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Leveraging generative hallucination and biophysics-informed modeling for unified biomolecular sequence-structure co-design

Xuefeng Liu, Mingxuan Cao, Xiao Luo, Songhao Jiang, Tobin Sosnick, Jinbo Xu, Louis Maher, Rick Stevens

arXiv:2608.17381v1q-bio.QMcs.AIcs.LGq-bio.BM

TL;DR

De novo biomolecular interaction design remains difficult, particularly for DNA/RNA systems with scarce complex data and demanding geometric and chemical constraints. MCTH addresses this by using uncertainty-aware Monte Carlo Tree Search over hallucinated sequence–structure states, and matched-budget experiments show improved search outcomes across modalities with transfer to held-out predictors.

  • Problem

    De novo biomolecular interaction design remains challenging, especially beyond proteins, because sequence–structure coupling is difficult to optimize across heterogeneous modalities and DNA/RNA data are scarce.

  • Method

    MCTH uses Monte Carlo Tree Search to allocate a fixed inference budget over hallucinated sequence–structure states produced by frozen folding, inverse-folding, and optional biophysical models.

  • Results

    Across protein–RNA, protein–DNA, protein–protein, and protein–ligand design, matched-budget experiments favor adaptive search over simpler strategies, with held-out AlphaFold3 retaining the highest mean ipTM at 0.884.

  • Takeaways & Limitations

    MCTH provides a shared planning layer for multimodal biomolecular co-design while allowing task-specific expert backends and biophysical terms.

  • Takeaways & Limitations

    Inference-time optimization remains coupled to the search-time oracle, so evaluation must test both equal-budget alternatives and predictors outside the optimization loop.

Abstract

from arXiv · show

Biomolecular design underpins applications from molecular recognition to therapeutics and synthetic biology, yet de novo interaction design remains challenging-especially for DNA/RNA, underexplored non-protein modalities with scarce, heterogeneous complex data and sharper geometric and chemical constraints. We introduce MCTH (Monte Carlo Tree Hallucination), an inference-only framework that casts all-atom sequence-structure co-design as uncertainty-aware planning over hallucinated states from pretrained folding and inverse-folding models, with optional biophysical control within the same decision loop. MCTH treats these models as frozen black-box operators and uses Monte Carlo Tree Search to allocate a fixed inference budget across competing design trajectories, incorporating model confidence and uncertainty, as well as cross-expert consensus/disagreement when multiple predictors are available. Across protein-RNA, protein-DNA, protein-protein, and protein-ligand design, matched-budget experiments show that adaptive search improves over simpler sampling and cycling strategies, while held-out AlphaFold3 and Chai-1 evaluations demonstrate transfer beyond the search-time oracle. MCTH provides a shared planning layer across modalities while allowing task-specific folding, inverse-folding, and biophysical modules, requiring no fine-tuning or backpropagation through component models.

1 Introduction

MCTH addresses the difficulty of de novo biomolecular interaction design by treating sequence–structure co-design as uncertainty-aware, finite-budget planning over hallucinated states. It coordinates frozen folding, inverse-folding, and optional biophysical modules through a shared Monte Carlo Tree Search framework across biomolecular modalities.

  • Motivation: De novo interaction design remains challenging beyond proteins because sequence and structure are tightly coupled in rugged, high-dimensional landscapes.Small sequence changes can cause large structural or functional shifts, making joint optimization of specificity, sequence, and structure computationally demanding.
  • Motivation: Diffusion-model hallucination enables plausible conformations from underspecified inputs, but existing cycling-based approaches have limitations.Cycling between hallucinated structure prediction and sequence redesign can produce designable biomolecules without fine-tuning.
  • MCTH framework: MCTH casts hallucination-based design as finite-budget planning over sequence–structure states, using MCTS to allocate folding evaluations across competing trajectories.Pretrained folding and inverse-folding models remain frozen black-box operators that propose and evaluate candidate transitions.
  • MCTH framework: Uncertainty-aware selection combines model confidence, expert consensus or disagreement, and optional biophysical feasibility signals within the planning loop.Geometric, thermodynamic, and energy-like cues can guide selection, proposal refinement, and evaluation rather than only post-hoc filtering.
  • General planning layer: MCTH reuses the same planning logic across protein–RNA, protein–DNA, protein–protein, and protein–ligand design tasks.Task-specific folding, inverse-folding, and biophysical modules are dispatched within a shared general planning layer.

