🔥 Protein Folding – Thermodynamics & Denaturation

1️⃣ Folding as an Equilibrium Process

Protein folding is treated as a reversible equilibrium:

U ightleftharpoons N

• U = unfolded
• N = native (folded)

The equilibrium constant for unfolding:

K_U = rac{U}{N} = rac{k_}{k_}

Thermodynamics connects equilibrium to free energy:

Delta G = -RT ln K

And also:

Delta G = Delta H - TDelta S

So if we know:

• ΔH (enthalpy)
• ΔS (entropy)

we can determine ΔG and therefore folding stability.

2️⃣ How Do We Measure These Parameters?

🔬 Differential Scanning Calorimetry (DSC)

This is the central method described.

Principle:

• One cell: buffer + protein
• One reference cell: buffer only
• Temperature is increased gradually
• The instrument measures how much heat is required to keep both cells at the same temperature

What we measure: Heat capacity (Cp) vs Temperature

3️⃣ Why is Heat Capacity (Cp) Higher Without Protein?

You asked:

“Is Cp higher without protein because water alone can take the molecule without changing something?”

Not exactly — but you're close.

Correct explanation:

Water has:

• Extremely high flexibility
• Extensive hydrogen-bond network
• Many degrees of freedom

Because of this, pure water absorbs heat very efficiently → high Cp.

Now when you add protein:

• Water molecules must organize around the protein surface
• Especially around hydrophobic residues
• This ordering reduces their freedom

👉 Less freedom = lower heat capacity

So:

Important correction:

It is NOT because "less water molecules can do something."

It is because:

• Water molecules become more ordered
• Ordering reduces configurational freedom
• Reduced freedom lowers heat capacity

4️⃣ Extracting Thermodynamics from DSC

From the thermogram:

• 🔺 Area under peak → ΔH_cal (calorimetric enthalpy)
• 📍 Peak midpoint → Tm (melting temperature)
• 📈 Baseline difference before/after → ΔCp (heat capacity change)

5️⃣ Two-State vs Non-Two-State Folding

The ratio:

rac{Delta H_}{Delta H_}

If ratio ≈ 1 → Two-state folding If > 1 → Multiple domains / intermediates If < 1 → Cooperativity effects

So deviation from 1 = not a simple two-state process.

6️⃣ Temperature Dependence of Stability

At melting temperature:

Delta G = 0

So:

T_m = rac{Delta H}{Delta S}

As temperature increases:

• ΔG decreases
• Unfolding becomes favorable

🧪 Ligand Effects on Stability

Two cases:

Case 1️⃣ Ligand binds native state

Effect:

• Stabilizes folded protein
• Decreases KU
• Increases Tm

Example in the file: Fibroblast Growth Factor (FGF)

Phosphate/sulfate binding increases Tm.

Case 2️⃣ Ligand binds unfolded state

Effect:

• Stabilizes unfolded protein
• Increases KU
• Decreases Tm

Example: Low pH and proton binding in lysozyme lowers Tm.

🧂 Guanidinium Chloride & Urea – How They Denature

You asked:

“Can guanidium chloride denaturate fibroblast?”

Yes — and it is used exactly for that purpose.

But important nuance:

In the experiment described, it was used at low concentration to slightly destabilize FGF to improve resolution of melting transitions.

Why do urea and guanidinium denature?

Not mainly because of hydrogen bonding.

The key is:

They preferentially solubilize exposed side chains, especially:

• Large hydrophobic residues
• Trp
• Tyr
• Phe

Graph in file shows:

Transfer free energy becomes more negative as side chain size increases.

Meaning:

ext{Hydrophobic side chains are more soluble in urea/GdmCl than in water}

This stabilizes the unfolded state.

🔥 Why Does Denaturation Increase with Concentration?

Free energy of folding becomes:

Delta G = Delta G_0 - m ext{denaturant}

• m-value depends on hydrophobic surface area
• Larger hydrophobic exposure → larger m

At high concentration:

• ΔG becomes 0
• Unfolding dominates

🧬 Tryptophan & Fluorescence

You asked:

“By increasing temperature, Trp becomes exposed — will find its hydrophilicity?”

Correction:

Trp is hydrophobic, not hydrophilic.

In folded protein:

• Trp usually buried in hydrophobic core
• Fluorescence emission ~330 nm

When unfolded:

• Trp exposed to water
• Emission shifts toward ~350 nm
• Fluorescence intensity changes

This is used to monitor unfolding.

Is Trp “highest energy” and “hardest to denature”?

This is partially misunderstood.

✔ Trp is highly hydrophobic ✔ It contributes strongly to stability when buried

But:

❌ It is not “highest energy” ❌ It does not make protein hardest to denature by itself

Denaturation depends on:

• Total hydrophobic surface area
• Hydrogen bonds
• Packing
• Salt bridges
• Overall fold

One Trp alone does not determine stability.

🧊 Osmolytes – Opposite of Denaturants

Examples:

• TMAO
• Betaine
• Sucrose
• Trehalose

They stabilize folded state by:

• Excluding themselves from protein surface
• Favoring compact structures
• Increasing ΔG of unfolding

📊 Summary of Stability Effects

🔎 Final Corrections to Your Understanding

❌ “Water alone can take molecule without changing something”

→ It is about flexibility and hydrogen-bond network, not absence of change.

❌ “Less water molecules can do something”

→ It is reduced molecular freedom, not number of molecules.

❌ “Trp finds its hydrophilicity”

→ Trp is hydrophobic. It becomes solvated in water when unfolded.

❌ “Trp highest energy”

→ Stability is collective; Trp contributes but is not sole determinant.

✔ Correct:

• Denaturants stabilize exposed hydrophobic residues.
• Increasing temperature exposes Trp.
• Ligand binding shifts melting temperature depending on which state is stabilized.