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Interaction of lac repressor with inducer. Kinetic and equilibrium measurements
J. Mol. Biol. (1977) l l l , 27-39
Interaction of lac Repressor with Inducer. Kinetic and Equilibrium Measurements B. ELLEN FRIEDMAN, JOHN S. OLSON AND KATHLEEN S. M.ATTHEWS
Department of Biochemistry, Rice University, Houston, Texas 77001, U.S.A. (Received 7 October 1976) The rates of binding and dissociation of the inducer isopropyl-fl,D-thiogalaetoside to the lactose represser protein of Escherichia cell were studied by monitoring changes in tryptophan fluorescence in a stopped-flow spectrometer. At p H 8.5 the association rate constant for inducer binding was found to be 1.7 • 10~ ~ - 1 s -1 and that for dissociation to be 0.53 s -1 in 1.0 ~-Tris.HC1 buffer. These kinetic measurements were made over a range of conditions, and a small but reproducible dependence on p H and ionic strength was observed. The presence of bound calf thymus DNA was fmmd to affect only slightly the rate of inducer binding to the protein. The kinetically determined rate constants were used to calculate dissociation constants for the interaction between represser and inducer. The calculated values were in agreement with those determined directly by equilibrium dialysis and ultraviolet spectral titration of represser with inducer. I t appears that represser and inducer interact by a simple equilibrium process, the characteristics of which are similar whether represser is free in solution or non-specifically bound to ])NA.
1. I n t r o d u c t i o n The lactose represser protein of Escherichia coli is the genetic control protein responsible for negative regulation of the lactose operon. As the only regulatory protein isolable in quantities sufficient for physical and chemical work (Miiller-Hill et al., 1968), it has been the target for extensive studies of gene regulation. The represser, a tetrameric protein of molecular weight 150,000 (Mtiller-Hill, 1971), apparently undergoes a conformational change on binding small inducer molecules, which results in the loss of specific binding to the D N A operator region of t h e / a c operon (Riggs et al., 1970). This sequence of events is thought to be the basis for the repressor's genetic control function in rive. Evidence for the existence of a conformational change in represser is derived in p a r t from spectral data (Matthews et al., 1973; Laiken et al., 1972; Sams et al., unpublished results). Of particular interest is the alteration in the ultraviolet absorption and fluorescence spectra of the protein when inducer is bound. These spectral changes apparently are not the result of direct interaction of chromophores with the inducer molecule; binding of anti-inducers does not result in these characteristic spectral alterations. Changes in t r y p t o p h a n absorbance, in t r y p t o p h a n fluorescence (Laiken et al., 1972), and in the absorbanee of various chromophorie probes on binding of inducer to the represser have been used to measure association rates in stopped-flow 27
28
B . E . F R I E D M A N , J. S. OLSON AND K. S. M A T T H E W S
rapid mixing experiments (Friedman et al., 1976). The rate constants observed were identical regardless of the type of spectral alteration monitored. This fact suggested t h a t the second-order combination of inducer with repressor causes a very rapid conformational isomerization t h a t is transmitted throughout the protein molecule (Friedman et al., 1976). While the fluorescence change observed corresponds to an isomerization of the protein structure, the second-order rate determined represents the rate of inducer binding, which is slower t h a n the conformational change and consequently is rate limiting. Our kinetic results differed from those reported b y Laiken et al. (1972). These authors observed a slow fu'st-order decay following the fast fluorescence change. They attributed this slow transition to a conformational change in repressor, possibly the one responsible for the dissociation of the protein from the operator DNA. Laiken et al. (1972) also estimated a value of 0.2 to 1-1 s -~ for the rate of dissociation of inducer from repressor, but no direct measurement has been made. We felt t h a t direct measurement of this dissociation rate would be of value in understanding the interaction between these two molecules. Such an investigation would provide another opportunity to check for evidence of a slow isomerization of repressor analogous to t h a t reported b y Laiken et al. (1972). Furthermore, knowledge of the inducer dissociation rate would allow an estimation of a minimum time limit for de-induction. Therefore, we determined the inducer dissociation rate directly by rapid dilution of isopropyl-fl, D-thiogalactoside-repressor mixtures in the stopped-flow spectrometer. Several workers have suggested t h a t the repressor protein m a y be sensitive to p H fluctuations, particularly in regard to the ability of the protein to bind inducer. Ohshima et al. (1974) reported a p H dependence of various parameters of inducer binding measured by equihbrium dialysis over a small range of p H values. Additional evidence for the possible influence of p H on inducer binding to repressor comes from the temperatm'e-jump experiments of Wu et al. (1976). These investigators observed a pH-dependent fluorescence change which was associated ~dth a very rapid isomerization between two forms of the protein. W u et al. further suggested the existence of a substantial variation in inducer binding rates as a function of pH. In addition, the protein molecule appears to undergo a conformational transition in response to p H conditions, which is apparent b y a shift in the wavelengths of m a x i m u m absorbance of specifically modified residues (Sams et al., unpublished results). On the basis of these indications, we felt it was important to examine the effects of p H on inducer binding to repressor by kinetic and equilibrium methods.
2. Materials and Methods (a) Purification and assay Lactose repressor was isolated from frozen cells of E. coli M96 using the procedure of Mfiller-Hill et al. (1971) as modified by Plattet al. (1972). The purified repressor was concentrated to 2.5 to 10 mg/ml by ammonium sulfate precipitation, dialyzed, and frozen in 0.1 M-Tris.HC1 (pH 7-5 to 8.0), 1.0 M-NaC1, with l0 -4 M-dithiothreitol added. At the time of each experiment, repressor was either dialyzed or diluted into the appropriate buffer. Protein concentration was determined by I P T G t binding activity assays using the ammonium sulfate precipitation method, described by Bourgeois (1971), and by standard Lowry determinations. I P T G was obtained from Sigma. t Abbreviation used : IPTG, isopropyl-fl, D-thiogala~toside.
INTERACTION
OF
lac REPRESSOR
WITH
INDUCER
29
(b) Kinetic measurements Kinetic measurements were carried out with a Gibson-Durrum stopped-flow spectremeter equipped with a fluorescence cuvette. Fluorescence changes were displayed on an oscilloscope, recorded photographically, enlarged and analyzed graphically. (c) Spectral titration A Cary 118 spectrophotometer was used to perform the ultraviolet titration of represser (1-2• l0 -~ M) with inducer in 1.0 M-Tris.HC1 (pH 8.1 at 20~ with 3• 10 -4 M-dithiothreitol. Self-masking quartz cuvettes with a path-length of 1.0 cm were used. The scan was made on auto-gain with a slitwidth of 0.5 ram. A baseline was recorded from 250 to 350 um and additious of 10 -3 g-IPTG were made with a Hamilton syringe. (d) Equilibrium dialysis Represser (0-4 ml; ~0.5 mg/ml) was placed in dialysis bags and dialyzed at 25~ overnight against solutions containing [14C]IPTG (2 • 10-7 M) and varying concentrations of unlabeled IPTG. The protein (0.1 ml) was removed from the bags and_ the amotmt of ligand inside and outside was determined. Protein concentration was measured by the Lowry method, and the Kd was determined by plotting the data as described by Scatchard (1949).
3. Results (a) Kinetic determination of dissociation constant I n order to measure the rate of dissociation of inducer from lactose represser, protein partially saturated with I P T G was rapidly mixed with a tenfold larger volume of buffer in the stopped-flow spectrometer. This rapid dilution of the represser solution resulted in dissociation of most of the inducer from the protein, and the ensuing increase in t r y p t o p h a n fluorescence was measured. Dilution of represser in the absence of ligand produced no change in the fluorescence signal. I n general, the observed rate constant (/cobs) for the dissociation of inducer is given by kobs ---- k' [IPTG] Jr k,
(1)
where k' is the association rate constant, and k is the dissociation rate constant. I n order to avoid the complication of observing any contribution of the association rate, it was necessary to work at inducer concentrations which corresponded to ~ 5 0 % or less saturation of sites, as calculated from the equilibrium K d values. Under these conditions, dilution of the protein reduces the level of saturation from ~ 5 0 % to 15%, and the contribution from the forward reaction, k' [IPTG], is minimized so t h a t kobs ~ k. I n all the kinetic experiments, the wavelength of excitation was 290 nm, and all fluorescence longer than 350 nm was recorded. As shown in Figure l(a), the observed time-course corresponded to a transition exhibiting essentially first-order behavior. The observed half-time was 1.3 s, corresponding to a dissociation rate of 0.53 s-1 at p H 8.5. The second-order association rate for I P T G binding was measured by mixing equal volumes of a fixed concentration of represser (1.3• 10 -e M) with various I F T G concentrations under pseudo first-order conditions. A time-com'se for the association of ligand with protein is shown in Figure l(b). From the exponentially decreasing fluorescence signal t h a t was observed (Fig. l(b)), a plot of the log of the fluorescence change versus time was made in order to determine the apparent rate of reaction. The pseudo first-order constant was then plotted versus inducer concentration, and the slope was determined by linear regression in order to calculate the second-order rate.
