1️⃣ Page 1 – Title: Molecular Forces and Protein Folding

Image: Unfolded green chain → folded compact structure.

Meaning: Proteins go from a random coil (unfolded) to a well-defined 3D structure (native state). This transformation is governed by molecular forces and thermodynamics.

2️⃣ Page 2 – Overview of Topics

The lecture covers:

• Covalent bonds
• Noncovalent interactions
• Electrostatics
• Hydrophobicity
• Folding energetics
• Calorimetry
• Kinetics
• Folding pathways
• Chaperones

This means we move from basic forces → to whole-protein thermodynamics and folding behavior.

3️⃣ Page 3 – Covalent Bonds: Potential Energy Curve

Table shows bond lengths and bond enthalpies.

Example:

• C–C: 348 kJ/mol
• C=C: 614 kJ/mol
• C≡C: 839 kJ/mol

Graph explanation:

Y-axis: Potential energy X-axis: Interatomic distance

• At large distance → energy ≈ 0 (no interaction)
• As atoms approach → energy decreases (attraction)
• At minimum → optimal bond length
• Too close → energy rises steeply (repulsion from electron overlap)

🔑 Covalent bonds are very strong compared to noncovalent interactions.

4️⃣ Page 4 – Post-Translational Modifications

Disulfide bond formation (Cys–S–S–Cys)

• Forms via oxidation of thiols
• Stabilizes protein structure
• Stable in neutral to acidic conditions

Other PTMs:

• Glycosylation
• Phosphorylation
• Acylation
• Proteolysis

These modify stability, activity, localization.

5️⃣ Page 5 – Charge-Charge Interactions (Coulomb's Law)

Electrostatic energy:

E ∝ (Z₁Z₂) / (D r)

D = dielectric constant

Dielectric values:

• Vacuum: 1
• Nonpolar solvent: 2
• Water: 80

Meaning:

Water strongly weakens electrostatic interactions.

Ion-ion interaction ~60 kJ/mol in vacuum → much weaker in water.

6️⃣ Page 6 – Electrostatics on Protein Surface

Image: Myoglobin surface with ion pairs.

Charged residues form:

• Salt bridges
• Ion pairs

These stabilize structure, especially on surfaces.

7️⃣ Page 7 – Ionic Strength Effects

Three regimes:

Low ionic strength

• Charges unshielded
• Can repel → denaturation

Moderate ionic strength

• Shielding stabilizes
• Protein soluble

High ionic strength

• Water competition
• Precipitation (“salting out”)

8️⃣ Page 8 – pH and Unfolding

Low pH:

• Carboxyl groups protonated
• Lose negative charge

High pH:

• Amino, imidazole, phenol deprotonated

Result:

• Charge repulsion
• Protein unfolds

Graph shows favorable vs unfavorable charge arrangements.

9️⃣ Page 9 – Charge-Dipole Interactions

Weaker than ion-ion (~8 kJ/mol).

Energy depends on:

• Distance (1/r²)
• Orientation (θ)

Important for:

• Ion hydration
• Protein–water interactions

🔟 Page 10 – Induced Dipoles & Dispersion

Temporary fluctuations in electron clouds → London dispersion forces.

All atoms experience these.

Stronger in:

• Large atoms
• Polarizable groups

1️⃣1️⃣ Page 11 – Summary of Electrostatics

Strength order:

Ion–ion (~60 kJ/mol) Ion–dipole Dipole–dipole Induced dipole Dispersion

Distance dependence increases rapidly:

• Ion-ion ~1/r
• Dispersion ~1/r⁶

1️⃣2️⃣ Page 12 – van der Waals Potential

Graph shows:

E = A/r¹² − B/r⁶

Blue curve:

• Attraction at moderate distance
• Repulsion at short distance

Minimum = van der Waals contact distance.

This is the balance of:

• Attractive dispersion
• Repulsive electron overlap

1️⃣3️⃣ Page 13 – Polarizability

Table shows:

• Larger atoms → more polarizable
• More outer electrons → stronger dispersion

Sulfur > oxygen > hydrogen

Important in hydrophobic cores.

1️⃣4️⃣ Page 14 – vdW Radii

Optimal H–O distance:

Sum of radii (~1.4 + 1.7 Å ≈ 3.1 Å)

Graph shows:

• Too close → repulsion spike
• Optimal distance → energy minimum

1️⃣5️⃣ Page 15 – Hydrogen Bonds

Energy: 4–13 kJ/mol

Distance: ~1 Å shorter than vdW contact

Directional (~180° ideal angle)

Hydrogen donor shares partial electron density with acceptor.

1️⃣6️⃣ Page 16 – Electronegativity & Donor/Acceptor Tables

Higher electronegativity:

• Stronger hydrogen bonding

O > N > S

Shows common donor–acceptor pairs and typical bond lengths.

1️⃣7️⃣ Page 17 – Peptide Bond Dipole

Peptide bond:

• Partial positive on N
• Partial negative on O

Planarity due to resonance.

These dipoles interact in helices.

1️⃣8️⃣ Page 18 – α-Helix Macro-Dipole

Helix has:

• Positive N-terminus
• Negative C-terminus

Due to aligned peptide dipoles.

Explains:

• Why acidic residues often near N-term
• Basic residues near C-term

1️⃣9️⃣ Page 19 – Hydrogen Bonds in Stability

Interior H-bonds:

• Replace water interactions
• Stabilize core

Breaking internal H-bonds costs 3–5 kcal/mol.

