All-atom inverse protein folding through discrete flow matching
Authors: Kai Yi
Kiarash Jamali
Sjors HW Scheres
Venue: ICML 2025 poster (2025)
Keywords: discrete diffusion
inverse folding
proteins
nucleotides
ions
guidance
nmr
dynamic structure
Primary area: applications->health_medicine

Abstract: The recent breakthrough of AlphaFold3 in modeling complex biomolecular interactions, including those between proteins and ligands, nucleotides, or metal ions, creates new opportunities for protein design. In so-called inverse protein folding, the objective is to find a sequence of amino acids that adopts a target protein structure. Many inverse folding methods struggle to predict sequences for complexes that contain non-protein components, and perform poorly with complexes that adopt multiple structural states. To address these challenges, we present ADFLIP (All-atom Discrete FLow matching Inverse Protein folding), a generative model based on discrete flow-matching for designing protein sequences conditioned on all-atom structural contexts. ADFLIP progressively incorporates predicted amino acid side chains as structural context during sequence generation and enables the design of dynamic protein complexes through ensemble sampling across multiple structural states. Furthermore, ADFLIP implements training-free classifier guidance sampling, which allows the incorporation of arbitrary pre-trained models to optimise the designed sequence for desired protein properties. We evaluated the performance of ADFLIP on protein complexes with small-molecule ligands, nucleotides, or metal ions, including dynamic complexes for which structure ensembles were determined by nuclear magnetic resonance (NMR). Our model achieves state-of-the-art performance in single-structure and multi-structure inverse folding tasks, demonstrating excellent potential for all-atom protein design. The code is available at https://github.com/ykiiiiii/ADFLIP .

All- inverse protein folding through discrete flow matching
Kai Yi Kiarash Jamali
Sjors H. W. Scheres
Abstract
1. Introduction
The introduction of AlphaFold2 (Jumper et al., 2021) repre- sented breakthrough in the prediction of three-dimensional protein structures from amino acid sequence. AlphaFold2 also catalysed advances in de novo protein design, where one aims to design amino acid sequence that adopts given taree-dimensiona structure, in a process called in- verse protein folding (Dauparas et al., 2022). Combined with diffusion- methods to generate protein structures (Watson et al., 2023), inverse folding methods have opened new frontiers in the design of proteins with specific struc- tural and functional properties, with profound implications for enzyme engineering (Lauko et al., 2024), antibody devel- opment (Bennett et al., 2024), and therapeutic interventions (Glögl et al., 2024).
The recent breakthrough of AlphaFold3 in model- ing complex biomolecular interactions, including those between proteins and ligands, nucleotides, or metal ions, creates new opportunities for pro- tein design. In so-called inverse protein fold- ing, the objective is to find sequence of amino acids that adopts a target protein structure. Many inverse folding methods struggle predict se- quences for complexes that contain non-protein components, and perform poorly with complexes that adopt multiple structural states. To address these challenges, we present ADFLIP (All-atom Discrete FLow matching Inverse Protein fold- ing), a generative model based on discrete flow- matching for designing protein sequences condi- tioned on all-atom structural contexts. ADFLIP progressively incorporates predicted amino acid side chains as structural context during sequence generation and enables the design of dynamic pro- tein complexes through ensemble sampling across multiple structural states. Furthermore, ADFLIP implements training-fre free classifier guidance sam- pling, which allows the incorporation of arbitrary pre-trained models to optimise the designed se- quence for desired protein properties. We evalu- ated the performance of ADFLIP on protein com- plexes with mmollemolecule ligands, nucleotides, or metal ions, including dynamic complexes for which structure ensembles were determined by nuclear magnetic resonance (NMR). Our model achieves ofte-ooftthe-rt performance in single- structure and multi-structure inverse folding tasks, demonstrating excellent potential for all-atom pro- tein design. The code is available at https: / //github... com/ htmm///iiiiii/AA//...
