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Conformational transitions of the lac repressor from Escherichia coli
J. Mol. Biol. (1976) 100, 459-472
Conformational Transitions of the lac Repressor from Escherichia coli FELICIA Y . - H . W u , PRADIP BANDYOPADHYAY AND CHENG-WEN W u
Department of Biophysics, Division of Biological Sciences Albert Einstein College of Medicine Bronx, N . Y . 10461, U.S.A. (Received 10 June 1975) T e m p e r a t u r e - j u m p studies of the lac represser were performed monitoring the intrinsic t r y p t o p h a n fluorescence of the protein. A single relaxation process with a time constant of 1.36 • 104 s - 1 was observed for lac represser solutions at p H 7.5 in the absence of inducer. The relaxation time is independent of the concentration of lac represser indicating a conformational transition between two states of the represser (R* r R). Although the binding of an inducer, isopropyl-fl-D-thiogalactoside, is too slow (as shown b y stopped-flow studies) to influence the rate of the rapid interconversion between these two states of the lac represser, the relaxation amplitude decreases with increasing I P T G ~ concentration. The rate of this conformational transition is altered b y protonation of the represser. T e m p e r a t u r e - j u m p d a t a obtained for lac represser at various p H values can be analyzed in terms of a concerted mechanism in which a proton binds preferentially to one of the two states of lac represser (R). We propose t h a t I P T G also binds selectively to the R state. This is consistent with our observation t h a t addition of 1O-3 M-IPTG shifts the p K of a specific group of amino acid residues in the lac represser. Furthermore, the mechanism provides satisfactory explanations for previous reports t h a t the bimolecular rate-constant for the IPTG-lac represser interaction is extremely low a n d t h a t the inducer binding m a y exhibit various degrees of co-operativity a t different p H values. Thus the allosteric transition of lac represser effected by proton and inducer m a y p l a y a significant role in the regulation of lac transcription. 1. I n t r o d u c t i o n T h e c o n t r o l s y s t e m o f t h e / a c o p e r o n in Escherichia coli has b e e n t h e focus for t h e s t u d y o f gene r e g u l a t i o n in t h e p a s t decade. T h e n e g a t i v e c o n t r o l e l e m e n t o f t h i s s y s t e m , t h e / a c represser, is now a v a i l a b l e in r e a s o n a b l e q u a n t i t i e s (Yliiller-Hill et al., 1968) for p h y s i c o - c h e m i c a l studies. T h e r e p r e s s e r is a t e t r a m e r i c p r o t e i n w i t h molec u l a r w e i g h t of 150,000 (Miiller-Hill et al., 1971 ; B e y r e u t h e r et al., 1973). R e c e n t l y , L a i k e n et al. (1972) h a v e e x p l o i t e d t h e change in t h e t r y p t o p h a n fluorescence o f / a c r e p r e s s e r in e q u i l i b r i u m a n d k i n e t i c studies o f t h e r e p r e s s e r - i n d u c e r i n t e r a c t i o n . T h e s t o p p e d - f l o w k i n e t i c d a t a a r e c o n s i s t e n t w i t h a simple t w o - s t e p m e c h a n i s m in which a b i m o l e e u l a r b i n d i n g o f t h e i n d u c e r (I) t o t h e r e p r e s s e r (R) is followed b y a slow i s o m e r i z a t i o n o f t h e i n d u c e r - r e p r e s s e r c o m p l e x ( R I a n d R I ' ) . R ~- 1
" RI.
" RI'.
(1)
H o w e v e r , t w o of t h e p h y s i c a l consequences o f t h e i r m e c h a n i s m are n o t a p p e a l i n g . First, the bimolecular rate constant (6• M -1 s -1) is t h r e e to four orders o f m a g n i t u d e s m a l l e r t h a n e x p e c t e d for a diffusion-controlled r e a c t i o n i n v o l v i n g t Abbreviation used: IPTG, isopropyl-fl-D-thiogalactoside. 31 459
460
F.Y.-H.
WU, P. B A N D Y O P A D H Y A Y AND C.-W. WU
molecules of the size of t h e / a c represser and the inducer. Second, their mechanism invokes direct contact between the inducer and the t r y p t o p h a n residue of the represser, yet observations with model compound suggest t h a t this will lead to quite a different effect on t r y p t o p h a n fluorescence t h a n t h a t actually observed. The authors have pointed out t h a t both these problems m a y be overcome b y an additional, non-rate-limiting, isomerization o f / a c represser before inducer binding. I R*
fast
' g
gI
" gl'.
(2)
I n this mechanism, the fluorescence change which appears to be associated with the bimolecular step is due to a rapid intereonversion between two existing forms of represser, thus obviating the necessity for direct contact between iuducer and tryptophan. Moreover, if the ratio of equilibrium concentrations of R* and R is of the order of 102, the bimolecular rate constant will approach the usual diffusioncontrolled values. Although a rapid conformational transition of t h e / a c represser as described above is critical in revealing the molecular mechanism, the authors claim t h a t a n y fast process occurring outside the time resolution of the stopped-flow instrument (~-~1 ms) is unlikely to result in significant change of fluorescence, since the entire fluorescence change observed b y equilibrium methods is accounted for b y the kinetic signal observed. I t is often true t h a t the information obtained from equilibrium studies cannot be used to resolve a detailed kinetic mechanism. To further elucidate the molecular mechanism of the represser-inducer interaction, in particular to detect elementary steps in the time range faster t h a n a millisecond, we have undertaken temperaturejump studies o f / a c represser monitoring the intrinsic t r y p t o p h a n fluorescence. We report here t h a t a rapid equilibrium exists between two conformational states of lac represser. Evidence will be presented t h a t this conformational equilibrium is affected by proton and the inducer. The possible role of this t y p e of allosterie transition in gene regulation will be discussed.
2. Materials and Methods (a) Reagents Isopropyl-fl-I)-thiogalactoside was obtained from Calbiocliem and 14C-labeled IPTG~ (17 Ci/mol) was purchased from Schwartz/Mann Biochemical. DNase I (pancreatic) was the electrophoretic grade product from Worthington Biochemical Co. All other chemicals were reagent grade. (b) Buffers All buffers used in purification of lac represser were the same as described by Platt et al. (1973). IPTG-binding assay (giggs & Bourgeois, 1968) was carried out in 0-01 ~t-Tris (pH 7-4), 0.2 ~-KC1, 0.01 M-magnesium acetate, 0.1 ml~-EDTA and 1 mI~-mercaptoethanol. All temperature-jump experiments were performed in buffer I (0.1 M-potassium phosphate, 0.1 m~t-dithiotkreitol and 0.1 ml~-MgC12); p H was adjusted to the desired value in each experiment. (c) Purification of lae represser The represser was isotatod from E. cell K I 2 (strain M96) following the procedure of Platt et al. (1973) with slight modification. The potassium phosphate gradient from 0.10 M to 0.24 M was used in the last phosphoeellulose column. The purified represser See footnote to p. 459.
C O N F O R M A T I O N A L C H A N G E S OF lae R E P R E S S E R
461
revealed a single protein b a n d and was better t h a n 98~o pure as judged by sodium dodecyl sulfate/polyacrylamide gel electrophoresis. Represser concentrations were determined using the method of Bticher (1947) and the molar extinction coefficient of 9 x 1 0 4 ~ - 1 cm-1 at 280 n m (Butler et al., 1975). The represser in small portions was stored in 1 M-Tris (pH 7.6), 0.3 mM-dithiothreitol and 30% (v/v) glycerol at --70~ (d) Assay of I P T G binding to the represser I P T G - b i n d i n g activity was determined both b y equilibrium dialysis (Gilbert & MfillerHill, 1966) and b y Millipore filter assay (Riggs & Bourgeois, 1968) using [14C]IPTG (30 ets/rnin per pmol).
(c) Potentiometric titration of lac represser A Radiometer PHM-26 p H meter and a Titrograph SBR2-C were used for the continuous potentiometric titration. The electrodes used were G2222C a n d 4112 (reference). The lac represser was dialyzed extensively against 0"2 M-KC1 solution. I t was i m p o r t a n t to preadjust the p H of the solution slightly above 6 to prevent precipitation of the protein. A portion of the protein solution (2 to 5 mg/ml) was placed in the reaction vessel (0.5 ml). After temperature equilibration (10 ~ or 25~ nitrogen was blown over the surface of the solution during the titration. The titration was performed using 0"05 ~-KOI.I standardized with potassium hydrogen phthalate, the solution being constantly stirred with a magnetic stirrer. As a blank, 0.2 M-KC1 solution was also titrated in the same manner. After correction for the blank, titration results were expressed as moles of proton dissociated per mole of protein (Perlmann, 1972). Discontinuous potentiometric titration was also carried out b y adding portions of K O H to the protein solution. The behavior of the protein was the same under these two different procedures of titration. (f) Spectrophotometric measurements Absorption spectra were measured with a Cary 118-C recording spectrophotometer. Fluorescence spectra were recorded on a n Hitachi P e r k i n - E l m e r MPF-3 spectrofluorometer equipped with a corrected spectra accessory. All spectral measurements were made at 25~ with represser concentrations of at least 10 -6 ~. (g) Temperature-jump experiments The equipment used for the temperature-jump relaxation measurements was a combined stopped-flow temperature-jump apparatus constructed in this laboratory (Wu & Wu, 1974). The reaction cell of this apparatus is about 0-3 ml in volume a n d utilizes two conical lenses a t right-angles to each other. A n exciting wavelength of 295 n m from a 200 W I-Ianovia xenon/mercury arc lamp was isolated with a Bausch a n d Lomb grating monochromator. The emission wavelength was isolated from the exciting wavelength by Corning 7-51 a n d 0-52 filters. The changes in fluorescence wore detected with a n E M I 9635QB photomultiplier tube. Signal-to-noise ratios of 1000~3000 were routinely obtained. Temperature j u m p s of 7.5~ were applied to the solution b y discharge of a 0.1 /~F capacitor which had been charged to 10 kV. The resolution time of the apparatus is approximately 10/~s. The temperature-jump was from 17.5 ~ to 25~ in all eases. The kinetic information was recorded on a Tektronix 543 storage oscilloscope and transferred directly on-line to a PDP-11 digital computer b y a Biomation Model 802 transient recorder. The relaxation times a n d amplitudes were calculated b y a least-squares analysis in terms of one or two relaxation processes. The data of successive measurements on the same reaction mixture were accumulated to enhance the signal-to-noise ratio. I n some eases the oscilloscope traces were photographed a n d analyzed graphically. The results were in good agreement with the computer analysis. The experimental u n c e r t a i n t y in the relaxation times was estimated to be a b o u t 10~/o.
