{"id":"83e9cfd8-d737-41e3-a901-970e9ad652c2","arxiv_id":"2412.14341","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Folding mechanisms of globular proteins can be inferred from evolutionary sequence alignments by mapping sequence-based energies onto an Ising chain of exon-defined folding elements.","lead":"This paper predicts how proteins fold by treating each protein as a chain of cooperative folding units, with the units' energies learned from evolutionary sequence data. The method captures diverse folding behaviors across 15 protein families and could help engineers predict how mutations change protein stability and folding cooperativity.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The untested 'folding-dominance' assumption is load-bearing: if RBM fields encode functional constraints at active sites, the inferred foldon energetics and mechanisms are contaminated. A stratified mutational ΔΔG test on a functionally constrained family would settle it.","rationale":"The reader's weakest_assumption correctly identifies the folding-dominance assumption as the most load-bearing point: the entire method converts RBM sequence statistics into folding free energies, and every conclusion about mechanisms inherits that conversion. My independent reading confirms this is the weakest link. Other concerns—T_sel calibration, entropy parameter s, linear-fit mutation predictions, weak ΔT_f correlations—are real but secondary: a global scaling of T_sel would mostly shift absolute T_f without changing relative foldon order, and the alternative-partition control partially addresses robustness to foldon definition. Functional contamination, by contrast, changes local energies non-uniformly and can directly reorder the predicted folding pathway. The paper deserves credit for useful controls (no-interaction, vanilla models, alternative partitions) and for the r=0.88 EcDHFR comparison against a structure-based model, but that comparison is a single model-model check using the same foldon partition and does not test whether the RBM fields are folding energies rather than functional constraints. The m-value and ΔT_f validations are aggregated and partly exclude or fail on functionally constrained families, which is consistent with the concern rather than against it. The proposed TEM-1 test is concrete, feasible, and would distinguish between the two hypotheses; until such a test is done, CONDITIONAL is the appropriate verdict.","tokens_in":21271,"tokens_out":6420,"duration_ms":62829,"concrete_test":"Train the RBM and run the full foldon-Ising pipeline on a family with a large independent experimental ΔΔG dataset, such as TEM-1 β-lactamase (Stiffler et al., Cell 2015, or Firnberg et al., MBE 2014). Predict ΔΔG for all single mutants, then stratify the predicted-vs-experimental correlation by whether the mutated residue lies in a known functional site (active site or substrate-binding pocket) versus the rest of the protein. If the correlation is significantly worse for functional-site mutations (e.g., via Fisher z-test on r values, or an interaction term in a regression), the RBM fields encode functional constraints and the 'only sequence information' claim fails. If the correlations are statistically indistinguishable, the folding-dominance assumption holds for this test case. Repeat on PDZ (the calibration family) as a positive control.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim, stated in the Abstract, is that 'only sequence information' can infer folding mechanisms, via the Eq. 2 mapping from RBM evolutionary energy fields to foldon Ising energies. That mapping is valid only if the RBM fields are dominated by folding stability. The Introduction asserts this, and the Concluding remarks admit: 'this framework assumes that folding stability is locally the main evolutionary constraint... sequence positions strongly conserved and conditioned by other selection forces besides folding may affect local stability and some cooperativity predictions.' The paper never tests this. This is load-bearing because all downstream results—foldon stabilities, cooperativity scores, mutation effects—are computed from those fields. For families like DHFR or RNase H, active sites are under strong functional selection; if the RBM fields encode catalytic constraints, the foldon containing the active site will have distorted internal and surface energies, changing the predicted folding order and cooperativity. Red flags already appear in the validation: the m-value correlation (Fig. S12) excludes CytochromeC because of heme binding, and the paper notes that active-site mutations in RNase H break the ΔT_f correlation (Table S2, Kanaya 1996 r=0, Lim 1992 r=0.14). These are exactly the signatures of non-folding constraints, yet no control is provided to separate functional from folding signals.