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J. Phys. Chem. B 2006, 110, 20664-20670
Analysis and Parametric Optimization of 1H Off-Resonance Relaxation NMR Experiments Designed to Map Polypeptide Self-Recognition and Other Noncovalent Interactions Julijana Milojevic, Veronica Esposito, Rahul Das, and Giuseppe Melacini* Departments of Chemistry, Biochemistry and Biomedical Sciences, McMaster UniVersity, 1280 Main Street West, Hamilton, Ontario, L8S 4M1, Canada ReceiVed: May 24, 2006; In Final Form: July 21, 2006
The measurement of 1H off-resonance nonselective relaxation rates (Rθ,ns) has been recently proposed as an effective method to probe peptide self-recognition, opening new perspectives in the understanding of the prefibrillization oligomerization processes in amylodogenesis. However, a full analysis and parametric optimization of the NMR experiments designed to measure Rθ,ns relaxation rates is still missing. Here we analyze the dependence of the Rθ,ns rates upon three critical parameters: the tilt angle of the effective field during the spin lock, the static magnetic field, and finally the repetition delay. Our analysis reveals that the tilt angle θ ) 35.5° not only minimizes spin-diffusion, but also avoids experimental artifacts such as J-transfer and poor adiabaticity. In addition, we found that when the dominant relaxation mechanism is caused by uncorrelated pairwise 1H dipole-1H dipole interactions the R35.5°,ns rate is not significantly affected by static field variations, suggesting a wide applicability of the 1H off-resonance nonselective relaxation experiment. Finally, we show that the self-recognition maps based on the comparative analysis of the R35.5°,ns rates can tolerate decreases in the interscan delays without significantly compromising the identification of critical self-association loci. These considerations not only provide a better understanding of the 1H off-resonance nonselective relaxation, but they also serve as guidelines for the optimal setup of this experiment.
Introduction We have recently proposed1 a nonselective off-resonance 1H relaxation NMR experiment (Figure 1) designed to map at residue resolution polypeptide self-recognition during the early stages of oligomerization. The proposed nonselective offresonance 1H relaxation NMR pulse sequence (Figure 1) is obtained from the well-established 1D-Watergate (Figure 1a) or 2D-TOCSY (Figure 1b) experiments2-5 inserting an adiabatic spin-lock6-9 between the interscan delay and the first 90° pulse of the 1D or 2D detection block (Figure 1). One of the most significant applications of these pulse sequences is to the growing class of amyloidogenic peptides related to several neurodegenerative diseases such as Alzhemier’s and Parkinson’s for which the reversible self-association preceding full fibrillization represents a promising target for early pharmacological treatment.10-15 Other NMR experiments such the CPMG pulse train designed to measure spin-spin (R2) relaxation rates and the selective R1 (R1,s) measurements can be used to probe selfrecognition16 because, when the main relaxation mechanism arises from 1H-1H dipolar-dipolar interactions, these rates are linearly proportional to the spectral density term evaluated at zero frequency, which in turn is linearly proportional to the correlation time (τc).16-20 However, the implementation of both CPMG and R1,s NMR measurements is experimentally challenging due to concurrent scalar coupling (J) evolution during CPMG sequences and to the necessary selectivity for R1,s experiments that limits their application only to small molecules and requires multiple measurements for multiple resolved protons. All these limitations are overcome by the proposed nonselective off-resonance 1H relaxation NMR experiment. The * To whom correspondence should be addressed. E-mail: melacin@ mcmaster.ca.
Figure 1. Pulse sequences for the measurement of nonselective offresonance relaxation rates with one- (a) and two-dimensional (b) detection. The phases, gradients, and other parameters for the pulse sequence in panel b are the same as those in Figure 2 of ref 1. For the 1D version of the experiment (i.e. panel a) φ1 ) (x)2(-x)2 and φrec ) (x)2(-x)2, while all the remaining parameters are as in panel b.
