JOURNAL O F T H E AMERICAN CHEMICAL SOCIETY (Registered in U. S . P a t e n t Office)
VOLUME
(0Copyright, 1957, b y t h e American Chemical Society) APRIL 5 , 1957
79
NUMBER ’7
PHYSICAL AND INORGANIC CHEMISTRY [CONTRIBUTIO.UFROM
THE
DEPARTMENT O F CHEMISTRY, UXIVERSITY O F LVISCONSIX]
Studies of the Enzyme Fumarase. 1V.l The Dependence of the Kinetic Constants at 25 O on Buffer Concentration, Composition and pH2 B Y CARL
FRIEDEN, RAYMOND G. WOLFE, JR.,3 AND ROBERT d.,\LBERTY RECEIVEDNOVEMBER 19, 1956
The Michaelis constants and maximum steady-state velocities for the forward and reverse reactions catalyzed by fumarase depend upon the hydrogen ion concentration in a simple way in the range p H 5 5-8.,5 when tris-(hydroxvmethy1)-aminomethane acetate buffers are used. Altogether 10 kinetic parameters for the reaction a t a particular buffer concentration may be calculated using the equations which have been derived earlier for the two Michaelis constants and two maximum steady-state velocities. The dependencies of these parameters on the concentration of tris-(hydroxymethy1)-aminomethane acetate and the effect of added sodium chloride have been determined. The “PH-independent” Michaelis constants are found to be a linear function of the acetate concentration.
It has been shown4 that the Michaelis constants and maximum steady-state velocities for both the forward and reverse reactions catalyzed by fumarase vary in a simple way with pH in the range 5.5-8.5 in “tris’I5 acetate buffers of 0.01 ionic strength. The pK values and pH-independent Michaelis constants and maximum steady-state velocities are expected to depend upon the composition6 and ionic strength7,*of the buffer. In order to explore these effects the various kinetic parameters for “tris” acetate buffers of 0.001, 0.005, 0.01, 0.02 and 0.05 ionic strength have been determined. They have also been determined for a 0.10 ionic strength buffer containing 0.09 N sodium chloride and 0.01 ionic strength “tris” acetate. Data of a similar nature were reported earlier for phosphate buffers,‘ but it was not possible to make a simple interpretation of the effect of PH, apparently because of the complications due to the change of the ratio of the concentrations of the mono- and divalent phosphate ions with pH. (1) T h e preceding article in this series is R . A. Alberty, V. Massey,
C. Frieden a n d A. R . Fuhlbrigge, THISJOURNAL, 76, 2485 (1954). (2) T h i s research was supported b y grants from t h e National Science Foundation a n d t h e Research Committee of t h e G r a d u a t e School of t h e University of Wisconsin f r o m funds supplied b y t h e Wisconsin Alumni Research Foundation. (3) Fellow of t h e S a t i o n a l Foundation for Infantile Paralysis. (4) C. Frieden a n d R . A. Alberty, J. B i d . Chem., 212, 859 (1955). ( 5 ) T h e abbreviation “tris” will be used for tris-(hydroxyrnethy1)aminomethane cation. (6) R. A. Alberty, THISJOURNAL, 76, 2494 (1954). (7) G. B. Kistiakowsky a n d W . H. R. Shaw, ibid.,76, 2731 (1953). (8) G. B. Kistiakowsky and IX’. E. Thompson, ibid.,1 8 , 4821 (195G).
The “tris” acetate buffers have the very great advantage that the ionic composition of the buffer medium is independent of pH except for the changes in (H+) and (OH-). Altogether 10 kinetic parameters may be evaluated a t a given buffer concentration from the initial velocities of the forward and reverse reactions over a range of p H values. The interpretation of these parameters in terms of a mechanism which has been proposed4 is discussed in detail in the following a r t i ~ l e . ~
Experimental Crystalline fumarase was isolated from pig heart muscle by the method described earlier.Io The enzyme is quite stable when stored frozen in dilute buffer or in the crystalline form suspended in 50% saturated ammonium sulfate solution in a refrigerator. Small volumes of fumarase solution, containing about 0.1 mg. of enzyme per ml., were frozen and then thawed for use as needed. Fumaric acid was crystallized twice from water and had a melting point of 287-292”. L-Malic acid (Pfanstiehl C.P.) was decolorized with activated charcoal and recrystallized twice from ethyl acetate-petroleum ether (boiling range 55-65’), The temperature of the solution was not allowed above 65” during the crystallization. The crystallized Lmalic acid melted at 102.2-102.4° and had molar absorbancy indices at 210, 230 and 250 mp of 124, 30 and 0.8 L I P cm.-’, respectively. These indices are identical with those of L-malic acid purified by chromatography.” The Michaelis constants and maximum steady-state velocities at 25” were obtained as described earlier’ using a (9) R . A. Alberty a n d W. H. Peirce, ibid , 79, 1320 (1087). (10) C. Frieden, R. M. Bock a n d R. A. Alberty, ibid., 76, 2482 (1954). ( 1 1 ) Personal communic;iiion of \Y.R . l l i l l e r .
