Solution dynamics of the trp repressor: A study of amide proton exchange by T1 relaxation

J. MoL BioL (1995) 246, 618-627

JMB Solution Dynamics of the trp Repressor: A Study of Amide Proton Exchange by Relaxation Michael R. Gryk, Michael D. Finucane, Zhiwen Zheng and Oleg Jardetzky* Stanford Magnetic Resonance Laboratory, Stanford University, Stanford CA 94305-5055, U.S.A.

The amide proton exchange rates of Escherichia coli trp repressor have been measured through their effects on the longitudinal relaxation rates of the amide protons. Three types of exchange regimes have been observed: (1) slow exchange (on a minute/hour time-scale), measurable by isotope exchange, but not by relaxation techniques in the core of the molecule; (2) relatively rapid exchange, with the rates on a T, relaxation time-scale (seconds) in the DNA-binding region and (3) very fast exchange at the N and C termini. The results have been analyzed in terms of the two-site exchange model originally proposed by Linderstrom-Lang, and of a three-site extension of the model. The values of the intrinsic exchange rates calculated using the two-state model agree with the values expected from the studies of Englander and co-workers for the very fast case of the chain terminals, but disagree with the literature values by two orders of magnitude in the intermediate case found in the DNA-binding region. The implication of these findings is that the "open" state of the two-state model in the DNA-binding region is not completely open and has an intrinsic exchange rate different from that of a random coil peptide. Alternatively, if the literature values of the intrinsic exchange rates are assumed to apply to the open states in all parts of the repressor molecule, two "closed" helical states have to be postulated, in slow exchange with each other, with only one of them in rapid exchange with the open state and hence with the solvent. Kineticall}~ the two models are indistinguishable.

*Corresponding author

K~/words: hydrogen exchange; trp repressor; protein stability; NMR

Introduction The trp repressor from Escherichia coli is an intertwined dimer of two chains, each consisting of six alpha helices (A to F). Structural studies of the trp repressor have characterized three subdomains of the homodimer (Schevitz et al., 1985; Zhao et al., 1993). The N-terminal residues appear to be unstructured in both the solution and crystal studies. The hydrophobic core formed by the intertwining of helices A, B, C and F of the two monomers appears highly helical in both the crystal and solution structures. The DNA-binding domain (helices D and E) adopts a helix-turn-helix conformation in the crystal structure (Schevitz et al., 1985), but is not well defined in the solution structures determined by Zhao et al. (1993) due to the lack of sufficient NOEs along the backbone. On the other hand, the chemical Abbreviations used: NOE, nuclear Overhauser enhancement; HMQC, heteronuclear multiple quantum coherence. 0022-2836/95/100618-10 $08.00/0

shifts of the C '~protons of the DE region (Zhao et al., 1993), the uniformity of the '~N T, and T2 relaxation rates along the entire backbone, and the heteronuclear NOEs for residues in the DNA-binding region (Zheng et al., 1995) indicate that the DNAbinding region is helical in solution as well. The lack of sufficient NOEs for an accurate structure determination is explained by the observation reported by Czaplicki et al. (1991), who found that the rate of proton exchange from the DNA-binding region was too fast to be measured by isotope exchange techniques, which yielded commonly found lifetimes of many hours for NH protons in the core of the molecule. The DNA-binding region must therefore be viewed not as unstructured, but rather as unstable with well-defined helices opening frequently to allow rapid amide proton exchange. The binding of L-tryptophan to the trp repressor results in both structural and dynamic changes in the macromolecule and slows the backbone proton exchange (Zhang et al., 1987; Arrowsmith et al., 1991a,b; Zhao et al., 1993). The recent publication of © 1995 AcademicPress Limited

Amide Proton Exchange in trp Repressor

619

the solution structure of the repressor/DNA complex has shown that more extensive conformational changes are needed to bind to the operator DNA sequence than result from ligand binding alone (Zhang et al., 1994). The instability of the DNAbinding region may play a crucial role in bringing about such additional conformational changes. For protons with rapid exchange (>0.2Hz), saturation transfer, T, relaxation, and lineshape analysis can be used to quantify the rates associated with the exchange process (Krishna et al., 1979; Jardetzky & Roberts, 1981; Spera et al., 1991). Due to the large number of protons observed in the amide region of a spectrum of trp repressor, one-dimensional lineshape analysis is out of the question. Saturation transfer and relaxation techniques in heteronuclear two-dimensional spectra (HMQC) are applicable, but have been used only with limited models of amide proton exchange (Spera et al., 1991). Here, we describe the analysis of amide proton exchange in the trp repressor using a combination of saturation transfer and T, relaxation techniques. The analysis of the results in terms of the widely used Linderstrom-Lang model (Scheme 1) made it apparent that the customary formulation of the model does not apply to all cases that can be observed. To evaluate the individual exchange parameters, the model has to be either extended or conceptually reinterpreted. The validity of the Linderstrom-Lang model for amide proton exchange is discussed.