2 Background and Problem Setup

This section positions MCTH as an inference-time planning layer that combines pretrained folding and inverse-folding experts with optional biophysical guidance. It formulates biomolecular sequence–structure co-design as finite-horizon search over hallucinated all-atom states, evaluated by learned confidence and task-specific feasibility signals.

  • Related method families: Physics-first frameworks provide explicit energetic priors but scale poorly in large multimodal design spaces, whereas learning-based predictors and generative tools broaden biomolecular modeling and redesign.The referenced tool families include Rosetta/MD, AF2/Multimer, AF3/RFAA, RFdiffusion, ProteinMPNN, and RNA pipelines.
  • Method positioning: MCTH wraps pretrained folding and inverse-folding experts with plug-in biophysical cues and allocates inference through Monte Carlo Tree Search.Biophysical cues participate in selection, expansion, and proposal reweighting rather than serving only as post-hoc filters.
  • Problem formulation: Biomolecular design is represented as finite-horizon planning over sequence–structure states containing sequences, all-atom coordinates, and interacting components when complexes are present.Actions are stochastic hallucination operators, including inverse-fold proposals, under task conditioning such as binding partners, motifs, or ligands.
  • Search and evaluation: MCTS expands a search tree through selection, expansion, evaluation, and backpropagation, using model-derived value signals instead of long stochastic rollouts.Value signals can include confidence, interface quality, and optional feasibility terms.
  • Design objectives: MCTH encodes foldability, binding confidence, constraint satisfaction, and lead optimization in a state value V(s).The framework searches hallucinated sequence–structure states using learned confidence and optional biophysical feasibility signals rather than explicit end-to-end energy minimization.

3 Methodology

MCTH frames biomolecular sequence–structure co-design as uncertainty-aware, finite-budget planning over hallucinated all-atom states. It combines inverse folding, structure hallucination, MCTS, model confidence and uncertainty, and optional biophysical guidance without fine-tuning or backpropagation.

  • Search formulation: MCTH represents each design hypothesis as a sequence–structure state s = (S, X), evaluating branches by both proposed sequences and their folded all-atom complexes.The search is conditioned on task-specific components such as receptors, motifs, ligands, or binding partners.
  • Actions and transitions: Each MCTS transition adaptively proposes a redesigned sequence by inverse folding, then predicts its corresponding complex structure through folding or hallucination.Adaptive inverse folding can refine promising structures or repair inconsistencies introduced during hallucination, unlike fixed iterative pipelines.
  • State evaluation: Child values aggregate predictor-derived signals including pLDDT, pTM, ipTM, interface quality, and optional geometric or biophysical feasibility terms.All signals come from forward inference, and the framework does not require gradients or backpropagation through component models.
  • Uncertainty-aware selection: CU-PUCT selection separates sequence-design ambiguity from folding uncertainty and can penalize physically implausible proposals while exploiting consensus across folding experts.With multiple experts, agreement supplies a consensus signal and disagreement supplies structural uncertainty; with one expert, the planner reduces to confidence-based search.
  • Interface-aware mutation strategy: Mutations are restricted to non-interface positions, defining interface residues by predicted target contacts exceeding a heavy-atom distance threshold such as < 8 Å.This interface-aware strategy is intended to avoid disrupting the binding surface.

4 Experiments

Experiments test MCTH under matched-budget search-time optimization and held-out evaluation with independent predictors and physical metrics. Across protein–RNA, protein–DNA, and protein–protein design, adaptive search generally improves oracle scores and retains advantages beyond the search-time evaluator.

