quantification of dynamics in the...

Quantification of Dynamics in the Solid-State

Bernd Reif

Technische Universität München Helmholtz-Zentrum München

Biomolecular Solid-State NMR Winter School Stowe, VT January 10-15, 2016

• Is there dynamics in the solid-state?

• How does local dynamics compare between solution- and solid-state ?

• How can we quantify dynamics in the solid-state ?

In solutionIn solids

€

R1 (15N) =

d2

10J0 ωH −ωN( ) + 3J1 ωN( ) + 6J2 ωH +ωN( )[ ] +

215c 2J1 ωN( )

€

J(ω) =S2τR

1+ω 2τR2 + 1− SF

2( ) τF1+ω 2τF

2 + SF2 1− SS

2( ) τ S1+ω 2τ S

2

Solution-state: Relaxation is due to molecular tumbling

Solid-state: Relaxation is due to local structural fluctuations

Motivation

1. Solid samples are more susceptible to local structural fluctuations

τc

Measurement of 15N-T1

Solid-State Solution

Chevelkov et al. JCP 128 052316 (2008)

Motivation

2. Temperature dependence of 1H,15N correlations in α-SH3

N-Src loopRT loop

distal loop N- and C-terminus

In solution, things get worse with larger molecular weight

τc

Observables for the quantification of dynamics

- INEPT vs CP based experiments

- T1 Spin-Lattice Relaxation

- T2 Spin-Spin Relaxation

- Order Parameter measurements

- CPMG / R1ρ Relaxation Dispersion

- Heteronuclear NOE

- off- magic angle spinning

⬅ affected by spin density

⬅ rotating methyl groups act as sinks for relaxation

⬅ trivial, but very useful

⬅ spin density ?

⬅ low resolution

⬅ classical observable

!

"

"

"

!

!

⬅ similar to CP/INEPT, quantitative

?

What determines T2 in the solid-state ?

In solution-state: Overall tumbling, τC (local fluctuations, chemical exchange)

In the solid-state:

Not an issue in deuterated samples

LW (adamantane) ≈ 2 Hz

€

T2* = T2

1) Acquisition time

- Insufficient decoupling power - Insufficient MAS frequencies - Probe design

2) Shimming

3) Crystal imperfections

4) Local dynamics ?

LW(1H,13C @ 24 kHz, 600 MHz) > 17 Hz, 4 Hz

τc

Quantification of Dynamics

Relaxation of longitudinal 15N magnetization:

€

R1 (15N) =

d2

10J0 ωH −ωN( ) + 3J1 ωN( ) + 6J2 ωH +ωN( )[ ] +

215c 2J1 ωN( )

€

J(ω) = 1− SF2( ) τF1+ω 2τF

2 + SF2 1− SS

2( ) τ S1+ω 2τ S

2

S: order parameter τ: correlation time τS/τF : Slow and fast motional time scale

In general:

In solution:

τC

€

Cα,α(m, # m )(τ ) = exp −τ /τC( )

€

Y2,mα Ω(0)( ), Y2, $ m

β Ω(τ )( )[ ]

€

J m− # m ωm −ω # m ( ) = dτ0

t

∫ Cα ,β(m, # m )(τ) ⋅ exp i ωm −ω # m ( )τ[ ]

Definition of the spectral density function J(ω):

Quantification of Dynamics in the Solid-State

In Solution-State NMR, relaxation is determined by the tumbling of the molecule in water

In solution

In solids

€

J(ω) = 1− SF2( ) τF1+ω 2τF

2 + SF2 1− SS

2( ) τ S1+ω 2τ S

2€

R1 (15N) =

d2

10J0 ωH −ωN( ) + 3J1 ωN( ) + 6J2 ωH +ωN( )[ ] +

215c 2J1 ωN( )

τS

In Solid-State NMR, relaxation is determined by local structural fluctuations only

τF

1. Measurement of 15N-T1 in the solid-state

Chevelkov et al. J Chem Phys 128 052316 (2008)

€

R1 (15N) =

d2

10J0 ωH −ωN( ) + 3J1 ωN( ) + 6J2 ωH +ωN( )[ ] +

215c 2J1 ωN( )

2. Can we learn something on J(0) in the solid-state ?

Chevelkov et al. JACS 129 10195 (2007)

1) Coherent, Static effect (CSA-dipole correlation) [MAS dependent] 2) Incoherent, Dynamic effect due to Dipole-CSA cross-correlated relaxation [MAS independent]

1) Static effect (CSA-dipole correlation) [MAS dependent]

Composition of Multiplet Intensities

€

δNNz + DHNHzNz = δN + DHN12

+ Hz

#

$ %

&

' ( −

12−Hz

#

$ %

&

' (

*

+ ,

-

. /

0 1 2

3 4 5 Nz

=δN + DHN Hα[ ]δN −DHN H β[ ]0 1 8

2 8

Hβ

Hα

1JNH

Center band

1st spinning side band



Hβ

Hα

1JNH

Center band


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+ Hz

#

$ %

&

' ( −

12−Hz

#

$ %

&

' (

*

+ ,

-

. /

0 1 2

3 4 5 Nz


2 8



Hβ

Hα

1JNH

Center band


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+ Hz

#

$ %

&

' ( −

12−Hz

#

$ %

&

' (

*

+ ,

-

. /

0 1 2

3 4 5 Nz


2 8



Hβ

Hα

1JNH

Center band


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+ Hz

#

$ %

&

' ( −

12−Hz

#

$ %

&

' (

*

+ ,

-

. /

0 1 2

3 4 5 Nz


2 8


Is there a contribution due to dynamics ?

