Characterizing millisecond motions in proteins using
CPMG-relaxation dispersion measurements
Tony Mittermaier
Aug, 2007 CCPN
McGill
conformationen
ergy
Dynamics are important for protein function
• Weakly populated protein states are often not directly observable in NMR spectra.
Two-site conformational exchange
major state minor state
Carr-Purcell-Meiboom-Gill(CPMG) pulse sequences
time
prec
essi
on
Two-site conformational exchange
• In the absence of exchange, magnetization remains in phase
• Conformational exchange on the millisecond timescale leads to dephasing of the signal.
• Peaks become broad or even disappear.
• The signal decays (relaxes) more rapidly.
time
prec
essi
on
Two-site conformational exchange
• 180 RF pulses reverse the effective direction of precession.
• By increasing the pulse repetition rate (CPMG), one can decrease dephasing and therefore the rate of signal loss (R2,eff) time
prec
essi
on
CPMG pulse train
180 180
180 180 180 180 180 180
Two-site conformational exchange
15N (ppm)
1H (ppm)
Constant time CPMG
full set in less than 24h
Constant time CPMGνCPMG
R2
νCPMG
Two-site exchange equations
Bk
kA
BA
AB
ωA ωB
022 ,,,, RkkfR ABBAABCPMG
R2
νCPMG
Two-site exchange equations
R2 1 / cp 12
R2A0 R2B
0 kex 1 cp
cosh 1 D cosh D cos
D 12
1 2 2
2 2 1/2
cp
2 (2 2 )1/2
1/2
(R2A0 R2B
0 pAkex pBkex )2 2 4 pA pBkex
2
2(R2A0 R2B
0 pAkex pBkex )
General equation:
We can extract kAB kBA Δω2 separately
ex
BAA
ex
ABB
BAABex
kkp
kkp
kkk
Carver & Richards, R.E. J. Magn. Reson 1972 6 89
Two-site exchange equationsFast timescale: kex>>Δω
CPMG
ex
ex
CPMG
ex
BA kkk
ppRR4
tanh412
022
We can extract kex
pB and Δω appear in the same term:inseparable.
Meiboom, Luz & D. Gill J. Chem. Phys. 1957 27 1411.
Two-site exchange equationsSlow timescale: kex<<Δω
CP
CPABkRR sin10
22
Curve is independent of kBA
We can only extract kAB and Δω2
Tollinger et. al J Am Chem Soc. 2001 123 11341.
kex (s–1) 341 327 750 2020
(s–1) 1540 1640 1770 1674pB 6% 7% 4% 3%
R20 (s–1) 15.6 15.3 12.6 11.3
CPMG Parameter Dependence
trouble
Kovrigin, Kempf, Grey, & Loria J Magn Reson. 2006 180 93
Occ
urre
nce Input Parameters
kex = 1000 s–1
= 1500 s–1
pa = 0.95R2
0 = 15 s–1
error=5%
Single-Field Dispersion Curves
Kovrigin, Kempf, Grey, & Loria J Magn Reson. 2006 180 93
Input Parameters
kex = 1000 s–1
= 1500 s–1
pa = 0.95R2
0 = 15 s–1
error=5%
Single-Field Dispersion Curves
Kovrigin, Kempf, Grey, & Loria J Magn Reson. 2006 180 93
Single-Field Dispersion Curves
• We need additional non-redundant data to resolve ambiguity in dispersion curves.
kex field independent
pA field independent
Δω field dependent= Δω(ppm)*ωspectrometer(MHz)
Occ
urre
nce
Input Parameters
kex = 1000 s–1
= 1500 s–1
pa = 0.95R2
0 = 15 s–1
error=5%
Two-Field Dispersion Curves
Kovrigin, Kempf, Grey, & Loria J Magn Reson. 2006 180 93
From CPMG data to protein motions
R2,eff νCPMG pB kex
Two state fitting: T4 lysozyme L99A
• peaks in the region of engineered cavity show broadening.
• Dispersion profiles were fit to a two-site exchange equation: pB, kex, Δω
• Similar values suggest concerted motions.