3. Results and Treatment o f Data W h e n t h e fluorescence i n t e n s i t y change a t 360 n m was followed, a single r e l a x a t i o n process could be d e t e c t e d w i t h t h e t e m p e r a t u r e - j u m p for solutions c o n t a i n i n g /ac represser i n buffer I ( p i t 7-5) i n t h e absence of inducer. A t y p i c a l oscilloscope trace
462
F. Y.-H.
WU,
P. BANDYOPADHYAY
AND
C.-W.
WU
of the relaxation process following a temperature-jump is given in Figure 1. No relaxation was seen in the absence of the protein. Figure 2 shows t h a t the reciprocal relaxation time, 1]T ~ 13,600 s -z, associated with this relaxation effect is independent of the concentration o f / a c repressor, suggesting the existence of a conformational equilibrium between two different forms of the repressor. kr
R*.
" R.
(3)
1/T = kf +/c~
(4)
kr
The relaxation time for this mechanism
is not dependent on the repressor concentration. I n the presence of the inducer, isopropyl-fl-D-thiogalactoside, two relaxation effects were seen, a fast one in the time range of about 50 ~s and a slow one in the time range longer t h a n 100 ms. The slower relaxation is probably associated with the bimolecular reaction of I P T G and lac repressor, since it occurs in the time scale similar to t h a t of the bimolecular binding of the same concentrations of these molecules observed b y the stopped-flow measurements (Laiken et al., 1972). However, because of its overlap with the optical changes associated with the convection of the solution, this slow relaxation process cannot be reliably analyzed using temperature-jump procedures. The fast relaxation process is essentially the same as t h a t observed in the absence of the inducer. I n addition, the relaxation time for the fast
tl.
<3 c
o El.
Time (50p.s/div) FIG. 1. A typical oscilloscope t r a c e of t h e t e m p e r a t u r e - j u m p r e l a x a t i o n effect o f t h e lac r e p r e s s e r in buffer I ( p H 7.5). T h e c o n c e n t r a t i o n of lac r e p r e s s e r w a s 8 • 1 0 - 6 M. T h e t e m p e r a t u r e - j u m p w a s f r o m 17"5 ~ to 25~ T h e v e r t i c a l scale is fluorescence i n t e n s i t y c h a n g e a t 360 n m in a r b i t r a r y u n i t s (5 m V f l a r g e division). T h e h o r i z o n t a l scale is t h e t i m e axis (50 ~s/large division).
CONFORMATIONAL
CHANGES
OF
lac R E P R E S S O R
463
20
16
i
12 I-,
I
o
8
4 -
0
I
l
2
4 10 6
I
6
I
8
I0
[/OC repressor] (M)
Fro. 2. T h e r e c i p r o c a l r e l a x a t i o n t i m e , l / r , as a f u n c t i o n of t h e i n d i c a t e d c o n c e n t r a t i o n of lac r e p r e s s e r in buffer I.
process is not altered b y changing I P T G concentration. This is expected since the bimoleeular binding is too slow (a factor of 103) to influence the rapid relaxation associated with the eortformational transitions. Nevertheless, the amplitude of the fast relaxation effect decreases with increasing I P T G concentration (Fig. 3) and no relaxation effect is observed when I P T G is saturating. This indicates that I P T G binds to one or both forms of the represser and therefore decreases the relaxation amplitude by reducing the populations of R and R*. I f the mechanism such as equation (2) exists for the/ac repressor-IPTG interaction, namely, I P T G binds only to R but not to R*, a pertinent question to probe is the magnitude of the equilibrium constant for the R* @ R transition. The value of this equilibrium constant kr/k~, could not be solved by equation (4) using the kinetic data of Figure 2. In order to obtain the forward and reverse rate constants, one needs a ligand, the binding of which to the represser is rapid enough to perturb the relaxation effect associated with the interconversion between the two forms o f / a c represser. A proton is such a ligand. Thus we have examined the effect of p H o n / a c represser. T h e / a c represser precipitates from solution below p H 6 and above p H 10. Hence potentiometric titrations of lac represser were performed between p H 6.5 and 9. The results are shown in Figure 4. Both in the presence and absence of IPTG, about 22 residues per represser molecule were titrated between p H 6-5 and 8.1. The results obtained by titrating samples from p H 6.5 to higher p i t values and from p H 9 to lower p H values agreed within the limit of experimental error. The difference curve between titrations in the presence and absence of I P T G provides information concerning the p K of certain specific residues which have been affected b y the addition of the inducer. It can be seen from Figure 4 that the averaged p K value of these residues is about 7.3; however, the analysis of the difference titration curve is not straightforward. Three cases are considered in Figure 5 in which the p K values of the specific residues are shifted in various degrees. When the p K shift is not very small (cases I I and III), the amplitude of the peak of the difference curve will give the
464
F . Y . - H . W U , P. B A N D Y O P A D H Y A Y
AND C.-W. WU 20
2O
16
12
% q
8
4 @
I
Oq
I
2
I
4
6
I
8
106[Zo](M) FIo. 3. The dependence of relaxation amplitude on I P T G concentration, Io, for bhe relaxation effect associated with the conforrnational transition of the lac repressor. Solutions contained 4 • 10- 6 M lac repressor and IPTG, concentrations as indicated, in buffer I. AV is the experimentally measured amplitude. The total signal strength was 3 V in all experiments. The solid line is the theoretical relaxation amplitude expressed by a thermodynamic parameter F (Hammes & Schimmel, 1970). F was calculated from the equilibrium concentrations of lac repressor and I P T G according to the mechanism o f e q n (3) and assuming that I P T G binds to the R but not to the R* state of the repressor.
50
~25
//I"
7/~
~ 20 ~ ~5
~ E
I0
5
S.Y ".
H
."
~ , . .."
0 ; 6-5
:.
-~
"-,. o~176176176~176176 "~176 I 7.0
I 7.5
"'f', 8-0
~"I:: I 8.5
<3 9.0
pH ~IG. 4. The potentiometric titration of the lac repressor with KOH. The solid line is the titration curve in the presence of 10 -3 M-IPTG, the broken line is that in the absence of inducer, and the dotted llne is the difference between these two titration curves. Solutions and titration procedures are described in Materials and Methods.
CONFORMATIONAL
CHANGES
(i}
$
6
Z
{n)
O F lac R E P R E S S O R
465
(m)
//
/ I t
i I
pH FIG. 5. A n a l y s i s o f difference p H t i t r a t i o n c u r v e s . T h e u p p e r c u r v e s a r e h y p o t h e t i c a l p H t i t r a t i o n c u r v e s o f a m i n o acid r e s i d u e s i n v o l v e d in p K shift. T h r e e c a s e s are c o n s i d e r e d : (I) s m a l l p K shift, (II) m o d e r a t e p K shift, a n d (III) large p K shift. I n e a c h case, one c u r v e r e p r e s e n t s t h e t i t r a t i o n c u r v e before s h i f t a n d t h e o t h e r a f t e r shift. T h e lower c u r v e s a r e t h e difference c u r v e s b e t w e e n t i t r a t i o n s b e f o r e a n d a f t e r shift. T h e o r d i n a t e s a r c n u m b e r s o f r e s i d u e s a n d t h e a b s c i s s a e are pH units.
number of residues involved, while the midpoints on the rising and falhng sides of the difference curve represent the pK before and after the shift, respectively. In the c~se of a small pK shift (case I), the peak will give the lower limit of the number of residues involved and the pK values estimated will not be accurate. Also in this ease the peak will be quite broad. Unfortunately, inspection of data such as those given in Figure 4 does not allow us to draw a clear-cut distinction between these cases. Nevertheless, the relatively sharp peak in the observed difference titration curve (Fig. 4) suggests that the magnitude of the pK shift might be moderate (e.g. case II in Fig. 5). Thus from this difference curve it was estimated that a:ldition of 10 -a •IPTG shifts the pK of at least two specific residues per repressor molecule (more than two residues for case I) from approximately 7.0 to 7.6. Moreover, there is a "cross-over" part of the potentiometric titration curves around pH 8.5, which should lead to an inverted difference peak, suggesting the possible deprotonation of other residues at this pH range on IPTG binding to the repressor. However, in this analysis we only dealt with the data in the pH range (6-5 to 8.1) Used in the kinetic experiments described below. To gain further insight into the effect of proton binding to/ac repressor, temperature-jump studies of the represser were carried out at various pH values. Figure 6 shows the reciprocal relaxation time (l/r) as a function of the proton concentration. Since pH is held constant by buffer in each experiment, it represents the free proton concentration. This is justified by the fact that no relaxation effect was observed for the buffer in the time range longer than 10 tts as monitored by a fluorescence p i t indicator (umbelliferone) in the temperature-jump. As can be seen in Figure 6, the reciprocal relaxation time decreases rapidly as the proton concentration increases
466
F.Y.-H.
