{"id":"d05d5b65-544c-49e6-a452-9c90e5ca33d7","arxiv_id":"2608.01143","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Selection for a localized functional motif alone can produce funnel-like protein energy landscapes, but only within an intermediate temperature range.","lead":"A two-dimensional lattice model of 20-residue proteins shows that selecting only for a local active-site motif can create funnel-shaped energy landscapes, the signature of foldable proteins. This happens only at intermediate temperatures; at low temperature, high-fitness sequences remain rugged and glassy instead.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Low-temperature comparison uses an f<0.9 cap rather than true maximum fitness, leaving the high-fitness tail explicitly untested.","rationale":"The reader's verdict is CONDITIONAL, and this stress-test identifies a specific, load-bearing gap that supports keeping that condition: the T=0.1 comparison is made at f<0.9 rather than at maximum fitness, and the authors explicitly defer examination of the extreme high-fitness tail. This is a correctness risk for the claim that intermediate temperatures are uniquely capable of generating funnel-like landscapes. The reader noted the f<0.9 issue in the rationale, but the reader's stated weakest assumption was model realism, so agreement is partial. The paper otherwise has substantial strengths: the sequence-space multicanonical sampling is well described, the supplement validates the contact-number restriction against the full ensemble, and the evolutionary consistency check in Fig. S3 supports the relevance of the multicanonical results. No circularity or fraud concerns arise. The proposed concrete test would settle the unresolved tail question and either confirm or weaken the central temperature-dependent conclusion.","tokens_in":11225,"tokens_out":4044,"duration_ms":37406,"concrete_test":"Repeat the energy- and free-energy-landscape analysis of Figs. 4-5 for the true maximum-fitness sequences at T=0.1 (or the highest fitness reachable by the multicanonical sampler, reporting its f value), using the same native-contact order parameter and the same visual and, ideally, quantitative funnel criteria. If the maximum-fitness low-temperature landscapes show a significant energy-versus-native-contact correlation and a two-state free-energy profile, the central temperature-dependent claim collapses; if they remain glass-like, the claim is strengthened. Report the actual fitness values compared at T=1.0 and T=0.1 so the comparison is matched.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central temperature-dependent claim depends on the contrast between high-fitness sequences evolved at T=1.0 and T=0.1. At T=1.0, the paper analyzes 'the highest-fitness sequence' and the 100 highest-fitness sequences. At T=0.1, however, the Methods state that analyses focus on sequences with fitness around f≃0.9, taken as 'the sequences of highest fitness among those with f < 0.9.' The two sets are therefore not at matched fitness values, and the low-temperature conclusion is not tested at the true maximum-fitness limit. The Supplemental Information explicitly concedes this: 'Whether the energy landscapes in this regime nevertheless acquire partial funnel-like character remains to be examined.' Because the paper's headline conclusion is that funnel-like landscapes emerge only within an appropriate temperature range, the untested f→1 tail at T=0.1 is load-bearing: if landscapes become funnel-like at very high fitness even at low temperature, the claim would need to be weakened to a statement about typical, not maximal, high-fitness sequences, and the proposed thermodynamic mechanism would require revision. The missing quantitative funnel metric compounds this, but the deferral in the Supplement is the clearest self-identified limitation.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript asks whether funnel-like protein energy landscapes can arise solely from selection for a local functional motif, without any explicit selection for foldability. Using a 20-residue two-dimensional lattice protein with four residue types, the authors define fitness at environmental temperature T as the equilibrium probability that a prescribed four-residue active-site motif is realized (Eq. 3). They sample the sequence space with a sequence-space multicanonical Monte Carlo method and construct energy and free-energy landscapes of high-fitness sequences. The main finding is that at an intermediate temperature (T = 1.0), high-fitness sequences show funnel-like energy landscapes and two-state free-energy landscapes, whereas at a low temperature (T = 0.1), sequences with fitness near 0.9 show rugged, glass-like landscapes. At T = 1.4 no highly functional