NeuralPLexer3: Accurate Biomolecular Complex Structure Prediction with Flow Models
Authors: Zhuoran Qiao
Feizhi Ding
Thomas Dresselhaus
Mia A. Rosenfeld
Xiaotian Han
Owen Lewis Howell
Aniketh Iyengar
Stephen Opalenski
Anders S Christensen
Sai Krishna Sirumalla
Fred Manby
Thomas Miller
Matthew Welborn
Venue: NeurIPS 2025 poster ()
Keywords: Co-folding
flow matching
biomolecules
computational drug discovery
Primary area: machine_learning_for_sciences
TL;DR: We introduce NeuralPLexer 3, a physics‑guided flow‑based generative model that delivers state‑of‑the‑art, seconds‑fast predictions of diverse biomolecular complex structures.

Abstract: Biomolecular structure determination is essential to a mechanistic understanding of diseases and the development of novel therapeutics. Machine-learning-based structure prediction methods have made significant advancements by computationally predicting protein and bioassembly structures from sequences and molecular topology alone. Despite substantial progress in the field, challenges remain to deliver structure prediction models to real-world drug discovery. Here, we present NeuralPLexer3 -- a physics-inspired flow-based generative model that achieves state-of-the-art prediction accuracy on key biomolecular interaction types and improves training and sampling efficiency compared to its predecessors and alternative methodologies. Examined through existing and new benchmarks, NeuralPLexer3 excels in areas crucial to structure-based drug design, including blind docking, physical validity, and ligand-induced protein conformational changes.

NeuralPLexer3: Accurate Biomolecular Complex Structure Prediction with Flow Models
Zhuoran Qiao* lambic Therapeutics San Diego, CA 92121
Feizhi Ding lambic Therapeutics San Diego, CA 92121
Thomas Dresselhaus" lambic Therapeuties San Diego, CA 92121
Mia A. Rosenfeld lambic Therapeutics San Diego, CA 92121
Xiaotian Han"
Owen Howell
lambic Therapeutics San Diego, CA 92121
lambic Therapeutics San Diego, CA 92121
Aniketh Iyengar lambic Therapeutics San Diego, CA 92121
Stephen Opalenski
Anders S. Christensen lambic Therapeutics San Diego, CA 92121
lambic Therapeuties San Diego, CA 92121
Sai Krishna Sirumalla lambic Therapeutics San Diego, CA 92121
Frederick R. Manby lambic Therapeutics San Diego, CA 92121
Thomas F. Miller III Iambic Therapeutics San Diego, CA 92121
Matthew Welborn
lambic Therapeutics San Diego, CA 92121
Abstract
Biomolecular structure determination is essential to mechanistic understanding of diseases and the development of novel therapeutics. Machine-learning leaiiie--eeanin-aaeeeeeee based structure prediction methods have made significant advancements by computation- ally predicting protein and bioassembly structures from sequences and molecular topology alone. Despite substantial progress in the field, challenges remain deliver structure prediction models to real-world drug discovery. Here, we present NeuralPLexer3 physics inssiire flw--baee generative model that achieves srate-of-the-at prediction accuracy on key biomolecular interaction types and improves training and sampling efficiency compared to its predecessors and alter- native methodologies 212). Examined through existing and new benchmarks, Neu- ralPLexer3 excels in erucial structure-basee drug design, including blind protein conformational changes.
docking, physical validity, and
Introduction
For decades, predicting the 3D structures of proteins has been transformative goal in structural biology and drug discovery. Experimental techniques like X-ray crystallography and cryo-electron microscopy have provided invaluable structural data. Still, these methods inttrcceentensive and time-consuming, making it challenging to scale their application across the immense diversity of
"Core contributors.
'Conespondence matt@iambic.e ai.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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proteins and small molecules. Most drug development programs still rely on these experimental structures, leaving countless therapeutic opportunities and hypotheses unexplored.
Breakthroughs in AI-driven structure prediction, notably with AlphaFold2 (AF2) [3] brought the field closer experimental accuracy. Despite this progress, significant challenge remained: accurate modeling of interactions between proteins and different biomolecules, particularly small molecules, nucleic acids, and other proteins. Understanding and accurately modeling these interactions is essential for adapting structure prediction models into effective drug discovery workflows.
NeuralPLexer (NP) [4] one of the first Al models to directly address these complex interactions by pioneering the use Al for pootein-ligant structures, with NeuralPLexer2 (NP2) (2) advancing further in prediction accuracy and covering all essential categories of biomolecules including protein complexes, nucleic acids, small molecules, and covalent modifications.
AlphaFold3 (AF3) (1] recently set new standard in interaction modeling. While taking another step further for drug discovery applications, this geometrical approach to interaction prediction still limits its usability. Drug discovery requires precise, atom-level details how small molecules interact with specific protein atoms and how these interactions induce conformational changes. Rapid screening of large numbers of potential compounds is also necessary.
Specifically, several technical challenges persist in state-of-the ofethherrtt structure prediction models:
Unphysical hallucinations: AF3 and related methods 51 sometimes generate structures
that are not physically plausible, such as ligands with incorrect chiral centers, unrealistic torsion angles, or misfolded chains for disordered regions.
The resource-intensive nature of current diffusion-based structure predictors can limit their scalability in large-scale studies, such as virtual screening.
Computational cost:
Performance assessment for drug discovery: There is need for thorough model eval- uation in drug discovery contexts, particularly in predicting ligand-induced protein con- formational changes and the recovery of physical interactions such as hydrogen bonds 7
Here we present NeuralPLexer3 (NP3), offering the following key contributions:
NP3 improves protein- ligand binding structure prediction with greater accuracy than AF3 while retaining broad applicability across all categories of biomolecular interactions.
By combining physics-inneee informed priors, fast sampling alorithms, and hardware-awarr aware opti- mizations, NP3 typically delivers prediction within seconds of GPU time while preserving accuracy.
We introduce novel benchmarks to evaluate conformational predictions related binding pocket/ligand interactions and their potential effects on protein conformation across a diverse dataset. For specific protein classes, such as kinases, NP3 provides downstream functional insights, such as predicting protein inactivation from ligand binding.
We also present scaling studies for flow-based encoder- structure prediction models and estimate the compute-optimal frontier, improving training efficiency relative AF3 and related methods. This detailed breakdown of model performance offers insights about learning behaviors across various biomolecular modalities and identifies future areas for improvement.
2 Results
NeuralPL.exer3 (NP3) (Figure TA) a generative modeling framework for the de novo prediction and sampling of generalized biomolecular complex structures composed of, but not limited to, proteins, nucleic acids, ligands, ions, and post-translational modifications (PTMs). The system also designed provide all-atom and pairwise confidence estimation of predicted complexes.
2.1 Model architecture
Underpinning NP3 conditional flow-based generative model that samples the 3D coordinates of all heavy atoms of the complex from model distribution [10 I1]

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NeuralPL.eser Architecture
Multi-seale Polymer Prior
Ground structure (rcihing))
dynamics
(64 stops)
Optimal transport permutation
Confidance
rnto
(32x)
(24k)
Stopolymers/ PTMs
Eatract chemical features
Global Attention ass
Fladh- Trannutar Anent
Difluston Attention igiona)
Drivaiion Attention Isparse)
Small moceecules
Prediction
Conditioning Modules
Row COE 140 horations)
MSA
Protein Lenguigge
Language
RNA
PoseBusters v2, Ground Truth Strueture Provided
Inference Time
100
100
400
SPU-secands (1024-resiuu protein)
350
Correct Sterenchemistty
Succiss Rato (5)
85-
250
85.6
200
40"
94-
190
100
(A100
0.408
Figure 1: NeuralPLexer3 (NP3) accurately predicts biomolecular structures with improved physical quality and prediction speed. (A) Schematics of the NP3 system. To perform predic- tion, NP3 uses molecular topology extracted from input biopolymer sequences and small molecule graphs primitive inputs, with additional conditioning signals from sequence language models and multiple sequence alignments (MSAs). NP3 adopts a flow www-mahhiing framework that samples from an informative globular polymer prior (Algorithm S3 (B) Performance of NP3 the Pose- Busters benchmark [9]. Left panel: success rate for predicting the ligand-protein structures to within 2 Å RMSD, with and without additionally requiring that the structures are physically reasonable (PB-valid). Center panel: percentage of predicted structures where ligand stereochemistry is correct. Right panel: timing for running a single inference on 1024-residue protein. Comparisons are made to NeuralPLexer2 (NP2) and AlphaFold (AF3).
Continuous normalizing flows: The core model of NP3 a flow-based generative model that uses continuous normalizing flows (CNFs) (10) and is trained without the use of simulations. CNFs transform simple probability distributions into complex ones through continuous-time dynamics. CNFs sample new data by integrating an ordinary differential equation (ODE) using initial conditions from prior distribution:
Io + f (x(x)) ds
Flow matching: Flow matching enables efficient and stable training of CNFs by aligning the model's vector field with a target vector field derived from predefined conditional probability paths:
((() 1E..100.11BB-00 [l x) u(t,x)) [1
(2)
3

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improvement
A
G AF3
@ NP1
NP3
OPP3 scaling
B
Improved Integ
Inference compute
10/
Decoder FLOPs Step
70-
PoseBusters
SRMSD x2
60
10
10%
30
101
10"
10"
10
5TM parems model
703M parame nodel
Adal Zaro OK Hore
Entty summetry prrection
Graph syometry correct porrction
Flaw timentop shittngg
improved sigementt tregitte incrassed crop size- EMA
Confilence based rarking
Energy crisity fetering
Encoder FLOPy Per Step (o)
Figure 2: (A) Comparison of relative encoder/decoder capacity in terms of floating ppint operations per second (FLOPs) among different methods. The asterisk indicates an estimate based on our reproduction of AF3. (B) Key model training and inference improvements included during the full course of model development and their impact on PoseBusters accuracy.
Improving flow matching for biomolecular structure prediction: We introduce several key enhancements to make flow matching more suitable for probabilistic structure prediction:
First, we take advantage of physically informed priors. Flow matching offers greater flexibility in choosing the prior distribution functional form, and we reason that more appropriate prior distributions will better capture the underlying data structure. In NP3, we introduce polymer prior that preserves the distance structure among linked atoms and residues belonging the same chain (Figure[[A) This informative prior is efficiently implemented by relaxing random atom configurations with a limited number of Langevin dynamics iterations using an energy model with harmonic connectivity terms (Algorithm
globular
Second, by incorporating optimal transport principles, flow matching can create simpler flows that are more stable to train and lead to faster inference 14). We introduce simulation-Fin -freenefeeeee symmetry correction module to straighten the conditional flow trajectories that connect the prior samples and ground truth structures. The symmetry correction module permutes equivalent entities, then permutes local atom indices while preserving the underlying chemical graph structures (Section (S.5).
Finally, instead of directly fitting the vector field u, we predict the denoised coordinates and estimate the vector field following an optimal rigid structure alignment. Following previous work (4), also apply a rigid alignment against the previous-step structure estimate to improve trajectory continuity (Algorithm (2)..
Altogether, these contributions led to two main advantages: (1) substantial reduction in the number of integrator steps needed to sample from the model, leading to improved inference efficiency; and (2) alleviating the need for expensive diffusion rollouts (T) before each optimizer step, which both speeds up and simplifies the procedure for training the main model and confidence modules.
More details on model training and inference can be found in Algorithms S2 and SI
We have implemented several architectural enhancements to support these contributions.
Model architecture: Leveraging components from both its predecessors and recent structure predic- tion methods 15). we adopt an encoder-decoder architecture that separates the tasks of anchor-level conditioning and atom-level structure generation (Figure SI). Anchors are selected with prespec- ified budget from all atoms, with priority given to residue backbones and ligand atoms. Paired multiple sequence alignment (MSA) [16 [7] features obtained via an improved pairing algorithm are assigned to these anchor atoms. The encoder comprises embedding layers to project all atom, bond and stereochemistry features; a hierarchical MSA Module; and AF3-style PairFormer blocks. The decoder consists of flow blocks using a diffusion transformer (18) (DiT) architecture with additional geometric bias and modern normalization layers and layer initialization techniques. Each flow block operates first on anchor atoms using dense attention and then on all heavy atoms using linear-scaling sliding window attention (19), both using bias terms from input topology and encoder representations. Refer to the Supplementary Information sections S.3 and S.4 for further details.

