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The molecular kinetics of the urea-urease system. V. Relationship between activity and concentration of urease solutions
The Molecular Kinetics of the Urea-Urease System. V. Relationship Between Activity and Concentration of Urease Solutions Mary Colman Wall and Keith J. Laidler From the Department
of Chemistry, The Catholic University of America, Washington, D. C. Received August 11, 1952
Several investigat,ors have commented on the lack of linearity between the activity and concentration of urease solutions (1, 5, S) and have suggested explanations. All previous work on this was carried out in the presence of inhibiting buffers, and Fasman and Niemann (2) have accepted the explanation of Strauss and Goldstein (3, 7) that the variation in specific activity of&he enzyme is due to the changing relative concentrations of enzyme, activator, and inhibitor. The present paper describes a reinvestigation of the phenomenon using trishydroxtiethylaminomethane (THMAM)-HzSOd buffer at pH 7.13; the effects observed here must be true properties of the urea-urease system since the buffer acts neither as activator nor as inhibitor (Part IV). EXPERIMENTAL
AND RESULTS
The experimental procedure was exactly as described in Part IV (8). The work was all done in 0.25 M urea and 0.035 M buffer. A considerable number of determinations were made of activity as a function of concentration, and the data in Table I are typical of many other results; they represent four different initial enzyme concentrations, diluted progressively by factors of two. If activity is plotted as a function of concentration it is found that: (1) Each curve has a point of inflection; below the concentration of enzyme corresponding to it the rate increases much more rapidly than the enzyme concentration. (2) Above this concentration the rate increases less rapidly than the enzyme concentration. 307
308
MARY
C. WALL
AND
KEITH
J.
LAIDLER
TABLE I0 Rates of Ammonia Production at Various Enzyme Concentrations Ammonia N liberated in 10 min.
SUllDle
I
II
III
IV
Relative enzyme EOIICIL.
a
b
(amt. observed)
(amt. required that the relationship between concn. and activitv be linear)
w. 1.000 42-O 48.0 0.500 29.8 24.0 0.250 18.1 12.0 0.125 10.5 6.0 ************************************************************** 0.031 1.76 1.5 0.015 0.15 0.75 1.000 38.0 38.0 0.250 11.2 9.5 0.125 6.1 4.75 ************************************************************~* 0.062 1.8 2.38 0.031 0.3 1.19 0.016 0.03 0.60 l.ooo 9.8 9.8 0.500 5.5 4.9 *************************************+****************~***** 0.250 2.5 2.45 0.125 0.92 1.22 0.062 0.25 0.61 0.031 0.05 0.30 0.015 0.01 0.15 1.000 15.0 15.0 0.500 8.75 7.5 ************************************************************** 0.250 4.1 3.8 0.125 1.6 1.9 0.062 0.55 0.95 0.031 0.12 0.48
b/a
1.0 0.80 0.66 .57 0.85 5.0 1.0 0.84 0.78 1.31 4.0 20.0 1.0 0.86 0.98 1.32 2.46 6.0 15.0 1.0 0.86 0.93 1.18 1.72 4.0
DThe line of asterisks for each sample separates approximately two regions; i.e., it represents a transition from a region in which one effect is more important to another in which a second effect predominates.
At concentrations above the line of asterisks in Table I effect (2) is observed; below it, effect (1). The ratio b/a would be 1.0 in every case
UREA-UREASE
SYSTEM.
309
V
were the activity of enzyme solution directly proportional to the first power of the concentration. Furthermore, if effect (2) occurred for all dilutions, b/a would decreasesteadily with dilution. Effect (1) is due to the fact, found by us on many occasions, that urease is very much more rapidly inactivated at high dilutions; there is therefore appreciable inactivation at low concentrations by the time the first reading is made. That this is the explanation is indicated by the fact that the lower the absolute concentration of the original solution, the higher the relative concentration corresponding to the inflection point in the rate curve. Thus it will be noted in Table I that the line of demarcation is drawn below 0.125 for the two samples of higher Rates of Ammonia
TABLE II Production at Various
Enzyme
Concentrations
Ammonia N liberated in 10 min.
