14. Special topic: Full thermodynamic “balance sheet” for lysozyme (folded vs unfolded) across temperature 🧮🌡️

Core idea: The folded state is only slightly more stable than the unfolded state, because it’s the difference between two huge numbers: enthalpy (H) and entropy term (T·S).

What Figure 21 is showing (and why it’s a big deal)

Figure 21 breaks the thermodynamics into four panels:

• Panel A (H vs T): Enthalpy of folded and unfolded lysozyme as temperature changes.
• Panel B (T·S vs T): The entropy contribution scaled by temperature.
• Panel C (G vs T): Since G = H − T·S, you get two curves (folded and unfolded free energies).
• Panel D (ΔGfold vs T): The actual stability difference: ΔGfold = G(unfolded) − G(folded) (stability of folded state).

The key “aha”

• The melting temperature (Tm) is where ΔGfold = 0, meaning folded and unfolded are equally populated.
• The figure emphasizes the “zooming” of scales: panels A/B are huge, C is smaller, D is tiny—showing how small ΔG is relative to H and T·S.
• So protein stability is a delicate cancellation: large favorable terms and large unfavorable terms nearly cancel, leaving a small net stability.

15. Special topic: Heat and cold denaturation (yes—proteins can unfold when it’s too cold) ❄️🔥

Core idea: Many proteins are stable only in a temperature window. Too hot unfolds them (common), but too cold can also unfold them (surprising).

Why heating usually denatures proteins

• As temperature rises, the entropy term (T·ΔS) tends to dominate.
• Even if folding has favorable enthalpy, at high enough T the entropy penalty wins → unfolding.

Why cold denaturation can happen

This hinges on the hydrophobic effect changing with temperature:

• Hydrophobic core formation has a special thermodynamic behavior: its enthalpy can be positive over part of the range (unlike “normal” bond formation).
• At low temperatures, the hydrophobic effect weakens enough that unfolding can become favorable.
• Cold denaturation is explained as water becoming more able/willing (entropically/enthalpically) to solvate exposed nonpolar surface when the protein unfolds.

Figure 22 (apomyoglobin calorimetry) interpretation

• They cool apomyoglobin down to around −10 °C in a supercooled solution.
• A negative deflection indicates heat release as cold denaturation occurs (protein unfolds).
• When warming back up:
  • there’s heat uptake as it refolds near the cold transition,
  • and later a second heat uptake peak for the usual high-temperature unfolding (~55 °C region).
• Physical intuition given: cold unfolding reflects the tendency of water to order around / solvate nonpolar areas exposed by unfolding.

19. Special topic: Heme-induced refolding of human α-globin (ligand binding can create the fold) 🩸🧲

Core idea: Binding a ligand (heme) doesn’t just “dock” onto a rigid protein—it can drive folding, and folding can occur in multiple kinetic phases.

Starting point: apo vs holo α-globin

• Native α-chain + heme is ~75% α-helix (CD double minimum at 208/222 nm).
• Remove heme → helix drops to ~30% (partially unfolded).
• Add equimolar heme back → CD returns to native-like spectrum (structure restored).

Why Trp fluorescence is a clever probe (Figure 33)

• α-globin has one Trp (A14) near the heme.
• In the holo protein: Trp fluorescence is quenched because energy transfers to heme quickly.
• In apo form: Trp fluoresces normally. So: loss of fluorescence reports on heme becoming positioned near Trp in a native-like geometry.

What the stopped-flow experiments reveal

They observe fast + slow phases, depending on what signal they track:

1) Trp fluorescence quenching (Figure 34)

• First ~85% fits fast second-order kinetics → consistent with a binding event dependent on reactant concentrations.
• The remaining part fits a slower first-order process → suggests a slower conformational “settling.”
• Reported rate constants:
  • fast: 3.3 × 10^7 M⁻¹ s⁻¹
  • slow: 2.3 × 10⁻² s⁻¹

2) Soret band appearance at 418 nm (Figure 35)

• Very rapid initial absorbance increase (first ~50–55%) too fast to measure in that setup.
• The remaining change clearly follows first-order kinetics:
  • 1.7 × 10⁻² s⁻¹, similar to the slow fluorescence phase.