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Compute-optimal scaling: The Chinchilla project [20] introduced compute-optimal scaling laws, demonstrating that an optimal balance between model size and training data can be identified by extrapolating from a series of iso-training-comy
Pareto frontiers. However, applying these frameworks to structure prediction models presents unique challenges due to their (1) heterogeneous architectures; (2) the simultaneous training of conditioning and structure generation modules (Figure ST]; (3) the use of decoder parallelism, where multiple independent coordinate initializations are passed to the decoder network within each training iterations to improve efficiency (Figure [2); and (4) the vast number of modalities corresponding to each category of biomolecular interaction. To resolve these challenges, reason that the total computational cost, measured in floating point operations (FLOPs), serves as a more accurate indicator of model capacity than parameter count.
To optimize the computational efficiency of training our encoder-decoder architecture, we conducted a series of experiments and determined the ideal balance (Figure(S44) (S4): an mucoder-decode FI.OP ratio of 10 with 20 decoder replicas. While intra-molecular prediction accuracy tends to saturate upon reaching a critical decoder size, inter-molecular interaction prediction continues to benefit from jointly scaling the model and data up to the production model size. We plot the relative encoder/decoder capacity among different methods, including NP3 scaling models and the production 100M-paramete model, and an estimated result for AF3 based on our reimplementation in Figure 2
Reaching full model scale required custom triangular attention kernel. See Supplementary Informa- tion section S.6 for details of its implementation and computational performance.
Model ablations: We illustrate the impact of each modification included during the full course of model development on PoseBusters accuracy, categorized into data engineering, training loss improvements, improvements the flow sampler, and better sample ranking protocols (Figure 2B.. Key improvments came from weighting interface- based training data sampling and cropping, AdaLN-Zero (18), QK-Norm (2I). an improved weighting scheme in rigid structure alignment that improves training (Algorithm S2 and the incorporation of clash and chirality penalties in conformer ranking.
2.2 Protein Structure and Interaction Accuracy
NP3 achieves state-of-the-ee accuracy in predicting protein- ligand complexes. This benchmark evaluates two critical aspects that determine whether model truly enables structure-basse drug discovery: whether the predicted structures match experimental data to within the necessary accuracy (<2 À RMSD) and whether their molecular geometries are physically valid (PB-valid).
On the PoseBusters benchmark [9]
Given only a protein sequence and a ligand's chemical structure, without prior knowledge of the protein's s structure, binding site location, ligand conformation, NP3 achieves 78.4% combined success rate across both metrics, outperforming AF3's 73.1% (Figure [ On the coordinate error (% RMSD 2 A), NP3 achieves similar performance to AF3 (80.2% versus 80.4%, shown in Table 1). NP3 similarly demonstrates substantial performance advantages over traditional docking methods that rely on experimental holo structures and explicitly defined pocket residues, including Vina (59.7%), GOLD (58.1%) and Uni-Mol (21.8%) [22 24). Newer Al-based approaches, such as EquiBind, TankBind, and DiffDock (7), which eliminate the need for explicitly defined pockets but still depend reference protein structures, achieved lower success rates of 1.9%, 15.9%, and 38%, respectively.
Importantly, NP3 also achieves 98.8% accuracy in predicting ligand stereochemistry (Figure BB)) This is critical for downstream drug design applications, as accurate stereochemical predictions are es- sential for optimizing ligand binding affinity and pharmacological activity, ensuring the development of effective and selective therapeutic compounds.
To further evaluate NP3's performance on nucleic acids, covalent ligands, and protein interaction accuracies, we introduced new benchmarking suite, NPBench. NPBench addresses several limita- tions in existing benchmarks for structure prediction. Standard molecular docking benchmarks are typically limited to binary interactions (single target, single ligand) and therefore fail to capture the diversity of biomolecular interactions and stoichiometry inherent to molecular biology. Moreover, many of these benchmarks exhibit significant overlap with training structures, which can lead to an overestimation of model performance on novel targets.
5

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Table 1: Quantitative model performance across biomolecule and interaction types. Protein- ligand interaction prediction aceuracy evaluated on the PoseBusters- V2 dataset (9). Nucleic acids, covalent ligands, and protein prediction accuracies are evaluated using 1,143 chains interfaces from low-homology, high-resolution, and deduplicated Protein DataBank (PDB) structures released after 2023. Sub- and super-scripts in the value column indicate the 95% confidence interval. Unless otherwise stated, no structural input is provided. "Holo protein structure input provided. *Pocket
residues specified. RRequires human input.
Task
Dataset
Metric
Method
N
Value
RMSD < 2 Á
NP3
308
77 77.9
and ralid
AF3 (2019 cutoff)
308
73.1
% RMSD < 2 Á
NP3
308
80 24.8 28
AF3 (2019 cutoff)
308
80.575.6
RMSD < 2
EquiBind
308
1.94-2
Ligands
PoseBusters V2
TankBind
308
15.920.5
DiffDock
308
38.0
RMSD < 2
Vina on AF-M 2.3
308
15.3
DeepDock
308
19.5
Uni-Mol
308
21.817:3
GOLD
308
58. 58.152.
58.1
52.4
Vina
308
59. 59.765.3 765.3
Low-homology
Noncovalent ligands
% RMSD < 2 Å
NP3
572
60.7 56.6
Ligands
Covalent ligands
% RMSD < 2 Å
NP3
584
69. 69.6
675
Modified residues
% RMSD < 2
NP3
320
82. 82.676.7
688.5
Protein-Protein
% DockQ > 0.23
AF-M 2.3
239
52.358
NP3
239
52. 02.720 46.3
700.
Protein Protein-Peptide
% DockQ > 0.23
AF-M
47
76.6
Proteins
NP3
47
85. 15.1 74.5
95.7
LDDT
AF-M 2.3
123
87.1
78.5
NP3
123
86.2
Monomers
TM-score
AF-M
123
90.9 93.0
NP3
123
89. 87.7
Protein-RNA Protein-DNA
DockQ > 0.23
NP3
32.746.3
DockQ > 0.23
NP3
116
56.263.9
RNA Monomers CASP RNA
LDDT
NP3
20
53.3 30-
Nucleic Acids
LDDT
NP3
12
49.957.
CASP 15 RNA
LDDT
NP3
46.557.3
(AF3 version)
AF3
47.325
Alchemy_RNAL
54.582-
While AF3 provided a RecentPDBEEal evaluation protocol that covers diverse molecular interactions, the associated code is not publicly available, limiting its accessibility for broader benchmarking efforts (T). In parallel, PLINDER introduced a comprehensive collection of protein-ligand interactions with stratified splits: however, does not currently support nucleic acids, generalized stoichiometry, or holdout splits aligned with the time-based evaluation splits commonly used in modern structure prediction models (28].
To address these gaps, NPBench comprises 1,143 chains or interfaces derived from hww-ooooog, high-resolution. and deduplicated PDB structures released after 2023. Further details of this bench- mark are described in section [S.2] and the code will be made publicly available to support repro- ducibility and future advancements in the field.
On this benchmark, NP3 exhibited overall strong performance across diverse biomolecular targets and interactions:

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Protein monomers and protein-proteid interactions (PPIs): NP3 demonstrated compara- ble performance predicting protein- protein interactions, achieving a success rate of 52.7% on low-homology interfaces with DockQ [29] scores greater than 0.23, closely matching AlphaFoldD-Multtier v2.3 (AF2-M 2.3) [30], which achieved 52.3%. For monomers, NP3 and AF2-M 2.3 also showed similar results, with success rates of 87.1 % and 86.2%,
respectively, as measured by LDDT.
Protein-peptide interfaces:
On protein-peptice interfaces-when peptides are defined as standard or modified polypeptide chains with fewer than 20 amino acids-NPP largely outperformed AF2-M, achieving an 85.1% success rate compared to AF2-M'ss 76.6%.
Noncovalent ligands: NP3 achieved a success rate of 60.7% (ligand RMSD <2 A) for noncovalent ligands in the evaluation set, compared to 80.2% on the PoseBusters benchmark. Notably, the evaluation set consists of ligand-target interfaces where either the binding pocket or the ligand exhibits significant structural dissimilarity from the training data. These results demonstrate NP3's ability to generalize effectively to unseen targets and novel molecules, maintaining satisfactory performance under more stringent evaluation criteria.
Covalent ligands and PTMs: For covalent ligands, NP3 achieved a high success rate of 69.6%, while for modified residues it reached 82.6%. These results underscore NP3's ability generalize to proteins with chemical modifications and covalent chemistry, making particularly relevant for drug discovery applications targeting chemically modified proteins.
Nucleic acids: On CASP15 RNA targets [31 32), NP3 demonstrated comparable performance AF3 (46.5% versus 47.3%, respectively) and slightly below that of Saahemy_RNAy (33 (54.8%), which relies on explicitly curated human inputs. While AF3 conditions its predictions on RNA MSAs, NP3 uses RNA language models (LMs) and achieves similar performance-a noteworthy result, as MSAs are typically considered more effective than LMs for conditioning structure predictions. This outcome also highlights the potential of utilizing LM-based approaches in scenarios where RNA MSAs are unavailable or impractical to generate. For protein- DNA interactions, NP3 achieved accuracy compara- ble to protein-protein protein interactions (56.2% versus 52. 22.7 respectively) and lower, though reasonable, accuracy for protein-RN. -NNA interactions (32.7%).
Intericc Proditiess
Fovetar finds rimes
8212
1254
14.02
12.92
12%0
Figure 3: Model confidence estimation. (A) Scatter plot of ligand RMSD against ligand pLDDT and on PoseBusters. (B) PoseBusters ligand RMSD success rate statistics grouped into NP3 confidence percentiles. Prediction success rates are consistently higher for higher confidence prediction bins. (C) Scatter plot of DockQ score against the pDockQ score on NPBench moteiin-proted and protein- nucleic acid interfaces.
(D) PPI DockQ success rate statistics grouped into NP3 confidence percentiles. Vertical lines on the scatter plot indicate the median prediction confidence. 95% confidence intervals are indicated by error bars in panels and D.
A strong correlation was also observed between NP3's model-estimated confidence and true pre- diction accuracy, highlighting its ability to effectively gauge the reliability of its outputs (Figure 3). Confidence for ligand predictions was quantified using the PLDDT score, while fillmerr-pllyyae interface predictions were assessed using the newly introduced pDockQ score (see SI. S.9...9). To further analyze the relationship between confidence and accuracy under a cutoff that defnes prediction successful-ness, prediction success rates were aggregated into percentiles based on model-estimated confidence. Results showed that higher confidence predictions achieved substantially better outcomes. Specifically, for predictions in the top 50% confidence subset, NP3 achieved 96.7% RMSD success rate on the PoseBusters benchmark and 93.1% % DockQ success rate on the NPBench dataset.
7

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Apo/Hoolo Protein Conformational Changes
Apo Proteins
100
%: Correct ConfBenchh
nu30
600
SLIX n-00
Ape (unbound)
404
(bound)
B Apo/Holo Structural Data Benchmark Curation
global IgadelliVOD beineen Apoltr
AF2
NP3
377K FUNDER
220K Bloossmaly Intages
77K Meocurable
NP3: All Proteins
52K pocket Cont BennBench entrles Apailic a 155
100+
67.4%
98.0%
n-95
n-528
ConfBench
Chain mapping
600
ApoiHille
Hterate through all possibie Tignns
Map chain asocelated with ligand to analogguus motrics
similarlyy
40-
Conformationatioaal Analysis for Predicted Hoo/oolo Structures
Apo
Holo
NP3: Kinase Subset
1004
6-45
72.5%
Query Structure apo
Structural Processing and Pockat
and
Global Pocket Alignment for
ContBench
Structure Mapping Aligniant
60-
Score)
Apo (ref)
(nef)
TUMSD
TOMSD query
(RMSD2
RMSD
RMSD
Holo
Figure 4: ConfBench conformational prediction. (A) Schematic illustration of types of conforma- tional changes of interest.
(B) Benchmark target statisties. 57k global and 52k pocket rearrangement entries with meaningful motions and biologically relevant ligands are identified. (C) The ConfBench scoring protocol. (D) Conformational prediction success rate statistics comparison. A correct confor- mational prediction is defined as a ConfBench score greater than NP3 outperforms AF2-M 2.3 in predicting pocket conformations on apo targets, while maintaining similar success targets and holo targets. 95% confidence intervals are indicated by error bars in panel In the top panel, the 90 apo structures correspond the subset of the 95 apo structures in ConfBench for which AF2 predictions were possible.
on apo
2.3 Ligand-induce Conformational Change Prediction
To this point, we have considered benchmarks of biomolecular systems in isolation. Also of interest assessment of accuracy in predicting the structural change of proteins from apo (non-ligand-bouml to holo (ligand-bound) structures. Accurate conformational predictions, both globally and locally around the binding site, are of acute importance drug discovery by assisting in identifying allosteric binding sites and optimizing interactions for improved efficacy and selectivity.
Several groups have discussed AlphaFold's limitations in predicting complete conformational ensem- bles of proteins of interest 34 38). Even so, there a lack of standard benchmarks to quantitatively measure the prediction accuracy of proteins with induced conformational changes.
To address this need, we developed ConfBench, conformational benchmark that systematically evaluates ligand-induced conformational changes across the proteome and assesses model conforma- tional biases by comparing predictions against reference apo and holo states (Figure ConfBench consists of rigorously curated selection of chain and figand-specific apo/holo PDB pairs that

