5898
J. Phys. Chem. B 2008, 112, 5898-5904
An Improved 15N Relaxation Dispersion Experiment for the Measurement of Millisecond Time-Scale Dynamics in Proteins† D. Flemming Hansen, Pramodh Vallurupalli, and Lewis E. Kay* Departments of Medical Genetics, Biochemistry, and Chemistry, The UniVersity of Toronto, Toronto, Ontario, Canada, M5S 1A8 ReceiVed: June 20, 2007; In Final Form: August 15, 2007
A new 15N constant-time relaxation dispersion pulse scheme for the quantification of millisecond time-scale exchange dynamics in proteins is presented. The experiment differs from previously developed sequences in that it includes 1H continuous-wave decoupling during the 15N Carr-Purcell-Meiboom-Gill (CPMG) pulse train that significantly improves the relaxation properties of 15N magnetization, leading to sensitivity gains in experiments. Moreover, it is shown that inclusion of an additional 15N 1800 refocusing pulse (phase cycled (x) in the center of the CPMG pulse train, consisting of 15N 1800y pulses, provides compensation for pulse imperfections beyond the normal CPMG scheme. Relative to existing relaxation-compensated constant-time relaxation dispersion pulse schemes, νCPMG values that are only half as large can be employed, offering increased sensitivity to slow time-scale exchange processes. The robustness of the methodology is illustrated with applications involving a pair of proteins: an SH3 domain that does not show millisecond time-scale exchange and an FF domain with significant chemical exchange contributions.
It has long been recognized that solution NMR spectroscopy is a powerful probe of molecular dynamics over a wide range of time scales.1-4 In the case of applications involving proteins, early pioneering experiments by Snyder, Rowan, and Sykes,5 Wu¨thrich and Wagner,6 as well as Dobson, Moore, and Williams7 foreshadowed the important role that NMR would play. These authors studied the positions and intensities of peaks in one-dimensional (1D) 1H NMR spectra of aromatic residues in globular proteins as a function of temperature, and found compelling evidence for the rotation of bulky aromatic side chains within the hydrophobic core. Results of this sort established unequivocally that proteins are in fact dynamic over a spectrum of time scales, and, in the past 30 years since their publication, increasingly sophisticated NMR methodology has evolved8-10 that has significantly enhanced our understanding of the relation between motion and function in this important class of biomolecule. Among the most useful of relaxation experiments are those that probe microsecond-millisecond time-scale dynamics in proteins because information about ‘excited states’ that cannot be directly observed in NMR spectra can often be obtained.11,12 In the Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion class of experiment, which forms the basis of what will be discussed here, the transverse relaxation rate, R2,eff, of a spin probe is monitored as a function of the number of refocusing pulses applied in a fixed time.13,14 From fits of the appropriate model of exchange to the resulting relaxation profile, the rates of exchange and the populations of the exchanging states can be quantified and chemical shift differences between states can be determined, leading to structural insights.15 Although the CPMG experiment was originally proposed many years ago16,17 and used in 1D NMR studies that focused on isolated spins as †
Part of the “Attila Szabo Festschrift”. * Corresponding author. Address: 1 King’s College Circle, Toronto, ON, M5S 1A8, Canada. Phone: +1 (416) 978-0741. Fax: +1 (416) 978-6885. E-mail:
[email protected].