1523
modificd Beckman DUR spectropliotometer. Cuvettes having light paths of 1, 5 and 10 cm. were employed as required to determine velocities during the first several pcr ccnt. reaction. Substrate activation12 was avoided by using substrate concentrations less than about five times the Michaelis constant. The activities of the enzyme in different experiments were compared by use of a standard assay. Sincc the turnover number at 25” is 1.7 X l o 3set.-' for 0.05 d l phosphate buffer of pH 7.3 containing 0.05 M L-malate, it is possible to express all maximum velocities as turnover Iiumbers.10 T h e stock solution of fumarase was held in ail ice-bath during the experiment, and it was always allowed to stand at least one hour before starting the experiment. The rate of iriactivation after the first hour was about 8-15% per hour and was dcterniined at regular intervals by use of tlic standnrtl assay.
Results In the pH range of about 5.5 to 8.5 the maximum steady-state velocities for fumarate (F) and Linalate (51) may be represented by the equations
where the molar concentration of the enzyme is represented by (E)o, the pH-independent turnover numbers are represented by V’,and the apparent first and second acid dissociation constants by K‘, and K ’ b . The acid dissociation constants were calculated from the pH-dependence of the maxii i i u n i steady-state velocities using the hydrogen ion concentrations, and ( H + ) b , a t which half the maximum velocity was obtained and the hydrogen ion concentration, (H+)maxrat the niaxiniuin of the plot of 1-F or i7ar C‘CYSZLSpH.l3 K t a = (H-), 4- ( H + ) b - J(H+)maX (3) =
K’b
(H+)*m*JK’a
(1)
‘I‘lic pH-independent turnover numbers J.’F and 1 -’AI were calculated with the equation
v‘ = v”,,,, (1
2 4 ~ ~ 7 ~ : )
(5)
Irma, is the turnover number a t the peak of the plot of maximum steady-state velocity veysus
n here
pH. In the pH range of about 5.3 to 8.3 the Xichaelis roristants a t a given buffer concentration may be represented by the equations
+
+ +
Ku = Klb, - _1 _ ~(~ H~ +_ ) /_ K_ ~E _ _KLE/(H+) (7) 1 (H+)/K’%E\I K ’ ~ E u I ( H + )
+
where the pH-independent Michaelis constants are represented by K’. The values of K a E and I ‘ b E were calculated from plots of V M / K Mand ’[iF/4.4KFI4 versus PH. As required by the Haldane relationi5 (12) R. A. Alberty a n d R. R I . Bock, Pvoc. S a f l . Acad. Sci., 39, 895 (1953). (13) R. A. Alberty a n d V. Massey, Biochim. Biophys. Acta, 13, 347 (1954). (14) T h e equilibrium constant for t h e over-all reaction a t 25‘ a n d f o r low ionic strength values i s Keq = 4.4. T h e ratios of maximum steady-state velocities t o Michaelis constants m a y b e f u r t h e r corrected b y multiplying b y factors providing f o r t h e secondary ionizations of t h e substrates.4 However, these corrections are negligible a t t h e lowest p H values used here. (15) J . D , S . I < d d n n c , “ E n z y i i i c s , ” I.[X
108 ( M )
1.8
7.9
2.0 1.8 1.0 8.1
1.7 2.6
0.0
IN
0.02 G.3
0.05
O.I(P 7.4
5,(j li8 (i.9
5,7
&!I
6.9
7.3 8.7 3.2 1.8
7.4
4.5 11.1
..
7.7 7 .4 7.6 9.0 2.2 1.8 30 It5
.. ..
8.4
3.8 2.3
The values iri ref. t j have been corrected. Tlie buffer contained 0.09 A 1 FaC1 and 0.01 ionic strength “tris” acetate.
dificulties in determining V.D a t low PH values a t 0.10 ionic strength the position of the 1 ’ ~versus PH curve in this region was calculated from the other three kinetic parameters using equation S with K,,= 4.4. At pi-I values above about 5.3 the hlichaelis constants deviate from equations G and 7 by considerably more than the experimental error. In making the present calculations these deviations were ignored since it is not yet certain whether these deviations are due to an additional dissociation or to electrostatic repulsion of the substrate ions by the fumarase molecule which has a fairly large negative charge a t such high pH values.’O The magnitude and significance of these deviations will be discussed in a future publication. I n order to permit a comparison of the kinetic parameters for “tris” acetate buffers with those for phosphate buffersi the kinetic constants for 0.005 Ad sodium phosphate and “tris” acetate buffers a t pH 7.0 and 25’ are given in Table 11. It is evident that the niaxiniuni steady-state velocities are affected to a very much smaller extent than the Michaelis constants by the change of buffer. The fact that the Xichaelis constants are 20-30 fold (16) R . A. Alhertp, J . Ccll.
