Model-Free Approach to Internal Motions in Proteins

Transcription

1 Model-Free Approach to Internal Motions in Proteins Lipari & Szabo, JACS 104, 4546 (1982) Palmer AG. Ann. Rev. Biophys. Biomol. Struc., 30, (2001) Palmer AG, Kroenke CD, Loria JP, Meth. Enzymol. 339, (2001)

2 Spin Relaxation: Result of Modulation of Spin Interactions by Molecular Motion: D-D Example: R 1S = 1/T 1 = (µ 2 0 h2 γ I2 γ S2 r IS -6 / 64π 4 )(J(ω I - ω S ) + 3J(ω S ) + 6J(ω I + ω S )) R 2S = 1/T 2 = (µ 2 0 h2 γ I2 γ S2 r IS -6 / 128π 4 )(4J(0)+J(ω I - ω S )+3J(ω S )+6J(ω I )+6J(ω I + ω S )) J(ω) = (2/5)τ c /(1 + ω 2 τ c2 ) Note: if τ c is small (small molecule), R 1S = R 2S. if τ c is large, R 2S >> R 1S Can probe structure, but also molecular motion

3 Generalized Order Parameters and Internal Motion Basis: fast internal motions scale interactions that are then modulated by molecular tumbling Methyl rotation a model specific example: B 0 θ θ θ 1 (t) (3cos 2 (θ (t) 1) 1 (t) (3cos 2 (θ (t) 1)(3cos 2 (θ 1)/2 1 (t) (3cos 2 (θ (t) 1)(-0.34) 1 (t) (3cos 2 (θ (t) 1) S Order Parameter

4 Scaling due to motions too fast to affect relaxation directly Efficiency of relaxation due to tumbling is reduced Scaling factor is an order parameter 0 if isotropic, 1 if no internal motion τ -1 = τ m -1 + τ i -1, if τ I is very short, it dominates τ For small τ first term can also dominate

5 S 2 and τ m are parameters often measured for proteins using 15 N 1 interactions where r is fixed at the bond length and γs are known 15 N T 1,T 2, and heteronuclear NOEs are usually measured. τ m can be estimated from T 1,T 2 for a large molecule, ω τ m is large implying: (1/ T 2 ) (dd /4){2J(0)}, (1/ T 1 ) (dd /4){3J(ω N )} J (2/5)S 2 τ m / (1 + (τ m ω) 2 ), (T 1 / T 2 ) (2/3)(τ m ω N ) 2 Once τ m is known, S 2 can be calculated from T 1,T 2 or NOE S 2 in a structured region is about 0.8, in loops less

6 Example from binding of phosphopeptides to S2 domain Biochemistry, 33, 5987 (1994)

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9 Changes in Order Parameters on Complexation

10 Other Contributions to T 2 can Complicate Analysis (R ex ) Extracting and Exploiting R ex is also Useful Structures of invisible, excited protein states by relaxation dispersion NMR spectroscopy, Vallurupalli P, ansen DF, Kay LE, PNAS, 105, (2008) Characterization of enzyme motions by solution NMR relaxation dispersion, Loria JP, Berlow RB, Watt ED, Acc. Chem. Res., 41, (2008) Observing biological dynamics at atomic resolution using NMR, Mittermaier AK, Kay LE, Trends Biochem. Sci., 34, (2009)

11 NMR senses dynamics on many time scales Chemical exchange (R ex ) is particularly useful in the 100µs- 10 ms range R ex = τ ex p A p B Δω 2 τ ex -1 = τ A -1 + τ B -1 Mittermaier & Kay, Trends Biochem. Sci (2009)

12 Carr-Purcell Meiboom-Gill Sequence Can Remove Effects of Exchange τ 2τ 2τ 2τ 2τ 2τ 90x 180x 180x 180x 180x 180x Long τ includes exchange; short τ removes exchange Relaxation dispersion a study as a function of τ R 2 (1/τ) ) = R ϕ ex /k ex [1-2tanh(k ex τ/2) (k ex τ)] ϕ ex /k ex = p A p B Δω 2

13 Field Dependent Measurement Separates Δω and P A,B information (Kay, PNAS, 2008)

14 Detection of 5-10% minor species of peptide bound to S3 domain

15 Internal Dynamics can Improve Resolution Cross-Correlation Effects TROSY - Pervushin, Riek, Wider & Wuthrich, PNAS 94, (1997) TROSY na CRINEPT - Riek, Pervushin & Wuthrich TIBS, 25, 462 (2000) Cα-N torsion angles -Reif, ennig & Griesinger Science, 276, (1997)

16 Deuteration and TROSY Greatly Improve Resolution Differential Line Broadening due to cross-correlation N SQC A N TROSY B 15 N 2 TROSY C

17 Other Cross-Correlated Relaxation Phenomena A general approach 1/T 1,2 V 1 2 J 11 (ω) + V 2 2 J 22 (ω) + V 1 V 2 J 12 (ω) Jij(ω) = fi(t + τ) fj(t) exp(iωτ) If motions are uncorrelated, latter average is zero Correlated example: 2 α protons on a 13 C methylene 1 Fields cancel 13 C 1 13 C 1 1 Fields cancel

18 The effects are geometry dependent 1 Fields add 13 C 1 13 C 1 1 Fields add Use in structure determination: Reif, ennig, Griesinger, Science, 276, (1997) 1 1 2Q coherence split by both 1 s 13 C 15 N ββ sharp αβ,βα αα broad

19 Example: Acyl Chain Rotation in Lipid Bilayers 13 C αα αβ+βα ββ α α 13 C 13 eff = 0 C β α αα αβ+βα ββ eff = f(t)v

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21 Selective Labeling of Methyl Groups Provides Sensitivity and Resolution Gardner &Kay (1997) JACS Goto et al. (1999) J Biomol NMR Tugarinov & Kay (2003) JACS

22 Methyl-TROSY another example of cross-correlation effects V. Tugarinov, R. Sprangers and L.E. Kay J. Am. Chem. Soc. 126, (2004) Double and zero quantum coherences between 13 C and 1 evolve with the effects of coupling to the remaining 2 protons 1 Proton coupled ZQ (-C) spectrum 13 C 1 1 αα αβ/βα ββ

23 Comparison of MQC and ZQC Data