€

ΓNH ,Nc ∝

γ HγNrNH3 ⋅ γNB0δN ⋅ (3cos

2 β −1)*τ c

2) Dynamic effect due to Dipole-CSA cross-correlated relaxation [MAS independent]

15N

1JNH

Chevelkov et al. Mag Res Chem 45 S156-160 (2007) Skrynnikov Mag Res Chem 45 S161-173 (2007)

N-Hα/N-Hβ Differential Line Broadening due to Dynamics

MAS = 13 kHz = const

1JNH

Broad Lines in „traditional“ solid-state NMR experiments

Columns

along 15N

T2 decay of 15N-Hα/β allows to access the timescale of local dynamics

Chevelkov et al. MRC 45 S156-160 (2007)

€

ηCSA /DD =12Δln

Iβ

Iα&

' ( (

)

* + + =

dc15

4J0(0) + 3J1(ωN ){ }P2 (cosθ)

Differential T2 decay of α/β multiplet components Teff = 12°C; MAS = 24 kHz

€

ηCSA /DD =12Δln

Iβ

Iα&

' ( (

)

* + + =

dc15

4J0(0) + 3J1(ωN ){ }P2 (cosθ)Chevelkov et al. MRC 45 S156 (2007)

3. 1H-15N dipolar coupling measurements yield Order Parameters

Simulation Parameters:

MAS = 20 kHz Ideal condition: ωRF(1H)/2π = 56 kHz ωRF(15N)/2π = 76 kHz

ΔωRF(15N)/2π = -6 kHz

Wu and Zilm, JMR A 104, 154 (1993) Dvinskikh, Zimmermann, Maliniak and Sandstrøm, JCP 122, 044512 (2005)

Chevelkov, Fink, Reif, J Am Chem Soc 131, 14018 (2009)

Experimental CPPI spectra for α-spectrin SH3

kHz

Error estimation in the determination of 1H,15N dipolar couplings (K18)

LB = Line Broadening of the Exponential Apodization; Dapp = apparent dipolar splitting; DHN = true dipolar coupling (without scaling factor of the pulse sequence)

1H,15N dipolar couplings in α-spectrin SH3

H-bond acceptor

Are variations in the size of the 1HN-15N dipolar coupling due to a variation in the HN-N bond length or

due to dynamics ?

1.035 Å = 11087.8 Hz 1.045 Å = 10772.5 Hz 1.055 Å = 10468.1 Hz

€

DNH = −µ0γ HγN!rNH3

Correlation between the scalar coupling across a hydrogen bond 3hJNC‘ and the1HN isotropic chemical shift

from Cordier and Grzesiek, JACS 121 1601 (1999)

Correlation between the 1HN,15N dipolar couplings and the 1HN isotropic chemical shift

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DNH = −µ0γ HγN!rNH3

Mob

ility

Increased dynamicsfor weak hydrogen bonds

However: N-H bond length shouldbe increased in a H-Bond

No effect of H-bonding on the N-H bond length

Schanda P, Meier BH, Ernst M Accurate measurement of one-bond H-X heteronuclear dipolar couplings in MAS solid-state NMR. J. Magn. Reson. 210: 246-259 (2011).

Alternatively: Order Parameters via REDOR type experiments

Schanda P, Huber M, Boisbouvier J, Meier BH, Ernst M. Solid-State NMR Measurements of Asymmetric Dipolar Couplings Provide Insight into Protein Side-Chain Motion. Angew. Chem. Int. Ed. 50: 11005-11009 (2012)

Order Parameters via REDOR type experiments

Model-free Analysis to decribe Motion in the Solid-State

€

J(ω ) = 1− SF2( ) τF1+ω 2τF

2 + SF2 1− SS

2( ) τS1+ω 2τS

2

Let's assume that you have slow and fast motions in your protein

There are 4 unknown parameters S2S, S2

F, τS and τF What can we measure?