3) CD recovery at 222 nm (Figure 36)

• Secondary structure (α-helix) grows in two first-order phases (no fast phase):
  • 2.6 × 10⁻² s⁻¹ (phase 1)
  • 6.0 × 10⁻³ s⁻¹ (phase 2)

Their mechanistic interpretation (sequence of events)

• Fast step: heme binds when protein fluctuations transiently create a pocket-like hydrophobic site.
• Binding stabilizes local tertiary structure → Trp begins to quench.
• Then structure propagates outward: helicity grows and heme/Trp geometry becomes fixed.
• The slow CD phases suggest secondary-structure recovery is not instantaneous; folding “ripples” outward from the heme pocket.
• Conclusion: the heme pocket acts as a folding nucleus.

22. Special topic: Simulating folding mechanisms (MD + Φ-values + NMR) 🧪💻

Core idea: Even “two-state folding” (macroscopically) can hide a rich microscopic story with transient structures, multiple nucleation attempts, and only late formation of the true folding nucleus.

What MD simulations show (example: chymotrypsin inhibitor 2)

• In the “unfolded” ensemble, there can still be:
  • small hydrophobic clusters,
  • fluctuating native-like helices, even though it’s globally unfolded.
• As folding begins, the gross topology starts emerging early, but not as a single clean pathway.

Figures 41–42: linking simulation to experiment

• Figure 41: snapshots during unfolding simulation show a “two-state” appearance overall, yet atomistically there are many transient structures.
• Figure 42: experimental Φ-values (and simulated equivalents) line up, validating the simulated transition state:
  • high Φ-values in certain residue regions imply a native-like folding “core” is already formed there in the transition state.

26. Special topic: Misfolding and chaperones (the crowded cell changes everything) 🧷🧯

Core idea: Proteins often can fold spontaneously, but in cells the environment is so crowded that misfolding/aggregation becomes a serious competing pathway—and chaperones help manage that.

Why folding is harder in vivo

• The cytosol is extremely crowded: macromolecules ~300–400 mg/mL.
• Partially folded states can collide and form aggregates.

What chaperones do (and do NOT do)

• They do not encode the final fold.
• They act more like catalysts:
  • prevent off-pathway aggregation,
  • “anneal” misfolded forms,
  • lower activation barriers so proteins can find the native basin.
• Many were discovered as heat-shock proteins, because stress increases misfolding risk and triggers their expression.

Figure 47 and Figure 48: folding vs aggregation landscapes

• Figure 47: many possible fates—native fold, intermediates, degradation, aggregation, amyloid, complexes.
• Figure 48: “double funnel” idea:
  • one funnel leads to native folding,
  • another leads to aggregation,
  • the environment (including chaperones) biases which funnel dominates.

Disease connection

• Some diseases arise because proteins misfold and lose function (e.g., some cases of cystic fibrosis, cancers).
• Others arise from toxic aggregates (Alzheimer’s, Parkinson’s).
• Failures in chaperone/proteostasis systems contribute to pathology.

27. Special topic: Aggregation and amyloid formation (a “generic” risk of polypeptides) 🧱🧬

Core idea: Amyloid formation isn’t unique to a few “bad” proteins—it seems to be a generic property of polypeptide chains under conditions where the backbone can form extensive β-sheet hydrogen bonding networks.

Figure 49: a generalized pathway

1. unfolded/partially unfolded proteins → small soluble aggregates
2. protofibrils/protofilaments
3. mature fibrils
4. larger deposits (plaques, Lewy bodies, etc.)

• Often: lag phase then rapid growth (nucleation-like, similar to crystallization).
• Seeding with preformed aggregates can remove the lag phase.

Why amyloids look similar across different sequences

• The main chain is chemically the same across proteins.
• Amyloid cores are stabilized mainly by backbone hydrogen bonds arranged in β-sheets (strands perpendicular to the fibril axis).
• This explains why diverse sequences can yield structurally similar fibrils.