30
B.E.
FRIEDMAN,
J.
S. O L S O N
AND
K.
S. M A T T H E W S
F i e . 1. T i m e - c o u r s e s for t h e i n t e r a c t i o n of i n d u c e r w i t h r e p r e s s o r (in 1.0 ~ - T r i s - H C 1 , w i t h 3 • 10 . 4 ~ - d i t h i o t h r e i t o l , a d j u s t e d to p H 8.5, a t 2 0 ~ as d e s c r i b e d in M a t e r i a l s a n d M e t h o d s . E x c i t a t i o n w a s a t 290 n m , u s i n g a 75 V~ x e n o n l a m p a n d a s l i t - w i d t h o f 3 r a m . A g l a s s c u t - o f f filter w a s e m p l o y e d so t h a t fluorescence e m i s s i o n a t w a v e l e n g t h s l o n g e r t h a n 350 n m could be recorded. C o n c e n t r a t i o n s g i v e n are before m i x i n g . (a) D i s s o c i a t i o n o f i n d u c e r f r o m repressor. A s o l u t i o n of r e p r e s s o r ( 3 . 3 • 10 . 6 M) w i t h I P T G (2 • 10 . 5 M) w a s d i l u t e d 1:11 into t h e a b o v e buffer. A t i m e c o n s t a n t o f 5 m s w a s u s e d . M a r k e r c o r r e s p o n d s to 0.5 s. (b) B i n d i n g o f I P T G ( 4 • 10 . 3 M) to r e p r e s s o r (1.3 • 10 . 6 M). A t i m e c o n s t a n t o f 0.1 m s w a s u s e d . M a r k e r c o r r e s p o n d s to 10 m s .
INTERACTION
O F lac R E P R E S S O R
WITH
INDUCER
31
T~Br.~. 1
Kine$iv and equilibrium ~arameters for the interaction of represser with I P T G Condition 9
pH
k 'b (M-is -1)
k ~ (s -1)
7.0 7.5 9.0
6.8• 104 5-7 • 104 5.1• 1.7• 0.7 • 104
(0.21) f (0.21) 0.43 0.53 0.63
3.1 • -s 11 • 10 -5
7.2 7.5
8"OX 104 8-0 X 104
(0"17) (0-17)
---
8"0 8"5
7 . 0 • 104 5 . 9 x 104
(0-21) (0.22)
---
9"0
5"0• 104h
(0'24)
~
0.21 • 10 -5r 0-21 X 10 -5 0 - 3 0 X 10 -5 0"37• 10 -5 0-49• 10 -5
0.1 M-Tris.HC1, 0.5 ~-NaCI
7.5 8.0 8"5
7.8 • 1 0 4 . 6 " 4 • 104 3.6•
(0-15) (0"28) (0"26)
----
0"21 • 10 - 5 0 . 4 4 • 10 - 6 0-72• -5
0.1 M-Tris.HC1
7.4
7.8• 104
(0.24)
0.31 •
0-1 M-Tris.HC1 DNA-bound
7-5
12.1 • 104
(0.52)
0.43 • 10 -5
1"0 ~-Tris" HCI
8.0 8.5
0.1 M-Tris.HCl, 1.0 ~i-NaC1
Kd =
~';
(~)
--0.84•
Ka" (M) 0-31 • 10 -s 0-37 • 10- a
-~
0-71 • 10 -s 2 - 8 • 10 -Sw
8-0 • 10 -5~
10 - s
All buffers contain 3 • 10-4 M-dithiothreitol. b Second-order association rate constant measured as described in the legends to Figs 1 and 3, and in the text. a First-order dissociation constant measured as described in the legend to Fig. 1 and in the text. d KineticaUy determined dissociation constant calculated from values measured for k and k'. e Dissociation constant determined by equilibrium dialysis as described in Materials and Methods. f Values in parentheses are calculated from measured values: k = Kd • k'. f Values taken from plots in Figs 3 and 5. h Buffer used was 0.1 M-glycine-NaOH, 1.0 M-NaC1.
I n 1.0 M-Tris. HC1 ( p H 8.5 a t 20~ 3 • 1 0 - 4 M - d i t h i o t h r e i t o l , a s e c o n d - o r d e r association rate of 1.7• M -1 s -1 a n d a f i r s t - o r d e r d i s s o c i a t i o n r a t e o f 0.53 s - 1 w e r e d e t e r m i n e d . N o a c c e l e r a t i o n w a s a p p a r e n t i n t h e t r a c e s r e c o r d e d i n t h i s m a n n e r for either process, nor did we observe a significant contribution of a slow transition a n a l o g o u s t o t h a t r e p o r t e d b y L a i k e n et al. (1972). T h e r a t e c o n s t a n t s m a y t h e n b e u s e d t o c a l c u l a t e a d i s s o c i a t i o n c o n s t a n t for a g i v e n p H : Kd -~ k[k'. A s s e e n i n T a b l e 1, t h e s p e c t r a l d i s s o c i a t i o n c o n s t a n t c a l c u l a t e d f r o m t h e s e k i n e t i c p a r a m e t e r s as d e t e r m i n e d a t p H 8.5 (3-1 • 1 0 - 5 M) is in e x c e l l e n t a g r e e m e n t w i t h t h a t d e t e r m i n e d b y t h e e q u i l i b r i u m m e t h o d s d e s c r i b e d b e l o w (2.8 • 1 0 - s ~ ) . (b) Ultraviolet titration A n i n d e p e n d e n t d e t e r m i n a t i o n o f t h e e q u i l i b r i u m d i s s o c i a t i o n c o n s t a n t for i n d u c e r binding to represser was carried out by measuring the resulting changes in the a b s o r b a n e e o f p r o t e i n in t h e u l t r a v i o l e t r e g i o n . T h e c h a r a c t e r i s t i c u l t r a v i o l e t d i f f e r e n c e spectrum was produced incrementally by additions of IPTG and recorded over the r a n g e 250 t o 350 n m (Fig. 2(a)). A final a d d i t i o n o f c o n c e n t r a t e d I P T G (10 - 1 M)
32
B. E. F R I E D M A N ,
J . S. O L S O N A N D K . S. M A T T H E W S
0
.Q
-+ol
<3
-0-02
(o) I
I
I
i
290
270
I
l
I
310 Wavelength (nm)
l
330
350
4.0
//,..o~,'''''-'-//
3.0
"o X
~ 9Q
._
/"
2.0
<~
/
I-0
/
/
./. 2
I
I
i
i
i
4
6
8
I0
12
//
i
l
(b) i
20
22
24
[IPTG] (MX IOs )
FIG. 2. Ultraviolet titration of repressor with inducer. (a) A difference spectrum produced by titration of repressor (1-2 • 10 -5 ~) with I P T G (10 -3 M) in 1.0 M-Tris.HC1 buffer, with 3 • 10 -4 M-dithiothreitol adjusted to p H 8.1, at 20~ and recorded as described in Materials and Methods. (b) A saturation curve generated from the original data in Fig. 2(a).