1H,15N dipole 15N CSA cross-correlated relaxation "15N-T2" 1H,15N dipolar couplings S2

F S2S

15N T1 @ 2 fields

Rmsd minimization of S2S, S2

F, τF and τS

Q16

€

rmsd =1R1,iexp R1,i

theo − R1,iexp( )

#

$ %

&

' (

2

i∑ +

1ηexp

η theo −ηexp( )#

$ % %

&

' ( (

2+ , -

. -

/ 0 -

1 -

1/ 2

Data used for fitting: 15N-T1 (900 MHz) 15N-T1 (600 MHz)

Data used for fitting: 15N-T1 (900 MHz) 15N-T1 (600 MHz) η (15N-CSA / 1H-15N)

S2SS2

F = 0.776; S2S = 0.92

τF = 26 ps

Rmsd minimization of S2S, S2

F, τF and τS

€

rmsd =1R1,iexp R1,i

theo − R1,iexp( )

#

$ %

&

' (

2

i∑ +

1ηexp

η theo −ηexp( )#

$ % %

&

' ( (

2+ , -

. -

/ 0 -

1 -

1/ 2

Data used for fitting: 15N-T1 (900 MHz) 15N-T1 (600 MHz)

Data used for fitting: 15N-T1 (900 MHz) 15N-T1 (600 MHz) η (15N-CSA / 1H-15N)

S2SS2

F = 0.349; S2S = 0.479

τF = 3.9 ns

D62

Order Parameter and τS in α-spectrin SH3

τS and τF in α-spectrin SH3

τS and τF in α-spectrin SH3

Is TROSY beneficial for solid-state NMR?

Observation 1: INEPT based experiments allow to detect residues in mobile regions

Linser et al., J. Am. Chem. Soc. (2010)

Observation 2: Regions which are not detectable in CP experiments undergo a ns-µs time scale dynamics

Quantification of ηCSA/DD using INEPT based experiments


TROSY experiments are beneficial in the solid-state for regions undergoing slow dynamics


Intensities in 2D-HSQC/TROSY and 3D-HNCO/TROSY-HNCO

Using TROSY experiments, the S/N in dynamic regions of the protein can be increased by x2-5

4. heteronuclear NOE measurements: Additional dynamics information in the solid-state

Lopez et al. JBNMR 59 241-249 (2014)

1H,13C heteronuclear NOE measurements

1H,15N heteronuclear NOE measurements

Deuteration is required to avoid spin diffusion

2H R1 rates in Solids and Solution

15N R1 rates in a protonated and deuterated SH3 sample

J. Am. Chem. Soc. 128 12354 (2006)

J. Chem. Phys. 128 052316 (2008)

Aliphatic protons (RAP, Reduction of Adjoining Protonation)

Asami et al., J. Am. Chem. Soc. 2010; Asami et al., Acc. Chem. Res. 2013

✓ 15NH4Cl ✓ [2H,13C]-glucose ✓ 5-30 % H2O (95-70 % D2O)

Experimental 13C T1 decay curves are bi-exponential(25% SH3 RAP sample, 24 kHz MAS)

1. Orientation dependence yieldsfrequency dependent R1 rates→ Mono-exponential initial-rate approximation (Torchia)

2. Spin Diffusion:efficient magnetization transfer to methyls which act as „relaxation sinks“

Dilution of the proton AND carbon spin system 1H,13C correlations of α-SH3: RAP-glucose vs. RAP 2-glycerol

25% RAP-glucose (25 % H2O / 75 % D2O, 2H,13C glucose in M9)

10% RAP-glycerol (10 % H2O / 90 % D2O, [u-2H, 2-13C]-glycerole in M9)

✓ improved resolution (no evolution of J couplings)

✓ simplified spectra: e.g. no Cα labeling for R, Q, E, L, Pno methyl labeling for A, I-γ2, V, L, M

13Cα T1 Decay Curves

25% RAP-glucose, 24 kHz MAS10% RAP-glycerol, 24 kHz MAS10% RAP-glycerol, 50 kHz MAS (mono-exponential)

13Cα T1 in α-spectrin SH3 and MD derived order parameters

Hologne et al. (2005) JACS 127, 11208

3D 2H-13C-13C correlation using 13C-13C RFDR mixing and 2H-13C CPapplied to α-spectrin SH3

5. Protein Side Chain Dynamics

3D-2H,13C,13C Correlation of α-spectrin SH3

2H Pake Pattern for Valine-CD3 in α-spectrin SH3

Conformational exchange is directly reflected in the anisotropy δ and the asymmetry η of the 2H pake pattern (τc < 1/ 52 kHz)

Motional Model for the Side Chain Dynamics of Val-23

Best fit: 2-site jump,jump angle 140° (Center band intensities are not well reproduced in the simulations)

2Hβ Pake Pattern for different Valines in α-spectrin SH3

Lower intensities for V23 indicates motion (τc <≈ 1/160 kHz )

But, ... there are many methyls indicating motion ... ... and no second conformation is visible in the X-ray structure

η=0

η=0 η=1δ1

Comparison of X-Ray Analysis at 100K and RT

Ile-30, 100K Ile-30, RT

Crystal dimensions: RT: 34.5 Å, 42.5 Å, 50.8 Å100 K: 33.6 Å, 42.3 Å, 49.6 Å

B-factors (Å2)main chain RT: 26.9 ; 100K: 13.9side chain RT: 29.6 ; 100K: 17.1whole RT: 28.3 ; 100K: 15.6

ResolutionRT: 1.90 Å; 100 K: 1.49 Å

Acknowledgement

Vipin Agarwal Sam Asami Veniamin Chevelkov Rasmus Linser

Purdue University Nikolai Skrynnikov

quantification of dynamics in the...

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