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript presents a coarse-grained Ising model of protein folding in which proteins are partitioned into foldons (defined by Minimal Common Exons) and the internal and interfacial free energies are obtained by mapping the one- and two-body fields of a family-specific Restricted Boltzmann Machine to folding energies via Eq. (2), scaled by a family selection temperature T_sel. The authors simulate thermal unfolding for 15 PFAM families (500 sequences each), characterize each family's folding temperature and cooperativity score, and report that within-family cooperativity variability is limited for beta and alpha/beta topologies but larger for alpha proteins. They also compute the effect of single-point mutations on folding temperature and cooperativity, comparing against experimental m-values and Delta-T_f data from ProTherm. The central claim is that folding mechanisms can be inferred from sequence information alone.","tokens_in":21513,"tokens_out":8099,"duration_ms":73736,"significance":"The framework is original and the paper includes several useful controls: reproduction of EcDHFR foldon stabilities against a structure-based model (r=0.88), robustness to alternative foldon partitions (Fig. S4), a family-level correlation of cooperativity variance with short/long-range contact ratio, and a set of clear falsifiable predictions for point mutants. The code and data are deposited on GitHub, which supports reproducibility. However, the validity of the entire pipeline rests on the assumption that the RBM fields are dominated by folding stability rather than by functional constraints; this assumption is acknowledged but not tested. If that assumption holds, the approach could be a valuable way to connect evolutionary sequence records to folding mechanisms and to rank mutants by stability and cooperativity.","major_comments":[{"comment":"The mapping from sequence to folding energetics in Eq. (2) assumes that the RBM fields are dominated by folding stability, an assumption stated in the Introduction ('we will make the approximation...') and acknowledged in the Concluding remarks as potentially affecting 'local stability and some cooperativity predictions.' This assumption is load-bearing because all downstream quantities--foldon internal energies, surface couplings, T_f, and cooperativity scores--are computed from these fields. The paper's own validations contain red flags: the m-value correlation in Fig. S12 excludes CytochromeC because of heme binding, and Table S2 reports r=0 (Kanaya 1996) and r=0.14 (Lim 1992) for RNase H and Trp syntA, which the authors attribute to active-site mutations. No control is provided that separates functional constraints from folding constraints. I request a stratified analysis: e.g., compare inferred energies against experimental Delta-Delta-G separately for functional-site and non-functional-site mutations, or recompute the model with active-site/gap columns masked, and report how the EcDHFR and m-value validations change. Without such a control, the abstract's claim that folding mechanisms are inferred from 'only sequence information' is premature.","section":"Introduction; Eq. (2); Fig. S12; Table S2; Concluding remarks"},{"comment":"Because Eq. (2) scales all Ising energies by T_sel, the folding temperature T_f of any sequence scales linearly with T_sel for fixed dimensionless energy patterns. The near-linear relationship between the standard deviation of T_f and T_sel reported in Fig. 3B therefore holds largely by construction, and it does not independently support the evolutionary interpretation that families with low T_sel 'only permit' sequences with T_f close to the family average. The authors should report the distribution of the dimensionless ratio T_f/T_sel across families, or equivalently residual variation after removing the multiplicative T_sel factor, and should test the sensitivity of the results to the Miyazawa assumption of constant sigma(Delta-Delta-G) underlying Eq. (3). As written, the claim in the text is at risk of being a scaling artifact rather than a biological finding.","section":"Eq. (3); Fig. 3B"},{"comment":"The predicted changes in cooperativity upon mutation are obtained from a linear fit of the cooperativity score in the heterogeneity-interaction plane (Fig. 5A) that is itself fitted to the 7500 simulated sequences; predictions from this fit are then compared to the model outputs again in Fig. S11. This is not an independent test of the model's ability to predict mutational Delta-rho. The only experimental observable linked to rho is the m-value correlation in Fig. S12, which pools many proteins and excludes CytochromeC because of the heme cofactor. I ask for an out-of-sample evaluation: cross-validate the linear surrogate, report per-family and per-mutant m-value correlations, and show the m-value comparison with CytochromeC included and without exclusion. The mutation-prediction section should clearly distinguish what is a computational shortcut from what is experimentally validated.","section":"Fig. 5A; Fig. S11; Fig. S12"},{"comment":"The central claim that topology limits cooperativity variability within a family rests on the correlation in Fig. 4C between cooperativity variance and N_short/N_long. This is a