a
SSIDDl.5
I
III
b
bla
Relative concentration of mzyme
(amt. observed)
(amt. required that the relationship between coocn. and activity of enzyme be linear)
0.125 0.250 0.500 1.000
1:5 18.1 2Q.8 48.0
w. 10.5 21.0 42.0 84.0
1.0 0.86 0.61 0.57
0.500 l;ooO
5.5 9.8
5.5 11.0
1.0 0.89
initial activity (samples I and II), but after 0.500 for the other two samples of lower initial activity. Effect (2) predominates in a region of enzyme concentration in which urease is relatively stable (i.e., effect (1) is negligible), and thus it must be distinctive of the enzyme-substrate system since the buffer takes no active part in the reaction. It will be observed that the greater the activity of the initial enzyme solution, i.e., the greater the amount of ammonia N liberated in unit time, the more pronounced is the departure from the linear relationship between enzyme concentration and activity. To make this more readily apparent a somewhat different analysis of part of the data in Table I has been made and is presented in Table II. Hoare and Laidler (4) have shown that ammonium ion, produced in the reaction, is an inhibitor of the enzyme, and have demonstrated that
310
MARY
C. WALL
this inhibition by ammonium follows the rate law:
AND
KEITH
J.
LAIDLER
ion in the phosphate-buffered
solutions
(1) where I represents the inhibitor. THMAM-H2SOd system which would be
The equivalent expression for the obeys the Michaelis-Menten law
koWEloPI ’ = (1 + KISl)(l + K’ [II)
(2)
These equations indicate that the greater the concentration of the inhibitor, the greater the resulting reduction in rate. But it is in solutions of high activity that the greatest amount of the inhibitor (ammonium ion) is produced. The values quoted were all obtained for lo-min. runs. Where the enzyme concentration was high, large amounts of the ammonium ion would be produced from the 0.25 M urea solution in the first few minutes of the run. Thereafter the rate in these samples would be more greatly inhibited by products than in those in which less ammonium ion was present. (In Table I compare sample I with sample III; for the former, the value of b/a becomes as low as 0.57; for the latter, 0.86 is the lowest value.) Thus it would seem that enzyme inactivation and inhibition by products adequately explain the failure of the rate to be a linear funcThese effects must also furnish tion of the enzyme concentration. partial explanations of the results which have been obtained using inhibiting buffers; however, here there is probably an additional contribution due to the presence of inhibitors (and in some cases of activators) as postulated by Strauss and Goldstein (3, 7). There is a narrow range of enzyme concentration in which the activity of the urease solution is directly proportional to its concentration; all sets of values of b/a in Table I would pass again through 1.0 as dilution is carried out. At such concentrations the amount of ammonium ion produced in the time of the runs is not great enough to cause appreciable inhibition, and yet the solution is sufficiently concentrated that inactivation with time is not very rapid. It is at such enzyme concentrations that the most easily reproducible results can be obtained.
UREA-UREASE
SYSTEM.
V
311
SUMMARY
The effect of the dilution of urease solutions on its specific activity has been studied using the trishydroxymethylaminomethane-H2S04 buffer, which has no activating or inhibiting action. It is shown that the activity is not proportional to the concentration; at low.concentrations the activity increases more rapidly than the concentration, at high concentrations less rapidly. The low concentration effect is shown to be due to the rapid inactivation of the enzyme, the high concentration effect to inhibition of the reaction by the ammonium ions produced. REFERENCES 1. AMBROSE, J. F., KISTIAKOWSKY, G. E., AND KRIDL, A. G., J. Am. Chem. Sot. 72, 317 (1950). 2. FASMAN, G. D:, AND NIEMANN, C., J. Am. Chem. Sot. 73, 1646 (1951). 3. GOLDSTEIN, A., J. Gen. Physiol. 27, 529 (1944). 4. HOARE, J. P., AND LAIDLER, K. J., J. Am. Chem. Sot. 72,2487 (1959). 5. HOFSTEE, B. H. J., J. Gen. Physiol. 32, 339 (1948). 6. PETERSON, J., HARMON, K. M., AND NIEMANN, C., J. Biol. Chem. 176,l (1948). 7. STRAUSS, 0. H., AND GOLDSTEIN, A., J. Gen. Physiol. 26,559 (1943). 8. WALL, M. C., AND LAIDLER, K. J., Arch. Biochem. and Biophys. 43,,299 (1953).