W U , P. B A N D Y O P A D H Y A Y
AND C.-W. WU
2.0
t-5 X~i,pH ~ 7-5 1.0
o
.3 -
_
..........
.
:i.'_~"_:~_ ~_~,--
o
I
I
I
0
I
2
I5
I
] 4
Io 7 [H+] ( M ) :FIo. 6. The offect of pH on ~he reciprocal relaxation time, ]/r, associated with the conformational transitions of the Zac reprcssor. The equilibrium concentrations of free proton were calculated from the pYI values of solutions. The lines arc the best-fit curves calculated based on a nonlinear least-squares analysis according to (a) (. . . . ) the non-co-operative model (cqn (5)), (b) ( ) a model of highly co-operative binding of two protons to R (cqn (7)), (c) (. . . . . ) a model similar to (b) but with 4 protons binding to R, and (d) (. . . . . ) a concerted model of 4 protons binding to the repressor (cqn (9)).
a n d a p p r o a c h e s a c o n s t a n t level a t h i g h e r p r o t o n c o n c e n t r a t i o n s . This t y p e of conc e n t r a t i o n d e p e n d e n c e is c h a r a c t e r i s t i c o f a m e c h a n i s m i n v o l v i n g a n i s o m e r i z a t i o n o f t h e p r o t e i n , w i t h a s s o c i a t e d r a t e c o n s t a n t s t h a t a r e d e p e n d e n t on t h e degree o f s a t u r a t i o n o f t h e p r o t e i n w i t h ligand. A simple m o d e l o f t h i s sort is t h a t a g r o u p o f p r o t o n s b i n d t o one o f t h e t w o isomeric forms o f lac reprcssor, t h e b i n d i n g site for each p r o t o n b e i n g i d e n t i c a l a n d i n d e p e n d e n t : H +
R*.
' R.
RH,
(5)
kr
where K D is t h e dissociation c o n s t a n t for b i n d i n g o f a p r o t o n t o t h e R f o r m o f t h e repressor. I f t h e p r o t o n a t i o n s t e p is f a s t e r t h a n t h e i s o m e r i z a t i o n s t e p a n d t h e p H o f t h e s o l u t i o n is c o n s t a n t , t h e r e l a x a t i o n t i m e o f t h e c o n f o r m a t i o n a l c h a n g e c o u p l e d to p r o t o n a t i o n c a n be w r i t t e n as kr [H+] " I t - KD
(6)
A n a t t e m p t t o fit t h e d a t a of F i g u r e 6 t o e q u a t i o n (6) using p K D = 7.3 g a v e a c u r v e w h i c h is n o t c o n s i s t e n t w i t h t h e e x p e r i m e n t a l o b s e r v a t i o n (curve (a)). I f t h e a s s u m p t i o n is m a d e t h a t t h e i s o m e r i z a t i o n is c o u p l e d t o h i g h l y c o - o p e r a t i v e b i n d i n g o f t w o p r o t o n s t o t h e R form o f t h e r e p r e s s o r a c c o r d i n g to t h e following scheme,
C O N F O R M A T I O N A L C H A N G E S OF l a c R E P R E S S O R
467
2H + R*.
kr kr
'
R. ~
(7)
RH2,
where K D' is the dissociation constant for the co-operative two-fold protonation, the relaxation time is then kr [H+] 2 " I + - -
1/~ --/~f +
(8)
K D'
This expression fits the data with p K D' 2 • (7.3), kr llO0 s -z, and kr 1.55 • 104 s -z (Fig. 6, curve (b)). Since/ac repressor is a tetramer of identical subunits, we have also tried to fit the data to a mechanism equivalent to equation (7) but assuming highly co-operative binding of four protons to the repressor. The result is less satisfactory (curve (c)) compared to the fit to equation (7) (curve (b)). However, the data are also compatible with a less co-operative binding of more than two protons as analyzed by a concerted mechanism similar to that proposed b y Monod et al. (1965) for allosteric regulation. For a tetrameric lac repressor ~nolecule binding four protons, the concerted mechanism can be formulated as follows: =
=
ko
R9
=
R
k-o
J
+_H+
-_._+_ H+
kl ReH
RH
k-t Roe
_+H+
• +
k2
(9)
RH2
ReH2 k-2 +14+
F
k3
J
+H +
RH3
ReH3 k- 3 _+H+
k4
r RH4
R~H4
k-4
Ko
_+H+
468
F. Y.-H.
WU,
P. BANDYOPADHYAY
AND
C.-W.
WU
where Ka and Ka* are the intrinsic dissociation constants for the binding of a proton to the R and R* states, respectively, and the ]C~terms are the rate constants associated with the interconversions between the R and R* states. The general expression for the relaxation time associated with the conformational transitions is quite complex in this case. Thus an analysis of the data is made based on the following simplifying assumptions. (1) The vertical steps equilibrate rapidly relative to the horizontal steps; this is a reasonable assumption since protonation-deprotonation reactions are known to be extremely rapid and in m a n y cases cannot be detected by temperaturejump measurements (Amdur & Hammes, 1966). (2) The concentration changes of free proton during equilibration are negligible; this is valid since the p H of the solution is fixed by buffer. (3) All transitions from the R* to R states are characterized b y identical rate constants; this is a quite arbitrary assumption and is discussed further below. With these assumptions, the reciprocal relaxation time associated with the conformational transitions can be expressed as (Hammes & Wu, 1974)
+
(10)
There are four unknown parameters in this equation: ]c_o, ]co, Ka and Ka*. I t is apparent from equation (1O) that 1/r decreases with increasing the proton concentrations if Ka is smaller than Ka*. ]c-o can then be estimated b y the value of 1/7 when the proton concentrations are very high. A computer program based on a nonlinear least-squares analysis was used to fit the experimental data in Figure 6 to equation (10). B y varying three parameters (]co, Ka and Ka*) the best-fit curve (curve (d)) is sho~m as a dotted line in Figure 6. The best-fit kinetic parameters are listed in Table 1. TABLE 1
Kinetic parameters for the concerted mechanism of equation (9) k-o (s -1)
520
ko (s -I)
1"15• 105 220 2.5 • 10- a 1"0 • 10- ~ 0.25 8"7• 10 -s
L (=]co/k_o) Ks (~) K~ (M)
c (=ga/g'~) Ko.s (M)
(pKa ~
7.6)
( p g ~ = 7.0) (pKo. s = 7"1)
Ko.5 d e n o t e s t h e c o n c e n t r a t i o n of p r o t o n for h a l f s a t u r a t i o n o f t h e specific a m i n o acid r e s i d u e s in lac represser.
