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Department of Biochemistry and Molecular Biophysics, Columbia University, New York, New York 10032, USA
(RECEIVED June 13, 2006; FINAL REVISION September 12, 2006; ACCEPTED September 18, 2006)
| Abstract |
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-helices B and C. This Gly insertion is conserved among thermophilic RNases H, and allows the formation of additional intrahelical hydrogen bonds. A Gly residue inserted between
-helices B and C appears to relieve unfavorable interactions in the transition state and alternate conformer(s) and represents an important adaptation to adjust conformational changes within RNase H for activity at high temperatures. Keywords: nuclear magnetic resonance; ribonuclease H; protein dynamics; thermal stability
| Introduction |
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Ribonucleases H (RNases H, EC 3.1.26.4 [EC] ) from the mesophile Escherichia coli (ecRNH) and thermophile Thermus thermophilus (ttRNH) share significant amino acid sequence and structural similarity, but display differences in thermal stability and catalytic activity. Typical of other mesophilic and thermophilic proteins (Jaenicke and Böhm 1998; Kumar et al. 2001; Vieille and Zeikus 2001), ttRNH is more resistant to thermal (and chemical) denaturation (Kanaya and Itaya 1992; Hollien and Marqusee 1999a,b) and is significantly less catalytically active than ecRNH at mesophilic temperatures (Kanaya and Itaya 1992). One source for these differences may stem from altered dynamic properties between these enzymes: Several regions display localized differences in dynamics on the picosecond-to-nanosecond (psns) and microsecond-to-millisecond (µsms) time scales (Butterwick et al. 2004).
Chemical exchange line broadening is observed for nuclear spins in a highly basic loop between
-helices C (
C) and D, termed the handle (see Fig. 1), in both ecRNH and ttRNH (Mandel et al. 1995, 1996; Kroenke et al. 1998; Yamasaki et al. 1998; Butterwick et al. 2004), suggesting that µsms time scale conformational changes in this region are an integral property of both enzymes. Residues in
C and the handle are important for RNA:DNA hybrid recognition (Kanaya et al. 1991), although they are not essential for catalytic activity (Keck and Marqusee 1995). Nuclear magnetic resonance (NMR) spectroscopy and circular dichroism studies suggest that the handle changes conformation with respect to the catalytic domain upon complex formation (Oda et al. 1993; Iwai et al. 1996). The structural details of these transitions remain elusive; however, based on chemical shift changes upon RNA:DNA hybrid titration and models of the substrate-bound complex, residues between
B and
C have been suggested as a possible hinge in ecRNH (Oda et al. 1993). This region contains a single amino acid insertion in ttRNH relative to ecRNH: Gly85 is in a left-handed helical conformation (backbone dihedral angles
= 70° and
= 9°), and allows an additional hydrogen bond between the Gly85 carboxyl and Gly89 amide, forming the N-terminal cap of
C (Ishikawa et al. 1993d).
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relaxation dispersion experiments show that conformational changes within the handle of both enzymes occur with similar kinetic exchange rate constants at 300 K. Analysis of the relaxation dispersion suggests an altered thermodynamic equilibrium among exchanging conformers exists between ecRNH and ttRNH. Reciprocal Gly insertion/deletion mutations within the putative
B/
C hinge are used to probe the role of this residue in modulating conformational changes within RNases H. Insertion of Gly80b into ecRNH between Gln80 and Trp81 (iG80b) or deletion of Gly85 from ttRNH (dG85) significantly alters µsms time scale dynamic processes compared to the wild-type (WT) enzymes. 15N R 1
dispersion experiments suggest that the thermodynamic distribution observed for WT ttRNH is largely recapitulated in the iG80b ecRNH mutant. Thus, the Gly insertion represents an important contribution in the adaptation of conformational changes within RNase H for activity at high temperatures. | Results |
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B and
C is conserved in thermophilic RNases H. Furthermore, this insertion is largely absent from mesophilic sequences: Only RNase H enzymes from mesophiles Lactobacillus plantarum and Deinococcus radiodurans contain this insertion.
