Day 3 part 2

Protein chemistry

🧠 Protein Folding – Thermodynamics, Cooperativity & Stability


1️⃣ Leventhal’s Paradox – Why Proteins Don’t Fold Randomly

If a 100-residue protein had only 2 conformations per residue, it would have:

2^{100} approx 10^{30}

possible conformations.

If it sampled each conformation in 10⁻¹³ s, it would take 10⁹ years to find the native state.

But real proteins fold in seconds to minutes.

✅ Conclusion:

Proteins do not search randomly. Folding is guided.


2️⃣ Hydrogen Bonds Guide Folding

You asked:

H-bonding of secondary structure guides folding?

Yes — but with nuance.

In early folding:

  • Local hydrogen bonds form quickly
  • α-helices and β-sheets appear early
  • These act as nucleation points

These pre-formed secondary structures reduce conformational space.

⚠ Important: Hydrogen bonds do not drive folding alone — they guide structure formation within the larger thermodynamic landscape.

Hydrophobic collapse and entropy of water are equally critical.


3️⃣ Force Fields & Folding Simulations

Modern molecular dynamics simulations include:

  • Bond stretching
  • Angle bending
  • Torsion angles
  • Electrostatics
  • Van der Waals interactions

These are encoded in force field equations.

Small proteins (~40 aa) can now fold in silico in milliseconds.


4️⃣ Chemical Denaturation – Guanidinium Chloride

You asked:

Can guanidinium chloride replace hydrogen bonds?

Yes — partially.

Guanidinium chloride:

  • Forms hydrogen bonds
  • Solubilizes hydrophobic residues
  • Stabilizes unfolded state

Water also forms hydrogen bonds — but water alone does not denature because:

  • It does not solubilize hydrophobic cores as effectively.
  • Guanidinium stabilizes exposed peptide backbone better.

5️⃣ Two-State Folding Model

Simple case:

N ightleftharpoons U

Only two states:

  • Fully folded
  • Fully unfolded

The sharp transition indicates:

🔁 Cooperative process Either folded or unfolded — no stable intermediates.


❓ Your Question:

2-state process means 2 independent units that have different denaturation?

No.

Two-state = one cooperative unit.

If a protein has multiple domains:

  • Each domain may unfold separately
  • Then you get multiple transitions
  • That is not a two-state system

6️⃣ Thermal Denaturation

You asked:

Protein unfolding by heating related to interactions vibrating?

Yes.

Heating increases molecular motion:

  • Ionic interactions weaken
  • Dipole interactions weaken
  • Hydrogen bonds break
  • Hydrophobic packing loosens

When thermal energy exceeds stabilizing interactions → unfolding occurs.


7️⃣ Gibbs Free Energy & Stability

Delta G = Delta H - TDelta S

If:

  • ΔG < 0 → folded favored
  • ΔG > 0 → unfolded favored

You asked:

Free energy positive → unfolded?

Yes — for folding reaction.

If ΔG_folding > 0 → folding is unfavorable → protein unfolds.


Magnitude of Stability

Typical folding ΔG: -20 ext{ to } -60 ext{ kJ/mol}

This equals only a few hydrogen bonds!

⚠ Important: Proteins are marginally stable.


8️⃣ Do Hydrogen Bonds “Give” Gibbs Free Energy?

Not directly.

Hydrogen bonds contribute to:

  • ΔH (enthalpy)

But ΔG depends on both:

  • ΔH (bond formation)
  • ΔS (entropy change)

You cannot look at hydrogen bonds alone.


9️⃣ Entropy & Enthalpy Contributions

Enthalpy (ΔH)

Favorable:

  • Hydrogen bonds
  • Electrostatic interactions
  • Hydrophobic packing

Unfavorable:

  • Breaking interactions with water

Entropy (ΔS)

Now the important correction:

You asked:

Unfolded → ΔG decreases because entropy bigger than enthalpy? But aromatic rings exposed reduce entropy?

This is where many students get confused.

Key distinction:

There are two entropies involved:

1️⃣ Chain entropy

  • Unfolded chain = very flexible
  • High entropy
  • Folding reduces chain entropy (unfavorable)

2️⃣ Water entropy

  • Hydrophobic residues force water to become ordered
  • This decreases water entropy
  • When folding buries hydrophobic residues:
    • Ordered water is released
    • Water entropy increases
    • Favorable

So what dominates?

For folding:

  • ΔH is favorable
  • Chain entropy is unfavorable
  • Water entropy is strongly favorable

Net result: Delta G < 0


Important Correction to Your Thought

You said:

Aromatic ring exposed → entropy decreases → unfolded unfavorable?

Correct locally for water.

But in unfolded state:

  • Chain entropy is very large and positive
  • Many water interactions exist

The full balance determines stability.

It is not dependent on one amino acid. It is a global thermodynamic balance.


🔥 10️⃣ Heat Capacity & Calorimetry

In Differential Scanning Calorimetry (DSC):

We measure heat capacity vs temperature.

When protein unfolds:

  • Energy goes into breaking bonds
  • Temperature does not increase as expected
  • Heat capacity spikes

You asked:

Some of the temperature unfolds the protein?

Correct — but more precisely:

Energy input goes into:

  • Breaking non-covalent bonds
  • Not increasing temperature

The area under the peak = ΔH_unfolding


1️⃣1️⃣ Heat Capacity & Protein Size

You asked:

Smaller protein → lower heat capacity? Why?

Because:

  • Larger proteins expose more surface upon unfolding
  • More solvent interaction change
  • Larger ΔCp

Heat capacity scales roughly with:

  • Nonpolar surface area
  • Protein size

Smaller protein → smaller hydrophobic core → smaller heat capacity change


1️⃣2️⃣ Temperature Dependence of Stability

ΔH and ΔS are temperature dependent.

At melting temperature (Tm):

Delta G = 0

So: T_m = rac{Delta H}{Delta S}


❄ Cold Denaturation

Important concept from your file:

Proteins can also unfold at low temperature.

Because:

  • Hydrophobic effect weakens at low temperature
  • Water entropy effect changes

Thus:

  • ΔG becomes positive again
  • Cold denaturation occurs

This surprises many students.


1️⃣3️⃣ Why ΔG is Small but Folding is Strongly Favored

Even if ΔG = -10 kcal/mol:

K = e^{-ΔG/RT}

At 298K:

→ ~10⁷ folded per unfolded

Small energy difference = huge equilibrium shift.


📊 Summary of Energy Contributions

ContributionFavors Folding?
Hydrogen bondsYes
ElectrostaticsYes
Hydrophobic effectStrong yes
Chain entropyNo
Water release entropyYes

Net result: Small negative ΔG → strong folded population.


🧬 Final Conceptual Picture

Protein folding is:

  • Guided by early secondary structure
  • Driven by hydrophobic effect
  • Stabilized by hydrogen bonds
  • Cooperative
  • Marginally stable
  • Temperature dependent
  • Both heat and cold sensitive

Quiz

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