sequences exist. The authors conclude that functional selection alone can generate foldability as a thermodynamic consequence of maintaining function under thermal fluctuations, and that environmental temperature is a key determinant. The manuscript includes consistency checks: four independent multicanonical runs, a complete-ensemble check for representative sequences, explicit evolutionary simulations at T = 1.0, and an analysis of native-structure degeneracy.","tokens_in":11369,"tokens_out":3564,"duration_ms":35282,"significance":"If the central claim holds, the paper is significant: it offers a concrete statistical-mechanical mechanism by which local functional constraints can organize a global energy landscape, connecting functional selection to the funnel picture of protein folding. The study goes beyond earlier spin-model work by constructing genuine structural order parameters and landscape profiles for a chain molecule. The authors are explicit that they are not claiming direct selection for foldability, and they identify the low-temperature extreme-fitness regime as an open question in the Supplemental Information. The computational approach is well suited to the question, and the inclusion of explicit evolutionary simulations and exhaustive enumeration checks strengthens the evidence. However, the main temperature-dependent comparison is not made at matched fitness values, and the funnel/glass distinction is assessed visually rather than quantitatively; these issues bear directly on the paper's headline claim.","major_comments":[{"comment":"The central temperature comparison is made between unmatched fitness regimes. At T = 1.0 the analysis uses the highest-fitness sequence and the 100 highest-fitness sequences, whereas at T = 0.1 the text and Fig. 5 analyze the sequence with the highest fitness among those with f < 0.9, and the 100 highest among those with f < 0.9. The Supplemental Information explicitly states that 'Whether the energy landscapes in this regime nevertheless acquire partial funnel-like character remains to be examined.' Because the abstract and Discussion conclude that funnel-like landscapes emerge only within an appropriate temperature range, the untested f → 1 tail at T = 0.1 is load-bearing: if maximal-fitness low-temperature sequences turn out to be funnel-like, the claim must be weakened to a statement about typical, rather than maximal, high-fitness sequences. Please analyze sequences at the true maximum fitness (or at least at matched fitness values) at T = 0.1 and report the corresponding landscapes.","section":"Results and Supplemental Information"},{"comment":"The classification of energy landscapes as 'funnel-like' versus 'glass-like' is made by visual inspection of energy spectra and free-energy profiles, with no quantitative order parameter. The central claim is precisely that funnel-like organization emerges at intermediate temperature and not at low temperature, so a quantitative measure is needed: for example, the correlation between energy and the number of native contacts, a roughness or frustration statistic, or a Z-score against randomized sequences. Such a metric would also make the deferred question of 'partial funnel-like character' in the Supplemental Information well posed. Please compute a quantitative funnel measure for all analyzed sequences at both temperatures.","section":"Results, Figs. 4 and 5"},{"comment":"The claim that funnel-like landscapes emerge 'only within an appropriate range of environmental temperatures' is supported by only three temperature values (T = 0.1, 1.0, 1.4), with exactly one temperature in the purported intermediate regime. While the three points bracket a nonmonotonic behavior, the phrase 'range' implies a more systematic dependence than the data establish. A scan over additional intermediate temperatures, or otherwise a clear statement that only the three values were examined, would make the temperature-dependence claim commensurate with the evidence.","section":"Results and Discussion"}],"minor_comments":[{"comment":"The full-text header contains an apparent line-break typo, 'functio nal evolution', which should be corrected.","section":"Title/header"},{"comment":"The sentence 'The environmental temperature is the only parameter of the present model' is imprecise: the contact-energy matrix in Table I and the restriction to conformations with 9–12 contacts are also model parameters and approximations. Please rephrase to clarify that T is the only evolutionary-selection parameter varied in the study.","section":"Methods, Eq. (3) and Table I"},{"comment":"The term 'native conformation' is used for low-temperature sequences whose ground states are described as one of many arbitrary members of a degenerate set; please state