Because AlphaFold2 only considered proteins, most pro- tein design efforts to date have also focused on structures that exclusively comprise proteins. However, many bio- logical reactions that are necessary to sustain life employ much wider range of chemistry. For example, chemical modification of the amino acids that make proteins may be used to signal distinct functional states; the binding of small-molccule ligands in specific protein pockets often af- fects function; many proteins interact with nucleic acids that carry genetic information; and many chemical reactions are catalysed by metal ions that are bound to enzymes. Re- cently, AlphaFold3 (Abramson et al., 2024) expanded the prediction of biological structures beyond proteins by mod- elling complex assemblies that also include nucleic acids, small molecules, metal ions, and chemical modifications of amino acids. This advance in structure prediction again created parallel opportunities for inverse folding (Dauparas et al., 2023), but the design of amino acid sequences for biomolecular complexes that contain wide range of chem- ical entities remains more challenging than the design of proteins only.
An additional complication in protein design that many biomolecular complexes are also structurally dynamic. Much like machines in daily life, the functional cycle of such complexes involves multiple structural states, even though their amino acid sequence is fixed. Although current models for inverse folding perform relatively well on static protein structures, they often struggle with complexes that
'Equal contribution 'MRC Laboratory of Molecular Biol- ogy, Cambridge, UK. Correspondence to: Sjors H. W. Scheres <scheres wwweemrrem...memeemee lww.cam.ac..k>...
Proceedings of the 4 International Conference on Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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All-atom inverse protein folding through discrete flow matching
adopt multiple structural states, e-g. dynamic proteins that studied by solution-state nuclear magnetic resonance (NMR) (Nikolaev et al., 2024; Yi et al., 2024).
Discrete generative model Because mapping protein's s structure to its sequence represents one-to-many mapping task, the sampling strategy for sequence generation presents an important design choice. Protein sequences, unlike natu- ral language, do not have an inherent left-to-right ordering. Thus, although autoregressive generation (Ingraham et al., 2019; Hsu et al., 2022) was initially the dominant approach, various alternative sampling strategies have been proposed. ProteinMPNN (Dauparas et al., 2022) employs random or- dering for sequence generation, while PiFold (Gao et al., 2023b) predicts amino acid probabilities in one step with independent sampling at each position.
In this paper, we present ADFLIP: a discrete flow cow-matching model for generating protein sequences based on the struc- ture of bio-molecular complexes that can involve non- protein elements. As shown in Figure 1, ADFLIP generates sequences by jointly considering protein backbone struc- ture and non-protein elements, such as nucleotides, ligands, or metal ions, while progressively incorporating predicted amino acid side chains as structural context during sequence generation. Because amino acid side chains often provide the chemical entities that define specific interactions with other molecules, considering the full information of the side chains is crucial for designing protein-ligand interac- tions. Our approach employs a multi-scale graph neural network as the denoising backbone, integrating both atom and residue-level information. Our iterative flow-based sam- pling framework enables ensemble sampling across different structural states, and it facilitates the integration of guidance signals to steer sample generation toward desired outcomes. The resulting model allows the design of biomolecular com- plexes with diverse chemical entities that adopt multiple conformational states and with defined protein properties.
Discrete generative models have undergone major recent developments. Discrete diffusion models were first in- troduced by Austin et al. (2021) and Hoogeboom et al. (2021), enabling diffusion- based generation of categorical data through forward corruption processes with Markov transition kernels. Campbell et al. (2022) extended this to continuous time by formulating discrete diffusion through Continuous Time Markov Chains. Recently, two indepen- dent works by Campbell et al. (2024) and Gat et al. (2024) proposed discrete flow matching, providing a simpler frame- work that allows faster training convergence. Here, we fol- low the discrete flow matching setting proposed in Campbell et al. (2024).
