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Light-scattering study on subunit association-dissociation equilibria of bovine liver glutamate dehydrogenase
144
Biochimica et Biophysica A eta, 786 (1984) 144 - 150 Elsevier
BBA 31861
L I G H T - S C A T r E R I N G STUDY ON SUBUNIT A S S O C I A T I O N - D I S S O C I A T I O N EQUILIBRIA OF BOVINE LIVER GLUTAMATE D E H Y D R O G E N A S E T O H R U I N O U E *, K O H S U K E F U K U S H I M A , T O M O K O T A S T U M O T O and R Y O S U K E S H I M O Z A W A
Department of Chemistry, Faculty of Science, Fukuoka University, Nakakuma, Fukuoka 814-01 (Japan) (Received September 2nd, 1983) (Revised manuscript received January 10th, 1984)
Key words: Glutamate dehydrogenase," Subunit dissociation," Dissociation; Light scattering," (Bovine liver)
The subunit dissociation of bovine liver glutamate dehydrogenase (L-glutamate: NAD(P) + oxidoreductase (deaminating), EC 1.4.1.3) induced by guanidine hydrochloride (GdnHCI) in 0.2 M phosphate buffer (pH 7.3) was investigated by light-scattering molecular-weight measurements. With increasing GdnHCI concentration, two-step transition was observed in the molecular weight change. The dissociation behavior was well described by assuming the dissociation-association equilibria expressed as
K1
H ~
K2
2T ~
6M
where H, T,
and M represent the hexameric, trimeric and monomeric forms of the enzyme, respectively. GdnHCI concentration dependence of the two equilibrium constants was interpreted in terms of the binding of GdnHCI on the protein. According to this treatment, the numbers of amino acid residues present at the trimer-trimer contact area within hexamer, N3, and at the monomer-monomer contact area within trimer, NI, were estimated to be as follows; N 3 = 21 + 2 and N I = 27 + 5. These values seem to be reasonable considering the physical model proposed for this enzyme.
Introduction Bovine liver glutamate dehydrogenase (Lglutamate: NAD(P) + oxidoreductase (deaminating), EC 1.4.1.3) is an oligomeric enzyme composed of six identical subunits [1,2]. Many oligomeric proteins undergo dissociation into the constituent subunits under the action of various salts and reagents which work as subunit-dissociating agents. The subunit dissociation-association phenomena of oligomeric proteins are of general interest in connection with the understanding of the protein-protein interaction and the self-assembly of proteins to form a higher-ordered structure. Recently, Herskovits and co-workers [3-9] have * To whom correspondence should be addressed. Abbreviation: GdnHC1, guanidine hydrochloride. 0167/4838/84/$03.00 © 1984 Elsevier Science Publishers B.V.
shown that the studies of the effects of the dissociating agents on the dissociation behavior give information not only about the forces maintaining the quarternary structure but also the number of amino-acid residues at the contact areas of the subunits. Previously, we studied the subunit dissociation of bovine liver glutamate dehydrogenase induced by guanidine hydrochloride, where it was found that with increasing GdnHCI concentration, the native hexamer of enzyme dissociates to monomer via an intermediate of trimer and the discussion was mainly concerned with the dissociation kinetics [10]. In the present work, the equilibrium light-scattering measurements were made in order to supplement the previous data and give more detailed and quantitative analysis of the association-dissociation equilibria of glutamate dehydrogenase hexamer.
145 Materials and Methods
Bovine liver glutamate dehydrogenase (EC 1.4.1.3) was purchased from Sigma Chemicals. The a m m o n i u m sulfate suspension was centrifuged and the residue was dissolved in 0.2 M phosphate buffer (pH 7.3)/10 -4 M EDTA. The solution was dialyzed against the same buffer for about 24 h at 5°C, and was passed through a 1 ~m membrane filter to give a stock solution of 3 4 m g / m l . The enzyme concentration was determined spectrophotometrically using an extinction coefficient C279n mlmg/ml = 0.97 [11]. The sample solutions were prepared by diluting the stock solution with the buffer solution containing GdnHC1 at the desired concentration. All the reagents were the best in available commercial grades and were used without further purification. Light scattering was measured with JASCO L S P - 1 light-scattering photometer mantained at 10°C. The wavelength of the incident light was 436 nm, and the intensity of the scattered light at the angle of 90 ° to the incident was observed. The sample cell was thoroughly cleaned with dust-free water and the buffer solution. Sample solutions were introduced into the sample cell through a 1 /~m membrane filter. Light scattering data were analyzed according to the method described by Parr and H a m m e s [12]. The ratios of molecular weight in the presence of GdnHC1, M~, to that in the absence of GdnHCI, M 0, were determined from Eqn. 1: 2
2
M~i = (no) (On /ac°)~'( c°)( l"9°) 2 2 M0 (n~) (a,/ac,)~(c,)(10.~0)
(1)
where n represents the refractive index, (~n/Oc)~, the refractive index increment at constant chemical potential, c the enzyme concentration, 190 the scattered light intensity at 90 °, and the subscipts 0 and i refer to the quantities in the absence and presence of GdnHCI, respectively. Since bovine liver glutamate dehydrogenase hexamer undergoes a reversible self-association to form aggregates above a critical concentration [1,2], the enzyme concentration was kept at low level, 0.075-0.10 m g / m l , where the enzyme exists predominantly as a hexameric form and the reference state in Eqn. 1 corresponds to the hexamer. Eqn. 1 was derived assuming that the second