J evolution typical of the CPMG train is avoided by setting the relaxation spin-lock off-resonance6-9,21,22 and the selectivity requirements of R1,s experiments are effectively eliminated since the relaxation of all protons is monitored simultaneously in the proposed off-resonance experiment.1 The efficiency of the nonselective off-resonance 1H relaxation NMR experiment1 has been demonstrated by its application to the Aβ (12-28) peptide in acetate buffer (pH 4.7), which has been shown to be a good model for the early stages of the Aβ fibrillization.23 Specifically, the nonselective off-resonance 1H relaxation NMR measurement identified the 16 ( 1 to 22 ( 1 segment as the main site of self-recognition in agreement with
10.1021/jp063194z CCC: $33.50 © 2006 American Chemical Society Published on Web 09/23/2006
Mapping Polypeptide Self-Recognition previous mutagenesis studies.24,25 However, despite the promising potential of the nonselective off-resonance 1H relaxation NMR experiments for mapping prefibrillization equilibria a full analysis and parametric optimization of this pulse sequence is still not available. Here we focus on the analysis of the nonselective off-resonance 1H relaxation experiments with respect to three key parameters, i.e., the static magnetic field (Bo), the tilt angle (θ) of the effective field, and finally the interscan relaxation delay that precedes the spin-lock influencing the initial spin polarization state at the beginning of the offresonance relaxation. On the basis of these analyses we propose general guidelines for the optimal setup of this experiment. Materials and Methods 2D Nonselective Off-Resonance Experiments. All data were collected with an AV700 Bruker spectrometer operating at 700 MHz. Off-resonance relaxation data were acquired with use of the recently published nonselective off-resonance relaxation 2DTOCSY pulse sequence.1 The off-resonance spin lock with the trapezoidal shape including two adiabatic pulses of 4 ms duration was applied at the angle of 35.5° for 5, 23, 42, 60, and 80 ms. The relaxation delay between the end of the acquisition and the start of the first adiabatic pulse was 1 s. The strength of the off-resonance spin lock was 8.23 kHz. For the detection a 45 ms long DIPSI-2 pulse train with strength of 10 kHz was used. For each experiment 16 scans and 128 dummy scans were employed; two replicas were collected for each data set both for 1 mM Aβ (12-28) and for 0.1 mM Aβ (12-28). The spectral widths for both dimensions were 8389.26 Hz with 256 and 1024 t1 and t2 complex points, respectively. Water suppression was achieved through a Watergate scheme implemented with the binomial 3-9-19 pulse train.2 All 2D replica sets were added and processed with Xwinnmr (Bruker Inc.). The 2D cross-peak intensities were measured with Sparky 3.11126 by Gaussian line fitting and determination of fit heights.1 The fit heights error was estimated by calculating the standard deviation for the distribution of differences in intensities of identical peaks in duplicate spectra.27 After the addition of the replicate spectra the error was scaled up proportionally to the square root of the total number of scans. For residues [15-19], [21-24], and [26-28] the TOCSY HR,iHN,i cross-peaks were used for data analysis, whereas for the N-terminal residues V12 and H14, the HR,12-HMe,12 and the HR,14-Hβh,14 cross-peaks were used since the HR,i-HN,i crosspeaks were affected by the fast exchange with water. Similarly, the weak HR,20-HN,20 and the strong HR,26-HN,26 cross-peaks were partially overlapped and therefore required the use of the HR,20-Hβl,20 cross-peak as reporter of the signal decay during the off-resonance spin-lock. Due to the overlap of its degenerate HR protons, G25 was omitted from the analysis of the offresonance relaxation rates.1 The initial rates of decay were obtained through the program Curvefit28 that implements a Levenberg-Marquardt nonlinear least-squares exponential fitting of the fit height decay measured for each cross-peak. The related errors were obtained as previously published.1 The rates and errors obtained were normalized with respect to the largest measured rate and smoothed by an i,i+1 moving window.1 No averaging was possible for V12, V24, and K28 due the lack of data at the following residues and actual values were used. In all analyses the previously established assignment1,23 was employed. The off-resonance relaxation data with a relaxation delay of 2 s were measured previously.1 Nonselective T1 Measurements. Nonselective T1 values for the HR protons of Aβ (12-28) were estimated by using the
