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**Characterizing millisecond motions in proteins using CPMG-relaxation dispersion measurements**

Tony Mittermaier McGill Aug, 2007 CCPN

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**Dynamics are important for protein function**

energy conformation

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**Two-site conformational exchange**

Weakly populated protein states are often not directly observable in NMR spectra.

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**Carr-Purcell-Meiboom-Gill (CPMG) pulse sequences**

major state minor state

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**Two-site conformational exchange**

In the absence of exchange, magnetization remains in phase precession time

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**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

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**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

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

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Constant time CPMG νCPMG R2 νCPMG

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**Two-site exchange equations**

R2 ωA ωB νCPMG

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**Two-site exchange equations**

General equation: We can extract kAB kBA Δω2 separately Carver & Richards, R.E. J. Magn. Reson

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**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

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**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

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**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

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**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

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**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

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**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)

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**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

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**From CPMG data to protein motions**

R2,eff νCPMG pB kex

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**Two state fitting: T4 lysozyme L99A**

peaks in the region of engineered cavity show broadening.

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**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

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**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

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**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)

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**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)

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**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)

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**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

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**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

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**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

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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. punfolded 5% kfolding 500 s-1

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**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

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**Three states: Fyn SH3 domain G48 mutants**

global parameters (entire protein) kAB, kBA, kBC, kCB 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 x-magnetization y-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**

180 τ τ n

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**Three-state dispersion profiles**

180 τ τ n

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**Three-state dispersion profiles**

180 τ τ n

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**Three-state dispersion profiles**

180 τ τ n

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**Three-state dispersion profiles**

180 τ τ 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 D F R2 H B C G vCPMG E

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**Three states: Fyn SH3 domain G48 mutants**

Three site model agrees with data. 2-site 3-site 2 3883 2131 DF 3975 3948

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**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

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**Three states: Hard to fit**

10,000 trial grid search varying global params. initiate minimizations from 20 best points. χ2 model parameters

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**Three states: Hard to fit**

Several of the grid points converge to the same, lowest χ2 solution. χ2 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. T independent ΔωAC ΔωAB T dependent

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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 νCPMG ( Hz) correct solution χ2 χ2 ΔωAB (ppm) ΔωAC (ppm) Neudecker, Korzhnev, & Kay J Biomol NMR

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**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

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**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

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**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.

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**Characterizing minor states using CPMG chemical shift information**

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**Obtaining the signs of chemical shift differences**

15N ppm ±Dw ? 1H ppm

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**Obtaining the signs of chemical shift differences**

800 MHz (≥ .006 ppm 15N) minor peak invisible 500 MHz Skrynnikov, Dahlquist, & Kay J Am Chem Soc

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**Obtaining the absolute signs of chemical shift differences**

kex << Dw slow exchange fast exchange kex >> Dw ωA ωB Δω

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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

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**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

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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 1H 15N ΔωAC ΔωA-random coil Mittermaier, Korzhnev & Kay Biochemistry

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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 A (folded) |ΔωAB| |ΔωCB| (Hz) B C (unfolded) residue Mittermaier, Korzhnev & Kay Biochemistry

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**G48M summary (25°C) 97% folded 1% partly-folded intermediate 2%**

unfolded kex=1500 s-1 kex=5000 s-1

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**Work in progress: PBX homeodomain**

1LFU Ca secondary chemical shifts Jabet et al (1999) JMB 291, 521

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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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**Work in progress: PBX homeodomain**

identify optimal conditions: temperature affects exchange rates and populations. R2,eff DR2,eff νCPMG

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**Work in progress: PBX homeodomain**

15C 20C 25C DR2 (s-1) 30C 35C 40C peaks (sorted)

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**Work in progress: PBX homeodomain**

15N SQ 20°C 800 MHz 500 MHz

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**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

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**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

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**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

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**Relaxation Compensated CPMG**

Nx -Nx 2NyHz 2NyHz 2NyHz Nx Magnetization is in-phase half the time, independent of τ Loria, Rance, Palmer, JACS

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