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The HMQC spectrum of the trp holorepressor is clearly pH-dependent (Figure 1). Many more peaks are seen at pH 6.1 (Figure l(a)) than at pH 8.7 (Figure l(b)). The assignments have been published (Arrowsmith et aI., 1990; Czaplicki et al., 1991). It is noteworthy that all of the assigned peaks from residue 73 to residue 79 seen at pH 6.1 are absent at pH 8.7 and those from residues 71 and 82 to 86 are considerably attenuated relative to their intensities at pH 6.1. A similar loss of intensity with increased pH is seen for residues in the N-terminal region, which are already affected at pH 5.1 and 6.1, and the C-terminal residue 108. In contrast, the intensity of residues in the core region (residues 25 to 60, 96 to 105) does not change with pH, indicating that this effect is limited to the peaks that disappear rapidly in a deuterium exchange experiment (Czaplicki et al., 1991). A pH-dependence of peak intensity is expected for residues exchanging on the time-scale of relaxation experiments, inasmuch as the intrinsic exchange rate is strongly pH-dependent and becomes very large (>50 Hz) at pH 8 or above. Similarl}~ a pH-dependence is seen when solvent presaturation is applied, so that the recovery rate of

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Figure 1. 'H-'SN HMQC spectra at pH 6.1 (a) and 8.7 (b). Some of the peaks that are present at pH 6.1 but not at 8.7 are indicated in (a), and some of the peaks that have reduced intensity at pH 8.7 are indicated in (b). the longitudinal magnetization of the amide protons is slowed by exchange with the presaturated solvent. The effect of presaturation on the recovery rate is shown in Figure 2 for residues 82 (Figure 2(b)) and 108 (Figure 2(c)), both of which are exchanging, and the non-exchanging residue 42 (Figure 2(a)), which is used as a control. All data are summarized in a plot of relative peak intensity as a function of residue number and pH, shown in Figure 3. As with peak disappearance, the N-terminal residues are affected at pH values 5.1 and 6.1; the residues in the DNA-binding region begin to show saturation transfer effects when the pH is 7.2 or greater, while the residues in the slowly exchanging core show no intensity changes at any pH. It is possible to obtain a rough estimate of the effective exchange rate k~, from the McConnell equation (McConneI1, 1958): 1 Tlapp

1 -

TI

+ k~,

(1)

620

Amide Proton Exchange in trp Repressor

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where T, is the intrinsic longitudinal relaxation time, T~,~ppis the observed longitudinal relaxation time, and k~.~is the effective amide proton exchange rate. According to Krishna et al. (1979) and Spera et al. (1991), a similar estimate can be made from the ratio of intensities measured with and without presaturation: M,, _ 1 + k~.,T,,

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where M,, and M~ are the equilibrium intensities of the amide proton crosspeaks in the absence and presence of solvent presaturation, respectively However, equation (2) is valid only in the limiting case of rapid exchange between the closed and open states (high motility limit, Krishna et al., 1979), which applies to small peptides but need not apply to proteins. In fact, a comparison of the effective exchange rates calculated from equations (1) and (2) can be used as a test of the applicability of the high motility assumption: if the assumption holds, the values of k~.~calculated by the two methods should agree. If they do not, the fast exchange limit and equation (2) do not apply Figure 4a shows the apparent relaxation rates for residues 22 to 108 at pH 7.6. These rates were

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Figure 3. The ratio of the peak intensity (@) measured with and without presaturation (Mo/Mp~) for the amide protons of trp repressor at all 6 pH values used in this study is shown. Large values of Mu/Mp~ reflect fast proton exchange while slow proton exchange yields a value of 1.

determined through a three-parameter fit of the inversion recovery equation: Mz = M~Q[1 - (1 - cos ~b)exp( - t/Tt,pp)],

(3)

fitting for the apparent relaxation time T1app, the equilibrium magnetization ME% and the pulse efficiency in terms of the flip angle qb. Using the average T~ (0.593 second) of the residues in the core that have measurable exchange lifetimes at pH 5.7 (Czaplicki et al., 1991) as an estimate of the intrinsic relaxation rate allows us to calculate the amide proton exchange rate, kex, from both the saturation transfer profile of Figure 3 and from the apparent T, of Figure 4a, using equations (1) and (2). A comparison of the results is shown in Figure 4b, clearly indicating that the exchange rate calculated from the saturation transfer ratio is consistently smaller for the DNA-binding region than the exchange rate calculated from the apparent T~. The only possible explanation for the difference between the two measurements is that the intrinsic relaxation

Amide Proton Exchange in trp Repressor

621

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Figure 4. Observed relaxation and exchange rates for trp repressor at pH 7.6. (a) The apparent relaxation rate 1/Tlapp (m). (b) k,.,as calculated from kL.~= 1/T,,~pp 1/T~ (O) and kL~ as calculated from k,.~= (M,,/M~ - 1)/T~ ([~). -

rate of the DNA-binding region is much faster than that of the core. However, the uniformity of the 15N T1 suggests that the intrinsic proton T~ values are similar as well and the assumption of the "high motility" limit and equation (2) cannot be applicable to our case. (This is not the case for the mobile C-terminal residue 108, which has a much slower intrinsic relaxation rate accounting for the discrepancy.) Nevertheless, it is clear that backbone protons of the N-terminal region, the DNA-binding helix-turn-helix DE and the C-terminal residue 108, exchange on a time-scale comparable with the relaxation rate (-2 Hz). At high pH values the intrinsic exchange rates are known from the work of Bai et al. (1993) and Englander & Mayne (1992) to be at least two orders of magnitude higher than the estimates of k~x,except for the C-terminal residue 108, which behaves like a random coil peptide. This is a clear indication that the exchange observed in the relaxation experiment for the DE region is not that of a random coil peptide, but is hindered, most likely by the rates of formation and breakage of secondary structure, as postulated in the model described by Linderstr~m-Lang. The decrease in the exchange rate for residue 106 can be explained by its proximity to