( oiiifl.
Z’h)siol., 47, 216 (I!l5(9
April 3, 1937
.\SD PH EFFECTS ON FUMARASE BUFFERCONCENTRATIOS, CONPOSITIOK
1525
TABLE I1 MICHAELISCONSTANTSA N D MAXIMUMV E L O C I T ~ FOR S 0.1105>If SODIUM PHOSPHATE A N D “TRIS”ACETATEBCFFERS AT PEI 7 0 AND 25” KF (pM)
[v’~/[E)ol x 10-3 (sec.-1)
Phosphate 72 1.9 Acetate 2.4 0.75 Calculated using equation 8.
[VM;(E)ol K M
x
10-3
(~.ld)
(sec.-i)
Kma
190 10
1.1 0.81
4.6 4.1
larger for phosphate buffer suggests that the phosphate ions are much better competitive inhibitors of fumarase than acetate ions.
Discussion The pH-independent maximum velocities for fumarate and L-malate increase somewhat with increasing “tris” acetate concentration. The activating effect may be a consequence of the binding of acetate ions a t binding sites neighboring the enzymatic site. It would not be expected that the experimental data should conform exactly with equations derived for such a mechanism6 0 0 0.01 0.02 since the ionic strength was not held constant in the present experiments. However, the effect is (ACETATE), very similar to that which would be expected. Fig. 1.-Dependence of pH-independent Michaelis conThe pH-independent Michaelis constants for fumarate and L-malate increase linearly with in- stants for fumarate (0) and L-malate ( 0 ) oti “tris” acetate creasing “tris” acetate concentration as shown in concentration (moles of salt per liter). Fig. 1. According to these plots the pH-independent Michaelis constants a t zero buffer con- effect of the greater negative charge on the fumacentration would be 1 p M for fumarate and 7.5 p rase molecule a t 0.10 ionic strength due to a greater M for L-malate. While the change of the pH- extent of anion binding. The fact that the pK, independent Michaelis constants with “tris” ace- values are shifted about twice as much as the pKb tate concentration is not inconsistent with equa- values when 0.09 Ad sodium chloride is added is tions6 derived on the assumption of simple activa- something which will have to be explained by future tion and inhibition the fact that the ionic strength theories of the enzyme structure. The differences p K l a ~ s- P K a E and PK’bEs varies precludes any simple interpretation of the PKbE do not vary greatly with ionic strength with present data. The apparent pK values calculated using equa- the exception of PK‘aEF - PKaE although the pK tions l , 2 and 9 are nearly independent of “tris” values are considerably higher for the 0.10 ionic acetate concentration but are markedly different strength buffer. The shifts a t 0.01 and 0.10 ionic for the 0.10 ionic strength buffer containing 0.09 strengths are summarized in Table IV. The conM sodium chloride. Since the probable errors in TABLE IV the apparent pK values are somewhat largerJ3 than the experimental errors in the determination of the DIFFERENCES IN pK’ VALUESAT 26“ pH values a t which half the maximum velocity is Ionic strength 0 . 0 0 1 0.0O.i 0 . 0 1 0.0-3 0.10 obtained, changes in pK values of 0.3 are not con- P K ‘ a ~ ~p.Ti,,E 0 -0.5 -0.9 - 0 . 7 -0.5 sidered significant. In all cases ~ K ‘ , E F P K a ~ . p K ‘ u ~ ~PK.F 0.6 0.8 0.1 0.5 0,:j The pK values are consistently higher a t 0.10 p h - ‘ b E F - p f ; h E 0.2 0.1 0.5 0.1 0.1 ionic strength as shown by the differences in Table PK’bEM - PA-bE 1.6 1.5 1.7 1.8 1.6 111. This is probably due to the acid-weakening centration of “tris” acetate was the same for the TABLE I11 DIFFERENCEIN pK‘ VALUES AT 0.1” A N D 0.01 IONIC 0.01 and 0.1 ionic strength buffers. The fact that the binding of fumarate by the enzyme causes a STRENGTH AT 25” lowering of pK, indicates a more profound change I3 EF E31 upon formation of the enzyme-substrate complex PK. 1.2 1.6 1.1 than simple ion pair formation. PKb 0.6 0.G 0.6
