Characterizing millisecond motions in proteins using CPMG-relaxation dispersion measurements

Characterizing millisecond motions in proteins using

CPMG-relaxation dispersion measurements

Tony Mittermaier

Aug, 2007 CCPN

McGill

conformationen

ergy

Dynamics are important for protein function

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

Two-site conformational exchange

major state minor state

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

time

prec

essi

on


• In the absence of exchange, magnetization remains in phase

• 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

prec

essi

on


• 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 (R2,eff) time

prec

essi

on

CPMG pulse train

180 180

180 180 180 180 180 180


15N (ppm)

1H (ppm)

Constant time CPMG

full set in less than 24h

Constant time CPMGνCPMG

R2

νCPMG

Two-site exchange equations

Bk

kA

BA

AB

ωA ωB

022 ,,,, RkkfR ABBAABCPMG

R2

νCPMG

Two-site exchange equations

R2 1 / cp 12

R2A0 R2B

0 kex 1 cp

cosh 1 D cosh D cos

D 12

1 2 2

2 2 1/2

cp

2 (2 2 )1/2

1/2

(R2A0 R2B

0 pAkex pBkex )2 2 4 pA pBkex

2

2(R2A0 R2B

0 pAkex pBkex )

General equation:

We can extract kAB kBA Δω2 separately

ex

BAA

ex

ABB

BAABex

kkp

kkp

kkk

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

Two-site exchange equationsFast timescale: kex>>Δω

CPMG

ex

ex

CPMG

ex

BA kkk

ppRR4

tanh412

022

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 equationsSlow timescale: kex<<Δω

CP

CPABkRR sin10

22

Curve is independent of kBA

We can only extract kAB and Δω2

Tollinger et. al J Am Chem Soc. 2001 123 11341.

kex (s–1) 341 327 750 2020

(s–1) 1540 1640 1770 1674pB 6% 7% 4% 3%

R20 (s–1) 15.6 15.3 12.6 11.3

CPMG Parameter Dependence

trouble

Kovrigin, Kempf, Grey, & Loria J Magn Reson. 2006 180 93

Occ

urre

nce Input Parameters

kex = 1000 s–1

= 1500 s–1

pa = 0.95R2

0 = 15 s–1

error=5%

Single-Field Dispersion Curves


Input Parameters

kex = 1000 s–1

= 1500 s–1

pa = 0.95R2

0 = 15 s–1

error=5%




• 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)

Occ

urre

nce

Input Parameters

kex = 1000 s–1

= 1500 s–1

pa = 0.95R2

0 = 15 s–1

error=5%

Two-Field Dispersion Curves


From CPMG data to protein motions

R2,eff νCPMG pB kex

Two state fitting: T4 lysozyme L99A

• peaks in the region of engineered cavity show broadening.

• 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


• Collected CPMG data at a range of temperatures• We expect K = pA/pB to follow the van’t Hoff

equation:

TR

HRSK 1ln

ln{K}

1/T Mulder, Mittermaier, Hon, Dahlquist, & Kay Nat Struct Biol. 2001 11 932


• Data were fit as a group: pB kex Δω R2

0(500) R20(800)

global local

pB kex Δω R20(500) R2

0(800)pB kex Δω R2

0(500) R20(800)



0(500) R20(800)



0(500) R20(800)



0(500) R20(800)

pB kex

n individualresidue fits

n χ2indiv


• What about residues not participating in the global process?

globalfit

n χ2group

donediscard res. with largest

χ2group/χ2

indiv

maximum?22

2

indiv

group

yes no(10% discarded)


• Experimental data are in good agreement with global fit.

CH3 (2) 600 MHz CH3 (2) 800 MHz

NH 500 MHz NH 800 MHz

R2,eff (s-1)

CPMG (Hz)

T (°C)

• Extracted CPMG parameters follow the van’t Hoff equation.


H = 7 kcal·mol-1S = 17 cal·mol-1 ·K-1

ln{K}

1/T

CH3

NH

• Extracted exchange rates are similar to rates of ligand binding in cavity.


koff = 800 s-1

90˚

kex 1000 s-1


• 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

Three states: Fyn SH3 domain G48 mutants

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

• punfolded 5%

• kfolding 500 s-1

• residues have very different apparent ku & kf

• elimination based on χ2

group/χ2indiv

discards ≈ 50% data.

• folding is not two state.


log10{ku}

log 1

0{k f

}

G48M

G48V

Korzhnev, Salvatella, Vendruscolo, Di Nardo, Davidson, Dobson, & Kay LE Nature. 2004 430 586


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.