virial coefficient term is negligibly small. At low concentrations as in the present case, this approximation may be quite reasonable. Refractive index increments were taken from the data for bovine serum albumin [13], assuming that the refractive index increments are similar for all globular proteins under similar conditions. The refractive index of 0.2 M phosphate buffer was measured, and that of GdnHC1 solution was obtained from the literature [14[. Results and Discussion
The molecular weight ratio obtained from Eqn. 1 is shown in Fig. 1 as a function of GdnHC1 concentration. As seen in this figure, two-step transition is observed in the molecular wieght ratio with increasing GdnHC1 concentration. That is, M i / M o changes form 1 (which corresponds to hexamer) to about 0.16 (monomer) through an intermediate state 0.5 (trimer). The open circles in the figure represent the data obtained from reassociation experiments which were designed to check the reversibility of hexamer-trimer transition. In reassociation experiments, the enzyme was initially dissolved in 1.0-1.8 M G d n H C I and incubated for about 20 min, during which the dissociation is completed as determined from the dissociation rate constant [10], and then the enzyme solution was diluted by buffer solution to the desired GdnHC1 concentration levels. It is proved that the reassociation from trimer to hexamer takes place by removing the denaturant. The trimer-monomer transition requires some comments. At higher GdnHC1 concentration region, the unfolding of polypeptide chain occurs in addition to the subunit dissociation. Fig. 2 shows the variation of mean residue ellipticity at 222 nm, [0]222, which reflects the conformational change of the polypeptide backbone, as functions of GdnHC1 concentration and time after mixing of the enzyme with GdnHCI. It is seen from this figure that at the GdnHC1 concentration region of trimer-monomer transition the unfolding rate is relatively slow, although it increases at higher GdnHC1 concentration. Most light-scattering measurements were made within about 30 min after the preparation of sample solution, which is sufficient for dissociation to take place. Hence, in solution employed to
146
_o ° ,
•
molecular weight observed in the mixture of the three species is given by:
,
£
M i = fHMH + fTMT + fMMM 05
0.5
~0
15 20 Gan HCI (mot I1 )
25
30
where f values are the weight fractions of respective species and M values are the molecular weights ( M H = 2 M T = 6M M), the molecular weight ratio derived from Eqn. 1 is related to c~ and/3 by Eqn. 4:
~Y~40
Fig. 1. Variation of the molecular weight ratio of glutamate dehydrogenase determined from Eqn. 1 with the GdnHCI concentration at pH 7.3 (0.2 M phosphate b u f f e r / 1 . 1 0 4 M EDTA) and 10°C. e, dissociation experiments; O, reassociation experiments, i.e., sample solutions were prepared by diluting the enzyme in 1.0-1.8 M GdnHCI solution with buffer solution after about 20 min incubation. The solid line is the calculated curve based on Scheme I (see text).
light-scattering measurements, unfolding of polypeptide chain is not so significant that the present light-scattering data may be considered to monitor approximately the dissociation into subunits with folded structure. The dissociation profile of glutamate dehydrogenase hexamer under the action of GdnHC1 may be explained most simply by assuming the dissociation-association equilibria represented by the following scheme. K I
H co(1
~ a)
K1
K3, I = K 1 / 2
On
6 - 3 a - 2afl
6
(4)
According to the dissociation profile shown in Fig. 1, at a low concentration of GdnHCI (under 1.5 M), it is considered that the species predominantly present in solution are hexamer and trimer. Hence, it may be reasonably assumed that in this GdnHC1 concentration range/3 is close to 0, and Eqn. 4 leads to: ,~=2(1-~
(5)
which permits the estimation of a from the molecular weight data. Furthermore, in this case, Eqn. 2 is reduced to: 4a 2 4c~2 c~ K6"3= ~ "Co= ] - ot " 336000
(6)
K 2
2T 2coa(1
~ -- f l )
6M
(Scheme I)
6 C o a fl
where H, T, and M are the hexamer, the trimer, and the monomer of the enzyme, respectively, and K 1 and K 2 are the equilibrium constsnts of the respective step. Then, the equilibrium constants of hexamer-trimer transition, K6,3, and trimer-monomer transition, K3A a r e expressed as Eqns. 2 and 3 in terms of the total enzyme concentration as a hexameric form in mol/1, c 0, the degree of dissociation of hexamer, a, and that of trimer,/3 [15].
K6"3 =
Mi
Mo
4CoO~2(1 __fl)2 1- a
108c~a2fl 3
1 -/~
the other hand,
(2)
(3)
since the weight-average
where c(') represents the enzyme concentration in 0 10
£ zf 0.5 -10
10
2.0 GdnHCI ( m o L / I )
30
40
Fig. 2. Variation of the mean residue ellipticity at 222 nm of glutamate dehydrogenase with the GdnHC1 concentration at pH 7.3 (0.2 M phosphate b u f f e r / 1 . 1 0 -4 M EDTA) and room temperature (25 + I°C). Time after mixing of the enzyme with GdnHCI is 5 min (O), 1 h (ll L and 4 h (zx). Enzyme concentrations are 0.019-0.024 m g / m l . The dashed line shows the variation of M i / M 0 calculated with the enzyme concentration of 0.02 m g / m l according to the same procedure in Fig. 1.