INTERACTION
OF l~
REPRESSOR
WITH
INDUCER
33
was made to insure t h a t saturation had been reached. The saturation curve was generated b y plotting the change in absorbance measured at the 290 nm trough versus the concentration of I P T G for each addition (Fig. 2(b)). Because this ligand exhibits such tight binding, the usual analysis of the data b y a Scatchard t y p e plot proved unsuccessful. However, an approximate dissociation constant could be determined b y noting the concentration of unbound I P T G which corresponds with half saturation. The Kd value estimated under these conditions was H 1 • 10 -B ~ for p H 8.1. This figure is similar to values obtained b y equilibrium dialysis under the same conditions. Perhaps more significant is the fact that the decrease in absorbance occurs lmiformly at all wavelengths, implying t h a t a single reaction is responsible for the spectral changes. This observation, in conjunction with the lack of acceleration in stopped-flow traces, suggests t h a t a simple equilibrium exists between I P T G and repressor. The similarity between Kd values determined by these different methods is a necessary condition for such an equilibrium to exist. (c) Dependence of inducer binding on TH and ionic strength An extensive study of the effects of p H on the interaction of inducer with repressor was undertaken b y kinetic and equilibrium methods. In order to determine the dependence of the binding affinity on pH, equilibrium dialysis was carried out at 22~ using repressor at a concentration of 3.3 • 10 -6 ~ and [14C]IPTG (2 • 10 -7 M). Measurements were made in 0.1 M-Tris.HC1, 3 • 10 -a M-dithiothreitol, adjusted to the appropriate p H ; 1.0 M-NaC1 or 0-5 M-NaCI was added to insure a constant ionic strength over the p H range examined (6.5 to 9.5). Resulting data were analyzed b y standard Scatchard plot treatment. As seen in Figure 3, the affinity of repressor for I P T G decreases with increasing pH, the inflection of each curve being between p H 8.3 and 8.5. Kinetic measurements were also made over the same p H range in 0.1 ~-Tris.HCl, 3 • 10 -4 M-dithiothreitol, 1.0 M-NaC1 or 0.5 M-NaC1. In a few cases a slow phase representing a very small percentage (_<5%) of the total change was observed. I n these instances the change in fluorescence resulting from this minor slow phase was subtracted before a rate for the fast phase was determined. The results, presented in Figure 3 as plots of the second-order rate versus pH, indicate that the rate of I P T G binding decreases with increasing pH. Again, the mid-point of the transition is ~ p H 8-3. In order to examine the effect of ionic strength, kinetic and equilibrium measurements were made in solutions of various salt concentrations under conditions of constant pH. Buffers of 0.1 M-Tris.HC1, 10 -4 M-dithiothreitol were adjusted to a specific p H with HG1, and NaC1 was added at concentrations from 0 to 1.0 M. The results, summarized in Figure 4, indicate that the ionic strength effects differ at different p H values. Generally a higher ionic strength results in increased affinity of ligand for repressor, with small effects on the second-order association rates. Because repressor is stabilized by high concentrations of Tris buffer, m a n y studies have used this buffer at concentrations of 0.5 to 1.0 ~. Our initial p H studies were also carried out in 1.0 M-Tris.HC1 (3• -4 M-dithiothreitol) and the results are shown in Figure 5. As before, the affinity of repressor for I P T G decreases with increasing p H and the association rate decreases in going from p H 7.0 to p H 9.0. In both cases the inflection point is between p H 8.3 and p H 8.7. The major difference between these results and those presented in Figure 3 is that in 1.0 M-Tris there is a greater change in the equilibrium and rate constants as the p H is raised to 9.0. I n 8
34
B. E. F R I E D M A N , J. S. OLSON AND K. S. M A T T H E W S (a)
A._._.&~&/ I 0
I
I
~e_
I
I
I
"2
I
O x
(b) 8
~
4
|
I
7.0
t
I
8-0 pH
i
I
i
9.0
Fro. 3. Rates and affinities of inducer binding as a function of pH. Dissociation constants (Ka values) for IPTG were determined by equilibrium dialysis at 22~ as described in Materials and Methods. Kinetic measurements were made at 20~ by mixing represser at a fixed concentration (1.3 • 10-6 M before mixing} with various concentrations of IPTG in the manner described in Fig. 1. Second-order rate constants (k') were derived by linear regression from plots of the observed first-order rate constant v e r s u s IPTG concentration. - - O - - O - - , Second-order rate constants (k'); - - & - - A - - , dissociation constants (Kd values). (a) Measurements were made in 0.1 M-buffer, 3• 10 -4 ~-dithiothreitol, with 1.0 ~-NaCI adjusted to the appropriate pH. The buffer used was Tris 'HC1, except for the kinetle measurements made at pH 9.0 and pH 9.5, in which case the buffer used was glycine-NaOH. (b) All measurements were made in 0.1 ~-Tris.ttC1 buffer, 3• 10 -4 ~-dithiothreitol, with 0.5 M-NaC1, adjusted to the appropriate pH with I-ICl.
view of the results shown i n F i g u r e 4, p a r t of this effect is p r o b a b l y the result of t h e m a r k e d change i n ionic s t r e n g t h i n t h e Tris buffer, going from p H 7.0 where it is fully p r o t o n a t e d to p H 9.0, where it is m o s t l y d e p r o t o n a t e d . I t is also possible t h a t there are more specific i n t e r a c t i o n s b e t w e e n Tris a n d the protein. T a b l e 1 presents a s u m m a r y of our k i n e t i c a n d e q u i l i b r i u m data. A t the higher p H values i n 1.0 M-Tris it was possible to m e a s u r e b o t h the association a n d dissociation velocity c o n s t a n t s for I P T G b i n d i n g . I n these cases, comparisons were m a d e b e t w e e n k i n e t i c a l l y d e t e r m i n e d e q u i l i b r i u m c o n s t a n t s a n d those m e a s u r e d directly b y e q u i l i b r i u m dialysis. A t lower pH, the high affinity of represser for I P T G p r e v e n t e d m e a s u r e m e n t of the dissociation rate c o n s t a n t , since this c o n d i t i o n required t h e use of c o n s i d e r a b l y lower p r o t e i n c o n c e n t r a t i o n , which i n t u r n resulted i n a fluorescence change t h a t was too small to be m e a s u r e d accurately. Thus, at t h e low p H values, the dissociation rate c o n s t a n t (in parentheses) was calculated from the second-order association rate a n d t h e e q u i l i b r i u m c o n s t a n t m e a s u r e d b y dialysis techniques.
INTERACTION
OF 16
-
lac REPRESSOR
WITH
INDUCER
,$5
(a)
12 0 x
1
8
! 12
[
I
I 0
I 0"5
I
(b)
A
T o
8
x
T "~
4
I I-0
-
[NaCI] (M)
Fxo. 4. R a t e s a n d affinities of inducer b i n d i n g as a f u n c t i o n of ionic s t r e n g t h . All m e a s u r e m e n t s were m a d e in 0-1 M-Tris.HC1 buffer, 3 • 10 -4 M-dithiotlu'eitol, a d j u s t e d to t h e indicated p H , w i t h a d d i t i o n s of NaCI fl'om 0 to 1.0 ~. (a) Dissociation c o n s t a n t s (Kd values) for I P T G were d e t e r m i n e d b y e q u i l i b r i u m dialysis as described elsewhere : - - 9 9 p H 7"5 ; - - 9 9 p H 8.0 ; - - 9 9 p H 8.5. (b) Second-order rate c o n s t a n t s (k') for I P T G b i n d i n g were m e a s u r e d as described in Fig. 3: - - O - - C ) - - , p H 7.5; - - A - - A - - , p H 8-0; - - [ ~ - - [ ~ - - , p H 8.5.
(d) Effect of bound D N A o~ association rate The binding of inducer to represser free in solution probably does not occur in rive. Represser has been shown to bind inducer while the protein is bound to operator DNA to form a ternary complex (Barldey et al., 1975). Even the inducer/protein complex is likely to be associated with the DNA in a non-specific binding interaction (von Hippel et al., 1975). In order to examine for the effects of non-specific DNA binding, the association rate for inducer binding was determined in the presence of fragmented calf thymus DNA (Mr ~ 15 • 106). The unavailability of operator DNA prevented examination of the influence of specific operator activity on inducer binding. A 3.3• 10 -6 M-solution of represser in 0-1 M-Tris.HC1, 3 • 10 -4 M-dithiothreitol buffer, with DNA at ~-~0.3 mg/ml was reacted with various concentrations of I P T G in the stopped-flow spectrometer under pseudo first-order conditions. The exponential change in t r y p t o p h a n fluorescence was recorded as before. The secondorder rate measured in the presence of DNA was 12• M-~s -~ at p H 7-5 and 9.1 • 104 M - ~ s - ~ at p H 8.0, while the inducer binding rate determined in the absence of DNA was 7-8• 104 M-~s -~ at p H 7.4 and p H 8.0. A comparison of these rates
36
B. E. F R I E D M A N ,
J. S. O L S O N A N D K. S. I~IATTHEWS
suggests that inducer binding is not greatly altered when repressor is non-specifically bound to DNA. As shown in Table 1, the equilibrium constant for inducer binding also appears to be little affected by the presence of caff thymus DNA.
