martin-luther-universität halle-wittenberg institut für physik nmr group multi-frequency proton...

Martin-Luther-Universität Halle-Wittenberg Institut für Physik

NMR group

Multi-Frequency Proton NMR Relaxation for the Study of Protein

Rotational Diffusion: Applications to Crowded Solutions

M. Roos, M. Hofmann, § E.A. Rössler,§ A. Krushelnitsky, Kay Saalwächter

Martin-Luther-Universität Halle-Wittenberg Institut für PhysikNMR group

§ Universität BayreuthPhysikalisches InstitutExperimentalphysik II


NMR group

Multi-Frequency Proton NMR Relaxation for the Study of Protein Rotational

Diffusion

M. Roos, M. Hofmann, E.A. Rössler, A. Krushelnitsky, Kay Saalwächter

¨ Eye lens crystallins and cataract

¨ NMR methods for (translational and) rotational diffusion

¨ aB-crystallin aggregates- self-diffusion, tr, RH and size scaling- dynamics upon crowding

¨ Crowded dynamics of other proteins

¨ Conclusions

Brownian motion:

translation vs tumbling


NMR group

a

b

g

crystallins(c ~ 0.4 mg/ml)

The vertebrate eye lens: a crowded environment

after P. Schurtenberger, 2010

S. Jehle, …, H. Oschkinat, Nat. Struct. Mol. Biol. 17 (2010) 1037.C. N. Kingsley, …, H. Oschkinat, R. W. Martin, Structure 21 (2013) 2221.

0.5 nm

aB-crystallin: a surfactant/chaperone- polydisperse but well-structured

aggregates- 800 kDa ~40-mers (monomer ~20

kDa)- co-aggregates with other

mutated/misfolded proteins (shielding)


NMR group

a

b

g

concentrate

global dynamics?

interactions?

inducecataract

phase separation?colloidal crystallization?

amyloid formation?

Cataract – a puzzling, multi-faceted desease

e.g.: cold cataractin a bovine eye lensat 4°C (reversible)


NMR group

Translation vs. rotation : Stokes-Einstein(-Debye)

effective medium viscosity h

2RH

tr

Dt

validity of the effective-medium approach for

highly concentrated (“crowded”) protein solutions?


NMR group

Stokes-Einstein and viscosity beyond Einstein

h from capillary viscosimetry

fit result: apparent protein density

in hydrodynamic volume rapp » 377±8 g/cm³(true density rprotein » 1.35 g/cm³)

consider protein dimensions:RH,eff = 9.5±0.3 nm from Dt (RH,lit = 9.5 nm)with MW » 800 kDa Þ rapp » 380 g/cm3

D.J. Thomas, J. Colloid Sci. 20 (1965) 267

volume fraction f = fapp = c/rapp

0 50 100 150 200

5

10

15

200.0 0.1 0.2 0.3 0.4 0.5 0.6

fapp

= c/ rapp

visc

osity

/

mP

as

concentration / mg/ml

Einstein

)

G. Foffi, …, P. Schurtenberger, Proc. Nat. Acad. Sci. USA 111 (2014) 16748

hard-sphere-like colloidal glass transition!


NMR group

0.0 0.5 1.0 1.5 2.00.01

0.1

1

Q / 1012 s/m2

D=25 ms D=300 ms

norm

. int

ensi

tyTranslational diffusion: pulsed-gradient NMR

G

PGSTE, 1H @ nL=400 MHz

<Þ Dt>

Ea ~ 19 kJ/mol (ºwater!)

RH = 95±3 nm ¹ f(T) (ºlit.!)

testing Stokes-Einstein

Dt viscosity h

3.2 3.4 3.6

1

10

visc

osi

ty / mP

as

3.2 3.4 3.61

10

100

27, 354565

11685

189 mg/ml

D2O

185

113

85

35

LYZ 180 mg/ml

SD

C x

10-1

2 /

m²/

s

1000/T / 1/K


NMR group

Rotational diffusion by NMR

- isotropic Brownian tumbling removes orientation-dependent intercations from spectra

- but: relaxation times (T1, T2) depend on the timescale of these fast (tr ~ ns) orientation fluctuations

H

H

e.g. dipole-dipole coupling

q(t)

B0

tr

- described in terms of rotation autocorrelation functions, e.g. C2,0(t) = <P2[cos q(t)]P2[cos q(t+t)]> t

~ exp{-t/ tr}

- BPP/Redfied theory predicts, e.g., where the spectral density Jr(w) = FT{C(t)} Þ

spectral density and Ri

R 1 , NOE

(tint)-1

(t r )-1

log w

J(w

)

R 2 (J(0))

(ts)-1

a problem!


NMR group

Rotational motion – the common approach

L. E. Kay, D. A. Torchia, Ad Bax, Biochemistry 28 (1989) 8972.

staphylococcal nucleasecorrelation function including internal motions

a “by-product” from high-resolultion 1H-15N NMR!

