Protein Motions Studied by CPMGRelaxation Dispersion Experiments

50th ENC-Asilomar March 30th 2009

Patrick LoriaYale University, Depts. of Chemistry

and Molecular Biophysics and Biochemistry

Biological Function = Structure +σ Structure(t)

-14 -12 -10 -8 -6 -4 -2 0 2

Type of motion

log t (sec)

TorsionalLibration of Buried Groups

Large/Buried Side ChainRotation, Binding, and Catalysis

Domain and Loop MotionsFolding and Allosterism

SurfaceSide ChainRotation

Timescale for Protein Motions

(T2, R2, spin-spin, transverse relaxation)

Conformational orchemical exchange

Relaxation dispersion: the variation in R2 values with changes in spin-echo pulse spacing

Conformational exchange in proteins

History1963 Luz & Meiboom, J.Chem.Phys 39 366

(Protolysis of trimethylammonium ion)

1954 Carr & Purcell, Phys. Rev 94 6301946 NMR

1965Wells & Gutowsky, J.Chem.Phys 43 3414 (modulation of spin-echo decay by scalar coupling)Allerhand, et al. J.Chem.Phys 42 3040 (chair-chair interconversion of d11-cyclohexane)

1964/5 Allerhand & Gutowsky, J.Chem.Phys 41 2115Allerhand & Gutowsky, J.Chem.Phys 42 1587 (R2, τcp, Δω, kex, populations-fast limit)

1994 Orekhov, et al. Eur. J. Biochem. 219 887 (1H-15N, vary τcp in spin-echo)

1999Loria, et al. JACS. 121 2331 (Relaxation-compensated CPMG, NH groups)Loria, et al. JBNMR. 15 151 (TROSY version)Brutscher, et al. JBNMR 14 241 (TROSY nucleic acids)

2001 Mulder, et al. JACS. 123 967 (Application to NH2 groups)Skrynnikov, et al. JACS 123 4556 (Application to CH3 groups)

Orekhov, et al. JACS. 126 1886 (DQ/ZQ dispersion experiments)Korzhnev, et al. JACS. 126 7320 (MQ dispersion experiments)Ishima, et al. JBNMR. 29 187 (C’ dispersion experiments)

2004

2007 Tugarinov & Kay JACS 129 9514 (1H CH3 SQ dispersion)

2007Igumenova, et al. JACS 129 13396 (Dispersion in aligned media)Vallurupalli, et al. PNAS 104 18473 (Dispersion in aligned media)

2000 Hill, et al. JACS. 122 11610 (Cα dispersion)

2003 Ishima, et al. JBNMR. 25 243 (1H dispersion experiments)Grey, et al. JACS 125 14324 (multisite exchange)

FT and multi-dimensional NMR, Redfield theory,protein structure by NMR, isotope labeling

Conformational exchangeµs - ms motions

70:30

Timescale of exchange determines the ‘look’ of the NMR spectrum

Δω

{pa

Ωa Ωb Ωa Ωb Ωa Ωb

90:10 Δω

pa kex < Δω

kex ~ Δω

kex > Δω

kex = ka + kb

Slow

Intermediate

Fast

ωa ωbA

B

Palmer, Kroenke,& Loria Meth.Enzymol. 2001 339 204Kempf & Loria Prot NMR Tech. 2004 287 185

Conformational Exchangeby CPMG motion between

molecular conformers

R2 = R20A

τ τ τττ ττ ττ τ τ τ

τ τ τ τ τ τ τ τ

τ τ τ τ

τ τ

Expt #1

Expt #n

Expt #3

Expt #2

–y τx

τ180ºωaτ

ωaττ

n Jim Kempf, 2002

Conformational Exchangeby CPMG motion between

molecular conformers

R2 = R20A

τ τ τττ ττ ττ τ τ τ

τ τ τ τ τ τ τ τ

τ τ τ τ

τ τ

Expt #1

Expt #n

Expt #3

Expt #2

–y τx

τ180ºωaτ

ωaτ

+ RexBA

Rex = f(pa,Δω,kex, τ)