4. D i s c u s s i o n
The physiological role of lactose repressor protein as a regulator of transcription of the structural genes of the lactose operon in E. coli rests on the ability of the protein to undergo a conformational change in response to inducer binding. This conformational isomerization is believed to trigger release of the protein from the operator region of the DNA molecule. Therefore it is important to characterize thoroughly the interaction of repressor with inducer and to understand the influence of factors such as ionic strength and pH on the inducer binding rates, on binding affinity, and on the conformational state of the protein. The dilution of repressor containing bound IPTG in the stopped-flow, rapid-mixing spectrometer provides a convenient method for the measurement of the rate constant for dissociation of inducer, a value which has not previously been determined directly. Measurement of the dissociation rate makes possible calculation of the K d value for inducer binding independent of equilibrium studies (see Table 1). The K d data determined by the various methods are in good agreement, a result which is to be expected for a simple protein-ligand equilibrium. The need for responsiveness of this system to environmental stimuli makes it unlikely that either the dissociation of inducer or its association with repressor is a slow process, particularly since a large number of complex reactions must take place before inductdon is complete. However, monitoring changes in tryptophan fluorescence at one emission wavelength (360 nm), Laiken et al. (1972) observed a fast second-order change (6• M-is -1) followed by a much slower first-order decay with a rate measured as 0.12 s -1. These authors assumed that the faster rate represented the rate of binding inducer, while the slower rate reflected the rate of the conformational change associated with the induction process. We did occasionally observe a slow change in tryptophan fluorescence, but even when present in our experiments, this slow phase always represented a very small percentage of the total fluorescence change (usually less than 5%). Furthermore, the appearance of the slow decay was erratic and corresponded generally with the age of the protein sample being observed. Freshly thawed samples always exhibited monophasic, fast fluorescence changes. Consequently, the slow changes appear to reflect some alteration in the protein structure indicative of decay of the molecule. Since the same rapid rate is observed when monitoring probes in different parts of the protein (Friedman et al., 1976), we have concluded that the rapid change in tryptophan fluorescence represents a conformational change in repressor which is rate-limited by inducer binding, hence the second-order nattlre of the change. This alteration of the protein structure is most likely the one respofisible for the induction process. From the results reported here, it is apparent that both the rate and affinity of IPTG binding vary with pH and ionic strength to a small but measurable extent. In view of the ionic strength effect, it is important to note the buffering system used before comparing results of studies on repressor conducted under different conditions. Wu et al. (1976) have suggested the possible significance of pH variations in the genetic control function of repressor. This type of regulation seems unlikely, as the magnitude of the changes observed in binding rates or dissociation constants with pH are not
INTERACTION OF /ac REPRESSOR WITH INDUCER
37
large. Furthermore, the effects of pH are decreased at higher ionic strength, such as that expected in the local environment of the DNA molecule. The decrease in K d values at high salt concentrations indicates that IPTG binding affinity increases with ionic strength, a situation which seems reasonable for a protein which interacts with DNA. Consistent with this view is the fact that the rate of inducer binding was not dramatically altered by the presence of non-operator DNA. More important, this result also shows that the binding measurements made on repressor free in solution may closely approximate the conditions in vivo, where the protein remains associated with non-specific regions of the DNA molecule. Wu et al. (1976) have demonstrated the existence of a pH dependent, rapid isomerization of repressor molecules by fluorescence, temperature-jump techniques. The magnitude of the fluorescence change decreased either by raising the pH of the solution or by adding high concentrations of IPTG. These results were interpreted by assuming that there are two forms of repressor: R*, a form that does not bind inducer and exhibits a lower affinity for protons than I~, a form which binds IPTG tightly and exhibits a higher affinity for protons. Thus, at high pH, the R* form predominates, whereas at low pit or in the presence of IPTG, the equilibrium favors the R form. In either case, no fluorescence change would be observed by equilibrium perturbation techniques. The interpretation by Wu et al. (1976) further predicts the dependence of the apparent second-order rate constant for IPTG binding on pH. According to these workers, the apparent rate for inducer binding, ktapp (the rate observed in our steppedflow experiments), is proportional to the fraction of R conformations present:
5R
k's,, = k' ~ R + ~ R * '
(2)
where k' represents the theoretical rate constant for binding to the R conformation of the protein. Inherent in equation (2) is the assumption that inducer binds only to the R form, since there is no term to take into account binding to the It* conformation. The pit dependence of k'~pp can be calculated from the expression proposed by Wu et al. (1976) to account for the pH dependence of the R to It* transition: ~R
= L
-{- (H+)/K~ } ,
(3)
where L represents the isomerization equilibrium constants in the absence of protons and Ks, Ks* are acid dissociation constants for the tt and It* forms, respectively. Using values from Wu et al. for Ka, Ka*, and L (pK~ = 7.6, pK~* = 7.0, ]5 = 220), the fraction of R states is predicted to change from 0.160 to 0.005 in going from pH 7.0 to pH 9.0. This requires a 30-fold decrease in the association rate for IPTG binding. As shown in Figures 3 and 5, the observed decrease is about sevenfold in 1.0 M-Tris.HC1 and only two- to fourfold in 0.5 M- or 1-0 M-NaC1, 0.1 M-Tris.HC1 in going from pit 7.0 to pH 9.0. Furthermore, the inflection point predicted from equation (3) is around pH 7.3, whereas the data in Figures 3 and 5 indicate a transition centered around pH 8.3. Our results indicate that inducer can bind to both of the forms of the protein described by Wu et al. Consequently, an additional term must be added to the righthand side of equation (2) to take into account binding to the R* form. In addition, the pH dependence of the isomerization equilibrium must be modified to take into account ionizations with pK~ values greater than pH 8.0. This latter modification is
38
B. E. F R I E D M A N , J. S. OLSON AND K. S. MATTHEWS 10 8
f0
"~ 4
6
O --
4
2
7.0
8.0
9-0
pH Fie. 5. Effects of high molarity Tris buffer on rate and affinity of inducer binding as a function of pH. Measurements were made using IPTG, as described in the legend to Fig. 3, except that experiments were carried out in 1.0 M-Tris.HCI buffer, 3 • 10 -* ~I-dithiothreitol, adjusted to the appropriate pit. - - 0 - - 0 - - , Second-order rate constants (k') ; - - A - - A--, dissociation constants (Kd values). required both by our data for the p H dependence of the rate constants for I P T G binding and by potentiometric data of W u et al. at high pHI, where I P T G was shown to decrease the fractional amount of protons bound to represser. I n spite of the problems discussed above, the data of Wu et al. are consistent with our previous observation (Friedman et al., 1976) that the represser undergoes a conformational transformation that is much more rapid than the binding of inducer molecules. Whether the fluorescence changes observed in these two studies represent the same or independent conformational transitions of the protein is not known. The fluorescence change we measured could result from a rapid conformational transition in the protein which occurs either before or after inducer binding. However, several conclusions about the system can be made. The binding of inducer to represser is apparently the rate-limiting step in the sequence of events in which the protein assumes a new conformation in response to inducer. The binding of I P T G to represser is, to a small extent, a function of the p H and ionic strength of the environment. No slow conformational isomerizations are detected in this process. This fact, combined with the absence of acceleration in the time-course of I P T G binding and dissociation, indicates that the binding of I P T G to represser does not exhibit cooperative subunit interactions. Furthermore, the simple equilibrium combination of inducer with represser protein occurs in a similar fashion either when the protein is free in solution or non-specifically bound to DNA. This work was supported by" grants from the National Science Foundation (BMS7301570 A01 to K.S.M.) and the National Institutes of Health (GM-22441 to K.S.M. and HL-16093 to J.S.O.).
REFERENCES Barkley, M. D., Riggs, A. D., Jobe, A. & Bourgeois, S. (1975). Biochemistry, 14, 17001712. Bourgeois, S. (1971). Methods Enzymol. 21D, 491-500. Friedman, B. E., Olson, J. S. & Matthews, K. S. (1976). J. Biol. Ohem. 251, 1171-1174. Laiken, S. L., Gross, C. A. & yon Hippel, P. H. (1972). J. Mol. Biol. 66, 143-155.
I N T E R A C T I O N OF lac R E P R E S S O R W I T H I N D U C E R
39
Matthews, K. S., Matthews, H. R., Thielmann, H. W. & Jardetzky, O. (1973). Biovhim. Biophys. A eta, 295, 159-165. Mfiller-Hfll, B. (1971). Angew. Chem. Internat. Ed. 10, 160-171. Mfiller-Hfll, B., Crapo, L. & Gilbert, W. (1968). Proe. Nat. Acad. Sci., U.S.A. 59, 1259-1264. Mfiller-Hill, B., Beyreuther, K. & Gilbert, W. (1971). Method8 Enzymol. 21D, 483-487. Ohshima, Y., Mizokoshi, T. & Horiuchi, T. (1974). J. Mol. Biol. 89, 127-136. Platt, T., Weber, K., Ganem, D. & Miller, J. (1972). Proc. Nat. Acad. Sei., U.S.A. 69, 897-901. l%iggs, A. D., Newby, R. F. & Bourgeois, S. (1970). J. Mol. Biol. 51,303-314. Scatchard, G. (1949}. Ann. N . Y . Aead. Sci. 51,660-672. von Hippel, P. H., Revzin, A., Gross, C. A. & Wang, A. C. (1975). In Protein-Ligand Interactions (Sand, I-L & Blauer, G., eds), pp. 270-288, W. de Gruyter, Berlin. Wu, F., Bandyopadhyay, P. & Wu, C.-W. (1976). J . Mol. Biol. 100, 459-472.