2. Related work
3. Methods
Inverse protein folding Predicting a sequence of amino acids that folds to a given structure using machine learn- ing approaches was pioneered in (O'Connell et al., 2018; Wang et al., 2018), but the current paradigm of using graph neural networks (Dauparas et al., 2022; Hsu et al., 2022; Gao et al., 2023b; Yi et al., 2024; Zhu et al., 2024) was first proposed in (Ingraham et al., 2019). These methods typically encode the protein backbone as a graph and use graph neural networks to extract geometric information. Re- cently, SuriPro (Song et al., 2024) extended this approach by incorporating desired surface properties into the sequence design. Other methods, like LMdesign (Zheng et al., 2023) and KWdssign (Gao et al., 2023a), have leveraged both geometric information and information from evolutionarily related protein homologues through the combined use of structural information with protein language models. Saport (Su et al., 2024) introduced a structure-awar vocabulary to encode protein structures as discrete tokens, enabling general protein language models to generate sequences di- rectly from structures. While most existing methods focus on protein-only backbone structures, LigandMPNN (Dau- paras et al., 2023) broadened the scope of inverse folding by considering all-atom structures that also contain non-protein components like ligands, ions, and nucleotides.
ADFLIP is generative model po (S) with parameters 6, for protein sequence design that samples discrete pro- tein sequences S E {1,..., (1,...,00]+ conditioned on protein- complex structural inputs X {X protein; X non-protein ) where X presein E RLx4x3 represents the protein backbone coordinates of atoms (N, C, O). and protein E x is the non-protein structure components with m atoms, L is the length of protein sequence. During sam- pling, ADFLIP progressively incorporates side chain infor- mation x RLx4 while generating the sequence. ADFLIP consists of three key components: discrete flow model for protein sequence generation; a multi-scale graph neural network denoiser that captures both residuc-level and atom- level information; and a property guidance mechanism that enables controlled generation without model retraining.
3.1. Discrete flow model all-atom inverse folding
We construct the sequence generating probability flow Pt (s:) at time / that interpolates from a noise distribution po (8o) to the data distribution Pi (s1) (saa Since modelling Pt directly is complex, we instead define it through simpler conditional flow Pap (-Isı) that interpolates from noise to the target sequence. This conditional flow has closed form:
(s)((((ss) (s1) = Cat(t5(s), st) + (1 - -)6 sc)),
2

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All-atom inverse protein folding through discrete flow matching
t=0
t=0.5
t=0.99
XXXX
Sequence (kuly masked)
XTXVV
ADFLIP
(partally masked)
ADFLIP
(pardally masked)
ADFLIP
QLEVV
XEVGE
Figure 1. Overview of ADFLIP. ADFLIP is flow matching generative framework for protein sequence design. Starting from 0, progressively generates the protein sequence through sequential denoising using only the protein backbone and non-protein structure as inputs. The process hegins with all amino acid positions masked (X) and gradually unmasks them reveal the sequence. As amino acids are sampled, their corresponding side chain structures are predicted, providing additional structural context to guide subsequent denoising steps.
where m represents a mask token, t E [0, 1] is the time parameter, Cat is the categorical distribution, and o(i,j) f} the delta function. At 0, all positions are masked, while at t 1, the sequence matches the target $1. With the conditional flow model, define the marginal distribution by taking the expectation over the data distribution:
Sampling As shown Algorithm 1, we initialise all se- quence positions with mask tokens. Given N protein back- bone conformations and non-protein structure information, employ two-stage sampling process that integrates both sequence design and side chain packing, For each conformation, we first estimate the conditional probability y" (s1 (sx) using our denoising network fo. These individual predictions are then ensembled obtain a more robust esti- mate the sequence probability ps)) To generate the next sequence state, we compute the rate matrix Rg (Sc. j) by taking the expectation over the conditional rate matrix with respect to predicted [s:). The next sequence state is then sampled according to categorical distribution defined by the current state and the rate matrix.
pr = (p (Pe) (s& [s)].