probes,18 there have been some very significant improvements in the recent past that have facilitated its more general use as a site-specific tool in the study of protein dynamics.13,19 One of the major problems that emerges in applications to complex biomolecules, such as proteins, is spectral resolution, and the need for higher dimensionality NMR is therefore critical. Thus, one-bond coupled 1H-15N or 1H-13C spin pairs are employed so that high-sensitivity two-dimensional (2D) correlation maps can be recorded. Although this circumvents to some extent the issue of resolution, and greatly improves sensitivity in heteronuclear applications, a problem emerges. The large one-bond heteronuclear coupling leads to an “exchange” of magnetization between in-phase and anti-phase during the CPMG pulse train that is quite distinct from the chemical exchange process that is to be quantified. Because in-phase and anti-phase magnetization components relax at rates that can be quite different in macromolecules, R2,eff becomes dependent on the rate of application of CPMG refocusing pulses purely from evolution due to scalar coupling. Separation of this effect from the exchange process of interest is thus critical. Loria et al. have devised an elegant approach that ensures that magnetization resides as in-phase and anti-phase for equal periods of time during the CPMG pulse train so that the effective intrinsic relaxation time becomes independent of pulse rate.13 In this way robust measures of chemical exchange can be obtained. Since the important paper of Loria et al. where the technical difficulties associated with the measurements were surmounted,13 many applications have emerged that focus on a wide range of biological problems.15,20-24 Most studies make use of 15N relaxation dispersion CPMG methods since it is easy to prepare uniformly 15N labeled proteins and since the 1H-15N data sets that quantify exchange are of high sensitivity and resolution. With this in mind we have revisited the 15N CPMG dispersion experiment and present a new version with improved signal-to-noise and improved sensitivity to slow exchange processes. An application to the wild-type (wt)-Fyn SH3 domain,
10.1021/jp074793o CCC: $40.75 © 2008 American Chemical Society Published on Web 00/00/0000
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Figure 1. Pulse scheme of the 15N constant-time relaxation dispersion experiment for measuring millisecond time-scale dynamics in proteins with 1H CW decoupling during the CPMG element (CW CPMG). For comparison, the constant-time relaxation-compensated (RC CPMG) experiment is shown as well, which has been described in detail previously.14 All 1H and 15N 90° (180°) rf pulses are shown as narrow (wide) black bars and are applied at the highest possible power levels, with the exception of the 15N refocusing pulses of the CPMG element, along with the 90° sandwiching pulses that are applied at a slightly lower power level (∼ 6 kHz). The 1H 180° pulse of the P element (RC CPMG) is applied as a composite pulse.33 The shaped 90° 1H pulses are water-selective and make use of the EBURP1 profile34 (7 ms; first selective pulse) or are rectangular in shape (∼1.6 ms; other selective pulses). A 1H spin-lock is applied at a field strength of approximately 15 kHz (ωSL/2π) during the CPMG period (SLx); the exact field strength varies slightly (∼10%) for different values of N, as described in the text (N can be any integer for the CW CPMG sequence and even for the RC CPMG scheme). To keep the heating effects constant, a spin-lock element is applied immediately after acquisition for N ) 0 (in the CW CPMG scheme and for all RC CPMG experiments). 15N decoupling during acquisition is achieved with a 1.3 kHz WALTZ16 scheme.35 All pulse phases are assumed to be x, unless indicated otherwise. In the CW CPMG scheme, the 1H carrier is placed on the water signal and moved to the middle of the amide region at the end of the first equilibration (τeq) period and subsequently returned to the water frequency at the start of the second equilibration period (point e). The 1H 180° pulse applied simultaneously with the 15N pulse of phase φ3 refocuses the evolution of water magnetization (note that the 1H carrier is off-resonance at this point), leading to the placement of water magnetization along the +Z axis at the end of the pulse scheme. The phase cycling used is: φ1 ) 2{y},2{-y}; φ2 ) {x,-x}; φ3 ) 2{x},2{-x}; φ4 ) 2{-y},2{y}; φ5 ) 4{y},4{-y}; φ6 ) x; and receiver ) 2{x,-x},2{-x,x} for the CW scheme, and φ2 ) {x,-x}; φ5 ) 2{y},2{-y}; φ6 ) x; and receiver ) x,-x,-x,x for the RC scheme (see ref 14 for more details). The delays used are τa ) 2.25 ms, τb ) 1/(4JNH) ) 2.68 ms, τeq ) (2-3)/(kex) ∼ 5 ms, χ ) 1/ωSL - (4/π)pw, ζ ) pwn - (2/π)pw, where pw (pwn) is the 1H (15N) high power 90° pulse width, and ∆ ) 0.5 ms. A value of Trelax is chosen such that the signal is reduced by approximately a factor of 2 relative to Trelax ) 0, as described previously.28 Gradient strengths (G/cm; length in ms) are g0 ) 5.0(1.0), g1 ) 4.0(0.5), g2 ) -6.0(1.0), g3 ) 18.0(0.5), g4 ) 9.0(0.5), g5 ) 15.0(0.8), g6 ) 0.5(t1/2), g7 ) 15(1.1), g8 ) 3.5(0.4), g9 ) 2.5(0.3), and g10 ) 29.4(0.11); gradients g7 and g10 are used for coherence selection and should be optimized to obtain the maximum signal. Quadrature detection in the indirect dimension is obtained using the sensitivity enhancement approach36,37 by recording two sets of spectra with (φ6,g10) and (φ6+π,-g10) for each t1 increment. The phase φ5 is incremented along with the receiver by 180° for each complex t1 point.38
a small protein that lacks exchange on the millisecond time scale, is presented to verify the methodology, followed by studies of the FF domain from the human protein HYPA/FBP11 that shows pervasive chemical exchange on the millisecond time scale. Materials and Methods NMR Samples. Both 15N-labeled wt-Fyn SH3 and FF domain (from the human protein HYPA/FBP11) samples were expressed and purified as described previously.25,26 A wt-Fyn SH3 sample that was 1.0 mM protein, 50 mM sodium phosphate, 0.05% NaN3, 0.2 mM EDTA, pH 7, and 90% H2O/10% D2O was employed along with a 1.0 mM FF domain sample, 50 mM sodium acetate, 100 mM NaCl, 0.05% NaN3, 0.2 mM EDTA, pH 5.7, and 90% H2O/10% D2O. NMR Experiments. 15N relaxation dispersion experiments were recorded on the wt-Fyn SH3 domain, 800 MHz (1H frequency), 20 °C, using (i) the CPMG scheme that includes 1H decoupling (Figure 1, continuous-wave (CW) CPMG) and (ii) the relaxation-compensated13 sequence14 (Figure 1, RC CPMG). Both odd and even numbers of spin echoes (N of Figure o 1) were recorded on each side of the 180φ3 pulse (CW CPMG)
or P element (RC CPMG). Each relaxation dispersion profile was composed of 21 points, Trelax ) 30 ms, with νCPMG values (see below) ranging from 33.3 to 1000 Hz. A pair of duplicate points was obtained for error analysis, as described previously.15 Each 2D data set, corresponding to one νCPMG value, was recorded with acquisition times of (36, 64) ms in (t1, t2) and a pre-scan delay of 2.5 s, giving rise to a net acquisition time of 0.9 h. 15N relaxation dispersion profiles were obtained for the FF domain (25 °C) at static magnetic field strengths of 500 and 800 MHz (1H frequency), using both the CW and RC CPMG schemes. Only even values of N were employed. Sixteen νCPMG values ranging from 66.6 to 1000 Hz were obtained (Trelax ) 30 ms), along with three duplicate points for error analysis. Data sets were recorded with acquisition times of (41,64) ms in (t1,t2), along with a pre-scan delay of 2.5 s for a net acquisition time of 0.9 h/spectrum (800 MHz; similar parameters for the 500 MHz data sets). An important consideration in the experimental design is that the amount of sample heating be the same for each value of N. For the 1H CW CPMG experiment (N ) 0), a 1H CW element (duration of Trelax) is placed immediately after the acquisition
5900 J. Phys. Chem. B, Vol. 112, No. 19, 2008 period, as shown in Figure 1, ensuring that this is the case. Moreover, in comparing data sets recorded with both the CW and RC CPMG schemes, the same effective sample temperature must be used. This is accomplished by inserting a CW element immediately after acquisition in the RC CPMG experiment at the same power level and for the same duration as used in the CW CPMG scheme. The extent of heating is evaluated by comparing a pair of 1D data sets obtained where the first spectrum is recorded immediately after steady-state has been achieved for the CPMG experiment (16-32 scans). The movement in peak positions between the two 1D spectra provides an accurate measure of the temperature change (since a plot of peak movement with temperature can be constructed a priori). In the case of the FF domain sample considered here (50 mM sodium acetate, 100 mM NaCl), an increase in temperature of 0.7 °C for Trelax ) 30 ms (800 MHz) is noted for both RC (with the CW element, as described above) and CW CPMG schemes. We also found for both CPMG experiments a temperature increase of 0.6 °C in a study of an SH3 domain that employed Trelax ) 20 ms (at 800 MHz); the sample was dissolved in buffer comprising 100 mM NaCl and 50 mM sodium phosphate. Of course, in any temperature-dependent study, the sample heating could be easily compensated by a concomitant decrease in the setting of the variable temperature unit (this was done here). Data Analysis. All NMR spectra were processed and analyzed using the NMRPipe/NMRDraw27 suite of programs and associated