Interaction of lac Repressor with Inducer. Kinetic and Equilibrium Measurements B. ELLEN FRIEDMAN, JOHN S. OLSON AND KATHLEEN S. M.ATTHEWS
Department of Biochemistry, Rice University, Houston, Texas 77001, U.S.A. (Received 7 October 1976) The rates of binding and dissociation of the inducer isopropyl-fl,D-thiogalaetoside to the lactose represser protein of Escherichia cell were studied by monitoring changes in tryptophan fluorescence in a stopped-flow spectrometer. At p H 8.5 the association rate constant for inducer binding was found to be 1.7 • 10~ ~ - 1 s -1 and that for dissociation to be 0.53 s -1 in 1.0 ~-Tris.HC1 buffer. These kinetic measurements were made over a range of conditions, and a small but reproducible dependence on p H and ionic strength was observed. The presence of bound calf thymus DNA was fmmd to affect only slightly the rate of inducer binding to the protein. The kinetically determined rate constants were used to calculate dissociation constants for the interaction between represser and inducer. The calculated values were in agreement with those determined directly by equilibrium dialysis and ultraviolet spectral titration of represser with inducer. I t appears that represser and inducer interact by a simple equilibrium process, the characteristics of which are similar whether represser is free in solution or non-specifically bound to ])NA.
1. I n t r o d u c t i o n The lactose represser protein of Escherichia coli is the genetic control protein responsible for negative regulation of the lactose operon. As the only regulatory protein isolable in quantities sufficient for physical and chemical work (Miiller-Hill et al., 1968), it has been the target for extensive studies of gene regulation. The represser, a tetrameric protein of molecular weight 150,000 (Mtiller-Hill, 1971), apparently undergoes a conformational change on binding small inducer molecules, which results in the loss of specific binding to the D N A operator region of t h e / a c operon (Riggs et al., 1970). This sequence of events is thought to be the basis for the repressor's genetic control function in rive. Evidence for the existence of a conformational change in represser is derived in p a r t from spectral data (Matthews et al., 1973; Laiken et al., 1972; Sams et al., unpublished results). Of particular interest is the alteration in the ultraviolet absorption and fluorescence spectra of the protein when inducer is bound. These spectral changes apparently are not the result of direct interaction of chromophores with the inducer molecule; binding of anti-inducers does not result in these characteristic spectral alterations. Changes in t r y p t o p h a n absorbance, in t r y p t o p h a n fluorescence (Laiken et al., 1972), and in the absorbanee of various chromophorie probes on binding of inducer to the represser have been used to measure association rates in stopped-flow 27
28
B . E . F R I E D M A N , J. S. OLSON AND K. S. M A T T H E W S
rapid mixing experiments (Friedman et al., 1976). The rate constants observed were identical regardless of the type of spectral alteration monitored. This fact suggested t h a t the second-order combination of inducer with repressor causes a very rapid conformational isomerization t h a t is transmitted throughout the protein molecule (Friedman et al., 1976). While the fluorescence change observed corresponds to an isomerization of the protein structure, the second-order rate determined represents the rate of inducer binding, which is slower t h a n the conformational change and consequently is rate limiting. Our kinetic results differed from those reported b y Laiken et al. (1972). These authors observed a slow fu'st-order decay following the fast fluorescence change. They attributed this slow transition to a conformational change in repressor, possibly the one responsible for the dissociation of the protein from the operator DNA. Laiken et al. (1972) also estimated a value of 0.2 to 1-1 s -~ for the rate of dissociation of inducer from repressor, but no direct measurement has been made. We felt t h a t direct measurement of this dissociation rate would be of value in understanding the interaction between these two molecules. Such an investigation would provide another opportunity to check for evidence of a slow isomerization of repressor analogous to t h a t reported b y Laiken et al. (1972). Furthermore, knowledge of the inducer dissociation rate would allow an estimation of a minimum time limit for de-induction. Therefore, we determined the inducer dissociation rate directly by rapid dilution of isopropyl-fl, D-thiogalactoside-repressor mixtures in the stopped-flow spectrometer. Several workers have suggested t h a t the repressor protein m a y be sensitive to p H fluctuations, particularly in regard to the ability of the protein to bind inducer. Ohshima et al. (1974) reported a p H dependence of various parameters of inducer binding measured by equihbrium dialysis over a small range of p H values. Additional evidence for the possible influence of p H on inducer binding to repressor comes from the temperatm'e-jump experiments of Wu et al. (1976). These investigators observed a pH-dependent fluorescence change which was associated ~dth a very rapid isomerization between two forms of the protein. W u et al. further suggested the existence of a substantial variation in inducer binding rates as a function of pH. In addition, the protein molecule appears to undergo a conformational transition in response to p H conditions, which is apparent b y a shift in the wavelengths of m a x i m u m absorbance of specifically modified residues (Sams et al., unpublished results). On the basis of these indications, we felt it was important to examine the effects of p H on inducer binding to repressor by kinetic and equilibrium methods.
2. Materials and Methods (a) Purification and assay Lactose repressor was isolated from frozen cells of E. coli M96 using the procedure of Mfiller-Hill et al. (1971) as modified by Plattet al. (1972). The purified repressor was concentrated to 2.5 to 10 mg/ml by ammonium sulfate precipitation, dialyzed, and frozen in 0.1 M-Tris.HC1 (pH 7-5 to 8.0), 1.0 M-NaC1, with l0 -4 M-dithiothreitol added. At the time of each experiment, repressor was either dialyzed or diluted into the appropriate buffer. Protein concentration was determined by I P T G t binding activity assays using the ammonium sulfate precipitation method, described by Bourgeois (1971), and by standard Lowry determinations. I P T G was obtained from Sigma. t Abbreviation used : IPTG, isopropyl-fl, D-thiogala~toside.
INTERACTION
OF
lac REPRESSOR
WITH
INDUCER
29
(b) Kinetic measurements Kinetic measurements were carried out with a Gibson-Durrum stopped-flow spectremeter equipped with a fluorescence cuvette. Fluorescence changes were displayed on an oscilloscope, recorded photographically, enlarged and analyzed graphically. (c) Spectral titration A Cary 118 spectrophotometer was used to perform the ultraviolet titration of represser (1-2• l0 -~ M) with inducer in 1.0 M-Tris.HC1 (pH 8.1 at 20~ with 3• 10 -4 M-dithiothreitol. Self-masking quartz cuvettes with a path-length of 1.0 cm were used. The scan was made on auto-gain with a slitwidth of 0.5 ram. A baseline was recorded from 250 to 350 um and additious of 10 -3 g-IPTG were made with a Hamilton syringe. (d) Equilibrium dialysis Represser (0-4 ml; ~0.5 mg/ml) was placed in dialysis bags and dialyzed at 25~ overnight against solutions containing [14C]IPTG (2 • 10-7 M) and varying concentrations of unlabeled IPTG. The protein (0.1 ml) was removed from the bags and_ the amotmt of ligand inside and outside was determined. Protein concentration was measured by the Lowry method, and the Kd was determined by plotting the data as described by Scatchard (1949).
3. Results (a) Kinetic determination of dissociation constant I n order to measure the rate of dissociation of inducer from lactose represser, protein partially saturated with I P T G was rapidly mixed with a tenfold larger volume of buffer in the stopped-flow spectrometer. This rapid dilution of the represser solution resulted in dissociation of most of the inducer from the protein, and the ensuing increase in t r y p t o p h a n fluorescence was measured. Dilution of represser in the absence of ligand produced no change in the fluorescence signal. I n general, the observed rate constant (/cobs) for the dissociation of inducer is given by kobs ---- k' [IPTG] Jr k,
(1)
where k' is the association rate constant, and k is the dissociation rate constant. I n order to avoid the complication of observing any contribution of the association rate, it was necessary to work at inducer concentrations which corresponded to ~ 5 0 % or less saturation of sites, as calculated from the equilibrium K d values. Under these conditions, dilution of the protein reduces the level of saturation from ~ 5 0 % to 15%, and the contribution from the forward reaction, k' [IPTG], is minimized so t h a t kobs ~ k. I n all the kinetic experiments, the wavelength of excitation was 290 nm, and all fluorescence longer than 350 nm was recorded. As shown in Figure l(a), the observed time-course corresponded to a transition exhibiting essentially first-order behavior. The observed half-time was 1.3 s, corresponding to a dissociation rate of 0.53 s-1 at p H 8.5. The second-order association rate for I P T G binding was measured by mixing equal volumes of a fixed concentration of represser (1.3• 10 -e M) with various I F T G concentrations under pseudo first-order conditions. A time-com'se for the association of ligand with protein is shown in Figure l(b). From the exponentially decreasing fluorescence signal t h a t was observed (Fig. l(b)), a plot of the log of the fluorescence change versus time was made in order to determine the apparent rate of reaction. The pseudo first-order constant was then plotted versus inducer concentration, and the slope was determined by linear regression in order to calculate the second-order rate.
