1. Characterizing millisecond motions in proteins using CPMG-relaxation dispersion measurements
Tony Mittermaier
McGill
Aug, 2007 CCPN

2. Dynamics are important for protein function
energy
conformation

3. Two-site conformational exchange
Weakly populated protein states are often not directly observable in NMR spectra.

4. Carr-Purcell-Meiboom-Gill (CPMG) pulse sequences
major state
minor state

5. Two-site conformational exchange
In the absence of exchange, magnetization remains in phase
precession
time

6. Two-site conformational exchange
Conformational exchange on the millisecond timescale leads to dephasing of the signal.
Peaks become broad or even disappear.
The signal decays (relaxes) more rapidly.
precession
time

7. Two-site conformational exchange
180 RF pulses reverse the effective direction of precession.
By increasing the pulse repetition rate (nCPMG), one can decrease dephasing and therefore the rate of signal loss (R2,eff)
CPMG pulse train
180
180
180
180
180
180
180
180
precession
time

8. Constant time CPMG
15N (ppm)
1H (ppm)
full set in less than 24h

9. Constant time CPMG
νCPMG R2
νCPMG

10. Two-site exchange equationsR2 ωA ωB
νCPMG

11. Two-site exchange equations
General equation:
We can extract kAB kBA Δω2 separately
Carver & Richards, R.E. J. Magn. Reson

12. Two-site exchange equations
Fast timescale: kex>>Δω
We can extract kex
pB and Δω appear in the same term:
inseparable.
Meiboom, Luz & D. Gill J. Chem. Phys

13. Two-site exchange equations
Slow timescale: kex<<Δω
Curve is independent of kBA
We can only extract kAB and Δω2
Tollinger et. al J Am Chem Soc

14. CPMG Parameter Dependence
trouble
kex (s–1)
341
327
750
2020
Dw (s–1)
1540
1640
1770
1674 pB 6% 7% 4% 3%
R20 (s–1)
15.6
15.3
12.6
11.3
Kovrigin, Kempf, Grey, & Loria J Magn Reson

15. Single-Field Dispersion Curves
Occurrence
Input Parameters
kex = 1000 s–1
Dw = 1500 s–1
pa = 0.95
R20 = 15 s–1
error=5%
Kovrigin, Kempf, Grey, & Loria J Magn Reson

16. Single-Field Dispersion Curves
Input Parameters
kex = 1000 s–1
Dw = 1500 s–1
pa = 0.95
R20 = 15 s–1
error=5%
Kovrigin, Kempf, Grey, & Loria J Magn Reson

17. 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)

18. Two-Field Dispersion Curves
Occurrence
Input Parameters
kex = 1000 s–1
Dw = 1500 s–1
pa = 0.95
R20 = 15 s–1
error=5%
Kovrigin, Kempf, Grey, & Loria J Magn Reson

19. From CPMG data to protein motions
R2,eff νCPMG
pB kex

20. Two state fitting: T4 lysozyme L99A
peaks in the region of engineered cavity show broadening.

21. Two state fitting: T4 lysozyme L99A
Dispersion profiles were fit to a two-site exchange equation: pB, kex, Δω
Similar values suggest concerted motions.
Mulder, Mittermaier, Hon, Dahlquist, & Kay Nat Struct Biol

22. 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:
ln{K}
1/T
Mulder, Mittermaier, Hon, Dahlquist, & Kay Nat Struct Biol

23. Two state fitting: T4 lysozyme L99A
Data were fit as a group:
pB kex Δω R20(500) R20(800)
pB kex Δω R20(500) R20(800)
pB kex Δω R20(500) R20(800)
pB kex Δω R20(500) R20(800)
pB kex Δω R20(500) R20(800)
pB kex
global
local
pB kex Δω R20(500) R20(800)
pB kex Δω R20(500) R20(800)
pB kex Δω R20(500) R20(800)
pB kex Δω R20(500) R20(800)