family-level scatter with only 15 points, and the manuscript does not report a correlation coefficient, p-value, or confidence interval for this relationship. The Copper-bind family is acknowledged as escaping the trend, but no explanation is offered. Please report the statistics (e.g., Spearman r, p), test the robustness of the relationship to the contact definition and to the choice of reference PDB, and discuss whether the result persists when the two or three least well-behaved families are removed.","section":"Fig. 4C"}],"minor_comments":[{"comment":"There is a typo in Eq. (1): 'Kroeneker' should be 'Kronecker'.","section":"Eq. (1)"},{"comment":"The first DHFR entry in Table S2 has 'No ID' in the PMID column; the reference should be completed or the column removed.","section":"Table S2"},{"comment":"The Methods sentence 'For minimizing the phylogenetic bias within each MSA, we clustered by full sequence similarity using CD-hit at 90% cutoff and we assigned a weight to each sequence defined as being the number of sequences in the th cluster' is incomplete and the subscript is missing; it should read '...defined as 1/n_i, where n_i is the number of sequences in the i-th cluster.'","section":"Methods (Data curation)"},{"comment":"The 'Statement of significance' is quite generic; it could more specifically state the discovered topology-dependence of cooperativity variability and its implications for protein engineering and for interpreting natural sequence diversity.","section":"Statement of significance"},{"comment":"Several correlations are described only by panels without reporting the corresponding coefficients and p-values in the main text (e.g., Fig. 4C, Fig. S8, Fig. S10); adding these statistics would make the strength of the trends easier to assess.","section":"Fig. 4C and supplemental figures"}],"recommendation":"major_revision","confidential_remarks":"The paper has a solid core and is likely to become a well-cited work if the functional-vs-folding constraint issue is addressed. I recommend asking the authors for the stratified Delta-Delta-G analysis, the T_sel scaling controls, and an out-of-sample evaluation of the mutation-cooperativity predictions. The political statement in the Acknowledgements is not a technical flaw but may draw attention; I leave it to the editor's judgment."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know this paper is a solid, incremental extension of the group's earlier repeat-protein Ising work to 15 globular families. What's genuinely new: they generalize the evolutionary-energy-plus-Ising framework to aperiodic topologies using exon-defined foldons, introduce a simple topology descriptor (N_short/N_long) that correlates with cooperativity variability, and extend predictions to mutation-induced changes in both T_f and cooperativity. The paper ships code and data, runs sensible controls (no-interaction, vanilla models, alternative foldon partitions), and validates against a structure-based model for EcDHFR (r=0.88) and against experimental m-values (r=0.74). The controls matter, and the transparent acknowledgment of limitations is refreshing.\n\nThe soft spots are real but proportional. The load-bearing assumption that folding stability dominates the evolutionary sequence record is stated but never tested. The stress-test note is on target: if RBM fields encode functional constraints at active sites, the inferred foldon energetics are contaminated. Red flags already appear in their own validation—CytochromeC needs to be excluded for the m-value correlation, and active-site mutations in RNase H break the ΔT_f correlation. That said, they flag these failures explicitly in the SI and concluding remarks, so it's not hidden. The selection temperatures for non-PDZ families rest on Miyazawa's scaling assumption, and the Δρ predictions are read off a fitted linear surface, which is a shortcut rather than a mechanistic prediction. Fig. 4C lacks error bars/statistics in the main text, which is a legitimate missing piece, not a fatal flaw.\n\nThe central topology result does not look circular because it relies on an external structural descriptor, and the model is tested against independent experimental data. The paper is internally consistent and honestly argued. The main unresolved question is whether the sequence-based energies are really reporting folding stability rather than mixed functional constraints; that is addressable with a stratified mutational ΔΔG test on a functionally constrained family.