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exhibit measurable conformational differences in one or more of the following ways: global RMSD > 1.5A, pocket alpha carbon RMSD 1.5A, or pocket alpha carbon plus sidechain heavy atom RMSD > 1.5Å. Additionally, we propose a conformational scoring function that a measure of conformational accuracy which is insensitive to absolute variance between reference structures and also agnostic of structural accuracy of conformationally irrelevant domains.
To enable the PDB-wide measurement of conformational change down to atomic level of accuracy, a stringent alignment protocol was required prior to RMSD calculation. Starting from PLINDER (28). implemented an exhaustive, bidirectional search of all linkages, examining all possible chain combinations and distinct ligand binding sites in multi-liganded complexes. Optimal chain mapping was comprehensively validated with PLINDER chain similarity metrics, namely pocket sequence identity (pocket_fident), fident), thain-wise local distance difference test (LDDT), and chain-wise backbone local distance difference test (bbLDDT).
For apo/holo pairs that have conformational changes greater than 1.5 i.e. changes that are mea- surable and relevant, NP3 outperforms AF2-M in conformational prediction success rates. NP3 outperformed AF2-M for 54 unique linkages with a correctness rate of 51.9% of predictions. compared to 29.6% of AF2-M predictions. This is true across the board, whether that be global conformational changes. pocket alpha carbon atom conformational changes, or pocket including sidechain confor- mational changes. Compared to context-unavee unaware methods like AF2-M, this result demonstrates the potential of using all-atom structure prediction algorithms to capture conformational variations induced by ligand binding and change in physiological conditions.
NP3 achieves consistent performance for apo and holo structures. Across all evaluated proteins, NP3 achieved correctness rates of 67.4% for apo structures (Minkages 95) and 69.0% (Niinkgees 528) for holo structures. further evaluate performance within high-value therapeutic target class, the benchmark dataset was refined to focus on kinases. Within this subset, NP3 achieved correctness rates of 77.8% for apo structures and 72.5% for holo structures.
There are some limitations: (I) imperfect ConiBench scores for NP predictions and (2) apo structures used for scoring do not always imply fully ligand-free free structure. We recognize that ligand-fres structures in the PDB are relatively limited [28 399; we expect more work to enable conformational benchmark that is diverse, biologically relevant, and leakage free.
Discussion
Accurately determining protein-ligand structures and their conformational distributions remains significant challenge, especially at the fine scale required for drug discovery. Along these lines, one notable contribution of NP3 is its high accuracy the PB-valid metrics that assess the prediction of physically plausible structures. This capability is essential for generating meaningful insights and avoiding unreliable results, as physically realistic predictions directly impact the translational success of computational models in drug discovery. NP3's high accuracy in predicting PTMs further represents a step forward in modeling biological processes such as signaling, immune response, and protein folding (40). These targets are historically underexplored in structure- drug discovery due to experimental challenges, where NP3 may open new opportunities for drug targeting.
In modeling specific conformations, particularly apo and holo states, NP3 also demonstrates improved accuracy compared to AF-M 2.3. Notably, NP3 shows similar fraction of correct conformational predictions between its predictions on apo targets and holo targets. These precise predictions, such the successful modeling of kinase conformations, and deepening the understanding of target protein behavior in structure- based drug design, and we anticipate the evaluation framework of this work be a basis for fairly measuring and improving conformation modeling ability.
critical for optimizing lead compounds
Finally, NP3 delivers predictions in seconds. This speed advantage may enable researchers to virtually screen extensive chemical libraries and iterate on ligand designs with significantly greater scalability. Moreover, NP3 achieves this efficiency while maintaining compatibility with standard hardware, reducing computational resource requirements and making advanced structure prediction more accessible.
NP3's performance is limited by its training data: PDB entries are resolved under artificial exper- imental conditions, whereas the model's intended use is to predict structures in native biological

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environments. Model capacity is a second limiting factor. Figure S4 shows that scaling the network would boost accuracy, yet such expansion is challenging on current GPUs. Finally, this study did evaluate NP3's accuracy on antibody structures.
4 Broader Impacts
NP3 offering a powerful in-silico complement to existing wet-lab methods in biology and medicine. Potential positive impacts include (i) accelerating the design of more selective and effective therapeu- tics, (ii) reducing experimental screening cycles, thereby lowering cost and environmental footprint, and (iii) enabling biologists without extensive structural resources to generate testable hypotheses. We anticipate downstream benefits for health.
The same capabilities also pose dual-use concerns. High-fidelity complex modeling could aid design of novel toxins, immune-evasive variants, or delivery vehicles. We will not release model weights, substantially mitigating these concerns.
NP3 will used in virtual screening of drug molecules. Compared to existing co-folding models, NP3 is much more computationally and therefore environmentally efficient.
5 Code and Data Availability
Code for the NPBench benchmark is available https://gt* thub. structures and corresponding model inferences are available on Zenodo at https://zenodo. 4rr
on GitHub NPBench reference
6
Acknowledgments
This work used computational resources provided by the National Energy Research Scientific Com- puting Center (NERSC) under Contract No. ERCAP0029432.
References
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Supplementary Information
S.1 Comparison to previous work
NeuralPLexer2
NeuralPLexer2 is a diffusion-based model using an equivariant graph-based denoising decoder, based on a continual development of the original NeuralPLexer model [T]. NeuralPLexer3 instead is flow matching model with multimodal conditioning module and a conditional diffusion transformer decoder. NeuralPLexer2 employs a Gaussian prior while NeuralPLexer3 employs more physical globular polymer prior (described in Algorithm (S.4). Compared to NeuralPL.xxr22, NeuralPL trained with greatly expanded training data and model size, and shows substantially improved performance.
AlphaFold
The main architectural components of AlphaFold 3 and NeuralPLexer3 are the same: MSA and Pairformer are used by both models. NeuralPLexer3 conditions additionally on protein and RNA language model embeddings. From scaling studies (Figure S4), we identified a different pareto- optimal choice for encoder/decoder size. We also using sliding window attention instead of ad-hoc block-based operations for token-to-atom communication.
NeuralPlexer3 employs flow matching to allow sampling from any prior distribution, and introduces novel physics-based prior (Algorithm (S.4). NeuralPLexer3 does not use AlphaFold 3's hand-crafted positional encoding among entities and atoms. NeuralPLexer3 does not rely on reference RDKit conformers, allowing encode molecules of all chemistries.
During training, no mini-rollouts are needed in NeuralPLexer3 because of the prior alignment step, which dramatically reduces the complexity of the training pipeline compared to Alphafold 3. We also introduce a fused triangular attention kernel absent AlphaFold 3, leading to faster and more memory-efficient training and inference.
S.2 Methods
Structure Prediction Benchmarks: We evaluated NP3's structural prediction performance on three benchmarks the PoseBusters-V V2 dataset (2) for protein-ligant interaction prediction accuracy, NPBench for diverse interaction types and stoichiometry on low-homology structures, and CASP15 for RNAs 3
Baselines: We conducted comparisons across multiple benchmark datasets to evaluate performance. For the PoseBusters ligand dataset [2]. we compared NP3 to traditional docking methods that require holo receptor structures, including Vina (4) and GOLD (5). as well as machine learning-basse methods with similar holo structure requirements, such as EquiBind (6). TankBind (7), and DiftDock (8). Additionally, we benchmarked against structure prediction methods that use only sequence and graph information, including AF3. Baseline numbers for these methods were derived from Abramsom et al
(Extended Data Table 1) [9].
For protein targets from the dataset of recent PDB structures (NPBench), NP3's performance was compared to SpphaFold-Multime 2.3 using ColabFold [TO]. Five seeds were generated per target, and the top-ranked conformers were scored using both NP3 metrics and the "multimer" metric provided by AlphaFold-Mulinn Multimmer [TI).
12] Baseline metries for these methods were sourced from the AF3 publication, which originally evaluated eight CASPI5 RNA targets (9). With all CASPI5 RNA targets now publicly available, NP3's average RNA LDDT scores were reported across both the original subset and the complete dataset, with no significant differences in performance between subsets.
For CASP15 RNA targets, NP3 was benchmarked against AF3 and
Evaluation Criteria: To evaluate model performance across this diverse set of biomolecules and structures, we utilized several well-established metrics:
RMSD <2 À success rate: The fraction of predictions with pocket-aligned ligand RMSD below 2 Angstrom, widely used metric for assessing structural prediction accuracy.
20

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PB- Pa-vali success rate: The proportion of PoseBusters predictions that pass physical validity checks implemented in PoseBusters (PB).
Local distance difference test (LDDT): An alignment- free metric for assessing the accuracy of local structures across cutoff all biomolecules. 25 À inclusion cutoff is used for DNAs and RNAs, and 15 À is used for proteins.
DockQ >0.23 success rate: The fraction of DockQ interfaces for evaluation, metric for evaluating the accuracy of polymer- pooyymer interaction predictions using acceptable thresholds from CAPRI [3
greater than 0.23 across all
Conformational Benchmarks: To develop the ConfBench benchmark, which assesses conforma- tional accuracy, all PLINDER (14) linkages were filtered for entries with only experimental structures from the PDB. These linkages were further distilled to curate a dataset of protein-ligand systems exhibiting measurable conformational changes between apo and holo states (4A and B). Systems with "lock-and-ked -nd--ayndd binding, where the protein structure remains largely unchanged upon ligand binding, or those with minimal allosteric shifts, were excluded. This step ensures the benchmark focuses on clear, quantifiable ligand-induced structural transitions that are significant enough to measure and therefore evaluate prediction accuracy and enable effective model performance assessment.
We next employed a systematic approach to identify precise chain-level correspondences between apo and holo protein structures- a critical metric for reliably evaluating ligand -eaandidduced conformational shifts in multichain, multi-liganded oligomeric systems:
Extract chain information from PLINDER's structured identifiers;
2. For each protein chain with an associated ligand chain, identify all possible mappings between holo protein chain and linked apo protein chains;
3. Rank these mappings based on quantitative structural metries:
Pocket_fident. Sequence identity within the binding pocket
LDDT: Local distance difference test
bb LDDT: Backhone local distance difference
To evaluate structural predictions, we employed scoring formula designed quantify the similarity between predicted (query) and ground truth (reference) structures. The score is calculated as:
RMSD query all RMSD query_ rel
score
(3)
(RMSD2 query_att + RMSD?
query_ref + RMSD alt
where:
1 when the query RMSD is O, indicating the prediction is identical the reference
state
score -1
indicates the prediction is identical to the linked alternative state
score 0 indicates the prediction is equally distant from the reference the apo/holo states.
Between 0 and the score scales smoothly, reflecting the degree of similarity to the reference state.
S.3 Data and Input Pipelines
Molecular Topology Featurization:
The initial structural features passed to the NP3 inference pipeline are a complete representation of the molecular topology. These input features include:
Atom-wise features: atom types and residue types. Residue types include a one-hot encoding of the 1-letter residue name for atoms from standard amino acids and nucleotides, and one-hot encoding for any other residues.
Atom-pal features: bond orders, and bond orientations:
21

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For bonded atom pair (ž,j),, we evaluate the bond orientations by first constructing local frame based on two nearest bonded atoms (ik, il) using the generalized Gram- Schmidt procedure described in [ and assign the bond orientation feature as the direction of the displacement vector between atom and atom expressed in the assigned local frame
We assign the bond order to 0 and bond orientation features to (0, 0, 0) for any non- bonded atom pairs.
Disulfides, ionic bonds, hydrogen bonds, and halogen bonds are excluded from featur- ization and solely inferred by the model.
Heavy atoms of bioassembly are split into levels of treatment: atoms and anchors. Only the anchors and anchor pairs among them are being processed by the encoder block to produce conditionings, while all atoms are passed through the flow blocks produce denoised coordinates of the entire assembly. Given a fixed context size budget, anchors are selected as follows:
1. Biopolymer backhones are prioritized. We label all Ca atoms of amino acid residues and C1' atoms for nucleic acids as anchors, unless the budget filled in which case perform a sampling without replacement;
2. Then we perform additional sampling without replacement from all atoms from ligands, non-standard residues, and PTMs;
3. If any budget is left, we perform atom sampling from the remaining standard protein, DNA, and RNA residues until the budget limit is reached.
Evolutionary sequence features: NP3 additionally leverages conditioning from MSAs, protein language models, and nucleic acid language models, For training, we follow the MSA generation protocol from AF3, combining jackhmmer MSAs [13] on uniref30 [T6], reduced BFD, and uniref 00; and hhblits MSAs [17] for BFD 18). We do not include RNA MSAs. We use 3B- 18-arameter language language model for RNAs (RiNalMo) (20).
model for proteins (ESM-2) 2) [19 and 350M-paramen
We introduce a compactified MSA pairing algorithm to capture cross-chain coevolutionary genetics while efficiently utilizing a fixed token context window of most 16,384 sequences. The method proceeds by first sorting sequences from all databases with decreasing sequence similarity w.r.t the query sequence, then pairing sequences by taxonomical ID (2I), and finally backfilling the blank spaces with unpaired monomer sequences.
Data filtering and preprocessing pipeline: For structures obtained from the PDB, generally follow the mmcif-level filtering protocol that has been described for AlphaFold 19, with the following minor differences:
We skip structures where either the asymmetric unit cif file size or the bioassembly cif file size exceeds 20 MB;
We do not need to remove leaving group atoms based on information about the residue in the CCD;
We do not limit the structures passed the training pipeline 20 chains.
To obtain correct connectivity and bond types, we make use of the information provided in the CCD for non-standard residue names via ParmED's 'all hall_residue_tnme taapceemmllleeepeeeee saatreemaathhhaaaeeaeeeeeaaarrhr (22). Furthermore, we read the bonds present in the 'struct_com section in the cif file for the asymmetric unit, which usually missing in cif files for bioassemblies. We then identify matching atom pairs in the bioassemblies and add the corresponding bonds.
S.4 Model architecture and inference
In ST we outline NP3's structure sampling procedure. CNFs integrate learned velocity field to transform a prior distribution and sample new data. Our conformer sampling protocol iteratively refines structures through time-conditioned decoding, rigid-body structure between integrator steps alignment to reduce discretization errors, and graph-preserving atom permutation corrections. In practice, we also apply a timestep shifting trick using a polynomial transform /" f1.15, which found beneficial to reduce exposure bias 23
22

