🧲 PART I – Introduction

Slide 1 – Title

Protein NMR Spectroscopy II Reinhard Wimmer – Aalborg University Focus: how NMR data becomes 3D structure.

Slide 2 – Protein Structure Determination

Key themes:

• What NMR data is structurally relevant?
• NMR vs X-ray crystallography

The Escher artwork symbolizes structural ambiguity — multiple possible interpretations depending on perspective.

Slide 3 – NMR Investigation Workflow

Protein NMR structure determination follows this pipeline:

1. Sample preparation
2. Optimization
3. Resonance assignment (huge NMR time investment)
4. Collect NOEs, couplings, etc.
5. Structure calculation (huge computer time)
6. Structure known → study:
   • Function
   • Dynamics
   • Mechanism

Important message: 📌 Data collection is long. Computation is long. Interpretation is iterative.

Slide 4 – What Structural Information Can NMR Give?

Three fundamental types:

1️⃣ Distances

• From NOEs
• From PREs
• From H-bonds

→ Define secondary, tertiary, quaternary structure

2️⃣ Dihedral angles

• Mainly backbone (φ, ψ)
• From scalar couplings and chemical shifts

→ Define local conformation

3️⃣ Relative orientations

• From residual dipolar couplings (RDCs)

→ Define global fold and domain orientation

Important distinction:

• Distances = local + global
• Angles = mostly local
• Orientations = mostly global

Slides 5–7 – The Puzzle Analogy 🧩

Solving NMR structures is like:

• A puzzle
• With missing pieces
• And extra pieces

Meaning:

• Some restraints are ambiguous.
• Some regions lack data.
• Some peaks are overlapped.
• There are multiple possible conformations.

Structure determination = constraint satisfaction under uncertainty.

Slides 8–10 – NMR vs X-ray Crystallography

Advantages of NMR:

• No crystal required
• Solution conditions (closer to physiological)
• Easy to change buffer, add ligands
• Study dynamics
• Study folding/unfolding

Disadvantages:

• Size limitation (~ <20–30 kDa typically)
• Time consuming
• Requires isotope labeling (¹⁵N, ¹³C)
• Expensive instrumentation

Size distribution slide:

• NMR → small proteins
• X-ray → broader size range
• EM → very large complexes

Clear methodological niches:

• NMR = small + dynamic
• X-ray = high resolution static
• EM = large complexes

Slides 11–12 – Workflow Comparison

NMR:

• Expression
• Isotope labeling
• Sample optimization
• Data collection
• Structure calculation

X-ray:

• Expression
• Crystallization
• Heavy atom derivative
• Data collection
• Phasing
• Refinement

X-ray easier once crystal obtained. NMR allows more functional studies.

Slide 13 – When Should You Choose NMR?

Use NMR when:

• No crystal available
• Interested in dynamics
• Studying ligand binding
• Studying mechanism
• Studying pKa
• Folding pathways

Slide 14 – Take-home Messages

There are three main structural data types:

• Distances
• Dihedral angles
• Orientations

Distances are often the most important.

🧪 PART II – Distances as Structural Information

Slides 15–16 – Distances Overview

Same classification repeated:

• NOEs
• H-bonds
• PREs

Distances define structure extremely well.

Slide 17 – Distances from NOESY

Each cross peak = one distance constraint.

But problem: 👉 WHO IS WHO?

This requires:

• Full resonance assignment

Without assignment, NOE peaks are meaningless.

Slide 18 – Why Distances Are Useful

Because structure = spatial arrangement.

If you know enough pairwise distances → geometry is constrained.

Slides 19–20 – Distance Network

Example:

• 68 amino acids
• 993 NOE distances
  • 201 intraresidual
  • 277 sequential
  • 218 medium range
  • 297 long range

Long-range NOEs are most important for defining tertiary structure.

Slide 21 – Types of NOESY Experiments

• 2D NOESY (all protons)
• 3D ¹⁵N NOESY
• 3D ¹³C aliphatic
• 3D ¹³C aromatic
• 4D NOESY

Higher dimensions = better resolution.

Slide 22 – Automated NOE Assignment

Programs:

• CANDID
• ATNOS
• FLYA

They:

• Take peak list
• Take assignments
• Assign NOEs + calculate structure simultaneously

Requires near-complete resonance assignment.

Slide 23 – Distances from NOEs 📏

Key equation:

V = rac{k}{r^6}

Thus:

r = left(rac{k}{V} ight)^{1/6}

But practically:

• Motion
• Spin diffusion
• Overlap

So instead of exact distance: 👉 Use upper distance limits

Empirically often behaves like:

V le rac{k}{r^4}

Important: NOEs are converted to distance restraints, not exact values.

Slide 24 – NOEs from Secondary Structure

Characteristic patterns:

α-helix:

• i → i+3
• i → i+4
• HN–HN
• HN–Hα

β-sheet:

• Inter-strand NOEs
• HN–HN
• Hα–Hα across strands

These patterns help identify secondary structure.