\n\nWho is this for? Anyone working in evolutionary biophysics, coarse-grained folding models, or mutational effect prediction. It deserves a serious referee. I would ask for sensitivity analyses on s and T_sel, proper statistics for Fig. 4C, and a direct test of the folding-dominance assumption on families with known functional sites. Those are revisions, not grounds for rejection.","headline":"A well-controlled extension of the foldon Ising model to globular proteins, with real validation and honest caveats; the folding-dominance assumption is the main soft spot, but the paper deserves a serious referee.","tokens_in":22118,"tokens_out":1022,"would_cite":true,"duration_ms":11824,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Using only the evolutionary record in a protein family's sequences, the paper infers how individual globular proteins fold — the order of their folding elements, how cooperatively they fold, and how single mutations rewire both.","keywords":["protein folding mechanisms","evolutionary energy","Ising model","Potts model","Restricted Boltzmann Machine","foldons","folding cooperativity","protein topology"],"falsifier":"Measure experimental folding-temperature shifts ($\\Delta T_f$) for a set of single mutants located in and around a strongly conserved functional site — for example the active site of a DHFR or RNase H family member — and compare them with the model's per-site predictions: if the correlation between predicted and measured $\\Delta T_f$ is systematically worse for functional-site mutations than for surface mutations, or collapses when the conserved functional positions are masked out of the alignment, the central assumption that folding dominates the sequence record is broken.","tokens_in":21001,"feed_emoji":"🧬","tokens_out":17176,"duration_ms":123008,"temperature":0.7,"pith_summary":"This paper attempts to show that the evolutionary record in protein sequences carries enough information to infer the folding mechanisms of globular proteins — not just their native structures or global stabilities, but which parts fold first, which fold together, and how mutations change that choreography. The authors learn one- and two-body evolutionary energy fields from each family's sequence alignment, map them onto a coarse-grained Ising chain of folding elements called foldons, and simulate thermal unfolding for 500 sequences in each of 15 protein families. They find that native topology sets limits on how much folding cooperativity can vary within a family: beta and alpha/beta folds allow only a few mechanisms despite high sequence diversity, while alpha topologies permit diverse folding scenarios among family members. They further claim that mutation-induced changes in folding temperature and cooperativity can be computed directly from the evolutionary model, and report correlations with experimental denaturation data ($r=0.74$ between predicted cooperativity and experimental m-values). If the claims hold, protein engineers could rank natural variants by folding stability, cooperativity, or both using sequence information alone.","feed_headline":"Sequences alone predict how proteins fold, not just their shape","feed_subtitle":"Across 15 families and 7,500 proteins, folding order and mutation effects emerge from sequence alignments alone.","key_machinery":"The central object is the foldon Ising model: a finite chain of $N$ two-state elements (foldons, each folded or unfolded) whose Hamiltonian combines an internal folding free energy per element, a pairwise interaction energy between folded elements, and an entropic cost for unfolded elements. What carries the argument is the mapping of sequence information onto those energies: a Restricted Boltzmann Machine is learned on each family's multiple sequence alignment and converted into Potts-model couplings and local fields, which are summed over the residues of each foldon to yield the Ising energy terms, scaled by a family-specific selection temperature $T_{sel}$ — the apparent temperature at which nature selected the family's sequences, calibrated against experimental stability data and extrapolated via an empirical scaling rule. The foldon partition itself is supplied by Minimal Common Exons, conserved exon-intron boundaries that divide each alignment into common folding elements. From Monte Carlo simulations, the model extracts thermal unfolding curves, free-energy profiles over the number of folded elements $Q$, per-element folding temperatures $T_f$, and a cooperativity score $\\rho = Q_{barrier}/(N-1)$ counting the intermediate $Q$ values that are never free-energy minima. Topology-only 'vanilla' models serve as controls that isolate the contribution of the amino-acid-level evolutionary fields.","core_discovery":"On its own terms, the paper establishes that the evolutionary energy fields inferred from a multiple sequence alignment can be quantitatively mapped onto a coarse-grained folding Hamiltonian. Each protein is divided into contiguous folding elements — foldons, defined by conserved exon boundaries called Minimal Common Exons — and the sequence-derived energies fix the internal stability of each foldon and the interactions between foldons. Simulating this finite Ising chain, the authors report that the folding temperature $T_f$ varies within a family in proportion to the family's selection temperature $T_{sel}$, and that the variance of the cooperativity score $\\rho$ across family members is governed by native topology, quantified by the ratio of short-range to long-range contacts in the reference structure: compact $\\beta$ and $\\alpha$/$\\beta$ proteins can realize only