1️⃣ How can we study protein folding? (p.1)

The slide shows a folded green protein structure transitioning into an unfolded chain.

Key idea:

It is easier to study unfolding than folding.

Why?

• Folding starts from many possible conformations.
• Unfolding starts from one well-defined native structure.

Two main approaches:

• 🔥 Thermal unfolding
• 🧪 Chemical unfolding

We measure unfolding and infer folding by thermodynamics (reversibility).

2️⃣ Overview of the course (p.2)

Lecture I:

• Covalent bonds
• Noncovalent interactions
• Electrostatics
• Hydrophobic effect
• Folding basics

Lecture II:

• Energetics
• Calorimetry
• Kinetics
• Folding pathways
• Two-state vs multi-state
• Structured vs unstructured proteins

This lecture focuses heavily on:

• Thermodynamics
• Calorimetry
• Denaturants
• Folding kinetics
• Transition state analysis

3️⃣ Folding equilibrium and kinetics (p.3)

Reaction:

U leftrightarrow N

Rates:

• kf = folding rate
• ku = unfolding rate

Equilibrium constant: K = rac{U}{N} = rac{k_u}{k_f}

Thermodynamics: Delta G = -RT ln K

Key concept:

• If ΔG < 0 → folded favored
• If ΔG = 0 → 50% folded (Tm)

4️⃣ Determining ΔH°, ΔS°, ΔG° (p.4)

Delta G° = Delta H° - TDelta S°

Van’t Hoff plot:

Plot: ln K ext{ vs } 1/T

Slope = −ΔH°/R Intercept = ΔS°/R

The graph on the slide shows a straight line — meaning enthalpy and entropy can be extracted from temperature dependence.

5–6️⃣ Calorimeter (DSC) (p.5–6)

The schematic shows:

• Sample cell
• Reference cell
• Heat compensation system

Principle: If unfolding absorbs heat, more power must be supplied to keep both cells at same temperature.

Modern DSC:

• ~0.5 mL sample
• ~0.2–1 mg/mL protein

Page 6 shows the real instrument.

7️⃣ Calorimetric raw data (p.7)

Graph shows:

• Cp vs temperature
• Sharp peak at Tm

Important:

✔️ Area under the peak = ΔHcal (Model independent)

Why is Cp higher without protein? Because buffer contributes baseline heat capacity.

The unfolding peak represents:

• Cooperative transition
• Energy absorbed to break stabilizing interactions

8️⃣ Van’t Hoff enthalpy (p.8)

Tm = 50% folded.

Important ratio:

rac{Delta H_}{Delta H_}

Interpretation:

• = 1 → Two-state folding
• < 1 → Intermediate(s)

• 1 → Aggregation

This ratio checks cooperativity.

9–12️⃣ Temperature dependence (p.9–12)

Graph shows:

• ΔH increases with T
• TΔS increases with T
• ΔG crosses zero at Tm

T_m = rac{Delta H}{Delta S}

ΔCp introduces curvature in ΔG vs T.

Key insight: If we know:

• ΔH(Tm)
• ΔCp

We can calculate ΔG at any T.

13–14️⃣ Scanning calorimetry (p.13–14)

Graph features:

• Native baseline
• Denatured baseline
• Peak = transition

ΔCp(unfolding) is difference between baselines.

Area under transition region = ΔHd.

Peak width reflects cooperativity.

15–20️⃣ Ligand binding effects on Tm

Two cases:

Case 1: Ligand binds native state (p.16–17)

Stabilizes N → Tm increases.

Graph (FGF example): Control Tm = 35.2°C With phosphate = 40.9°C With sulfate = 46.2°C

Clear rightward shift.

Case 2: Ligand binds denatured state (p.18–19)

Stabilizes U → Tm decreases.

Lysozyme at low pH: Protons bind U → destabilization.