  • Evaluation protocol: Matched-budget controls compare MCTH with greedy cycling and best-of-N alternatives using the same initialization, folding oracle, inverse-folding backend, and evaluation budget.Held-out evaluations use predictors and physical metrics excluded from the corresponding search, including AlphaFold3, Chai-1, and Rosetta InterfaceAnalyzer.
  • Protein–RNA aptamer benchmark: 0.946 mean best ipTM: MCTH exceeds ODesign (0.894) and RNAFrameFlow + NA-MPNN (0.923), ranking highest on 6 of 7 protein–RNA targets.Under held-out AlphaFold3, MCTH retains the highest mean ipTM at 0.884 versus 0.824 for ODesign and 0.794 for RNAFrameFlow + NA-MPNN.
  • Protein–DNA aptamer benchmark: 0.925 mean best ipTM: MCTH exceeds ODesign@100 (0.908) on eight non-degenerate protein–DNA targets and scores highest on 7 of 8.Across all 10 targets under held-out AlphaFold3, MCTH achieves mean ipTM 0.721 versus 0.665 for BoltzDesign and 0.644 for ODesign.
  • Protein–protein binder design: 0.864 highest mean best ipTM: MCTH exceeds Complexa (0.853), ODesign (0.816), and BoltzDesign1 (0.539) across 11 available protein–protein binder targets.The matched-budget result indicates that MCTH’s gain cannot be attributed simply to greater access to folding-model evaluations.
  • Protein–protein binder design: 0.57 held-out Chai-1 mean ipTM: dual-expert MCTH improves from 0.18 for the original Boltz-only configuration and outperforms it on 9 of 11 targets, tying on one.Across shared targets, dual-expert values are 0.74/0.61/0.57 under Boltz-2/AF2/Chai-1, versus 0.69/0.19/0.18 for Boltz-only MCTH.
  • Protein–protein binder design: 37.3% pass rate: dual-expert MCTH yields 41 passing designs out of 110 versus 20.0% (22/110) for RFDiffusion, a 17.3 percentage-point or 1.86× increase.Both methods produce at least one passing design on 8 of 11 targets under the equal output budget.

5 Conclusion … B.2 Biophysical Penalty

MCTH unifies inference-only biomolecular sequence–structure co-design as uncertainty-aware Monte Carlo planning over hallucinated states, integrating pretrained experts and optional biophysical feasibility. Its modular design spans multiple biomolecular modalities while avoiding task-specific fine-tuning and backpropagation.

  • 5 Conclusion: MCTH coordinates frozen folding, inverse-folding, and optional biophysical operators within fixed-budget MCTS across protein–RNA, protein–DNA, protein–protein, and protein–ligand design.The framework allocates expensive structure evaluations using confidence, uncertainty, and cross-expert consensus/disagreement signals.
  • A Related works: Prior biomolecular design families span physics-based energy modeling, deep-learning structure prediction, diffusion and inverse folding, iterative hallucination, and search-based generation, but typically lack unified all-atom multimodal co-design.Physics-based approaches offer interpretability but face computational and scalability limits, while prior planning methods are commonly restricted to one modality.
  • A Related works: MCTH is positioned as a planning layer combining explicit sequence–structure states, broad modality coverage, biophysical feasibility, and no task-specific fine-tuning.This distinguishes its combination from physics-first optimization, direct all-atom generation, and gradient-based or fixed-schedule hallucination methods.
  • B.1 Uncertainty-Aware MCTS over Sequence–Structure States: MCTH represents each hypothesis as s = (S, X), proposes sequence updates through inverse folding, obtains structures through folding or hallucination experts, and searches under a finite folding-call budget.Multiple experts can provide cross-expert agreement as an explicit uncertainty signal.
  • B.1 Uncertainty-Aware MCTS over Sequence–Structure States: CU-PUCT combines empirical action values with consensus priors, inverse- and forward-folding uncertainty, and optional biophysical penalties to balance exploration and exploitation.Lower confidence or greater structural disagreement increases exploration of under-resolved states, while cached terms keep selection lightweight.
  • B.2 Biophysical Penalty: The biophysical term Ephys down-weights candidates that are high-confidence under learned priors but physically implausible, including clashes, strained geometry, and infeasible pockets.Ephys is modular, ranges from near 0 for feasible to near 1 for implausible candidates, and can use proposed sequences and/or predicted coordinates.
  • B.2 Biophysical Penalty: For DNA aptamers, Ephys uses a soft nearest-neighbour self-folding free-energy window with boundaries ∆Gl = −10 kcal mol−1 and ∆Gu = −2 kcal mol−1 and steepness kl = ku = 0.75.The favourable interval avoids both overly stable self-folds that require unfolding and insufficient structure that increases binding entropy costs; these parameters derive from random DNA-sequence free-energy distributions.

