Characterizing millisecond motions in proteins using cpmg relaxation dispersion measurements
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McGill. Characterizing millisecond motions in proteins using CPMG-relaxation dispersion measurements. Tony Mittermaier. Aug, 2007 CCPN. Dynamics are important for protein function. energy. conformation. Two-site conformational exchange.

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Characterizing millisecond motions in proteins using cpmg relaxation dispersion measurements

McGill

Characterizing millisecond motions in proteins using CPMG-relaxation dispersion measurements

Tony Mittermaier

Aug, 2007 CCPN



Two site conformational exchange
Two-site conformational exchange

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


Carr purcell meiboom gill cpmg pulse sequences
Carr-Purcell-Meiboom-Gill(CPMG) pulse sequences

major state

minor state


Two site conformational exchange1
Two-site conformational exchange

  • In the absence of exchange, magnetization remains in phase

precession

time


Two site conformational exchange2
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


Constant time CPMG

15N (ppm)

1H (ppm)

full set in less than 24h


Constant time CPMG

νCPMG

R2

νCPMG


Two site exchange equations
Two-site exchange equations

R2

ωA

ωB

νCPMG


Two site exchange equations1
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 equations2
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 equations3
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.


Cpmg parameter dependence
CPMG Parameter Dependence

trouble

Kovrigin, Kempf, Grey, & LoriaJ Magn Reson. 2006 180 93


Single field dispersion curves

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


Single field dispersion curves1
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 curves2
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

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



Two state fitting t4 lysozyme l99a
Two state fitting: T4 lysozyme L99A

  • peaks in the region of engineered cavity show broadening.


Two state fitting t4 lysozyme l99a1
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 l99a2
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 l99a3
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 l99a4
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 l99a5
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 l99a6
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


Two state fitting t4 lysozyme l99a7

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 l99a8
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
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 mutants1
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 mutants2
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
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 profiles1
Three-state dispersion profiles

x-magnetization

x-magnetization

y-magnetization

y-magnetization

exchange

chemical shift evolution

autorelaxation


Three state dispersion profiles2
Three-state dispersion profiles

matrix exponential can be calculated numerically – MATLAB, etc.







Three state dispersion profiles8
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 mutants3
Three states: Fyn SH3 domain G48 mutants

  • Three site model agrees with data.


Three states hard to fit
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 fit1
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 fit2
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
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 possible1
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 possible2
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 15 n
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 15 n1
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 15 n2
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
Obtaining the signs of chemical shift differences information

15N ppm

±Dw ?

1H ppm


Obtaining the signs of chemical shift differences1
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
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 differences2
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
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
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 states1
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 c
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
Work in progress: PBX homeodomain information

1LFU

Ca secondary chemical shifts

Jabet et al (1999) JMB 291, 521


Work in progress pbx homeodomain1
Work in progress: PBX homeodomain information

  • broadened peaks throughout protein in the absence of DNA



Work in progress pbx homeodomain3
Work in progress: PBX homeodomain information

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

R2,eff

DR2,eff

νCPMG


Work in progress pbx homeodomain4
Work in progress: PBX homeodomain information

15C

20C

25C

DR2

(s-1)

30C

35C

40C

peaks (sorted)


Work in progress pbx homeodomain5
Work in progress: PBX homeodomain information

15N SQ 20°C

800 MHz

500 MHz


Work in progress pbx homeodomain6
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
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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