the carboxy terminus. Rosevear et al. (1985) have noticed a similar effect on am•de proton exchange for residues that neighbor the carboxy termini of peptides. This explanation cannot hold for the DNA-binding region. A careful examination of its three-dimensional solution structure shows that no comparable charge exists near either of the D and E helices. Thus, the decrease in the exchange rates for the DNA-binding region implies a structural hindering of exchange of the same kind, though obviously weaker than is seen in the hydrophobic core. This is not unexpected, as the (x-proton chemical shifts and 'SN relaxation data support the notion that the DE region is largely helical. Since our calculation shows that the simplified model of am•de proton exchange (Krishna et al., 1979; Spera et al., 1991) does not apply and the generalized Linderstrom-Lang model contains at least three exchange rates, we have to conclude that the measurement of the presaturation factor alone is insufficient to determine all three rates. An estimate of the three exchange parameters and of the average relaxation rate (k,, k2, k~,,r~,.,~and R~) can be obtained for each residue by examining the complete longitudinal relaxation profiles at each pH, both with and without solvent saturation. The relaxation profiles observed for trp repressor fall into one of three classes. (1) Single exponential without pH dependence. This is the pattern characteristic of the ABCF core indicating that there is no exchange on the relaxation time-scale. (2) Single exponential with pH dependence. This is the pattern observed for the C-terminal residue 108 and expected either for random coil peptides or for fast exchange (fast on the relaxation time-scale) between a closed and an open form. (3) Double exponential with pH dependence seen in the DE region. This indicates that the limiting rates are of the same order of magnitude as the relaxation rate, and the general solution of the McConnell equations for the Linderstrom-Lang model (see Materials and Methods) must be used for the analysis of the data. The method used to determine all four rates for the am•de protons that show bi-exponential pH-dependent relaxation profiles is outlined below. The intrinsic relaxation rate of the open state is expected to be approximately the same as that of the closed state. For simplicity of calculation, the two rates were assumed to be identical within experimental error. As a first step it was determined whether the crosspeak originated from the closed state or the sum of the two (an average of the two requires the fast exchange limit and would result in a single exponential, as would the open state). This was a rather simple matter, for the expected relaxation profiles are quite distinct depending on which state is being observed. If only the closed state is being observed, both the presaturation and no-presaturation profiles should show only a weak pH-dependence, an initial slow and a later appearing fast component. In contrast, the sum of the two would give an initial fast and a later slow component, corresponding to exchange from the open and closed

622

Amide Proton Exchange in trp Repressor

Table

1

Solutions to the modified Bloch equations for relaxation in the presence of Linderstrom-Lang exchange MT(t) = M A ( t ) + M t ~ MA(t)= MAO(1-- PA) + C, exp( - l,t) + C_~exp( - K.,t) M , ( t ) = M~(1 - P,) + D. exp( - K,t) + D., exp( - K:t) t, = ½(R,~+ R ,

- x / ( R a - R,~)'- + 4k,~,,.~kd,,~.)

t2 = ½(R,,+ R., + v/(R,,-

R,)" + 4kop,.°k,.,o,.)

R,, = R,,, + k,,p,., RB = RI. + K,.~. + k,., PA =

k,~....k..f

p , = R,~k~.,f

l, 12 where

f

for experiment with no solvent saturation. -.

for experiment

with

solvent

saturation.

c [ M A . - M A o ( 1 - P A ) I ( R ~ - k~) + [ M I ~ , - M , o ( 1 - P,)]k~,..,.

C2 = [MA, - M A u ( 1 - P , O ] ( R R - K_~) + [ M , i - M B o ( l - PR)]k,.i,~.

D, = [MA,-MAo(1-

P.O]k.w. + [M., -

M1~(1- P.)](RA- KI)

D_, = [Ma~ - M , ~ ) ( 1 - Pa)]k,,,,,,. + [ M , . - M ~ ( 1

- P , ) ] ( R A - ~.,)

L - K~

states, respectively. All of the bi-exponential profiles found were of the fast-slow type and strongly pH-dependent, allowing the conclusion that one is observing a superposition of the closed and open states at the same chemical shift. For this case tile strong pH-dependence of the relaxation profile seen in the absence of solvent presaturation is expected to vanish when the solvent is presaturated, and this was indeed found to be the case for most residues in the DE region. Next, the data were analyzed semi-quantitatively by inspection to obtain estimates of the four rate parameters. To estimate the intrinsic relaxation rate, we simply estimate the relaxation rate at low pH (5.1) where exchange is expected to be negligible. Next, for the data acquired with solvent saturation, the difference in the apparent relaxation rates between high and low pH values gives an estimate of the opening rate, kopek,. The closing rate, k~,.... is then estimated by determining the relative weights of the two rates in the bi-exponential recovery. Lastl)~ k~,,n~ is estimated by measuring the fast rate of the biphasic recovery. Finally; the entire data set for each residue, i.e. all recovery curves, with and without solvent presaturation at all pH values, was fitted to the general solution of the McConnell equations for the Linderstrom-Lang model shown in Table 1, using the Marquardt nonqinear, least-squares fitting routine. This routine uses a combination of the inverse Hessian method and steepest descent and thus minimizes the problem of local minima. The pooling

of the data at different pH values can be justified by the fact that very few chemical shift differences are found when varying the pH from 5.1 to 8.7. Chemical shifts in proteins are generally good indicators of intact tertiary structure (Jardetzky & Roberts, 1981). Thus the chemical shift invariance implies that there are no structural changes occurring within the pH range of this study. A comparison of the estimates obtained by inspection with those obtained by the fitting procedure is given in Table 2. Brief inspection of the Table shows a marked difference between residues in the N terminus and those in the DNA-binding region. The residues in the N-terminus are observable only at lowest pH values, are seen to exist largely in the open state and therefore show a ko~ greater than k,.~...... However, residues in helices D and E are observed to be the superposition of the open and closed states. From the magnitude of k,~, and k~,~. we see that the two states are in intermediate exchange, and that the average population of each state is approximately 50%. If the closed and open states in the generalized Linderstrom-Lang model are naively equated with "helix" and "coil," this finding contradicts the finding based on 'SN relaxation and c(-CH chemical shift data that the DE helices are largely helical. The resolution of this apparent contradiction is discussed below. A second point of interest is that the estimated intrinsic exchange rates agree with those calculated for random coils by the rules of Bai e t a l . (1993) for the N and C termini, but differ from the calculated values by two orders of magnitude in the DE region. A comparison of the experimental and calculated values of k~.,~,,_~cas a function of sequence is shown in Figure 5. This finding also contradicts the naive interpretation of the kinetic closed and open states as helix and coil, and requires further analysis.