---

Table S1: Comparison of data processing pipeline details.
Training Data Processing Step
AF3
NP3 (Ours)
Keep structures of reported resolution of 9 Å less
Remove structures with 300 more polymer chains
Remove polymer chains containing fewer than 4 resolved residues
Remove hydrogen atoms
Remove clashing chains (those with >30% of atoms within 1.7 Å an atom in another chain)
Remove atoms outside of the CCD code's defined set atom names
Remove leaving atoms for covalent ligands
Not needed
Filter out protein chains with consecutive Ca atoms greater than 10 distance
Truncate closest 20 chains relative random token for large bioassemblies
Keep all chains
For structures from crystallography. remove crys- tallization aid molecules
Algorithm S1 Sampling from NP3 with symmetry-correeted flow. CFM: Conditional flow matching.
1: function MPSSAWPPLLSTRUCTTEEEPPPMGC T 100) b T: Number of integrator steps
2: Xg f MuitchhannPoyymeeerrrraaappp
b Sample initializations from the
physics-inspired prior
3: x Xp. Al 1/T,1
4: Zatom; Zanchor; paair
for timestep Ppair-anchor; anchor, Apair local NP3Fnccderrcc)
5:
do
6:
next f- + At
7:
pred f- NP3Decoder(xx, l' ZaIzoo Zanchor; Zpair- anchor, Zpair-local), 1' = (2.15 pred clast
8: Topt: topt GetKabschTransform/ss ,x1 Walign)
Global superpsuppooninooon to
improve continuity pred
9:
x peed
Topt Lopt
X
pred
OptimalGraphPeermttttttttt
pred lostt
Atom permutation correction using
graph isomorphism pred
11:
l t- x
Xtrest CFMSampleStep(x pred N4, Xx,,t, fnext)
CFMSamplcStepp(21..au tnext)
lnex I1 (1 Inext) 1-2
13:
t t tnext
end for
15: return æ1
end function
When sampling initial coordinates from the prior, we incorporate constraints at multiple scales. Bonded connectivity ensures that linked atoms form coherent polymer-like chains: Entity-level and residue-level scale constraints guide atomic positions to cluster in manner consistent with coarse-graines structural motifs; and global spherical confinement maintains compact, globular arrangement.
23

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Algorithm S2 NP3 main model training iteration.
1: function NPSTRAINNNGITTTRNPPPMM xf I, c, ddata 16.0A, 0.01) D xf Ground
truth structure
2: Xo f MuttchaiiiPoylymerrrrtssaapp
b Sample initializations from the
physics-inspired prior
3: f- OptimalEEtiyyeermaattioo.oo x(r)
Apply entity permutation on prior sample
4:
X₁ + (1 - 1) X + --x
5:
x <- NP33odel(xx
> Encoder + decoder forward pass
6: Topts topt GeiKabschTraasffmm((
pred xnd Walign)
Global SE(3)-spperposition using
backbone trace
7:
X1 t x Topt + topt
8:
x1 +
pred x! D. Atom permutation correction using graph
isomorphism
9:
x1 t STOP GRAD(x
w(t 1/(c (1 t)o
Loss weighting following [24]
11:
C
(t) (xeudooHuuerLLos((f xx²) + W2 S1ToothLDDT(x!" xxp) + W/3
FAPE(x] x
Backpropagate on L
13: end function
Algorithm S3 Sampling from Globular Polymer Prior via Short Langevin Dynamics
Require: Xo E N x3 dt 0.25, sphere_ res = 4.0, ent r 10.0
Require: Matrices Spood, Sentity Sresidue define neighbor and group structure
1: for = - 64 do
2: dbond (Sp Xo
3: demiiy t (Seniyy Xo)
Xu
4: dres (Sresidue Xo) Xo
5:
drift -- 2 dbond + en res
dann + dis
sphere_r 1r with e ((,
6: No +- Xo + di- drift 2v
7:
end for
8: return Xo
Starting from random atomic positions, the algorithm iteratively applies drift updates derived from these constraints and adds small thermal noise. After brief relaxation period, the resulting coordi- nates serve as a well-structured initialization that respects chemical connectivity, coarse geometric organization, and global compactness. This initialization naturally breaks inter-chain symmetry for copies of the same biopolymer. During training, at the end of the initialization we apply a greedy permutation of the prior entities such that the nearest neighbor entity index of each entity maximally agrees with the nearest neighbors derived from the ground truth.
ST we provide detailed view of the NP3 model architecture. The production model uses the following configuration: 350M encoder parameters, 350M decoder parameters, 50M confidence module parameters. We highlight the following architecture details:
Standard block details: We
single representation embedding size of 384, pair representation embedding size of 128, atom representation embedding size of 256, and atom pair representation size of 128. For MLP blocks, we use hidden size that is 4 times the embedding size similar to the design choices made in Llama-2 [25]. RMSNorm 26 is used for all MLPP blocks; LayerNorm (2 without learnable bias is used for all MSA module blocks, pair bias attention, triangular attention, and triangular multiplication blocks.
U-Shaped MSA Module: NP3 uses an MSA Module consisting blocks, each with the architecture described in [9]. The MSA latent dimension progressively scales from 32 to 512 with multiplier of 2 after each block, optimizing memory usage with minimal representation capacity tradeoff.
24

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Flow Blocks (24x)
Single representation
MLP Narm
MLP Norm
DifusionAttention llangraaner dilated)
DiffusionAttentio
Islicing window, W-128)
Select anchor atoms
representation
Noley coordinstes [NLatom, 3]
Embed coordinates
Apply local mask
(Fourier pos. enc.)
Flow timestop? 1
Embed timestte
(Fourier pos, enc.)
Single representation
reprosentation on
Encoder Blocks (32x)
MLP
Triangular Atrantion (1x)
AltentionWit
Trianguler Multipiicatlon (2x)
Conditioning Modules
Protoin & RNA LM embeddingg (Trozen)
U-shaped MSA Module
Single representation anchors, DJ
Pair represantation anchors, anchors,
Multiple sequence alignments
Select anchor atoms
Select anchor peirs
regresentation INLatom, DJ
peir representation INLatom, N_atom, D
Molecular topology: Atom types, bond types orientations
Figure $1: Architecture details. Dg: atom representative latent dimension; D,: single representation latent dimension; Dp: pair representation latent dimension; Dap: sliding window atom pair represen- tation latent dimension.
Independent timestep/ coordinate
Decoter
*Loss
Pander
Decoeer
Figure S2: Schematics of decoder parallelism for training encoder-decoder structure prediction models.
25

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Table S2: Notation used in the symmetry-correeted alignment.
Symbol
Meaning
Noisy prior sample drawn at diffusion timestep T One-step denoised coordinates predicted from XT Ground-truth (noise-free) label structure
Xo
D= (D,....,DD D
Set of entity groups; each Dx contains indices of chemically identical chains or ligands Root-mean-saue -quare deviation between coordinate sets 6 Rotation matrix and translation vector returned by Kabsch alignment
RMSD(a,
R, t
P
Block-diagonal permutation matrix acting inside each D3:
Sliding window attention with sparse pair bias: We employ an efficient implementation of sliding window attention compatible with pairwise attention bias, maintaining linear asymptotic inference time and memory scaling with respect to the number of heavy atoms. The atom pair features (bonds and orientations) are projected by a linear layer and collated to the sliding window mask. The biased sliding window masks are shared across all decoder replicas when using decoder parallelism during training.
S.5 Flow Trajectory Symmetry Correction
We incorporate a simulation-fire symmetry correction module motivated to align the conditional flow trajectories with displacement interpolation paths that approximate the optimal transport geodesics between the prior and target distributions. The details are as follows:
1. Denoise the prior with pre-computed conditioning:
fo(x., T).
2. Rigidly align each indistinguishable entity. For every entity group D3:
(a) For each index pair (i.j) E Dx Da (e.g., (), (0, .). identical):
... (2, 1) when entities 0, 1,
i. Compute (Rij, kij) = Kabsch ( x(i)
ii Obtain an aligned label copy x(1) Ruj x(1)
+ tij.
(b) Greedy in- group permutation search (cf. choose the permutation zž that minimises
11
Sec. 7.3): for each entity group De-
Σ RMSD
x (mell))) xx))
LDD
3. Global objective. For each global alignment (Rij. tij), compute
RMSD = RMSD(P &o),
and retain the permutation//lignmeen pair (P*, {R ig: bly)) with the lowest RMSD
4. Apply the optimal permutation to the label:
x = P'x.
5. Final alignment applied to the prior (optional with SEv3)-invrriant losses), Align the permuted label X to the original noisy sample x7:
(Rr, tr) <- Kabsch( x7),
x = R, tr.
The resulting X (or X in an invariant setting) is used as the target in the flow-matching loss, reducing the transport cost between the prior and target data distribution and maintaining consistent frame across sampling iterations.
26

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A hash-TriangulrrAttenttoo
B
Nedive Tranngaarraktteeennnn
Natlee Pytarch Flash- Trannngarntttttteeetennn
TTbkan:
50
Model Forward Time (ms]
Peak Memory (GB)
30
Bios Nrr
(sqquiics gradiont)
14404
SRAM HBM, Input
HBM Output
Number of Residues (N)
Number of Residues (N)
Figure S3: Illustration of Flash- Priangular-Attention kernel and experimental comparison on the peak memory usage and the inference time. (A) The workflow for Flash-Triang TriangularAtteniin The main goal is to reduce peak memory usage, which is the bottleneck of triangular attention. Our implementation avoids this explicit broadcast, which is required while using other memory-efficied implementations, thus enabling longer crop size training. (B) Peak memory usage comparison between Flash- Maash-TriangularAttee Attention and PyTorch built-in SDPA. Our implementation significantly reduces peak memory usage for longer residues, enabling samples with residues exceeding 1024 to run on one H100 GPU (80GB). (C) the inference time of the Flash- Flash-TriangularAA TriangularAttention and Pytorch built-in SDPA. The figure shows that our implementation significantly reduces inference runtime- for example, by 38% at a residue of 1024.
S.6 Computational Efficiency and Prediction Speed
To address the computational challenges of molecular structure prediction, introduced Flash- TriangulaAAttnttion. a novel attention mechanism optimized for efficient training and inference ([A and S3 The method leverages implicit bias broadcasting within the kernel during the QK" Bias operation, which eliminates unnecessary bias replication, significantly reducing memory overhead and enabling scalability for large structures.
In more detail, the triangular attention mechanism requires a gradient- tracked Bias term. The query (Q), key (K), and value (V) tensors each have the shape (B * N, d), and the Bias tensor has the shape (B * H, N, N), where B is the batch size, H is the number of attention heads, N is the crop size, and d is the head dimension. In a naive approach, during the QK" + Bias operation, Bias is broadcasted from (B = H, NN, .N to (B * N, N,,, N, .N.. Current optimized solutions, such [28] and PyTorch's 's scaled dot-product attention (SDPA) and FlexAttention [29], either do not support gradient-tracke
as FlashAttention
Bias or require explicit bias broadcasting which dramatically increases peak memory usage. To train models with larger structural crop sizes, seek to avoid this broadcasting step.
Flash-Triang Teahh-Trrinnaurttteeeee Attention leverages implicit bias broadcasting within the kernel during the QKT Bias operation. For each channel, the bias is loaded once from the bias matrix during the forward pass, while the backward pass accumulates gradients into a shared bias matrix. This eliminates unnecessary bias replication, significantly reducing memory overhead and enabling scalability for large values. Our Triton kernel implementation, a language and compiler for writing highly efficient custom Deep-Leeriing primitives, enhances efficiency, allowing for training on larger sequences and crop sizes while staying within GPU memory constraints. Experimental results underscore the effectiveness of Flash- Flash-Triangun Traangularrttteniion (S3). Peak memory usage decreases by 5x compared to a naive implementation as crop size increases, enabling the model to scale effectively, while the forward pass inference time is improved by 50% on average. These improvements make NP3 capable of processing large, complex structures without compromising computational efficiency.
Building on these advancements. NP3 delivers predictions 15x faster than inference timing statistics reported by AF3 (3.. Unlike AF3 p which requires approximately six A 1000minutes per prediction, NP3 generates results in approximately 30 seconds using a single L40S GPU. This efficiency is also attributed to removing the expensive trunk recycling operations and cutting the number of sampling steps to 40 by leveraging qgiimal-trnnsoor flow samplers (SI).
27