4. D i s c u s s i o n
The independence of the single relaxation time on the concentration of lac represser (Fig. 2) suggests a unimolecular isomerization between two conformational states of /ac represser. The effect of p H on the reciprocal relaxation time associated with this conformational transition (Fig. 6) is consistent with a mechanism of two protons binding highly co-operatively to one of the two conformational states (R) of the represser (eqn (7)) and a mechanism of four protons binding in a less co-operative fashion to the represser tetramer as formulated b y the concerted model in equation
C O N F O R M A T I O N A L C H A N G E S OF lac R E P R E S S O R
469
(9). A non-co-operative model such as that shown in equation (5) is inconsistent with the data. The data were also analyzed in terms of concerted mechanisms similar to equation (9) but with less than four protons binding to the repressor (best-fit curves not shown). Again the case of single proton binding does not agree with the observed data. In the case of two protons binding to the repressor, the value of Ka* obtained is extremely large (or Ka/K* ~ 0). This indicates that proton has little affinity for the R* form, in accord with the strongly co-operative model of equation (7). In general the degree of co-operativity can he expressed by the ratio of the Hill coefficient to the number of ligand binding sites (Hammes & Wu, 1974). The degree of co-operativity is 1 for the strongly co-operative model of equation (7). The degree of cooperativity in the concerted model of equation (9), however, is dependent on the values of L, Ka, Ka* and the number of proton binding sites per repressor molecule. Using the parameters in Table 1, this value is estimated to be about 0.4. At the present time, we are not able to disting~sh between these two models (or other co-operative models, e.g. 3 protons binding to the repressor with the degree of co-operativity somewhere between 0.4 and 1) from our kinetic data. However, as will be discussed later, detailed kinetic analysis according to equation (9) provides more insights into some molecular aspects of the/ac repressor. In principle, three relaxation effects should be observed for the mechanism of equation (9), but the two relaxation effects related to the bimolecular binding steps could not be detected. Either the relaxation times are too fast (<~ 10 ~s), or no fluorescence change is accompanying proton binding, or the amplitudes are too small for detection. The first alternative appears to apply in this case, since most of the secondorder rate constants for protonation reactions are in the range 101~ to 1011 M-1 s -1 (Amdur & Hammes, 1966). The quantitative analysis of the data in terms of equation (9) is quite restrictive because of the uncertainty in exact stoichiometry of protonations and the arbitrary assumption that the k_ ~terms are equal. The parameters given in Table 1 m a y not be a unique fit of the data and should only be given semiquantitative significance. Nevertheless, the analysis that has been carried out shows unequivocally that a concerted mechanism of equation (9) is consistent with the data, i.e. a mechanism in which two different eonformationaI states of the repressor exist and proton binding is tighter for one state (R) than that for the other (R*). Physically this means t h a t the repressor has a higher p K value for certain specific amino acid residues in the R states and a lower pK value in the R* states. The pK values of the R and R* states were estimated from the kinetic data to be 7.6 and 7.0, respectively. Using these and other parameters in Table 1, one can calculate the saturation function, ~, for this mechanism by the relationship (Monod et al., 1965): :F :
Lcoc(1 + c~) 3 -}- a(1 ~-
ft.)3
L(1 + c a ) a + ( l + C r
4 '
(11)
where ~ ---- [H+]/K,, c : Ka/K*, and L ---- ko/k_o. The concentration of proton for half saturation ( l ~ : 0-5) calculated for equation (11) is 8.7 • 10- s M, or pK0.5 ---- 7.1. This is in good agreement with the pK of the specific residues of/ac repressor in the absence of inducer estimated by potentiometric titration (Fig. 4). Thus the mechanism of equation (9) is consistent with the available kinetic and equilibrium data. The primary structure of/ac repressor has been elucidated (Beyreuther et aI., 1973). The repressor molecule contains 4 cr terminal (methionine), 28 histidine, 12
470
F . Y . - H . WU, P. BANDYOPADHYAY AND C.-W. WU
cysteine and 44 lysine residues, some of which might possess p K values within the range of 6.5 to 8.1. However, it is not known which amino acid residues are responsible for binding the protons that accompany the conformational transitions of the repressor. Since t r y p t o p h a n fluorescence was monitored for the conformational transition, it is likely t h a t these specific amino acid residues are spatially adjacent to one of the two t r y p t o p h a n residues in the repressor. These two tryptophans have been implicated to occupy positions (190 to 209) in a region which may be involved in inducer binding (Beyreuther et al., 1973). Probably the most interesting phenomenon observed is the shift of the p K of certain specific amino acid residues from 7.0 in the absence of I P T G to 7.6 in its presence. It provides independent evidence for the IPTG-induced conformational change of the htc repressor. Moreover, the p K value of the repressor at saturating concentration of I P T G is the same as that of the R form of repressor (pK~) determined by kinetic analysis (Table 1). This suggests that I P T G binds preferentially to the R forms and that virtually no R* form of the repressor is present in this situation. Thus it appears that both proton and I P T G bind preferentially to the same form of lac repressor. An interesting point here is the observation that not all the subunits of repressor are active in binding inducer under all circumstances. Depending on the environmental conditions, A. P. Butler, A. Revzin & P. H. yon Hippel, manuscript in preparation, and Ohshima et al. (1974) showed that the maximum number of I P T G binding per repressor molecule, n~, varies from 2 to 4. Probable explanations for less n~ than four are based on the assumption that there are at least two molecular species of the repressor, one of which has less than four binding sites. For this purpose, a mechanism such as equation (2) with four I P T G binding sites on R and none or less than four sites on R* is certainly very attractive. Furthermore, our results also imply that the non-inducible subunits may be those which are frozen into a "non-protonable" conformation. Gilbert & MiilIer-Hill (1966) and Barkley et al. (1975) found no co-operativity for inducer binding to the lac repressor as determined by equi'ibrium dialysis at 4~ On the other hand, Ohshima et al. (1974) reported that the mode of binding of I P T G varied with conditions, exhibiting no co-operativity, positive co-operativity or negative co-operativity dependent on p H and temperature. Our kinetic results tend to support the latter observations. I f both I P T G and proton stabihze one of the two conformations of the repressor, one would expect that multiple binding of either one of these two hgands in the presence of the second can give rise to a co-operative effect, the extent of which is dependent on the concentration of the second ligand (Weber, 1972). However, it is more difficult to explain the negative co-operative binding of I P T G to the repressor based on the concerted model (Monod et al., 1965) used in our analysis. It should be pointed out that although our data are consistent with the concerted model, one cannot exclude the possibihty of a sequential allosteric model such as that proposed by Koshland et al. (1966), since the complete relaxation spectrum is not observed. According to this model, the reciprocal relaxation time associated with a conformational transition may also decrease with increasing hgand concentration similar to that shown in Figure 6 (Loudon & Koshland, 1972). Alternatively, a more complex mechanism than the two hmiting models described here m a y be operative (Hammes & Wu, 1974). I f the mechanism of equation (9) is vahd and I P T G binds preferentially to the R forms, the true and apparent bimolecular rate constants for the IPTG-repressor
C O N F O R M A T I O N A L CHANGES OF lac R E P R E S S E R
471
interaction are related to t h e equilibrium concentrations of the R and R* forms at certain p H values b y
k = k' (1 + ~[R*]/~[R~]),
(12)
where k is the true and k' is the apparent bimolecular rate constant for I P T G binding to the represser. At pI-I 7.5, the ratio ~[R*]/~.[R,] was estimated to be about 22 using the parameters in Table 1 (a value of 10 was obtained according to the mechanism of equation (7)). Taking It'----6• M-1 s -1 (Laiken et al., 1972) the true bimolecular rate constant for the I P T G - l a c represser interaction is calculated to be 1.4 • l0 s M- ~ s-1, which is not unreasonable in light of the known bimolecular rates of protein-ligand interactions (Hammes, 1968). The results presented in this paper indicate t h a t t h e / a c represser is an allosteric protein. The binding of inducer to t h e / a c represser alters the p K of certain specific amino acid residues in the protein. I n addition, the inducer-represser interaction, which stimulates the expression of /ac genes, m a y be modulated b y the proton concentration. Whether such regulation also exists i n rive is an open question. Because of a constant intraccllular p H the i n rive control of gene expression b y the proton concentration seems unlikely. Nevertheless, the "microscopic" p H near or at a macromolecule has not been revealed. I n a previous paper we have reported t h a t the positive-control element of the lac operon system, the cyclic AMP receptor protein, also exists in two conformational forms, although the rates of its conformational transitions are much slower t h a n t h a t of lac represser (Wu & Wu, 1974). An i m p o r t a n t aspect of the cyclic AMP receptor protein system is t h a t cyclic AMP stimulates lac transcription b y shifting the conformational equilibrium from the biologically inactive form of the cyclic AMP receptor protein to the active form. On the other hand, cyclic GMP, which is the competitive inhibitor of cyclic AMP, shifts the equilibrium in the opposite direction. I t seems likely t h a t an allosteric regulation m a y also play a significant role in the negative control of lac transcription. This work was supported by grants from the National Institutes of Health (GM-19062) and the American Cancer Society (BC94B). One of us (C.-W. W.) is a Research Career Development awardee of the National Institutes of Health. The authors thank Dr B. Mfiller-Hill for a generous gift of E. coli K12 (strain M96). They are also grateful to Mr David Rogerson of the National Institutes of Health for cultivation of E. coli cells.
REFERENCES Amdur, I. & Hammes, G. G. (1966). In Chemical Kinetics, pp. 148-152, McGraw-Hill Book Company, New York. Barkley, M. D., Riggs, A. D., Jobe, A. & Bourgeois, S. (1975). Biochemistry, 14, 1700-1712. Beyreuther, K., Adler, K., Geisler, M. & Klemm, A. (1973). Prec. Nat. Acad. ,.%i., U.S.A. 70, 3576-3580. B(icher, T. (1947}. Bioehim. Biophys. Acta, 1, 292-314. Gilbert, W. & Miiller-Hill, B. {1966). Prec. Nat. Acad. Sci., U.S.A. 56, 1891-1898. Hammes, G. G. (1968). Advan. Protein Chem. 23, 1-57. Hammes, G. G. & Sehimmel, P. (1970). In The Enzymes (Boyer, P. D., ed.}, 3rd edit., vol. 2, pp. 67-114, Academic Press, New York. Hammes, G. G. & Wu, C.-W. (1974}. A n n u . Rev. Biophys. Bioeng. 3, 1-33. Koshland, D. E., Jr, Nemethy, G. & Filmer, D. (1966). Biochemistry, 5, 365-385. Lalken, S. L., Gross, C. A. & v o n Hippel, P. H. (1972). J. Mol. Biol. 66, 143-155. Loudon, G. M. & Koshland, D. E., J r (1972). Biochemistry, l l , 229-240.
472
F.Y.-tt.
W U , P. B A N D Y O P A D H Y A Y AND C.-W. W U
Monod, J., Wyman, J. & Changeux, J.-P. (1965). J. Mol. Biol. 12, 88-118. Mfiller-Hill, B., Cropo, B. L. & Gilbert, W. (1968). Prov. Nat. Aead. Sei., U.S.A. 59, 1259-1264. Mfiller-I-Iill, B., Beyreuther, K. & Gilbert, W. ( 1971 ). Metho'ds in Enzymology, 21,483-490. Ohshima, Y., Mizokoshi, T. & Horiuchi, T. (1974). J . Mol. Biol. 89, 127-136. Perlmann, G. E. (1972). Method8 in Enzymology, 26, 413-423. Platt, T., Files, J. G. & Weber, K. (1973). J. Biol. Chem. 248, 110-121. Riggs, A. D. & Bourgeois, S. (1968). J. Mol. Biol. 34, 361-364. Weber, G. (1972). Biochemistlry, 11,864-878. Wu, C.-W. & Wu, F. Y.-H. (1974). Biochemistry, 13, 2573-2578.