30
B.E.
FRIEDMAN,
J.
S. O L S O N
AND
K.
S. M A T T H E W S
F i e . 1. T i m e - c o u r s e s for t h e i n t e r a c t i o n of i n d u c e r w i t h r e p r e s s o r (in 1.0 ~ - T r i s - H C 1 , w i t h 3 • 10 . 4 ~ - d i t h i o t h r e i t o l , a d j u s t e d to p H 8.5, a t 2 0 ~ as d e s c r i b e d in M a t e r i a l s a n d M e t h o d s . E x c i t a t i o n w a s a t 290 n m , u s i n g a 75 V~ x e n o n l a m p a n d a s l i t - w i d t h o f 3 r a m . A g l a s s c u t - o f f filter w a s e m p l o y e d so t h a t fluorescence e m i s s i o n a t w a v e l e n g t h s l o n g e r t h a n 350 n m could be recorded. C o n c e n t r a t i o n s g i v e n are before m i x i n g . (a) D i s s o c i a t i o n o f i n d u c e r f r o m repressor. A s o l u t i o n of r e p r e s s o r ( 3 . 3 • 10 . 6 M) w i t h I P T G (2 • 10 . 5 M) w a s d i l u t e d 1:11 into t h e a b o v e buffer. A t i m e c o n s t a n t o f 5 m s w a s u s e d . M a r k e r c o r r e s p o n d s to 0.5 s. (b) B i n d i n g o f I P T G ( 4 • 10 . 3 M) to r e p r e s s o r (1.3 • 10 . 6 M). A t i m e c o n s t a n t o f 0.1 m s w a s u s e d . M a r k e r c o r r e s p o n d s to 10 m s .
INTERACTION
O F lac R E P R E S S O R
WITH
INDUCER
31
T~Br.~. 1
Kine$iv and equilibrium ~arameters for the interaction of represser with I P T G Condition 9
pH
k 'b (M-is -1)
k ~ (s -1)
7.0 7.5 9.0
6.8• 104 5-7 • 104 5.1• 1.7• 0.7 • 104
(0.21) f (0.21) 0.43 0.53 0.63
3.1 • -s 11 • 10 -5
7.2 7.5
8"OX 104 8-0 X 104
(0"17) (0-17)
---
8"0 8"5
7 . 0 • 104 5 . 9 x 104
(0-21) (0.22)
---
9"0
5"0• 104h
(0'24)
~
0.21 • 10 -5r 0-21 X 10 -5 0 - 3 0 X 10 -5 0"37• 10 -5 0-49• 10 -5
0.1 M-Tris.HC1, 0.5 ~-NaCI
7.5 8.0 8"5
7.8 • 1 0 4 . 6 " 4 • 104 3.6•
(0-15) (0"28) (0"26)
----
0"21 • 10 - 5 0 . 4 4 • 10 - 6 0-72• -5
0.1 M-Tris.HC1
7.4
7.8• 104
(0.24)
0.31 •
0-1 M-Tris.HC1 DNA-bound
7-5
12.1 • 104
(0.52)
0.43 • 10 -5
1"0 ~-Tris" HCI
8.0 8.5
0.1 M-Tris.HCl, 1.0 ~i-NaC1
Kd =
~';
(~)
--0.84•
Ka" (M) 0-31 • 10 -s 0-37 • 10- a
-~
0-71 • 10 -s 2 - 8 • 10 -Sw
8-0 • 10 -5~
10 - s
All buffers contain 3 • 10-4 M-dithiothreitol. b Second-order association rate constant measured as described in the legends to Figs 1 and 3, and in the text. a First-order dissociation constant measured as described in the legend to Fig. 1 and in the text. d KineticaUy determined dissociation constant calculated from values measured for k and k'. e Dissociation constant determined by equilibrium dialysis as described in Materials and Methods. f Values in parentheses are calculated from measured values: k = Kd • k'. f Values taken from plots in Figs 3 and 5. h Buffer used was 0.1 M-glycine-NaOH, 1.0 M-NaC1.
I n 1.0 M-Tris. HC1 ( p H 8.5 a t 20~ 3 • 1 0 - 4 M - d i t h i o t h r e i t o l , a s e c o n d - o r d e r association rate of 1.7• M -1 s -1 a n d a f i r s t - o r d e r d i s s o c i a t i o n r a t e o f 0.53 s - 1 w e r e d e t e r m i n e d . N o a c c e l e r a t i o n w a s a p p a r e n t i n t h e t r a c e s r e c o r d e d i n t h i s m a n n e r for either process, nor did we observe a significant contribution of a slow transition a n a l o g o u s t o t h a t r e p o r t e d b y L a i k e n et al. (1972). T h e r a t e c o n s t a n t s m a y t h e n b e u s e d t o c a l c u l a t e a d i s s o c i a t i o n c o n s t a n t for a g i v e n p H : Kd -~ k[k'. A s s e e n i n T a b l e 1, t h e s p e c t r a l d i s s o c i a t i o n c o n s t a n t c a l c u l a t e d f r o m t h e s e k i n e t i c p a r a m e t e r s as d e t e r m i n e d a t p H 8.5 (3-1 • 1 0 - 5 M) is in e x c e l l e n t a g r e e m e n t w i t h t h a t d e t e r m i n e d b y t h e e q u i l i b r i u m m e t h o d s d e s c r i b e d b e l o w (2.8 • 1 0 - s ~ ) . (b) Ultraviolet titration A n i n d e p e n d e n t d e t e r m i n a t i o n o f t h e e q u i l i b r i u m d i s s o c i a t i o n c o n s t a n t for i n d u c e r binding to represser was carried out by measuring the resulting changes in the a b s o r b a n e e o f p r o t e i n in t h e u l t r a v i o l e t r e g i o n . T h e c h a r a c t e r i s t i c u l t r a v i o l e t d i f f e r e n c e spectrum was produced incrementally by additions of IPTG and recorded over the r a n g e 250 t o 350 n m (Fig. 2(a)). A final a d d i t i o n o f c o n c e n t r a t e d I P T G (10 - 1 M)
32
B. E. F R I E D M A N ,
J . S. O L S O N A N D K . S. M A T T H E W S
0
.Q
-+ol
<3
-0-02
(o) I
I
I
i
290
270
I
l
I
310 Wavelength (nm)
l
330
350
4.0
//,..o~,'''''-'-//
3.0
"o X
~ 9Q
._
/"
2.0
<~
/
I-0
/
/
./. 2
I
I
i
i
i
4
6
8
I0
12
//
i
l
(b) i
20
22
24
[IPTG] (MX IOs )
FIG. 2. Ultraviolet titration of repressor with inducer. (a) A difference spectrum produced by titration of repressor (1-2 • 10 -5 ~) with I P T G (10 -3 M) in 1.0 M-Tris.HC1 buffer, with 3 • 10 -4 M-dithiothreitol adjusted to p H 8.1, at 20~ and recorded as described in Materials and Methods. (b) A saturation curve generated from the original data in Fig. 2(a).