Page 20 shows Tm vs pH:

• Low pH → low Tm
• Neutral pH → high Tm

21–22️⃣ Methods for thermal denaturation

Methods:

• DSC → thermodynamics
• CD → secondary structure
• Fluorescence → tertiary structure
• Differential scanning fluorimetry (DSF)

Graph on p.21 shows:

• DSC peak
• CD signal change
• Both transition at same temperature

If transitions overlap → likely two-state.

23–26️⃣ Denaturants vs osmolytes

Denaturants:

• Urea
• GdmHCl Stabilize unfolded state.

Osmolytes:

• TMAO
• Betaine
• Trehalose Stabilize folded state.

Key equation (p.25):

Delta G_ = Delta G_ + mD

m-value reflects:

• Exposure of surface area
• Interaction with denaturant

27–29️⃣ m-values

Good correlation: m-value ↔ ΔCp

Meaning: Both reflect change in solvent-accessible surface area.

Same ΔG but different m: Different exposure patterns.

30️⃣ Beware of urea

Urea can:

• Decompose
• Carbamylate proteins
• Change pH

32–37️⃣ Folding kinetics

Rate law:

rac{dU}{dt} = -k_fU + k_uN

Stop-flow allows:

• Millisecond mixing
• Monitoring fluorescence or CD

Exponential behavior:

A(t) = A_0 e^{-kt}

38–39️⃣ Chevron plots (VERY IMPORTANT)

A chevron plot =

Plot: ln k_ ext{ vs } denaturant

Two linear arms:

Left arm: ln k_f = ln k_f^{water} + m_f D

Right arm: ln k_u = ln k_u^{water} + m_u D

Shape looks like a "V" → chevron.

What does it tell us?

1. Folding rate in water (intercept)
2. Unfolding rate in water
3. Equilibrium constant: K = rac{k_f}{k_u}
4. Transition state sensitivity to denaturant

From p.39: kf(water) ≈ 320 s⁻¹ ku(water) ≈ 0.0005 s⁻¹

Thus: K ≈ 640,000

Very stable protein.

Interpretation of slopes:

• mf reflects structure formation in transition state.
• If slope small → transition state less native-like.

If plot is curved:

• Folding intermediate present.

40–46️⃣ Transition state & Φ-values

Transition state cannot be directly observed.

We use mutagenesis.

Φ-value:

Phi = rac{DeltaDelta G^{‡}}{DeltaDelta G}

Interpretation:

Φ ≈ 0: Residue not structured in transition state.

Φ ≈ 1: Residue fully structured in transition state.

Page 45 example: Mutant increases ku but not kf → Φ ≈ 0

Residue not native-like in transition state.

47️⃣ Two-state folding is simplified

MD simulation shows: Many microscopic conformations.

Macroscopic two-state ≠ atomic two-state.

48–50️⃣ Folding pathway

Unfolded state:

• Some residual structure
• Hydrophobic clusters

Early folding:

• Topology emerges
• Local structures fluctuate

Transition state:

• Native folding nucleus
• Long-range interactions

51–52️⃣ Folding funnel

Energy landscape:

Wide top → many conformations Narrow bottom → native state

Many pathways → same native state.

53–56️⃣ Molten globule

Characteristics:

• Compact
• Secondary structure intact
• No tight tertiary packing
• Hydrophobic core exposed

CD evidence (p.56):

Far UV CD: Secondary structure present.

Near UV CD: No tertiary structure.

Thus: Molten globule retains helices but loses packing.

57️⃣ Exercises

References: Dobson 2003 Nature review on misfolding and fibrils.

🔥 Big Picture Summary

Protein folding involves:

Thermodynamics:

• ΔG = ΔH - TΔS
• DSC measures ΔH
• m-values reflect exposure

Kinetics:

• kf and ku from stop-flow
• Chevron plots reveal mechanism

Transition state:

• Studied by Φ-value analysis
• Reveals folding nucleus

Energy landscape:

• Funnel model
• Multiple pathways

Intermediates:

• Molten globule