Conformational Transitions of the lac Repressor from Escherichia coli FELICIA Y . - H . W u , PRADIP BANDYOPADHYAY AND CHENG-WEN W u
Department of Biophysics, Division of Biological Sciences Albert Einstein College of Medicine Bronx, N . Y . 10461, U.S.A. (Received 10 June 1975) T e m p e r a t u r e - j u m p studies of the lac represser were performed monitoring the intrinsic t r y p t o p h a n fluorescence of the protein. A single relaxation process with a time constant of 1.36 • 104 s - 1 was observed for lac represser solutions at p H 7.5 in the absence of inducer. The relaxation time is independent of the concentration of lac represser indicating a conformational transition between two states of the represser (R* r R). Although the binding of an inducer, isopropyl-fl-D-thiogalactoside, is too slow (as shown b y stopped-flow studies) to influence the rate of the rapid interconversion between these two states of the lac represser, the relaxation amplitude decreases with increasing I P T G ~ concentration. The rate of this conformational transition is altered b y protonation of the represser. T e m p e r a t u r e - j u m p d a t a obtained for lac represser at various p H values can be analyzed in terms of a concerted mechanism in which a proton binds preferentially to one of the two states of lac represser (R). We propose t h a t I P T G also binds selectively to the R state. This is consistent with our observation t h a t addition of 1O-3 M-IPTG shifts the p K of a specific group of amino acid residues in the lac represser. Furthermore, the mechanism provides satisfactory explanations for previous reports t h a t the bimolecular rate-constant for the IPTG-lac represser interaction is extremely low a n d t h a t the inducer binding m a y exhibit various degrees of co-operativity a t different p H values. Thus the allosteric transition of lac represser effected by proton and inducer m a y p l a y a significant role in the regulation of lac transcription. 1. I n t r o d u c t i o n T h e c o n t r o l s y s t e m o f t h e / a c o p e r o n in Escherichia coli has b e e n t h e focus for t h e s t u d y o f gene r e g u l a t i o n in t h e p a s t decade. T h e n e g a t i v e c o n t r o l e l e m e n t o f t h i s s y s t e m , t h e / a c represser, is now a v a i l a b l e in r e a s o n a b l e q u a n t i t i e s (Yliiller-Hill et al., 1968) for p h y s i c o - c h e m i c a l studies. T h e r e p r e s s e r is a t e t r a m e r i c p r o t e i n w i t h molec u l a r w e i g h t of 150,000 (Miiller-Hill et al., 1971 ; B e y r e u t h e r et al., 1973). R e c e n t l y , L a i k e n et al. (1972) h a v e e x p l o i t e d t h e change in t h e t r y p t o p h a n fluorescence o f / a c r e p r e s s e r in e q u i l i b r i u m a n d k i n e t i c studies o f t h e r e p r e s s e r - i n d u c e r i n t e r a c t i o n . T h e s t o p p e d - f l o w k i n e t i c d a t a a r e c o n s i s t e n t w i t h a simple t w o - s t e p m e c h a n i s m in which a b i m o l e e u l a r b i n d i n g o f t h e i n d u c e r (I) t o t h e r e p r e s s e r (R) is followed b y a slow i s o m e r i z a t i o n o f t h e i n d u c e r - r e p r e s s e r c o m p l e x ( R I a n d R I ' ) . R ~- 1
" RI.
" RI'.
(1)
H o w e v e r , t w o of t h e p h y s i c a l consequences o f t h e i r m e c h a n i s m are n o t a p p e a l i n g . First, the bimolecular rate constant (6• M -1 s -1) is t h r e e to four orders o f m a g n i t u d e s m a l l e r t h a n e x p e c t e d for a diffusion-controlled r e a c t i o n i n v o l v i n g t Abbreviation used: IPTG, isopropyl-fl-D-thiogalactoside. 31 459
460
F.Y.-H.
WU, P. B A N D Y O P A D H Y A Y AND C.-W. WU
molecules of the size of t h e / a c represser and the inducer. Second, their mechanism invokes direct contact between the inducer and the t r y p t o p h a n residue of the represser, yet observations with model compound suggest t h a t this will lead to quite a different effect on t r y p t o p h a n fluorescence t h a n t h a t actually observed. The authors have pointed out t h a t both these problems m a y be overcome b y an additional, non-rate-limiting, isomerization o f / a c represser before inducer binding. I R*
fast
' g
gI
" gl'.
(2)
I n this mechanism, the fluorescence change which appears to be associated with the bimolecular step is due to a rapid intereonversion between two existing forms of represser, thus obviating the necessity for direct contact between iuducer and tryptophan. Moreover, if the ratio of equilibrium concentrations of R* and R is of the order of 102, the bimolecular rate constant will approach the usual diffusioncontrolled values. Although a rapid conformational transition of t h e / a c represser as described above is critical in revealing the molecular mechanism, the authors claim t h a t a n y fast process occurring outside the time resolution of the stopped-flow instrument (~-~1 ms) is unlikely to result in significant change of fluorescence, since the entire fluorescence change observed b y equilibrium methods is accounted for b y the kinetic signal observed. I t is often true t h a t the information obtained from equilibrium studies cannot be used to resolve a detailed kinetic mechanism. To further elucidate the molecular mechanism of the represser-inducer interaction, in particular to detect elementary steps in the time range faster t h a n a millisecond, we have undertaken temperaturejump studies o f / a c represser monitoring the intrinsic t r y p t o p h a n fluorescence. We report here t h a t a rapid equilibrium exists between two conformational states of lac represser. Evidence will be presented t h a t this conformational equilibrium is affected by proton and the inducer. The possible role of this t y p e of allosterie transition in gene regulation will be discussed.
2. Materials and Methods (a) Reagents Isopropyl-fl-I)-thiogalactoside was obtained from Calbiocliem and 14C-labeled IPTG~ (17 Ci/mol) was purchased from Schwartz/Mann Biochemical. DNase I (pancreatic) was the electrophoretic grade product from Worthington Biochemical Co. All other chemicals were reagent grade. (b) Buffers All buffers used in purification of lac represser were the same as described by Platt et al. (1973). IPTG-binding assay (giggs & Bourgeois, 1968) was carried out in 0-01 ~t-Tris (pH 7-4), 0.2 ~-KC1, 0.01 M-magnesium acetate, 0.1 ml~-EDTA and 1 mI~-mercaptoethanol. All temperature-jump experiments were performed in buffer I (0.1 M-potassium phosphate, 0.1 m~t-dithiotkreitol and 0.1 ml~-MgC12); p H was adjusted to the desired value in each experiment. (c) Purification of lae represser The represser was isotatod from E. cell K I 2 (strain M96) following the procedure of Platt et al. (1973) with slight modification. The potassium phosphate gradient from 0.10 M to 0.24 M was used in the last phosphoeellulose column. The purified represser See footnote to p. 459.
C O N F O R M A T I O N A L C H A N G E S OF lae R E P R E S S E R
461
revealed a single protein b a n d and was better t h a n 98~o pure as judged by sodium dodecyl sulfate/polyacrylamide gel electrophoresis. Represser concentrations were determined using the method of Bticher (1947) and the molar extinction coefficient of 9 x 1 0 4 ~ - 1 cm-1 at 280 n m (Butler et al., 1975). The represser in small portions was stored in 1 M-Tris (pH 7.6), 0.3 mM-dithiothreitol and 30% (v/v) glycerol at --70~ (d) Assay of I P T G binding to the represser I P T G - b i n d i n g activity was determined both b y equilibrium dialysis (Gilbert & MfillerHill, 1966) and b y Millipore filter assay (Riggs & Bourgeois, 1968) using [14C]IPTG (30 ets/rnin per pmol).
(c) Potentiometric titration of lac represser A Radiometer PHM-26 p H meter and a Titrograph SBR2-C were used for the continuous potentiometric titration. The electrodes used were G2222C a n d 4112 (reference). The lac represser was dialyzed extensively against 0"2 M-KC1 solution. I t was i m p o r t a n t to preadjust the p H of the solution slightly above 6 to prevent precipitation of the protein. A portion of the protein solution (2 to 5 mg/ml) was placed in the reaction vessel (0.5 ml). After temperature equilibration (10 ~ or 25~ nitrogen was blown over the surface of the solution during the titration. The titration was performed using 0"05 ~-KOI.I standardized with potassium hydrogen phthalate, the solution being constantly stirred with a magnetic stirrer. As a blank, 0.2 M-KC1 solution was also titrated in the same manner. After correction for the blank, titration results were expressed as moles of proton dissociated per mole of protein (Perlmann, 1972). Discontinuous potentiometric titration was also carried out b y adding portions of K O H to the protein solution. The behavior of the protein was the same under these two different procedures of titration. (f) Spectrophotometric measurements Absorption spectra were measured with a Cary 118-C recording spectrophotometer. Fluorescence spectra were recorded on a n Hitachi P e r k i n - E l m e r MPF-3 spectrofluorometer equipped with a corrected spectra accessory. All spectral measurements were made at 25~ with represser concentrations of at least 10 -6 ~. (g) Temperature-jump experiments The equipment used for the temperature-jump relaxation measurements was a combined stopped-flow temperature-jump apparatus constructed in this laboratory (Wu & Wu, 1974). The reaction cell of this apparatus is about 0-3 ml in volume a n d utilizes two conical lenses a t right-angles to each other. A n exciting wavelength of 295 n m from a 200 W I-Ianovia xenon/mercury arc lamp was isolated with a Bausch a n d Lomb grating monochromator. The emission wavelength was isolated from the exciting wavelength by Corning 7-51 a n d 0-52 filters. The changes in fluorescence wore detected with a n E M I 9635QB photomultiplier tube. Signal-to-noise ratios of 1000~3000 were routinely obtained. Temperature j u m p s of 7.5~ were applied to the solution b y discharge of a 0.1 /~F capacitor which had been charged to 10 kV. The resolution time of the apparatus is approximately 10/~s. The temperature-jump was from 17.5 ~ to 25~ in all eases. The kinetic information was recorded on a Tektronix 543 storage oscilloscope and transferred directly on-line to a PDP-11 digital computer b y a Biomation Model 802 transient recorder. The relaxation times a n d amplitudes were calculated b y a least-squares analysis in terms of one or two relaxation processes. The data of successive measurements on the same reaction mixture were accumulated to enhance the signal-to-noise ratio. I n some eases the oscilloscope traces were photographed a n d analyzed graphically. The results were in good agreement with the computer analysis. The experimental u n c e r t a i n t y in the relaxation times was estimated to be a b o u t 10~/o.
