Protein Structure

Lecture 5 Video 2

📘 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:

Does binding occur?
Where does the ligand bind?
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:

Protein alone
Protein + micelle
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:

Record protein HSQC
Add ligand gradually
Monitor peak movement or splitting
Map shifting residues
Fit binding curve
Extract Ka / Kd

Simple in theory — powerful in practice.

Quiz

Score: 0/30 (0%)

Q0. What fundamental property does a chemical shift report in NMR during protein–ligand binding studies?

The mass of the nucleus

The local electronic environment averaged over time and ensemble

The temperature of the sample

The molecular weight of the protein

Q1. Why do residues near a ligand binding site typically show chemical shift changes?

Because they change molecular weight

Because their electronic environment changes upon binding

Because they rotate faster

Because they lose protons

Q2. How is the association constant (Ka) related to kinetic rates?

Ka = koff / kon

Ka = kon + koff

Ka = kon / koff

Ka = 1 / kon

Q3. What is the relationship between Ka and Kd?

Kd = Ka

Kd = kon × koff

Kd = 1 / Ka

Kd = Ka²

Q4. In diffusion-controlled binding, the typical order of magnitude of kon is:

10^2 M⁻¹s⁻¹

10^5 M⁻¹s⁻¹

10^7 M⁻¹s⁻¹

10^10 M⁻¹s⁻¹

Q5. In slow exchange (kex ≪ Δω), what is observed in the NMR spectrum?

A single averaged peak

No peak at all

Two separate peaks for free and bound states

Only the bound peak

Q6. In fast exchange (kex ≫ Δω), the observed chemical shift corresponds to:

Only the bound state

Only the free state

A weighted average of free and bound states

A random value

Q7. If a peak moves 75% of the total shift distance in fast exchange, what fraction of protein is bound?

25%

50%

75%

100%

Q8. Which experiment is typically used to monitor backbone amide shifts in CSP mapping?

COSY

HSQC

NOESY

TOCSY

Q9. What equation must be solved to determine [PL] when fitting binding curves?

Linear equation

Cubic equation

Quadratic equation

Exponential decay equation

Q10. Why can very tight binding (very small Kd) be difficult to study by NMR?

Protein concentration required for NMR is often similar to or higher than Kd

NMR cannot detect bound states

Ligands always degrade

Exchange is always slow

Q11. What does integrating peaks in slow exchange allow you to determine?

Molecular weight

Relaxation rate

Population fractions of free and bound states

Diffusion coefficient

Q12. What limitation exists when interpreting chemical shift changes?

They always directly identify hydrogen bonds

They provide atomic-resolution structures automatically

They only indicate that something changed, not precisely what

They measure molecular weight changes

Q13. In the plectasin study, why were micelles required?

To increase temperature

To solubilize lipid-2 and mimic a membrane

To denature the protein

To remove water

Q14. If kex is much smaller than Δω, the system is in:

Fast exchange

Slow exchange

Intermediate exchange

No exchange

Q15. Chemical shift perturbation mapping can be used to extract binding constants.

True

False

Q16. In fast exchange, two distinct peaks are visible simultaneously.

True

False

Q17. The dissociation rate (koff) depends on ligand concentration.

True

False

Q18. Association rate (kon) depends on the concentration of reactants.

True

False

Q19. In slow exchange, peak intensity ratios reflect population ratios.

True

False

Q20. Chemical shift magnitude always correlates perfectly with distance to the binding site.

True

False

Q21. NMR CSP mapping provides a full 3D structure of the protein–ligand complex.

True

False

Q22. In fast exchange, Δδobs/Δδmax equals the fraction of bound protein.

True

False

Q23. Very weak interactions are generally easier to fit accurately than very tight interactions in NMR titrations.

True

False

Q24. Micelle binding and ligand binding can be distinguished by analyzing which residues shift at each step.

True

False

Q25. If no peaks shift upon ligand addition, binding is unlikely.

True

False

Q26. In diffusion-controlled binding, conformational rearrangements slow down kon.

True

False

Q27. In slow exchange, the observed peak position is a weighted average of free and bound states.

True

False

Q28. Chemical shift perturbation mapping works only for weak interactions.

True

False

Q29. Large conformational changes upon binding can complicate interpretation of CSP data.

True

False