Structural and functional consequences of Gly insertion
Although the Gly insertion is conserved in thermophilic RNases H, insertion of Gly80b into ecRNH provides only a moderate increase in thermal stability of 0.1 kJ/mol (Kimura et al. 1992b). However, this insertion leads to a drastic decrease in catalytic efficiency, increasing the binding affinity by 50-fold and decreasing the catalytic rate constant (k cat) by 10-fold at 30°C (Ishikawa et al. 1993c), such that the activity of iG80b ecRNH is similar to the activity of ttRNH (Kanaya and Itaya 1992). Structurally, Gly80b is nicely accommodated between
B and
C, and adopts a similar left-handed helical conformation (
= 52°,
= 46°) as Gly85 in ttRNH (Fig. 1B). In addition to the expected N-terminal cap hydrogen bond between Gly80b and Asn84, another hydrogen bond is present between the Ile78 carboxyl and Gly80b amide forming the C-terminal cap of
B (Ishikawa et al. 1993c). The additional Gly also shifts the Gly77 carboxylIle82 amide hydrogen bond to Gly77Trp81. Given the minimal structural perturbations and marginal stabilization induced by the Gly80b insertion, the drastic decrease in activity may be due to modification of dynamic processes involving the substrate-binding handle.
Backbone amide 1H and 15N resonances for the iG80b ecRNH and dG85 ttRNH mutant enzymes were assigned by comparison to WT spectra complemented with an HMQC-NOESY-HSQC spectrum recorded at 300 K. Chemical shift differences between WT and mutant spectra are small outside the site of mutation, suggesting that insertion or removal of the Gly residue does not significantly alter the protein structure. In addition, NOESY cross-peaks are observed between backbone amide protons separated by one or two residues throughout both
B and
C, confirming the helical nature of these regions (data not shown). The largest 15N chemical shift differences between WT and iG80b ecRNH are for residues Thr79 and Ile82:
iG80b
WT = 4.94 ppm and 3.77 ppm, respectively. These shift changes are the correct sign and magnitude as expected for gain of a hydrogen bond involving the Ile78 carboxyl and switch of the hydrogen bond involving the Ile82 amide (Xu and Case 2002).
Interestingly, the equivalent residues also exhibit similar 15N chemical shift differences between WT and dG85 ttRNH, but with the opposite sign:
dG85
WT = 4.78 ppm for Thr83 and 3.89 ppm for Leu87. Chemical shift changes for residues in
B,
C and the handle between WT and mutant ecRNH and ttRNH are negatively correlated overall (Fig. 2A). Not only are the changes in chemical shift similar in magnitude for these proteins, but the iG80b ecRNH chemical shifts resemble WT ttRNH, and dG85 ttRNH shifts resemble WT ecRNH (Fig. 2B). Thus, the hydrogen bonding pattern and backbone geometry is similar between WT ttRNH and iG80b ecRNH and between WT ecRNH and dG85 ttRNH. These results are in slight disagreement with the crystal structure of WT ttRNH (Fig. 2C) (Ishikawa et al. 1993d): Based on chemical shift changes, hydrogen bonds would be expected between carboxyls of Phe82 and Gly77 and amides of Gly85 and Leu87. These interactions appear to be present in solution and slight packing rearrangements may prevent these hydrogen bonds from being recognized in the crystalline state.
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2.5 sec1): Lys60 in the
A/
4 loop and Trp90 in the handle (Mandel et al. 1995, 1996; Kroenke et al. 1998; Yamasaki et al. 1998). WT ttRNH is characterized by an increase in both the number of residues influenced by chemical exchange and the magnitude of R ex. Specifically, Lys80, Thr83, Gly85, and Trp86 surrounding the
B/
C hinge, Trp95 and Arg96 within the handle, and His124 and Val 126 in
5 have significant values of R ex at 300 K (Butterwick et al. 2004).