3. Results and Treatment o f Data W h e n t h e fluorescence i n t e n s i t y change a t 360 n m was followed, a single r e l a x a t i o n process could be d e t e c t e d w i t h t h e t e m p e r a t u r e - j u m p for solutions c o n t a i n i n g /ac represser i n buffer I ( p i t 7-5) i n t h e absence of inducer. A t y p i c a l oscilloscope trace
462
F. Y.-H.
WU,
P. BANDYOPADHYAY
AND
C.-W.
WU
of the relaxation process following a temperature-jump is given in Figure 1. No relaxation was seen in the absence of the protein. Figure 2 shows t h a t the reciprocal relaxation time, 1]T ~ 13,600 s -z, associated with this relaxation effect is independent of the concentration o f / a c repressor, suggesting the existence of a conformational equilibrium between two different forms of the repressor. kr
R*.
" R.
(3)
1/T = kf +/c~
(4)
kr
The relaxation time for this mechanism
is not dependent on the repressor concentration. I n the presence of the inducer, isopropyl-fl-D-thiogalactoside, two relaxation effects were seen, a fast one in the time range of about 50 ~s and a slow one in the time range longer t h a n 100 ms. The slower relaxation is probably associated with the bimolecular reaction of I P T G and lac repressor, since it occurs in the time scale similar to t h a t of the bimolecular binding of the same concentrations of these molecules observed b y the stopped-flow measurements (Laiken et al., 1972). However, because of its overlap with the optical changes associated with the convection of the solution, this slow relaxation process cannot be reliably analyzed using temperature-jump procedures. The fast relaxation process is essentially the same as t h a t observed in the absence of the inducer. I n addition, the relaxation time for the fast
tl.
<3 c
o El.
Time (50p.s/div) FIG. 1. A typical oscilloscope t r a c e of t h e t e m p e r a t u r e - j u m p r e l a x a t i o n effect o f t h e lac r e p r e s s e r in buffer I ( p H 7.5). T h e c o n c e n t r a t i o n of lac r e p r e s s e r w a s 8 • 1 0 - 6 M. T h e t e m p e r a t u r e - j u m p w a s f r o m 17"5 ~ to 25~ T h e v e r t i c a l scale is fluorescence i n t e n s i t y c h a n g e a t 360 n m in a r b i t r a r y u n i t s (5 m V f l a r g e division). T h e h o r i z o n t a l scale is t h e t i m e axis (50 ~s/large division).
CONFORMATIONAL
CHANGES
OF
lac R E P R E S S O R
463
20
16
i
12 I-,
I
o
8
4 -
0
I
l
2
4 10 6
I
6
I
8
I0
[/OC repressor] (M)
Fro. 2. T h e r e c i p r o c a l r e l a x a t i o n t i m e , l / r , as a f u n c t i o n of t h e i n d i c a t e d c o n c e n t r a t i o n of lac r e p r e s s e r in buffer I.
process is not altered b y changing I P T G concentration. This is expected since the bimoleeular binding is too slow (a factor of 103) to influence the rapid relaxation associated with the eortformational transitions. Nevertheless, the amplitude of the fast relaxation effect decreases with increasing I P T G concentration (Fig. 3) and no relaxation effect is observed when I P T G is saturating. This indicates that I P T G binds to one or both forms of the represser and therefore decreases the relaxation amplitude by reducing the populations of R and R*. I f the mechanism such as equation (2) exists for the/ac repressor-IPTG interaction, namely, I P T G binds only to R but not to R*, a pertinent question to probe is the magnitude of the equilibrium constant for the R* @ R transition. The value of this equilibrium constant kr/k~, could not be solved by equation (4) using the kinetic data of Figure 2. In order to obtain the forward and reverse rate constants, one needs a ligand, the binding of which to the represser is rapid enough to perturb the relaxation effect associated with the interconversion between the two forms o f / a c represser. A proton is such a ligand. Thus we have examined the effect of p H o n / a c represser. T h e / a c represser precipitates from solution below p H 6 and above p H 10. Hence potentiometric titrations of lac represser were performed between p H 6.5 and 9. The results are shown in Figure 4. Both in the presence and absence of IPTG, about 22 residues per represser molecule were titrated between p H 6-5 and 8.1. The results obtained by titrating samples from p H 6.5 to higher p i t values and from p H 9 to lower p H values agreed within the limit of experimental error. The difference curve between titrations in the presence and absence of I P T G provides information concerning the p K of certain specific residues which have been affected b y the addition of the inducer. It can be seen from Figure 4 that the averaged p K value of these residues is about 7.3; however, the analysis of the difference titration curve is not straightforward. Three cases are considered in Figure 5 in which the p K values of the specific residues are shifted in various degrees. When the p K shift is not very small (cases I I and III), the amplitude of the peak of the difference curve will give the
464
F . Y . - H . W U , P. B A N D Y O P A D H Y A Y
AND C.-W. WU 20
2O
16
12
% q
8
4 @
I
Oq
I
2
I
4
6
I
8
106[Zo](M) FIo. 3. The dependence of relaxation amplitude on I P T G concentration, Io, for bhe relaxation effect associated with the conforrnational transition of the lac repressor. Solutions contained 4 • 10- 6 M lac repressor and IPTG, concentrations as indicated, in buffer I. AV is the experimentally measured amplitude. The total signal strength was 3 V in all experiments. The solid line is the theoretical relaxation amplitude expressed by a thermodynamic parameter F (Hammes & Schimmel, 1970). F was calculated from the equilibrium concentrations of lac repressor and I P T G according to the mechanism o f e q n (3) and assuming that I P T G binds to the R but not to the R* state of the repressor.
50
~25
//I"
7/~
~ 20 ~ ~5
~ E
I0
5
S.Y ".
H
."
~ , . .."
0 ; 6-5
:.
-~
"-,. o~176176176~176176 "~176 I 7.0
I 7.5
"'f', 8-0
~"I:: I 8.5
<3 9.0
pH ~IG. 4. The potentiometric titration of the lac repressor with KOH. The solid line is the titration curve in the presence of 10 -3 M-IPTG, the broken line is that in the absence of inducer, and the dotted llne is the difference between these two titration curves. Solutions and titration procedures are described in Materials and Methods.
CONFORMATIONAL
CHANGES
(i}
$
6
Z
{n)
O F lac R E P R E S S O R
465
(m)
//
/ I t
i I
pH FIG. 5. A n a l y s i s o f difference p H t i t r a t i o n c u r v e s . T h e u p p e r c u r v e s a r e h y p o t h e t i c a l p H t i t r a t i o n c u r v e s o f a m i n o acid r e s i d u e s i n v o l v e d in p K shift. T h r e e c a s e s are c o n s i d e r e d : (I) s m a l l p K shift, (II) m o d e r a t e p K shift, a n d (III) large p K shift. I n e a c h case, one c u r v e r e p r e s e n t s t h e t i t r a t i o n c u r v e before s h i f t a n d t h e o t h e r a f t e r shift. T h e lower c u r v e s a r e t h e difference c u r v e s b e t w e e n t i t r a t i o n s b e f o r e a n d a f t e r shift. T h e o r d i n a t e s a r c n u m b e r s o f r e s i d u e s a n d t h e a b s c i s s a e are pH units.
number of residues involved, while the midpoints on the rising and falhng sides of the difference curve represent the pK before and after the shift, respectively. In the c~se of a small pK shift (case I), the peak will give the lower limit of the number of residues involved and the pK values estimated will not be accurate. Also in this ease the peak will be quite broad. Unfortunately, inspection of data such as those given in Figure 4 does not allow us to draw a clear-cut distinction between these cases. Nevertheless, the relatively sharp peak in the observed difference titration curve (Fig. 4) suggests that the magnitude of the pK shift might be moderate (e.g. case II in Fig. 5). Thus from this difference curve it was estimated that a:ldition of 10 -a •IPTG shifts the pK of at least two specific residues per repressor molecule (more than two residues for case I) from approximately 7.0 to 7.6. Moreover, there is a "cross-over" part of the potentiometric titration curves around pH 8.5, which should lead to an inverted difference peak, suggesting the possible deprotonation of other residues at this pH range on IPTG binding to the repressor. However, in this analysis we only dealt with the data in the pH range (6-5 to 8.1) Used in the kinetic experiments described below. To gain further insight into the effect of proton binding to/ac repressor, temperature-jump studies of the represser were carried out at various pH values. Figure 6 shows the reciprocal relaxation time (l/r) as a function of the proton concentration. Since pH is held constant by buffer in each experiment, it represents the free proton concentration. This is justified by the fact that no relaxation effect was observed for the buffer in the time range longer than 10 tts as monitored by a fluorescence p i t indicator (umbelliferone) in the temperature-jump. As can be seen in Figure 6, the reciprocal relaxation time decreases rapidly as the proton concentration increases
466
F.Y.-H.
