The Molecular Kinetics of the Urea-Urease System. IV. The Reaction in an Inert Buffer’ Mary Colman Wall and Keith J. Laidler From the Department
of Chemistry, The Catholic Washington, D. C. Received
August
University
of America,
11, 1952
In Parts I, II, and III of this series of papers (7, 9, lo), a systematic study was presented of the molecular kinetics of the urease-catalyzed hydrolysis of urea. The work was carried out in phosphate buffer, but in 1951 Fasman and Niemann (3) showed that this buffer affects the reaction, the sodium and potassium ions acting as inhibitors and the phosphate ion [contrary to an earlier report (S)] as an activator. It was therefore decided to repeat the work in a buffer which would have no effect on the rate of reaction. The choice of suitable buffer was complicated by the fact that the demonstrated effects of sodium, potassium and phosphate ions precluded the use of the usual buffer systems. It was necessary to find a buffer containing no metal ions, and a search of the literature produced three possibilities: trishydroxymethylaminomethane, 5-collidine, and 2amino-2-methyl-1,3-propanediol (4). The first of these was selected for study since it is readily available in pure form (obtainable from the G. Frederick Smith Chemical Co., Columbus, Ohio). It was found that trishydroxymethylaminomethane sulfate (THMAM-H&04) had no activating or inhibiting effect and the present paper describes a molecularkinetic study using this buffer. 1 The present paper and two following papers in this series are abstracted from a dissertation submitted by Mother Mary Colman Wall, S. H. C. J., to t,hct Graduate School of The Catholic University of America in partial fulfillment, of the requirements for the degree of Doctor of Philosophy. The work wan eupported under Contract NS onr-05309 with the Office of Naval Research, Biochemistry Branch. 299
300
MARY C. WALL AND KEITH J. LAIDLER EXPERIMENTAL
PROCEDURE
The experimental procedure used was essentially as in previous work (9), the reaction being followed by determining the ammonia concentration using Nessler’s method. The urease was prepared from jack-bean meal and once crystallized according to the method of Sumner (13). THMAM-HCl and THMAM-H$04 buffers were prepared by mixing 0.2 M THMAM solution with 0.2 N HCl or H&SO,, the final pH being determined using a Beckman pH meter. All rates quoted are initial rates. RESULTS
The first work undertaken was that of finding a suitable buffer. ‘I‘HMAM-HCl was first tried; 0.070, 0.035, 0.018, 0.009, and 0.004 A1 solutions of this buffer were used, with the reaction mixture 0.25 M in urea. The rates were found to increase markedly with increasing buffer concentration, indicating an activating effect (presumably due TABLE Typical
Data Showing
Urea concentration M
0.25 0.25 0.25 0.00125 0.00125 0.00125
I
the Independence
Temperature OC.
9.9 20.8 25.3 9.9 19.7 25.3
of Rate on Buffer
Initial M = 0.070
2.49 3.68 5.10
Concentration
rates (moles/l./sec.) X 106 at following THMAM-H&O4 concentrations 0.035 0.018 0.009 0.094
5.7 10.2 13.7 2.49 3.80 5.05
5.7 13.8 2.40 -
5.6 10.0 13.6 5.15
5.65 10.2 13.6 2.59 3.68 5.22
to the chloride ions). The buffer was then changed by substituting HzSOa for HCl, and no activating or inhibiting effect was then found. This was demonstrated to be the case at five temperatures (from 10 to 30°C.) and at two urea concentrations (0.25 and 0.00125 M) ; some typical data at pH 7.13 are shown in Table I. The THMAM-HBOt buffer was therefore used in all subsequent work, at a concentration of
0.035 M. In all of the work care was taken that there were no significant pH changes during the course of a run. Since the rates are initial rates measured during the very early stages of reaction, not much ammonia accumulates, so that this can neither inhibit much (7) nor bring about much change in pH. It was found by direct measurement that during the course of a run the pH changed only by a few tenths, even when the lowest buffer concentrations were used. The buffer concentration of
UREA-UREASE
SYSTEM.
IV
301
0.035 M was chosen because it was sufficient to maintain the pH constant (to the accuracy of its determination) in the studies both at pH 7.13 and at pH 8.0. The next objective was the determination of the optimum pH with the THMAM-H&SO4 buffer at a substrate concentration of 0.25 M. Rates were measured at 20.8%. in solutions for which the pH varied over the range from pH 6.5 to 9.0. The results are shown in Fig. 1, from
FIG.