24. Two state fitting: T4 lysozyme L99A
What about residues not participating in the global process?
n individual
residue fits
n χ2indiv
global
fit
n χ2group
maximum
discard res.
with largest
χ2group/χ2indiv
done
yes no
(10% discarded)

25. Two state fitting: T4 lysozyme L99A
Experimental data are in good agreement with global fit.
CH3 (2) 600 MHz
CH3 (2) 800 MHz
R2,eff (s-1)
T (°C)
NH 500 MHz
NH 800 MHz
CPMG (Hz)

26. Two state fitting: T4 lysozyme L99A
Extracted CPMG parameters follow the van’t Hoff equation.
ln{K}
CH3 NH
H = 7 kcal·mol-1
S = 17 cal·mol-1 ·K-1
1/T

27. Two state fitting: T4 lysozyme L99A
Extracted exchange rates are similar to rates of ligand binding in cavity.
koff = 800 s-1
90˚
kex  1000 s-1

28. 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

29. Two state fitting: T4 lysozyme L99A
Global fitting to a 2-state model produces physically reasonable results.
temperature dependence
kinetics
About 10% of residues appear to participate in alternate processes.

30. Three states: Fyn SH3 domain G48 mutants
Several G48 mutants having folding kinetics amenable to CPMG studies.
punfolded  5%
kfolding  500 s-1

31. Three states: Fyn SH3 domain G48 mutants
residues have very different apparent ku & kf
elimination based on χ2group/χ2indiv discards ≈ 50% data.
folding is not two state.
G48M
log10{kf}
G48V
log10{ku}
Korzhnev, Salvatella, Vendruscolo, Di Nardo, Davidson, Dobson, & Kay LE Nature

32. Three states: Fyn SH3 domain G48 mutants
global parameters (entire protein)
kAB, kBA, kBC, kCB
local parameters (each amide group)
AB, AC

33. Three-state dispersion profiles
Two-state exchange described by analytical expressions.
Three-state exchange profiles can be calculated numerically using modified Bloch-McConnell equations.

34. Three-state dispersion profiles
x-magnetization
x-magnetization
y-magnetization
y-magnetization
exchange
chemical shift evolution
autorelaxation

35. Three-state dispersion profiles
matrix exponential can be calculated numerically – MATLAB, etc.

36. Three-state dispersion profiles
180 τ τ n

37. Three-state dispersion profiles
180 τ τ n

38. Three-state dispersion profiles
180 τ τ n

39. Three-state dispersion profiles
180 τ τ n

40. Three-state dispersion profiles
180 τ τ n

41. Three-state dispersion profiles
This general procedure allows dispersion profiles to be calculated for dynamical models of arbitrary complexity. A D F R2 H B C G
vCPMG E

42. Three states: Fyn SH3 domain G48 mutants
Three site model agrees with data.
2-site
3-site 2
3883
2131 DF
3975
3948

43. Three states: Hard to fit
Most χ2 minimization algorithms are downhill.
To find the correct answer, we need to start near the correct answer χ2
model parameters

44. Three states: Hard to fit
10,000 trial grid search varying global params.
initiate minimizations from 20 best points. χ2
model parameters

45. Three states: Hard to fit
Several of the grid points converge to the same,
lowest χ2 solution. χ2
model parameters

46. How much data do you need? (as much as possible)
Vary conditions such that some of the physical parameters change while others remain constant. T
independent
ΔωAC
ΔωAB T
dependent

47. How much data do you need? (as much as possible)
Vary conditions such that some of the physical parameters change while others remain constant.
only one rate
depends
on [L]

48. How much data do you need? (as much as possible)
simulated SQ data
two static magnetic fields
νCPMG ( Hz)
correct
solution χ2 χ2
ΔωAB (ppm)
ΔωAC (ppm)
Neudecker, Korzhnev, & Kay J Biomol NMR