To sample sequence from p(s), we need access rate matrix Rg that defines the frequency and destination of state transitions, with the constraint that its off off-diagonal elements are non-negative. The probability that state x, will jump to a different state for the next infinitesimal time step dt is R (st. The transition probability can be written as:
Although many existing protein inverse folding methods do not consider side chains, side chain-ligand interactions are often crucial for designing functional proteins. Therefore, perform side chain packing concurrently with sequence sampling (see Figure 1). For each sampled sequence 81, we predict its side chain conformations using a dedicated side chain packing network PIPPACK (Randolph & Kuhlman, 2024) that takes into account both the protein backbone and the current sequence state. Then, for positions where 8t contains mask tokens, we remove the corresponding side chain atoms maintain consistency between the sequence and structure representations. This iterative process con- tinues until t reaches 1, at which point we obtain our final sequence 81.
Pitsa)e(lss:) o(s j) + (s..
In practice, we simulate the sequence trajectory with finite time intervals At using Euler steps:
At ~ Cat( st+a + R, At). (1)
We represent the rate matrix Re(se, j) as an expectation over a simpler conditional rate matrix:
R₂ (s,,, j) pprs(erle)) [e(st,j(ss)],
where the conditional rate matrix has the form: R2 (s(.s)))s d(e.)tff..m) Here, (si((s)ss) is the de- noising distribution that predicts the clean sequence given the noisy sequence, which we approximate using a neural network.
I-t
We also propose an adaptive sampling scheme that takes advantage of the varying uncertainty amino acid predic- tions across different positions. Given backbone structure,
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All-atom inverse protein folding through discrete flow matching
Algorithm 1 ADFLIP Sampling Process
side chains. The neural network then extracts information both the atom and residue level to predict the probability dis- tribution over amino acids at each position $1. We optimise the network parameters using the cross-entropy loss:
Input:
N protein and non-protein structures (#1, ..., "N Initial sequence 80 = (m....,,m) m)) Initial side chains Xo =
Time step At
Denoising network Se. side chain packing network In Initialise =0 0 while < do for n = to N do Compute y" (8:) T(x
LCE = F P (LtO) [1gg (f St, x,, xt)
3.2. Multi-scale GNN denoiser
The GNN denoiser is a multi-scale network that aims to mix information between two different hierarchies - residues and their constituent atoms. It takes inspiration from Al- phaFold3 (Abramson et al., 2024) and LigandMPNN (Dau- paras et al., 2023). The GNN has two types of nodes: residue nodes and atom nodes. Each amino acid and nuclcotide is represented residue node, while each non-hydrogen atom is represented as an atom node. Residue features have information about the arrangement of residues in the wider context of the protein backbone, whereas local information about the arrangement of atoms is contained in atom fea- tures. The network divided into three main parts: an initial input embedding; multiple layers of processing on both the atom and residue features; and, finally, multiple decoding layers to translate the features to sequence prediction logits, Key to our approach is the information transfer between the atom and residue node types, as we alternate between the processing of local information on atom nodes and the processing of global context in residue nodes (Figure 2a).
end for
p(81)=
1 (3))) N
Sample 81 -p($1)
for n = to N do
Compute Xi = g(1, k.)
end for
Compute (s: (mls))))))))) (Ro
Sample S by Equation 1
6 1-1+A. A
end while
Return: Final sequence 81
many of the side chains inside the core of the protein have constrained amino acid choices due to the available space.
These residues display peaked categorical distributions in the demoiser's prediction. To exploit this property, we com- pute the purity score (maximum probability in the categor- ical distribution) for each masked position. As shown in Algorithm 2 (see Appendix B), positions where the purity score exceeds a threshold т. are sampled first, as these rep- resent high high-confidennc predictions. After these positions are sampled, their side chain conformations are predicted and incorporated as additional structural context for subsequent steps. The time increment is then computed proportionally to the number of positions sampled. This process iterates until the remaining positions reach the purity threshold or the sampling process converges. For positions that never achieve the confidence threshold, we perform independent sampling at the final step. This adaptive scheme allows the model to progress more quickly through high-confidence positions, while expending more compute on challenging positions. Concurrent work, such (Peng et al., 2025), adopts a similar strategy by using path planning to adap- tively sample time steps, where denoiser entropy is used to determine the next step in the diffusion process.