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B/
C hinge significantly alters chemical exchange line broadening. iG80b ecRNH shows an increase in both the number of residues influenced by chemical exchange line broadening and magnitude of R ex for residues within the handle and
B/
C hinge. In particular, Ile82, Arg88, Lys95, Lys99, and Asn100 show significant R ex not seen in the WT enzyme, while Trp90 shows a significant increase in R ex (over 10-fold). Relative to changes in the handle, chemical exchange for Lys60 is only moderately perturbed (decreased by 0.8-fold) in the iG80b ecRNH mutant. Conversely, dG85 ttRNH shows a significant decrease in R ex for residues in both the handle and
5. Specifically, residues near the Gly85 deletion no longer show significant R ex, and Trp95 in the handle and His124 and Val126 in
5 show decreased R ex, relative to the WT enzyme. Importantly, changes in R ex for both mutants are not localized solely to the site of mutation, but are distributed throughout the handle and other regions of the protein, suggesting that µsms time scale motions are highly coupled events that affect much of the enzyme.
Temperature dependence of chemical exchange
The temperature dependence of R ex provides information on the time scale and energetics of conformational transitions (Mandel et al. 1996; Evenäs et al. 1999; Butterwick et al. 2004). R ex measurements were repeated at temperatures between 285 K and 310 K for WT ecRNH and mutant RNases H; data for WT ttRNH have been reported previously (Butterwick et al. 2004). Values of R ex increase with decreasing temperature in both WT enzymes, indicating that chemical exchange is intermediate to fast on the chemical shift time scale (Fig. 4A; Mandel et al. 1996; Butterwick et al. 2004). In addition, although R ex is not a kinetic rate constant per se, the temperature dependence of R ex displays Arrhenius behavior over the temperature ranges studied, where the thermophilic enzyme is characterized by a larger "apparent" activation energy barrier (Ê a) (Fig. 4B; Butterwick et al. 2004). At T
290 K, Ile82 and Asn100 have significant R ex in WT ecRNH, but accurate Ê a could not be determined for these residues (see Materials and Methods).
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5 near the active site. Removal of Gly85 from ttRNH likely disrupts this connection, but leaves motion within the handle relatively unperturbed. Although the relatively large uncertainty in Ê a for dG85 ttRNH renders quantitative comparisons difficult, the similarity between Trp95 in WT and dG85 ttRNH suggests that interactions within the handle determine the kinetic and thermodynamic properties of motion. In contrast to the WT proteins, R ex for both mutants deviate from Arrhenius behavior at low temperatures; these data are not included in the determination of Ê a.
Relaxation dispersion of backbone amide nuclei
To further characterize the exchange kinetics within WT and mutant RNases H, backbone amide 15N R 2(
e) relaxation dispersion was measured at a temperature of 300 K for WT ecRNH, WT ttRNH, and iG80b ecRNH using R 1
spin relaxation techniques. The magnitude of exchange broadening in the dG85 ttRNH mutant is too small for accurate relaxation dispersion measurements (see Materials and Methods). All dispersion data are well described by a two-state exchange model
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characterized by a kinetic exchange rate constant k ex = k AB + k BA, where k AB and k BA are the forward and reverse rate constants between exchanging conformers A and B. On- and off-resonance R 1
experiments (Akke and Palmer 1996; Mulder et al. 1998; Massi et al. 2004) were combined to span effective fields of
e
102104 sec1 at static magnetic fields of 11.7 and 18.8 T. For all exchanging residues in WT ecRNH and ttRNH, R ex(
e) is barely suppressed at the highest
e obtained, such that k ex >> 104 sec1 for residues in both enzymes (Fig. 5; Table 2). In this regime, the individual forward and reverse rate constants and the thermodynamic and structural characteristics of the exchange process cannot be separated and only k ex and
ex = p A p B
2 can be determined, where p A and p B are the fractional populations of the conformers A and B, respectively (p A
p B), and 
is the chemical shift difference between exchanging conformers (Palmer 2004).
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e) could be quantified for Lys60 in the
D/
4 loop, and Trp90 and Asn100 in the handle. Residues in the handle were individually fit with similar k ex
40,00045,000 sec1; subsequent global analysis of these residues yielded k ex = (42 ± 8) x 103 sec1. In agreement with its reduced Ê a, Lys60 exhibited much faster kinetics with k ex = (100 ± 23) x 103 sec1. Surprisingly, residues in WT ttRNH exhibited very similar exchange kinetics to residues in WT ecRNH. Individual fits of residues Lys80, Phe82, Thr83, Gly85, Trp86, Gly89, and Trp90 near the
B/
C hinge and Trp95, Arg96 and Arg106 in the handle region were characterized by k ex
30,00050,000 sec1. Interestingly, residues His124 and Val126 in
5 were also individually fit with k ex
40,000 sec1, suggesting a common motional process affects residues in the handle and near the active site. In a similar manner for WT ecRNH, these residues could be globally described by k ex = (40 ± 4) x 103 sec1. Thus, the larger values of R ex for residues in WT ttRNH are due to approximately threefold larger
ex values and either the population distribution or chemical shift differences between the exchanging conformers are altered between the two enzymes.
