Bernd Reif Quantification of Dynamics in the Solid-State Technische Universität München Helmholtz-Zentrum München Biomolecular Solid-State NMR Winter School Stowe, VT January 0-5, 206 Motivation. Solid samples are more susceptible to local structural fluctuations Is there dynamics in the solid-state? How does local dynamics compare between solution- and solid-state? How can we quantify dynamics in the solid-state? Solution-state: Relaxation is due to molecular tumbling τ c Solid-state: Relaxation is due to local structural fluctuations R ( 5 N) = d 2 [ ( ) + 3J ( ω N ) + 6J 2 ( ω H + ω N )] + 2 0 J 0 ω H ω N J(ω) = S 2 τ R + ω 2 τ + S 2 2 ( F ) R + ω 2 τ + S 2 2 2 F ( S S ) F + ω 2 2 τ S τ F τ S ( ) 5 c 2 J ω N In solids In solution
Measurement of 5 N-T Solid-State Solution Chevelkov et al. JCP 28 05236 (2008) Motivation 2. Temperature dependence of H, 5 N correlations in α-sh3 RT loop N-Src loop distal loop N- and C- terminus
In solution, things get worse with larger molecular weight τ c Observables for the quantification of dynamics - INEPT vs CP based experiments - T Spin-Lattice Relaxation - T2 Spin-Spin Relaxation - Order Parameter measurements - CPMG / Rρ Relaxation Dispersion - Heteronuclear NOE - off- magic angle spinning trivial, but very useful spin density? affected by spin density classical observable similar to CP/INEPT, quantitative rotating methyl groups act as sinks for relaxation low resolution! " "!!? "
What determines T 2 in the solid-state? In solution-state: Overall tumbling, τ C (local fluctuations, chemical exchange) τ c In the solid-state: LW( H, 3 C @ 24 khz, 600 MHz) > 7 Hz, 4 Hz ) Acquisition time - Insufficient decoupling power - Insufficient MAS frequencies - Probe design Not an issue in deuterated samples 2) Shimming 3) Crystal imperfections LW (adamantane) 2 Hz T 2 * = T 2 4) Local dynamics? Quantification of Dynamics Relaxation of longitudinal 5 N magnetization: R ( 5 N) = d 2 [ ( ) + 3J ( ω N ) + 6J 2 ( ω H + ω N )] + 2 0 J 0 ω H ω N ( ) 5 c 2 J ω N Definition of the spectral density function J(ω): J m # ( ) = dτ m ω m ω m # t 0 [ Y α 2,m ( Ω(0) ), Y β 2, m $ ( Ω(τ) )] [ ] (m, m # C ) α,β (τ) exp i( ω m ω m # )τ τ C In solution: (m, m # C ) α,α (τ) = exp( τ /τ C ) In general: ( ) τ F ( ) 2 J(ω) = S F + ω 2 τ + S 2 2 2 F S S F + ω 2 2 τ S τ S S: order parameter τ: correlation time τ S /τ F : Slow and fast motional time scale
Quantification of Dynamics in the Solid-State In Solution-State NMR, relaxation is determined by the tumbling of the molecule in water τ S R ( 5 N) = d 2 [ ( ) + 3J ( ω N ) + 6J 2 ( ω H + ω N )] + 2 0 J 0 ω H ω N ( ) 5 c 2 J ω N ( ) τ F ( ) 2 J(ω) = S F + ω 2 τ + S 2 2 2 F S S F + ω 2 2 τ S τ S In solution In solids In Solid-State NMR, relaxation is determined by local structural fluctuations only τ F. Measurement of 5 N-T in the solid-state R ( 5 N) = d 2 [ ( ) + 3J ( ω N ) + 6J 2 ( ω H + ω N )] + 2 0 J 0 ω H ω N ( ) 5 c 2 J ω N Chevelkov et al. J Chem Phys 28 05236 (2008)
2. Can we learn something on J(0) in the solid-state? ) Coherent, Static effect (CSA-dipole correlation) [MAS dependent] 2) Incoherent, Dynamic effect due to Dipole-CSA cross-correlated relaxation [MAS independent] Chevelkov et al. JACS 29 095 (2007) Composition of Multiplet Intensities ) Static effect (CSA-dipole correlation) [MAS dependent] 0 *# δ N N z + D HN H z N z = δ N + D HN % 2 + H & # z ( % $ ' 2 H &- 3, z (/ 4 2 + $ '. 5 N z [ ] [ ] 0 8 = δ N + D HN H α 28 δ N D HN H β H β Center band J NH st spinning side band H α
Composition of Multiplet Intensities ) Static effect (CSA-dipole correlation) [MAS dependent] 0 *# δ N N z + D HN H z N z = δ N + D HN % 2 + H & z $ ' ( # % $ 2 H &- 3, ( + z / 4 2 '. 5 N z [ ] [ ] 0 8 = δ N + D HN H α 28 δ N D HN H β H β Center band J NH st spinning side band H α Composition of Multiplet Intensities ) Static effect (CSA-dipole correlation) [MAS dependent] 0 *# δ N N z + D HN H z N z = δ N + D HN % 2 + H & # z ( % $ ' 2 H &- 3, z (/ 4 2 + $ '. 5 N z [ ] [ ] 0 8 = δ N + D HN H α 28 δ N D HN H β H β Center band J NH st spinning side band H α