B.3 Parameter derivation. · B.4 Additional details: multi-modality representation and expert dispatch · B.5 Inference-time structural guidance for nucleic acids

The appendix calibrates nucleic-acid self-folding parameters from observed thermodynamic extremes, while MCTH extends across modalities through unified all-atom modeling and target-specific inverse-folding dispatch. For nucleic acids, seqfold-derived secondary-structure contacts guide Boltz-2 structure generation during inference, preserving non-interface scaffolds while leaving interfaces flexible.

  • B.3 Parameter derivation.: Random DNA sequences spanning 20–80 nt showed ∆Gself values from approximately −14 to +2 kcal mol−1, with a median near −2.5 kcal mol−1.Calibration uses nearest-neighbour thermodynamics with seqfold and SantaLucia parameters at 37 °C.
  • B.3 Parameter derivation.: The calibration sets ∆Gu = −2 kcal mol−1, because sequences above this threshold cannot maintain even one stable secondary-structure element.A minimal stable hairpin has ∆G ≈−2 to −3 kcal mol−1 under nearest-neighbour parameters.
  • B.3 Parameter derivation.: The lower boundary is ∆Gl = −10 kcal mol−1, corresponding to the 1st–5th percentile, below which multiple stable stem-loops reduce effective binding affinity.The cumulative unfolding cost of these stem-loops substantially reduces effective binding affinity.
  • B.4 Additional details: multi-modality representation and expert dispatch: MCTH supports proteins, peptides, DNA/RNA, small molecules, ions, and post-translational modifications without modality-specific fine-tuning or architectural changes.This generality combines a unified all-atom folding representation with modular, modality-aware inverse-folding dispatch.
  • B.4 Additional details: multi-modality representation and expert dispatch: The planner keeps state representation, tree policy, and value computation fixed, changing only the inverse-folding call for the design target.Examples include ProteinMPNN for proteins and peptides, NA-MPNN for nucleic acids, and LigandMPNN for ligand-pocket-aware protein redesign.
  • B.5 Inference-time structural guidance for nucleic acids: For candidates satisfying ∆Gl ≤∆Gself(S′) ≤∆Gu, seqfold provides self-folding free energy and MFE base-pair assignments in one call taking <1 ms.These outputs are ∆Gself(S′), the minimum free energy of intramolecular self-folding, and P(S′), the predicted intramolecular base-pair set.
  • B.5 Inference-time structural guidance for nucleic acids: MCTH injects seqfold’s non-interface base pairs as soft constraints into Boltz-2 inference, guiding denoising so aptamer scaffolds retain secondary structure away from binding sites.Interface bases remain unconstrained, allowing adaptation at the protein-contact region; the contact guidance adds no extra computational overhead.

B.6 Reproducibility and Hyperparameters

The main experiments use one audited configuration across four design tasks without dataset-specific search-hyperparameter tuning. MCTH consistently selects the highest-ipTM design evaluated during search.

  • Configuration: Table 8 defines the audited configuration used across RNA aptamer, DNA aptamer, protein–protein binder, and ligand-conditioned design tasks.The same configuration applies unless otherwise stated.
  • Configuration: Search hyperparameters are not tuned per dataset; modality differences enter only through the inverse-folding backend and task conditioning passed to the folding expert.This keeps the search setup fixed while allowing modality-specific components.
  • Candidate selection: The reported candidate is the state with the highest ipTM among all internal and leaf states evaluated during search.This selection rule is fixed across all reported MCTH runs.

C Additional Experiments … D.1 Ligand-aware vs. ligand-blind inverse folding

Additional experiments extend MCTH to protein–ligand binding, where it outperforms the evaluated baselines under Boltz-2 refolding. A ligand-aware inverse-folding proposal improves both interface confidence and precision over ligand-blind redesign.

