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

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conformation energy Dynamics are important for protein function

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

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

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

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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

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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

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

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Constant time CPMG ν CPMG R2R2

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Two-site exchange equations ωAωA ωBωB R2R2 ν CPMG

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Two-site exchange equations General equation: We can extract k AB k BA Δω 2 separately Carver & Richards, R.E. J. Magn. Reson 1972 6 89

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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. 1957 27 1411.

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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. 2001 123 11341.

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k ex (s –1 )3413277502020 (s –1 ) 1540164017701674 pBpB 6%7%4%3% R 2 0 (s –1 )15.615.312.611.3 CPMG Parameter Dependence trouble Kovrigin, Kempf, Grey, & Loria J Magn Reson. 2006 180 93

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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. 2006 180 93

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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. 2006 180 93

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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)

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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. 2006 180 93

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

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

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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. 2001 11 932

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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. 2001 11 932

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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

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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)

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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)

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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

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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

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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

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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.

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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

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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. 2004 430 586

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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

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

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

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

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Three-state dispersion profiles ττ 180 n

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Three-state dispersion profiles ττ 180 n

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Three-state dispersion profiles ττ 180 n

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Three-state dispersion profiles ττ 180 n

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Three-state dispersion profiles ττ 180 n

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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

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Three states: Fyn SH3 domain G48 mutants Three site model agrees with data. 2-site3-site 22 38832131 DF39753948

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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

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

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Several of the grid points converge to the same, lowest χ 2 solution. Three states: Hard to fit χ2χ2 model parameters

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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

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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]

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How much data do you need? (as much as possible) simulated SQ data two static magnetic fields ν CPMG (50-1000Hz) Δω AC (ppm) Δω AB (ppm) χ2χ2 χ2χ2 correct solution Neudecker, Korzhnev, & Kay J Biomol NMR. 2006 34 129

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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. 2005 127 15602

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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. 2006 34 129

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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

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Characterizing minor states using CPMG chemical shift information

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

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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. 2002 124 12352

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

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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. 2005 127 15602

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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. 2005 127 15602

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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 2005 44 15430

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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 2005 44 15430

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

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

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

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Work in progress: PBX homeodomain ?

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

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

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

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Work in progress: PBX homeodomain p B = 5.5% k ex = 1600 s -1 14 residues consistent with 2-state global process 3 residues with χ 2 group / χ 2 indiv > 2

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Simple dynamic models ABAB k ex pBpB ωBωB global param.Δω param. 2121 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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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!

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Loria, Rance, Palmer, JACS 1999 121 2331 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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