In a similar manner to the WT enzymes, chemical exchange for all residues in iG80b ecRNH are fast on the chemical shift time scale (Fig. 5; Table 2). Residues in
C and the handle region were generally individually fit with slower kinetics than WT ecRNH with k ex
15,00040,000 sec1; subsequent global analysis of Trp81, Ile82, Arg88, Trp90, Thr92, Lys95, Lys99, and Asn100 yielded k ex = (27 ± 2) x 103 sec1. The reduced k ex does not completely account for the increased R ex relative to WT ecRNH, and residues in iG80b ecRNH are fit with approximately fourfold larger
ex. Relaxation dispersion for Lys60, however, yields k ex = (101 ± 30) x 103 sec1, which is identical within experimental uncertainties to the value obtained for WT ecRNH. Thus, reduced R ex for Lys60 in iG80b ecRNH compared to WT is due to an
0.8-fold reduction in
ex.
Interpreting chemical exchange effects
In the fast exchange regime, only k ex and
ex can be determined from relaxation dispersion measurements; consequently, the underlying energetics and chemical shift changes of the conformational transition cannot be determined. However, ratios of k ex and
ex provide information on the relative changes in the free energy difference between exchanging conformers (
G) and between transition states (
G
) for two proteins. Assuming that k AB and k BA are described by transition state theory, k AB = k oexp[
G
/RT] and k BA = k oexp[(
G
G)/RT], and that site populations follow a Boltzmann distribution, p B/p A = exp[
G/RT], then
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where the subscripts 1 and 2 represent the two proteins of interest, k o is the preexponential factor for k AB and k BA, R is the universal gas constant, and
G and
G
are the energy differences of the minor conformer and transition state relative to the major conformer, respectively, and 
G =
G 1
G 2 and 
G
=
G 1
G 2
. The second equalities in Equations 2 and 3 arise if p A p B
1 for either protein.
Given the small chemical shift changes between WT and iG80b ecRNH outside the site of mutation, the exchanging conformer structures probably are similar for both proteins, such that 
WT

iG80b. In this case, using R 1
results for Trp90 (
N,iG80b
N,WT = 0.41 ppm), 
G =
G iG80b
G WT = 3.6 ± 0.1 kJ/mol and 
G
=
G
iG80b
G
WT = 2.5 ± 0.5 kJ/mol at 300 K. Thus, insertion of Gly80b reduces the stability difference between exchanging conformers, increasing p B relative to WT ecRNH (Fig. 6). The decreased stability difference between conformers is slightly larger than the decrease in activation energy, leading to slower kinetics in the mutant enzyme. Virtually identical results are obtained with data from Asn100.