W U , P. B A N D Y O P A D H Y A Y
AND C.-W. WU
2.0
t-5 X~i,pH ~ 7-5 1.0
o
.3 -
_
..........
.
:i.'_~"_:~_ ~_~,--
o
I
I
I
0
I
2
I5
I
] 4
Io 7 [H+] ( M ) :FIo. 6. The offect of pH on ~he reciprocal relaxation time, ]/r, associated with the conformational transitions of the Zac reprcssor. The equilibrium concentrations of free proton were calculated from the pYI values of solutions. The lines arc the best-fit curves calculated based on a nonlinear least-squares analysis according to (a) (. . . . ) the non-co-operative model (cqn (5)), (b) ( ) a model of highly co-operative binding of two protons to R (cqn (7)), (c) (. . . . . ) a model similar to (b) but with 4 protons binding to R, and (d) (. . . . . ) a concerted model of 4 protons binding to the repressor (cqn (9)).
a n d a p p r o a c h e s a c o n s t a n t level a t h i g h e r p r o t o n c o n c e n t r a t i o n s . This t y p e of conc e n t r a t i o n d e p e n d e n c e is c h a r a c t e r i s t i c o f a m e c h a n i s m i n v o l v i n g a n i s o m e r i z a t i o n o f t h e p r o t e i n , w i t h a s s o c i a t e d r a t e c o n s t a n t s t h a t a r e d e p e n d e n t on t h e degree o f s a t u r a t i o n o f t h e p r o t e i n w i t h ligand. A simple m o d e l o f t h i s sort is t h a t a g r o u p o f p r o t o n s b i n d t o one o f t h e t w o isomeric forms o f lac reprcssor, t h e b i n d i n g site for each p r o t o n b e i n g i d e n t i c a l a n d i n d e p e n d e n t : H +
R*.
' R.
RH,
(5)
kr
where K D is t h e dissociation c o n s t a n t for b i n d i n g o f a p r o t o n t o t h e R f o r m o f t h e repressor. I f t h e p r o t o n a t i o n s t e p is f a s t e r t h a n t h e i s o m e r i z a t i o n s t e p a n d t h e p H o f t h e s o l u t i o n is c o n s t a n t , t h e r e l a x a t i o n t i m e o f t h e c o n f o r m a t i o n a l c h a n g e c o u p l e d to p r o t o n a t i o n c a n be w r i t t e n as kr [H+] " I t - KD
(6)
A n a t t e m p t t o fit t h e d a t a of F i g u r e 6 t o e q u a t i o n (6) using p K D = 7.3 g a v e a c u r v e w h i c h is n o t c o n s i s t e n t w i t h t h e e x p e r i m e n t a l o b s e r v a t i o n (curve (a)). I f t h e a s s u m p t i o n is m a d e t h a t t h e i s o m e r i z a t i o n is c o u p l e d t o h i g h l y c o - o p e r a t i v e b i n d i n g o f t w o p r o t o n s t o t h e R form o f t h e r e p r e s s o r a c c o r d i n g to t h e following scheme,
C O N F O R M A T I O N A L C H A N G E S OF l a c R E P R E S S O R
467
2H + R*.
kr kr
'
R. ~
(7)
RH2,
where K D' is the dissociation constant for the co-operative two-fold protonation, the relaxation time is then kr [H+] 2 " I + - -
1/~ --/~f +
(8)
K D'
This expression fits the data with p K D' 2 • (7.3), kr llO0 s -z, and kr 1.55 • 104 s -z (Fig. 6, curve (b)). Since/ac repressor is a tetramer of identical subunits, we have also tried to fit the data to a mechanism equivalent to equation (7) but assuming highly co-operative binding of four protons to the repressor. The result is less satisfactory (curve (c)) compared to the fit to equation (7) (curve (b)). However, the data are also compatible with a less co-operative binding of more than two protons as analyzed by a concerted mechanism similar to that proposed b y Monod et al. (1965) for allosteric regulation. For a tetrameric lac repressor ~nolecule binding four protons, the concerted mechanism can be formulated as follows: =
=
ko
R9
=
R
k-o
J
+_H+
-_._+_ H+
kl ReH
RH
k-t Roe
_+H+
• +
k2
(9)
RH2
ReH2 k-2 +14+
F
k3
J
+H +
RH3
ReH3 k- 3 _+H+
k4
r RH4
R~H4
k-4
Ko
_+H+
468
F. Y.-H.
WU,
P. BANDYOPADHYAY
AND
C.-W.
WU
where Ka and Ka* are the intrinsic dissociation constants for the binding of a proton to the R and R* states, respectively, and the ]C~terms are the rate constants associated with the interconversions between the R and R* states. The general expression for the relaxation time associated with the conformational transitions is quite complex in this case. Thus an analysis of the data is made based on the following simplifying assumptions. (1) The vertical steps equilibrate rapidly relative to the horizontal steps; this is a reasonable assumption since protonation-deprotonation reactions are known to be extremely rapid and in m a n y cases cannot be detected by temperaturejump measurements (Amdur & Hammes, 1966). (2) The concentration changes of free proton during equilibration are negligible; this is valid since the p H of the solution is fixed by buffer. (3) All transitions from the R* to R states are characterized b y identical rate constants; this is a quite arbitrary assumption and is discussed further below. With these assumptions, the reciprocal relaxation time associated with the conformational transitions can be expressed as (Hammes & Wu, 1974)
+
(10)
There are four unknown parameters in this equation: ]c_o, ]co, Ka and Ka*. I t is apparent from equation (1O) that 1/r decreases with increasing the proton concentrations if Ka is smaller than Ka*. ]c-o can then be estimated b y the value of 1/7 when the proton concentrations are very high. A computer program based on a nonlinear least-squares analysis was used to fit the experimental data in Figure 6 to equation (10). B y varying three parameters (]co, Ka and Ka*) the best-fit curve (curve (d)) is sho~m as a dotted line in Figure 6. The best-fit kinetic parameters are listed in Table 1. TABLE 1
Kinetic parameters for the concerted mechanism of equation (9) k-o (s -1)
520
ko (s -I)
1"15• 105 220 2.5 • 10- a 1"0 • 10- ~ 0.25 8"7• 10 -s
L (=]co/k_o) Ks (~) K~ (M)
c (=ga/g'~) Ko.s (M)
(pKa ~
7.6)
( p g ~ = 7.0) (pKo. s = 7"1)
Ko.5 d e n o t e s t h e c o n c e n t r a t i o n of p r o t o n for h a l f s a t u r a t i o n o f t h e specific a m i n o acid r e s i d u e s in lac represser.