J. Phys. Chem. B, Vol. 110, No. 41, 2006 20665 inversion recovery (IR) experiment with delays of 100, 300, 450, and 600 ms and a relaxation delay of 4 s. For each experiment 16 scans and 128 dummy scans were collected. A composite (90x 180y 90x) pulse was employed for the nonselective inversion to minimize pulse imperfections. For the detection of the inversion recovery, a 2D-TOCSY was used and set up as the previous 2D-TOCSY employed as a detection block of the nonselective off-resonance measurements. Due to the long repetition delay necessary for inversion recovery experiments, the data acquisition for each IR point took on the average about 10-12 h. The data were processed with Xwinnmr (Bruker Inc.). The intensities of the TOCSY HR,i-HN,i cross-peaks were obtained with Sparky26 fit heights and were plotted as a function of the inversion recovery delay, τ. The estimated T1,ns,eff values fell in the 0.5-0.9 s range. Theoretical Treatment At first-order approximation, the decay of the magnetization of a generic spin i (IiZ) aligned along the off-resonance spinlock axis (OZ) is:
IiZ,∆t ) IiZ,0 +
( )
dIiZ ∆t dt 0
(1)
where IiZ,0 and IiZ,∆t are the values of IiZ at the start and at the end of the ∆t delay (Figure 1), respectively, and (dIiZ/dt)0 is the value of dIiZ/dt at the start of the ∆t delay. Assuming that the only nonnegligible relaxation mechanism arises from uncorrelated pairwise 1H dipole-dipole interactions and that contributions from chemical exchange are negligible because weak binding affinities (KD > high µM) such as those previously measured for the Aβ (12-28) peptide23,29 fall within the fast exchange regime,16 (dIiZ/dt)0 can be computed through the Solomon equations for the multitilted rotating frame of n homonuclear spins Ii:6-9
dIiZ
)-
dt
∑j Fij/IiZ - ∑j σij/IjZ + c∑j (Fij + σij)Ieq.
(2)
with
F′ij ) c2Fij + s2λij
(3)
σ′ij ) c2σij + s2µij
(4)
where j is any spin different from spin i, c ) cos(θ), s ) sin(θ) (where θ is the tilt angle, i.e., the angle formed by the longitudinal axis of the laboratory frame and the effective spinlock axis), Fij and σij are the laboratory frame rates of longitudinal direct and cross relaxation, respectively, while λij and µij are the rotating frame rates of transverse direct and cross relaxation, respectively. F′ij and σ′ij are the respective effective rates of direct and cross relaxation along the direction of the effective field and Ieq is the equilibrium magnetization of spin i. At the beginning of the ∆t delay, eq 2 becomes
( ) dIiZ dt
0
)-
∑j F′ijIiZ,0 - ∑j σ′ijIjZ,0 + c∑j (Fij + σij)Ieq
(5)
If the interscan delay is significantly longer than 1/R1,ns, then IiZ,0 = IjZ,0 = Ieq and eq 1 becomes
IiZ,∆t ) IiZ,0{1 - [
∑j F′ij + ∑j σ′ij - c∑j (Fij + σij)]∆t}
(6)
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This means that the initial rate of decay for spin i in the i ) is nonselective off-resonance experiment (defined as Rθ,ns i Rθ,ns )
∑j F′ij + σ′ij - c(Fij + σij)
(7)
Based on eqs 3 and 4, eq 7 can be recast as i ) (c - 1)c Rθ,ns
∑j (Fij + σij) + s2∑j (λij + µij)
(8a)
Considering that Ri1,ns ) ∑j(Fij + σij) and that Ri2 ) ∑j(λij + µij), eq 8a can in turn be rewritten as eq 8b:29,30 i Rθ,ns ) (c - 1)cRi1,ns + s2Ri2
(8b)
Both eqs 8a and 8b can be evaluated by using the spectral densities computed on the assumption that the relaxation is caused by the modulation of 1Hi-1Hj dipole-dipole interactions through isotropic Brownian rotations:31
Fij ) J(0) + 3J(ω0) + 6J(2ω0) σij ) -J(0) + 6J(2ω0) 9 5 λij ) J(0) + J(ω0) + 3J(2ω0) 2 2 µij ) 2J(0) + 3J(ω0)
information similar to that provided by a more experimentally challenging selective measurement.