Atom encoder Information about atoms is embedded in the Atom Encoder module, which contains Fourier embed- dings (Abramson et al., 2024) and word embedding layers. The Fourier embeddings embed the sequence position of each node: atoms in their residues and residues within the overall complex. The chain identity of each node is also embedded through the chain index. The word embedding layers embed categorical variables that specify the identity of the node, such as the class of the residue, the element, and the type of the residue whether it is protein, nucleotide, or an ion. These features are concatenated, pro- jected and then processed by module that is similar to the Transition Block in AlphaFold3 (Abramson et al., 2024). Furthermore, we encode the time step of the flow matching process similarly to Nichol et al. (2021).
Residue encoder Information about residues is encoded through the Residue Encoder module, which is similar to the encoder used in LigandMPNN (Dauparas et al., 2022). Briefly, each protein residue receives distance and orienta- tion information from its nearest protein residue neighbours, together with distance information from all non non-protein atoms. Each protein residue's 's k nearest neighbours are calculated using the positions of their Ca atoms. Next, dis-
Training We train denoising network, fol. t), to ap- proximate (s |s., x, Xt). The neural network takes as input the protein complex structure x and the partial side chain structure information Xt- During training, we first sample a noisy sequence s, ~ Pip (s:[s: using the closed- form conditional distribution, and we remove its current
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All-atom inverse protein folding through discrete flow matching
b
Residue
Radiaa Encodar
Azcei Encodar
Time stop
Previous sequence
Residue festures
features
Multiple Layers
Raikke Enstadder
Ausen Attention
Atom
features
Self Attention Decoder
Scatter
All Non-protein
Content
Trassionn
Maoc
Mean
Residue
Atom
Catggrical
requerce
features
features
probabiiiiss
Figure 2. Architecture of the ADFLIP denoiser. a. The information flow between residue features and atom features. Updating residue features from atom features involves averaging over all atoms residue; updating atom features from residue features requires scattering the same residue feature over all atoms in that residue. b, Schematic showing the main blocks of the graph neural network (GNN) encoder. c, Schematic showing the inputs output self-attention decoder.
lances are calculated between the backbone atoms of these protein residues and the backbone atoms of their neighbours, and the resulting distances are encoded through a radial ba- sis function. Distances between the backbone atoms of each protein residue and all non-protein atoms calculated and encoded similarly. In addition, for each non con-protein atom, we also calculate tetrahedral angle with the Co, N, and C atoms of each protein residue. Node features for protein residues consist of a token-encoding of the residue type, along with learned embedding of the distance features described above. Node features for the non- non-protein atoms include their positioning in the table of periodic elements and additional tokenisation that encodes the identity of the atom in one-hot manner. Edge features are projections of the distance and angle features described earlier.
and then all the atom features corresponding to residue are averaged and then added to the residue features. The
updated features are integrated in the GNN Block, which is a message passing layer similar to the one used in Lig- andMPNN. We apply diffusion-time modulation (Peebles Xie, 2023) to the features of this message passing network, to condition the network to treat early time steps during sampling and later ones differently. The updated informa- tion from the residue nodes then feeds back to the atom nodes through the Residue to Atom Embedder module. This module transforms residue features using linear layer fol- lowed by ReLU activation. The output is then scattered to the atom features corresponding to each residue. This is followed by the Transition Block and the optional Context Block, which does message passing from the non non-protein atom features to all protein features. We included this block to further increase the amount of information that flows from the non- con-protein context to the protein residues.
