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)

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

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

•  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

•  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

Example from binding of phosphopeptides to SH2 domain Biochemistry, 33, 5987 (1994)

Changes in Order Parameters on Complexation

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)

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)

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

Field Dependent Measurement Separates Δω and PA,B information

(Kay, PNAS, 2008)

Detection of 5-10% minor species of peptide bound to SH3 domain

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)

Deuteration and TROSY Greatly Improve Resolution

15N HSQC 15N TROSY 15N 2H TROSY A B C

Differential Line Broadening due to cross-correlation

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

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

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

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

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

Comparison of HMQC and HZQC Data