(9)
with ωo being the proton Larmor frequency and J(ω) being the Lorentzian spectral density function:
J(ω) )
γH4h2
τc
40π rij 1 + ω2τc2 2
6
(10)
In eq 10 h is the Planck constant, γH is the proton gyromagnetic ratio, τc is the correlation time, and rij is the internuclear distance between protons i and j.16 In principle the θ values are in the range 0-90°. However, the θ ) 35.5° value is particularly interesting because when θ ) 35.5° the off-resonance spin-lock effective dipolar crossrelaxation rate approaches zero in the spin-diffusion limit (σ′ij = 0) due to NOE/ROE compensation (Figure 2b).1 As a result the cross-talk between spins with different nonselective offresonance relaxation rates is minimized. Furthermore, in the spin-diffusion limit Ri1,ns approaches zero as well (Figure 2a,b) and hence eq 7 simplifies to: i = R35.5°,ns
∑j F′ij
(in the spin-diffusion limit) (11)
Since the term on the right is the selective self-relaxation rate along the spin-lock field tilted at 35.5°, eq 11 can be recast as: i i = R35.5°,s R35.5°,ns
Figure 2. Static magnetic field (Bo) dependence of relaxation rates vs the correlation time (τc) for a model two-spin system where K ) p2γH4/ 10rij6. (a) τc dependence of the nonselective (R1,ns) and selective (R1,s) longitudinal relaxation rates as well as of the transverse relaxation rate for in-phase magnetization (R2) and of the nonselective off-resonance relaxation rate at the tilt angle θ ) 35.5° (R35.5°,ns) at different Bo fields. The proton Larmor frequencies are color coded as indicated in the two panels. (b) τc dependence of the self-relaxation (F′, dashed line), crossrelaxation (σ′, dot-dashed line), and equilibrium (-cos(35.5°)R1,ns, dotted line) components of R35.5°,ns (solid line) at different Bo fields.
(in the spin-diffusion limit) (12)
In other words, for θ ) 35.5° the nonselective off-resonance relaxation rate in the spin-diffusion limit does not differ significantly from the selective off-resonance self-relaxation rate. In conclusion, in the spin diffusion limit and when θ ) 35.5° an easily implementable nonselective NMR experiment offers
Results and Discussion On the basis of the theoretical framework described above we have analyzed how the static magnetic field (Bo), the effective field tilt angle (θ), and finally the interscan relaxation delay affect the nonselective off-resonance 1H relaxation rates i ). Given the importance of the 35.5° tilt angle as men(Rθ,ns tioned above, we will start the analysis assuming θ ) 35.5°. The Effect of the Static Magnetic Field Bo. The plots of the 1H relaxation rates R2, R1,s, R1,ns, and R35.5°,ns vs the logarithm of τc in seconds have been calculated at five static fields ranging from 300 to 700 MHz, using the model discussed above (Figure 2a). Figure 2a reveals that the effect of Bo on the τc dependence of the calculated 1H relaxation rates follows three distinct patterns in different τc regions. First, for low τc values (i.e., log (τc/s) < ca. -10) all 1H relaxation rates (i.e., R2, R1,s, R1,ns, and R35.5°,ns) are only minimally and almost negligibly dependent on Bo (Figure 2a). This result common to all the simulated 1H relaxation rates is explained by the previous model considering that all spectral densities are computed through eq 10 in which the Bo dependence is formalized by the (ωτc)2 term in the denominator. When log (τc/s) < ca. -10, then the (ωτc)2 term in eq 10 becomes less relevant in explaining the absence of significant Bo dependence at low τc values (Figure 2a). A similar quasi-Bo independent behavior is observed also at high τc values (i.e., log (τc/s) > ca. -8.5), however, with the exception of R1,ns, which is still significantly affected by Bo even for log (τc/ s) > ca. -8.5 (Figure 2a). This observation is accounted for by the previous model considering that the R2, R1,s, and R35.5°,ns rates but not the R1,ns rate contain a J(0) term that increases proportionally with τc and does not depend on the static field as indicated by eq 10 explaining the absence of significant Bo dependence at high τc values for R2, R1,s, and R35.5°,ns. On the contrary, Ri1,ns ) ∑j(Fij + σij) and therefore based on eq 9 does not depend on J(0) terms. In the other spectral density functions that define R1,ns the (ωτc)2 term in eq 10 introduces a significant
Mapping Polypeptide Self-Recognition
Figure 3. Plots of relaxation rates vs static magnetic field (Bo) for selected values of the correlation time τc. (a) Bo dependence of R1,ns, R1,s, R2, and R35.5°,ns relaxation rates at the τc values 10-9.25 and 10-8.5 s. The color and the solid/dashed line coding are as indicated in panel a. (b) Bo dependence of the components of the R35.5°,ns relaxation rate at the τc values 10-9.25 (red) and 10-8.5 s (black). The coding for solid, dashed, dotted, and dot-dashed lines is as explained for panel b of Figure 2.