Composition of Multiplet Intensities ) Static effect (CSA-dipole correlation) [MAS dependent] 0 *# δ N N z + D HN H z N z = δ N + D HN % 2 + H & z $ ' ( # % $ 2 H &- 3, ( + z / 4 2 '. 5 N z [ ] [ ] 0 8 = δ N + D HN H α 28 δ N D HN H β H β Center band J NH st spinning side band H α Composition of Multiplet Intensities 2) Dynamic effect due to Dipole-CSA cross-correlated relaxation [MAS independent] c Γ NH,N γ Hγ N γ 3 N B 0 δ N (3cos 2 β )*τ c r NH J NH 5 N Is there a contribution due to dynamics? Chevelkov et al. Mag Res Chem 45 S56-60 (2007) Skrynnikov Mag Res Chem 45 S6-73 (2007)
N-H α /N-H β Differential Line Broadening due to Dynamics MAS = 3 khz = const J NH Columns along 5 N Broad Lines in traditional solid-state NMR experiments T 2 decay of 5 N-Hα/β allows to access the timescale of local dynamics η CSA / DD = & 2Δ ln I β ) ( ' I α + = dc { * 5 4J (0) + 3J (ω ) 0 N }P 2 (cosθ) Chevelkov et al. MRC 45 S56-60 (2007)
Differential T 2 decay of α/β multiplet components T eff = 2 C; MAS = 24 khz η CSA / DD = & 2Δ ln I β ) ( ' I α + = dc { * 5 4J 0(0) + 3J (ω N )}P 2 (cosθ) Chevelkov et al. MRC 45 S56 (2007) 3. H- 5 N dipolar coupling measurements yield Order Parameters Simulation Parameters: MAS = 20 khz Ideal condition: ω RF ( H)/2π = 56 khz ω RF ( 5 N)/2π = 76 khz Δω RF ( 5 N)/2π = -6 khz Wu and Zilm, JMR A 04, 54 (993) Dvinskikh, Zimmermann, Maliniak and Sandstrøm, JCP 22, 04452 (2005) Chevelkov, Fink, Reif, J Am Chem Soc 3, 408 (2009)
Experimental CPPI spectra for α-spectrin SH3 khz Error estimation in the determination of H, 5 N dipolar couplings (K8) LB = Line Broadening of the Exponential Apodization; D app = apparent dipolar splitting; D HN = true dipolar coupling (without scaling factor of the pulse sequence)
H, 5 N dipolar couplings in α-spectrin SH3 H-bond acceptor γ D NH = µ H γ N! 0 3 r NH.035 Å = 087.8 Hz.045 Å = 0772.5 Hz.055 Å = 0468. Hz Are variations in the size of the H N - 5 N dipolar coupling due to a variation in the H N -N bond length or due to dynamics? Correlation between the scalar coupling across a hydrogen bond 3h J NC and the H N isotropic chemical shift from Cordier and Grzesiek, JACS 2 60 (999)
Correlation between the H N, 5 N dipolar couplings and the H N isotropic chemical shift γ D NH = µ H γ N! 0 3 r NH However: N-H bond length should be increased in a H-Bond Mobility Increased dynamics for weak hydrogen bonds No effect of H-bonding on the N-H bond length Alternatively: Order Parameters via REDOR type experiments Schanda P, Meier BH, Ernst M Accurate measurement of one-bond H-X heteronuclear dipolar couplings in MAS solid-state NMR. J. Magn. Reson. 20: 246-259 (20).
Order Parameters via REDOR type experiments Schanda P, Huber M, Boisbouvier J, Meier BH, Ernst M. Solid-State NMR Measurements of Asymmetric Dipolar Couplings Provide Insight into Protein Side-Chain Motion. Angew. Chem. Int. Ed. 50: 005-009 (202) Model-free Analysis to decribe Motion in the Solid-State Let's assume that you have slow and fast motions in your protein ( ) J(ω ) = S F 2 τ F ( ) τ S +ω 2 τ + S 2 2 2 F S S F +ω 2 2 τ S There are 4 unknown parameters S 2 S, S2 F, τ S and τ F What can we measure? H, 5 N dipole 5 N CSA cross-correlated relaxation " 5 N-T 2 " H, 5 N dipolar couplings S 2 F S2 S 5 N T @ 2 fields
Rmsd minimization of S 2 S, S2 F, τ F and τ S Q6 + 2 - # & # rmsd =, % R theo exp (,i R exp,i )( + % $ R.- i,i ' $ % 2 / 2 & ( η exp ηtheo η exp )( / - 0 '( - Data used for fitting: 5 N-T (900 MHz) 5 N-T (600 MHz) Data used for fitting: 5 N-T (900 MHz) 5 N-T (600 MHz) η ( 5 N-CSA / H- 5 N) S 2 S S2 F = 0.776; S2 S = 0.92 τ F = 26 ps Rmsd minimization of S 2 S, S2 F, τ F and τ S D62 + 2 - # & # rmsd =, % R theo exp (,i R exp,i )( + % $ R.- i,i ' $ % 2 / 2 & ( η exp ηtheo η exp )( / - 0 '( - Data used for fitting: 5 N-T (900 MHz) 5 N-T (600 MHz) Data used for fitting: 5 N-T (900 MHz) 5 N-T (600 MHz) η ( 5 N-CSA / H- 5 N) S 2 S S2 F = 0.349; S2 S = 0.479 τ F = 3.9 ns
Order Parameter and τ S in α-spectrin SH3 τ S and τ F in α-spectrin SH3
τ S and τ F in α-spectrin SH3 Is TROSY beneficial for solid-state NMR?
