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Characterizing millisecond motions in proteins using CPMG-relaxation dispersion measurementsPowerPoint Presentation

Characterizing millisecond motions in proteins using CPMG-relaxation dispersion measurements

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

Tony Mittermaier

Aug, 2007 CCPN

Two-site conformational exchange

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

Two-site conformational exchange

- In the absence of exchange, magnetization remains in phase

precession

time

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

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

Two-site exchange equations

General equation:

We can extract kAB kBAΔω2 separately

Carver & Richards, R.E. J. Magn. Reson 1972 6 89

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.

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.

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

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

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)

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

Two state fitting: T4 lysozyme L99A

- peaks in the region of engineered cavity show broadening.

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

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

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)

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)

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)

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

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

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

Three states: Fyn SH3 domain G48 mutants

- Several G48 mutants having folding kinetics amenable to CPMG studies.

- punfolded 5%
- kfolding 500 s-1

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

Three states: Fyn SH3 domain G48 mutants

global parameters (entire protein)

kAB, kBA, kBC, kCB

local parameters (each amide group)

AB, AC

Three-state dispersion profiles

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

Three-state dispersion profiles

x-magnetization

x-magnetization

y-magnetization

y-magnetization

exchange

chemical shift evolution

autorelaxation

Three-state dispersion profiles

matrix exponential can be calculated numerically – MATLAB, etc.

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

Three states: Fyn SH3 domain G48 mutants

- Three site model agrees with data.

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

Three states: Hard to fit

10,000 trial grid search varying global params.

initiate minimizations from 20 best points.

χ2

model parameters

Three states: Hard to fit

Several of the grid points converge to the same,

lowest χ2 solution.

χ2

model parameters

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

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]

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

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

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

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.

Obtaining the signs of chemical shift differences information

800 MHz

(≥ .006 ppm 15N)

minor peak

invisible

500 MHz

Skrynnikov, Dahlquist, & Kay J Am Chem Soc. 2002 124 12352

Obtaining the absolute signs of chemical shift differences information

kex << Dw

slow

exchange

fast

exchange

kex >> Dw

ωA

ωB

Δω

Obtaining the signs of chemical shift differences information

- 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

Reconstructing spectra of invisible states information

A

- |Δω| from CPMG
- sign of Δω from HSQCs at two fields.

B

C

Korzhnev, Neudecker, Mittermaier, Orekhov & Kay J Am Chem Soc. 2005 127 15602

Structures of invisible states information

- 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 2005 44 15430

Structures of invisible states information

- 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 2005 44 15430

G48M summary (25 information°C)

97%

folded

1%

partly-folded

intermediate

2%

unfolded

kex=1500 s-1

kex=5000 s-1

Work in progress: PBX homeodomain information

1LFU

Ca secondary chemical shifts

Jabet et al (1999) JMB 291, 521

Work in progress: PBX homeodomain information

- broadened peaks throughout protein in the absence of DNA

Work in progress: PBX homeodomain information

?

Work in progress: PBX homeodomain information

- identify optimal conditions: temperature affects exchange rates and populations.

R2,eff

DR2,eff

νCPMG

Work in progress: PBX homeodomain information

14 residues consistent with

2-state global process

3 residues with

χ2group/χ2indiv > 2

pB = 5.5%

kex = 1600 s-1

Simple dynamic models information

global param.Δω param.

pB

kex

21

A B

ωB

pB

pC

kex

kex

42

A B C

ωB

ωC

pB

kex

A B

ωB

52

kex

kex

C

pC

ωC

ωB

kex

A B

pB

43

kex

C BC

pC

ωBC

ωC

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