📘 Lecture 4 – Video 3

Protein Structure Determination by NMR (Part 3)

Topic: Dihedral Angles & Orientational Information from NMR

This lecture focuses on how we extract dihedral angles and overall molecular orientation from NMR data — two critical ingredients for determining protein structures.

File reference:

🧬 1. Chemical Shifts & Secondary Structure

🔎 Key Idea:

Backbone chemical shifts are highly sensitive to secondary structure.

If you compare:

• Cα in α-helices
• Cα in β-sheets

You see clear differences (some overlap, but distinct trends). This applies not only to:

• Cα
• Cβ
• Hα
• Carbonyl (C’)
• Nitrogen (N)

👉 Essentially all backbone atoms show structural dependence.

🧪 Secondary Chemical Shift

To use this information quantitatively:

extbf{Secondary Shift} = ext{Observed Shift} - ext{Random Coil Shift}

What is a random coil shift?

The chemical shift the atom would have in a completely disordered conformation.

Any deviation = structural influence.

You calculate secondary shifts typically for:

• Cα
• Cβ
• N
• C’
• Hα

Sometimes also include neighboring residues (i-1 and i+1) for better prediction.

🧠 TALOS: Predicting Dihedral Angles from Shifts

Software evolution:

• TALOS
• TALOS+
• TALOS-N

Same core idea, progressively improved.

💡 How TALOS Works:

1. Calculate secondary shifts for residue triplets.
2. Search a database of proteins with:
   • Known structures
   • Known chemical shifts
3. Find best matches (usually top 10).
4. Extract their φ (phi) and ψ (psi) angles.
5. Predict your residue’s allowed Ramachandran region.

Even the amino acid type does not have to match — it matches based on secondary shifts.

📊 Example Outcome

If all 10 best matches cluster in a β-sheet region of the Ramachandran plot:

→ Very likely your residue is also β-sheet.

If matches scatter across different regions:

→ No reliable prediction.

🎯 Why This Is Powerful

• You already measure chemical shifts for assignment.
• No extra experiment required.
• Gives backbone angle restraints for structure calculation.
• Often defines secondary structure very well.

Because of this efficiency: 👉 J-coupling-based angle measurements are now rarely used.

🔁 2. Scalar Couplings (J-Couplings) & Dihedral Angles

Scalar couplings depend on local geometry.

They follow Karplus curves — sinusoidal relationships between: J = f( ext{dihedral angle})

📐 Example: φ Angle

The coupling between:

• HN
• Hα

depends on φ.

If you measure:

• J = 10 Hz → φ ≈ 120° (well-defined)
• J = 4 Hz → ambiguous (could correspond to multiple angles)

⚠️ Problem:

• Many angles give the same coupling.
• Small couplings are difficult to measure.
• ψ and χ1 couplings are even harder (small values).

Conclusion:

Chemical shifts are:

• Easier
• Already measured
• More reliable

Hence: TALOS dominates.

🧭 3. Orientational Information: Residual Dipolar Couplings (RDCs)

Now comes something very powerful.

Normally:

Proteins tumble freely in solution. All orientations equally probable. Dipolar couplings average to zero.

Because the angular term:

3cos^2 heta - 1

averages to zero over all orientations.

🧲 What if We Partially Align the Protein?

Use anisotropic media like:

• Liquid crystalline solvents
• Stretched polyacrylamide gels
• Lipid bicelles
• Bacteriophages

These align in the magnetic field.

Dissolve protein in such media → protein becomes slightly oriented.

📏 Residual Dipolar Couplings (RDCs)

Now dipolar couplings no longer fully average to zero.

You observe small, non-zero couplings: → Residual Dipolar Couplings

They depend on:

• Internuclear distance (fixed for NH bond)
• Angle θ between bond vector and magnetic field

So for an NH pair:

• Distance is known.
• Measure RDC → determine orientation angle.

You can do this for:

• NH bonds
• CH bonds
• (theoretically HH)

🧩 What Does This Give You?

You now get orientation of many bond vectors relative to:

• The laboratory frame (magnetic field axis)

This provides:

• Long-range angular information
• Global structural constraints
• Domain orientation information

🧱 Domain Orientation Problem

Imagine:

• Two domains
• Each domain has a well-defined structure
• You don’t know how they orient relative to each other

RDCs allow:

• Assigning coordinate frames to each domain
• Comparing them
• Finding orientation where coordinate systems coincide

Only one orientation satisfies both RDC datasets.

This is extremely powerful for:

• Multi-domain proteins
• Flexible linkers
• Assemblies

📌 Summary of Information Sources

🎓 Big Picture

In protein NMR structure determination:

1. Assign chemical shifts
2. Extract:
   • Dihedral angle restraints (TALOS)
   • Distance restraints (NOEs, earlier video)
   • Orientational restraints (RDCs)
3. Feed all restraints into structure calculation
4. Obtain 3D model

This lecture covered the angular and orientational components.

🔑 Core Takeaways

• Chemical shifts encode secondary structure.
• Secondary shifts → TALOS → φ/ψ restraints.
• J-couplings follow Karplus curves but are ambiguous.
• Partial alignment enables measurement of RDCs.
• RDCs give global orientation information.
• Especially powerful for multi-domain proteins.

Next step (Video 4): Structure calculation and validation.