of Chemistry, The Catholic University of America, Washington, D. C. Received August 11, 1952
Several investigat,ors have commented on the lack of linearity between the activity and concentration of urease solutions (1, 5, S) and have suggested explanations. All previous work on this was carried out in the presence of inhibiting buffers, and Fasman and Niemann (2) have accepted the explanation of Strauss and Goldstein (3, 7) that the variation in specific activity of&he enzyme is due to the changing relative concentrations of enzyme, activator, and inhibitor. The present paper describes a reinvestigation of the phenomenon using trishydroxtiethylaminomethane (THMAM)-HzSOd buffer at pH 7.13; the effects observed here must be true properties of the urea-urease system since the buffer acts neither as activator nor as inhibitor (Part IV). EXPERIMENTAL
AND RESULTS
The experimental procedure was exactly as described in Part IV (8). The work was all done in 0.25 M urea and 0.035 M buffer. A considerable number of determinations were made of activity as a function of concentration, and the data in Table I are typical of many other results; they represent four different initial enzyme concentrations, diluted progressively by factors of two. If activity is plotted as a function of concentration it is found that: (1) Each curve has a point of inflection; below the concentration of enzyme corresponding to it the rate increases much more rapidly than the enzyme concentration. (2) Above this concentration the rate increases less rapidly than the enzyme concentration. 307
308
MARY
C. WALL
AND
KEITH
J.
LAIDLER
TABLE I0 Rates of Ammonia Production at Various Enzyme Concentrations Ammonia N liberated in 10 min.
SUllDle
I
II
III
IV
Relative enzyme EOIICIL.
a
b
(amt. observed)
(amt. required that the relationship between concn. and activitv be linear)
w. 1.000 42-O 48.0 0.500 29.8 24.0 0.250 18.1 12.0 0.125 10.5 6.0 ************************************************************** 0.031 1.76 1.5 0.015 0.15 0.75 1.000 38.0 38.0 0.250 11.2 9.5 0.125 6.1 4.75 ************************************************************~* 0.062 1.8 2.38 0.031 0.3 1.19 0.016 0.03 0.60 l.ooo 9.8 9.8 0.500 5.5 4.9 *************************************+****************~***** 0.250 2.5 2.45 0.125 0.92 1.22 0.062 0.25 0.61 0.031 0.05 0.30 0.015 0.01 0.15 1.000 15.0 15.0 0.500 8.75 7.5 ************************************************************** 0.250 4.1 3.8 0.125 1.6 1.9 0.062 0.55 0.95 0.031 0.12 0.48
b/a
1.0 0.80 0.66 .57 0.85 5.0 1.0 0.84 0.78 1.31 4.0 20.0 1.0 0.86 0.98 1.32 2.46 6.0 15.0 1.0 0.86 0.93 1.18 1.72 4.0
DThe line of asterisks for each sample separates approximately two regions; i.e., it represents a transition from a region in which one effect is more important to another in which a second effect predominates.
At concentrations above the line of asterisks in Table I effect (2) is observed; below it, effect (1). The ratio b/a would be 1.0 in every case
UREA-UREASE
SYSTEM.
309
V
were the activity of enzyme solution directly proportional to the first power of the concentration. Furthermore, if effect (2) occurred for all dilutions, b/a would decreasesteadily with dilution. Effect (1) is due to the fact, found by us on many occasions, that urease is very much more rapidly inactivated at high dilutions; there is therefore appreciable inactivation at low concentrations by the time the first reading is made. That this is the explanation is indicated by the fact that the lower the absolute concentration of the original solution, the higher the relative concentration corresponding to the inflection point in the rate curve. Thus it will be noted in Table I that the line of demarcation is drawn below 0.125 for the two samples of higher Rates of Ammonia
TABLE II Production at Various
Enzyme
Concentrations
Ammonia N liberated in 10 min.