147 m g / m l and 336 000 is the molecular weight of the hexameric oligomer. Thus, the value of K6, 3 can be determined from a and c~. On the other hand, at a higher GdnHC1 concentration (over 1.5 M), trimer and monomer are considered to be predominant species and a may be assumed close to 1. Then, Eqn. 4 leads to: m i
according to which /3 can be estimated from the molecular weight data. The value of K3A can also be determined by use of Eqn. 8 which is derived from Eqn. 3: K,,
108c2/33 108/33( c~ / 2 1-# ~ - ~ ~,3 3 ~ 6 ]
(8)
With the data of M i / M o and c6 = 0.08 m g / m l (most measurements were made at the enzyme concentration of about 0.08 m g / m l ) , the values of a, /3, K6, 3 and K3,1 were determined at different GdnHC1 concentrations by applying Eqns. 5-8. It was found experimentally that the GdnHC1 concentration dependence of K6. 3 and K3, ~ was expressed by the following equations:
tions suggest that the dissociated forms are more stabilized relative to the associated forms by the binding of more G d n H C I induced by the presence of GdnHC1 at higher concentration on the newly exposed surface resulting from the dissociation, and consequently reassociation is retarded. Herskovits et al. [6] have analyzed the subunit dissociation-association equilibria of hemoglobin in the presence of various denaturants in terms of the binding of the denaturant on the protein. According to their treatment, the dissociation-association equilibria in the present system are expressed by the following scheme: H HD
+ +.
D~HD D ~.HD 2
HDk_ 1
+
D ~:HDkr
KI ~2
T TD
+ + •
D D 21 D ~~ TTD •
TDI 1
+
D ~'TD t ]
t
M K~6 MD k MD,,,_ 1
log K6.3 = 6 log [D]-5.7
+ +.
D D t D ~~ M .MD2
+
D ~'MD,,]
(9a) Scheme II
log K3,1 =
24 log [D]-20.6
(9b)
where [D] represents the GdnHC1 concentration in mol/1. Eqns. 9a and 9b reproduce the values of K6, 3 and Ks, 1 at different GdnHC1 concentrations, from which a and/3 are obtained by solving Eqns. 6 and 8. Then, M ~ / M o at different GdnHC1 concentrations can be calculated by Eqn. 4. The solid line in Fig. 1 represents the simulated curve thus obtained. The agreement between calculated curve and experimental data seems to be satisfactory, and thus the dissociation profile of glutamate dehydrogenase under the action of GdnHC1 can be well described by Scheme I. It was found previously that the dissociation rate constants from hexamer to trimer and from trimer to monomer are independent of GdnHC1 concentration [10]. On the other hand, the equilibrium c o n s t a n t s K6, 3 and K3A increase with increasing GdnHC1 concentration. These observa-
In Scheme II, D represents G d n H C l and k, l, and rn the number of binding sites of GdnHC1 on the hexamer, trimer and monomer, respectively. The total concentrations of respective species are given by: k
CH=C ° H (I+K,[D]) /
cT = c° 17 (1+ Ki[D]) i=l
and
cM=c ° ~ O+ K, ID]) i=l
0o)
where K~ is the binding constant of GdnHC1 to the individual binding site and c o is the concentration of each species free from G d n H C I binding. Let N 3
148
and N~ represent the number of binding sites at the contact areas of trimer constituent within hexamer, and of monomer constituent within trimer, respectively. These may be related to k, l, and rn by k=2(l-N3)
and l = 3 ( m - N x )
because binding sites in the contact area are considered to be inaccessible to denaturant molecule and begin to interact with the reagent after the dissociation takes place. Hence, we can rewrite Eqn. 10 to the forms distinguishing explicitly the two kinds of binding site in associated forms: k
1I 0+ &,,[D])
,.=4
i=l
k/2
,CT=C O
N
II ( I + K , , i [ D ] ) - H (I+K,.i[D]) i-1
i=1
I/3
NI
CM=C ° II ( l + K ~ , i [ D ] ) . H ( I + K ¢ . i [ D ] ) i=1
(11)
t=l
where s and c in the subscripts represent the binding site at the surface and at the contact area, respectively. Then, the dissociation constants are expressed as:
K~,3=4
[ */z
c--d = [c°iU=l (1 + K~, i [D])
• H (I+K~.i[D
,=1
/
c° H (I+K~.i[D])
i=1
(12a)
I/3 K3, I
c3 -
correspond to the dissociation constants in the absence of GdnHC1. Taking logarithms of Eqn. 13, one obtains: log K6. 3 = log K~3 + 2 N:~ log( 1 + K n [D])
(]4a)
l°g K3., = l°g K'~3.,+3N, log(l + K , [ D ] )
(14b)
Eqn. 14 predicts that the plot of log K against log(1 + KB[D]) gives a straight line from which we can estimate the value of N~ and N~, the number of binding sites which are at the contact areas in associated forms and will be exposed to solvent after the dissociation. (If the unfolding of polypeptide chain is significant in monomeric form, N~ may correspond to the difference in the number of binding sites between unfolded monomer and folded trimer. However, as mentioned before, the unfolding of polypeptide chain may be negligible for the present analysis of the light-scattering data. Hence, N~ may be regarded as approximately the number of binding sites on the newly exposed area of monomer resulting from the dissociation.) Figs. 3a and 3b show the plots of Eqns. 14a and 14b, respectively, where the intrinsic binding constant of GdnHC1 to protein, K B, was assumed to be 0.2 [9]. Several points which deviated greatly from the solid line in Fig. 1 were omitted in these figures. The straight lines were obtained by the least-squares method from which the values of N 3 and N 1 were estimated to be as follows; N 3 = 21 + 2 and N~ = 27 _+ 5. Furthermore, from the intercepts of these straight lines the standard free energies of dissociation from hexamer to trimer, AG6O.``' and ,3 '
cO H ( I + K , , , i [ D ] )
-
C'I
,
i = 1
II ( I + K ~ . i [ D ] )
I=1
]/
c ° H ( 1 + K,.i[D])
-6
2N~
(13a)
K3, , = K~a(1 + KB[D]) 3N'
where K "6 , ( =
(13b)
°)
and
8~
/
(12b)
t=l
Under the assumption that all the binding sites are independent and equivalent, with an identical binding constant, K B, (i.e., K~,i = K~,i = K B ) , Eqn. 12 is reduced to: K6,3 = K6.3(1 + K,[DI)
[
(a) 5
1 (=
°)
~-7
f
(b)
°[
/
/o
-14
8 -9
o/
16
/
j
18
-10 i
i
005
0.1
l o g ( 1 • Ke[D] )
01
015
02
l o g (1 * KB[D] )
Fig. 3. Plots of (a) logK6. 3 and (b) logK3a against log(l + KB[D]). The value of K B was assumed to be 0.2. Lines represent the best-fit straight lines derived from least-squares analysis.