explicitly how the native conformation was chosen for the T = 0.1 cases, since the low-temperature sequences are said to be individually diverse.","section":"Results, Fig. 4 and Fig. 5"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a serious and readable contribution, and the main mechanism is plausible. The decisive issue for me is the unmatched fitness comparison between T = 1.0 and T = 0.1, which the authors themselves flag in the Supplemental Information. This is fixable within the scope of the paper by analyzing maximum-fitness low-temperature sequences and reporting a quantitative funnel metric. I do not see circularity in the fitness definition; the concern is the completeness of the stated temperature-dependent claim."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: the paper earns its central point for T=1.0, and the T=0.1 contrast is suggestive but incomplete. The authors directly compute energy and free-energy landscapes for a 2D lattice protein under selection for a local active-site motif, and show that high-fitness sequences at intermediate temperature have funnel-like spectra and two-state free-energy profiles, while at low temperature they look glassy. This is a step beyond Saito et al. and Sakata et al., who inferred funnel organization from spin models or from kinetics/frustration. Using native-contact number as a structural order parameter and constructing landscapes from the equilibrium ensemble is a real improvement.\n\nWhat is done well: the multicanonical sequence-space sampling is carefully checked (four independent runs; complete-ensemble checks for representative sequences; explicit evolutionary simulations reproduce the same high-fitness sequences). The observation that 500 high-fitness sequence patterns collapse into four native folds at T=1.0 is striking, and the comparison with 187 distinct folds at T=0.1 is a nice quantitative contrast. Citation of prior work is fair.\n\nSoft spots, in order of importance. First, the low-temperature branch is not tested at maximal fitness. The main text analyzes 'the sequences of highest fitness among those with f < 0.9' at T=0.1, and the Supplement explicitly defers whether the extreme tail becomes funnel-like ('remains to be examined'). That is load-bearing because the headline conclusion is that funnel-like landscapes emerge only in an intermediate temperature range. If the f→1 tail at T=0.1 turns funnel-like, the claim weakens to 'typical high-fitness sequences'. This is not fatal, but it is a genuine gap the authors should be asked to close. Second, only three temperatures are examined, and T=1.4 yields no high-fitness sequences, so the 'appropriate range' is essentially one temperature. Third, the funnel assessment is visual; a quantitative metric would make the claim sharper. Fourth, code and data are not released, which matters for a simulation paper of this type.\n\nOverall, this is a competent, honest study. The limitations are mostly acknowledged, and the core T=1.0 result appears solid. I would send it to peer review with a request for the T=0.1 f→1 tail, more temperatures, and a quantitative funnel measure. Worth reading.","headline":"Direct landscape construction supports the claim that functional selection alone can build a funnel, but the low-temperature leg is tested only up to f<0.9, and the authors explicitly defer the f→1 tail.","tokens_in":11943,"tokens_out":2598,"would_cite":true,"duration_ms":22258,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Selecting only for a local active-site motif generates funnel-like folding landscapes in a lattice protein model, but only at intermediate environmental temperatures.","keywords":["protein folding","energy landscape","functional selection","lattice protein model","multicanonical Monte Carlo","thermal fluctuations","two-state folding","native contacts"],"falsifier":"Repeat the same sequence-space sampling in a three-dimensional or off-lattice model with the same fitness definition and check whether intermediate-temperature high-fitness sequences still display funnel-like energy spectra and cooperative two-state free-energy profiles; if they do not, the proposed thermodynamic mechanism fails to generalize. Alternatively, run explicit folding kinetics on the $T = 1.0$ high-fitness sequences: if they relax slowly and non-cooperatively despite funnel-shaped equilibrium landscapes, the paper's identification of funnel landscapes with foldability would be contradicted.","tokens_in":10949,"feed_emoji":"🧬","tokens_out":14688,"duration_ms":111952,"temperature":0.7,"pith_summary":"The paper asks whether foldability is a direct evolutionary target or a by-product of selection for function. In a 20-residue two-dimensional lattice protein model with four amino-acid types, the