model-free approach to internal motions in...
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Model-Free Approach to Internal Motions in Proteins
• Lipari & Szabo, JACS 104, 4546 (1982) • Palmer AG. Ann. Rev. Biophys. Biomol.
Struc., 30, 129-155 (2001) • Palmer AG, Kroenke CD, Loria JP, Meth.
Enzymol. 339, 204-238 (2001)
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Spin Relaxation: Result of Modulation of Spin Interactions by Molecular Motion: D-D Example:
Can probe structure, but also molecular motion
R1S = 1/T1 = (µ20h2γI
2γS2rIS
-6 / 64π4)(J(ωI- ωS) + 3J(ωS) + 6J(ωI+ ωS))
R2S = 1/T2 = (µ2
0h2 γI2γS
2rIS-6 / 128π4)(4J(0)+J(ωI- ωS)+3J(ωS)+6J(ωI)+6J(ωI+ ωS))
J(ω) = (2/5)τc/(1 + ω2 τc2)
Note: if τc is small (small molecule), R1S = R2S. if τc is large, R2S >> R1S
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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:
H
H H
θ θ’
θ’’
B0
H1(t) ∝ (3cos2(θ’’(t) – 1) H1(t) ∝ (3cos2(θ’(t) – 1)(3cos2(θ – 1)/2 H1(t) ∝ (3cos2(θ’(t) – 1)(-0.34) H1(t) ∝ (3cos2(θ’(t) – 1) S
Order Parameter
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• 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 = τm-1 + τi
-1 , if τI is very short, it dominates τ For small τ first term can also dominate
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• S2 and τm are parameters often measured for proteins using 15N – 1H interactions where “r” is fixed at the bond length and γs are known
• 15N T1 ,T2 , and heteronuclear NOEs are usually measured.
• τm can be estimated from T1 ,T2 for a large molecule, ω τm is large implying:
• (1/ T2) ≅ (dd’/4){2J(0)}, (1/ T1) ≅ (dd’/4){3J(ωN)} • J ≅ (2/5)S2 τm / (1 + (τmω)2), (T1/ T2) ≅ (2/3)(τmωN)2
• Once τm is known, S2 can be calculated from T1 ,T2 or NOE
• S2 in a structured region is about 0.8, in loops less
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Example from binding of phosphopeptides to SH2 domain Biochemistry, 33, 5987 (1994)
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Changes in Order Parameters on Complexation
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Other Contributions to T2 can Complicate Analysis (Rex)
Extracting and Exploiting Rex is also Useful
• Structures of invisible, excited protein states by relaxation dispersion NMR spectroscopy, Vallurupalli P, Hansen DF, Kay LE, PNAS, 105, 11766-11771 (2008)
• Characterization of enzyme motions by solution NMR relaxation dispersion, Loria JP, Berlow RB, Watt ED, Acc. Chem. Res., 41, 214-221 (2008)
• Observing biological dynamics at atomic resolution using NMR, Mittermaier AK, Kay LE, Trends Biochem. Sci., 34, 601-611 (2009)
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NMR senses dynamics on many time scales
Chemical exchange (Rex) is particularly useful in the
100µs- 10 ms range
Rex = τex pApBΔω2
τex-1 = τA
-1 + τB-1
Mittermaier & Kay, Trends Biochem. Sci (2009)
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Carr-Purcell Meiboom-Gill Sequence Can Remove Effects of Exchange
90x 180x
τ 2τ
180x
2τ
180x
2τ
180x
2τ
180x
2τ
Long τ includes exchange; short τ removes exchange Relaxation dispersion – a study as a function of τ
R2(1/τ) ) = R20 + ϕex/kex[1 - 2tanh(kexτ/2)⁄(kexτ)] ϕex/kex = pApBΔω2
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Field Dependent Measurement Separates Δω and PA,B information
(Kay, PNAS, 2008)
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Detection of 5-10% minor species of peptide bound to SH3 domain
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Internal Dynamics can Improve Resolution – Cross-Correlation Effects
• TROSY - Pervushin, Riek, Wider & Wuthrich, PNAS 94, 12366 (1997)
• TROSY na CRINEPT - Riek, Pervushin & Wuthrich TIBS, 25, 462 (2000)
• Cα-N torsion angles -Reif, Hennig & Griesinger Science, 276, 1230-1233 (1997)
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Deuteration and TROSY Greatly Improve Resolution
15N HSQC 15N TROSY 15N 2H TROSY A B C
Differential Line Broadening due to cross-correlation
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Other Cross-Correlated Relaxation Phenomena A general approach
• 1/T1,2 ∝ |V1|2 J11(ω) + |V2|2 J22(ω) + |V1 V2 | J12(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 13C methylene
13C
13C
1H
1H Fields cancel
Fields cancel
1H
1H
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13C
The effects are geometry dependent
• Use in structure determination: Reif, Hennig, Griesinger, Science, 276, 1230-1233 (1997)
1H
1H
1H 1H 13C
Fields add
Fields add
13C 15N
1H 1H 2Q coherence split by both 1Hs
αα ββ αβ,βα
broad
sharp
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Example: Acyl Chain Rotation in Lipid Bilayers
H
H 13C
αα αβ+βα ββ
α
β 13C
α
α 13C Heff = 0
Heff = f(t)V
αα αβ+βα ββ
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Selective Labeling of Methyl Groups Provides Sensitivity and Resolution
Gardner &Kay (1997) JACS 119 7599 Goto et al. (1999) J Biomol NMR 13 369 Tugarinov & Kay (2003) JACS 125 13868
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Methyl-TROSY another example of cross-correlation effects
V. Tugarinov, R. Sprangers and L.E. Kay J. Am. Chem. Soc. 126, 4921-4925 (2004)
Double and zero quantum coherences between 13C and 1H evolve with the effects of coupling to the remaining 2 protons
13C
1H
1H
1H
αα αβ/βα ββ
Proton coupled ZQ (H-C) spectrum
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Comparison of HMQC and HZQC Data