software. Values of R2,eff have been calculated for each CPMG frequency as described below and in detail in previous publications.28,29 In the case of the FF domain, exchange parameters were extracted from fits of a two-site exchange model to dispersion data using home-written software that is available upon request. Results and Discussion NMR Methodology. Figure 1 shows the 1H-decoupled 15N CPMG-based relaxation dispersion pulse scheme (denoted CW CPMG) that has been developed for quantifying millisecond time-scale exchange processes in proteins. The basic sequence is similar to the RC13 constant-time CPMG experiment14 that was developed earlier, shown in Figure 1 for comparison (RC CPMG), with a number of significant improvements that are highlighted below. The initial portion of the scheme, between points a and b, transfers magnetization from 1H to 15N via a refocused INEPT,30 with the magnetization of interest residing along the z-axis at point b. During the subsequent delay, τeq, the magnetization of each exchanging state is restored to its equilibrium level, prior to the start of the CPMG pulse train. This can be accomplished in the case of a two-site exchanging kA
system A {\} B, for example, by choosing τeq ∼ 2-3/kex, kB
where kex ) kA + kB. In this manner, the populations of states A (pA) and B (pB) at the start of the CPMG train correspond to their equilibrium values, independent of differential relaxation between the states that might manifest during the INEPT transfers between points a and b. In order to preserve water magnetization, and hence enhance the sensitivity of the resulting spectra,31 a scheme is used (between points b and c) that we have discussed previously for aligning magnetization prior to a spin-locking element.32 Thus, immediately prior to the application of the 1H CW decoupling field that is operative during the constant-time CPMG relaxation element, Trelax, between points c and d, the water magnetization is placed along its effective field, given by the vector sum of the 1H CW spin-lock field
Hansen et al. (along x) and the effective Zeeman field in the rotating frame (along z). After the CPMG pulse train, the water magnetization is returned to the z-axis via the scheme between points d and e. Subsequently, 15N chemical shift evolution is recorded during incremented delay t1, and magnetization is transferred to amide protons for detection. In this manner, a series of 2D spectra are recorded as a function of the spacing between the centers of successive 15N 180° refocusing pulses, δ ) 2τcp + 2pwn, where 2pwn is the 15N 180° pulse width and νCPMG ) 1/(2δ). Peak intensities are converted into effective relaxation rates14 via R2,eff(νCPMG) ) -1/Trelax‚ln(I1(νCPMG)/I0), where I0 is the peak intensity in a reference spectrum recorded without the relaxation delay Trelax. In order to minimize errors in measured R2,eff(νCPMG) values, it is important that the strength of the 1H CW decoupling field during Trelax be chosen with care. An understanding of how this is achieved can be obtained by first thinking about the 1H CW decoupling element as a series of 180° back-to-back pulses. So that magnetization transfer between the scalar coupled 1H and 15N spins does not occur for any ν CPMG value, it is important that an integral number of such pulses be applied39 for each τcp + pwn. This is achieved by choosing the CW decoupling field strength, νCW, such that νCW ) 2kνCPMG, where k is an integer, and, as we have shown previously39 and will show below, robust dispersion profiles can be obtained using this approach. The selection of νCW in this manner means that values of the 1H decoupling field will, of course, vary for each νCPMG value. Typically, an average νCW field of between 12 and 15 kHz is chosen, and the variability in νCW as a function of νCPMG is small, on the order of 10%. The CW decoupling scheme described above ensures that 15N magnetization remains in-phase during the complete Trelax interval, SX, (15N ) S) with an effective decay rate of R2,IP. By contrast, in the RC scheme, the effective relaxation rate of transverse 15N magnetization is given by13 1/2(R2,IP + R2,AP), where R2,AP is the decay of 2SXIZ (1H ) I). Such anti-phase magnetization can relax very efficiently due to spin-flips between spin I and adjacent proton spins. When this occurs, R2,AP > R2,IP, and it is clear that the 1H decoupled scheme is preferred since the relaxation losses during the constant-time relaxation interval are smaller, leading to sensitivity gains (see below). Alternatively, the smaller intrinsic relaxation rates of in-phase magnetization can be “put to use” to monitor slower exchange processes than are otherwise possible since larger values of Trelax can be chosen. There is yet another important advantage of the new experiment that has to do with the self-compensatory nature of radio frequency (rf) pulse imperfections during the CPMG scheme between points c and d. This is described in what follows, where we have explicitly neglected relaxation and chemical exchange contributions since none of these impact the point that we wish to make, and we have assumed that the 1H CW field completely suppresses evolution due to the I-S scalar coupling (see above), although this is not necessary. It is straightforward to show that, under this set of conditions, the evolution of the magnetization operator O ˆ p during the CPMG pulse train is given by