a few mechanisms, whereas elongated $\\alpha$ proteins span the full range from all-or-none to downhill folding. For the benchmark enzyme EcDHFR, the model's per-element folding temperatures correlate at $r=0.88$ with a structure-based simulation and match the flexible regions seen in an atomistic molecular dynamics study. The same model predicts the effect of every single-point mutation on both $T_f$ and $\\rho$; predicted folding-temperature changes track experimental values for the families with available data, and the sequence-based cooperativity score correlates with experimental m-values ($r = 0.74$, $p = 3.62\\times 10^{-80}$).","pith_inferences":["A testable extension the paper does not run: hydrogen/deuterium exchange or NMR measurements on several members of an alpha family such as ACBP should show mechanism diversity matching the predicted spread in $\\rho$, while members of a beta family such as Trypsin should not — a direct experimental check of the topology-cooperativity claim.","The short-to-long contact ratio rule implies a design principle for protein engineering: folding-pathway control is far easier to engineer in alpha-topology scaffolds than in beta or alpha/beta scaffolds, since the latter relax back toward a narrow set of mechanisms.","The weakest assumption could be stress-tested by masking strongly conserved functional positions (active sites, binding interfaces) in the alignments and re-learning the model: if the predicted $T_f$ and $\\rho$ shift systematically when those positions are removed, the inferred energies are carrying functional signal rather than pure folding signal.","Because the model predicts per-element folding temperatures, it implicitly predicts non-native partially folded states; comparing the predicted order of element folding with experimental kinetic intermediates for a multi-domain protein would test whether the exon-defined foldons are the true cooperative units."],"forward_implications":["For any protein family with a deep multiple sequence alignment, the folding temperature and cooperativity of every natural sequence can be annotated without running folding simulations, because both observables are fitted as functions of the evolutionary energy.","Topology sets a ceiling on mechanism diversity: families with compact beta or alpha/beta folds can realize only a few folding mechanisms even when sequence diversity is high, so the reference sequence of a family is not necessarily representative of its members' mechanisms.","Single-mutation effects on both stability ($\\Delta T_f$) and mechanism ($\\Delta \\rho$) become computable for every possible amino acid substitution, providing a direct way to rank variants for protein engineering.","Cooperativity can be apparent rather than real: in families such as ACBP, Serpin, and Ubiquitin, all-or-none behavior can arise from similar internal stabilities of the folding elements even when inter-element interactions are removed.","The relationship between $T_f$ variability and $T_{sel}$ implies that the selection temperature estimated from sequences alone reports how strongly folding stability is constrained during a family's evolution."],"supporting_citations":[{"why":"Supplies the Minimal Common Exons — the conserved exon-boundary partition used to divide each family's alignment into foldons.","marker":"[25]"},{"why":"The predecessor repeat-protein model coupling evolutionary energies to an Ising chain; this paper generalizes it to globular topologies and reuses its entropy parameters.","marker":"[26]"},{"why":"The earlier one-dimensional Ising model of repeat-protein folding that defines the coarse-grained Hamiltonian this work adopts.","marker":"[27]"},{"why":"Provides the Restricted Boltzmann Machine learning scheme and its exact mapping to Potts-model couplings, the source of the evolutionary energy fields.","marker":"[28]"},{"why":"Defines the selection temperature and its relation to folding free energies, the framework used to scale evolutionary energies into folding energies.","marker":"[29]"},{"why":"Supplies the empirical observation that mutation-induced stability variance is nearly family-independent, the basis for extrapolating the selection temperature from PDZ to all other families.","marker":"[30]"},{"why":"Provides the experimental stability data on PDZ used to calibrate the reference selection temperature.","marker":"[44]"},{"why":"The atomistic molecular dynamics study of EcDHFR whose flexible regions match the model's predicted least-stable folding elements.","marker":"[33]"},{"why":"Reports microsecond subdomain folding in DHFR, supporting the multi-step folding mechanism the model predicts for the benchmark enzyme.","marker":"[34]"},{"why":"Establishes that native energetic heterogeneity influences transition-state fluctuations, grounding the short/long-range contact ratio as a predictor of mechanism variability.","marker":"[38]"}],"fun_headline_variants":["Sequence alignments decode protein folding mechanisms","Evolutionary sequences reveal folding order and cooperative transitions","Foldon