149
from trimer to m o n o m e r , AG3,0,w t , in the absence of G d n H C I were estimated according to the relation: (15)
AG °'w = - 2.303 R T log K w
°'W = 12.7 + 0.3 k c a l / m o l The results were AG 6.3 and AG3°'~~ = 36 + 4 kcal/mol. Estimation of above parameters by the use of Eqn. 14 may depend on the K B value to be used. Elaborate investigations have been made by Herskovits and co-workers on the dissociation of oligomeric proteins induced by various dissociating agents [3-9]. For the analysis of the dissociation behavior, they have used the K B values properly estimated from the interaction between respective ligand and average amino acid in protein, and obtained the results that the number of binding sites of the ligands at the contact area of cq3-dimer within tetramer of human hemoglobin ranged from 15 to 21 [5,7], which shows a good agreement with the number of amino-acid residues at the contact area suggested by the X-ray crystallographic structure. The values of N 3 and N 1 derived in the present work may also be regarded as the number of amino acid residues present at the contact areas in the associated state of the enzyme. A physical model of bovine liver glutamate dehydrogenase hexamer has been proposed on the basis of X-ray small-angle analysis, electron microscopy, light-scattering and hydrodynamic measurements [1,2]. In this model, the hexamer is formed by two layers, each composed of triangularly arranged three elongated subunits approximated by prolate ellipsoid, the major and minor semiaxes of which are about 33 A and 21 ,~ [16]. It is interesting to compare the present results of N 3 and N1 with this physical model. The number of amino-acid residues at the trimer-trimer contact area in hexamer is estimated to be about 7 per monomer, because N 3 corresponds to that per trimet. Whereas, monomers in trimeric form contact with each other by two surfaces, and hence, assuming that the two contact surfaces are identical, the number of amino-acid residues per single contact surface is estimated from the N~ value to be about 14. The ratio of the number of amino-acid residues present at the two different contact surfaces of monomer is almost comparable to that of the square of the two semiaxes of monomer, which -
-
might reflect the contact surface area at the two different faces. Thus, the results derived from the present analysis of the dissociation behavior of glutamate dehydrogenase seem to be consistent with the previously proposed physical model of this enzyme. Approximate correlation is also seen between the number of amino-acid residues at the contact areas and the standard free energies of dissociation in aqueous buffer solution. It may be considered that AG 6,3 °'w and AG3°'~" roughly correspond to the standard free energies required for 2N 3 ( = 42 + 4) and 3N 1 ( = 81 + 15) amino-acid residues to be released from the contact and exposed to the solvent, although an additional contribution from the mixing term is included, since these values were derived based on the molarity concentration scale. The ratios of AG°'3'~'/2N3 and AG°'~'/3N1 may be regarded as almost comparable taking into account the errors involved in respective quantities. Thus, the forces responsible for hexamer formation from trimers and trimer formation from monomers seem to be almost identical in nature.
Acknowledgement This work was supported financially in part by the Central Research Institute of Fukuoka University.