Rˆ O ˆ pRˆ -1
(1)
ˆ Rˆ ) K ˆ exp(-iπ Sˆ X)K
(2)
where
and
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J. Phys. Chem. B, Vol. 112, No. 19, 2008 5901
K ˆ ) {exp(-i∆Sˆ ZτCP) exp(-i(ω1Sˆ Y + ∆Sˆ Z)τp) ×
It follows that
exp(-i∆Sˆ ZτCP)} (3) N
In eqs 1-3, ∆Sˆ Z is the 15N Zeeman Hamiltonian where ∆ (rad/ sec) is the offset of spin S from the rf carrier in the rotating frame, ω1 is the 15N rf field strength (rad/sec), and τp is the duration of each refocusing pulse of the CPMG train. In the analysis below, we have also neglected pulse imperfections in o the 15N 180φ3 pulse (φ3 ) x) in the center of the CPMG train, Figure 1, but imperfections are not neglected for the pulses that make up the individual CPMG elements. Experimentally, o pulse can be compensated to a large imperfections in the 180φ3 extent by the phase cycle φ3 ) (x (see legend to Figure 1). It can be shown that
ˆ exp(iπSˆ X) exp(-iπSˆ X) ) Rˆ ) K ˆ exp(-iπSˆ X)K exp(-iπSˆ X) (4) since
ˆ exp(iπSˆ X) ) K ˆ -1 exp(-iπSˆ X)K
(5)
ˆ p exp(iπSˆ X) Rˆ O ˆ pRˆ -1 ) exp(-iπSˆ X)O
(6)
Hence,
Equation 6 shows that chemical shift evolution (and, it turns out, evolution due to 1H-15N scalar coupling also, were it to be present) is refocused, even in the presence of pulse imperfections during the CPMG element. This follows directly from the 15N o pulse (φ3 ) x) in the middle of the CPMG train 180φ3 (Y-pulses). That this is the case has been verified both in a series of simulations and by experiment using a sample that does not have millisecond time-scale exchange (see below). It is noteworthy that the total number of spin-echoes in the scheme of Figure 1, 2N, is even, but that there is no requirement as to whether an even or odd number of echoes proceed/follow the central refocusing pulse. Thus, the minimum νCPMG value is 1/Trelax. It is worth considering how pulse imperfections manifest in the case of the relaxation compensation scheme that has been used previously14 (RC CPMG of Figure 1). In this case, and with the same set of assumptions as above, evolution during Trelax can be written as
Rˆ O ˆ pRˆ -1
(7)
Rˆ ) K ˆ ′Pˆ exp(- iπ/2Sˆ Z)K ˆ ′ exp(iπ/2Sˆ Z)
It is convenient to write O ˆ p ) 2Sˆ YˆIZ, that describes the state of the magnetization at the start of the CPMG train, in terms of the individual I spin states, O ˆ p ) 2Sˆ YˆIZ ) 1/2{Sˆ Y(1ˆ + 2IˆZ) Sˆ Y(1ˆ - 2IˆZ)}, and subsequently consider how each of the two terms evolves independently (eq 7). We first note that, for O ˆ p,1 ) 1/2{Sˆ Y(1ˆ - 2IˆZ)},
K ˆ ′ exp(iπ/2Sˆ Z)O ˆ p,1 ×
(8)
)
(13)
where the appropriate multiplicative factors associated with each of the three terms on the right-hand side of eq 13 that account for pulse imperfections have been neglected, as has the factor of 1/2 in O ˆ p,1. That is, S pulse imperfections and evolution during the CPMG train will lead to the interconversion of {Sˆ X(1 - 2IˆZ), Sˆ Y(1 - 2IˆZ), Sˆ Z(1 - 2IˆZ)}. A similar equation holds for O ˆ p,2 ) 1/2{Sˆ Y(1ˆ + 2IˆZ)}. In order to simplify eq 12, it is useful to consider the following relations:
(
)
Sˆ X(1ˆ - 2IˆZ) Pˆ exp(-iπ/2Sˆ Z) Sˆ Y(1ˆ - 2IˆZ) exp(iπ/2Sˆ Z)Pˆ -1 ) Sˆ Z(1ˆ - 2IˆZ) Sˆ X(1ˆ - 2IˆZ) exp(-iπ(IˆY + Sˆ Y)) Sˆ Y(1ˆ - 2IˆZ) exp(iπ(IˆY + Sˆ Y)) (14.1) Sˆ Z(1ˆ - 2IˆZ)
(
(
)
)
Sˆ X(1ˆ + 2IˆZ) Pˆ exp(-iπ/2Sˆ Z) Sˆ Y(1ˆ + 2IˆZ) exp(iπ/2Sˆ Z)Pˆ -1 ) Sˆ Z(1ˆ + 2IˆZ) Sˆ X(1ˆ + 2IˆZ) exp(- iπ(IˆX + Sˆ X)) Sˆ Y(1ˆ + 2IˆZ) exp(iπ(IˆX + Sˆ X)) (14.2) Sˆ Z(1ˆ + 2IˆZ)
(
)
where τb ) 1/(4|JHN|) and JHN < 0 in Pˆ . In eq 14, it is understood that the equality holds separately for each element {Sˆ X(1ˆ ( 2IˆZ), Sˆ Y(1ˆ ( 2IˆZ), Sˆ Z(1ˆ ( 2IˆZ)}. Substituting eq 12 into Rˆ O ˆ p,1Rˆ -1 and making use of the relations in eqs 13-14.1, we obtain
ˆ ′ exp(iπ/2Sˆ Z) Rˆ ) K ˆ ′ exp(-iπ(IˆY + Sˆ Y))K
(15)
Rˆ ) K ˆ ′K ˆ ′′ exp(-iπ(IˆY + Sˆ Y)) exp(iπ/2Sˆ Z)
(16)
Finally,
and
K ˆ ) {exp(- i(2πJHNˆIZSˆ Z + ∆Sˆ Z)τCP) exp(- i(ω1Sˆ Y +
(
Sˆ X(1ˆ - 2IˆZ) ˆ ′)-1 f Sˆ Y(1ˆ - 2IˆZ) exp(-iπ/2Sˆ Z)(K Sˆ Z(1ˆ - 2IˆZ)
where
Rˆ ) K ˆ ′Pˆ K ˆ
(12)
where
∆Sˆ Z)τp) exp(- i(2πJHNˆIZSˆ Z + ∆Sˆ Z)τCP)} (9) N