ωbττ

n Jim Kempf, 2002

Δ

τ

Δ

τ τ τ

2n 2n

y

U

R2(1/ τ cp ) = εR2(in − phase) + (1− ε)R2(anti − phase) +Rex

τ τ τ τ

2n

Δ’ Δ’

if τ cp < 1/ (4JNH ); ε ≈ 1

Palmer, et al. (1992) Mol. Phys. 75 699 Loria, et al. (1999) JACS. 121 2331

15N

(ppm

)

1H (ppm)

Two-Dimensional-15N HSQCRNase A, pH 6.4, 298 K, 14.1 T

N–H

τcp = 1ms

τcp = 10 ms

τcp

n

Measuring Exchange Rates

2n2n

1/τcp

R 2 (τ

cp) s

–1

Dispersion Curve

Rex

The importance of pulsing slowly

τcp < 1/(4JNH)

case kex (s–1)

Δω (s–1)

pA

1 910 1435 0.95

2 200 1627 0.84

R2(1/ τ cp ) = εR2(in − phase) + (1− ε)R2(anti − phase) +Rex

if τ cp < 1/ (4JNH ); ε ≈ 1

Conformational exchangeµs - ms motions

70:30

Timescale of exchange determines the ‘look’ of the NMR spectrum

Δω

{pa

Ωa Ωb Ωa Ωb Ωa Ωb

90:10 Δω

pa kex < Δω

kex ~ Δω

kex > Δω

kex = ka + kb

Slow

Intermediate

Fast

ωa ωbA

B

Palmer, Kroenke,& Loria Meth.Enzymol. 2001 339 204Kempf & Loria Prot NMR Tech. 2004 287 185

R2(1/ τ cp ) = R2

0 + (pApBΔω2 / kex ) 1− 2tanh(kexτ cp / 2) / (kexτ cp )⎡⎣ ⎤⎦

R2 1 / τ cp( ) = 12 R2A0 + R2B

0 + kex −1τ cpcosh−1 D+ cosh η+( ) − D− cos η−( )⎡⎣ ⎤⎦

⎛

⎝⎜⎞

⎠⎟

D± =12

±1+ Ψ + 2Δω 2

Ψ2 +ζ 2( )1/2⎡

⎣⎢⎢

⎤

⎦⎥⎥

η± =τ cp2

±Ψ + (Ψ2 +ζ 2 )1/2⎡⎣ ⎤⎦1/2

Ψ = (R2A0 − R2B

0 − pAkex + pBkex )2 − Δω 2 + 4 pA pBkex

2

ζ = 2Δω (R2A0 − R2B

0 − pAkex + pBkex )

Fast-limit (kex > Δω)

General Equation

Exchange regime: data analysis

Luz & Meiboom, (1963) J. Chem. Phys. 39 366Carver & Richards (1972) J. Magn. Res. 6 89

Dispersion curves-parameterdependence

kex = 1500 s–1

Δω = 400, 700, 1500 s–1

pa = 0.95R2

0 = 15 s–1

kex = 1500, 1000, 500 s–1

Δω = 700 s–1

pa = 0.95R2

0 = 15 s–1

kex = 1500 s–1

Δω = 1000 s–1

pa = 0.98, 0.95, 0.90R2

0 = 15 s–1

R2 (

1/τ c

p) s

–1

1/τcp (s–1)

A system in slow exchange, yetF-test indicates the fast limit equation is

appropriate

Challenges of curve-fittingat a single static field

Millet et al. JACS 2000 122 2867

Challenges of curve-fittingat a single static field

Expt. kex (s–1) Δω (s–1) pA

1 1000 1500 0.95

2 2600 790 0.81

3 200 1510 0.83

Similar curves, different parameters

Kovrigin et al. JMR 2005

Making use of multiple staticmagnetic fields

Rex depends on the static field via the scaling parameter, α,which defines the chemical shift timescale

Millet et al. JACS 2000 122 2867

α =

d lnRex

d lnΔω=

B02 + B01

B02 − B01

⎛

⎝⎜⎞

⎠⎟Rex,2 − Rex,1

Rex,2 + Rex,1

⎛

⎝⎜

⎞

⎠⎟

For pA pB 0 ≤ α ≤ 20 ≤ α < 1 ; slow exchange α = 1 ; intermediate exchange1< α ≤ 2 ; fast exchange

Use of two fieldsand α

11.7 T14.1 T

ΔR2 (τcp: 64 ms – 1 ms)

Millet et al. JACS 2000 122 2867

300 K

Parameter correlations(input: kex = 1000 s–1, Δω = 1500 s–1, pA = 0.95output from 1000 fits to these synthetic data)

1 magnetic field 2 magnetic fields

Kovrigin et al J. Magn.Reson. 2006 180 93

How far can one go with the generaldispersion equation?

