0 ml. aliquots were withdrawn. 
Each aliquot was added immediately to an equal volume of formaldehyde 
solution contained in a 10 ml. beaker, and the beaker placed in the depres- 
sion of a rubber stopper which was mounted on the shaft of an inverted 
air-driven stirrer in such a way as to permit rotation of the beaker during 
the titration. The glass and reference electrodes immersed in the solu- 
tion facilitated stirring. The solution was titrated with standard 0.01 M 
sodium hydroxide in a semiautomatic burette graduated in 0.01 ml. and 
equipped with a capillary tip of sufficient length to permit introduction 
of the reagent beneath the surface of the solution being titrated; thus the 
disadvantages inherent in drop-wise transfer are avoided. The end- 
point of the titration (pH 8.1) was determined with the aid of a Beckman 
model G pH meter equipped with electrodes specially constructed for use 
in the limited space available. The glass electrode was of the type in- 
tended for use in alkaline solutions. After every titration the electrodes 
were washed with distilled water and checked against a standard buffer 
solution. The solutions were invariably titrated immediately after the 
aliquot had been added to the formaldehyde solution. Blank runs made 
with solutions containing no enzyme indicated that the substrate was 
not hydrolyzed in the absence of the enzyme under the conditions em- 
ployed. 
SUMMARY 
A reinvestigation of the kinetics of hydrolysis of N-benzoyl-n-arginina- 
mide by crystalline trypsin has led to the conclusion that the hydrolysis 
products enter into the over-all reaction as inhibitors. 
BIBLIOGRAPHY 
1. Hofmann, K., and Bergmann, M., J. Biol. Chem., 138, 243 (1941). 
2. Butler, J. A. V., J. Am. Chem. Sot., 63, 2971 (1941). 
3. Irving, G. W., Jr., Fruton, J. S., and Bergmann, M., J. Biol. Chem., 138, 231 
(1941). 
750 HYDROLYSIS OF BENZOYLARGININAMIDE 
4. Michaelis, L., and Menten, M. L., Biochem. Z., 49,333 (1913). 
5. Klotz, I. M., Arch. Biochem., 9, 109 (1946). 
6. Klotz, I. M., Walker, F. M., and Pivan, R. B., J. Am. Chem. Sot., 68,1486 (1946). 
7. Sohwert, G. W., Neurath, H., Kaufman, S., and Snoke, J. E., J. Biol. Chem., 172, 
221 (1948). 
8. Bergmann, M., Fruton, J. S., and Pollok, H., J. Biol. Chem., 127, 643 (1939). 
9. Van Slyke, D. D., and Kirk, E., J. Biol. Chem., 102,651 (1933). 
10. Levy, M., J. Biol. Chem., 99, 767 (1932-33). 
11. Dunn, M. S., and Loshakoff, A., J. Biol. Chem., 113,369 (1936). 


The hydrolysis of N-benzoyl-L-argininamide by crystalline trypsin

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The hydrolysis of N-benzoyl-L-argininamide by crystalline trypsin

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