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S.7 Model training
Dataset Splitting and sampling:
NP3 is trained on all PDB structures deposited before September 1, 2020, along with addi- tional synthetic datasets. The cutoff date is chosen ensure overlap with evaluation set structures. We process training samples based on contiguous and spatial cropping centered around each to ensure maximal training data mixture diversity. In our implementation, we always sort the chain numbers based on the minimum distance to the chain or interface of interest before applying contiguous cropping.
Weighted sampling of structure crops is employed to ensure inclusion of underrepresenteed molecule classes (e.g., nucleic acids, ligands). We mainly follow AF3 for clustering all chains and interfaces including 40% maximum similarity threshold for sequence clustering, with the notable difference of using 60% Tanimoto similarity cutoff for ligand clustering rather than the 100% CCD) identity cutoff employed in AF3.
Data augmentation strategies include spatial translation, rotation, MSA row-wise subsam- pling, and 15% residue masking rate for language model embeddings, and 15% masking rate for atom type, bond order, and bond orientation features.
Several synthetic datasets used to augment model training and improve generalization, with examples drawn from computational predictions:
Protein monomer distillation: With 30% probability, we sample structure from the Open-
ProteinSet dataset of OpenFold (30) predictions (N=270,000).
Disordered distillation set for protein multimers. With 1% probability, we sample a structure from NP2 predictions of bioassemblies containing more than one polymer chain, with the motivation to reduce hallucination for intrinsically disordered regions. These samples were generated by NP2 with full full-length sequence inputs and template coordinates guidance, for PDB structures with 50 or more contiguous missing residues (N=2,801).
OrbNet conformers: With 2% probability, we sample a single molecular conformer. These conformers are obtained from a comprehensive dataset of small molecule conformations refined at the w.B97X--D3/De22-TZVV level of DFT theory, expanded from OrbNet Denali
training data (N=12,706,496) 31
Model weight initialization: Within all attention layers, we adopt QK-normalization 32 to stabilize model training. For all PairFormer blocks, employ Zero-residual initialization motivated by recent works [33 344. For Flow blocks, we employ Adaro- initialization (35] to both the attention and MLP layers, with scale and shift parameters dependent timestep embedding.
Optimization Details: S2] we outline the procedure of a single optimization step for training NP3. Following Lee et al. [24). we found that pseudo-Huber loss combined with SmoothLDDT introduced in AlphaFold 3 yields the most stable training. Additional loss terms include a distance-normalize Frame-Alignee Point Error (FAPE) and distance-geometty loss to ensure accurate local and global structural alignments
We modified the alignment weights Walign used in the weighted Kabsch-Umsa Umeyama algorithm 36 37 which we found important to reduce numerical variations in late-stage training:
Atom weight 10.0 for the ligand of interest, when the training structure is generated based on a contiguous or spatial crop around a ligand-polymer polymer interface;
Atom weight 1.0 for Ca and C1" atoms, and all rest ligand atoms;
Atom weight 0.0 for all side-chain atoms.
Scaling studies
Optimization algorithm and training stages: The NP3 production model was trained on 56 H100 GPUs hosted on cluster that implements the NVIDIA NCP Reference Architecture for 24 days. Training is carried out using PyTorch FSDP (39] under BF16 automatic mixed precision. Over the full course of model training, we progressively seale the structure crop size to gradually capture longer contexts. The number of decoder replicas P is tuned for each stage:
28

---

40-2002 C-42, PH8 - 201 C-48, P-4
ofj-7A CHU1, PHO
-1-233 C-16.4, PHg
c7- 0:4.3,,,
274 CH6.8, Put8
w//-274, C.87,
-/9-25.2 CH177, P18
Intra-Ligand
Intra-Protein
07
0.4
1-L001
0.
10
10
10
10
10
10 10
10
10 10
10
10
Protein-Ligand
Protein-Protein
Protein- NA
NA-Ligand
0.8
0.
10
10 10 10P
10
10 10
Compute (FLOPs)
Figure S4: Model scaling behavior across molecule and interface types reported by the relation between the average validation set local distance difference test (LDDT) (38) scores and the total training floating-point operation count (FLOPs). While intra-molecular prediction accuracy tends to saturate upon reaching a critical model size, inter-molecular interaction prediction benefits from jointly scaling the model and data up to the production model size. C: Compute in GFLOPs; P: number decoder replicas.
Maximum cropping size for first 80% training iterations: 384 anchors 3072 atoms, P=32;
For 10% of training iterations: 512 anchors or 4096 atoms, P=32;
For 6% of training iterations: 640 anchors or 6400 atoms, P-24;
For the last 4% of training iterations: 1024 anchors or 15360 atoms, P-8.
Activation checkpointing is employed for all training stages with anchor crop size larger than 384. Note that training on structure crops of 1024 anchors or greater sizes was only possible when using the Arash-TriangulaAAtttnnin kernel, otherwise observe GPU OOM.
All inference results used either: one H100 GPU hosted on a cluster that implements the NVIDIA NCP Reference Architecture, one L40S GPU hosted AWS góe.xlarge instance.
29

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S.8 Training Strategy for Confidence Module
Algorithm S4 Schematics NP3 Confidence Module Training
Require: NP3Model, ground truth X conditions c
for each iteration n do
2: Sample t ~ Uniform (), 1)
Sample timestep from noise schedule
3: Sample noised structure X, < SampleFromPrior((c)
4: Compute denoised structure Xienniied < NP3Model(x:)
5: Compute flow matching loss: Laow (xef; Xdenoised)
6: LDDT < LDDT Xdenoised; X<ef)
Compute per-atom LDDT score
7:
DistanceErroor +
(map(Xaenisss) - Dmaa(xXet] >Compute anchor distance map errors Pass Xdenoised through confidence module and extract confidence_loge Jogiiss
8:
9: Leonfidence + CrossEntroppy (confidence_ logits, (LDDT, DistanceError))
DCCmppue
confidence loss
10:
Liota f- LLow + Leontidence
> Update model with total loss
11:
if 10 then
12:
Xsampled +
NPSSamplerrmauuuu(PPPMddddd c, T = 10) DApply rollout with limited
steps
13:
Pass Sampledd through confidence module and extract confidence_logit
Ciotal Lrotal Ceonfidence Xsampled: X confidence_logitt
15:
end if
end for
NP3 provides two types of confidence scores:
Predicted local distance difference test (pLDDT) for each heavy atom;
Predicted distance error (pDE) for each pair among anchors.
In NP v1-2 and AF3, confidence module training is performed by sampling bioassembly structures via full diffusion Stochastic Differential Equations (SDE) at predefined intervals N, followed by optimization steps to minimize deviations between model-estimated errors and true distance errors. We note that AF3 uses N=1 (perform diffusion rollout and optimize every iteration), while NP1, NP2, and NP3 use N=10.
Analysis of preliminary models revealed limited sensitivity of confidence scores to sampled confor- mations, despite good correlation between accuracy and confidence scores over diverse targets. We reasoned that the insensitivity of confidence scores stems from under-training and insufficient paired conformational data for the same molecular topology.
The improved training algorithm integrates additional optimization steps into the standard flow- matching procedure. This approach involves sampling noisy conformations, denoising them through the model, and optimizing confidence scores based on cross-entropy loss with calculated structural errors. Noise levels are varied, producing multiple hypotheses for the same molecular topology, enabling robust confidence estimation. The algorithm thus ensures efficiency while minimizing the need for costly resampling or simulation-based inference. the fine-tuning stages, we also incorporate InfoNCE [40] loss commonly adopted in contrastive learning to encourage the model to discern minor prediction quality differences across multiple conformations.
S.9 Aggregated Confidence Metrics and Sample Ranking
Aggregated confidence metrics are provided for entities and interfaces:
PLDDT for atomic-level predictions, averaged against atoms from the entity of interest.
DDockQ for self- or inter-molecular interactions between a chain pair.
pDockQ is calculated based on the following formula:
pDockQ = (iRMS_scaled + sRal_dc + Predicted_Fnatt)
where:
30

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iRMS SesSs_scled____ Ir= 1/ (1 + (mean(pDE ) /855)
iRMS_scaled_sr= / (mean(pDE / 1.59)
Predicted_Fnail mean(pDE 5.0)
Ranking Methodology: Sample ranking leverages adjusted pLDDT and pDockQ values. Scores are penalized for steric clashes, ensuring physically plausible configurations.
For ligand of interest, LG: Score PLDDT(LG) 1000 (is (is_clash + is chirality_
chirality_vvollaiion violation)
For chain A of interest: Score pDockQ(A, A)
For chain pair (A, B) of interest: Score pDoccQ(AA B).
S.10 Evaluation datasets and benchmarking (NPBench)
Curation of the recent PDB dataset is loosely based the strategy introduced by AF3 Supplemental Information Section 6.1-6.2 [9] The dataset construction started by taking all 10, 192 PDB entries deposited between 2022-05-01 and 2023-01-12. We filter non-NMR entries with resolution better than 4.5A. To choose the most representative sample from these candidates with strong protection against overlap from training set, we perform PDB clustering chain/igand/intefface index for all structures released before 2023-01-12, with maximum similarity cutoff of 40% sequence identity for polymers and 0.6 Tanimoto similarity for ligands and PTMs. Then, for the recent structures,
Include monomers from novel clusters (not covered by PDB clusters used during training);
Include polymer-polymme interfaces if at least one of the polymers is in novel clusters;
Include polymer-peptics interfaces if the receptor chain novel clusters;
Include all polymer-ligand, ion, and metal interfaces with additional labels:
is ligand unseen CCD, is plsite_ plsite_unseen, unseen cluster, is covalent, is modified residue.
Exclude all exotic not covered by criteria above. In particular, exclude all branch entities such as multi-residue glycosylations this benchmark release as there is no clear consensus their representations in the context of structure prediction model inputs.
We then created the benchmark input mmCIF files by removing solvents and crystallography artifacts from the original samples. Finally, we deduplicate the dataset by only keeping the first occurrence of chain interface from each cluster and removing all samples which ColabFold inference did complete within GPU hour, yielding 1,143 evaluation targets in total.
Benchmarking metrics The following metrics were used to assess the accuracy of the predictions on the benchmarking datasets:
Pocket-aligned ligand RMSD: We used rigorous alignment protocol compute the pocket-aligned ligand RMSD which is described as follows:
We define the reference pocket as all Ca atoms within 10 of the ligand atoms in the ground-truie truth structure. If the ligand-polymer interface is not specified (as in Posebusters benchmarking), the Ca atoms that belong to the chain with the most residues in the reference pocket are selected for alignment.
The same set Ca atoms in the predicted structure are selected based on the residue indices and the optimal chain mapping between the predicted and the ground-trui structures obtained using DockQ v2. If the optimal chain mapping is not provided will align each chain in the predicted pocket, defined in the same way as the reference pocket, and find the minimal RMSD.
(as in Posebusters benchmarking).
We use PyMOL 41 to align the selected Ca atoms and all ligand atoms in the predicted structure to those the ground-truie structure with zero refinement cycles.
The pocket-aligned ligand RMSD is computed using RDKit (42 CaleRMS between the aligned ligand and the reference ligand structures.
DockQ v2: The DockQ scores are computed for oolymer-polymer interfaces defined in the Recent PDB Evaluation Set using DockQ v2 43 package.
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Generalized RMSD: This is computed for each pollmd interface defined in the Recent PDB Evaluation Set as follows:
We first find the optimal chain mapping between the predicted and the ground-truth structures using DockQ v2.
We use the same algorithm as described above to compute the bocket--lligned ligand RMSD for given polyyer interface.
For structures with multiple identical ligands, we perform an exhaustive search over all pairwise permutations between the predicted and reference ligands (up to 10 ligands) and find the minimal pocket-aligned ligand RMSD. This leads to N² pocket-aligned R.MSD calculations where N is the number of ligands corresponding to the same CCD code in a gegand-polymee interface.
TM-score: This is computed using the USalign package. The TM-scores for both entire protein and each chain are calculated using the optimal chain mapping obtained from DockQ.
LDDT (local distance difference test): We compute the all-atom and backbone-only LDDT scores for both entire structure and each chain in the predictions with custom implementa- tion.
S.11
Conformational change benchmarking (ConfBench)
S.11.1
ConfBench Dataset Curation
The development of ConfBench required establishing a systematic protocol for identifying and validating apo-holo protein structure pairs that exhibit measurable conformational changes. Here we detail the technical implementation of our structure pair identification pipeline and the specific criteria used for quality control.
Structure Pair Database Integration: The curation pipeline was built on PLINDER's 's structured database schema, leveraging system id indexing that encodes both PDB identifiers and chain chain). We developed
information in standardized format (PDB model protein.chain a two-pass search algorithm that first identifies potential apo-holo relationships through system_id queries, then validates these relationships through detailed structural analysis.
For structures with multiple chains, our mapping algorithm evaluates all possible chain combinations using hierarchical sorting approach. The best mapping is selected by first sorting by pocket_f fiennt (binding site sequence conservation), followed by 1ddt (overall structural similarity) and bb 1ddt (backbone conformation) as successive tiebreakers. This prioritizes binding site similarity while still considering global structural features when discriminating between similar candidates.
Chain Mapping Protocol:
Conformational Change Validation: Structure pairs required to exhibit at least of the following:
Global RMSD > 1.5A
Pocket Ca RMSD 1.5À
Pocket all-atom RMSD 1.5À
S.11.2 ConfBench Scoring Protocol
The ConfBench scoring protocol introduces several key technical advances to address quantifying the quality of prediction of ligand-ing -nduuddd conformational changes:
A robust protocol for identifying and mapping binding site residues between structures that accounts for numbering discontinuities and chain breaks
A multi-level structural comparison approach that evaluates both global and local conforma- tional changes
A novel scoring function that enables fair comparison across protein systems with varying magnitudes of conformational change
32