  • C Additional Experiments: The supplement extends MCTH beyond the three main-text benchmarks to protein–ligand binding and an inverse-folding ablation.Only protein–ligand binding and its corresponding ablation are included in the reported additional experiments.
  • C.1 Protein–Ligand Binding Design: The benchmark contains 10 ligand-binding targets drawn from four PDB complexes, each pairing a fixed ligand with a specified binding-protein chain.The complexes are 5SDV, 7BKC, 7C7M, and 7V11.
  • C.1 Protein–Ligand Binding Design: MCTH combines Boltz-2 folding, LigandMPNN proposals, ipTM-dominant scoring, and MCTS expansion within a budget of up to 100 fold calls per target.Search starts from random sequences and iterates folding, scoring, and expansion.
  • C.1 Protein–Ligand Binding Design: Evaluation compares MCTH with RFDiffusion-AA + LigandMPNN and ODesign under a common Boltz-2 refolding protocol using ipTM.BoltzDesign1 is reported separately as a specialist comparison.
  • C.1 Protein–Ligand Binding Design: MCTH achieves a higher mean ipTM of 0.901 than RFDiffusion-AA at 0.850 and ODesign at 0.460.The main performance gap is concentrated on challenging FAD cofactor targets requiring greater pocket precision.
  • D.1 Ligand-aware vs. ligand-blind inverse folding: The ligand-aware LigandMPNN backend improves mean ipTM from 0.826 to 0.901 relative to ligand-blind ProteinMPNN.Both inverse-folding backends use identical MCTS, scoring, and Boltz-2 evaluation configurations.
  • D.1 Ligand-aware vs. ligand-blind inverse folding: Ligand-aware inverse folding reduces mean iPDE from 4.20 to 3.02 and yields the largest gains on FAD and SAM targets.Per-target results show improvements in both ipTM and iPDE on most targets, especially where pocket complementarity is critical.

D.2 Evaluation Protocol and Cross-Oracle Validation

The evaluation separates search-time optimization from held-out predictor and oracle-independent physical checks. Matched budgets and post hoc archive filtering assess search efficiency, transfer beyond the optimized oracle, physical plausibility, and design yield.

  • Search-time oracle evaluation: Search-time scores use each procedure’s available folding signals, with Boltz-2 as the modality-spanning oracle and common Boltz-2 refolding for comparable methods.ODesign, RFDiffusion, RFDiffusion-AA, and Complexa are re-scored with Boltz-2, while BoltzDesign1 uses native Boltz evaluation.
  • Search-time oracle evaluation: Search-time scores measure optimization under a shared computational proxy, not oracle-independent evidence of physical binding.This limitation distinguishes proxy optimization from direct physical-binding validation.
  • Matched-budget evaluation: Budgets are matched whenever possible, including up to 100 candidate or folding/evaluator calls for ODesign, RNAFrameFlow, Complexa, and BoltzDesign1.Additional identical-budget comparisons test exploration-off search, greedy cycling, and best-of-N sampling under shared initialization, proposal models, folding oracle, and evaluation budget.
  • Held-out predictor evaluation: Held-out evaluation uses AlphaFold3 for RNA and DNA aptamers and Chai-1 for protein-binder dual-expert searches guided by Boltz-2 and AlphaFold2.Held-out predictors are excluded from proposal, tree selection, and output ranking to test transfer beyond the optimized predictor.
  • Oracle-independent physical evaluation and final-design pass rate: Rosetta InterfaceAnalyzer checks protein-binder interface geometry and energetics, while held-out archive filtering measures final design yield beyond best-per-target ipTM.Reported physical metrics include size-normalized interface energy, packing, and buried unsatisfied hydrogen-bond statistics; pass rates are computed after archive construction.

D.3 Matched-Budget Search Ablations · D.4 Effective Convergence Diagnostic

Matched-budget ablations show that MCTH’s gains arise from search-guided compute allocation rather than iterative refinement or independent sampling alone. An effective-convergence diagnostic further shows that MCTH continues improving later in the evaluation budget while many non-adaptive or reduced-search runs stagnate immediately.

  • D.3 Matched-Budget Search Ablations: All variants use the same 100 folding-call budget, initialization, evaluation, scoring, folding oracle, and inverse-folding backend; only planning strategy differs.This isolates search-guided compute allocation as the experimental variable.
  • D.3 Matched-Budget Search Ablations: The ablations compare exploratory MCTH, exploitation-only tree search, single-trajectory greedy cycling, and feedback-free Best-of-N sampling.Greedy cycling tests refinement without branching, whereas Best-of-N tests independent sampling without feedback or iterative refinement.
  • D.3 Matched-Budget Search Ablations: MCTH achieves the highest final quality across all targets, with especially large gains on RNA and DNA tasks.The result supports search-guided compute allocation rather than iterative refinement or a larger independent candidate pool as the source of improvement.
  • D.4 Effective Convergence Diagnostic: Together, the matched-budget and convergence results indicate that tree search changes how useful evaluations are allocated, rather than merely adding iterative refinement.The convergence pattern links MCTH’s advantage to later useful search progress within the fixed budget.
  • D.4 Effective Convergence Diagnostic: The convergence diagnostic records the last folding call at which the incumbent score improves by more than ϵ = 0.002.Runs without improvement above this threshold receive a last-improvement call of zero and are counted as immediately stagnant.
  • D.4 Effective Convergence Diagnostic: Every MCTH run improves beyond the threshold, with the last improvement occurring at fold call 46.6 on average.This indicates that MCTH continues extracting useful improvements later in the evaluation budget.
  • D.4 Effective Convergence Diagnostic: 44–62% of non-adaptive or reduced-search runs never make a nontrivial improvement after initialization.These runs are contrasted with MCTH’s continued progress under the same evaluation budget.