K ˆ ′ ) {exp(- i(2πJHNˆIZSˆ Z + ∆Sˆ Z)τCP) exp(- i(ω1Sˆ X + ∆Sˆ Z)τp) exp(- i(2πJHNˆIZSˆ Z + ∆Sˆ Z)τCP)}N (10) Pˆ ) exp(- i(2πJHNˆIZSˆ Z + ∆Sˆ Z)τb) exp(- iπSˆ X) × exp(- iπIˆX) exp(- i(2πJHNˆIZSˆ Z + ∆Sˆ Z)τb) (11) In eqs 9-11, 2πJHNˆIZSˆ Z is the scalar coupling Hamiltonian connecting spins I and S, and JHN is the scalar coupling constant.
K ˆ ′′ ) {exp(-i(2πJHNˆIZSˆ Z - ∆Sˆ Z)τCP) exp(i(ω1Sˆ X + ∆Sˆ Z)τp) exp(-i(2πJHNˆIZSˆ Z - ∆Sˆ Z)τCP)}N (17) A similar relation, describing the evolution of O ˆ p,2, can be generated upon substitution of eq 14.2 for eq 14.1 above; the evolution of O ˆ p is subsequently obtained by summing the result for O ˆ p,1 and O ˆ p,2. Because K ˆ ′K ˆ ′′ * 1ˆ (eq 16), it is clear that evolution due to chemical shift and/or scalar couplings is not completely refocused (even in the absence of chemical exchange) in the general case of pulse imperfections during the
5902 J. Phys. Chem. B, Vol. 112, No. 19, 2008 CPMG train, in contrast to the CPMG scheme with 1H CW decoupling, presented above. With this in mind, it is necessary to choose an even number of spin-echoes on either side of the P element (Figure 1), as has been described previously,13 that has been shown to largely suppress imperfections.16,17 Thus, the minimal νCPMG value that can be used is 2/Trelax, twice as large as that of the CPMG scheme that employs 1H CW decoupling. Therefore, the new dispersion sequence is more sensitive to slow exchange events, both because of the improved relaxation characteristics during the CPMG pulse train and because smaller νCPMG values can be selected. As a final note, it is worth mentioning that, if the P element were modified by inclusion of an additional 1H 180° pulse at the end, eq 16 becomes Rˆ ) exp(-iπSˆ Y)exp(iπ/2Sˆ Z) for O ˆ p,1, and hence evolution due to chemical shift and I-S scalar coupling is refocused, even in the presence of pulse imperfections. This “modified” P element was proposed by Palmer and co-workers in their design of a TROSY-based 15N relaxation dispersion experiment.19 It is thus possible to record such experiments with any integral number of echoes on either side of the P element, halving the minimum νCPMG frequency that can be employed relative to the case where only even echoes are used. By contrast, evolution is not refocused for O ˆ p,2 unless the P element is modified yet again, by changing the phase of the 15N 180° pulse from X to Y. Interestingly, it is thus not possible to “refocus” pulse imperfections associated with TROSY and anti-TROSY magnetization components simultaneously. This will be discussed in more detail elsewhere. Experimental Verification. In order to establish that the relaxation dispersion experiment of Figure 1 with 1H CW decoupling during the CPMG train provides a robust measure of exchange, we have first recorded dispersion profiles on the wt-Fyn SH3 domain that does not show exchange on the millisecond time-scale. From the discussion above, flat dispersion profiles are expected, independent of whether the number o of spin-echoes, N, applied on either side of the 15N 180φ3 pulse in the middle of the CPMG train is odd or even. By contrast, on the basis of previous studies, flat dispersion profiles are expected for the RC scheme as long as an even number of spin echoes are employed before and after the P element.13 Figure 2 presents typical dispersion profiles recorded on the wt-Fyn SH3 domain, 800 MHz, using the CPMG dispersion experiment with 1H CW decoupling (experimental data points shown with squares), along with the corresponding profiles generated from the RC scheme14 (circles). The data points in blue are R2,eff(νCPMG) values generated from CPMG pulse trains with an odd number of spin echoes on each side of the central 15N 18 o pulse or P element, while points in red denote R2,eff values 0φ3 generated with an even number of echoes. The chemical shift displacement (in ppm) of each cross-peak, from which the dispersion profiles are derived, relative to the 15N carrier, is listed in the upper right-hand side of each plot. As expected, flat profiles are obtained for the 1H CW scheme, independent of whether N is odd or even, even for large displacements from the carrier. The situation is quite different for the dispersions measured using the RC scheme. Although flat profiles are obtained for even N, it is clear that odd values lead to elevated R2,eff rates for low νCPMG values. It is possible to quantify how “flat” the profiles are by calculating the pairwise root-meansquare deviation, rmsd ) xND-1∑i{Ri2,eff(νCPMG,i)-k}2, where Ri2,eff is the effective transverse relaxation rate at CPMG frequency VCPMG,i, k ) 〈R2,eff(νCPMG)〉, and ND is the number of data points in the dispersion profile. For the 53 correlations that were examined in the wt-Fyn SH3 domain, rmsd ) 0.12
Hansen et al.