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probably are similar between these enzymes. Using R 1
results for Trp90 (ecRNH) and Trp95 (ttRNH) (
N,ttRNH
N,ecRNH = 1.03 ppm), yields 
G =
G WT,Tt
G WT,Ec = 2.7 ± 0.1 kJ/mol and 
G
=
G
WT,Tt
G
WT,Ec = 2.6 ± 0.6 kJ/mol at 300 K. Similar exchange kinetics are observed between WT enzymes because 
G

G
; however, the minor conformer is stabilized relative to the major conformer in the thermophilic enzyme leading to a larger p B (Fig. 6). Most surprisingly, the increase in transition state and minor conformer stabilities seen in WT ttRNH is similar to that conferred by the Gly80b insertion into ecRNH. | Discussion |
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A Gly insertion between
B and
C is conserved in thermophilic RNases H that utilize a handle region for RNA:DNA hybrid recognition, suggesting that this residue is important for biological function at high temperatures. This insertion is a focal point for additional intrahelical hydrogen bonds that marginally stabilize the protein. Chemical shifts surrounding this region are similar between WT ttRNH and iG80b ecRNH and between WT ecRNH and dG85 ttRNH, suggesting that interactions within the iG80b ecRNH mutant are more "thermophilic-like" while those in dG85 ttRNH are more "mesophilic-like." The similarity between WT ttRNH and iG80b ecRNH is further reflected in their reduced catalytic efficiencies relative to WT ecRNH (Kanaya and Itaya 1992; Ishikawa et al. 1993c). dG85 ttRNH, however, does not show significantly increased catalytic activity at low temperatures (to resemble WT ecRNH), possibly due to the uncoupling of conformational changes between the handle and
5 near the active site (J.A. Butterwick and A.G. Palmer III, unpubl.). Thus, while the crystallographic structures of WT ttRNH and iG80b ecRNH display slight differences, both proteins likely incorporate the same additional hydrogen bonds in solution, compared to WT ecRNH and dG85 ttRNH.
Currently, the structural details of alternative conformations sampled in solution and leading to chemical exchange line broadening are unknown. Differences in R ex between WT and mutant RNases H are spread throughout residues in
C and the handle, suggesting that conformational changes within these regions are highly coupled. Large R ex are not observed for most residues, indicating that 
are small and the local structure in
C and the handle is maintained. Because chemical exchange line broadening is not observed for residues Thr79, Gly80b and Asn84 in iG80b ecRNH, the additional hydrogen bonds most likely are maintained during conformational changes about this region. Residues Trp90 and Asn100 may serve as hinges for motions of the handle: Trp90 is the first and Asn100 is the last residue in the handle, both Trp90 and Asn100 show significant increase in R ex in the iG80b ecRNH mutant, and both Trp90 and Asn100 have left-handed helical backbone dihedral angles in the observed major conformation.
The hypothesis that chemical exchange reflects movement of the entire handle as a whole is supported by the dynamic properties of a thermostabilized ecRNH quintuple G23A/H62P/V74L/K95G/D134H mutant (Yamasaki et al. 1998). Mutation of the left-handed Lys95 to Gly is well accommodated within the handle of ecRNH (Ishikawa et al. 1993a) and significantly stabilizes the protein (Kimura et al. 1992a). While no global changes in dynamics were observed in the quintuple mutant compared to the WT protein, several residues surrounding the sites of mutation experienced a change in dynamics across multiple time scales. Interestingly, an increase in R ex was observed for residues Ile82, Trp90, Lys91, and Asn100 in the quintuple mutant (Yamasaki et al. 1998), although to a lesser extent than seen in iG80b ecRNH. Lys95 is 514 Å away from these residues, yet removal of its bulky side chain likely alters the thermodynamics or kinetics of structural transitions across the handle.
The remarkable similarity between the free energy profiles of iG80b ecRNH and WT ttRNH (Fig. 6) suggests that the Gly insertion plays a major role in modulating conformational dynamics of the handle region of RNase H. In iG80b ecRNH, both the transition and minor states are stabilized by a similar extent relative to WT ecRNH. Thus, the Gly insertion does not drastically alter the kinetic rate constants, but rather adjusts the thermodynamic equilibrium between conformers. Lacking a C
atom, Gly occupies approximately threefold more Ramachandran space compared to other amino acids. This structural plasticity appears to alleviate unfavorable interactions in the transition state and minor conformer(s) in RNase H.
For RNases H, the kinetics of the chemical exchange process are likely too fast to be rate limiting for enzymatic activity. Previous characterization of the WT proteins using a nonanucleotide hybrid substrate at 30°C yielded k cat
1.5 and 0.3 sec1 for WT ecRNH and WT ttRNH, respectively (Kanaya et al. 1990; Kanaya and Itaya 1992). Given the current results, the lower limit for WT ecRNH is p B
1%, corresponding to k AB
400 sec1 and k BA
41,600 sec1, which are much faster than k cat. Thus, the altered thermodynamic distribution rather than changes in the kinetic rate constants afforded by the Gly insertion likely represents an important adaptation to fine tune conformational changes within RNase H for activity at high temperatures. The Gly80b insertion into ecRNH does not significantly stabilize the protein; thus, the mutant ecRNH enzyme is unfolded and inactive at the optimal temperature for activity in the wild-type thermophilic ttRNH enzyme (
343 K) (Kanaya and Itaya 1992). Additional amino acid substitutions, such as H62P and V74L (Kimura et al. 1992b; Ishikawa et al. 1993b), may be required to confer increased thermal stability in order for the effects of the Gly insertion to be seen at higher temperatures.