Two state fitting: T4 lysozyme L99A
Mulder, Mittermaier, Hon, Dahlquist, & Kay Nat Struct Biol. 2001 11 932
Two state fitting: T4 lysozyme L99A
• Collected CPMG data at a range of temperatures• We expect K = pA/pB to follow the van’t Hoff
equation:
TR
HRSK 1ln
ln{K}
1/T Mulder, Mittermaier, Hon, Dahlquist, & Kay Nat Struct Biol. 2001 11 932
Two state fitting: T4 lysozyme L99A
• Data were fit as a group: pB kex Δω R2
0(500) R20(800)
global local
pB kex Δω R20(500) R2
0(800)pB kex Δω R2
0(500) R20(800)
pB kex Δω R20(500) R2
0(800)pB kex Δω R2
0(500) R20(800)
pB kex Δω R20(500) R2
0(800)pB kex Δω R2
0(500) R20(800)
pB kex Δω R20(500) R2
0(800)pB kex Δω R2
0(500) R20(800)
pB kex
n individualresidue fits
n χ2indiv
Two state fitting: T4 lysozyme L99A
• What about residues not participating in the global process?
globalfit
n χ2group
donediscard res. with largest
χ2group/χ2
indiv
maximum?22
2
indiv
group
yes no(10% discarded)
Two state fitting: T4 lysozyme L99A
• Experimental data are in good agreement with global fit.
CH3 (2) 600 MHz CH3 (2) 800 MHz
NH 500 MHz NH 800 MHz
R2,eff (s-1)
CPMG (Hz)
T (°C)
• Extracted CPMG parameters follow the van’t Hoff equation.
Two state fitting: T4 lysozyme L99A
H = 7 kcal·mol-1S = 17 cal·mol-1 ·K-1
ln{K}
1/T
CH3
NH
• Extracted exchange rates are similar to rates of ligand binding in cavity.
Two state fitting: T4 lysozyme L99A
koff = 800 s-1
90˚
kex 1000 s-1
Two state fitting: T4 lysozyme L99A
• We could just average pB values over all residues, but there are several drawbacks:– The average value of pB will not in general
correspond to a best fit to experimental data.– It is difficult to identify residues that do not
participate in the global process.– Residues in fast exchange do not provide pB,
however kex is global, refines the fit.
pApB(Δω)2 kex pB Δω kex
fast exchange intermediate exchange
Three states: Fyn SH3 domain G48 mutants
• Several G48 mutants having folding kinetics amenable to CPMG studies.
• punfolded 5%
• kfolding 500 s-1
• residues have very different apparent ku & kf
• elimination based on χ2
group/χ2indiv
discards ≈ 50% data.
• folding is not two state.
Three states: Fyn SH3 domain G48 mutants
log10{ku}
log 1
0{k f
}
G48M
G48V
Korzhnev, Salvatella, Vendruscolo, Di Nardo, Davidson, Dobson, & Kay LE Nature. 2004 430 586
Three states: Fyn SH3 domain G48 mutants
global parameters (entire protein)kAB, kBA, kBC, kCB
local parameters (each amide group) AB, AC
Three-state dispersion profiles
• Two-state exchange described by analytical expressions.
• Three-state exchange profiles can be calculated numerically using modified Bloch-McConnell equations.
Three-state dispersion profiles
Cy
By
Ay
Cx
Bx
Ax
CBCBAC
CBBCBAABAB
BAAB
ACCBCB
ABCBBCBAAB
BAAB
Cy
By
Ay
Cx
Bx
Ax
MMMMMM
RkkkRkkk
kRkRkk
kRkkkkRk
MMMMMM
t
00000
0000000
000000
x-magnetization
y-magnetization
x-magnetization
y-magnetization
exchange
chemical shift evolutionautorelaxation
Three-state dispersion profiles
tMRtMt
ˆ
0ˆexp MtRtM
matrix exponential can be calculated numerically – MATLAB, etc.
Three-state dispersion profiles
τ τ180
n
0M
Three-state dispersion profiles
τ τ180
0ˆexp MRM
n
Three-state dispersion profiles
τ τ180
n
0ˆexp1801
11
11
1
MRM
Three-state dispersion profiles
τ τ180
n
0ˆexpˆexp1801
11
11
1
MRRM
Three-state dispersion profiles
τ τ180
n
0ˆexpˆexp1801
11
11
1
M
n
RRM n
Three-state dispersion profiles
• This general procedure allows dispersion profiles to be calculated for dynamical models of arbitrary complexity.
A
B C
D
E
F
G
H
vCPMG
R2
Three states: Fyn SH3 domain G48 mutants
• Three site model agrees with data.
2-site 3-site2 3883 2131
DF 3975 3948
2
2exp2
RRR calc
• Most χ2 minimization algorithms are downhill.– To find the correct answer, we need to
start near the correct answer
Three states: Hard to fit
χ2
model parameters
10,000 trial grid search varying global params.initiate minimizations from 20 best points.
Three states: Hard to fit
χ2
model parameters
Several of the grid points converge to the same,lowest χ2 solution.
Three states: Hard to fit
χ2
model parameters
How much data do you need?(as much as possible)
• Vary conditions such that some of the physical parameters change while others remain constant.
