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

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Presentation on theme: "Characterizing millisecond motions in proteins using CPMG-relaxation dispersion measurements Tony Mittermaier Aug, 2007 CCPN McGill."— Presentation transcript:

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

2 conformation energy Dynamics are important for protein function

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

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

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

6 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 precession Two-site conformational exchange

7 180  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 (R 2,eff ) time precession CPMG pulse train 180 Two-site conformational exchange

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

9 Constant time CPMG ν CPMG R2R2

10 Two-site exchange equations ωAωA ωBωB R2R2 ν CPMG

11 Two-site exchange equations General equation: We can extract k AB k BA Δω 2 separately Carver & Richards, R.E. J. Magn. Reson

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

13 Two-site exchange equations Slow timescale: k ex <<Δω Curve is independent of k BA We can only extract k AB and Δω 2 Tollinger et. al J Am Chem Soc

14 k ex (s –1 )  (s –1 ) pBpB 6%7%4%3% R 2 0 (s –1 ) CPMG Parameter Dependence trouble Kovrigin, Kempf, Grey, & Loria J Magn Reson

15 Occurrence Input Parameters k ex = 1000 s –1  = 1500 s –1 p a = 0.95 R 2 0 = 15 s –1 error=5% Single-Field Dispersion Curves Kovrigin, Kempf, Grey, & Loria J Magn Reson

16 Input Parameters k ex = 1000 s –1  = 1500 s –1 p a = 0.95 R 2 0 = 15 s –1 error=5% Single-Field Dispersion Curves Kovrigin, Kempf, Grey, & Loria J Magn Reson

17 Single-Field Dispersion Curves We need additional non-redundant data to resolve ambiguity in dispersion curves. k ex field independent p A field independent Δωfield dependent = Δω(ppm)*ω spectrometer (MHz)

18 Occurrence Input Parameters k ex = 1000 s –1  = 1500 s –1 p a = 0.95 R 2 0 = 15 s –1 error=5% Two-Field Dispersion Curves Kovrigin, Kempf, Grey, & Loria J Magn Reson

19 From CPMG data to protein motions R 2,eff ν CPMG p B k ex

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

21 Dispersion profiles were fit to a two-site exchange equation: p B, k ex, Δω Similar values suggest concerted motions. Two state fitting: T4 lysozyme L99A 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 = p A /p B 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: p B k ex ΔωR 2 0 (500)R 2 0 (800) globallocal p B k ex ΔωR 2 0 (500)R 2 0 (800) p B k ex

24 n individual residue fits n χ 2 indiv n individual residue fits n χ 2 indiv Two state fitting: T4 lysozyme L99A What about residues not participating in the global process? global fit n χ 2 group global fit n χ 2 group done discard res. with largest χ 2 group /χ 2 indiv discard res. with largest χ 2 group /χ 2 indiv maximum yesno (10% discarded)

25 Two state fitting: T4 lysozyme L99A Experimental data are in good agreement with global fit. CH 3 (  2) 600 MHzCH 3 (  2) 800 MHz NH 500 MHzNH 800 MHz R 2,eff (s -1 ) CPMG (Hz) T (°C)

26 Extracted CPMG parameters follow the van’t Hoff equation. Two state fitting: T4 lysozyme L99A  H = 7 kcal·mol -1  S = 17 cal·mol -1 ·K -1 ln{K} 1/T CH 3 NH

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

28 Two state fitting: T4 lysozyme L99A We could just average p B values over all residues, but there are several drawbacks: –The average value of p B 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 p B, however k ex is global, refines the fit. p A p B (Δω) 2 k ex p B Δωk ex fast exchangeintermediate 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. p unfolded  5% k folding  500 s -1

31 residues have very different apparent k u & k f elimination based on χ 2 group /χ 2 indiv discards ≈ 50% data. folding is not two state. Three states: Fyn SH3 domain G48 mutants log 10 {k u } log 10 {k f } G48M G48V Korzhnev, Salvatella, Vendruscolo, Di Nardo, Davidson, Dobson, & Kay LE Nature

32 Three states: Fyn SH3 domain G48 mutants global parameters (entire protein) k AB, k BA, k BC, k CB 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 y-magnetization x-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 ττ 180 n

37 Three-state dispersion profiles ττ 180 n

38 Three-state dispersion profiles ττ 180 n

39 Three-state dispersion profiles ττ 180 n

40 Three-state dispersion profiles ττ 180 n

41 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 v CPMG R2R2

42 Three states: Fyn SH3 domain G48 mutants Three site model agrees with data. 2-site3-site 2 DF

43 Most χ 2 minimization algorithms are downhill. –To find the correct answer, we need to start near the correct answer Three states: Hard to fit χ2χ2 model parameters

44 10,000 trial grid search varying global params. initiate minimizations from 20 best points. Three states: Hard to fit χ2χ2 model parameters

45 Several of the grid points converge to the same, lowest χ 2 solution. Three states: Hard to fit χ2χ2 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. Δω AB Δω AC T dependent T independent

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 ν CPMG ( Hz) Δω AC (ppm) Δω AB (ppm) χ2χ2 χ2χ2 correct solution Neudecker, Korzhnev, & Kay J Biomol NMR

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

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

51 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 15 N

52 Characterizing minor states using CPMG chemical shift information

53 15 N ppm 1 H ppm ±  ? Obtaining the signs of chemical shift differences

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

55 ωAωA ωBωB k ex <<  slow exchange fast exchange Δω Obtaining the absolute signs of chemical shift differences k ex >> 

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 A BC |Δω| from CPMG sign of Δω from HSQCs at two fields. 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 Δω A-random coil Δω AC 1H1H 15 N 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 residue |Δω AB | |Δω CB | (Hz) B A (folded) C (unfolded) Mittermaier, Korzhnev & Kay Biochemistry

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

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

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

63 Work in progress: PBX homeodomain ?

64 identify optimal conditions: temperature affects exchange rates and populations. R 2,eff ν CPMG  R 2,eff

65 Work in progress: PBX homeodomain 15C20C25C 30C35C40C  R 2 (s -1 ) peaks (sorted)

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

67 Work in progress: PBX homeodomain p B = 5.5% k ex = 1600 s residues consistent with 2-state global process 3 residues with χ 2 group / χ 2 indiv > 2

68 Simple dynamic models ABAB k ex pBpB ωBωB global param.Δω param ABCABC ABAB C k ex pBpB pCpC ωBωB ωCωC 4242 ωBωB ωCωC pCpC pBpB 5252 ABAB CBC k ex pBpB pCpC ωBωB ωCωC ω BC 4343

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72 Relaxation Compensated CPMG N x N x cos π Jτ + 2N y H z sin π Jτ N x cos π Jτ – 2N y H z sin π Jτ N x τ 180 x τ R 2 in-phase R 2 anti-phase ≠ Length of time spent in-phase depends on τ Evolution due to scalar coupling: Variation of R 2 with ν CPMG will depend not only on exchange!

73 Loria, Rance, Palmer, JACS Relaxation Compensated CPMG 2N y H z -N x NxNx 2N y H z NxNx Magnetization is in-phase half the time, independent of τ


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