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energie atomique • energies alternatives

instn

UNIVERSITÉ DE
VERSAILLES

ST-QUENTIN-EN-YVELINES

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UNIVERSITÉ
PARIS
SUD

Comprendre le monde.
construire l'avenir*

Experiment and Modelling in Structural NMR

November 28th – December 2nd 2011

INSTN – CEA Saclay, France

Nicolas Birlirakis

ICSN CNRS, France

3D modern techniques

[03002]

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Organized by

Thibault Charpentier
Patrick Berthault
Constantin Meis

thibault.chapentier@cea.fr
patrick.berthault@cea.fr
constantin.meis@cea.fr
## Lectures

History, General principles

M. Goldman, CEA Saclay

Formalism and Interactions

H. Desvaux, CEA Saclay

Molecular Modelling

M. Nilges, Institut Pasteur

Anisotropy for Conformational studies

M. Blackledge, CEA Grenoble

Oriented media

D. Merlet, Univ. Paris-Sud 11

Techniques of solid-state NMR

D. Massiot, CNRS Orléans

NMR crystallography

F. Taulelle, UVSQ

### 3D Modern Techniques

N. Birlirakis ICSN - CNRS

Interactions ligand-macromolecules

G. Lippens, University of Lille

Bio-Solid State NMR

H. Oschkinat, University of Berlin

Bioinformatics-protein assembly

R. Guérois, CEA Saclay

Materials Modelling & Simulations¹

C. Meis, INSTN - CEA, Saclay

DFT calculations of NMR parameters.

J. Yates, Oxford University

Inorganic Materials-Ceramics

S. Ashbrook, University of St Andrews

Amorphous materials

T. Charpentier, CEA Saclay

Hyper-polarization

G. De Paepe, CEA Grenoble

Fast NMR

N. Giraud, Univ. Paris-Sud 11

NMR Diffusometry : Dynamics in Complex Systems over many decades

R. Kimmich, University of Ulm

## ORGANISATION

* Coordinator for the INSTN - CEA Saclay
  Constantin MEIS, INSTN/DIR

* Coordinators for the CEA
  Patrick BERTHAULT, DSM/IRAMIS
  Thibault CHARDPENTIER, DSM/IRAMIS

* Coordinators for the Universities
  Pierre Richard DAHOO, Versailles Univ., UVSQ
  Francis TAULELLE, Versailles Univ., UVSQ
  Eric SIMONI University Paris-Sud 11
  Denis MERLET, University Paris-Sud 11

* Secretary, Information and Registration
  Dominique PARISOT,
  INSTN - CEA Saclay
  Bat. 395 - PC N°35
  Gif-sur-Yvette F-91191
  📧: +33 1 69084882
  email: dominique.parisot@cea.fr

A limited number of scholarships can be obtained for PhD students

contact : constantin.méis@cea.fr

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Winter-School

## “Experiment and Modelling in Structural NMR”

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The aim of the school is to provide basic understanding on the coupling of theoretical Modelling and Simulation methods to the Experiments in structural NMR, for biology and material science. It is composed of Seminars in the morning and Practical Training in the afternoon involving both the theoretical and experimental aspects.

November 28 - December 2, 2011
INSTN - CEA, Saclay

http://www-instn.cea.fr (events 2011)

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# 3D NMR experiments applied to proteins

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<figure><img src="image_14.png" /><figcaption>amino acid</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>peptide < 50aa < protein</figcaption></figure>

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Essential constituents of all living organisms

Linear chains consisting of 20 L-amino acids

Their folding to particular 3D structures triggers their biological function

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Attractive targets for therapeutic applications once their structure-activity relationship is understood
**General considerations**

- Chemically synthesized molecules (SPPS)

- Isotopic labelling expensive → homonuclear ¹H-¹H 2D experiments

**Spectral assignment**

- Starting point for magnetisation transfer: backbone NH protons (experiments in H₂O)

- Spin system identification via scalar couplings: 2D COSY, RELAYS, TOCSY

- Sequential assignment: 2D NOESY

**Extraction of geometrical informations**

- Dihedral angle $\phi$ determination from ³J<sub>HN-Hα</sub> couplings: 2D-COSY-DQF (Karplus equations)

- Interproton distance determination: 2D NOESY (build up with several $\tau_m$)

<figure><img src="image_18.png" /></figure>

**General considerations**

- Favorable $T_2$ relaxation

- Increased ¹H signal density → increased spectral complexity and peak overlapping (structuration dependent)

**Spectral assignment and structure elucidation**

- Same strategy as previously

- Addition of one more dimension to increase resolution: first 3D experiment NOESY-TOCSY, Nature 332, 374 (1988)