Processing trunk The main computation in the GNN hap- pens in its processing trunk (Figure 2b), where information flows between the two different types of nodes and edges. Processing occurs a hierarchical manner. Atom nodes first attend to their nearest neighbours the Local Atom Attention module. This module is similar to AlphaFold3's Invariant Point Attention module, except that also uses frame averaging (Puny al., 2021; Huang et al., 2024) to make it more robust to rotations. The resulting contextual information from nearby atoms is then propagated to the residue features using the Atom to Residue Embedding. In this module, the features are first processed by linear layer followed by a ReLU activation function (Fukushima, 1969)
Decoding layers The decoder (Figure 2c) consists of three
layers of a Transformer (Vaswani et al., 2017) with a GeLU activation (Hendrycks & Gimpel, 2016). is only applied to the residue nodes. From there, the logits are predicted using linear layer.
3.3. Training-free guidance sampling
A key advantage of flow matching its ability to incorpo- rate external regressors to guide the generative process to-
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All-atom inverse protein folding through discrete flow matching
Table Interaction residue recovery all-atom complex
ProteinMPNN
LigandMPNN
ADFLIP
structure.
Metrie/ Model
Ligand
Nucleotide
Metal Ion
Perplexity +
PIFOLD
4.03
7.26
7.55
PROTEINMPNN
4.46
6.48
4.59
LIGANDMPNN
3.84
4.97
2.73
ADFLIP
3.57
4.86
2.61
b
Recovery Rate (%) f
PIFOLD
59.20
38.41
47.55
PROTEINMPNN
54.48
40.29
54.09
LIGANDMPNN
59.21
46.14
69.31
ADFLIP
62.19
50.21
75.73
c
ward samples with desired properties. Traditional regressor- guided generation requires training regressor pyy s,) (Song et al., 2021; Vignac et al., 2023; Wang et al., 2024) predict properties from intermediate states. However, retraining sophisticated neural networks to handle interme- diate states s, instead of complete samples $1 is often pro- hibitively expensive. For example, AlphaFold2's confidence scores are widely used in protein design to assess foldability and protein-proteii interactions (Pacesa et al., 2024), but retraining AlphaFold2 use masked sequences as input would be impractical.
Figure 3. Comparison of the inverse folding of three structures with nucleotides and ligands generated with ProteinMPNN, Lig- andMPNN, and ADFL.P. The sequences are refolded (coloured) Theuueeee
with Chai-1 (Chai Discovery, 2024) and compared to the starting structure (black outline). a. Comparison for a helix loop- loop-helix helix transcriptional activator protein (PDB ID: 1AM9, Parraga et al., 1998), showing that ADFLIP's integration nucleotide con- text information allows superior performance ProteinMPNN, Comparison for a HNH homing endonuclease (PDB ID: IU3E, see Shen al., 2004) further demonstrating ADFLIP's performance for DNA-binding proteins. c, A closc-up of the anhibitor-binding pocket of Factor (PDB ID: 2UWP, see Young al.. 2007). demonstrating ADFLIP's superior performance for ligand binding proteins. The refolded ligand (yellow) is docked closer to the target (black outline) for the others.
Here, we propose training-free approach to leverage ex- isting regressors (3 $1) that only operate on complete, unmasked samples. Similar to how we define the marginal distribution Pi (St) through expectation over completions, we estimate the property predictions for intermediate states by taking the expectation of the regressor outputs (v s1) under the denoiser output (s( se):
protein, but not the
ply st) = E poo (po s1)].
the dataset curation protocol of LigandMPNN (Dauparas et al., 2023). Specifically, we include X-ray crystallography or cryo-EM entries that were deposited after 16 December 2022, with resolutions better than 3.5 Å, and total protein length less than 6,000 residues. We use the same validation and test 317 protein complexes with small molecule ligands, 74 complexes with nucleic acids, and 83 proteins with bound metal ions. Because LigandMPNN did not release their training clusters, we cluster the remaining structures using MMseqs2 at 30% sequence identity to prevent homology between training and test sets.
This approach enables leveraging powerful existing regres- sors in plug-and-play manner for guided generation, with- out requiring expensive retraining or architectural modifica- tions.