Water competes strongly.

2️⃣0️⃣ Page 21 – Water & Hydrophobic Effect

Water hydrogen-bonds extensively.

Water weakens polar interactions.

Hydrophobic groups cluster → hydrophobic effect.

2️⃣1️⃣ Page 22 – Hydrophobicity

Buried CH₂ group: ~6.2 kJ/mol stabilization.

Oil-water analogy.

Proteins bury hydrophobic residues in core.

2️⃣2️⃣ Page 23 – Water Structure

Water network dynamic.

Hydrogen bonds constantly form/break.

2️⃣3️⃣ Page 24 – Entropic Basis of Hydrophobic Effect

Water around hydrophobic groups:

• Ordered
• Entropically unfavorable

When hydrophobic groups cluster:

• Water released
• Entropy increases
• Folding favored

2️⃣4️⃣ Page 25 – ΔG = ΔH − TΔS

Graph explanation:

When hydrophobic solutes cluster:

• ΔS positive (water freedom increases)
• ΔG becomes negative

Folding driven by entropy of water.

2️⃣5️⃣ Page 27 – Hydrophobic Index

Ranking from most hydrophobic: Trp, Ile, Phe, Leu...

Used to predict:

• Membrane helices
• Transmembrane segments

2️⃣6️⃣ Page 28 – Free Energy vs Surface Area

Graphs show:

Transfer free energy correlates with accessible surface area.

Larger hydrophobic surface → larger ΔG.

2️⃣7️⃣ Page 30 – Proteins Are Dynamic

Ubiquitin NMR ensemble:

• Shows multiple conformations
• Termini disordered

Proteins are not rigid.

2️⃣8️⃣ Page 31 – Timescales of Motion

Range: 10⁻¹⁵ s (bond vibration) to seconds (folding)

Entropy from flexibility contributes to stability.

2️⃣9️⃣ Page 32 – Levinthal’s Paradox

Random search impossible: 100 residues → 10³⁰ conformations.

Folding must follow pathways.

3️⃣0️⃣ Page 33 – Folding Pathway Simulation

Preformed structural elements guide folding.

Energy landscape funnel model.

3️⃣1️⃣ Page 34 – Force Fields

Computational folding uses:

• Bonded terms
• Electrostatics
• vdW
• Torsion angles

3️⃣2️⃣ Page 36 – Millisecond Folding

Simulation of NTL9 for 1.5 ms.

Shows computational power.

3️⃣3️⃣ Page 37 – Chemical Denaturation

GdmCl unfolding.

Two-state: N ⇌ U

K = U/N

3️⃣4️⃣ Page 38 – Two-State Analogy

AcOH ⇌ AcO⁻ example.

Only two species present.

3️⃣5️⃣ Page 39 – Thermal Denaturation

Melting temperature (Tm): N = U

Midpoint of transition.

3️⃣6️⃣ Page 40 – Cooperativity

Steep unfolding curve.

All-or-none behavior.

3️⃣7️⃣ Page 41 – Folding Kinetics

Rate constants: kf (folding) ku (unfolding)

Equilibrium: K = kf / ku

3️⃣8️⃣ Page 42 – ΔG of Folding

ΔG = −RT lnK

Typical ΔG: −20 to −60 kJ/mol

Only equivalent to a few hydrogen bonds!

3️⃣9️⃣ Page 43 – Energy Diagram

Free energy landscape:

Unfolded → transition state → folded

ΔG‡ = activation barrier

Stability depends on ΔG.

4️⃣0️⃣ Page 44–45 – RNase Example

ΔH = −95 kcal/mol TΔS = −85 kcal/mol ΔG = −10 kcal/mol

Large enthalpy and entropy cancel → small ΔG.

Keq ≈ 2.2 × 10⁷

Protein mostly folded.

4️⃣1️⃣ Page 46 – Protein Comparisons

ΔH varies greatly. ΔG varies little.

Huge enthalpy–entropy compensation.

4️⃣2️⃣ Page 47–48 – Contributions to ΔG

Enthalpy:

• Electrostatics
• H-bonds
• vdW
• Disulfide

Entropy:

• Chain entropy (unfavorable)
• Hydrophobic effect (favorable)

Balance yields small net ΔG.

4️⃣3️⃣ Page 49 – Measuring Thermodynamics

ΔG from equilibrium.

ΔH & ΔS: Van’t Hoff equation.

Calorimetry measures ΔH directly.

4️⃣4️⃣ Page 50 – Differential Scanning Calorimetry

Graph shows:

Heat capacity vs temperature.

Peak area = ΔH.

Tm = peak midpoint.

4️⃣5️⃣ Page 51 – Heat Capacity Change

ΔCp increases upon unfolding.

Reason: Water orders around exposed hydrophobic surfaces.

ΔCp ~ residues × 50 J/mol·K

4️⃣6️⃣ Final Pages – Temperature Dependence

ΔG vs temperature curve:

Protein most stable at intermediate T.

At: Low T → cold denaturation High T → heat denaturation

Tm when ΔG = 0.

🧠 Overall Big Picture

Protein folding is governed by:

Strong forces:

• Covalent bonds

Weak but numerous forces:

• Electrostatics
• Hydrogen bonds
• van der Waals
• Hydrophobic effect

Thermodynamics:

• Large ΔH and ΔS
• Small net ΔG
• Cooperative transitions

Folding is:

• Fast
• Directed
• Funnel-shaped energy landscape
• Not random