Insertion of Gly80b into ecRNH has few effects on the ground-state structure outside of the
B/
C hinge region and insignificantly affects overall thermodynamic stability, but renders the structure of the
B/
C hinge region and enzymatic activity more similar to the hinge structure and enzymatic activity observed for WT ttRNH (Ishikawa et al. 1993c). The crystallographically observed structures of apo WT ecRNH, WT ttRNH, and iG80b ecRNH are consistent with the dominant conformations observed in solution by NMR spectroscopy, but these structures appear incapable of productive interactions between the handle and substrate (Iwai et al. 1996). The present results demonstrate that the potential energy surface controlling µsms time scale transitions to alternate higher energy conformations also is more similar in iG80b ecRNH to WT ttRNH than WT ecRNH. These observations imply that enzymatic activity of RNases H depends upon the structures and energetics of the alternative conformations that are sampled at equilibrium in solution.
| Materials and methods |
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NMR spectroscopy
All NMR data were collected at Columbia University (11.7 and 14.1 T) or the New York Structural Biology Center (16.4 and 18.8 T). Data at static magnetic fields of 11.7 and 18.8 T were acquired on Bruker DRX500 and AV800, respectively, equipped with triple-resonance probes and three-axis gradients. Data at static magnetic fields of 14.1 and 16.4 T were acquired on Bruker DRX600 and AV700, respectively, equipped with triple-resonance cryoprobes with Z-axis gradients. For all experiments, the temperature was calibrated using a 100% (v/v) methanol standard (Cavanagh et al. 1996). Data processing and analysis were performed with NMRPipe (Delaglio et al. 1995) and Sparky (T.D. Goddard and D.G. Kneller, Sparky 3, University of California, San Francisco) software, along with in-house written programs.
Resonance assignments for mutant RNases H
Backbone 1H and 15N resonance assignments for iG80b ecRNH and dG85 ttRNH were determined by comparison with WT spectra supplemented by HMQC-NOESY-HSQC spectra (Cavanagh et al. 1996) acquired at a static magnetic field of 16.4 T and a temperature of 300 K. The spectra were recorded using with (t 1 x t 2 x t 3) 48 x 32 x 768 complex points and 2.857 x 2.857 x 10 kHz spectral widths. Assignments, referenced to internal DSS, have been deposited to the BioMagResBank (http://www.bmrb.wisc.edu) under accession codes 7277 (dG85 ttRNH) and 7278 (iG80b ecRNH).
Analysis of chemical exchange line broadening
For residues subject to chemical exchange line broadening, R 2 = R 2° + R ex, where R 2° is the intrinsic transverse relaxation rate constant which is sensitive to motion on the psns time scale and the protein size. A TROSY-based Hahn-echo sequence (Wang et al. 2003) was used to measure R 2° and R ex at a static magnetic field of 14.1 T and temperatures between 285 K and 310 K. This method uses the transverse 15N chemical shift anisotropy/1H15N dipolar interference rate constant (
xy) to determine R 2° = 
xy, where
is the trimmed mean R 2/
xy ratio for nonexchanging residues. Values of
were between 1.31 and 1.47 at all temperatures for all proteins. Analysis of the data with a weighted mean
= 1.40 does not significantly change the results. Relaxation data were collected in an interleaved manner with (t 1 x t 2) 150 x 1024 complex points and 2.5 x 10 kHz spectral widths. A minimum of four experiments were acquired at each temperature for each protein. The average and standard deviation were taken as the relaxation rate constant and uncertainty, respectively.