T1 decay

the crucial ratio


NMR group

“Simple NMR”: the potential of integrated 1H signal

Fouriertransformation

HO–CH2–CH3

frequencyspectrum

N

S

spin-1/2

free induction

decay

acquisition time

inhom. low field: • no spectral resolution• couplings, broadening and

relaxation...

...encoded in time-domain signal decay


NMR group

Rotational motion – the easier (and better?) approach

focus on sampling integral 1H signal at low frequencies w(L)

log C

r(t)

log time

“normal” Brownian tumbling

local anisotropy

A. Krushelnitsky, Phys. Chem. Chem. Phys. 8 (2006) 2117

“electrostatic steering”

(from field-cycling NMR)

A. G. Krushelnitsky, V.D. Fedotov. J. Biomol. Struct. Dyn. 11 (1993) 121


NMR group

□ - T2 (@ 20 MHz low

field)

▲ - T1r @ 20 kHz spin lock

○ - T1r @ 40 kHz spin

lock

● - off-res. T1r @ 60 kHz

red lines – two-component C(t)

dashed blue lines – single-component C(t) Sr

2 = 0

Robust variable-temperature fitting

Þ tr(T), Ea ~ 17 kJ/mol (water again!)

0.1

1.0

T1r

, T2

/ m

s


NMR group

Consequences of weak local anisotropy

~ 1 ms

0.6 … 3.7 ms in the investigated c rangefor aB-crystallin


NMR group

retardation factors:

rt,r = Dt,r(35 mg/ml) / Dt,r(c)

aB-crystallin dynamics upon crowding

0 50 100 150 200

1

2

3

456

translational diffusion

viscosity

reta

rdati

on f

act

or

c / mg/ml

rotationaldiffusion

tetrahedral 24-mer(also other n-mers)

S. Jehle, …, H. Oschkinat, Nat. Struct. Mol. Biol. 17 (2010) 1037.

“cage effect”known from glass-forming colloids


NMR group

Size scaling: fractal dimension and compactness

J. Liang, K.A. Dill, Biophys. J. 81 (2001) 751-766

d=2.47

van-der-Waals volumeV ~ M ~ Rg/H

d

Rg: radius of gyration (from scattering/lit. structures)RH: hydrodynamic radius

(fractal) dimensiond = 3: compact sphered = 2: random coil

structural data from the PDB

translation:

rotation:


NMR group

Size scaling: fractal dimension and compactness

A. Krushelnitsky, Phys. Chem. Chem. Phys. 8 (2006) 2117

Dt ~ M-0.4 tR ~ M1.2

aB-crystallin is structurally similar to other global proteins!

10 100 1000

10

10 100 1000

10

100

1000

Dtx1

0-11 /

m2 /s

(20

0C

)

M / kDa

2t r /

ns

lysozymebinase

trp -repressor

BSA

aB-crystallin

5

tR ~ M1.1±0.2

from T1/T2

10 100

10

100

t r /

n

s

M / kDa


NMR group

Smaller proteins: also internal motions matter

e.g. lysozyme (14.4 kDa)T2, T1r plus T1(w) from fast field-cycling NMRspectral density representation Rx = 1/Tx ~ J(w)

R1~1/T1

slow tail!


NMR group

Various proteins: shape and interactions matter

aB-crystallin (~800 kDa)mel ~0 D (?)

BSA (~66 kDa)mel ~ 450 D

lysozyme (~14.4 kDa)mel ~ 200 D

forms transient clusters!

L. Procar et al., J. Phys. Chem. Lett. 1 (2010) 126.

dimer

mono-mer


NMR group

Slow tail: consequences for T1/T2 analysis

BSA (66 kDa) and lysozyme (14.4 kDa)

simulate 15N-1H T1/T2/NOE metadata, fit to model w/o slow tailÞ significant errors even for c ~ 50 g/L!

“rigid” “mobile”


NMR group

Summary

¨ aB-crystallin (800 kDa aggregate/multimer): same “compactness” (fractal dimension) as globular proteins

¨ strong decoupling of rotational from translational diffusion and viscosity resembles a spherical colloid with minimized

interactions¨ BSA and lysozyme exhibit lesss rot./trans. decoupling

Þ a matter of shape and interactions¨ rotational tumbling has local

anisotropy/slow component

Þ T1/T2-based tr-determination

critical at high c

! €€€:thanks to:Matthias Roos, Susanne Link, Alexey Krushelnitsky, Jochen Balbach (U Halle)Marius Hofmann, E. Rössler (U Bayreuth)

M. Roos, S. Link, J. Balbach, A. Krushelnitsky, K. Saalwächter,Biophys. J. 108 (2014) 98.

martin-luther-universität halle-wittenberg institut für physik nmr group multi-frequency proton...

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