<figure><img src="image_19.png" /></figure>

**Breakthrough**

- Recombinant protein expression → affordable ¹⁵N labelling (natural abundance 0.366%)

- The gene encoding the protein of interest is inserted to the plasmids

- Plasmids contain genes confering resistance to antibiotics (selection)

- Plasmids are inserted to the bacteria (transformation)

- Use of rich media (LB) for cell replication

- Induction in poor media (M9) containing ¹⁵NH₄Cl

- Rare codons

- Protein folding and inclusion bodies

- Post-translational modifications

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### Heteronuclear 3D experiments

- Resolve the ¹HN overlapping by the use of ¹⁵NH frequency : 4ppm versus 30-35ppm

### Sensitivity considerations (S/N)

S ~ nA (1/T) $B_0^{3/2} \gamma_{obs}^{3/2} \gamma_{exc} T_2 \sqrt{N_{scan}}$

Cryoprobe technology: $N_d$

n: sample quantity (v·c)

A: active nuclei abundance

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## Going from 2D to 3D

<figure><img src="image_25.png" /><figcaption>2D NOESY ($\tau_m$=150ms)
4 scans</figcaption></figure>

<figure><img src="image_26.png" /><figcaption>3D NOESY-HSQC H-H-N ($\tau_m$=150ms)
8 scans</figcaption></figure>

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Axial peak suppression: $\phi_1$ and rec cycled x, -x

Quadrature detection at the indirect dimension using $\phi_1$ incrementation:

TPPI (axial peak at the edges, folding)

States (axial peak in the middle, aliasing)

States-TPPI (axial peak at the edges, aliasing)
HMQC (J<sub>II</sub>, J<sub>SS</sub>, T<sub>2I</sub>, T<sub>2S</sub>)

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refocused HSQC (J<sub>SS</sub>, T<sub>2S</sub>)

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HSQC (J<sub>SS</sub>, T<sub>1I</sub>, T<sub>2S</sub>)

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sensitivity enhanced HSQC (J<sub>SS</sub>, T<sub>1I</sub>, T<sub>2S</sub>)

<figure><img src="image_35.png" /></figure>

- Due to increased spectral complexity, peak assignment is difficult through 3D H-H-N TOCSY/NOESY-HSQC experiments

- Slow molecular tumbling results in rapid T<sub>2</sub> proton relaxation: COSY and TOCSY HN → Hα magnetisation transfer fails especially in helical regions (³J<sub>HN-Hα</sub> ~ 3Hz)

<figure><img src="image_36.png" /></figure>
- Recombinant expression of ¹³C, ¹⁵N labelled proteins using ¹⁵NH₄Cl and ¹³C₆-glucose
  → access to triple-resonance experiments

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- Resolve the ¹HC overlapping by using ¹³CH frequency: 5ppm versus 65-70ppm for the aliphatics

- Use of heteronuclear couplings ¹H-¹⁵N, ¹H-¹³C, ¹³C-¹³C, ¹⁵N-¹³C (¹J and ²J) for unambiguous intra- and inter-residual assignment

- Magnetisation transfers implicating slowly relaxing nuclei

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Water magnetization at z prior to WATERGATE module

Proton decoupled version (longer T₂ relaxation for ¹⁵N, ¹³C nuclei)

Constant time at ¹⁵N dimension

¹J<sub>CαCβ</sub> couplings not refocused during t₂

$$ \Delta_1 = 1/4 J_{HN} = 2.7 \text{m} $$

$$ \Delta_2 = 12 \text{m} \text{ (relaxation optimized, } 1/4 J_{NC\alpha} \sim 22 \text{m)} $$

Same sequence for HNCO experiment (via Cα-CO channel interconversion)
- Shaped pulses

- Pulsed field gradients

- Water suppression

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<figure><img src="image_47.png" /><figcaption>Excitation profile of a rectangular
90° pulse $\tau_p = 1$ms</figcaption></figure>

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Rectangular hard pulses (polychromatic): $\gamma B_1/2\pi \gg\gg \Delta F$
Typical hard pulse lengths @ 800MHz, max admitted power:

<footnote>$^{1}$H $\rightarrow$ 7-...µs</footnote>

<footnote>$^{15}$N $\rightarrow$ 39.5µs</footnote>

<footnote>$^{13}$C $\rightarrow$ 14µs</footnote>
<figure><img src="image_49.png" /><figcaption>Amplitude modulation: first trials</figcaption></figure>

<figure><img src="image_50.png" /><figcaption>Amplitude modulation: peak selection</figcaption></figure>