1) generate 500 (x 2 fields) data sets incorporating 2% Gaussian distributed random error2) Fit the general equation to each data set3) How do the fit results compare with the input values?

The input: pa = 0.93, R20 = 15 s–1, kex ranged

from 500, 1000, 1500, 2000 s–1.

For each of these, 10 -20 Δω values ranging fromΔω/kex = 0.1 - 2.0.

Input values: kex = 1500 s–1, pa = 0.93, Δω is varied. Mean Values ± St. Dev for 500 simulations (2% Gaussianerror)

kex (s–1) pa Δω (s–1)Exchange

RegimeΔω/kex Δω (s–1)

Fast 0.133 200 1341 ± 347 0.92 ± 0.05 317 ± 232Fast 0.200 300 1604 ± 944 0.91 ± 0.07 345 ± 150Fast 0.233 350 1559 ± 813 0.91 ± 0.06 370 ± 129Fast 0.250 375 1500 ± 400 0.91 ± 0.05 393 ± 122Fast 0.267 400 1483 ± 152 0.91 ± 0.06 414 ± 129Fast 0.283 425 1734 ± 1411 0.90 ± 0.06 418 ± 123Fast 0.300 450 1504 ± 2572 0.90 ± 0.06 448 ± 111Fast 0.333 500 2240 ± 2485 0.91 ± 0.05 504 ± 100Fast 0.400 600 1638 ± 1328 0.92 ± 0.03 598 ± 85Fast 0.433 650 1623 ± 1345 0.92 ± 0.02 652 ± 79Fast 0.450 675 1493 ± 83 0.93 ± 0.02 675 ± 71Fast 0.600 900 1504 ± 73 0.93 ± 0.007 897 ± 49Fast 0.733 1100 1504 ± 71 0.93 ± 0.004 1099 ± 38Fast 0.867 1300 1501 ± 76 0.93 ± 0.002 1299 ± 34

Intermediate 1.000 1500 1501 ± 76 0.93 ± 0.002 1499 ± 33Slow 1.133 1700 1501 ± 78 0.93 ± 0.001 1699 ± 34Slow 1.333 2000 1490 ± 94 0.93 ± 0.001 1998 ± 39

Results for one group of input conditions

Fast

Intermediate

Slow

Δω

kex

pA

The raw data: kexInput: kex = 2000 s–1, pa = 0.93

Δω = 300Δω/kex = 0.15

Δω = 1200Δω/kex = 0.6

Δω = 4000Δω/kex = 2

2000

5000

7000

Simulation number

k ex (

s–1 )

Fast Intermediate Slow

The raw data: pa

Input: kex = 2000 s–1, pa = 0.93

Simulation number

p A

1.0

0.9

0.8

Δω = 300Δω/kex = 0.15

Δω = 1200Δω/kex = 0.6

Δω = 4000Δω/kex = 2

Fast Intermediate Slow

The raw data: ΔωInput: kex = 2000 s–1, pa = 0.93

Δω = 300Δω/kex = 0.15

Δω = 1200Δω/kex = 0.6

Δω = 4000Δω/kex = 2

Δω (s

–1)

2500

0 3000

5000

Fast Intermediate Slow

Simulation number

298 K

Apo RNase A (Dispersion Curves)kex = 1810 ± 90 s–1

pa = 0.93 ± 0.01ka = 1690 ± 85 s–1

kb = 130 ± 10 s–1

Δω = residue specifickcat = 1700 ± 100 s–1

koff = 1700 ± 150 s–1

Loria, Rance, Palmer, JACS 1999 121 2331

Cole & Loria, Biochemistry 2002 41 6072Kovrigin & Loria, Biochemistry 2006 45 2636Kovrigin & Loria J. Magn.Reson. 2006 180 93