Bo dependence on R1,ns due to the high τc values, accounting for the Bo effects on R1,ns observed at log (τc/s) > ca. -8.5 in Figure 2a. Finally, at intermediate τc values (i.e., ca. -10 e log (τc/s) e ca. -8.5) a third distinct pattern is seen (Figure 2a). Unlike the previous low and high τc regions, at -10 e log (τc/s) e ca. -8.5 all R2, R1,s, R1,ns, and R35.5°,ns relaxation rates are affected by Bo (Figure 2a). While for R2, R1,s, and R1,ns the Bo dependency is quite dramatic, for R35.5°,ns the effect of Bo is only minimal at intermediate τc values (Figures 2a and 3a,b). This unusual behavior specific of R35.5°,ns is explained by Figure 2b showing the dissection of R35.5°,ns in terms of self-relaxation (F′), crossrelaxation (σ′), and equilibrium (-cos(35.5°)R1,ns ) -c(Fij + σij)) components as indicated by eq 7. Inspection of Figure 2b reveals that the absolute values of all three R35.5°,ns components (i.e., F′, σ′, and cos(35.5°)R1,ns) increase at lower Bo. However, due to the negative sign of the equilibrium term in eq 7 the
J. Phys. Chem. B, Vol. 110, No. 41, 2006 20667 effect of Bo on F′ and σ′ is compensated by that on cos(35.5°)R1,ns explaining the marginal dependence of R35.5°,ns on Bo (Figure 2a,b). This compensatory mechanism explains also why the R35.5°,ns rates are minimally affected by Bo increases above 700 MHz, up to static fields of at least 900 MHz as seen in Figure 3 showing how R35.5°,ns depends on Bo at two representative τc values. As a result, for the remaining figures and related discussion we will assume a static field of 700 MHz. The Tilt Angle (θ) Dependence. The tilt angle (θ) defines the orientation with respect to the laboratory frame z-axis of the effective field generated by the off-resonance spin-lock. The effect of the tilt angle on the nonselective off-resonance i i ) is described by eq 8b, showing that Rθ,ns relaxation rates (Rθ,ns i results essentially from a linear combination of R1,ns and Ri2 with coefficients (c - 1)c and s2, respectively, where c ) cos(θ) and s ) sin(θ) with θ ranging in principle from 0° to 90°. If θ ) 0°, which corresponds to a negligible spin-lock strength i ) 0 (Figure relative to its offset, then eq 8b predicts that Rθ,ns 4a) consistently with the absence of significant perturbations caused by the spin-lock (Figure 1). If θ ) 90°, which corresponds to a negligible spin-lock offset relative to its i strength, then eq 8b predicts that Rθ,ns ) Ri2 (Figure 4a) consistently with the effective field being essentially in the xy i rate plane (Figure 1). As θ increases from 0° to 90°, the Rθ,ns increases monotonically from the τc independent zero value to i increments being more significant at lower θ Ri2, with the Rθ,ns values (Figure 4a). Among the θ angles in the 0-90° range, the θ value 35.5° is particularly interesting because, as mentioned above, at θ ) 35.5° and in the spin diffusion limit σ′ij = 0 (Figure 4b,c) due to NOE/ROE compensation thus minimizing the cross-talk between different spins during the relaxation. Furthermore, at θ ) 35.5° the nonselective and the selective off-resonance relaxation rates converge in the spin-diffusion limit (eq 12) (Figure 4b,c). Another tilt angle (θ) value at which the nonselective and the selective off-resonance relaxation rates are linearly proportional to each other in the spin-diffusion limit is θ ) 54.7°. At this θ value F′ij is equal to 2σ′ij independently of the correlation time τc.6-9 Therefore, considering again that in the spin-diffusion limit Ri1,ns is negligible as compared to the