Discussion The interpretation of the findings on the ABCF core and the N and C termini is straightforward and needs no further discussion. On the time-scale of a relaxation measurement there is no exchange in the core and rapid exchange at the terminals, which behave like a random coil with estimated intrinsic exchange rates similar to those calculated for random coils by the method of Bai e t a l . (1993). The analysis of the findings for the DE region presents more of a problem. The region is clearly unstable, compared with the core, but more structured and stable than the N and C termini. However, the simple notion that one is observing unstable helices, with the solvent exchange described by the generalized LinderstromLang model, as conventionally understood, leads to two difficulties: (1) the interpretation of kinetic data yielding a roughly 50%-50% distribution of the population between the helix and the coil is not compatible with the findings from chemical shift and ~SNrelaxation data, both of which suggest that the DE region is largely >90%, helical, and (2) the model as usually applied requires that the intrinsic exchange

Amide Proton Exchange in trp Repressor

623

Table 2

Results of dynamic parameters obtained both by inspection and by fit for residues with pH-dependent profiles By fit Calculated1" By inspection Residue number R~(Hz) k,,~,,,(Hz) k~,,,~,(Hz) log.~ko. R,(Hz) kop,,~(Hz) k~t,~.(Hz) log~, ko. log,0 koH 7 9 10 11 18 19 20 21 33 47 65 67 68 70 71 73 74 77 79 82 83 84 86 94 106 108

N/A~ N/A N/A N/A 2.3 2.1 N/A N/A 1.3 2.6 2.25 1,3 N/A 2.23 2.2 2.0 2.01 1.4 N/A 1,61 1.55 1.85 1.8 1.3 1.7 2.0

N/A N/A N/A N/A <0.1 II <0.1 N/A N/A <0.1 0.35 <0.1 1.29 N/A 0.16 0.52 0.18 0.45 0.93 N/A 0.60 0.45 0.75 0.37 <0.1 <0.1 N/A

N/A N/A N/A N/A <0.1 <0.1 N/A N/A <0.1 0.62 <0.1 0.61 N/A 0.11 0.35 0.15 0.37 0.36 N/A 0.73 0.22 0.57 0.I3 <0.1 <0.1 N/A

8.47 9.55 9.37 8.65 6.92 Z04 9.14 8.62 7.10 6,96 6.99 7.47 8.82 7.17 6.97 7.43 7.15 7.43 8.60 6.92 7.06 7.12 7.05 8.00 7.07 6.89

1.75 (0.15)§ 1.58 (0.13) 1.34 (0.15) 1.73 (0.31) 1.81 (0~35) 2.54 (0.43) 1.78 (0.17) 2.65 (0.42) 1.24 (0.11) 3.22 (0.22) 2.21 (0.17) 1.54 (0.26) 1.19 (0.24) 2.75 (0.19) 2.28 (0.10) 1.96 (0,19) 1.64 (0.17) 1.10 (0.13) 1.37 (0.16) 1.97 (0.12) 2.14 (0.21) 2.13 (0.11) 1.81 (0.18) 1.04 (0.17) 1.44 (0.12) 2.00 (0.06)

0.36 (0.38) 0.44 (0.18) 0.75 (0.54) 0.63 (1.28) 1.07 (0.37) 1.11 (0.47) 1.05 (3.25) 3.99 (14.39) 0.31 (0,14) 1.00 (0.32) 0.81 (0.20) 0.98 (0.23) 0.17 (0.25) 0.28 (0.26) 0.78 (0.33) 0.05 (0.24) 1.30 (0.39) 0.63 (1.29) 0.29 (0.24) 0.31 (0.20) 0.66 (0.61) 0.61 (0.27) 0.31 (0.56) 0.00 (0.19) 0.36 (0.31) 16.31(7.17)

0.26 (0.34) 0.24 (0.12) 0.35 (0.36) 0.07 (0.18) 1.31 (0.62) 3.03 (1.89) 0.41 (2.09) 0.28 (1.72) 0.95 (0.58) 5.71 (3.39) 1.44 (0.47) 3.34 (1.43) 0.09 (0.13) 0.19 (0.19) 0,63 (0,35) 0.04 (0.19) 0.98 (0.39) 0.10 (0.25) 0.27 (0.26) 0.38 (0.27) 0.43 (0.49) 0.46 (0.25) 0.32 (0.71) 0.00 (0.30) 0.12 (0.11) 4.93 (3.85)

8.53 (0.10) 9.66 (0.05) 9.36 (0.11) 8.59 (0.08) 7.44 (0.13) 8.68 (0.24) 8.90 (0.37) 8.58 (0.17) 7.18 (0.18) 7.21 (0.24) 7.69 (0.10) 9.94 (0.28) 9.12 (0.09) 7.32 (0.07) 6.99 (0.06) 7.71 (0,10) 7.38 (0.07) 7.39 (0.07) 8.75 (0.10) 7.14 (0.08) 7.13 (0.10) 7.16 (0.06) 7.42 (0.20) 8.57 (0.19) 7.15 (0.04) 7.12 (0.05)