authors define fitness as the equilibrium probability that a prescribed local active-site motif is populated at the environmental temperature $T$, and they sample sequences across the full fitness range with a sequence-space multicanonical Monte Carlo method. They find that high-fitness sequences evolved at an intermediate temperature ($T = 1.0$) spontaneously acquire funnel-like energy landscapes and cooperative two-state free-energy landscapes, although foldability never enters the fitness definition. At low temperature ($T = 0.1$), similarly fit sequences instead show rugged, glass-like landscapes with nearly one native conformation per sequence, and at high temperature ($T = 1.4$) no highly functional sequences exist. The contribution is a concrete, structural demonstration that local functional constraints, when maintained under thermal fluctuations, can organize the entire protein energy landscape.","feed_headline":"One local active-site motif can shape the whole folding funnel","feed_subtitle":"In a lattice-protein model, high-fitness sequences become cooperative two-state folders only at intermediate temperatures.","key_machinery":"The load-bearing object is the fitness function $$f(T) = \\frac{\\sum_C \\varphi(C) $e^{{-E(C)/T}}$}{\\sum_C $e^{{-E(C)/T}}$},$$ the equilibrium probability that a conformation $C$ contains the prescribed active-site motif, defined as two exposed polar residues backed by a hydrophobic pair with neighboring lattice sites empty; $\\varphi(C)$ is 1 for functional conformations and 0 otherwise. This fitness contains no term for the native structure, thermodynamic stability, or foldability. The method pairs this fitness with sequence-space multicanonical Monte Carlo using entropic sampling, which performs a random walk over fitness bins and yields representative sequences across the entire fitness range, and then reconstructs energy and free-energy landscapes from the equilibrium conformational ensemble, with the number of native contacts serving as the structural order parameter.","core_discovery":"The central discovery is that selection acting only on the equilibrium probability of a single prescribed local active-site motif is sufficient to generate funnel-like protein energy landscapes and cooperative two-state free-energy landscapes, but only in an intermediate range of environmental temperatures. At $T = 1.0$, the lowest-energy spectra of high-fitness sequences decrease systematically with the number of native contacts, and the free-energy landscape shows two minima separated by a barrier, the signature of two-state folding; the 100 highest-fitness sequences share the same overall organization, and 500 independent sequence patterns collapse onto only four native folds. At $T = 0.1$, high-fitness sequences achieve comparable fitness through glass-like, rugged energy landscapes, and essentially every sequence adopts its own native conformation. The paper concludes that foldability can emerge as a thermodynamic consequence of maintaining function under thermal fluctuations: the requirement that many thermally populated states preserve the active-site geometry converts a local functional constraint into a global constraint on the energy landscape, providing a common origin for the consistency principle and minimal frustration.","pith_inferences":["A natural extension would select on two or more functional motifs simultaneously and test whether funnel organization strengthens, weakens, or breaks; the paper only treats one motif.","If the mechanism scales to larger chains, one would expect a quantitative link between the environmental temperature during selection and the folding temperature of the resulting proteins; that link is a prediction, not a result of the paper.","The collapse of many sequences onto a few folds hints at a thermodynamic contribution to the limited fold repertoire of natural proteins, but the 20-residue lattice is too small to establish that claim for real proteins.","Replacing equilibrium fitness with a kinetic fitness, such as the probability of reaching the active site within a fixed time, could narrow or shift the intermediate-temperature window; this is an untested extension of the paper's logic."],"forward_implications":["Foldability can be viewed as an emergent thermodynamic property of maintaining a local functional motif, not as an independent target of selection.","There is a nontrivial temperature window for the emergence of foldability: low thermal noise removes the evolutionary pressure to organize the whole spectrum, while high thermal noise prevents high fitness from being realized at all.","Functional selection can strongly restrict the accessible fold space, since 500 independently sampled sequence patterns collapse onto only four