90° Gaussian δ and J evolution during pulse:
Amplitude/phase modulation: band selection (top-hat profile)
Gaussian Cascade and BURP famillies

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Amplitude/phase modulation: band selection (top-hat profile)

Gaussian Cascade family

- Universal pulses: Q5 (90°, 6.18) and Q3 (180°, 3.41/3.448)

- Excitation pulse: G4 (7.82)

- Inversion pulse: G3 (3.556)

BURP famillies

- Universal pulses: U-BURP (90°, 4.666) and RE-BURP (180°, 4.64/5.814)

- Excitation pulses: E-BURP1 (4.514) and E-BURP2 (4.952)

- Inversion pulses: I-BURP1 (4.498) and I-BURP2 (4.53)

Figure of merit (depends on the shape): $FM = \tau_p \Delta\Omega$

Frequency shifted (laminar) pulses: $\Delta\phi = 2\pi \tau_p \Delta F / k$
<figure><img src="image_52.png" /></figure>

### Advantages

* zoom into a precise spectral region

* suppression of indesired signals (solvent)

* speed-up experiments

* resolution increase
  - precise measurement of $\delta$ et $\Delta$
  - refocusing of homonuclear couplings

* possibility to direct transfers

* possibility to treat an homonuclear system as heteronuclear

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- Differentiation between ¹³Cα (or ¹³Caliph) and ¹³CO regions

Use of rectangular pulses: $τ_{180°} = \sqrt{3} / (2ΔΩ)$ and $τ_{90°} = \sqrt{15} / (4ΔΩ)$

where $ΔΩ$ is the difference of pulse carrier and the first null point

Problems: inhomogenous excitation/inversion and cryoprobe arcing if executed simultaneously high power ¹³C and ¹⁵N pulses

Use of universal top-hat pulses (or interleaved G4 and G4tr)

<figure><img src="image_54.png" /><figcaption>180° pulse comparison: 33µs square and 200µs Q3</figcaption></figure>

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**ATTENTION**
Offset-dependent
transient Bloch-Siegert
phase shifts in
homREFocusing

- Selective perturbation of ¹HN region (BEST experiments)

- Solvent selection (flipback or suppression)

- High field spectrometrs → large ¹³C spectral width in Hz → imperfect inversion/decoupling
  → use of adiabatic pulses: smoothed CHIRP and WURST families

<figure><img src="image_56.png" /><figcaption>180° pulse comparison: 28µs square and 500µs CA-WURST-4</figcaption></figure>

Adiabatic decoupling:

Use P4M5 supercycle

Use bi-level decoupling for reduction
of sidebands in ¹H-¹H-¹³C and ¹H-¹H-¹⁵N
experiments

Homonuclear decoupling → offset
dependent Bloch-Siegert frequency shifts

- Adiabatic ¹⁵N inversion and decoupling is used to reduce power and thus probe heating, important in rapid scan conditions

- Adiabatic pulses are tolerant to Rf inhomogeneity

- Interesting pseudoadiabatic pulses: Bip and power-BIBOP for inversion and power-BEBOP for excitation
Linear variation of B₀ at a certain direction

- Coherence transfer pathway selection: $\sum \gamma_i p_i G_i = 0$

- Artifact suppression per scan ie ¹H¹²C artifacts with short phase cycling (...subtraction)

- Solvent suppression and control of water magnetisation (radiation damping)

- *Translational diffusion measurements*

- *Magnetic Resonance Imaging*

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Strong water (~50M) signal deteriorates spectral dynamic range

High fields + cryoprobes → strong radiation damping → large water signal

Strategies

- Observe an heteroatom

- Presaturation: forbidden in the case of fastly exchangable protons

- Coherence selection with gradients

- Return of water at z axis: polynomial sequences (jump and return...), water selective flip-back pulses, manipulation of radiation dumping

- Dynamic filters: based on the differences in relaxation rates or diffusion coefficients

- Selective defocusing of water via a gradient echo (WATERGATE, excitation sculpting)

- Purging pulses: B₀ or Rf gradient

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INEPT version

$$ \Delta_1 = 1/4^1 J_{HN} = 2.7m $$

$$ \Delta_2 = 12m \text{ (relaxation optimized, } 1/4 J_{NC\alpha} \sim 22m \text{)} $$

$$ \Delta_3 = 3.5-4m \text{ (relaxation optimized, } 1/4 J_{COC\alpha} = 4.5m \text{)} $$