8.21 9.02 8.72 8.71 8.41 8.16 8.03 8.59 8.74 8.03 8.38 9.20 9.08 8.43 7.99 9.33 8.53 8.89 8.16 8.19 8.42 9.00 9.26 7.78 8.47 6.92

i- Log(ko.) calculated from Bai et al. (1993). :~ N / A means that the parameter cannot be determined. § Numbers shown in parentheses are the standard errors of the curve fit evaluated from the covarient matrix. II <0.1 means that the difference of the apparent T~ values with solvent saturation between low and high pH values is less than the experimental error.

rates correspond to those generally calculated for random coils on the basis of very extensive experimental data. The finding that the intrinsic exchange rate calculated for the DE region is smaller by two orders of magnitude than the intrinsic exchange rate usually found for an open state is in fact more consistent with the chemical shift and ~SN data suggesting that a truly open state is not perceptibly populated. The simplest way to reconcile all of our findings is to say that the kinetic equations of the LinderstromLang model appl)~ but the open state is not truly

1

T

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Residue

Figure 5. Comparison of calculated ( ) and observed (11) k~.,,..~i~(k~.,,.~i,= G. [OH - ]) values for trp repressor. The calculated values were obtained using the method of Bai et al. (1993).

open. It does not involve the unraveling of a helix, but only the opening of individual hydrogen bonds, one at a time, without a major departure from an overall helical conformation. This accounts for all the chemical shift and ~N relaxation findings indicating that the region exists largely in a helical conformation on both the relaxation and chemical shift time-scales, and for the finding that the intrinsic exchange rate calculated from the model does not correspond to the well-known random coil value: if the open state is only partially open, the proton in the broken hydrogen bond need not be freely exposed to the solvent and will show a slower intrinsic exchange rate. This leads to a picture of the DE helix-turn-helix consisting of two helices whose hydrogen bonds are broken half of the time (or half the hydrogen bonds are broken at any given time), but which retain their helical conformation all of the time. The picture is consistent with the finding that one is observing the superposition of two states that do not differ in chemical shift. Normall)4 one might expect significant differences in the chemical shift of the closed and open states for the hydrogen-bonded proton and its surroundings. This difference would reflect largely the configuration of the surroundings, since the hydrogen bond shift itself will not be very different in a hydrogen bond within the structure and a hydrogen bond to the solvent. If the overall helical configuration is preserved, only a small change in chemical shifts will be expected. No

624

Amide Proton Exchange in trp Repressor

k3

C-

kintrinsic

ks

,,- D _

-E_

k6

k4

-

H20

k'inmnsic

Scheme 2. Three-state model.

experimental finding to date contradicts this interpretation. It should be noted, however, that the interpretation is not unique and that other, kinetically indistinguishable, models can be proposed that are equally consistent with the reported observations. The simplest of these is an extension of the LinderstromLang model to three states: a "locked" helical state (C) from which no exchange is possible, in slow equilibrium (50%-50% population) with an " u n locked" helical state (D) that is in very rapid equilibrium with a truly open state (E), from which exchange with the solvent is free (Scheme 2). This model requires no differences in the intrinsic exchange rates, but explains the observed reduction in intrinsic exchange rate by the mass action effect of the'(very fast) helix-coil equilibrium, with k~..... >> k,.r..... so that the helical form predominates. Thus (k,,,n.,~.~) observed = k,w.,/kc,,,~, x (k,,,~.,~,.) calculated. The model is otherwise equally consistent with all chemical shift and ~N relaxation data that point toward a p r e d o m i n a n c e of the helical conformation as the two-state model requiring a restricted open state. The assumption of very rapid exchange b e t w e e n the D and E species in fact reduces the three-state model to the original two-state model with two changes in interpretation: (1) the apparent closing rate is slowed d o w n by (x, and (2) the apparent intrinsic exchange rate is slowed clown b y (1 - c 0 , w h e r e c~ is defined as [D]/([D] + [E]) (Scheme 3). In relation to the three state model (Scheme 2), state A is now state C, state B is the average of states D and E, k, is k3, k2 is c~k4,and k~,, is (1 - 00km,~,,,~. With this model, we expect the same magnetization r e c o v e r y / p H profiles as before and can derive the p a r a m e t e r s in exactly the same way. Only the interpretation of the calculated p a r a m e t e r s is different. Regardless of the model applied, we see that the DNA-binding region is actually quite structured and stable on the nanosecond time-scale, though unstable on a millisecond/second time-scale. Also, regardless of the model adopted, the reported results have an important consequence for the s t u d y of a m i d e proton exchange. It is c o m m o n l y a s s u m e d that the local unfolding of helices occurs simply by hydrogen bond breakage implicit

kl

](eft

k2

k'intrinsic

A

Scheme 3. Modified two-state model.

-

H20

in the simple Linderstrom-Lang model (Englander & Kallenbach, 1984). It is also c o m m o n to use the values of the intrinsic exchange rate calculated from the Molday rules (Bai et al., 1993). However, if the modified two-state model (Scheme 3) is correct, then the intrinsic exchange rate observed in proteins can be m u c h smaller than that found in peptides and peptide analogs. The effect of this is that closing rates calculated f r o m d e u t e r i u m exchange experiments m u s t b e treated only as an u p p e r limit and not as a precise estimate (Pedersen et al., 1993). If the three-state m o d e l (Scheme 2) is correct, the Molday rules are still valid, but the model implies that a m i d e proton exchange occurs through three processes instead of two and the interpretation of exchange data m u s t be modified accordingly. The functional significance of this relative instability m a y be inferred from the finding of Z h a n g et al. (1994) on the structure of the repressor-operator complex. It was found there that m o r e extensive conformational adjustments occur in the DE region u p o n complex formation with D N A than the simple relocation of the helix-turn helix observed in both the crystal and solution structures u p o n binding of the corepressor tryptophan. The relative instability of the D and E helices could p r o m o t e the additional adjustments.

