Modeling protein density of states: Additive hydrophobic effects are insufficient for calorimetric two-state cooperativity
Bibliographic record
Abstract
A well-established experimental criterion for two-state thermodynamic cooperativity in protein folding is that the van't Hoff enthalpy DeltaH(vH) around the transition midpoint is equal, or very nearly so, to the calorimetric enthalpy DeltaH(cal) of the entire transition. This condition is satisfied by many small proteins. We use simple lattice models to provide a statistical mechanical framework to elucidate how this calorimetric two-state picture may be reconciled with the hierarchical multistate scenario emerging from recent hydrogen exchange experiments. We investigate the feasibility of using inverse Laplace transforms to recover the underlying density of states (i.e., enthalpy distribution) from calorimetric data. We find that the constraint imposed by DeltaH(vH)/DeltaH(cal) approximately 1 on densities of states of proteins is often more stringent than other "two-state" criteria proposed in recent theoretical studies. In conjunction with reasonable assumptions, the calorimetric two-state condition implies a narrow distribution of denatured-state enthalpies relative to the overall enthalpy difference between the native and the denatured conformations. This requirement does not always correlate with simple definitions of "sharpness" of a transition and has important ramifications for theoretical modeling. We find that protein models that assume capillarity cooperativity can exhibit overall calorimetric two-state-like behaviors. However, common heteropolymer models based on additive hydrophobic-like interactions, including highly specific two-dimensional Gō models, fail to produce proteinlike DeltaH(vH)/DeltaH(cal) approximately 1. A simple model is constructed to illustrate a proposed scenario in which physically plausible local and nonlocal cooperative terms, which mimic helical cooperativity and environment-dependent hydrogen bonding strength, can lead to thermodynamic behaviors closer to experiment. Our results suggest that proteinlike thermodynamic cooperativity may require a cooperative interplay between local and nonlocal interactions. The prospect of using calorimetric data to constrain Z-scores of knowledge-based potentials is discussed.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".