ΔωABΔωAC
Tdependent
Tindependent
How much data do you need?(as much as possible)
Bk
kI
k
LkLF
BI
IB
off
on
• Vary conditions such that some of the physical parameters change while others remain constant.
only one ratedepends
on [L]
How much data do you need?(as much as possible)
• simulated SQ data• two static magnetic fields• νCPMG (50-1000Hz)
ΔωAC (ppm)
Δω
AB
(ppm
)χ2 χ2
correctsolution
Neudecker, Korzhnev, & Kay J Biomol NMR. 2006 34 129
• 1H 15N SQ DQ ZQ MQ experiments
CPMG experiments beyond amide 15N
1H SQ
ΔωH
ΔωN
15N SQ
ZQ
ΔωH-ΔωN
DQ
MQ(1H)
MQ(15N)
ΔωH+ΔωN
Korzhnev, Neudecker, Mittermaier, Orekhov & Kay J Am Chem Soc. 2005 127 15602
SQ1 temperature
true ΔωAB (ppm)best
fit Δ
ωA
B (p
pm)
• simulated data• two static magnetic fields• group fitting
CPMG experiments beyond amide 15N
SQ3 temperatures
SQ DQ ZQ MQ1 temperature
Neudecker, Korzhnev, & Kay J Biomol NMR. 2006 34 129
• In general, dispersion profiles are well-fit by two-site model.
• Even with 6 experiments, for single-residue fits, 3-site is better than 2-site model for only 14 out of 40 residues.
• Multi-site models explain inconsistencies between apparent two-site parameters for different residues.
CPMG experiments beyond amide 15N
Characterizing minor states using CPMG chemical shift information
15N ppm
1H ppm
±?
Obtaining the signs of chemical shift differences
minor peakinvisible
800 MHz
500 MHz
Obtaining the signs of chemical shift differences
(≥ .006 ppm 15N)
Skrynnikov, Dahlquist, & Kay J Am Chem Soc. 2002 124 12352
ωA ωB
kex << slowexchange
fastexchange
Δω
Obtaining the absolute signs of chemical shift differences
kex >>
Obtaining the signs of chemical shift differences
• In the case of three-site exchange the situation is a little more complicated but analogous.
• Imaginary parts of eigenvalues of R give the peak locations.
tVRtVt
ˆ
coherence instates A, B &C
Korzhnev, Neudecker, Mittermaier, Orekhov & Kay J Am Chem Soc. 2005 127 15602
Reconstructing spectra of invisible states
A
B C
• |Δω| from CPMG• sign of Δω from
HSQCs at two fields.
Korzhnev, Neudecker, Mittermaier, Orekhov & Kay J Am Chem Soc. 2005 127 15602
Structures of invisible states • Match reconstructed spectrum to reference state
with known spectrum:– unfolded state– ligand-bound state– phosphorylated form– etc.
state C is theunfolded state
ΔωA-random coil
ΔωAC
1H 15N
Mittermaier, Korzhnev & Kay Biochemistry 2005 44 15430
Structures of invisible states • Match reconstructed spectrum to reference state
with known spectrum:
state B is folded-like in center, unfolded in RT loop
residue
|ΔωAB||ΔωCB|(Hz)
B
A (folded)
C (unfolded)
Mittermaier, Korzhnev & Kay Biochemistry 2005 44 15430
G48M summary (25°C)
97%folded
1%partly-foldedintermediate
2%unfolded
kex=1500 s-1 kex=5000 s-1
1LFU
Work in progress: PBX homeodomain
Jabet et al (1999) JMB 291, 521
C secondary chemical shifts
Work in progress: PBX homeodomain• broadened peaks throughout protein in the
absence of DNA
Work in progress: PBX homeodomain
?
Work in progress: PBX homeodomain
• identify optimal conditions: temperature affects exchange rates and populations.
R2,eff
νCPMG
R2,eff
Work in progress: PBX homeodomain
15C 20C 25C
30C 35C 40C
R2
(s-1)
peaks (sorted)
Work in progress: PBX homeodomain
800 MHz
500 MHz
15N SQ 20°C
Work in progress: PBX homeodomain
pB = 5.5%kex = 1600 s-1
14 residues consistent with2-state global process
3 residues withχ2
group/χ2indiv > 2
Simple dynamic models
A Bkex
pBωB
global param. Δω param.
2 1
A B C
A B
C
kex kexpB pC
ωB ωC
4 2
ωB
ωCpC
pB
kexkex
kex
5 2
A Bkex
C BCkex
pB
pC
ωB
ωC ωBC
4 3