1. Plot of initial rate (moles/l./sec.) vs. pH for 0.25 M urea in THMAM-HzS04-buffered solutions at 20.8”C.
which it may be seen that the optimum pH is about 8.00. Subsequent work was done at this pH and also at pH 7.13, this being in the neighborhood of the apparent optimum when phosphate, acetate, and citrate buffers are used. The influence of substrate concentration on the rate was next determined. Rates were measured in THMAM-H&O, buffers at pH values of 7.13 and 8.09 at 20.8”C. over a range of urea concentrations from
302
MARY
C. WALL
AND
KEITH
J.
LAIDLER
0.00125 to 0.835 M. The data are shown in Figs. 2 and 3. Except at very high substrate concentrations, the plot of rate versus substrate concentration gives a curve of the form characteristic of reactions obeying the Michaelis-Menten law. This behavior is in sharp contrast to that found using the usual phosphate buffers in which the curves show no flat portion.
FIG.
2. Plota of initial rate (moles/l./sec.) vs. concentration of urea at 20.8”C.; THMAM-HeSO buffer at pH 7.13.
To obtain data from which the experimental activation energies in THMAM-H2S04 buffer could be determined, rates were measured at four temperatures for 0.25 and 0.005 M urea and at the two pH’s of 8.00 (optimum) and 7.13. The results are given in Table 11 and the resultant activation energies in Table III. All measurements were made using enzyme solutions of the same activity. The molarity of the enzyme solution was determined by comparison with its activity toward Sumner’s standard 30/, urea solution
UREA-UREASE
SYSTEM.
303
IV
FIG. 3. Plots of initial rate (moles/L/see.) vs. concentration urea at 20.8”C.; THMAM-HZSO, buffer at pH 8.00. TABLE
Rate
II
in THMAM-H&O4
cOn8tant8
of
Buffer
Rate constant‘X lo-’ “C.
12.3 12.8 13.2 20.8 25.3 30.1
TABLE
Experimental Urea concentration I4 0.005 0.250
0.005M urea l./?nok/sec. pH 8.00 pH 7.1 180 220 340, 240 410 290 530 350
0.25Y urea sec.-= pH 1.13 pH 8.00 1.3 1.8 2.0 3.1 2.7 4.1 3.7 5.3 III
Activation Energies Activation energy kcal./molc
pH 7.13 6.8 9.7
ocriac centers
pH 8.00 8.5 11.1
304
MARY
C. WALL
AND
KEITH
J.
LAIDLER
in phosphate buffer at a pH of 7.00 at 20°C. In 5 min. 0.330 mg. of ammonia nitrogen was produced under these conditions, so that 5 ml. of the enzyme solution employed contained 0.330 Sumner units of activity; the same solution in THMAM-HGSO, buffer at pH 7.13 liberated 0.440 mg. of ammonia nitrogen in 5 min. Utilizing Sumner’s result that 1 g. of pure urease is equivalent to 133,000 units of activity (13) and that the molecular weight of the enzyme is 483,000 (12), the molarity of the urease solution was determined as 5.1 X lo-lo. DISCUSSION
Applicability The Michaelis-Menten
of the Michaelis-Menten law may be written
Law
as
h NElo [Sl v = 1 + K[S] It is generally interpreted E+S
(1)
in terms of the reaction scheme
h h G==W X -+ k-l
products + enzyme
where E represents enzyme, S represents substrate and X represents the enzyme-substrate complex; kz is the rate constant for the decomposition of the complex and, if the steady-state treatment is employed (2>, K = kd(k-: + kz). It is seen that if such a law is obeyed the rate should increase with substrate concentration up to a certain point, after which it should remain constant when the substrate concentration is further increased. These conditions are fulfilled in the THMAM-H2S0, buffered ureaurease system up to a substrate .concentration of 0.33 M at pH = 7.13 (Fig. 2) and of 0.25 M at pH = 8.00 (Fig. 3). (It may be noted that here, as in other buffers (8), at the lower pH substrate inhibition occurs at a higher concentration of substrate than is the case in the solution at the higher pH value.) At higher urea concentrations there is a falling off of the rate, though to a smaller extent than in the phosphate buffer. Applicability of the Michaelis-Menten law in the lower concentration range was confirmed by the linearity of plots of l/v vs. l/[S]. The reciprocals of the Michaelis constants are given in Table IV.