References 1 Sund, H., Markau, K. and Koberstein, R. (1975) in Subunits in Biological Systems, Part C (Timasheff, S.N. and Fasman, G.D., eds.), pp. 225-287, Dekker, New York 2 Eisenberg, H., Josephs, R. and Reisler, E. (1976) Adv. Protein Chem. 30, 101-181 3 Elbaum, D. and Herskovits, T.T. (1974) Biochemistry 13, 1268-1278 4 Harrington, J.P. and Herskovits, T.T. (1975) Biochemistry 14, 4972-4976 5 Bhat, R.K. and Herskovits, T.T. (1975) Biochemistry 14, 1572-1578 6 Herskovits, T.T. and Ibanez, V.S. (1976) Biochemistry 15, 5715-5721 7 Herskovits, T.T., Cavanagh, S.M. and San George, R.C. (1977) Biochemistry 16, 5795-5801 8 Herskovits, T.T., San George, R.C. and Cavanagh, S.M. (1978) J. Colloid Interface Sci. 63, 226-234 9 Herskovits, T.T., San George, R.C. and Erhunmwunsee, L.J. (1981) Biochemistry 20, 2580-2587
150 10 Tashiro, R., lnoue, T. and Shimozawa, R. (1982) Biochim. Biophys. Acta 706, 129-135 11 Olson, J.A. and Anfinsen, C.B. (1952) J. Biol. Chem. 197, 67-72 12 Parr, G.R. and Hammes, G.G. (1975) Biochemistry 14, 1600-1605
13 Noelken, M.E. and Timasheff, S.N. (1967) J. Biol. Chem. 242, 5080-5085 14 Nozaki, Y. (1972) Methods Enzymol. 26, 43 50 15 Herskovits, T.T. and Harrington, J.P. (1975) Biochemistry 14, 4964-4971 16 Reisler, E. and Eisenberg. H. (1970) Biopolymers 9, 877-889
Biochimica et Biophysica A eta, 786 (1984) 144 - 150 Elsevier
BBA 31861
L I G H T - S C A T r E R I N G STUDY ON SUBUNIT A S S O C I A T I O N - D I S S O C I A T I O N EQUILIBRIA OF BOVINE LIVER GLUTAMATE D E H Y D R O G E N A S E T O H R U I N O U E *, K O H S U K E F U K U S H I M A , T O M O K O T A S T U M O T O and R Y O S U K E S H I M O Z A W A
Department of Chemistry, Faculty of Science, Fukuoka University, Nakakuma, Fukuoka 814-01 (Japan) (Received September 2nd, 1983) (Revised manuscript received January 10th, 1984)
Key words: Glutamate dehydrogenase," Subunit dissociation," Dissociation; Light scattering," (Bovine liver)
The subunit dissociation of bovine liver glutamate dehydrogenase (L-glutamate: NAD(P) + oxidoreductase (deaminating), EC 1.4.1.3) induced by guanidine hydrochloride (GdnHCI) in 0.2 M phosphate buffer (pH 7.3) was investigated by light-scattering molecular-weight measurements. With increasing GdnHCI concentration, two-step transition was observed in the molecular weight change. The dissociation behavior was well described by assuming the dissociation-association equilibria expressed as
K1
H ~
K2
2T ~
6M
where H, T,
and M represent the hexameric, trimeric and monomeric forms of the enzyme, respectively. GdnHCI concentration dependence of the two equilibrium constants was interpreted in terms of the binding of GdnHCI on the protein. According to this treatment, the numbers of amino acid residues present at the trimer-trimer contact area within hexamer, N3, and at the monomer-monomer contact area within trimer, NI, were estimated to be as follows; N 3 = 21 + 2 and N I = 27 + 5. These values seem to be reasonable considering the physical model proposed for this enzyme.
Introduction Bovine liver glutamate dehydrogenase (Lglutamate: NAD(P) + oxidoreductase (deaminating), EC 1.4.1.3) is an oligomeric enzyme composed of six identical subunits [1,2]. Many oligomeric proteins undergo dissociation into the constituent subunits under the action of various salts and reagents which work as subunit-dissociating agents. The subunit dissociation-association phenomena of oligomeric proteins are of general interest in connection with the understanding of the protein-protein interaction and the self-assembly of proteins to form a higher-ordered structure. Recently, Herskovits and co-workers [3-9] have * To whom correspondence should be addressed. Abbreviation: GdnHC1, guanidine hydrochloride. 0167/4838/84/$03.00 © 1984 Elsevier Science Publishers B.V.
shown that the studies of the effects of the dissociating agents on the dissociation behavior give information not only about the forces maintaining the quarternary structure but also the number of amino-acid residues at the contact areas of the subunits. Previously, we studied the subunit dissociation of bovine liver glutamate dehydrogenase induced by guanidine hydrochloride, where it was found that with increasing GdnHCI concentration, the native hexamer of enzyme dissociates to monomer via an intermediate of trimer and the discussion was mainly concerned with the dissociation kinetics [10]. In the present work, the equilibrium light-scattering measurements were made in order to supplement the previous data and give more detailed and quantitative analysis of the association-dissociation equilibria of glutamate dehydrogenase hexamer.