Observation : INEPT based experiments allow to detect residues in mobile regions Linser et al., J. Am. Chem. Soc. (200) Observation 2: Regions which are not detectable in CP experiments undergo a ns-µs time scale dynamics Quantification of η CSA/DD using INEPT based experiments Linser et al., J. Am. Chem. Soc. (200)
TROSY experiments are beneficial in the solid-state for regions undergoing slow dynamics Linser et al., J. Am. Chem. Soc. (200) Intensities in 2D-HSQC/TROSY and 3D-HNCO/TROSY-HNCO Using TROSY experiments, the S/N in dynamic regions of the protein can be increased by x2-5
4. heteronuclear NOE measurements: Additional dynamics information in the solid-state Lopez et al. JBNMR 59 24-249 (204) H, 3 C heteronuclear NOE measurements
H, 5 N heteronuclear NOE measurements Deuteration is required to avoid spin diffusion 5 N R rates in a protonated and deuterated SH3 sample 2 H R rates in Solids and Solution J. Am. Chem. Soc. 28 2354 (2006) J. Chem. Phys. 28 05236 (2008)
Aliphatic protons (RAP, Reduction of Adjoining Protonation) 5 NH 4 Cl [ 2 H, 3 C]-glucose 5-30 % H 2 O (95-70 % D 2 O) Asami et al., J. Am. Chem. Soc. 200; Asami et al., Acc. Chem. Res. 203 Experimental 3C T decay curves are bi-exponential (25% SH3 RAP sample, 24 khz MAS). Orientation dependence yields frequency dependent R rates Mono-exponential initial-rate approximation (Torchia) 2. Spin Diffusion: efficient magnetization transfer to methyls which act as relaxation sinks
Dilution of the proton AND carbon spin system H, 3 C correlations of α-sh3: RAP-glucose vs. RAP 2-glycerol 25% RAP-glucose (25 % H2O / 75 % D2O, 2 H, 3 C glucose in M9) 0% RAP-glycerol (0 % H2O / 90 % D2O, [u- 2 H, 2-3 C]-glycerole in M9) improved resolution (no evolution of J couplings) simplified spectra: e.g. no Cα labeling for R, Q, E, L, P no methyl labeling for A, I-γ2, V, L, M 3 Cα T Decay Curves 25% RAP-glucose, 24 khz MAS 0% RAP-glycerol, 24 khz MAS 0% RAP-glycerol, 50 khz MAS (mono-exponential)
3 Cα T in α-spectrin SH3 and MD derived order parameters 5. Protein Side Chain Dynamics 3D 2 H- 3 C- 3 C correlation using 3 C- 3 C RFDR mixing and 2 H- 3 C CP applied to α-spectrin SH3 Hologne et al. (2005) JACS 27, 208
3D- 2 H, 3 C, 3 C Correlation of α-spectrin SH3 2 H Pake Pattern for Valine-CD 3 in α-spectrin SH3 Conformational exchange is directly reflected in the anisotropy δ and the asymmetry η of the 2 H pake pattern (τ c < / 52 khz)
Motional Model for the Side Chain Dynamics of Val-23 Best fit: 2-site jump, jump angle 40 (Center band intensities are not well reproduced in the simulations) 2 H β Pake Pattern for different Valines in α-spectrin SH3 Lower intensities for V23 indicates motion (τ c < /60 khz )
But,... there are many methyls indicating motion...... and no second conformation is visible in the X-ray structure η=0 η= δ η=0 Comparison of X-Ray Analysis at 00K and RT Ile-30, 00K Ile-30, RT Resolution RT:.90 Å; 00 K:.49 Å Crystal dimensions: RT: 34.5 Å, 42.5 Å, 50.8 Å 00 K: 33.6 Å, 42.3 Å, 49.6 Å B-factors (Å 2 ) main chain RT: 26.9 ; 00K: 3.9 side chain RT: 29.6 ; 00K: 7. whole RT: 28.3 ; 00K: 5.6
Acknowledgement Vipin Agarwal Sam Asami Veniamin Chevelkov Rasmus Linser Purdue University Nikolai Skrynnikov