UREA-UREASE
SYSTEM.
305
IV
Thermodynamic Quantities At the high substrate concentration of 0.25 M, as may be seen from Eq. (1) and Figs. 2 and 3, the rate is given by v = kz[Elo
(2)
and from absolute rate theory (5) k2 is
k2 =kTe
AWIR
e-~~2*~~~
h
TABLE IV Values of the Thermodynamic Properties Thermodynamic
property
pH 7.13
pH 8.00
9.1 0.2 -7.2 -6.8 11.2 8.2 2.50
10.5 7.9 -2.2 -0.2 11.2 7.9 256
kcal. mole AH* kcal. mole A$ entropy units (e. u.) AS* entropy units (e. u.) AF: kcal. mole AF* kcal. mole K (reciprocal of Michaelis constant) AH:
where AH: is related to the Arrhenius activation energy E by AH2 = ERT. At low substrate concentrations the rate is
v = kz~[JWSl = @MS]
(4)
where k
=-e
kT
AN/R
e-AIi*IR~
h
Application of these equations to the data gave rise to the thermodynamic values listed in Table IV. The significance of the entropies of activation obtained at the pH optimum (8.00) may be considered first. The value corresponding to the breakdown of the enzyme-substrate complex, -2.2 e.u., falls into line with all other known cases in being negative; negative values may be attributed to a folding of the enzyme and to charge separation associated with electrostriction of solvent (1). The entropy of activation for the bimolecular reaction between enzyme and substrate, -0.2 e.u., is more positive than would be expected if there were no structural changes or electrostriction effects; the value therefore suggests either
306 some unfolding ization. Comparison at 7.13 shows entropy values
MARY C. WALL AND KEITH J. LAIDLER
or some release of water molecules due to charge neutralof the thermodynamic values at the pH’s of 8.00 and that the lower rates at 7.13 are associated with lower and not with higher energies of activation. SUMMARY
A kinetic study has been made of the urease-catalyzed hydrolysis of urea, the work being done in a trishydroxymethylaminomethane-H&SO4 buffer, which was shown to have no activating or inhibiting effect on the reaction. The rate was found to pass through a sharp maximum at pH 8.00, and detailed studies were made at pH values of 8.00 and 7.13, over a wide range of substrate concentrations and temperatures. The Michaelis law’ was found to be obeyed accurately up to a substrate concentration of 0.25 M at pH 8.00 and of 0.33 M at pH 7.13; at higher concentrations there was some falling off of the rate. The absolute enzyme concentration was determined by comparison with Sumner’s data in phosphate buffer, and values of entropies and heats of activation were calculated. REFERENCES 1. 2. 3. 4. 5.
BARNABD, M. L., AND LAIDLER, K. J., j. Am. Chem. Sot. 74, 6099 (1952). BRIQQS, G. E., AND HALDANE,J. B. S.,Biochem. J. (London)19, 338 (1925). FASMAN, G. D., AND NIEMANN, C., J. Am. Chem. Sot. 73, 1646 (1951). GAMORI, G., Proc. Sot. Ezptl. Biol. Med. 62, 33 (1946). GLASSTONE,S., LAIDLER, K. J., AND EYRINO, H., The Theory of Rate Processes, p. 199. McGraw-Hill Book Co., Inc., New York, N. Y., 1941. 6. HARMON, K. M., AND NIEMANN, C., J. BioE. Chem. 137, 601 (1949). 7. HOARE, J. P., AND LAIDLER, K. J., J. Am. Chem. Sot. 72,2437 (1950). 8. HOWELL, S. F., AND SUMNER,J. B.,J. BioE. Chem. 104, 619 (1934). 9. LAIDLER, K. J., AND HOARE, J. P., J. Am. Chem. Sot. 71, 2699 (1949). 10. LAIDLER; K. J., AND HOARE, J. P., J. Am: Chem. Sot. 72.2489 (1950). 11. MICHAELIS, L:, AND MENTEN,M. L., Biochem. 2. 49, 333 (1913). 12. SUMNER, J. B., GRABEN, N., AND ERIKSON-QUENSEL, I. B., J. Biol. Chem. 126, 37, (1938). 13. SUMNER, J. B., AND SOMERS, G. F., Chemistry and Methods of Enzymes. Academic PreTs, New York, 1947.