49. CPMG experiments beyond amide 15N
1H 15N SQ DQ ZQ MQ experiments ZQ
1H SQ
MQ(1H)
ΔωH
ΔωH-ΔωN
15N SQ
MQ(15N) DQ
ΔωN
ΔωH+ΔωN
Korzhnev, Neudecker, Mittermaier, Orekhov & Kay J Am Chem Soc

50. CPMG experiments beyond amide 15N
simulated data
two static magnetic fields
group fitting
SQ DQ ZQ MQ
1 temperature SQ
1 temperature SQ
3 temperatures
best fit ΔωAB (ppm)
true ΔωAB (ppm)
Neudecker, Korzhnev, & Kay J Biomol NMR

51. CPMG experiments beyond amide 15N
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.

52. Characterizing minor states using CPMG chemical shift information

53. Obtaining the signs of chemical shift differences
15N ppm
±Dw ?
1H ppm

54. Obtaining the signs of chemical shift differences
800 MHz
(≥ .006 ppm 15N)
minor peak
invisible
500 MHz
Skrynnikov, Dahlquist, & Kay J Am Chem Soc

55. Obtaining the absolute signs of chemical shift differences
kex << Dw
slow
exchange
fast
exchange
kex >> Dw ωA ωB Δω

56. 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.
coherence in
states A, B &C
Korzhnev, Neudecker, Mittermaier, Orekhov & Kay J Am Chem Soc

57. Reconstructing spectra of invisible states
|Δω| from CPMG
sign of Δω from HSQCs at two fields. B C
Korzhnev, Neudecker, Mittermaier, Orekhov & Kay J Am Chem Soc

58. Structures of invisible states
Match reconstructed spectrum to reference state with known spectrum:
unfolded state
ligand-bound state
phosphorylated form
etc.
state C is the
unfolded state 1H
15N
ΔωAC
ΔωA-random coil
Mittermaier, Korzhnev & Kay Biochemistry

59. Structures of invisible states
Match reconstructed spectrum to reference state with known spectrum:
state B is folded-like in center, unfolded in RT loop
A (folded)
|ΔωAB|
|ΔωCB|
(Hz) B
C (unfolded)
residue
Mittermaier, Korzhnev & Kay Biochemistry

60. G48M summary (25°C) 97% folded 1% partly-folded intermediate 2%
unfolded
kex=1500 s-1
kex=5000 s-1

61. Work in progress: PBX homeodomain
1LFU
Ca secondary chemical shifts
Jabet et al (1999) JMB 291, 521

62. Work in progress: PBX homeodomain
broadened peaks throughout protein in the absence of DNA

63. Work in progress: PBX homeodomain?

64. Work in progress: PBX homeodomain
identify optimal conditions: temperature affects exchange rates and populations.
R2,eff
DR2,eff
νCPMG

65. Work in progress: PBX homeodomain
15C
20C
25C
DR2
(s-1)
30C
35C
40C
peaks (sorted)

66. Work in progress: PBX homeodomain
15N SQ 20°C
800 MHz
500 MHz

67. Work in progress: PBX homeodomain
14 residues consistent with
2-state global process
3 residues with
χ2group/χ2indiv > 2
pB = 5.5%
kex = 1600 s-1

68. Simple dynamic models A B A B C A B C A B C BC global param. Δω param.pB
kex
A B
2 1 ωB pB pC
kex
kex
A B C
4 2 ωB ωC pB
kex
A B ωB
5 2
kex
kex C pC ωC
kex ωB
A B pB
4 3
kex
C BC pC ωC
ωBC

72. Relaxation Compensated CPMG
Length of time spent in-phase depends on τ
Evolution due to scalar coupling: ≠ Nx
NxcosπJτ + 2NyHzsinπJτ
NxcosπJτ – 2NyHzsinπJτ
R2in-phase
R2anti-phase τ
Variation of R2 with νCPMG will depend not only on exchange!
180x τ

73. Relaxation Compensated CPMGNx
-Nx
2NyHz
2NyHz
2NyHz Nx
Magnetization is in-phase half the time, independent of τ
Loria, Rance, Palmer, JACS