Figure 4. Tilt angle (θ) dependence of the relaxation rates vs the correlation time (τc) for a model two-spin system at 700 MHz. (a) Plots of Rθ,ns vs τc for θ ranging from 0° to 90°. (b) τc dependence of the nonselective off-resonance relaxation rates at the tilt angles θ ) 35.5° (R35.5°,ns) and 54.7° (R54.7°,ns). For reference purposes the nonselective (R1,ns) and selective (R1,s) longitudinal relaxation rates as well as the transverse relaxation rate for in-phase magnetization (R2) are shown. (c) τc dependence of the self-relaxation (F′, dashed line), cross-relaxation (σ′, dot-dashed line), and equilibrium (-cos(35.5°)R1,ns, dotted line) components of Rθ,ns (solid line) at the tilt angles θ ) 35.5° and 54.7°. Other details are as in Figure 2. The data referring to θ ) 35.5° are included in panels b and c as well for the purpose of facilitating the comparison between θ ) 35.5° and 54.7°. The tilt angles are color coded as indicated in panels b and c.
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effective dipolar self-relaxation rate F′ij, eq 8 leads to: i R54.7°,ns = 1.5
∑j F′ij
(in the spin-diffusion limit) (13)
Since ∑jF′ij is the selective self-relaxation rate along the spinlock field tilted at 54.7°, we have: i i R54.7°,ns = 1.5R54.7°,s
(spin-diffusion limit)
(14)
as can also be seen in Figure 4c. In other words, in the spindiffusion limit the nonselective off-resonance relaxation rate is linearly related to the selective self-relaxation rate both for θ ) 35.5° and for θ ) 54.7° (Figure 4b,c). When θ ) 35.5° there is the added advantage that the effective cross-relaxation rate is negligible (σ′ij = 0), as mentioned above, thus minimizing the cross-talk between different spins that is particularly efficient in the spin-diffusion limit. When θ ) 54.7° the effective crossrelaxation rate is not negligible any more and the nonselective off-resonance relaxation at θ ) 54.7° is faster than that at θ ) 35.5° (Figure 4b,c), increasing the probability that the peaks generated by the NMR pulse sequences displayed in Figure 1 decay under the noise for long ∆t relaxation delays. This problem could be avoided by using very short ∆t delays; however, when the ∆t duration approaches that of the adiabatic pulses (Figure 1), the θ angle is ill defined. On the basis of these considerations, the 35.5° value for the tilt angle θ is still preferred to θ ) 54.7°. Values of the θ angle significantly higher than 54.7° are not recommended as J-transfer effects and poor adiabaticity may compromise the off-resonance experiments described in Figure 1. Values of the θ angle significantly lower than 35.5° are not advisable because at θ < 35.5° the sensitivity i of Rθ,ns to τc increases is only minimal and again the cross-talk between different relaxing spins is active. In conclusion, 35.5° is still the preferred optimal value for the tilt angle θ and the remaining part of the discussion will assume θ ) 35.5°. The Repetition Delay Dependence. The time between the first digitized point and the beginning of the trapezoidal spinlock in the pulse sequences of Figure 1 defines the interscan repetition delay denoted as Tc (i.e., Tc ) relaxation delay + acquisition time). The main effect of Tc is on the initial polarization at the start of the off-resonance relaxation spinlock (Figure 1). If Tc is significantly (i.e., ca. 5-fold) longer than the effective time constant for the longitudinal relaxation during the interscan delay (1/R1,ns,eff) then the initial polarization at the start of the off-resonance relaxation spin-lock is similar to its equilibrium value: IiZ,0 = IjZ,0 = Ieq as assumed before to derive eq 6 from eq 5. However, if Tc is reduced to speed up the nonselective off-resonance measurement then the IiZ,0 = IjZ,0 = Ieq assumption does not apply any more. A better approximation is:
IiZ,0 = IjZ,0 = Ieq
(15)
≈ 1 - e-TcR1,ns,eff
(16)
where:
based on the Ernst angle theory.5 As a result, eq 7 above has to be modified to: i ) ( Rθ,ns
∑j F′ij + σ′ij) - c(Fij + σij)
(17)