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mixed INEPT / DQ version

$$ \Delta_1 = 1/4^1 J_{HN} = 2.7m $$

$$ \Delta_2 = 13.5m \text{ (relaxation optimized, } 1/4 J_{NCO} = 33m \text{)} $$

$$ \Delta_3 = 8m \text{ (relaxation optimized, } 1/2 J_{COC\alpha} = 9m \text{)} $$
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mixed INEPT / RELAY sequence

$$ \Delta_1 = 1/4 J_{HN} = 2.7m $$

$$ \Delta_2 = 12m \text{ (relaxation optimized, } 1/4 J_{NC\alpha} \sim 22m \text{)} $$

$$ \Delta_3 = 3.6m \text{ (relaxation optimized, } 1/4 J_{C\alpha C\beta} = 7.1m \text{)} $$

$^1J_{C\alpha C\beta}$ and $^1J_{C\beta C\gamma}$ couplings not refocused during $t_2$

$C_\alpha$, $C_\beta$ peaks of opposite sign

- In $^1H-^{15}N$ correlation experiments $^1HN$ longitudinal dipolar relaxation is accelerated if the rest of the protein protons (aliphatics) and $^1H_2O$ are unperturbed (at z axis)

- Substitution of $^1H$ hard pulses with shaped ones (top-hat).

SOFAST-HMQC ($J_{SS}$, $T_{2I}$, $T_{2S}$)

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BEST-HSQC ($J_{SS}$, $T_{1I}$, $T_{2S}$)

<figure><img src="image_65.png" /></figure>

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<figure><img src="image_67.png" /></figure>
## SOFAST-HMQC

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90° pulse → 1770µs Q5.1000

180° pulse → 1260µs Q3.1000

P5M4 <sup>15</sup>N decoupling using 2ms CA-WURST-2 adiabatic pulse

1scan, 128 transients, AQ=70ms, RD=300ms, Total Experimental Time: 55s

## BEST-HSQC

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<sup>1</sup>H carrier frequency @ 7.999ppm

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]: 180° broadband inversion pulse → 155µs power-BIBOP pulse
10kHz inversion, tolerant to 20% inhomogeneity
<figure><img src="image_71.png" /><figcaption>BEST-HNCO: 4scans, 58min</figcaption></figure>

<figure><img src="image_72.png" /><figcaption>BEST-HNCACB: 4scans, 3h 54min</figcaption></figure>

<figure><img src="image_73.png" /><figcaption>BEST-HN(CO)CA: 4scans, 2h</figcaption></figure>

<figure><img src="image_74.png" /><figcaption>BEST-HN(CA)CO: 4scans, 59min</figcaption></figure>

<figure><img src="image_75.png" /><figcaption>BEST-HN(CO)CACB: 4scans, 4h 9min</figcaption></figure>

<figure><img src="image_76.png" /></figure>

- Usefull for protonated proteins < 150aa (above, fractional deuteration is required)

- Other fast methods are based on reduced sampling at the indirect dimensions:

Spectrum compression through folding

Exponential sampling and maximum entropy

Projection reconstruction (radial sampling)

Hadamard transform

Filter Diagonalisation Method

Sharc NMR

...
HBHA(CBCACO)NH

<figure><img src="image_77.png" /><figcaption>In H₂O:</figcaption></figure>

(H)CC(CO)NH-TOCSY / H(CCCO)NH-TOCSY

<figure><img src="image_78.png" /><figcaption>In D₂O:</figcaption></figure>

HACACO

<figure><img src="image_79.png" /></figure>

HACACO-TOCSY

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H(C)CH-TOCSY / (H)CCH-TOCSY

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The HCCH-TOCSY experiment

$\delta \rightarrow t1$
$J \rightarrow 2\Delta1$

<figure><img src="image_82.png" /></figure>

Refocused INEPT / z-TOCSY

Constant time at both indirect dimensions

$\Delta_1 = 1/2 J_{HC} = 37$m (optimized for CH₂)

Purging of residual water magnetization with B₀ and RF gradients
- Decrease transverse <sup>13</sup>CH relaxation rates through deuteration:

Expression in D₂O → up to 70% deuteration (isotopic effect)

Expression in D₂O+U[¹³C, D]-glucose → up to ~100% deuteration

Use of pyruvate or α-ketobutyrate/α-ketoisovalerate for production
of methyl protonated perdeuterated proteins.

(back-exchange of ND to NH, introduction of D decoupling)

- Decrease transverse <sup>15</sup>N<sup>1</sup>H relaxation rates through TROSY effect at high field:

Selection of the slower relaxing component due to the destructive
interference of cross-correlated relaxation (DD - CSA)

<figure><img src="image_83.png" /></figure>

- At high fields transverse <sup>13</sup>CO relaxation rates increase due to CSA

Use i-HNCA instead of HN(CO)CA