INTERACTION
OF l~
REPRESSOR
WITH
INDUCER
33
was made to insure t h a t saturation had been reached. The saturation curve was generated b y plotting the change in absorbance measured at the 290 nm trough versus the concentration of I P T G for each addition (Fig. 2(b)). Because this ligand exhibits such tight binding, the usual analysis of the data b y a Scatchard t y p e plot proved unsuccessful. However, an approximate dissociation constant could be determined b y noting the concentration of unbound I P T G which corresponds with half saturation. The Kd value estimated under these conditions was H 1 • 10 -B ~ for p H 8.1. This figure is similar to values obtained b y equilibrium dialysis under the same conditions. Perhaps more significant is the fact that the decrease in absorbance occurs lmiformly at all wavelengths, implying t h a t a single reaction is responsible for the spectral changes. This observation, in conjunction with the lack of acceleration in stopped-flow traces, suggests t h a t a simple equilibrium exists between I P T G and repressor. The similarity between Kd values determined by these different methods is a necessary condition for such an equilibrium to exist. (c) Dependence of inducer binding on TH and ionic strength An extensive study of the effects of p H on the interaction of inducer with repressor was undertaken b y kinetic and equilibrium methods. In order to determine the dependence of the binding affinity on pH, equilibrium dialysis was carried out at 22~ using repressor at a concentration of 3.3 • 10 -6 ~ and [14C]IPTG (2 • 10 -7 M). Measurements were made in 0.1 M-Tris.HC1, 3 • 10 -a M-dithiothreitol, adjusted to the appropriate p H ; 1.0 M-NaC1 or 0-5 M-NaCI was added to insure a constant ionic strength over the p H range examined (6.5 to 9.5). Resulting data were analyzed b y standard Scatchard plot treatment. As seen in Figure 3, the affinity of repressor for I P T G decreases with increasing pH, the inflection of each curve being between p H 8.3 and 8.5. Kinetic measurements were also made over the same p H range in 0.1 ~-Tris.HCl, 3 • 10 -4 M-dithiothreitol, 1.0 M-NaC1 or 0.5 M-NaC1. In a few cases a slow phase representing a very small percentage (_<5%) of the total change was observed. I n these instances the change in fluorescence resulting from this minor slow phase was subtracted before a rate for the fast phase was determined. The results, presented in Figure 3 as plots of the second-order rate versus pH, indicate that the rate of I P T G binding decreases with increasing pH. Again, the mid-point of the transition is ~ p H 8-3. In order to examine the effect of ionic strength, kinetic and equilibrium measurements were made in solutions of various salt concentrations under conditions of constant pH. Buffers of 0.1 M-Tris.HC1, 10 -4 M-dithiothreitol were adjusted to a specific p H with HG1, and NaC1 was added at concentrations from 0 to 1.0 M. The results, summarized in Figure 4, indicate that the ionic strength effects differ at different p H values. Generally a higher ionic strength results in increased affinity of ligand for repressor, with small effects on the second-order association rates. Because repressor is stabilized by high concentrations of Tris buffer, m a n y studies have used this buffer at concentrations of 0.5 to 1.0 ~. Our initial p H studies were also carried out in 1.0 M-Tris.HC1 (3• -4 M-dithiothreitol) and the results are shown in Figure 5. As before, the affinity of repressor for I P T G decreases with increasing p H and the association rate decreases in going from p H 7.0 to p H 9.0. In both cases the inflection point is between p H 8.3 and p H 8.7. The major difference between these results and those presented in Figure 3 is that in 1.0 M-Tris there is a greater change in the equilibrium and rate constants as the p H is raised to 9.0. I n 8
34
B. E. F R I E D M A N , J. S. OLSON AND K. S. M A T T H E W S (a)
A._._.&~&/ I 0
I
I
~e_
I
I
I
"2
I
O x
(b) 8
~
4
|
I
7.0
t
I
8-0 pH
i
I
i
9.0
Fro. 3. Rates and affinities of inducer binding as a function of pH. Dissociation constants (Ka values) for IPTG were determined by equilibrium dialysis at 22~ as described in Materials and Methods. Kinetic measurements were made at 20~ by mixing represser at a fixed concentration (1.3 • 10-6 M before mixing} with various concentrations of IPTG in the manner described in Fig. 1. Second-order rate constants (k') were derived by linear regression from plots of the observed first-order rate constant v e r s u s IPTG concentration. - - O - - O - - , Second-order rate constants (k'); - - & - - A - - , dissociation constants (Kd values). (a) Measurements were made in 0.1 M-buffer, 3• 10 -4 ~-dithiothreitol, with 1.0 ~-NaCI adjusted to the appropriate pH. The buffer used was Tris 'HC1, except for the kinetle measurements made at pH 9.0 and pH 9.5, in which case the buffer used was glycine-NaOH. (b) All measurements were made in 0.1 ~-Tris.ttC1 buffer, 3• 10 -4 ~-dithiothreitol, with 0.5 M-NaC1, adjusted to the appropriate pH with I-ICl.
view of the results shown i n F i g u r e 4, p a r t of this effect is p r o b a b l y the result of t h e m a r k e d change i n ionic s t r e n g t h i n t h e Tris buffer, going from p H 7.0 where it is fully p r o t o n a t e d to p H 9.0, where it is m o s t l y d e p r o t o n a t e d . I t is also possible t h a t there are more specific i n t e r a c t i o n s b e t w e e n Tris a n d the protein. T a b l e 1 presents a s u m m a r y of our k i n e t i c a n d e q u i l i b r i u m data. A t the higher p H values i n 1.0 M-Tris it was possible to m e a s u r e b o t h the association a n d dissociation velocity c o n s t a n t s for I P T G b i n d i n g . I n these cases, comparisons were m a d e b e t w e e n k i n e t i c a l l y d e t e r m i n e d e q u i l i b r i u m c o n s t a n t s a n d those m e a s u r e d directly b y e q u i l i b r i u m dialysis. A t lower pH, the high affinity of represser for I P T G p r e v e n t e d m e a s u r e m e n t of the dissociation rate c o n s t a n t , since this c o n d i t i o n required t h e use of c o n s i d e r a b l y lower p r o t e i n c o n c e n t r a t i o n , which i n t u r n resulted i n a fluorescence change t h a t was too small to be m e a s u r e d accurately. Thus, at t h e low p H values, the dissociation rate c o n s t a n t (in parentheses) was calculated from the second-order association rate a n d t h e e q u i l i b r i u m c o n s t a n t m e a s u r e d b y dialysis techniques.
INTERACTION
OF 16
-
lac REPRESSOR
WITH
INDUCER
,$5
(a)
12 0 x
1
8
! 12
[
I
I 0
I 0"5
I
(b)
A
T o
8
x
T "~
4
I I-0
-
[NaCI] (M)
Fxo. 4. R a t e s a n d affinities of inducer b i n d i n g as a f u n c t i o n of ionic s t r e n g t h . All m e a s u r e m e n t s were m a d e in 0-1 M-Tris.HC1 buffer, 3 • 10 -4 M-dithiotlu'eitol, a d j u s t e d to t h e indicated p H , w i t h a d d i t i o n s of NaCI fl'om 0 to 1.0 ~. (a) Dissociation c o n s t a n t s (Kd values) for I P T G were d e t e r m i n e d b y e q u i l i b r i u m dialysis as described elsewhere : - - 9 9 p H 7"5 ; - - 9 9 p H 8.0 ; - - 9 9 p H 8.5. (b) Second-order rate c o n s t a n t s (k') for I P T G b i n d i n g were m e a s u r e d as described in Fig. 3: - - O - - C ) - - , p H 7.5; - - A - - A - - , p H 8-0; - - [ ~ - - [ ~ - - , p H 8.5.
(d) Effect of bound D N A o~ association rate The binding of inducer to represser free in solution probably does not occur in rive. Represser has been shown to bind inducer while the protein is bound to operator DNA to form a ternary complex (Barldey et al., 1975). Even the inducer/protein complex is likely to be associated with the DNA in a non-specific binding interaction (von Hippel et al., 1975). In order to examine for the effects of non-specific DNA binding, the association rate for inducer binding was determined in the presence of fragmented calf thymus DNA (Mr ~ 15 • 106). The unavailability of operator DNA prevented examination of the influence of specific operator activity on inducer binding. A 3.3• 10 -6 M-solution of represser in 0-1 M-Tris.HC1, 3 • 10 -4 M-dithiothreitol buffer, with DNA at ~-~0.3 mg/ml was reacted with various concentrations of I P T G in the stopped-flow spectrometer under pseudo first-order conditions. The exponential change in t r y p t o p h a n fluorescence was recorded as before. The secondorder rate measured in the presence of DNA was 12• M-~s -~ at p H 7-5 and 9.1 • 104 M - ~ s - ~ at p H 8.0, while the inducer binding rate determined in the absence of DNA was 7-8• 104 M-~s -~ at p H 7.4 and p H 8.0. A comparison of these rates
36
B. E. F R I E D M A N ,
J. S. O L S O N A N D K. S. I~IATTHEWS
suggests that inducer binding is not greatly altered when repressor is non-specifically bound to DNA. As shown in Table 1, the equilibrium constant for inducer binding also appears to be little affected by the presence of caff thymus DNA.
