📘 Lecture 5 – Video 2

Protein–Ligand Interactions by NMR: Chemical Shift Perturbation Mapping

This lecture focuses on one of the most powerful and conceptually simple methods for studying protein–ligand interactions:

🧪 Chemical Shift Perturbation (CSP) Mapping

It combines physical chemistry with NMR spectroscopy to answer three key questions:

1. Does binding occur?
2. Where does the ligand bind?
3. How strong is the binding (Ka / Kd)?

Below is a complete, structured, and detailed walkthrough of all topics covered.

🧠 1. The Core Idea: Chemical Shifts Reflect Environment

A chemical shift reports on the local electronic environment of a nucleus (e.g., ¹H, ¹⁵N).

• It is time-averaged
• It is ensemble-averaged (all molecules in solution)

Therefore:

🔄 Any change in surroundings → change in chemical shift

When a ligand binds:

• Residues near the binding site change environment
• Their peaks move in the NMR spectrum
• Residues far away usually don’t change

⚠️ In practice:

• You always see many changes near the binding site
• And almost always one unexpected shift somewhere else (This is common and not always easy to explain.)

📌 This method is simple:

• Record spectrum of protein alone
• Add ligand
• Record new spectrum
• Compare

If peaks move → binding occurs

⚖️ 2. Binding Thermodynamics and Kinetics

Binding is a reversible reaction:

P + L ightleftharpoons PL

Two rates:

• kon (association rate)
• koff (dissociation rate)

Important concepts:

🔹 Association constant (Ka)

K_a = rac{PL}{[P]L}

Also:

K_a = rac{k_}{k_}

Units: L/mol

🔹 Dissociation constant (Kd)

K_d = rac{1}{K_a}

Units: mol/L (M)

Biologists prefer Kd because molarity is intuitive.

🔹 Diffusion limit

If binding is diffusion-controlled:

k_ approx 10^7 , M^{-1}s^{-1}

If conformational changes are required (e.g. calmodulin), binding is slower.

Very small ligands (like ions) can bind even faster.

🔁 3. Exchange Regimes in NMR

The most important concept in CSP experiments is:

What does the NMR signal look like when molecules exchange between free and bound states?

Let:

• δω = frequency difference between free and bound
• kex = exchange rate

The relationship between kex and δω determines the observed spectrum.

🐢 Slow Exchange (kex ≪ δω)

You see:

• Two separate peaks
  • One for free
  • One for bound

Example:

• 1 ppm difference at 600 MHz → 600 Hz
• If exchange is much slower than 600 s⁻¹ → slow exchange

Peak intensities reflect populations:

Fraction bound = rac{I_}{I_+I_}

This allows direct quantification.

⚠️ But:

• Integration assumes equal relaxation
• That assumption is rarely perfectly true

⚡ Fast Exchange (kex ≫ δω)

You see:

• One peak
• It moves gradually during titration

Observed chemical shift is:

delta_ = weighted average

If peak moves 75% of total distance:

→ 75% of protein is bound

This is the most common case.

📊 4. HSQC Spectra and Titrations

Experiments are typically done using:

🧾 ¹H–¹⁵N HSQC spectra

Each peak = one backbone amide

🔴 Example: Fast Exchange Case

Protein alone → red spectrum Add ligand → peaks move

Observations:

• Some peaks move
• Some do not

Interpretation:

• Moving residues are near binding site
• Non-moving residues are far away

Important:

There is no strict correlation between magnitude of shift and distance to binding site — but generally closer residues shift more.

📈 5. Extracting Binding Constants

In fast exchange:

Define:

• Δδmax = shift at full binding
• Δδobs = shift at given ligand concentration

Then:

Fraction bound = rac{Deltadelta_}{Deltadelta_}

This equals:

rac{PL}{P_0}

You measure:

• P₀ (total protein)
• L₀ (total ligand)

You want:

• Ka (or Kd)

The binding equation becomes quadratic:

PL = rac{(P_0+L_0+K_d) - sqrt{(P_0+L_0+K_d)^2 - 4P_0L_0}}{2}

You fit this curve to your data to extract Ka or Kd

⚠️ Important Practical Considerations

• Protein concentration should be similar to Kd
• NMR requires high protein concentration
• Very tight binding (low Kd) is hard to fit accurately
• Fluorescence may be better for very strong interactions

Weaker binding curves are easier to fit accurately.

🧬 6. Case Study: Plectasin Binding

The lecture gives a real example:

🦠 Plectasin

• 42 amino acid antimicrobial protein
• Binds lipid-2 (bacterial cell wall precursor)

Problem:

• Lipid-2 is insoluble
• Requires micelles to mimic membrane

Step 1: Binding to Micelle (TPC)

Add dodecyl phosphocholine (TPC).

Some residues shift → micelle binding site identified.

Shifts cluster in one hydrophobic region.

Mapping shifts on structure:

• Hotspot at one end
• Mostly hydrophobic residues

Important insight:

Not all binding site residues shift Chemical shift reports environmental change, not direct contact.

Step 2: Add Lipid-2

Now three states:

1. Protein alone
2. Protein + micelle
3. Protein + micelle + lipid-2

Some residues:

• Change only with micelle
• Change only with lipid-2
• Change with both

Two binding hotspots identified:

• Around residue 8
• Around residue 33

Mapping shows:

• Protein inserts partly into membrane
• Lipid-2 sugar head interacts with specific ring of residues

This demonstrates how CSP mapping can dissect multi-step binding events

🧩 7. Strengths and Limitations

✅ Advantages

• Conceptually simple
• Easy experimental setup
• Works for weak and strong interactions
• Identifies binding site
• Gives Ka / Kd
• No complex structural calculations required

❌ Limitations

• Only tells you something changed
• Does NOT give full complex structure
• Cannot always distinguish direct contact from allosteric effects
• If protein undergoes large conformational change:
  • Many peaks shift everywhere
  • Binding site harder to identify

Rule of thumb:

You usually see the binding site plus a few extra residues.

Trying to rationalize every single shift is often not productive.

🎯 Final Big Picture

Chemical shift perturbation mapping is:

• One of the most straightforward NMR methods
• Highly informative
• Quantitative
• Structurally insightful
• Widely used in structural biology

Basic workflow:

1. Record protein HSQC
2. Add ligand gradually
3. Monitor peak movement or splitting
4. Map shifting residues
5. Fit binding curve
6. Extract Ka / Kd

Simple in theory — powerful in practice.