Apparent activation energies, Ê a, were determined from the temperature dependence of chemical exchange assuming an Arrhenius relationship for R ex:
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where
H
is the transition state enthalpy for the forward reaction and
H is the difference in enthalpy between the two exchanging states (Mandel et al. 1996; Evenäs et al. 1999; Butterwick et al. 2004). The second equality assumes that exchange is fast (k ex >> 
). For each residue, Ê a was determined from a linear fit of ln(R ex) versus 1/T using R ex data acquired at a minimum of three temperatures. At low temperatures, deviations from linearity may become apparent if the exchange kinetics slow to the intermediate regime (k ex

); these data are not included in the determination of Ê a.
R1
relaxation dispersion analysis
Chemical exchange line broadening is suppressed in the presence of an effective field,
e. In an R 1
experiment, magnetization is spin-locked parallel to
e by the application of a continuous radiofrequency (rf) field with frequency
rf and amplitude
1. The magnitude of the effective field is
e 2 =
1 2 + 
2, where 
=
o
rf is the observed resonance offset from the applied field. The relaxation rate constant, R 1
, for magnetization aligned parallel to
e is given by
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where R 1 is the longitudinal relaxation rate constant,
= arctan(
1/
) is the tilt angle of the effective field, and
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is the effective transverse relaxation constant where R ex(
e) is the residual R ex.
R 1 and on-resonance R 1
relaxation rate constants were measured at a temperature of 300 K and static magnetic fields of 11.7 and 18.8 T using relaxation time delays between 0 and 1.2 sec and 0 and 100 msec, respectively (Farrow et al. 1994; Massi et al. 2004). Seven to nine unique time points were sampled with three duplicates for estimation of the error in signal intensity. The relaxation rate constants were determined from the best single exponential fit to the data with the error estimated using a jackknife algorithm. Off-resonance R 1
relaxation rate constants were measured from pairs of interleaved spectra with relaxation delays of 2 msec and 60200 msec assuming a single exponential decay (Akke and Palmer 1996; Mulder et al. 1998); errors were estimated based on repeat experiments. For on-resonance experiments, magnetization was aligned using a free precession period of 1/
1 (Yamazaki et al. 1994; Massi et al. 2004), while off-resonance experiments utilized 10 msec tanh/tan adiabatic pulses each with a frequency sweep of 15 kHz (Mulder et al. 1998). For all R 1
experiments,
1 was calibrated using the residual scalar coupling in the presence and absence of the applied field (Palmer et al. 2001).
Analysis of relaxation dispersion data followed a similar protocol previously described (Grey et al. 2006). Initially, R 1 and R 1
relaxation data at both static magnetic fields along with R 2° and free precession R ex estimated from TROSY Hahn-echo experiments acquired at 11.7 and 18.8 T were analyzed on a per-residue basis using Equations 5 and 6. F-statistical testing (at
= 0.05 confidence level) was used to select the appropriate functional form for R ex(
e): either chemical exchange is not present, with R ex(
e) = 0; or exchange is fast on the chemical shift time scale (k ex >>
e), with
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Additional R ex(
e) models that include exchange outside the fast time scale regime (Trott and Palmer 2002), or a three-site exchange mechanism (Grey et al. 2003) did not significantly improve the fitted parameters. Optimization of R 1 and R 2° rate constants and
ex and k ex exchange parameters were accomplished with routines written in Mathematica (v4.1, Wolfram Research, Inc.) utilizing the Levenberg-Marquart algorithm. Off-resonance R 1
data were included only if 20°
65° while on-resonance R 1
data required 
|0.4
1/2
|. Residues characterized by similar k ex values by inspection were subsequently analyzed globally with a single k ex, maintaining individual
ex.
| Footnotes |
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Reprint requests to: Arthur G. Palmer III, Department of Biochemistry and Molecular Biophysics, Columbia University, 650 West 168 Street, Black Building 507, New York, NY 10032, USA; e-mail: agp6{at}columbia.edu; fax: (212) 305-6949.
Article published online ahead of print. Article and publication date are at http://www.proteinscience.org/cgi/doi/10.1110/ps.062398606.
| Acknowledgments |
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measurements and critical reviews of the manuscript. This work was supported by National Institutes of Health (NIH) Grant GM50291 (A.G.P.). A.G.P. is a member of the New York Structural Biology Center supported by NIH Grant GM66354. | References |
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