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Pocket residues were identified using a distance-based approach in PyMOL, selecting protein residues within 10Å of the ligand of interest. To ensure consistent pocket mapping between structures, we implemented robust sequence alignment- protocol that accounts for potential numbering discontinuities and chain breaks. The mapping algorithm uses local sequence alignment with the Sio.Align.Pairwise PaigneseAligner module, prioritizing sequence identity while handling insertions and deletions. Pocket mappings were validated by requiring at least 50% of the reference pocket residues to successfully mapped maintain structural context.
Pocket Detection and Mapping:
RMSD Calculations and Structural Alignment: implemented:
Three levels of structural comparison were
Global alignment using all Ca atoms
Pocket-specifie alignment using only pocket Ca atoms
Complete pocket alignment including both backbone and sidechain heavy atoms
Each alignment was performed using PyMOL's align command with cycles=O to prevent local optimization bias. For multi-chain structures, chain mapping was determined through hierarchical approach first attempting sequence-bai -assed matching, then falling back to spatial proximity to the ligand necessary.
Conformational Score Calculation: The conformational scoring function was designed to be:
Symmetric with respect to the reference structures
Normalized account for varying magnitudes of conformational change
Invariant global rigid body movements
For each alignment type (global, pocket, pocket+sidecchiin)) the score is calculated as:
RMSD_hol RMSD_app
score_apo_i
(4)
(RMSD_holo RMSD_apo + RMSD_ref²)
RMSD_apo RMSD_holo
score_holo_i (RMSD_apo' + RMSD_holo² RMSD_ref*
(5)
where RMSD ref is the RMSD between reference apo and holo structures, and RMSD_ DASD__ao/RMMDD holo are RMSDs between the query structure and respective references. This formulation ensures scores are bounded and comparable across different protein systems regardless of their absolute conformational differences.
S.11.3 Additional NP3 and AF2-M results
When limiting to "big" ConfBench wins (i.e. ConfBench scores > 0), NP3 achieves 47.7% of wins above ConfBench score of 0.5, whereas AF2-M achieves 32.22%.
Detailed distributions of prediction accuracy are presented through histograms of ConfBench scores and subsequent kernel density estimation plots comparing AlphaFold2-Multim and NP3 perfor- mance, providing comprehensive visualization of the complete prediction landscape beyond aggregate statistics.
For additional clarity, histograms of NP3 raw ConfBench score distribution data shared below, detailing the magnitude of win rates for the apo and holo dataset discussed the main text.
33

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CanfBench
rads
315
30*
Win Rotoo (56)
rude
Score
Pocke::
Foclet Score
Figure S5: Win rates for all ConfBench score types on query conformation = apo linkages where reference RMSD > 1.5 Å. A ConfBench win is defined as query structure score > O.
Soores JQ
Figure S6: Distribution of ConfBench score values for NP3 and AF2 multimer models with query conformation = apo and reference RMSD > 1.5 Á. The histograms display the frequency of scores across all metrics (global, pocket, and pocket-sidechain) within the range of -1 1.
Distribution of Scores (KDE) (Query Apo) Ref RMSD 1.5
Gobal Score
Fociet Score
Peciet Stedhain
Figure S7: Kernel density estimation plots depicting the score probability densities for NP3 and AF2 models where query conformation = apo and reference RMSD 1.5 A.
34

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Clebe: Score
Pediat
Tociat Steecheh
1
Figure S8: Distribution of ConfBench score values for NP3 with query conformation = apo or holo and reference RMSD 1.5 A. The histograms display the frequency of scores across all metrics (global, pocket, and pocket-sidechain) within the range of -1 to 1.
35