Slide 25 – Sequence Plot

Combines:

• NOE patterns
• Chemical shifts
• Couplings

To map:

• α-helices
• β-strands

Slide 26 – Hydrogen Bonds

Sometimes detectable via:

• Scalar couplings across H-bonds

But: ⚠️ H-bonds should NOT be added unless strong evidence exists.

Slides 27–29 – PREs (Paramagnetic Relaxation Enhancement) 🧲

Insert spin label (unpaired electron).

Effect:

• Increases relaxation rate (R2)
• Distance dependent (~1/r⁶)

Use:

• Engineer single Cys mutant
• Attach spin label
• Measure signal attenuation
• Compare oxidized vs reduced label

PREs give long-range distance information (up to ~25 Å).

Very powerful for domain orientation.

Slide 30 – Distance Take-Home

Three sources:

• NOEs
• PREs
• H-bonds

NOEs:

• Main information source
• Converted to upper distance limits
• Long-range NOEs define tertiary structure

📐 PART III – Dihedral Angles & Orientation

Slide 31 – Introduction

Angles and orientation add additional constraints.

Slide 32 – Chemical Shifts & Secondary Structure

Cα and Cβ shifts differ in:

• α-helix
• β-sheet

Secondary chemical shift: Observed − random coil value

Patterns:

• Helix → positive Cα shift
• Sheet → negative Cα shift

Slide 33 – TALOS

Programs:

• TALOS
• TALOS+
• TALOS-N

Use chemical shifts to predict:

• φ
• ψ

Machine learning + database comparison.

Provides torsion angle restraints.

Slides 34–35 – J-Coupling (Scalar Coupling)

Electron-mediated, through-bond interaction.

Karplus relationship:

J = Acos^2( heta) + Bcos( heta) + C

J depends on dihedral angle.

Common example: ³J(HN–Hα)

Large J (~8 Hz) → β-sheet Small J (~3–4 Hz) → α-helix

Thus J-couplings provide dihedral angle constraints.

Slides 36–38 – Measuring Orientations in Anisotropic Media

Normally:

• Molecules tumble isotropically
• Dipolar couplings average to zero

If weakly aligned:

• Residual dipolar couplings (RDCs) remain

How to align?

• Bicelles
• Bacteriophages
• Liquid crystals
• Polyacrylamide gels

RDCs give:

• Orientation of bond vectors (N-H, C-H)
• Relative domain orientation

Extremely valuable for multi-domain proteins.

🧮 PART IV – Structure Calculation & Validation

Slide 41 – Structure Calculation Software

Programs:

• CYANA
• CNS
• X-PLOR

Input:

• Distance constraints
• Angle constraints
• RDCs
• All other restraints

Procedure: Iterative:

• Calculate
• Evaluate
• Adjust
• Recalculate

Slide 42 – Target Function

Structure calculation minimizes deviation between:

• Measured restraints
• Calculated geometry

Many conformers generated.

Select best-fitting ensemble.

Slide 43 – Evaluation Metrics

1️⃣ Target function (restraint violations)

2️⃣ RMSD (precision of ensemble)

3️⃣ Ramachandran statistics

Slides 45–46 – RMSD

RMSD = root mean square deviation between structures.

Lower RMSD → tighter ensemble → higher precision.

But: Depends on:

• Superposition region
• Structured vs flexible regions

You can artificially lower RMSD by fitting only secondary structure.

Slide 47 – Method Dependence

NMR, X-ray, modeling can give different structures.

Solution vs crystal packing effects.

Slides 48–49 – Validation

Check:

• Ramachandran plot
• Side chain rotamers
• Bond geometry
• van der Waals contacts
• H-bond geometry

Use:

• PROCHECK
• ProQ
• WhatIf
• ProseSS

Use independent data (RDCs, unusual shifts) for validation.

Slide 50 – Ramachandran Plot

Allowed φ/ψ regions:

• α-helix
• β-sheet
• Left-handed helix

Low percentage in disallowed region = good structure.

Slide 51 – Example Structure Statistics

Example publication statistics:

• 1576 NOEs
• 20 conformers
• Target function ~4.6
• Max violation 0.14 Å
• 72.8% favored Ramachandran
• RMSD backbone ~1.19 Å
• RMSD secondary structure ~0.67 Å

Important: RMSD of structured core is more meaningful than full-length RMSD.

🎯 Overall Big Picture

Protein NMR structure determination integrates:

Distances (NOEs, PREs)

→ Define fold

Angles (J-coupling, chemical shifts)

→ Define local conformation

Orientations (RDCs)

→ Define global orientation

Then:

Structure calculation → Minimize violations → Select best ensemble → Validate geometry → Report RMSD + statistics

NMR structures are ensembles, not single static models.