Cy

By

Ay

Cx

Bx

Ax

CBCBAC

CBBCBAABAB

BAAB

ACCBCB

ABCBBCBAAB

BAAB

Cy

By

Ay

Cx

Bx

Ax

MMMMMM

RkkkRkkk

kRkRkk

kRkkkkRk

MMMMMM

t

00000

0000000

000000

x-magnetization

y-magnetization

x-magnetization

y-magnetization

exchange

chemical shift evolutionautorelaxation


tMRtMt

ˆ

0ˆexp MtRtM

matrix exponential can be calculated numerically – MATLAB, etc.


τ τ180

n

0M


τ τ180

0ˆexp MRM

n


τ τ180

n

0ˆexp1801

11

11

1

MRM


τ τ180

n

0ˆexpˆexp1801

11

11

1

MRRM


τ τ180

n

0ˆexpˆexp1801

11

11

1

M

n

RRM n


• This general procedure allows dispersion profiles to be calculated for dynamical models of arbitrary complexity.

A

B C

D

E

F

G

H

vCPMG

R2


• Three site model agrees with data.

2-site 3-site2 3883 2131

DF 3975 3948

2

2exp2

RRR calc

• Most χ2 minimization algorithms are downhill.– To find the correct answer, we need to

start near the correct answer

Three states: Hard to fit

χ2

model parameters

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


χ2

model parameters

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.

ΔωABΔωAC

Tdependent

Tindependent


Bk

kI

k

LkLF

BI

IB

off

on

• Vary conditions such that some of the physical parameters change while others remain constant.

only one ratedepends

on [L]


• simulated SQ data• two static magnetic fields• νCPMG (50-1000Hz)

ΔωAC (ppm)

Δω

AB

(ppm

)χ2 χ2

correctsolution

Neudecker, Korzhnev, & Kay J Biomol NMR. 2006 34 129

• 1H 15N SQ DQ ZQ MQ experiments

CPMG experiments beyond amide 15N

1H SQ

ΔωH

ΔωN

15N SQ

ZQ

ΔωH-ΔωN

DQ

MQ(1H)

MQ(15N)

ΔωH+ΔωN

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

SQ1 temperature

true ΔωAB (ppm)best

fit Δ

ωA

B (p

pm)

• simulated data• two static magnetic fields• group fitting


SQ3 temperatures

SQ DQ ZQ MQ1 temperature

Neudecker, Korzhnev, & Kay J Biomol NMR. 2006 34 129

• 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.


Characterizing minor states using CPMG chemical shift information

15N ppm

1H ppm

±?

Obtaining the signs of chemical shift differences

minor peakinvisible

800 MHz

500 MHz


(≥ .006 ppm 15N)

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

ωA ωB

kex << slowexchange

fastexchange

Δω

Obtaining the absolute signs of chemical shift differences

kex >>


• 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.

tVRtVt

ˆ

coherence instates A, B &C


Reconstructing spectra of invisible states

A

B C

• |Δω| from CPMG• sign of Δω from

HSQCs at two fields.


Structures of invisible states • Match reconstructed spectrum to reference state

with known spectrum:– unfolded state– ligand-bound state– phosphorylated form– etc.

state C is theunfolded state

ΔωA-random coil

ΔωAC

1H 15N

Mittermaier, Korzhnev & Kay Biochemistry 2005 44 15430

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

|ΔωAB||ΔωCB|(Hz)

B

A (folded)

C (unfolded)

Mittermaier, Korzhnev & Kay Biochemistry 2005 44 15430

G48M summary (25°C)

97%folded

1%partly-foldedintermediate

2%unfolded

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

1LFU

Work in progress: PBX homeodomain

Jabet et al (1999) JMB 291, 521

C secondary chemical shifts

Work in progress: PBX homeodomain• broadened peaks throughout protein in the

absence of DNA


?


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

R2,eff

νCPMG

R2,eff


15C 20C 25C

30C 35C 40C

R2

(s-1)

peaks (sorted)


800 MHz

500 MHz

15N SQ 20°C


pB = 5.5%kex = 1600 s-1

14 residues consistent with2-state global process

3 residues withχ2

group/χ2indiv > 2

Simple dynamic models

A Bkex

pBωB

global param. Δω param.

2 1

A B C

A B

C

kex kexpB pC

ωB ωC

4 2

ωB

ωCpC

pB

kexkex

kex

5 2

A Bkex

C BCkex

pB

pC

ωB

ωC ωBC

4 3

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Characterizing millisecond motions in proteins using CPMG-relaxation dispersion measurements

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