145 Materials and Methods
Bovine liver glutamate dehydrogenase (EC 1.4.1.3) was purchased from Sigma Chemicals. The a m m o n i u m sulfate suspension was centrifuged and the residue was dissolved in 0.2 M phosphate buffer (pH 7.3)/10 -4 M EDTA. The solution was dialyzed against the same buffer for about 24 h at 5°C, and was passed through a 1 ~m membrane filter to give a stock solution of 3 4 m g / m l . The enzyme concentration was determined spectrophotometrically using an extinction coefficient C279n mlmg/ml = 0.97 [11]. The sample solutions were prepared by diluting the stock solution with the buffer solution containing GdnHC1 at the desired concentration. All the reagents were the best in available commercial grades and were used without further purification. Light scattering was measured with JASCO L S P - 1 light-scattering photometer mantained at 10°C. The wavelength of the incident light was 436 nm, and the intensity of the scattered light at the angle of 90 ° to the incident was observed. The sample cell was thoroughly cleaned with dust-free water and the buffer solution. Sample solutions were introduced into the sample cell through a 1 /~m membrane filter. Light scattering data were analyzed according to the method described by Parr and H a m m e s [12]. The ratios of molecular weight in the presence of GdnHC1, M~, to that in the absence of GdnHCI, M 0, were determined from Eqn. 1: 2
2
M~i = (no) (On /ac°)~'( c°)( l"9°) 2 2 M0 (n~) (a,/ac,)~(c,)(10.~0)
(1)
where n represents the refractive index, (~n/Oc)~, the refractive index increment at constant chemical potential, c the enzyme concentration, 190 the scattered light intensity at 90 °, and the subscipts 0 and i refer to the quantities in the absence and presence of GdnHCI, respectively. Since bovine liver glutamate dehydrogenase hexamer undergoes a reversible self-association to form aggregates above a critical concentration [1,2], the enzyme concentration was kept at low level, 0.075-0.10 m g / m l , where the enzyme exists predominantly as a hexameric form and the reference state in Eqn. 1 corresponds to the hexamer. Eqn. 1 was derived assuming that the second
virial coefficient term is negligibly small. At low concentrations as in the present case, this approximation may be quite reasonable. Refractive index increments were taken from the data for bovine serum albumin [13], assuming that the refractive index increments are similar for all globular proteins under similar conditions. The refractive index of 0.2 M phosphate buffer was measured, and that of GdnHC1 solution was obtained from the literature [14[. Results and Discussion
The molecular weight ratio obtained from Eqn. 1 is shown in Fig. 1 as a function of GdnHC1 concentration. As seen in this figure, two-step transition is observed in the molecular wieght ratio with increasing GdnHC1 concentration. That is, M i / M o changes form 1 (which corresponds to hexamer) to about 0.16 (monomer) through an intermediate state 0.5 (trimer). The open circles in the figure represent the data obtained from reassociation experiments which were designed to check the reversibility of hexamer-trimer transition. In reassociation experiments, the enzyme was initially dissolved in 1.0-1.8 M G d n H C I and incubated for about 20 min, during which the dissociation is completed as determined from the dissociation rate constant [10], and then the enzyme solution was diluted by buffer solution to the desired GdnHC1 concentration levels. It is proved that the reassociation from trimer to hexamer takes place by removing the denaturant. The trimer-monomer transition requires some comments. At higher GdnHC1 concentration region, the unfolding of polypeptide chain occurs in addition to the subunit dissociation. Fig. 2 shows the variation of mean residue ellipticity at 222 nm, [0]222, which reflects the conformational change of the polypeptide backbone, as functions of GdnHC1 concentration and time after mixing of the enzyme with GdnHCI. It is seen from this figure that at the GdnHC1 concentration region of trimer-monomer transition the unfolding rate is relatively slow, although it increases at higher GdnHC1 concentration. Most light-scattering measurements were made within about 30 min after the preparation of sample solution, which is sufficient for dissociation to take place. Hence, in solution employed to
146
_o ° ,
•
molecular weight observed in the mixture of the three species is given by:
,
£
M i = fHMH + fTMT + fMMM 05
0.5
~0
15 20 Gan HCI (mot I1 )
25
30
where f values are the weight fractions of respective species and M values are the molecular weights ( M H = 2 M T = 6M M), the molecular weight ratio derived from Eqn. 1 is related to c~ and/3 by Eqn. 4:
~Y~40
Fig. 1. Variation of the molecular weight ratio of glutamate dehydrogenase determined from Eqn. 1 with the GdnHCI concentration at pH 7.3 (0.2 M phosphate b u f f e r / 1 . 1 0 4 M EDTA) and 10°C. e, dissociation experiments; O, reassociation experiments, i.e., sample solutions were prepared by diluting the enzyme in 1.0-1.8 M GdnHCI solution with buffer solution after about 20 min incubation. The solid line is the calculated curve based on Scheme I (see text).
light-scattering measurements, unfolding of polypeptide chain is not so significant that the present light-scattering data may be considered to monitor approximately the dissociation into subunits with folded structure. The dissociation profile of glutamate dehydrogenase hexamer under the action of GdnHC1 may be explained most simply by assuming the dissociation-association equilibria represented by the following scheme. K I
H co(1
~ a)
K1
K3, I = K 1 / 2
On
6 - 3 a - 2afl
6
(4)
According to the dissociation profile shown in Fig. 1, at a low concentration of GdnHCI (under 1.5 M), it is considered that the species predominantly present in solution are hexamer and trimer. Hence, it may be reasonably assumed that in this GdnHC1 concentration range/3 is close to 0, and Eqn. 4 leads to: ,~=2(1-~
(5)
which permits the estimation of a from the molecular weight data. Furthermore, in this case, Eqn. 2 is reduced to: 4a 2 4c~2 c~ K6"3= ~ "Co= ] - ot " 336000
(6)
K 2
2T 2coa(1
~ -- f l )
6M
(Scheme I)
6 C o a fl
where H, T, and M are the hexamer, the trimer, and the monomer of the enzyme, respectively, and K 1 and K 2 are the equilibrium constsnts of the respective step. Then, the equilibrium constants of hexamer-trimer transition, K6,3, and trimer-monomer transition, K3A a r e expressed as Eqns. 2 and 3 in terms of the total enzyme concentration as a hexameric form in mol/1, c 0, the degree of dissociation of hexamer, a, and that of trimer,/3 [15].