Materials and Methods

Sample preparation [UJ~N]trp repressor was isolated from E. coli strain CY15070 carrying the pJPR2 plasmid (Paluh & Yanovsk)~ 1986). The strain was grown on M9 minimal medium (Maniatis et al., 1982) containing 1 g of ~NH4C1 (99 atom% '~N, Isotec Inc.)/l as the sole nitrogen source, 10 g of unlabeled R-D-glucose/l and 200 mg of ampicillin/1. Cells were grown at 37°C to an A~7..of -0.5 at which time the production of trp repressor was induced with the addition of 1 mM isopropyl-~-D-thiogalactopyranoside (final concentration), trp repressor was extracted from the cells after a further ten hours growth essentially as described by Paluh & Yanofsky (1986). A yield of 160 mg of aporepressor was obtained from 4 1 of medium. The protein was transferred to the NMR buffer (500 mM NaC1, 50 mM NaH2PO4, pH 7) by repeated concentration and dilution into the buffer using an Amicon stirred pressure cell with a PM10 membrane, and finally concentrated to 5.14 mM monomer. The protein concentration was determined by A2~, using an extinction coefficient of 1.2 cm-' mg -~ ml (Joachimiak et al., 1983). The aporepressor was converted to the holo-form by adding a threefold molar excess of L-tryptophan, divided into five samples and the pH of each adjusted with 1 to 5pl increments of 1 M HC1 or I M NaOH with rapid stirring to prevent denaturation. The samples were then frozen, lyophilized and stored at - 6°C until use, when they were reconstituted to a 90% H20/10% 2H20 solution. Samples were heated to 60°C for five minutes to equilibrate the more slowly exchanging amide protons to the solvent and finally centrifuged before use. The sample prepared at pH 7.6 was prepared independently of the others, and had a concentration of 4.78 mM monomer.

Amide Proton Exchange in trp Repressor

NMR spectroscopy 1H-'~N HMQC spectra were recorded at 11.74 T on a Bruker AM-500. Data were acquired into 1024 data points in t2 (512 real) and into 200 points (all real) in t.. Quadrature detection was achieved using time-proportional phase incrementation (Marion & Wiithrich, 1983). The spectral width was 6493.5 Hz in t2 and 3012.1 Hz in the indirectly detected dimension, with 96 transients recorded for each of the 200 t~ experiments. Waltz-16 decoupling was used to decouple '~N during the acquisition period (Shaka et al., 1983). Water suppression was carried out using jumpreturn pulses (Plateau & Gueron, 1982) in all experiments, but in half of the experiments a presaturating pulse was also used at a power level of 35L, both during a constant presaturation delay of 2.5 seconds and also during the variable delay period. Inversion recovery profiles were obtained by recording a series of nine two-dimensional HMQC spectra with delays of 2.5, 2, 1, 0.5, 0.2, 0.1, 0.075, 0.050 and 0.025 seconds, except at pH 7.6 when eight delays (2.5, 1, 0.5, 0.2, 0.1, 0.05, 0.02 and 0.01 seconds) were used. At pH 5.1, 6.1, 7.2, 8.0 and 8.7 two inversion recovery experiments were carried out, one with presaturation and one without. At pH 7.6 only the recovery profiles without presaturation were measured; the presaturation factor was measured separately by recording two spectra, one with presaturation of the solvent, both using jump-return pulses and both using a 2.5 seconds relaxation delay between pulses. The pH of each sample was recorded before and after each experiment, and has not been corrected for the mole fraction of deuterium oxide present. The pH value reported is the average of the two readings. In most samples the pH varied less than 0.1 pH unit during the experiment; the exception is the sample at pH 8.7 which decreased 0.35 pH unit during the two week experiment. To ensure that the temperature of the experiments with and without solvent presaturation were identical (despite the high salt concentration present) the sample temperature was measured directly in an actual sample using a thermocouple installed in the NMR tube while the pulse sequences were tested. In each case, and for all delays used, the temperature was within 0.1°C of 43°C. All spectral processing was done on Silicon Graphics Iris Indigo workstation, using the FELIX NMR data processing package, version 2.0 developed by Hare Research. The residual water peak was removed by convolution of the signal, then the spectra were zero-filled to 1024 points in the proton dimension, linear predicted to 256 points and zero-filled to 512 points in the nitrogen dimension. The spectra were then apodized using a sine-bell squared window shifted by ~/2, Fourier transformed and phase and baseline corrected. Chemical shifts were measured relative to internal TSP in the proton dimension and relative to external ~NH4C1 (pH 0.6) in the nitrogen dimension.

Data fitting and error analysis Each relaxation profile without solvent presaturation was normalized such that the last data point acquired had a volume of 100. These data were used in a preliminary fitting to determine a rough estimation of the intrinsic exchange rate (k,,,r~,J. If the k~.,,~.c was small enough that the assumption that no exchange occurs at pH 5.0 is valid, the data acquired with solvent presaturation were normalized with reference to

625 the Mp~/Mo ratio at pH 5.0 to correct for spin diffusion effects. The data were fit to the relaxation equations using a non-linear least-squares algorithm implementing a combination of steepest descent and inverse Hessian methods (Press et al., 1989). This algorithm provides a measure of the standard error in the diagonal elements of the covarient matrix.