D.5 Cross-Oracle Agreement Analysis

Boltz-2 and AlphaFold3 show modality-dependent, imperfect agreement in ranking designs, with substantially stronger concordance for global folding quality than interface quality. Screening utility is strongest for DNA, while RNA agreement is limited by score saturation, supporting held-out evaluation alongside the search-time oracle.

  • Design-level agreement: Within-target agreement is moderate for DNA aptamers, weak but positive for protein binders, and indistinguishable from zero for RNA aptamers.The pooled raw ipTM correlation is ρ = 0.670, versus ρ = 0.261 within target, indicating substantial target-level difficulty effects.
  • Global folding versus interface ranking: For protein binders, global folding agreement exceeds interface agreement: pLDDT reaches ρ = 0.762, whereas ipTM reaches ρ = 0.252.For n = 255, the 95% CIs are [0.64, 0.85] for pLDDT and [0.05, 0.46] for ipTM.
  • Use as a screening proxy: Boltz-2 is a useful but imperfect screening proxy for DNA, with top-1 recovery and top-quartile precision approximately three times random baselines.Protein-binder screening is above random but weaker, while RNA top-quartile precision does not exceed random expectation.
  • RNA score saturation: RNA ranking agreement is constrained by score saturation: AlphaFold3 has an ipTM interquartile range of 0.080, Boltz-2 has 0.022, and Boltz-2’s median ipTM is approximately 0.946.Many RNA designs therefore lie near the Boltz-2 score ceiling, leaving little within-target ranking resolution.
  • Method-level rankings: Method-level rankings preserve broad performance direction but remain non-equivalent, with Kendall’s τ of 0.333 for DNA, 0.738 for protein binders, and 0.333 for RNA.These results motivate reporting held-out evaluation alongside the search-time oracle rather than treating either predictor as a ground-truth interface metric.

D.6 Dual-Expert Search and Final-Archive Yield

Dual-expert MCTH combines Boltz-2 and AlphaFold2 signals within the same fixed-budget search, improving transfer to AF2 and held-out Chai-1. In matched final-output comparisons, it yields more passing designs than RFDiffusion, while expanding archives trades precision for target coverage.

  • Dual-Expert Search: Dual-expert MCTH evaluates each candidate with Boltz-2 and AlphaFold2, incorporating agreement, disagreement, and uncertainty into CU-PUCT without fine-tuning or differentiation.Each dual-expert evaluation consumes two folding/evaluator calls, preserving fixed inference-budget accounting.
  • Cross-Predictor Transfer: 0.74/0.61/0.57: dual-expert MCTH’s mean best ipTM under Boltz-2/AF2/Chai-1, versus 0.69/0.19/0.18 for Boltz-only MCTH.The gain transfers to held-out Chai-1 while maintaining Boltz-2 performance across 11 shared CaoData targets.
  • Final-Archive Construction: The reward-ranked archive pools and deduplicates candidates by exact sequence identity, ranks them using only in-loop joint reward, and evaluates top-K archives for K ∈{5, 10, 25}.Chai-1 is applied only afterward as a held-out filter, with passing defined as ipTMChai ≥0.50.
  • Final-Archive Yield: 49.1% → 37.3% →30.5%: pass fraction as lower-ranked candidates enter the archive, while target coverage increases from 8/11 to 9/11.The pattern indicates a precision–coverage trade-off across archive sizes.

D.7 Oracle-Independent Rosetta Interface Evaluation

Rosetta InterfaceAnalyzer provides an oracle-independent evaluation of MCTH protein-binder designs across interface energetics, packing, and buried unsatisfied hydrogen bonds. MCTH is competitive in physical plausibility but does not establish superior binding energetics or experimental affinity.