By using this equation the R35.5°,ns vs log(τc/s) plots were recomputed for three different scenarios corresponding to Tc )
Figure 5. Interscan delay (Tc) dependence of the relaxation rates vs the correlation time (τc) plots for a model two-spin system. (a) Three different representative scenarios for the interscan delay (Tc) dependence are shown and color coded as indicated in the figure. The τc dependence of the self-relaxation (F′), cross-relaxation (σ′), and equilibrium (-cos(35.5°)R1,ns) components of R35.5°,ns are reported for each scenario at a static field of 700 MHz. Other details are as in the figure describing the tilt angle dependence (Figure 4). The effective time constant for the longitudinal relaxation during the interscan delay is 1/R1,ns,eff. (b) Percent change of R35.5°,ns vs τc at 1/R1,ns,eff ) 0.5 (red) and 0.9 s (green) relative to the 1/R1,ns,eff , Tc scenario.
1.122 s and increasing values of 1/R1,ns,eff (i.e., 1/R1,ns,eff ) 0.5 s and 1/R1,ns,eff ) 0.9 s) (Figure 5a). These R1,ns,eff values are representative for the range spanned by the HR protons of the Aβ (12-28) peptide as indicated by our inversion recovery measurements. Figure 5a shows that in all three scenarios considered (1/R1,ns,eff , Tc; 1/R1,ns,eff ) 0.5 s; 1/R1,ns,eff ) 0.9 s) the R35.5°,ns rate is monotonically increasing with log(τc/s) when τc is greater than subnanosecond. In other words, it is possible that R35.5°,ns is still able to probe self-recognition even when the condition 1/R1,ns,eff , Tc is not fully fulfilled. Figure 5a also shows that as R1,ns,eff decreases a negative offset is introduced in the R35.5°,ns vs log(τc/s) plots. The main cause of the negative offset is the modulation of the ∑jF′ij + σ′ij term in eq 17 above by the factor < 1 in eq 16. If this negative offset is expressed in terms of percentage change relative to the reference case of 1/R1,ns,eff , Tc (Figure 5b), then the effect of decreasing R1,ns,eff rates is more significant at shorter τc values rather than when the spin diffusion limit is approached (Figure 5b). This is true for both scenarios with 1/R1,ns,eff ) 0.5 and 0.9 s (Figure 5b). However, as the 1/R1,ns,eff values increase the percentage change becomes more and more significant (Figure 5b). The theoretical predictions illustrated by Figure 5 are supported by the observed nonselective R35.5°,ns rates at Tc ) 1.122 s and by the comparison with the experimental R35.5°,ns rates at Tc ) 2.122 s (Figure 6). Figure 6a displays the plots of R35.5°,ns vs residue number measured at Tc ) 1.122 s for both 1 mM (circles) and 0.1 mM (squares) Aβ (12-28). The trend seen in both Figure 6a plots is similar to that previously observed for the R35.5°,ns measurements at Tc ) 2.122 s:1 at mM concentrations the oligomers in equilibrium with the monomer enhance the R35.5°,ns rates especially for the central hydrophobic core, which is known to be one of the key sites of Aβ self-recognition; at sub-mM concentrations the oligomers dissociate decreasing the R35.5°,ns rates to values that are to good approximation residue independent. These results are consistent with our theoretical prediction that even after reducing Tc the R35.5°,ns rates are still monotonically increasing with τc. In addition, the Figure 6a plot measured at 1 mM concentrations (circles) is not significantly
Mapping Polypeptide Self-Recognition
J. Phys. Chem. B, Vol. 110, No. 41, 2006 20669