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Reviews:
[{"review_id": "f4hyGCEuZw", "reviewer": "Reviewer_TQha", "summary": "This paper presents NeuralPLexer3, an update to the family of biomolecular structure prediction models. Algorithmic components introduced include physical priors to constrain initial conformational embedding, optimal transport mechanisms to simplify training flows, and compute-optimal attention schemes to induce inference speedups. Performance for structure prediction in the PoseBusters benchmark is included and compared to AlphaFold 3. New benchmarks are proposed that assess performance in specialized modalities such as protein-peptide interfaces and post-translational modifications. An additional benchmark study assesses model performance for capturing conformational changes induced by ligand binding, measuring model accuracy for apo- and holo-state structure prediction.", "questions": "1. See Weaknesses 3. for several questions\n2. How are symmetry-correction and optimal rigid structure alignment modules applied at test time, i.e., without ground-truth structures? \n3. Where is the data that the percentages quoted in lines 237-244 refers to? I don't see those numbers in Figure 4", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. The algorithmic components applying physical constraints described in S.3 are nice, such as bonded-connectivity, entity-level and residue-level, and global spherical confinement constraints to ensure consistent clustering and compact arrangement at the polymer level\n2. The architecture (Figure S1) and arrangement of conditioning modules, encoder blocks, and flow blocks is nice\n3. The Flash-TriangularAttention implementation is innovative and the memory and speed improvements are significant\n4. The results in model development Figure 2B are nice and showcase a complex system\n5. PB performance (Figure 1B and Table 1) is impressive and significant\n6. New benchmarks with specialized modalities and performance therein (Table 1) is nice\n7. Calibrated uncertainties (results in Figure 3) are nice. Not perfect, but pretty good classifiers as indicated by dashed gridlines in Fig 3A & 3C \n8. Introducing ConfBench is nice and an important measurement of model fidelity with deep practical significance within the drug-discovery process.\n\nWeaknesses:\n1. The paper is not very detailed on the math or algorithms in the main text. E.g., details for “incorporating optimal transport principles” by adding “a simulation-free symmetry correction module to straighten the conditional flow trajectories that connect the prior samples and ground truth structures” (L82-86). This is a significant component that could be an impactful contribution to the field; it should be described with equations, as should training losses in much greater detail than is included in S.2 Flow matching (eqn 2). This would greatly increase the clarity, quality, and significance of the work and overall rating \n2. Related to 1., the organization and presentation of the paper is lacking. Direct comparison to AF3 architectural, algorithmic, and training components in the main text would be helpful to increase understanding of the novelty of what is proposed. An outline that presents such advancements in a stepwise fashion and points to the results that demonstrate their significance (with equations) would increase the significance and originality of the work\n3. Related to 1. and 2., the overall clarity of the work is lacking. Pointers to specific data and descriptions of exact experiments that tested hypotheses and describe exactly which data was assessed and why would increase clarity. For example, the ConfBench experiments are difficult to understand. There is very little detail on what subset of the benchmark is used to create the data in Figure 4. Specifically, what set does the, e.g., “n=90” refer to in the bar charts? Further, I don’t understand how the measurement of “Apo Proteins” in Figure 4D is conducted. Are these just the raw prediction results for the proteins in the curated dataset without bound ligands (i.e., in their apo state)? If so, why are the results substantially lower than the “Proteins.Monomers” results in Table 1, which would refer to the same type of experiment? Finally and given this, was there any analysis done to understand the distribution shift from training data of NP3 to the ConfBench set, either apo or holo? Is the majority of the ConfBench set actually a subset of training data?\n4. Qualitative results are lacking. Including visualizations of predicted and true complexes (protein-ligand, PPIs, etc.) generated by NP3 in comparison to AF3 or AF-M would increase the significance of the work and give confidence that the quantitative PB results that suggest NP3 complexes are accurate and physically plausible bear out in practice with interesting and significant interactions visible in predicted complexes", "was_revised": true, "final_justification": "The authors responses to weaknesses noted and questions raised resulted in increased clarity and understanding of the originality of the work. Each score was increased accordingly, and the overall rating increased to \"Accept\"", "rebuttal": "We appreciate the reviewer’s thoughtful evaluation and constructive feedback. Each weakness and question raised by the reviewer is reproduced in block quotes, followed by our responses in plain text.\n\n> Weakness 1: The paper is not very detailed on the math or algorithms in the main text. E.g., details for “incorporating optimal transport principles” by adding “a simulation-free symmetry correction module to straighten the conditional flow trajectories that connect the prior samples and ground truth structures” (L82-86). \n\nWe agree and will clarify on this point. In the revised manuscript, we will augment the relevant section (L82–86) with supporting information. Specifically, we incorporate a simulation-free symmetry correction module motivated to align the conditional flow trajectories with displacement interpolation paths that approximate the OT geodesics between the prior and target distributions. The details are as follows:\n\n\n|  Symbol | Meaning                                                                                                                       |\n| :--------------------------------------------------: | :---------------------------------------------------------------------------------------------------------------------------- |\n| $x_T$ | Noisy prior sample drawn at diffusion timestep $T$   |\n|  $\\hat{x}_0$| One‑step denoised coordinates predicted from $x_T$  |\n|  $x$   | Ground‑truth (noise‑free) label structure  |\n| $\\mathcal{D}= \\{\\mathcal{D}_1,\\dots,\\mathcal{D}_m\\}$ | Set of entity groups; each $\\mathcal{D}_k$ contains indices of chemically identical (indistinguishable) chains or ligands |\n|                 $\\mathrm{RMSD}(a,b)$  | Root‑mean‑square deviation between coordinate sets $a,b$ |\n|   $\\mathbf{R},\\mathbf{t}$| Rotation matrix and translation vector returned by Kabsch alignment  |\n|  $\\mathbf{P}$| Block‑diagonal permutation matrix acting inside each $\\mathcal{D}_k$  |\n\n---\n\n1. Denoise the prior with pre-computed conditoning: $\\hat{x}_0 = f (x_T,T)$\n\n2. Rigidly align each indistinguishable entity. For every entity group $\\mathcal{D}_k$:\n\n   1. For each index pair $(i,j)\\in\\mathcal{D}_k\\times\\mathcal{D}_k$ (e.g., $(0,0),(0,1),\\dots,(2,1)$ when entities $0,1,2$ are identical):\n\n      * Compute $(R_{ij},t_{ij})=\\mathrm{Kabsch}(\\hat{x}_0^{(i)},x^{(j)})$.\n      * Obtain an *aligned* label copy $ x^{(j)*} = R_{ij}x^{(j)} + t_{ij}.$\n\n   2. Greedy in‑group permutation search (c.f. doi:10.1101/2021.10.04.463034, section 7.3):\n      For all entity group $\\mathcal{D}_l$, choose the permutation $\\pi_l^\\star$ that minimises\n\n      $$\n        \\sum_{i\\in\\mathcal{D}_l}\\mathrm{RMSD} \\bigl(x^{\\bigl(\\pi_l(i)\\bigr)*},\\hat{x}_0^{(i)}\\bigr).\n      $$\n\n3. Global objective:\n   For each global alignment $\\bigl(R_{ij},t_{ij}\\bigr)$, compute\n\n   $$\n     \\mathrm{RMSD}_{\\text{tot}} = \\mathrm{RMSD}\\bigl(\\mathbf{P}x^{*},\\hat{x}_0\\bigr).\n   $$\n\n   Retain the permutation/alignment pair $\\bigl(P^\\star,\\{R_{ij}^\\star,t_{ij}^\\star\\}\\bigr)$ with the lowest $\\mathrm{RMSD}_{\\text{tot}}$.\n\n4. Apply the optimal permutation to the label.\n\n   $$\n     \\tilde{x}=\\mathbf{P}^\\star\\,x.\n   $$\n\n5. Final alignment applied to the prior:\n   Align the permuted label $\\tilde{x}$ to the *original noisy sample* $x_T$ (optional when using SE(3)‑invariant losses):\n\n   $$\n     \\bigl(\\mathbf{R}_T,\\mathbf{t}_T\\bigr)=\\mathrm{Kabsch}\\left(\\tilde{x},x_T\\right),\n     \\qquad\n     \\tilde{x}^{\\prime} = \\mathbf{R}_T\\tilde{x} + \\mathbf{t}_T.\n   $$\n\nThe resulting $\\tilde{x}^{\\prime}$ (or $\\tilde{x}$ in an invariant setting) is used as the target in the flow‑matching loss, reducing the transport cost between the prior and target data distribution and maintain a consistent frame across the sampling iterations.\n\nIn the revised manuscript, we will also include an additional algorithm subsection to clarify the implementation of this module.\n\n> Weakness 2: Related to 1., the organization and presentation of the paper is lacking. Direct comparison to AF3 architectural, algorithmic, and training components in the main text would be helpful to increase understanding of the novelty of what is proposed.\n\nWe agree that more explicit comparisons with AlphaFold 3 would improve the clarity and impact of our presentation. Our architectural, algorithmic, and training improvements over AlphaFold 3 are as follows:\n\n* Architecture: MSA and Pairformer are used by both models. We condition additional on protein and RNA language model embeddings. From scaling studies (Figure S4), we identified a different pareto-optimal choice for encoder / decoder size. We also using sliding window attention instead of ad-hoc block-based operations for token-to-atom communication.\n\n* Algorithms: We employ flow matching to allow sampling from any prior distribution, and introduce a novel physics-based prior (Algorithm S3). We do not use AlphaFold 3’s hand-crafted positional encoding among entities and atoms. \n\n* Conditioning: NeuralPLexer3 does not rely on reference RDKit conformers, allowing it to encode molecules of all chemistries.\n\n* Training components: No training-time mini-rollout is needed because of the prior alignment step, which dramatically reduces the complexity of the training pipeline.\n\n* Evaluation: We introduce better benchmarks for physical plausibility and conformational change. Unlike AlphaFold 3, we have made the code and structures for these benchmarks available.\n\n* Optimization: We introduce a fused triangular attention kernel absent in AlphaFold 3.\n\n> Weakness 3: Related to 1. and 2., the overall clarity of the work is lacking. Pointers to specific data and descriptions of exact experiments that tested hypotheses and describe exactly which data was assessed and why would increase clarity. For example, the ConfBench experiments are difficult to understand. There is very little detail on what subset of the benchmark is used to create the data in Figure 4. Specifically, what set does the, e.g., “n=90” refer to in the bar charts? Further, I don’t understand how the measurement of “Apo Proteins” in Figure 4D is conducted. Are these just the raw prediction results for the proteins in the curated dataset without bound ligands (i.e., in their apo state)? If so, why are the results substantially lower than the “Proteins.Monomers” results in Table 1, which would refer to the same type of experiment? Finally and given this, was there any analysis done to understand the distribution shift from training data of NP3 to the ConfBench set, either apo or holo? Is the majority of the ConfBench set actually a subset of training data?\n\nWe appreciate the reviewer’s comments. In Figure 4, n=90 refers to the number of apo–holo structure pairs that had AlphaFold 2 and NeuralPLexer3 structures available and that met ConfBench criteria: global or pocket RMSD change >1.5 Å. These represent a subset of PLINDER-derived complexes curated to measure meaningful ligand-induced conformational changes. Unlike Table 1, which reports standard fold similarity metrics (e.g., TM-score, LDDT) on diverse targets regardless of conformational state, ConfBench assesses relative accuracy of choosing the correct state (apo vs. holo) using a normalized, symmetric score insensitive to rigid-body shifts. “Apo Proteins” in Figure 4D shows ConfBench scores for NeuralPLexer3 predictions on apo structures, benchmarked against both apo and holo references; lower values compared to Table 1 reflect the greater difficulty of this task and stricter evaluation. Importantly, ConfBench ensures at least one structure in each apo/holo pair is held out from training, mitigating data leakage.\n\n> Weakness 4: Qualitative results are lacking. Including visualizations of predicted and true complexes (protein-ligand, PPIs, etc.) generated by NP3 in comparison to AF3 or AF-M would increase the significance of the work and give confidence that the quantitative PB results that suggest NP3 complexes are accurate and physically plausible bear out in practice with interesting and significant interactions visible in predicted complexes\n\nThank you for the suggestion. In the revised manuscript, we plan to include (1) examples from Posebusters, where AlphaFold 3 predicted the incorrect chirality while NeuralPLexer3 predicted the correct chiral center, and (2) examples where AlphaFold 2-Multimer and AlphaFold 3 predicted the wrong (apo v.s. holo) conformation while NeuralPLexer3 correctly predicted the conformational difference. In compliance with the rebuttal guideline this year, we omit images from this author response.\n\nIn addition, NeuralPLexer3 predictions corresponding to all structures in Figure 1, Table 1, and Figure 4 will be made available on Zenodo.\n\n\n> Question 1: See Weaknesses 3. for several questions\n\nPlease see our response to weakness 3 above.\n\n\n> Question 2: How are symmetry-correction and optimal rigid structure alignment modules applied at test time, i.e., without ground-truth structures?\n\nAt test time, these modules are only applied between subsequent steps of the roll-out trajectory. That is, we attempt to keep each step geometrically and permutationally matched to the previous step. This results in straighter trajectories that may otherwise have been confounded by identical polymer chains and/or permutational symmetry within chains.\n\n> Question 3: Where is the data that the percentages quoted in lines 237-244 refers to? I don't see those numbers in Figure 4\n\nWe thank the reviewer for pointing out this typo on lines 237-244. The correct values are listed in the Figure 4D. These typos will be fixed in the revised manuscript."}, {"review_id": "sS4CgXPfiB", "reviewer": "Reviewer_ZJv9", "summary": "The paper tackles the challenge of predicting three-dimensional structures of biomolecular complexes, such as protein–ligand and protein–protein assemblies, with high physical realism and speed. Experimental methods deliver accurate structures but are slow and resource-intensive.  To address this, the authors present NeuralPLexer3 (NP3), a flow-based generative model. NP3 uses optimal-transport-driven training with a symmetry-correction module to enforce realistic bond geometries, and an anchor-based encoder–decoder that first refines key anchor atoms before expanding to all heavy atoms via geometry-aware attention. Hardware-aware optimizations enable inference in seconds on a single GPU. Benchmarks show NP3 outperforms AlphaFold3 and earlier NeuralPLexer versions on PoseBusters and ConfBench, achieving higher docking success and conformational accuracy.", "questions": "1.\tThe authors emphasise that alternatives such as AF3 produce unrealistic torsion angles or bond lengths. Often AF3 structures are post processed and optimised using force fields which are fast and readily available. Could the authors compare their models performance to using this common AF3 pipeline.\n2.\t Would it be possible to also compare to Boltz-2?", "limitations": "-", "rating": 5, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "1.\tClear descriptions of the problem and architecture. \n2.\tTable 1 could be presented more clearly. Could the authors bold best performing models \n3.\tThe figures are clear and informative. \n4.\tThe choice of the range of y axis on figure 1B is misleading.\n5.\tThe reviewer does not have enough domain expertise to judge the significance of this work. How significant are the minor (eg Table 1 Pose Buster) improvements in accuracy. Does this correspond to a significant improvement of downstream tasks?", "was_revised": true, "final_justification": "The authors have responded to all comments and clarified some points. The score has been improved due to comments to other rebuttals. The difference between NP2 vs NP3 is more clear.", "rebuttal": "We appreciate the reviewer’s thoughtful evaluation and constructive feedback. Each weakness and question raised by the reviewer is reproduced in block quotes, followed by our responses in plain text.\n\n_In response to the strengths and weaknesses,_\n\n> Weakness 2: Table 1 could be presented more clearly. Could the authors bold best performing models\n\nThank you for this suggestion. In the revised version, we will indicate the best performing model for each evaluation metric and task category in boldface.\n\n\n\n> Weakness 4: The choice of the range of y axis on figure 1B is misleading.\n\nWe agree and intend to introduce an axis break to improve clarity in future versions of the manuscript. We feel that it is important to remain zoomed-in on this scale in the second panel of Figure 1B. Stereochemistry must be preserved for these models to be useful in drug discovery. In our experience, structure-based drug design scientists demand 100% correct stereochemistry.\n\n\n\n> Weakness 5: The reviewer does not have enough domain expertise to judge the significance of this work. How significant are the minor (eg Table 1 Pose Buster) improvements in accuracy. Does this correspond to a significant improvement of downstream tasks?\n\nImprovement of PoseBusters accuracy is itself one downstream task. Co-folding models are intended to reduce the need for structural experiments, and the read-off of these experiments is the protein-ligand structure. The key metric \"% RMSD < 2 Å and PB-valid\" is particularly important for downstream tasks because it requires structures to be both geometrically accurate AND physically reasonable (PB-valid). As shown in Figure 1B, NeuralPLexer3 achieves a 5.6% absolute improvement (77.9% vs 72.3%) compared to AlphaFold3. The combination of improved accuracy AND physical realism makes these gains particularly valuable for practical drug discovery applications where both geometric precision and chemical plausibility are essential.\n\nFor other downstream tasks, PoseBusters accuracy is at least well correlated with performance. For example, we find that the ability of the model to recapitulate protein ligand interactions (hydrogen bonds, salt bridges, pi-pi stacking, etc) is linearly correlated with the logarithm of the ligand RMSD measured in Posebusters. \n\nAs for the question of significance, we believe that the results we report are a meaningful improvement over AlphaFold 3. An even greater advancement compared to AlphaFold 3 is the far faster inference speed shown in the third panel of Figure 1B. Our faster model can screen more chemical space and enables semi-interactive design.\n\n\n\n_Regarding the reviewer’s questions,_\n\n>Question 1: The authors emphasise that alternatives such as AF3 produce unrealistic torsion angles or bond lengths. Often AF3 structures are post processed and optimised using force fields which are fast and readily available. Could the authors compare their models performance to using this common AF3 pipeline.\n\nWe agree that a force-field pipeline can sometimes be used to clean up structures. However, these cleanup steps are expensive compared to the inference cost of NeuralPLexer3, requiring about 30s seconds on an L40S GPU. Force-field cleanup can also be brittle, as it requires force fields that are parameterized to the system of interest. Finally, force fields are sensitive to unphysical initial structures, and their minimization can diverge, especially in cases where bond lengths are too short.\n\nPoseBench (arXiv:2405.14108v5) benchmarked the effect of force field relaxation on PoseBusters physical validity for multiple models including AlphaFold 3. Their results are mixed. In some tests (Figs 2, 4, G15, and G21), force field relaxation of AlphaFold 3 predictions offers small improvements to physical validity. In other tests (Figs 3, G17, and G25), force field relaxation results in worse physical validity. (Please note that “NeuralPLexer” refers to the model described in doi:10.1038/s42256-024-00792-z and not to NeuralPLexer3 as described in this work.)\n\n\n\n> Question 2: Would it be possible to also compare to Boltz-2?\n\nAt the time of submission, Boltz-2 had not been announced.\n\nBoltz-2's training set included all Posebusters samples. Its training date cutoff for PDB structures was June 1, 2023. Moreover, Boltz-2 have not released their evaluation code corresponding to the custom benchmark reported in their manuscript, so it is yet not possible to make a fair comparison.\n\nTo facilitate comparisons with current and future models, we have published all of our benchmark code (included in the SI) as well as our corresponding structure predictions. (The structure predictions are not included in the submission packet as they are hosted on Zenodo with author-identifying information.)"