4. D i s c u s s i o n
The physiological role of lactose repressor protein as a regulator of transcription of the structural genes of the lactose operon in E. coli rests on the ability of the protein to undergo a conformational change in response to inducer binding. This conformational isomerization is believed to trigger release of the protein from the operator region of the DNA molecule. Therefore it is important to characterize thoroughly the interaction of repressor with inducer and to understand the influence of factors such as ionic strength and pH on the inducer binding rates, on binding affinity, and on the conformational state of the protein. The dilution of repressor containing bound IPTG in the stopped-flow, rapid-mixing spectrometer provides a convenient method for the measurement of the rate constant for dissociation of inducer, a value which has not previously been determined directly. Measurement of the dissociation rate makes possible calculation of the K d value for inducer binding independent of equilibrium studies (see Table 1). The K d data determined by the various methods are in good agreement, a result which is to be expected for a simple protein-ligand equilibrium. The need for responsiveness of this system to environmental stimuli makes it unlikely that either the dissociation of inducer or its association with repressor is a slow process, particularly since a large number of complex reactions must take place before inductdon is complete. However, monitoring changes in tryptophan fluorescence at one emission wavelength (360 nm), Laiken et al. (1972) observed a fast second-order change (6• M-is -1) followed by a much slower first-order decay with a rate measured as 0.12 s -1. These authors assumed that the faster rate represented the rate of binding inducer, while the slower rate reflected the rate of the conformational change associated with the induction process. We did occasionally observe a slow change in tryptophan fluorescence, but even when present in our experiments, this slow phase always represented a very small percentage of the total fluorescence change (usually less than 5%). Furthermore, the appearance of the slow decay was erratic and corresponded generally with the age of the protein sample being observed. Freshly thawed samples always exhibited monophasic, fast fluorescence changes. Consequently, the slow changes appear to reflect some alteration in the protein structure indicative of decay of the molecule. Since the same rapid rate is observed when monitoring probes in different parts of the protein (Friedman et al., 1976), we have concluded that the rapid change in tryptophan fluorescence represents a conformational change in repressor which is rate-limited by inducer binding, hence the second-order nattlre of the change. This alteration of the protein structure is most likely the one respofisible for the induction process. From the results reported here, it is apparent that both the rate and affinity of IPTG binding vary with pH and ionic strength to a small but measurable extent. In view of the ionic strength effect, it is important to note the buffering system used before comparing results of studies on repressor conducted under different conditions. Wu et al. (1976) have suggested the possible significance of pH variations in the genetic control function of repressor. This type of regulation seems unlikely, as the magnitude of the changes observed in binding rates or dissociation constants with pH are not
INTERACTION OF /ac REPRESSOR WITH INDUCER
37
large. Furthermore, the effects of pH are decreased at higher ionic strength, such as that expected in the local environment of the DNA molecule. The decrease in K d values at high salt concentrations indicates that IPTG binding affinity increases with ionic strength, a situation which seems reasonable for a protein which interacts with DNA. Consistent with this view is the fact that the rate of inducer binding was not dramatically altered by the presence of non-operator DNA. More important, this result also shows that the binding measurements made on repressor free in solution may closely approximate the conditions in vivo, where the protein remains associated with non-specific regions of the DNA molecule. Wu et al. (1976) have demonstrated the existence of a pH dependent, rapid isomerization of repressor molecules by fluorescence, temperature-jump techniques. The magnitude of the fluorescence change decreased either by raising the pH of the solution or by adding high concentrations of IPTG. These results were interpreted by assuming that there are two forms of repressor: R*, a form that does not bind inducer and exhibits a lower affinity for protons than I~, a form which binds IPTG tightly and exhibits a higher affinity for protons. Thus, at high pH, the R* form predominates, whereas at low pit or in the presence of IPTG, the equilibrium favors the R form. In either case, no fluorescence change would be observed by equilibrium perturbation techniques. The interpretation by Wu et al. (1976) further predicts the dependence of the apparent second-order rate constant for IPTG binding on pH. According to these workers, the apparent rate for inducer binding, ktapp (the rate observed in our steppedflow experiments), is proportional to the fraction of R conformations present:
5R
k's,, = k' ~ R + ~ R * '
(2)
where k' represents the theoretical rate constant for binding to the R conformation of the protein. Inherent in equation (2) is the assumption that inducer binds only to the R form, since there is no term to take into account binding to the It* conformation. The pit dependence of k'~pp can be calculated from the expression proposed by Wu et al. (1976) to account for the pH dependence of the R to It* transition: ~R
= L
-{- (H+)/K~ } ,
(3)
where L represents the isomerization equilibrium constants in the absence of protons and Ks, Ks* are acid dissociation constants for the tt and It* forms, respectively. Using values from Wu et al. for Ka, Ka*, and L (pK~ = 7.6, pK~* = 7.0, ]5 = 220), the fraction of R states is predicted to change from 0.160 to 0.005 in going from pH 7.0 to pH 9.0. This requires a 30-fold decrease in the association rate for IPTG binding. As shown in Figures 3 and 5, the observed decrease is about sevenfold in 1.0 M-Tris.HC1 and only two- to fourfold in 0.5 M- or 1-0 M-NaC1, 0.1 M-Tris.HC1 in going from pit 7.0 to pH 9.0. Furthermore, the inflection point predicted from equation (3) is around pH 7.3, whereas the data in Figures 3 and 5 indicate a transition centered around pH 8.3. Our results indicate that inducer can bind to both of the forms of the protein described by Wu et al. Consequently, an additional term must be added to the righthand side of equation (2) to take into account binding to the R* form. In addition, the pH dependence of the isomerization equilibrium must be modified to take into account ionizations with pK~ values greater than pH 8.0. This latter modification is
38
B. E. F R I E D M A N , J. S. OLSON AND K. S. MATTHEWS 10 8
f0
"~ 4
6
O --
4
2
7.0
8.0
9-0
pH Fie. 5. Effects of high molarity Tris buffer on rate and affinity of inducer binding as a function of pH. Measurements were made using IPTG, as described in the legend to Fig. 3, except that experiments were carried out in 1.0 M-Tris.HCI buffer, 3 • 10 -* ~I-dithiothreitol, adjusted to the appropriate pit. - - 0 - - 0 - - , Second-order rate constants (k') ; - - A - - A--, dissociation constants (Kd values). required both by our data for the p H dependence of the rate constants for I P T G binding and by potentiometric data of W u et al. at high pHI, where I P T G was shown to decrease the fractional amount of protons bound to represser. I n spite of the problems discussed above, the data of Wu et al. are consistent with our previous observation (Friedman et al., 1976) that the represser undergoes a conformational transformation that is much more rapid than the binding of inducer molecules. Whether the fluorescence changes observed in these two studies represent the same or independent conformational transitions of the protein is not known. The fluorescence change we measured could result from a rapid conformational transition in the protein which occurs either before or after inducer binding. However, several conclusions about the system can be made. The binding of inducer to represser is apparently the rate-limiting step in the sequence of events in which the protein assumes a new conformation in response to inducer. The binding of I P T G to represser is, to a small extent, a function of the p H and ionic strength of the environment. No slow conformational isomerizations are detected in this process. This fact, combined with the absence of acceleration in the time-course of I P T G binding and dissociation, indicates that the binding of I P T G to represser does not exhibit cooperative subunit interactions. Furthermore, the simple equilibrium combination of inducer with represser protein occurs in a similar fashion either when the protein is free in solution or non-specifically bound to DNA. This work was supported by" grants from the National Science Foundation (BMS7301570 A01 to K.S.M.) and the National Institutes of Health (GM-22441 to K.S.M. and HL-16093 to J.S.O.).
REFERENCES Barkley, M. D., Riggs, A. D., Jobe, A. & Bourgeois, S. (1975). Biochemistry, 14, 17001712. Bourgeois, S. (1971). Methods Enzymol. 21D, 491-500. Friedman, B. E., Olson, J. S. & Matthews, K. S. (1976). J. Biol. Ohem. 251, 1171-1174. Laiken, S. L., Gross, C. A. & yon Hippel, P. H. (1972). J. Mol. Biol. 66, 143-155.
I N T E R A C T I O N OF lac R E P R E S S O R W I T H I N D U C E R
39
Matthews, K. S., Matthews, H. R., Thielmann, H. W. & Jardetzky, O. (1973). Biovhim. Biophys. A eta, 295, 159-165. Mfiller-Hfll, B. (1971). Angew. Chem. Internat. Ed. 10, 160-171. Mfiller-Hfll, B., Crapo, L. & Gilbert, W. (1968). Proe. Nat. Acad. Sci., U.S.A. 59, 1259-1264. Mfiller-Hill, B., Beyreuther, K. & Gilbert, W. (1971). Method8 Enzymol. 21D, 483-487. Ohshima, Y., Mizokoshi, T. & Horiuchi, T. (1974). J. Mol. Biol. 89, 127-136. Platt, T., Weber, K., Ganem, D. & Miller, J. (1972). Proc. Nat. Acad. Sei., U.S.A. 69, 897-901. l%iggs, A. D., Newby, R. F. & Bourgeois, S. (1970). J. Mol. Biol. 51,303-314. Scatchard, G. (1949}. Ann. N . Y . Aead. Sci. 51,660-672. von Hippel, P. H., Revzin, A., Gross, C. A. & Wang, A. C. (1975). In Protein-Ligand Interactions (Sand, I-L & Blauer, G., eds), pp. 270-288, W. de Gruyter, Berlin. Wu, F., Bandyopadhyay, P. & Wu, C.-W. (1976). J . Mol. Biol. 100, 459-472.