K6"3 =
Mi
Mo
4CoO~2(1 __fl)2 1- a
108c~a2fl 3
1 -/~
the other hand,
(2)
(3)
since the weight-average
where c(') represents the enzyme concentration in 0 10
£ zf 0.5 -10
10
2.0 GdnHCI ( m o L / I )
30
40
Fig. 2. Variation of the mean residue ellipticity at 222 nm of glutamate dehydrogenase with the GdnHC1 concentration at pH 7.3 (0.2 M phosphate b u f f e r / 1 . 1 0 -4 M EDTA) and room temperature (25 + I°C). Time after mixing of the enzyme with GdnHCI is 5 min (O), 1 h (ll L and 4 h (zx). Enzyme concentrations are 0.019-0.024 m g / m l . The dashed line shows the variation of M i / M 0 calculated with the enzyme concentration of 0.02 m g / m l according to the same procedure in Fig. 1.
147 m g / m l and 336 000 is the molecular weight of the hexameric oligomer. Thus, the value of K6, 3 can be determined from a and c~. On the other hand, at a higher GdnHC1 concentration (over 1.5 M), trimer and monomer are considered to be predominant species and a may be assumed close to 1. Then, Eqn. 4 leads to: m i
according to which /3 can be estimated from the molecular weight data. The value of K3A can also be determined by use of Eqn. 8 which is derived from Eqn. 3: K,,
108c2/33 108/33( c~ / 2 1-# ~ - ~ ~,3 3 ~ 6 ]
(8)
With the data of M i / M o and c6 = 0.08 m g / m l (most measurements were made at the enzyme concentration of about 0.08 m g / m l ) , the values of a, /3, K6, 3 and K3,1 were determined at different GdnHC1 concentrations by applying Eqns. 5-8. It was found experimentally that the GdnHC1 concentration dependence of K6. 3 and K3, ~ was expressed by the following equations:
tions suggest that the dissociated forms are more stabilized relative to the associated forms by the binding of more G d n H C I induced by the presence of GdnHC1 at higher concentration on the newly exposed surface resulting from the dissociation, and consequently reassociation is retarded. Herskovits et al. [6] have analyzed the subunit dissociation-association equilibria of hemoglobin in the presence of various denaturants in terms of the binding of the denaturant on the protein. According to their treatment, the dissociation-association equilibria in the present system are expressed by the following scheme: H HD
+ +.
D~HD D ~.HD 2
HDk_ 1
+
D ~:HDkr
KI ~2
T TD
+ + •
D D 21 D ~~ TTD •
TDI 1
+
D ~'TD t ]
t
M K~6 MD k MD,,,_ 1
log K6.3 = 6 log [D]-5.7
+ +.
D D t D ~~ M .MD2
+
D ~'MD,,]
(9a) Scheme II
log K3,1 =
24 log [D]-20.6
(9b)
where [D] represents the GdnHC1 concentration in mol/1. Eqns. 9a and 9b reproduce the values of K6, 3 and Ks, 1 at different GdnHC1 concentrations, from which a and/3 are obtained by solving Eqns. 6 and 8. Then, M ~ / M o at different GdnHC1 concentrations can be calculated by Eqn. 4. The solid line in Fig. 1 represents the simulated curve thus obtained. The agreement between calculated curve and experimental data seems to be satisfactory, and thus the dissociation profile of glutamate dehydrogenase under the action of GdnHC1 can be well described by Scheme I. It was found previously that the dissociation rate constants from hexamer to trimer and from trimer to monomer are independent of GdnHC1 concentration [10]. On the other hand, the equilibrium c o n s t a n t s K6, 3 and K3A increase with increasing GdnHC1 concentration. These observa-
In Scheme II, D represents G d n H C l and k, l, and rn the number of binding sites of GdnHC1 on the hexamer, trimer and monomer, respectively. The total concentrations of respective species are given by: k
CH=C ° H (I+K,[D]) /
cT = c° 17 (1+ Ki[D]) i=l
and
cM=c ° ~ O+ K, ID]) i=l
0o)
where K~ is the binding constant of GdnHC1 to the individual binding site and c o is the concentration of each species free from G d n H C I binding. Let N 3
148
and N~ represent the number of binding sites at the contact areas of trimer constituent within hexamer, and of monomer constituent within trimer, respectively. These may be related to k, l, and rn by k=2(l-N3)
and l = 3 ( m - N x )
because binding sites in the contact area are considered to be inaccessible to denaturant molecule and begin to interact with the reagent after the dissociation takes place. Hence, we can rewrite Eqn. 10 to the forms distinguishing explicitly the two kinds of binding site in associated forms: k
1I 0+ &,,[D])
,.=4
i=l
k/2
,CT=C O
N
II ( I + K , , i [ D ] ) - H (I+K,.i[D]) i-1
i=1
I/3
NI
CM=C ° II ( l + K ~ , i [ D ] ) . H ( I + K ¢ . i [ D ] ) i=1
(11)
t=l
where s and c in the subscripts represent the binding site at the surface and at the contact area, respectively. Then, the dissociation constants are expressed as:
K~,3=4
[ */z
c--d = [c°iU=l (1 + K~, i [D])
• H (I+K~.i[D
,=1
/
c° H (I+K~.i[D])
i=1
(12a)
I/3 K3, I
c3 -
correspond to the dissociation constants in the absence of GdnHC1. Taking logarithms of Eqn. 13, one obtains: log K6. 3 = log K~3 + 2 N:~ log( 1 + K n [D])
(]4a)
l°g K3., = l°g K'~3.,+3N, log(l + K , [ D ] )
(14b)