}, {"review_id": "TUwnJ2Y1qP", "reviewer": "Reviewer_VFzv", "summary": "This work proposes NeuralPLexer3, a generative model for biomolecular complex structure prediction. Many innovations are adopted to improve the accuracy and efficiency of the model over its predecessor, including physics-informed prior, flow-based objective and OT permutation, customized triangular attention kernel etc. The authors also propose new benchmark suites called NPBench and ConfBench to better evaluate the performance of structure-prediction models. Overall, this is a comprehensive and solid paper.", "questions": "Below are some questions and comments I have:\n\n1. Mis-predicted chirality is indeed a problem in AF models. The authors show that the NeuralPLexer3 is doing better than AF3 on this front. Which component in NP3 contributes the most to alleviating the chirality problem?\n1. The physics-informed prior from running Langevin dynamics is very interesting. The critical components of the drift are the bond, entity, and residue matrices $S$. Can authors elaborate on how they are constructed? \n1. From the result, it seems like the PoseBuster benchmark evaluates the ligand RMSD? It would be nice to also evaluate the receptor RMSD since the NP3 and some other baselines are co-folding models. \n1. Ablation study: There is no ablation study about the novel prior. I am very curious about how the prediction accuracy would change if simple Gaussian prior is used. \n1. Releasing the kernel for triangular attention can be highly valuable to the field. \n1. One important concern is that the manuscript is not comparing NP3 to many other open-sourced strong baselines such as the family of Botlz and Chai. Admittedly, NP3 scores very high on many evaluation tasks, but the authors can surely also evaluate those baselines on new benchmarks proposed in this work.", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strength**\n1. NeuralPLexer3 is a structure prediction model with strong performance and faster sampling speed.\n1. New comprehensive benchmarks are highly useful for the entire field if made publicly available. \n1. Some interesting innovations such as the physics-informed prior are proposed.\n1. Customized triangle attention can be valuable if also open-sourced.\n\n**Weakness**\n1. Some details can be better elaborated (See Questions) and more ablation study can be added for demonstration the effectiveness of some innovations.\n1. Lack of comparison to other open-sourced strong baselines such as the series models of Boltz and Chai.", "was_revised": true, "final_justification": "Great paper with substantial experiments. Suggest to accept.", "rebuttal": "We appreciate the reviewer’s thoughtful evaluation and constructive feedback. Each weakness and question raised by the reviewer is reproduced in block quotes, followed by our responses in plain text.\n\n_In response to the reviewer’s questions,_\n\n> Question 1: Mis-predicted chirality is indeed a problem in AF models. The authors show that the NeuralPLexer3 is doing better than AF3 on this front. Which component in NP3 contributes the most to alleviating the chirality problem?\n\nWithin the scope of this work, we do not have definitive evidence isolating any one factor. We believe that the primary drivers are:\n\n1. the use of flow matching with symmetry correction described on lines 82-86 of the main text, lines 519-524 of the SI, and in Algorithm S1;\n\n2. the inclusion of smoothed frame-aligned point error during training (Algorithm S2, L11), which assigns a greater penalty to violations of local molecular geometry;\n\n3. the selection of sampled poses from all rollouts at inference time based on an approximate energy model (Figure 2B, Section S.5 of the SI).\n\n> Question 2: The physics-informed prior from running Langevin dynamics is very interesting. The critical components of the drift are the bond, entity, and residue matrices.Can authors elaborate on how they are constructed?\n\nThe drift terms are constructed based on an idealized Gaussian polymer model. The values are selected such that the standard deviation of atom positions within each component is approximately 2Å for each bonded atom pair, 5Å for each residue, and 8Å for each biopolymer entity.\n\nTo understand the construction of the adjacency matrices, $S$, note that NeuralPLexer3 operates at two scales: anchors and atoms. Starting with atoms, $S_{bond}$ is a connectivity matrix for chemical bonds. Its entries are 1 and 0 corresponding to the presence and absence of bonds, respectively. For small molecule ligands, bond connectivity is provided as input. For amino acids, nucleotides, etc, bond connectivity is looked up in the Chemical Component Dictionary.\n\nAnchors correspond to amino acid residues, nucleotides, and small molecule heavy atoms. In addition, there are anchors for other miscellaneous monomers such as non-natural amino acids. We refer to all of these objects as “residues”. The $S_{residue}$ matrix has entries of 1 for consecutive anchors in the same biopolymer and 0 otherwise.\n\nFinally, “entities” refer to biopolymer chains, and the $S_{entity}$ matrix introduces a spring between each atom to the centroid coordinate of the entity it belongs to.\n\nThe result of this process is illustrated in the upper left of figure 1A. The physics-informed prior looks like globular clouds for each chain, with some incomplete separation between chains.\n\n\n\n> Question 3: From the result, it seems like the PoseBuster benchmark evaluates the ligand RMSD? It would be nice to also evaluate the receptor RMSD since the NP3 and some other baselines are co-folding models.\n\nPoseBusters evaluates the ligand RMSD after aligning the test and reference structures on the pocket. So, it implicitly tests for correct positioning of the ligand in the protein pocket in addition to explicitly measuring internal ligand structure. \n\nWe find that the PoseBusters (pocket-aligned ligand) RMSD is correlated with pocket RMSD, with a correlation coefficient R=0.7. The pocket RMSD is less than 2Å in 90% of PoseBusters structures.\n\n\n\n> Question 4: Ablation study: There is no ablation study about the novel prior. I am very curious about how the prediction accuracy would change if simple Gaussian prior is used.\n\nThis is a good point, and we did not carefully test a simple Gaussian prior. As this requires expensive model retraining, we reserve this exact experiment for a future work. \n\nMeanwhile, because we choose to not include the hand-crafted entity positional encoding from AlphaFold 3 to break symmetry, we anticipate that an isotropic Gaussian prior will lead to degenerate and qualitatively wrong behavior for symmetric assemblies such as protein homodimers. This behavior has been observed in Boltz-1 (doi:10.1101/2024.11.19.624167, Figure 7).\n\n\n\n> Question 5: Releasing the kernel for triangular attention can be highly valuable to the field.\n\nWe fully agree and appreciate the reviewer’s recognition of the potential impact of our Flash-TriangularAttention implementation. However, we choose not to release the code at this time.\n\nWe are encouraged by the community’s recent development of efficient triangular kernels, including Trifast (doi:10.1101/2024.11.19.624167), `triangle_attention` and `triangle_mutiplicative_update` in Nvidia’s cuEquivariance library, and the GPU MODE triangular multiplicative update competition.\n\n\n\n> Question 6: One important concern is that the manuscript is not comparing NP3 to many other open-sourced strong baselines such as the family of Boltz and Chai. Admittedly, NP3 scores very high on many evaluation tasks, but the authors can surely also evaluate those baselines on new benchmarks proposed in this work.\n\nWe are currently working on comparison to Boltz-2 and Chai-1. There are challenges: this is computationally expensive, we want to ensure fair comparison, and sometimes these models permute atom order, requiring careful checking and postprocessing of outputs. \n\nWith the submitted work, we have published the code and reference structures corresponding to our benchmarks to facilitate comparison with future models. We have also published corresponding NeuralPLexer3 predictions. (The structure predictions are not included in the submission packet as they are hosted on Zenodo with author-identifying information.)\n\nFurther, we would point the reviewer to PoseBench (arXiv:2405.14108v5), which makes comparisons between AlphaFold 3 and Chai-1 among other methods. (Please note that “NeuralPLexer” refers to the model described in doi:10.1038/s42256-024-00792-z and not to NeuralPLexer3 as described in this work.)"}, {"review_id": "OSRqh2fYHS", "reviewer": "Reviewer_E3XT", "summary": "This paper introduces NeuralPLexer 3 (NP3), a conditional flow-matching model that couples a physics-motivated globular-polymer prior with symmetry-corrected flows and a custom Flash-TriangularAttention kernel. NP3 delivers ligand-to-protein complex structures in ≈30 s on a single L40S GPU, while achieving. competitive performance across proteins, nucleic‐acids, PTMs and covalent ligands. Two new evaluation suites，NPBench and ConfBench are released to measure generalisation and ligand-induced conformational change, where NP3 outperforms AlphaFold-Multimer on pocket motions.", "questions": "There remain some areas of ambiguity that raise concerns regarding the clarity and completeness of the work.\n\n1) Have the authors systematically evaluated (or at least approximately assessed, given computational constraints) the contribution of each modality, such as MSAs, protein language models, and RNA-specific models, to the final performance?\n\n2) The claimed speed advantage over AlphaFold3 is compelling, but was the comparison conducted on the same hardware setup? A fair, hardware-consistent comparison would significantly strengthen this claim.\n\n3) What are the guiding principles behind the selection of sampling steps, algorithmic parameters, and physics-inspired priors? These choices appear somewhat ad hoc and could benefit from further justification or ablation.\n\n4) The authors state that the method \"excels in areas crucial to structure-based drug design,\" but this claim lacks clear empirical support. Could the authors provide more quantitative evidence to substantiate this assertion?", "limitations": "yes.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n1）By integrating physics priors and multiple molecular modalities (proteins, ligands, nucleic acids, PPIs) and multiple useful information (MSAs, PLM information) it directly mitigates the “unphysical hallucination” problem common to diffusion/flow generators and incorporates recent gains from modern structure-prediction models.It also reflects several recent advances in structure prediction, making it a valuable reference for future work in this area.\n\n2) The introduction of two new benchmarks, NPBench and ConfBench, represents a meaningful contribution to the evaluation of molecular and structural modeling methods.\n\n3) The manuscript is well-written, and the figures and tables are of high quality.\n\nWeakness:\n1) There are several minor issues that detract from the polish of the manuscript, such as inconsistent naming between “NP3” and “NPv3,” and formatting problems like the font size in Table 1.\n\n2) The training data is only described at a high level (e.g., “all PDB entries before September 2020” and synthetic datasets), and the authors note that model weights will not be released due to dual-use concerns. In addition, important implementation details—such as the custom Triton kernel code and hyperparameters—are proprietary, which limits reproducibility and independent validation.\n\n3) The novelty over NP2 appears to be incremental. A more detailed comparison and clarification of the specific improvements would be helpful to better assess the contribution.\n\n4) The scope of model comparison is relatively limited. For instance, in the nucleic acid category, only the performance of NP3 is discussed, without comparisons to other relevant baselines.", "was_revised": true, "final_justification": "After considering the paper and the author rebuttal, I confirm a final rating of 5. And I think 5 best reflects the current contribution.", "rebuttal": "We appreciate the reviewer’s thoughtful evaluation and constructive feedback. Each weakness and question raised by the reviewer is reproduced in block quotes, followed by our responses in plain text.\n\n_In response to the weaknesses,_\n\n> Weakness 1: There are several minor issues that detract from the polish of the manuscript, such as inconsistent naming between “NP3” and “NPv3,” and formatting problems like the font size in Table 1.\n\nThank you for pointing out these formatting issues. We will address these concerns in the revised manuscript.\n\n\n\n> Weakness 2: The training data is only described at a high level (e.g., “all PDB entries before September 2020” and synthetic datasets), and the authors note that model weights will not be released due to dual-use concerns. In addition, important implementation details—such as the custom Triton kernel code and hyperparameters—are proprietary, which limits reproducibility and independent validation.\n\nFor training data, we used all PDB entries before September 2020, which includes a wide range of protein structures. We also generated synthetic datasets to augment the training data. While we understand the importance of reproducibility, we are currently unable to release the model weights due to dual-use concerns. However, we are committed to providing detail about our methodology and implementation in the revised manuscript.\n\nDue to the proprietary nature of model weight of our custom Triton kernel code, we are unable to release these details at this time.\n\n\n\n> Weakness 3: The novelty over NP2 appears to be incremental. A more detailed comparison and clarification of the specific improvements would be helpful to better assess the contribution.\n\nThank you for the suggestion. We will include a section in the revised manuscript to highlight improvements made between NeuralPLexer2 and NeuralPLexer3. Among all technical differences, the most notable changes are:\n\n1. NeuralPLexer2 is a diffusion-based model using an equivariant graph-based denoising decoder, based on a continual development of the original NeuralPLexer model (doi:10.1038/s42256-024-00792-z). NeuralPLexer3 instead is a flow matching model with a multimodal conditioning module and a conditional diffusion transformer decoder.\n\n2. NeuralPLexer2 employs a Gaussian prior while NeuralPLexer3 employs a more physical globular polymer prior (described in Algorithm S3).\n\n3. Compared to NeuralPLexer2, NeuralPLexer3 is trained with greatly expanded training data and model size, and shows substantially improved performance.\n\n\n\n> Weakness 4: The scope of model comparison is relatively limited. For instance, in the nucleic acid category, only the performance of NP3 is discussed, without comparisons to other relevant baselines.\n\nA direct comparison for the nucleic acid category was challenging, and we decide to omit a extensive comparison to baselines within the scope of this work. At the time of submission the only work reporting accuracy for low-homology RNA-including structures is AlphaFold 3, and we do not have a license to run their code in order to reproduce their results. The best non-deep-learning baseline, Alchemy-RNA2, requires additional human expert inputs.\n\nTo facilitate fair evaluation of structure prediction models on all molecular modalities in this field, we will make all benchmarking entries and model evaluation code public.\n\nWe find that NeuralPLexer3's RNA and protein-RNA interaction prediction performance is overall far from experimental accuracy, which is unsurprising given that (1) the diversity of solved RNA structures in the PDB is limited and (2) we did not include domain-specific features such as RNA secondary structure.\n\n\n\n_In response to the reviewer’s questions,_\n\n> Question 1: Have the authors systematically evaluated (or at least approximately assessed, given computational constraints) the contribution of each modality, such as MSAs, protein language models, and RNA-specific models, to the final performance?\n\nThese conditioning signals are critical for model performance. The PDB is a comparatively small dataset (~250,000 structures). Cofolding models can be interpreted as learning the relationship between evolutionary signal (MSA, PLM) and structure.\n\nRemoval of protein MSA resulted in a drop in Posebusters pass rate from ~78% (Figure 1B) to ~27%. Use of more approximate MSA (MMSeqs2 on the ColabFold database) resulted in a pass rate of ~74%. We did not train NeuralPLexer3 to be robust to the removal of MSA.\n\nPoseBench (arXiv:2405.14108v5) examines the role of MSA in AlphaFold 3 and Chai-1, and reports similar accuracy loss upon the removal of MSA. See Figure 2 and note that “single-seq” is the no-MSA condition.\n\nNeuralPLexer3 has limited accuracy for RNA structure prediction, which remains an ongoing challenge in the field. In this work, we show that our model trained on RNA language model features are similar in accuracy to existing models trained on RNA MSA.\n\n\n\n> Question 2: The claimed speed advantage over AlphaFold3 is compelling, but was the comparison conducted on the same hardware setup? A fair, hardware-consistent comparison would significantly strengthen this claim.\n\nWe do not have license to run AlphaFold 3, so we cannot provide a perfectly controlled comparison. To address this, we run NeuralPLexer3 on the comparatively weaker L40S GPU and compare to AlphaFold 3’s reported timings on the A100 GPU.\n\nNeuralPLexer3 is around 20x faster on an L40S than is AlphaFold 3 on A100s (as reported in doi:10.1038/s41586-024-07487-w) for a 1024-residue protein. The majority of the compute is done in 16-bit precision, for which the maximum throughput is 300 TFlops for A100 and 180 TFlops for L40S. So even though AlphaFold 3 had a hardware advantage in this comparison, NeuralPLexer3 still exhibits a large speed advantage. \n\n\n\n> Question 3: What are the guiding principles behind the selection of sampling steps, algorithmic parameters, and physics-inspired priors? These choices appear somewhat ad hoc and could benefit from further justification or ablation.\n\nTraining of the NeuralPLexer3 model was expensive compared to our computational resources, requiring the use of our cluster for a full month. While we tested many parameters and architectures at small scale, we found that these results often did not translate to the full-scale model. (For example, we found that an equivariant decoder was preferred at small scale, but not at full scale.) As a result, the development of the model was indeed ad hoc in many places. \n\nIn the manuscript, we present two cases where we were able to confidently extrapolate conclusions from small scale to full scale. \n\n1. In Figure 2B, we provide a sequential set of improvements to the model and report the performance of each added improvement.\n\n2. In Figure S4, we report scaling curves for the model, varying the size of the encoder and decoder as well as the number of decoder replicas during training.\n\nWe hope that these cases will be helpful and transferable in future model design.\n\nWe note that better hyperparameters are possible, and their determination is an interesting future direction. Two important areas that we have not exhaustively investigated:\n\n1. Physics-inspired priors: our current choice of prior is certainly important to break symmetry e.g. in the case of protein homodimers. In our small-scale experiments, it was also found to substantially improve training stability when the FAPE loss is included. However, we have not examined the relationship between the quality of the prior and model accuracy.\n\n2. Number of sampling steps and noise schedule: we have anecdotally found our current number of sampling steps to be more than sufficient. We have not carefully examined the tradeoff between sampler parameters and downstream accuracy. \n\n\n\n> Question 4: The authors state that the method \"excels in areas crucial to structure-based drug design,\" but this claim lacks clear empirical support. Could the authors provide more quantitative evidence to substantiate this assertion?\n\nWe would point to the PoseBusters results presented in Figure 1B. PoseBusters (doi:10.1039/D3SC04185A) represents the current standard benchmark for structure-based drug design. In Figure 1, the authors report that traditional docking methods GOLD and Vina have success rates of 55% and 58% respectively, while requiring the ground-truth receptor structure as input. NeuralPLexer3 has a 78% success rate at this benchmark. NeuralPLexer3 is substantially faster than similar co-folding methods (AlphaFold 3, Chai-1, Boltz-2), which gives it greater screening power and enables interactive use."}]

Author rebuttal:

Meta-review: This submission presents NeuralPlexer3, an all-atom structure prediction model. The reviewers appreciated the architectural advances, the implementation of Flash-Triangular attention, strong performance, and thorough benchmarks, some of which are novel and significant in themselves. Reviewer concerns largely centered around clarity, organization, and presentation and comparisons to AF3. Discussions mainly focused on resolving these clarity concerns, with two reviewers raising the score and two others maintaining a positive rating. Altogether, the reviewer consensus is a clear accept.
Decision: Accept (poster)