Theory The Linderstrom-Lang model of amide proton exchange (Berger & Linderstrom-Lang, 1957) assumes that each amide proton exchanges between two states, an open state and a closed state. Although in the most general (triangular) form of the model solvent exchange from either state is allowed, a common additional assumption is that the amide hydrogen atom can be replaced by a solvent proton if and only if it is in the open state (linear model, see Scheme 1). The classic interpretation of the closed state is that it is a hydrogen-bonded state and the open state is random-coil-like with the amide hydrogen atom freely exposed to the solvent (Hvidt & Nielsen, 1966; Englander & Mayne, 1992). This model has been applied most successfully in the analysis of deuterium exchange experiments. Amide proton exchange rates can be measured using NMR to monitor deuterium exchange only if the amide proton exchange lifetime (1/k,~) is at least one minute for one-dimensional experiments or at least ten minutes for two-dimensional experiments (rates of -1.7 x 10-2 Hz and 1.7 x 10-3 Hz, respectively). To a more limited extent, the model has also been used in the analysis of T1 relaxation. Krishna et al. (1979) have solved the modified Bloch equations for amide proton relaxation in the presence of Linderstrom-Lang exchange and have applied a simplified solution to the analysis of T, relaxation in several small peptides. The simplified equations apply when there is a rapid equilibrium between the open and closed states or if the amide exists predominantly in the open state. This case is in contrast to the case of proteins studied by deuterium exchange, where a preponderance of the closed state is usually found or assumed, and the opening rate is usually found to be slow. Spera et al. (1991) proposed a two-dimensional method for obtaining the amide proton exchange rates in proteins using saturation transfer techniques. In their method, two HMQC spectra are taken, one with solvent presaturation and one without. By comparing the ratio of peak intensities with and without presaturation, one is able to calculate the amide proton exchange rates for rapidly exchanging protons. The fast exchange approximation is implicit in both the treatment described by Krisha et al. (1979) and by Spera et al. (1991), and the applicability of their methods is restricted to this special case. In general, it is impossible to determine the opening and closing rates by either method. Here, we have combined the T~ relaxation approach of Krishna et al. (1979) and the two-dimensional saturation transfer approach of Spera et al. (1991), extending the combined approach to the study of the pH dependence of both the TI and the magnetization ratios. Study of the pH dependence is essential to cover a broad range of intrinsic exchange rates, which are known to be strongly pH-dependent (Englander & Mayne, 1992). The general theory necessary to this approach has been submitted for publication and only a brief synopsis is given here.

626

Amide Proton Exchange in trp Repressor

The modified Bloch equations for amide proton relaxation in the presence of exchange according to the Linderstrom-Lang model are as follows: dMA ~ _ R~A(Ma - M~ Q) - k,,I,...(M^) + l~1.~.(Ml~) dt

Acknowledgements

This research has been supported by NIH grants GM33385 and RR07558. M. R. G. was supported on NIH training grant GM08294. The authors thank Dr Jerzy Czaplicki for the work he contributed to this project and for inspiring the use of most of the techniques used.

dM, - RIo(MB - M E°') + k,,p,.,(Ma) - k,.,,~(MB) dt =

References - ki.,..~i.(M~) + k~,,,.i,,~i~(M.:o)

dM,~Odt.= - R,,:o(Mn:o - M,:o)eQ- k:.,,,i,~i,(MH~o) + ki..ri.~i¢(MB) where MA, MD, and M,2o are the average magnetizations of the protons in the closed state, in the open state, and when bound to water, respectively The superscript EQ refers to the equilibrium magnetization of the state in the absence of any solvent saturation. R~A, R~8 and R,~:o are the respective intrinsic relaxation rates of the three species, and the other four rate constants have the same interpretation as in the Linderstrom-Lang model. The general solutions of these equations are given in Table 1. We have found that the relaxation profile behaves in one of three ways. One, it may be single exponential and invariant with pH. This reflects the observation of the helical peak only and a slow kop,,. Conversel)~ the profile may be a single exponential with a pH-dependence. This reflects the observation of either the coil peak only or a rapid average of both the helix and coil peaks. These two can be distinguished from the magnitude of the observed k~,. Finall~ the third possibility is that the relaxation may be biphasic and pH-dependent. This occurs if the opening and closing rates are similar to each other and of the same order of magnitude as the relaxation rates of the two species.

Effects of spin diffusion Spin diffusion can cause errors in two ways: it can change the equilibrium magnetization and also the rate of relaxation. Changes to the equilibrium magnetization can be corrected for residues in which no amide proton exchange occurs at pH 5.1 by using the Mr~/Mo ratio observed at pH 5.1 as a constant scale factor. For residues in which amide proton exchange does occur at pH 5.1, the small effect of spin diffusion will be negligible compared with the dominating influence of exchange. The influence of cross-relaxation on the rate of relaxation can also be neglected (Z. Zheng (unpublished results), who has calculated theoretically the effect of spin diffusion on R~ using the known atomic coordinates available from the NMR structures). In addition to the theoretical arguments, we were able to compare the saturated and unsaturated profiles for residues in which the alpha proton is superimposed on the water resonance. If spin diffusion were to be significant, these protons should show the greatest effect. The effect was negligible, suggesting that the contribution of spin diffusion may be safely ignored.

