Characterizing millisecond motions in proteins using CPMG-relaxation dispersion measurements

1. McGill Characterizing millisecond motions in proteins using CPMG-relaxation dispersion measurements Tony Mittermaier 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 equations R2 ωA ωB νCPMG

11. Two-site exchange equations General equation: We can extract kAB kBAΔω2 separately Carver & Richards, R.E. J. Magn. Reson 1972 6 89

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. 1957 27 1411.

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. 2001 123 11341.

14. CPMG Parameter Dependence trouble Kovrigin, Kempf, Grey, & LoriaJ Magn Reson. 2006 180 93

15. Occurrence 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, & LoriaJ Magn Reson. 2006 180 93

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, & LoriaJ Magn Reson. 2006 180 93

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. Occurrence Two-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, & LoriaJ Magn Reson. 2006 180 93

19. From CPMG data to protein motions R2,effνCPMG 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. 2001 11 932

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. 2001 11 932

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

24. Two state fitting: T4 lysozyme L99A • What about residues not participating in the global process? n individual residue fits nχ2indiv global fit nχ2group 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. koff = 800 s-1 90˚ Two state fitting: T4 lysozyme L99A • Extracted exchange rates are similar to rates of ligand binding in cavity. 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 pBΔω kex fast exchange intermediate exchange

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

30. Three states: Fyn SH3 domain G48 mutants • residues have very different apparent ku & kf • elimination based on χ2group/χ2indivdiscards ≈ 50% data. • folding is not two state. G48M log10{kf} G48V log10{ku} Korzhnev, Salvatella, Vendruscolo, Di Nardo, Davidson, Dobson, & Kay LE Nature. 2004 430 586

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

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

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

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

35. Three-state dispersion profiles 180 τ τ n

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 • 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

41. Three states: Fyn SH3 domain G48 mutants • Three site model agrees with data.

42. 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

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

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

45. 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

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. only one rate depends on [L]

47. How much data do you need?(as much as possible) • simulated SQ data • two static magnetic fields • νCPMG (50-1000Hz) correct solution χ2 χ2 ΔωAB (ppm) ΔωAC (ppm) Neudecker, Korzhnev, & Kay J Biomol NMR. 2006 34 129

48. CPMG experiments beyond amide 15N • 1H 15N SQ DQ ZQ MQ experiments ZQ 1H SQ MQ(1H) ΔωH-ΔωN ΔωH 15N SQ MQ(15N) DQ ΔωN ΔωH+ΔωN Korzhnev, Neudecker, Mittermaier, Orekhov & Kay J Am Chem Soc. 2005 127 15602

49. 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. 2006 34 129

50. 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.