  • Evaluation design: Rosetta InterfaceAnalyzer evaluates MCTH designs independently of proposal generation, MCTS selection, archive ranking, and other search components.The evaluation addresses the limitation that structure-predictor confidence is not a physical energy and may retain search-model biases.
  • Evaluation design: The evaluation covers six CaoData targets shared with RFDiffusion, including five targets with available BindCraft designs.Reported measures include interface separation energy ∆Gsep, area-normalized energy, packstat, and buried unsatisfied hydrogen bonds.
  • Results: −3.12 vs. −3.13 per 100 ˚A^2: MCTH essentially matches RFDiffusion on area-normalized interface separation energy, while BindCraft reaches −3.40.Area-normalized energy is treated as more interpretable than raw ∆Gsep because raw energy is sensitive to interface size.
  • Results: Packing and buried-unsatisfied-hydrogen-bond statistics are comparable across methods, but MCTH does not outperform the strongest baseline on packing quality.Table conventions indicate that more negative interface energy and higher packstat are favorable, while fewer buried unsatisfied hydrogen bonds are preferred.
  • Interpretation: MCTH produces interfaces with competitive physical plausibility under an evaluation outside the search loop, but the scores do not establish superior binding energetics or experimental affinity.The interpretation is deliberately conservative because Rosetta scores alone do not demonstrate experimental binding performance.

D.8 Compute and Search-Trajectory Diagnostics … NeurIPS Paper Checklist

MCTH’s diagnostics show that adaptive search improves designs by allocating expensive folding evaluations across trajectories rather than merely generating more states. The extended preliminaries formalize biomolecular states, folding and inverse-folding operators, confidence-guided inference, and MCTS planning, while the checklist documents limitations, compute, reproducibility, and responsible-use considerations.

  • D.8 Compute and Search-Trajectory Diagnostics: MCTH uses a nominal maximum of 100 folding calls, but early stopping after 10 unimproved iterations causes realized compute to vary across modalities.Protein-binder searches nearly exhaust the budget, whereas RNA and DNA aptamer searches often terminate earlier.
  • D.8 Compute and Search-Trajectory Diagnostics: For protein binders, held-forward mean best ipTM rises from 0.614 after one folding evaluation to 0.864 after 100 calls.Intermediate values are 0.724, 0.768, 0.803, and 0.830 after 5, 10, 25, and 50 calls, respectively.
  • D.8 Compute and Search-Trajectory Diagnostics: MCTH does not consistently evaluate more unique states than matched-budget independent sampling; its main difference is how evaluations are allocated within the search tree.Protein searches concentrate early on promising branches and broaden later, whereas RNA and DNA searches initially explore broadly before concentrating around elite neighborhoods.
  • E.1 Biomolecular representation: The framework represents biomolecular systems as sequences S paired with all-atom structures X, with multimolecular interactions encoded through spatial proximity and pairwise structural relationships.Components may include proteins, cyclic peptides, DNA/RNA, small molecules, ions, and post-translational modifications.
  • E.2 Forward folding (diffusion) and inverse folding: Pretrained forward-folding models hallucinate physically plausible structures from underspecified sequences, while inverse-folding models redesign sequences compatible with fixed or refined structures.MCTH applies these dual operators adaptively and repeatedly rather than enforcing a fixed alternation.
  • E.3 Confidence/value signals: Model confidence signals, including pLDDT, pTM, and ipTM, provide learned consistency-based value estimates, optionally combined with clash, geometry, and energy-like feasibility penalties.These values evaluate candidate designs rather than serving as explicit physical energies.
  • E.4 MDP notation and value functions: MCTH is inference-only: guided proposal resampling reweights candidate hallucinations by task-aware value signals, while multiple experts supply diverse proposals for planning.The MDP framing motivates MCTS-style evaluation and compute allocation over model-derived state values.
  • E.5 Diffusion models and guidance; E.5.1 Monte Carlo Tree Search details: MCTS expands and evaluates children with folding calls, backs up values through the tree, and balances exploration and exploitation across guided design hypotheses under an explicit fold-call budget.The method can use max backup for best-of-N objectives and returns high-value leaves after exhausting the rollout budget.
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