298 K

Location of the Isotope Sensitive Residues

KSIE = 2KSIE = 1

Active Site

Watt, Shimada, Kovrigin, Loria (2007) PNAS 104 11897Kovrigin & Loria, JACS 2006 128 7724

98% D2O

52% D2O

5% D2O

Functional insightsfrom relaxation dispersion analysis

Bound forms have opposite sign

and similar magnitude of Δω from apo form

Skrynnikov, Dahlquist, Kay, JACS 2002 124, 12352

apo

bound

Δω

1.5 kcal/mol

openclosed5 kcal/mol

Apo

openclosed5 kcal/mol

1.5 kcal/mol

ES

Beach, Cole, Gill, Loria, JACS 2005 127 9167

Disruption of motions by mutation

H48ARNaseA-ECP chimera

Conformational exchange in substrate-bound HisF by TROSY 15NH rcCPMG dispersion curves

kex=1939 ± 252 s-1

kex=1872 ± 286 s-1 kwz=2433 ± 486 s-1

kex=1746 ± 405 s-1

Limitations of NMR DispersionExperiments

Is the amino acid ‘moving’ or not?

Δω = 0

Δω ≠ 0

moving but not detectable

Rigid NH ‘appears’ to move

Solution: introduce anisotropic interactions in the R2 measurement

kex

Igumenova, et al. JACS 129 13396Vallurupalli, et al. PNAS 104 18473 Wang, et al. PNAS 98 7684

Igumenova, et al. JACS 129 13396

Dispersion in aligned systems

Contributions from NMR DispersionExperiments

Conformational motion in proteins, DNA and RNA, loop motions, cis/trans isomerization

Insight into enzyme function

Characterization of ligand binding

Protein folding

Two-site vs. three-site motion, identification of intermediates

H2O binding to macromolecules

Detection of lowly populated conformational states

Characterization of thermodynamics of conformational motion

Characterization of cation motions

Potential for structural information of spectroscopically invisible conformations

Recent papers related to relaxation dispersionexperiments and applications

Loria et al. Characterization of enzyme motions by solution NMR relaxation dispersion. Accounts Chem Res (2008) vol. 41 pp. 214-221

Palmer et al. Solution NMR spin relaxation methods for characterizing chemical exchange in high-molecular-weight systems. Meth. in Enzymol. (2005) vol. 394 pp. 430-465

Palmer et al. Nuclear magnetic resonance methods for quantifying microsecond-to-millisecond motions in biological macromolecules. Meth. Enzymol. (2001) vol. 339 Part B pp. 204-238

Neudecker et al. Assessment of the effects of increased relaxation dispersion data on theextraction of 3-site exchange parameters characterizing the unfolding of an SH3 domain. Journal of Biomol NMR (2006) vol. 34 (3) pp. 129-135

Yip et al. Improvement of duty-cycle heating compensation in NMR spin relaxation experiments. J Magn Reson (2005) vol. 176 (2) pp. 171-178

Yip et al. A phase cycle scheme that significantly suppresses offset-dependent artifacts in the R-2-CPMG N-15 relaxation experiment. J Magn Reson (2004) vol. 171 (1) pp. 25-36

Ishima et al. Accuracy of optimized chemical-exchange parameters derived by fitting CPMG R-2 dispersion profiles when R-2(0a) = R-2(0b). J Biomol NMR (2006) vol. 34 (4) pp. 209-219

Ishima et al. Error estimation and global fitting in transverse-relaxation dispersion experiments to determine chemical-exchange parameters. J Biomol NMR (2005) vol. 32 (1) pp. 41-54

Palmer et al. Characterization of the dynamics of biomacromolecules using rotating-frame spin relaxation NMR spectroscopy. Chem Rev (2006) vol. 106 (5) pp. 1700-19

NSF MCB0236966NIH R01 GM070823NIH R01 GM61239

Alfred P. Sloan Foundation, Camille &Henry Dreyfus, American Chemical Society, American Cancer Society, Yale University

Funding

Roger Cole, Evgenii Kovrigin, Jim Kempf, Michelle Gill, Heather BeachArt Palmer, Mark Rance

Rebecca

JamesYan

Eric TJ

GennadyNick

SeanPoster 149