Eqn. 14 predicts that the plot of log K against log(1 + KB[D]) gives a straight line from which we can estimate the value of N~ and N~, the number of binding sites which are at the contact areas in associated forms and will be exposed to solvent after the dissociation. (If the unfolding of polypeptide chain is significant in monomeric form, N~ may correspond to the difference in the number of binding sites between unfolded monomer and folded trimer. However, as mentioned before, the unfolding of polypeptide chain may be negligible for the present analysis of the light-scattering data. Hence, N~ may be regarded as approximately the number of binding sites on the newly exposed area of monomer resulting from the dissociation.) Figs. 3a and 3b show the plots of Eqns. 14a and 14b, respectively, where the intrinsic binding constant of GdnHC1 to protein, K B, was assumed to be 0.2 [9]. Several points which deviated greatly from the solid line in Fig. 1 were omitted in these figures. The straight lines were obtained by the least-squares method from which the values of N 3 and N 1 were estimated to be as follows; N 3 = 21 + 2 and N~ = 27 _+ 5. Furthermore, from the intercepts of these straight lines the standard free energies of dissociation from hexamer to trimer, AG6O.``' and ,3 '
cO H ( I + K , , , i [ D ] )
-
C'I
,
i = 1
II ( I + K ~ . i [ D ] )
I=1
]/
c ° H ( 1 + K,.i[D])
-6
2N~
(13a)
K3, , = K~a(1 + KB[D]) 3N'
where K "6 , ( =
(13b)
°)
and
8~
/
(12b)
t=l
Under the assumption that all the binding sites are independent and equivalent, with an identical binding constant, K B, (i.e., K~,i = K~,i = K B ) , Eqn. 12 is reduced to: K6,3 = K6.3(1 + K,[DI)
[
(a) 5
1 (=
°)
~-7
f
(b)
°[
/
/o
-14
8 -9
o/
16
/
j
18
-10 i
i
005
0.1
l o g ( 1 • Ke[D] )
01
015
02
l o g (1 * KB[D] )
Fig. 3. Plots of (a) logK6. 3 and (b) logK3a against log(l + KB[D]). The value of K B was assumed to be 0.2. Lines represent the best-fit straight lines derived from least-squares analysis.
149
from trimer to m o n o m e r , AG3,0,w t , in the absence of G d n H C I were estimated according to the relation: (15)
AG °'w = - 2.303 R T log K w
°'W = 12.7 + 0.3 k c a l / m o l The results were AG 6.3 and AG3°'~~ = 36 + 4 kcal/mol. Estimation of above parameters by the use of Eqn. 14 may depend on the K B value to be used. Elaborate investigations have been made by Herskovits and co-workers on the dissociation of oligomeric proteins induced by various dissociating agents [3-9]. For the analysis of the dissociation behavior, they have used the K B values properly estimated from the interaction between respective ligand and average amino acid in protein, and obtained the results that the number of binding sites of the ligands at the contact area of cq3-dimer within tetramer of human hemoglobin ranged from 15 to 21 [5,7], which shows a good agreement with the number of amino-acid residues at the contact area suggested by the X-ray crystallographic structure. The values of N 3 and N 1 derived in the present work may also be regarded as the number of amino acid residues present at the contact areas in the associated state of the enzyme. A physical model of bovine liver glutamate dehydrogenase hexamer has been proposed on the basis of X-ray small-angle analysis, electron microscopy, light-scattering and hydrodynamic measurements [1,2]. In this model, the hexamer is formed by two layers, each composed of triangularly arranged three elongated subunits approximated by prolate ellipsoid, the major and minor semiaxes of which are about 33 A and 21 ,~ [16]. It is interesting to compare the present results of N 3 and N1 with this physical model. The number of amino-acid residues at the trimer-trimer contact area in hexamer is estimated to be about 7 per monomer, because N 3 corresponds to that per trimet. Whereas, monomers in trimeric form contact with each other by two surfaces, and hence, assuming that the two contact surfaces are identical, the number of amino-acid residues per single contact surface is estimated from the N~ value to be about 14. The ratio of the number of amino-acid residues present at the two different contact surfaces of monomer is almost comparable to that of the square of the two semiaxes of monomer, which -
-
might reflect the contact surface area at the two different faces. Thus, the results derived from the present analysis of the dissociation behavior of glutamate dehydrogenase seem to be consistent with the previously proposed physical model of this enzyme. Approximate correlation is also seen between the number of amino-acid residues at the contact areas and the standard free energies of dissociation in aqueous buffer solution. It may be considered that AG 6,3 °'w and AG3°'~" roughly correspond to the standard free energies required for 2N 3 ( = 42 + 4) and 3N 1 ( = 81 + 15) amino-acid residues to be released from the contact and exposed to the solvent, although an additional contribution from the mixing term is included, since these values were derived based on the molarity concentration scale. The ratios of AG°'3'~'/2N3 and AG°'~'/3N1 may be regarded as almost comparable taking into account the errors involved in respective quantities. Thus, the forces responsible for hexamer formation from trimers and trimer formation from monomers seem to be almost identical in nature.
Acknowledgement This work was supported financially in part by the Central Research Institute of Fukuoka University.
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