4. D i s c u s s i o n
The independence of the single relaxation time on the concentration of lac represser (Fig. 2) suggests a unimolecular isomerization between two conformational states of /ac represser. The effect of p H on the reciprocal relaxation time associated with this conformational transition (Fig. 6) is consistent with a mechanism of two protons binding highly co-operatively to one of the two conformational states (R) of the represser (eqn (7)) and a mechanism of four protons binding in a less co-operative fashion to the represser tetramer as formulated b y the concerted model in equation
C O N F O R M A T I O N A L C H A N G E S OF lac R E P R E S S O R
469
(9). A non-co-operative model such as that shown in equation (5) is inconsistent with the data. The data were also analyzed in terms of concerted mechanisms similar to equation (9) but with less than four protons binding to the repressor (best-fit curves not shown). Again the case of single proton binding does not agree with the observed data. In the case of two protons binding to the repressor, the value of Ka* obtained is extremely large (or Ka/K* ~ 0). This indicates that proton has little affinity for the R* form, in accord with the strongly co-operative model of equation (7). In general the degree of co-operativity can he expressed by the ratio of the Hill coefficient to the number of ligand binding sites (Hammes & Wu, 1974). The degree of co-operativity is 1 for the strongly co-operative model of equation (7). The degree of cooperativity in the concerted model of equation (9), however, is dependent on the values of L, Ka, Ka* and the number of proton binding sites per repressor molecule. Using the parameters in Table 1, this value is estimated to be about 0.4. At the present time, we are not able to disting~sh between these two models (or other co-operative models, e.g. 3 protons binding to the repressor with the degree of co-operativity somewhere between 0.4 and 1) from our kinetic data. However, as will be discussed later, detailed kinetic analysis according to equation (9) provides more insights into some molecular aspects of the/ac repressor. In principle, three relaxation effects should be observed for the mechanism of equation (9), but the two relaxation effects related to the bimolecular binding steps could not be detected. Either the relaxation times are too fast (<~ 10 ~s), or no fluorescence change is accompanying proton binding, or the amplitudes are too small for detection. The first alternative appears to apply in this case, since most of the secondorder rate constants for protonation reactions are in the range 101~ to 1011 M-1 s -1 (Amdur & Hammes, 1966). The quantitative analysis of the data in terms of equation (9) is quite restrictive because of the uncertainty in exact stoichiometry of protonations and the arbitrary assumption that the k_ ~terms are equal. The parameters given in Table 1 m a y not be a unique fit of the data and should only be given semiquantitative significance. Nevertheless, the analysis that has been carried out shows unequivocally that a concerted mechanism of equation (9) is consistent with the data, i.e. a mechanism in which two different eonformationaI states of the repressor exist and proton binding is tighter for one state (R) than that for the other (R*). Physically this means t h a t the repressor has a higher p K value for certain specific amino acid residues in the R states and a lower pK value in the R* states. The pK values of the R and R* states were estimated from the kinetic data to be 7.6 and 7.0, respectively. Using these and other parameters in Table 1, one can calculate the saturation function, ~, for this mechanism by the relationship (Monod et al., 1965): :F :
Lcoc(1 + c~) 3 -}- a(1 ~-
ft.)3
L(1 + c a ) a + ( l + C r
4 '
(11)
where ~ ---- [H+]/K,, c : Ka/K*, and L ---- ko/k_o. The concentration of proton for half saturation ( l ~ : 0-5) calculated for equation (11) is 8.7 • 10- s M, or pK0.5 ---- 7.1. This is in good agreement with the pK of the specific residues of/ac repressor in the absence of inducer estimated by potentiometric titration (Fig. 4). Thus the mechanism of equation (9) is consistent with the available kinetic and equilibrium data. The primary structure of/ac repressor has been elucidated (Beyreuther et aI., 1973). The repressor molecule contains 4 cr terminal (methionine), 28 histidine, 12
470
F . Y . - H . WU, P. BANDYOPADHYAY AND C.-W. WU
cysteine and 44 lysine residues, some of which might possess p K values within the range of 6.5 to 8.1. However, it is not known which amino acid residues are responsible for binding the protons that accompany the conformational transitions of the repressor. Since t r y p t o p h a n fluorescence was monitored for the conformational transition, it is likely t h a t these specific amino acid residues are spatially adjacent to one of the two t r y p t o p h a n residues in the repressor. These two tryptophans have been implicated to occupy positions (190 to 209) in a region which may be involved in inducer binding (Beyreuther et al., 1973). Probably the most interesting phenomenon observed is the shift of the p K of certain specific amino acid residues from 7.0 in the absence of I P T G to 7.6 in its presence. It provides independent evidence for the IPTG-induced conformational change of the htc repressor. Moreover, the p K value of the repressor at saturating concentration of I P T G is the same as that of the R form of repressor (pK~) determined by kinetic analysis (Table 1). This suggests that I P T G binds preferentially to the R forms and that virtually no R* form of the repressor is present in this situation. Thus it appears that both proton and I P T G bind preferentially to the same form of lac repressor. An interesting point here is the observation that not all the subunits of repressor are active in binding inducer under all circumstances. Depending on the environmental conditions, A. P. Butler, A. Revzin & P. H. yon Hippel, manuscript in preparation, and Ohshima et al. (1974) showed that the maximum number of I P T G binding per repressor molecule, n~, varies from 2 to 4. Probable explanations for less n~ than four are based on the assumption that there are at least two molecular species of the repressor, one of which has less than four binding sites. For this purpose, a mechanism such as equation (2) with four I P T G binding sites on R and none or less than four sites on R* is certainly very attractive. Furthermore, our results also imply that the non-inducible subunits may be those which are frozen into a "non-protonable" conformation. Gilbert & MiilIer-Hill (1966) and Barkley et al. (1975) found no co-operativity for inducer binding to the lac repressor as determined by equi'ibrium dialysis at 4~ On the other hand, Ohshima et al. (1974) reported that the mode of binding of I P T G varied with conditions, exhibiting no co-operativity, positive co-operativity or negative co-operativity dependent on p H and temperature. Our kinetic results tend to support the latter observations. I f both I P T G and proton stabihze one of the two conformations of the repressor, one would expect that multiple binding of either one of these two hgands in the presence of the second can give rise to a co-operative effect, the extent of which is dependent on the concentration of the second ligand (Weber, 1972). However, it is more difficult to explain the negative co-operative binding of I P T G to the repressor based on the concerted model (Monod et al., 1965) used in our analysis. It should be pointed out that although our data are consistent with the concerted model, one cannot exclude the possibihty of a sequential allosteric model such as that proposed by Koshland et al. (1966), since the complete relaxation spectrum is not observed. According to this model, the reciprocal relaxation time associated with a conformational transition may also decrease with increasing hgand concentration similar to that shown in Figure 6 (Loudon & Koshland, 1972). Alternatively, a more complex mechanism than the two hmiting models described here m a y be operative (Hammes & Wu, 1974). I f the mechanism of equation (9) is vahd and I P T G binds preferentially to the R forms, the true and apparent bimolecular rate constants for the IPTG-repressor
C O N F O R M A T I O N A L CHANGES OF lac R E P R E S S E R
471
interaction are related to t h e equilibrium concentrations of the R and R* forms at certain p H values b y
k = k' (1 + ~[R*]/~[R~]),
(12)
where k is the true and k' is the apparent bimolecular rate constant for I P T G binding to the represser. At pI-I 7.5, the ratio ~[R*]/~.[R,] was estimated to be about 22 using the parameters in Table 1 (a value of 10 was obtained according to the mechanism of equation (7)). Taking It'----6• M-1 s -1 (Laiken et al., 1972) the true bimolecular rate constant for the I P T G - l a c represser interaction is calculated to be 1.4 • l0 s M- ~ s-1, which is not unreasonable in light of the known bimolecular rates of protein-ligand interactions (Hammes, 1968). The results presented in this paper indicate t h a t t h e / a c represser is an allosteric protein. The binding of inducer to t h e / a c represser alters the p K of certain specific amino acid residues in the protein. I n addition, the inducer-represser interaction, which stimulates the expression of /ac genes, m a y be modulated b y the proton concentration. Whether such regulation also exists i n rive is an open question. Because of a constant intraccllular p H the i n rive control of gene expression b y the proton concentration seems unlikely. Nevertheless, the "microscopic" p H near or at a macromolecule has not been revealed. I n a previous paper we have reported t h a t the positive-control element of the lac operon system, the cyclic AMP receptor protein, also exists in two conformational forms, although the rates of its conformational transitions are much slower t h a n t h a t of lac represser (Wu & Wu, 1974). An i m p o r t a n t aspect of the cyclic AMP receptor protein system is t h a t cyclic AMP stimulates lac transcription b y shifting the conformational equilibrium from the biologically inactive form of the cyclic AMP receptor protein to the active form. On the other hand, cyclic GMP, which is the competitive inhibitor of cyclic AMP, shifts the equilibrium in the opposite direction. I t seems likely t h a t an allosteric regulation m a y also play a significant role in the negative control of lac transcription. This work was supported by grants from the National Institutes of Health (GM-19062) and the American Cancer Society (BC94B). One of us (C.-W. W.) is a Research Career Development awardee of the National Institutes of Health. The authors thank Dr B. Mfiller-Hill for a generous gift of E. coli K12 (strain M96). They are also grateful to Mr David Rogerson of the National Institutes of Health for cultivation of E. coli cells.
REFERENCES Amdur, I. & Hammes, G. G. (1966). In Chemical Kinetics, pp. 148-152, McGraw-Hill Book Company, New York. Barkley, M. D., Riggs, A. D., Jobe, A. & Bourgeois, S. (1975). Biochemistry, 14, 1700-1712. Beyreuther, K., Adler, K., Geisler, M. & Klemm, A. (1973). Prec. Nat. Acad. ,.%i., U.S.A. 70, 3576-3580. B(icher, T. (1947}. Bioehim. Biophys. Acta, 1, 292-314. Gilbert, W. & Miiller-Hill, B. {1966). Prec. Nat. Acad. Sci., U.S.A. 56, 1891-1898. Hammes, G. G. (1968). Advan. Protein Chem. 23, 1-57. Hammes, G. G. & Sehimmel, P. (1970). In The Enzymes (Boyer, P. D., ed.}, 3rd edit., vol. 2, pp. 67-114, Academic Press, New York. Hammes, G. G. & Wu, C.-W. (1974}. A n n u . Rev. Biophys. Bioeng. 3, 1-33. Koshland, D. E., Jr, Nemethy, G. & Filmer, D. (1966). Biochemistry, 5, 365-385. Lalken, S. L., Gross, C. A. & v o n Hippel, P. H. (1972). J. Mol. Biol. 66, 143-155. Loudon, G. M. & Koshland, D. E., J r (1972). Biochemistry, l l , 229-240.
472
F.Y.-tt.
W U , P. B A N D Y O P A D H Y A Y AND C.-W. W U
Monod, J., Wyman, J. & Changeux, J.-P. (1965). J. Mol. Biol. 12, 88-118. Mfiller-Hill, B., Cropo, B. L. & Gilbert, W. (1968). Prov. Nat. Aead. Sei., U.S.A. 59, 1259-1264. Mfiller-I-Iill, B., Beyreuther, K. & Gilbert, W. ( 1971 ). Metho'ds in Enzymology, 21,483-490. Ohshima, Y., Mizokoshi, T. & Horiuchi, T. (1974). J . Mol. Biol. 89, 127-136. Perlmann, G. E. (1972). Method8 in Enzymology, 26, 413-423. Platt, T., Files, J. G. & Weber, K. (1973). J. Biol. Chem. 248, 110-121. Riggs, A. D. & Bourgeois, S. (1968). J. Mol. Biol. 34, 361-364. Weber, G. (1972). Biochemistlry, 11,864-878. Wu, C.-W. & Wu, F. Y.-H. (1974). Biochemistry, 13, 2573-2578.