a
SSIDDl.5
I
III
b
bla
Relative concentration of mzyme
(amt. observed)
(amt. required that the relationship between coocn. and activity of enzyme be linear)
0.125 0.250 0.500 1.000
1:5 18.1 2Q.8 48.0
w. 10.5 21.0 42.0 84.0
1.0 0.86 0.61 0.57
0.500 l;ooO
5.5 9.8
5.5 11.0
1.0 0.89
initial activity (samples I and II), but after 0.500 for the other two samples of lower initial activity. Effect (2) predominates in a region of enzyme concentration in which urease is relatively stable (i.e., effect (1) is negligible), and thus it must be distinctive of the enzyme-substrate system since the buffer takes no active part in the reaction. It will be observed that the greater the activity of the initial enzyme solution, i.e., the greater the amount of ammonia N liberated in unit time, the more pronounced is the departure from the linear relationship between enzyme concentration and activity. To make this more readily apparent a somewhat different analysis of part of the data in Table I has been made and is presented in Table II. Hoare and Laidler (4) have shown that ammonium ion, produced in the reaction, is an inhibitor of the enzyme, and have demonstrated that
310
MARY
C. WALL
this inhibition by ammonium follows the rate law:
AND
KEITH
J.
LAIDLER
ion in the phosphate-buffered
solutions
(1) where I represents the inhibitor. THMAM-H2SOd system which would be
The equivalent expression for the obeys the Michaelis-Menten law
koWEloPI ’ = (1 + KISl)(l + K’ [II)
(2)
These equations indicate that the greater the concentration of the inhibitor, the greater the resulting reduction in rate. But it is in solutions of high activity that the greatest amount of the inhibitor (ammonium ion) is produced. The values quoted were all obtained for lo-min. runs. Where the enzyme concentration was high, large amounts of the ammonium ion would be produced from the 0.25 M urea solution in the first few minutes of the run. Thereafter the rate in these samples would be more greatly inhibited by products than in those in which less ammonium ion was present. (In Table I compare sample I with sample III; for the former, the value of b/a becomes as low as 0.57; for the latter, 0.86 is the lowest value.) Thus it would seem that enzyme inactivation and inhibition by products adequately explain the failure of the rate to be a linear funcThese effects must also furnish tion of the enzyme concentration. partial explanations of the results which have been obtained using inhibiting buffers; however, here there is probably an additional contribution due to the presence of inhibitors (and in some cases of activators) as postulated by Strauss and Goldstein (3, 7). There is a narrow range of enzyme concentration in which the activity of the urease solution is directly proportional to its concentration; all sets of values of b/a in Table I would pass again through 1.0 as dilution is carried out. At such concentrations the amount of ammonium ion produced in the time of the runs is not great enough to cause appreciable inhibition, and yet the solution is sufficiently concentrated that inactivation with time is not very rapid. It is at such enzyme concentrations that the most easily reproducible results can be obtained.
UREA-UREASE
SYSTEM.
V
311
SUMMARY
The effect of the dilution of urease solutions on its specific activity has been studied using the trishydroxymethylaminomethane-H2S04 buffer, which has no activating or inhibiting action. It is shown that the activity is not proportional to the concentration; at low.concentrations the activity increases more rapidly than the concentration, at high concentrations less rapidly. The low concentration effect is shown to be due to the rapid inactivation of the enzyme, the high concentration effect to inhibition of the reaction by the ammonium ions produced. REFERENCES 1. AMBROSE, J. F., KISTIAKOWSKY, G. E., AND KRIDL, A. G., J. Am. Chem. Sot. 72, 317 (1950). 2. FASMAN, G. D:, AND NIEMANN, C., J. Am. Chem. Sot. 73, 1646 (1951). 3. GOLDSTEIN, A., J. Gen. Physiol. 27, 529 (1944). 4. HOARE, J. P., AND LAIDLER, K. J., J. Am. Chem. Sot. 72,2487 (1959). 5. HOFSTEE, B. H. J., J. Gen. Physiol. 32, 339 (1948). 6. PETERSON, J., HARMON, K. M., AND NIEMANN, C., J. Biol. Chem. 176,l (1948). 7. STRAUSS, 0. H., AND GOLDSTEIN, A., J. Gen. Physiol. 26,559 (1943). 8. WALL, M. C., AND LAIDLER, K. J., Arch. Biochem. and Biophys. 43,,299 (1953).