When amyloid becomes possible

• In globular proteins, backbone and hydrophobics are buried.
• Amyloid needs exposure of these features, e.g.:
  • partial unfolding (low pH),
  • fragmentation (proteolysis),
  • destabilizing mutations.

Evolutionary angle

• Selection may avoid sequences that strongly favor amyloid-like β-structures (e.g., alternating polar/hydrophobic patterns).

Prions and transmission

• In prion disorders, ingestion/exposure to pre-aggregated states can increase aggregation via seeding, enabling transmissibility.

28. Special topic: Cooperativity in folding as an entropy phenomenon (effective concentration) 🤝📈

Core idea: A single weak interaction inside a floppy chain is usually unstable. Folding becomes cooperative because once one interaction forms, it raises the effective concentration of other groups, making subsequent interactions much more likely and stronger.

Effective concentration: the key conceptual tool

Compare:

• intermolecular association (A + B ↔ AB): K has units (concentration)⁻¹
• intramolecular contact (A···B within same chain): K is dimensionless Their ratio behaves like a concentration: the “effective concentration” of B near A in that chain conformation.

Important punchline: effective concentrations can be much higher than 55 M, so intramolecular contacts can be dramatically favored compared with bringing two separate molecules together.

Why one interaction isn’t enough in an unfolded chain

For a single contact in an unfolded polypeptide:

• effective concentrations often ~10⁻² to 10⁻⁵ M
• predicted observed equilibrium constants for one H-bond/salt bridge can be ~10⁻³ to 10⁻⁷ So: one interaction alone is usually not stable unless groups are already close in sequence/geometry.

Cooperativity with multiple interactions (Figures 53–54)

• If A–B forms, it can increase the effective concentration for C–D.
• This mutual reinforcement is captured by a Coop factor.
• Net stability is multiplicative: Knet = (KAB·A/BU)(KCD·C/DI)(...)
• This produces the classic cooperative behavior:
  • partially formed states can be less stable than either end state,
  • once enough interactions accumulate, Knet crosses >1 and the folded state dominates.

29. Special topic: Calorimetry of a multidomain protein (plasminogen) — domains as “beads-on-a-string” (sometimes) 🧩🔥

Core idea: In large multidomain proteins, unfolding can occur as multiple transitions, revealing whether domains unfold independently or cooperatively. Plasminogen is used as a detailed case study.

Plasminogen architecture (Figure 55)

• 791 aa precursor of plasmin.
• Contains:
  • N-terminal region + five kringle domains (1–5),
  • plus a trypsin-like serine protease domain.
• Various fragments (kringles 1–3, kringle 4, kringle 5–protease “miniplasminogen”) can be produced by elastase cleavage and studied separately.

Castellino et al. at pH 7.4 (Figure 56): complex, partly irreversible behavior

• Intact plasminogen shows a broad melting curve → multiple overlapping transitions.
• Individual fragments show simpler (but still broad) patterns.
• Adding ligand ε-aminocaproic acid raises Tm values and changes transitions—implying ligand interactions across fragments.
• But interpretation is limited because transitions were not fully reversible, with insoluble denatured protein forming.

Novokhatny et al. at pH 3.4 (Figure 57): cleaner, reversible transitions → stronger conclusions

At low pH where transitions were reversible:

• Intact plasminogen: multiple close melting transitions.
• Kringles 1–3: deconvolution suggests three transitions → each kringle unfolds like an independent folding unit.
• Kringle 1 alone confirms “miniprotein-like” independent behavior.
• Kringle 5 + serine protease: suggests three components; kringle 5 corresponds to one lower-temperature transition, and the protease contributes two (consistent with the protease having two domains).
• Overall message: at pH 3.4, plasminogen behaves like modular beads-on-a-string (weak interdomain coupling).

They note that at physiological pH (7.4) plasminogen likely has stronger interdomain interactions and a different overall shape—still flexible, and influenced by ligand binding to kringles (e.g., C-terminal Lys on fibrin fragments).