energies from alignments predict folding pathways","Natural sequences map to foldon interactions, predicting folding and mutations","Sequence diversity alone forecasts protein folding cooperativity"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that folding stability is the main evolutionary pressure recorded in a protein family's sequences, so the statistical energies learned from the alignment genuinely describe folding; if binding, catalysis, allostery, or other functional demands shape any part of the sequence record more strongly, the inferred folding energies, temperatures, and cooperativity scores would be distorted.","fun_headline_variants_meta":{"raw":{"variants":["Sequence alignments decode protein folding mechanisms","Evolutionary sequences reveal folding order and cooperative transitions","Foldon energies from alignments predict folding pathways","Natural sequences map to foldon interactions, predicting folding and mutations","Sequence diversity alone forecasts protein folding cooperativity"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000171,"raw_usage":{"total_tokens":1297,"prompt_tokens":995,"completion_tokens":302,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":611,"completion_tokens_details":{"reasoning_tokens":231}},"tokens_in":611,"tokens_out":302,"duration_ms":3222,"temperature":1.0,"reasoning_tokens":231,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T12:19:31.181552+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure experimental folding-temperature shifts ($\\Delta T_f$) for a set of single mutants located in and around a strongly conserved functional site — for example the active site of a DHFR or RNase H family member — and compare them with the model's per-site predictions: if the correlation between predicted and measured $\\Delta T_f$ is systematically worse for functional-site mutations than for surface mutations, or collapses when the conserved functional positions are masked out of the alignment, the central assumption that folding dominates the sequence record is broken.","supporting_citations":[{"cited_title":"Reassessing the exon–foldon correspondence using frustration analysis,","cited_arxiv_id":null,"evidence_quote":"Supplies the Minimal Common Exons — the conserved exon-boundary partition used to divide each family's alignment into foldons."},{"cited_title":"Evolution and folding of repeat proteins,","cited_arxiv_id":null,"evidence_quote":"The predecessor repeat-protein model coupling evolutionary energies to an Ising chain; this paper generalizes it to globular topologies and reuses its entropy parameters."},{"cited_title":"The energy landscapes of repeat-containing proteins: Topology, cooperativity, and the folding funnels of one-dimensional architectures,","cited_arxiv_id":null,"evidence_quote":"The earlier one-dimensional Ising model of repeat-protein folding that defines the coarse-grained Hamiltonian this work adopts."},{"cited_title":"Learning protein constitutive motifs from sequence data,","cited_arxiv_id":null,"evidence_quote":"Provides the Restricted Boltzmann Machine learning scheme and its exact mapping to Potts-model couplings, the source of the evolutionary energy fields."},{"cited_title":"Coevolutionary information, protein folding landscapes, and the thermodynamics of natural selection,","cited_arxiv_id":null,"evidence_quote":"Defines the selection temperature and its relation to folding free energies, the framework used to scale evolutionary energies into folding energies."},{"cited_title":"Selection originating from protein stability/foldability: Relationships between protein folding free energy, sequence ensemble, and fitness,","cited_arxiv_id":null,"evidence_quote":"Supplies the empirical observation that mutation-induced stability variance is nearly family-independent, the basis for extrapolating the selection temperature from PDZ to all other families."},{"cited_title":"Frustration, dynamics and catalysis","cited_arxiv_id":"2505.00600","evidence_quote":"Provides the experimental stability data on PDZ used to calibrate the reference selection temperature."},{"cited_title":"Thermal unfolding molecular dynamics simulation of Escherichia coli dihydrofolate reductase: Thermal stability of protein domains and unfolding pathway,","cited_arxiv_id":null,"evidence_quote":"The atomistic molecular dynamics study of EcDHFR whose flexible regions match the model's predicted least-stable folding elements."},{"cited_title":"Microsecond Subdomain Folding in Dihydrofolate Reductase,","cited_arxiv_id":null,"evidence_quote":"Reports microsecond subdomain folding in DHFR, supporting the multi-step folding mechanism the model predicts for the benchmark enzyme."},{"cited_title":"Quantitative criteria for native energetic heterogeneity influences in the prediction of protein folding kinetics,","cited_arxiv_id":null,"evidence_quote":"Establishes that native energetic heterogeneity influences transition-state fluctuations, grounding the short/long-range contact ratio as a predictor of mechanism variability."}],"review_version":1}