Figure 2. Comparison of 15N relaxation dispersion profiles recorded using the CPMG scheme with 1H CW decoupling (squares) and using the RC (circles) experiment,14 both illustrated in Figure 1. Profiles were measured at a spectrometer field of 800 MHz (1H frequency), 20 °C, on a sample of the wt-Fyn SH3 domain that does not show exchange on the millisecond time-scale. Both odd (blue) and even (red) numbers o of spin echoes are recorded on each side of the central 15N 180φ3 pulse or P element, as described in the text. The offset of the correlation from which the dispersion profile was derived, relative to the 15N carrier, is listed in the upper right-hand side of each panel.
( 0.06 s-1 and 0.11 ( 0.06 s-1 (mean ( 1 standard deviation), calculated from dispersion profiles composed of either both “odd” and “even” points (0.12) or just “even” points (0.11) that were generated with the 1H CW decoupling scheme. The corresponding values for the RC experiment are 0.40 ( 0.21 s-1 and 0.19 ( 0.11 s-1, which largely reflect the substantial rmsd’s that are obtained from dispersion curves derived from spins with large offsets from the 15N carrier. A second striking feature of the comparison illustrated in Figure 2 is that the intrinsic relaxation rates, R2,eff(νCPMG ) ∞), are notably different between the two methods, as expected from the discussion above. This difference translates into a noticeable sensitivity gain in dispersion spectra obtained with 1H CW decoupling during the CPMG element, even for the wt-Fyn SH3 domain that tumbles with a small correlation time under the conditions of the experiments (6.8 ns, 20 °C). For a constanttime relaxation delay of Trelax ) 30 ms, a relative sensitivity gain of 10.5 ( 2.5% (53 profiles quantified) is obtained on average, with individual values ranging from 6% to 17%. As a second control, we have recorded relaxation dispersion profiles on the FF domain from the human protein HYPA/ FBP11. In this example, large dispersion profiles are obtained for many of the residues in the protein that can be well fit to a kA
} B. The extracted values global two-site exchange model, A {\ kB of kex () kA + kB), pB, and the per-residue differences in chemical shifts between states A and B, |∆ω j |, that are obtained from fits of profiles recorded using the two approaches of Figure 1 have been compared. Values of (kex, pB) ) (1960 ( 24 s-1,1.56 ( 0.03%) and (2155 ( 39 s-1,1.53 ( 0.03%) are obtained for the 1H CW decoupled and the RC experiments, respectively, from separate fits of the 22 residues for which |∆ω j|
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Figure 4. Correlation between 15N chemical shift differences, |∆ω j |, obtained from global fits of RC14 (Y axis) and 1H CW decoupled CPMG (X axis) data sets with (kex,pB) values fixed to (1960 ( 24 s-1,1.56 ( 0.03%) in both fits or allowed to vary freely (inset). The line y ) x is shown. The coefficient of linear correlation, R ) σxy/(σyyσxx) is shown, where σνµ ) ∑(νi - 〈ν〉)(µi - 〈µ〉)/ND and ND is the number of points, along with δ, the systematic deviation from y ) x, δ ) ∑(yi - xi)/xi.
Figure 3. Comparison of selected relaxation dispersion profiles recorded on the FF domain, 25 °C, at 800 (top) and 500 MHz (bottom) using the 1H CW decoupled CPMG (left) and RC CPMG14 (right) pulse schemes. Shown in solid lines are the independent global two-state fits of each data set, along with the obtained chemical shift differences (ppm) between each of the exchanging states.