Arrowsmith, C. H., Pachter, R., Altman, R. B., Iyer, S. B. & Jardetzk)~ O. (1990). Sequence-specific 'H NMR assignments and secondary structure in solution of Escherichia coli trp repressor. Biochemistry, 29, 6332-6341. Arrowsmith, C. H., Czaplicki, J., Iyer, S. B. & Jardetzky, O. (1991a). Unusual dynamic features of the trp repressor from Escherichia coli. J. Amer. Chem. Soc. 113, 4020-4022. Arrowsmith, C., Pachter, R., Altman, R. & Jardetzk~; O. (1991b). The solution structures of Escherichia coil trp repressor and trp aporepressor at an intermediate solution. Eur. J. Biodzem. 202, 53-66. Bai, Y., Milne, J. S., Mayne, L. & Englander, S. W. (1993). Primary structure effects on peptide group hydrogen exchange. Proteins: Struct. Funct. Genet. 17, 75-86. Berger, A. & Linderstrom-Lang, K. (1957). Deuterium exchange of poly-DLoalanine in aqueous solution. Arch. Biochem. Biophys. 69, 106-118. Czaplicki, J., Arrowsmith, C. & Jardetzk); O. (1991). Segmental differences in the stability of the trp-repressor peptide backbone. J. Biomol. N M R , 1, 349-361. Englander, S. W. & Kellenbach, N. R. (1984). Hydrogen exchange and structural dynamics of proteins and nucleic acids. Quart. Rev. Biophys. 16, 521-655. Englander, S. W. & Mayne, L. (1992). Protein folding studied using hydrogen-exchange labeling and two-dimensional NMR. Annu. Rev. Biophys. Biomol. Struct. 21, 243-265. Hvidt, A. & Nielsen, S. O. (1966). Hydrogen exchange in proteins. Advan. Protein Chem. 21, 287-386. Jardetzk~ O. & Roberts, G. C. K. (1981). Relaxation in multispin systems: spin diffusion. In N M R in Molecular Biology, pp. 60-68, Academic Press, Inc., New York, NY. Joachimiak, A., Kelle~ R. L., Gunsalus, R. P., Yanofsk)~ C. & Sigler, P. B. (1983). Purification and characterization of trp aporepressor. Proc. Nat. Acad. Sci., U.S.A. 80, 668--672. Krishna, N. R., Huang, D. H., Glickson, J. D., Rowan, R., III & Walter, R. (1979). Amide hydrogen exchange rates of peptides in H20 solution by 1H nuclear magnetic resonance transfer of solvent saturation method. Biophys. ]. 26, 345-366. Maniatis, T., Fritsch, E. F. & Sambrook, J. (1982). Propagation and maintenance of bacterial strains and viruses: media and antibiotics. In Molecular Cloning: A Laboratory Manual. pp. 55-73, Cold Spring Harbor Laborator~ Cold Spring Harbor, NY. Marion, D. & WLithrich, K. (1983). Application of phase-sensitive correlated spectroscopy for measurement of proton-proton spin-spin coupling constants in proteins. Biochem. Biophys. Res. Commun. 113, 967-974.

Amide Proton Exchange in trp Repressor

McConnell, H. (1958). Reaction rates by nuclear magnetic resonance. J. Chem. Phys. 28, 430-431. Paluh, J. L. & Yanofsk34C. (1986). High level production and rapid purification of the E. coli trp repressor. Nuct. Acids Res. 14, 7851-7860. Pedersen, T. G, Thomsen, N. K., Andersen, K. V., Madsen, J. C. & Poulsen, F. M. (1993). Determination of the rate constants kl and k2 of the Linderstrom-Lang model for protein amide hydrogen exchange. J. Mol. Biol. 230, 651-660. Plateau, P. & Gu6ron, M. (1982). Exchangeable proton NMR without baseline distortion, using new strongpulse sequences. J. Amer. Chem. Soc. 104, 7310-7311. Press, W. H., Flanner~ B. P., Teukolsk~ S. A. & Vetterling, W. T. (1989). Numerical Recipes, Cambridge University Press, Cambridge. Rosevear, P. R., Fr~ D. C. & Mildvan, A. S. (1985). Temperature dependence of the longitudinal relaxation rates and exchange rates of the amide protons in peptide substrates of protein kinase. J. Magn. Reson. 61, 102-115. Schevitz, R. W., Otwinowski, Z., Joachimiak, A., Lawson, C. L. & Sigler, P. B. (1985). The three-dimensional structure of trp repressor. Nature (London), 317, 782-786.

627 Shaka, A. J., Keeler, J. & Freeman, R. (1983). Evaluation of a new broadband decoupling sequence: WALTZ-16. J. Magn. Reson. 53, 313-340. Spera, S., Ikura, M. & Bax, A. (1991). Measurement of the exchange rate of rapidly exchanging amide protons: application to the study of calmodulin and its complex with a myosin light chain kinase fragment. J. Biomol. NMR, 1, 155--165. Zhang, H., Zhao, D., Revington, M., Lee, W., Jia, X., Arrowshmith, C. & Jardetzk34 O. (1994). The solution structures of the trp repressor-operator DNA complex. ]. Mol. Biol. 238, 592-614. Zhang, R.-G., Joachimiak, A., Lawson, C. L., Schevitz, R. W., Otwinowski, Z. & Sigler, P. B. (1987). The crystal structure of trp aporepressor at 1.8 A shows how binding tryptophan enhances DNA affinity. Nature (London), 327, 591-597. Zhao, D., Arrowsmith, C. H., Jia, X. & Jardetzk~ O. (1993). Refined solution structures of the Escherichia coli trp holo- and aporepressor. J. MoL Biol. 229, 735-746. Zheng, Z., Czaplicki, J. & Jardetzk~ O. (1995). Backbone dynamics of trp repressor studied by 15N NMR relaxation. Biochemistry, in the press.

Edited by R. Huber (Received 16 August 1994; accepted 21 November 1994)