Figure 6. Plot of the relative R35.5°,ns relaxation rates vs residue number in Aβ (12-28) with sequence H3N+-VHHQ15KLVFF20AEDVG25SNKCOO-. All rates were measured at 20 °C in 50 mM acetate-d4 buffer at pH 4.7 and at 700 MHz. (a) Relative relaxation rates acquired at 1 (circles) and 0.1 mM (squares) Aβ (12-28) concentrations with a 1.122 s interscan delay (Tc). (b) Difference between the relative R35.5°,ns relaxation rates of the 1 mM Aβ (12-28) sample acquired with 2.122 and 1.122 s interscan delays. (c) Difference between the relative R35.5°,ns relaxation rates of the 0.1 mM Aβ (12-28) sample acquired with the 2.122 and 1.122 s interscan delays. Solid and dashed lines indicate mean ( the standard error, respectively. (d) Refers to the difference between the two plots shown in panel a. The horizontal solid and dashed lines indicate the mean ( the standard error, respectively. All rates and the related errors were computed as previously explained.1
different from the related plot previously measured for longer Tc values (i.e., 2.122 s),1 as shown in Figure 6b. However, a different scenario is observed at 0.1 mM concentrations. In the dilute sample the variation of Tc from 1.122 to 2.122 s causes a significant change in the measured R35.5°,ns rates (Figure 6c). These observations are fully consistent with our simulations (Figure 5b) predicting that Tc variations affect more significantly the R35.5°,ns rates at lower τc values. The difference plot (Figure 6d) between the two sets of measurements at Tc ) 1.122 s (Figure 6a) is qualitatively similar to that previously observed at Tc ) 2.122 s.1 Both measurements of R35.5°,ns rates at Tc ) 1.122 and 2.122 s1 provide similar results for the identification of the residue segment responsible for selfrecognition: residues (16 ( 1, 22 ( 1) for Tc ) 2.122 s and residues (15 ( 1, 22 ( 1) for Tc ) 1.122 s (Figure d), which are within error from each other. We therefore conclude that decreases in the interscan repetition delays (Tc) do not necessarily lead to significantly different self-recognition maps. However, despite the time saving achieved by lowering the Tc value, at lower Tc values the signal-to-noise ratio obviously decreases and the probe and sample heating caused by the spinlock is less efficiently dissipated. Conclusions In summary, we have analyzed how the 1H off-resonance nonselective relaxation rates (Rθ,ns) depend on three key parameters: the tilt angle for the effective field during the off-
resonance spin-lock, the static magnetic field, and the interscan delay. We have found that the tilt angle θ ) 35.5° is optimal not only for the suppression of spin-diffusion effects but also for the preservation of good adiabaticity, the J-transfer suppression, and the sensitivity to peptide self-recognition. Our analysis also revealed that the effect of the static magnetic field on R35.5°,ns is minimal as compared to other typical 1H relaxation rates (i.e., R1,ns, R1,s, and R2) due to the compensation between the equilibrium (cos(35.5°)R1,ns) term and the self- (F′) and crossrelaxation (σ′) terms. As a result, the proposed 1H off-resonance nonselective R35.5°,ns experiment is applicable over a wide range of magnetic fields (i.e., 300-900 MHz) as the sensitivity and resolution allow. Finally, we show that short interscan delays are expected to preserve the monotonic increase of R35.5°,ns vs τc within a wide range of τc values. However, as the interscan delay decreases with respect to 1/R1,ns a negative offset is introduced mainly due to the down-scaling of the self- and crossrelaxation rates F′ and σ′. In relative terms the effect of this negative offset is more significant at short τc values, but the proposed experiment is still able to provide reliable selfrecognition maps. Overall the 1H off-resonance nonselective R35.5°,ns measurement emerges as a robust NMR method suitable to probe a variety of noncovalent interactions. Acknowledgment. We are grateful to the NSERC for financial support and to Hao Huang and Dr. Alex Bain for helpful discussions. V.E. was supported by a fellowship from
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