native conformations at $T = 1.0$.","The consistency principle and minimal frustration can be derived from the same mechanism: competing low-energy conformations are selectively disfavored because they reduce the equilibrium probability of maintaining the active site.","The maximum-target-probability design criterion becomes a special case of this framework, suggesting a complementary function-oriented design strategy in which only the functional motif is specified."],"supporting_citations":[{"why":"Supplies the earlier model study that first suggested functional selection alone can produce foldable sequences.","marker":"[6]"},{"why":"Identifies thermal noise level as the factor that determines funnel-like versus glassy organization in an abstract spin model.","marker":"[10]"},{"why":"Motivates the four-letter amino-acid alphabet by pointing out the excessive accidental degeneracy of the two-letter HP model.","marker":"[11]"},{"why":"Provides the reference inter-residue contact-energy matrix from which Table I is constructed.","marker":"[14]"},{"why":"Supplies the sequence-space multicanonical method that samples sequences across the fitness range.","marker":"[15–18]"},{"why":"Provides the original multicanonical Monte Carlo scheme underlying the sequence-space sampling.","marker":"[19, 20]"},{"why":"Supplies the entropic-sampling algorithm used for the production random walks in fitness space.","marker":"[21]"},{"why":"Provides the flat-histogram weight-determination algorithm used to fix the multicanonical weights.","marker":"[22, 23]"},{"why":"Defines the maximum-target-probability design criterion that the paper shows is a special case of its framework.","marker":"[24–26]"}],"fun_headline_variants":["Function alone can shape folding funnels at moderate temperatures","Active-site selection at right temperature yields two-state folding","Thermal midpoint: where function begets foldability","No foldability pressure? No problem at intermediate T","One local function, one global funnel, one temperature range"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument would collapse if real protein function cannot be represented by the equilibrium probability of a single local active-site motif in a 20-residue two-dimensional lattice model with four amino-acid types and the hand-set contact energies of Table I; under that representation, the claim that foldability emerges purely from functional selection may not generalize to real proteins.","fun_headline_variants_meta":{"raw":{"variants":["Function alone can shape folding funnels at moderate temperatures","Active-site selection at right temperature yields two-state folding","Thermal midpoint: where function begets foldability","No foldability pressure? No problem at intermediate T","One local function, one global funnel, one temperature range"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000223,"raw_usage":{"total_tokens":1468,"prompt_tokens":968,"completion_tokens":500,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":584,"completion_tokens_details":{"reasoning_tokens":423}},"tokens_in":584,"tokens_out":500,"duration_ms":5628,"temperature":1.0,"reasoning_tokens":423,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T15:11:37.140922+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Repeat the same sequence-space sampling in a three-dimensional or off-lattice model with the same fitness definition and check whether intermediate-temperature high-fitness sequences still display funnel-like energy spectra and cooperative two-state free-energy profiles; if they do not, the proposed thermodynamic mechanism fails to generalize. Alternatively, run explicit folding kinetics on the $T = 1.0$ high-fitness sequences: if they relax slowly and non-cooperatively despite funnel-shaped equilibrium landscapes, the paper's identification of funnel landscapes with foldability would be contradicted.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the earlier model study that first suggested functional selection alone can produce foldable sequences."},{"cited_title":"Nagao, T","cited_arxiv_id":null,"evidence_quote":"Identifies thermal noise level as the factor that determines funnel-like versus glassy organization in an abstract spin model."},{"cited_title":"Sakata, K","cited_arxiv_id":null,"evidence_quote":"Motivates the four-letter amino-acid alphabet by pointing out the excessive accidental degeneracy of the two-letter HP model."},{"cited_title":"Wang and W","cited_arxiv_id":null,"evidence_quote":"Provides the reference inter-residue contact-energy matrix from which Table I is constructed."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the entropic-sampling algorithm used for the production random walks in fitness space."}],"review_version":2}