> 1 ppm. When the RC data set is fit using pB and |∆ω j | values from the 1H CW decoupled experiment, a best fit kex value of 2015 ( 30 s-1 is extracted that agrees even more closely with kex ) 1960 ( 24 s-1 obtained from the 1H CW scheme (with little increase in reduced χ2 of the fit). It is important to reemphasize that the RC experiment included 1H CW decoupling for a duration of Trelax immediately after signal acquisition to equalize the amount of heating in each of the two experiments that were compared (see Materials and Methods). Figure 3 shows a comparison of dispersion profiles for Ala 5, Asp 46, and Ala 64 that were recorded at 800 MHz (top) and 500 MHz (bottom) (25 °C) along with fits of the data (solid lines) that were generated from separate global analyses of all dispersion profiles from each of the two data sets. Only even values of N were recorded for each experiment. Values of |∆ω j | that are extracted for each residue are shown as well. As observed for the wt-Fyn SH3 domain, it is clear that the intrinsic 15N relaxation rates measured in the 1H CW decoupled experiment are lower, translating into an average sensitivity gain of 7.7 ( 2.9% (τC ) 5.2 ns at 25 °C), with minimum and maximum enhancements of 0 and 20%, respectively (Trelax ) 30 ms for each data set). Figure 4 shows a correlation plot of |∆ω j | values extracted from fits of RC (Y-axis) and 1H CW decoupled (X-axis) data sets where (kex,pB) were fixed to a common set of values, (1960 ( 24 s-1,1.56 ( 0.03%; see above) to ensure that any correlation between extracted values of pB and |∆ω j | does not lead to differences in extracted chemical shift values between separate data sets. Shown in the inset is the correlation plot obtained when (kex,pB) values were not fixed between profiles measured using the two schemes of Figure 1. The agreement between extracted values is excellent, again confirming that the dispersion experiment with 1H CW decoupling provides a robust measure of exchange. In summary, a new 15N relaxation dispersion pulse scheme is presented for the accurate measurement of chemical exchange
in proteins. The self-compensating nature of the CPMG element with respect to pulse imperfections, independent of whether the number of echoes, N, is odd or even, is described; such advantages are not obtained with the RC scheme. A series of experiments on a pair of proteins establishes that the CPMG element with 1H CW decoupling is robust. Modest gains in sensitivity relative to existing methodology are noted for the small proteins studied here, with potentially more significant gains for larger proteins. Because both odd and even values of N can be chosen, the minimum νCPMG value is half that in previous experiments, providing increased sensitivity to slow exchange processes. Alternatively, the same range of νCPMG values can be recorded with half the duration of Trelax, relative to the RC sequence,14 translating into substantial sensitivity gains in applications to proteins with large intrinsic relaxation rates. The CPMG relaxation dispersion scheme with 1H CW decoupling presented here is a significant improvement over the previous 15N constant-time dispersion method14 and, as such, will be a valuable addition to the growing family of experiments that quantify millisecond time-scale dynamic processes in proteins. Acknowledgment. This work is supported by a grant from the Canadian Institutes of Health Research (L.E.K). D.F.H. is the recipient of a postdoctoral fellowship from the Danish Agency for Science, Technology and Innovation (J. no. 27205-0232) and P.V. has a postdoctoral fellowship from a CIHR Training Grant on Protein Folding in Health and Disease. We thank Mr. Arash Zarrine-Afsar (University of Toronto) and Dr. Tomasz Religa (University of Cambridge) for preparation of the wt-Fyn and FF domain samples, respectively. L.E.K. holds a Canada Research Chair in Biochemistry. D.F.H. and P.V. contributed equally to this work. References and Notes (1) Palmer, A. G.; Williams, J.; McDermott, A. J. Phys. Chem. 1996, 100, 13293-13310. (2) Ishima, R.; Torchia, D. A. Nat. Struct. Biol. 2000, 7, 740-743. (3) Peng, J. W.; Wagner, G. Methods Enzymol. 1994, 239, 563-596. (4) Kay, L. E. Nat. Struct. Biol. NMR Supplement 1998, 5, 513-516. (5) Snyder, G. H.; Rowan, R., III; Sykes, B. D. Biochemistry 1976, 15, 2275-2283. (6) Wuthrich, K.; Wagner, G. Trends Biochem. Sci. 1978, 3, 227230. (7) Dobson, C. M.; Moore, G. R.; Williams, R. J. FEBS Lett. 1975, 51, 60-65. (8) Jarymowycz, V.; Stone, M. Chem. ReV. 2006, 106, 1624-1671.
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