LigandMPNNN for evaluation, comprising
4. Experiments
We evaluated ADFLIP in three scenarios of inverse folding: on all-protein complexes with small molecule ligands, nu- cleotides and metal ions; on ensembles of structures from dynamic complexes; and on protein-ligand complexes where we guided sequence generation towards higher predicted binding affinities.
We evaluated the quality of predicted protein sequences using two metries: perplexity and recovery rate. Perplexity is calculated as the exponential of the average negative log- likelihood of the sequence. Lower perplexity indicates a better of the predicted amino acid probabilities and the original sequence. The recovery rate measures sequence identity between the generated sequence that is sampled
4.1. All-atom inverse folding
Test design
We evaluated ADFLIP on all-atom protein structures from the Protein Data Bank (PDB), following
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All-atom inverse protein folding through discrete flow matching
from the predicted probabilities and the original sequence. Both metrics are calculated only on residues that close to the non-protein molecules, i.e. which have atoms within 5.0 A of any of the non-pron non-protein atoms. For each complex structure, we sampled 10 sequences and computed the mean sequence recovery rate.
showed good performance for complexes with small molecule ligands, achieving average RMSD scores below 1.3 A. TM-scores above 0.95, and foldability exceeding 98%. For nucleotide complexes, we observed higher RMSDs (around 5 Å), with 78-79% of the generated sequences suc- cessfully folding into structures similar to the reference. For complexes with metal ions, both methods achieve RMSDs around 2 Á and foldability scores above 80 %. Notably, both methods achieved high pLDDT scores (bigger than 95%), indicating high confidence in structure prediction.
We compared our method against several baselines. Our pri- mary comparison was with LigandMPNN (Dauparas et al., 2023)', which also considers the atom-level details of non- protein molecules. We retrained LigandMPNN with the same clustering we used. For a more comprchensive evalua- tion, we also included methods that only consider protein backbone information: PiFold (Gao et al., 2023b)?, and ProteinMPNN (Dauparas et al., 2022)²
Across all three types of complexes, ADFLIP outperformed LigandMPNN, with RMSD reductions of 0.06 Á for small molecule ligands, 0.44 Å for nucleotides, and 0.1 A for metal ions.
Table 2. Numerical comparison between generated sequence struc- ture and the native structure.
Sequence recovery As shown in Table I, methods that incorporate all-atom information of non-protein molecules significantly outperformed backbone-only approaches. For metal binding sites, sequence recovery improved from 40% with ProteinMPNN to 69% with LigandMPNN, and further to 75% with ADFLIP. This improvement is likely due to the highly conserved nature of metal-binding amino acids. For example, in many natural metalloproteins, metal ions are coordinated by the side chains of only few amino acids, such as histidine, cysteine, methionine, tyrosine, aspartate or glutamate (Trindler& & Ward, 2017). The inclusion of explicit ligand information also improved performance for ligand- binding residues, ADFLIP achieved 62.9% recovery compared to 59.2% for LigandMPNNN, 54.98% for Protein- MPNN, and 59.2% for PiFold. Similarly, for nucleotide- binding residues, ADFLIP reached 50.21% % recovery, out- performing LigandMPNN (46.1%% 1)), ProteinMPNN (40.2%), and PiFold 1%).
Model
RMSD (A)
TM-score
PLDDT
Foldability
Small Molecule
LigandMPNN ADFLIP
1.21
0.95
94.6
98.8%
1.15
0.96
90.6
100.0%
Nucleotide LigandMPNN
5.99
0.76
84.7
79.4%
ADFLIP
5.55
0.77
87.5
83.5%
Metal Tons
LigandMPNN ADFLIP
2.37
0.79
97.85
83.7%
2.27
0.78
98.38
85%1%
4.2. Inverse folding on structure ensembles
Test design To assess the performance of ADFLIP for inverse folding of structurally dynamic complexes, constructed a new dataset of protein structure ensembles that were determined by solution-state NMR spectroscopy. Specifically, we selected PDB entries that were deposited after January 2015, which contained more than 100 residues, and least two conformational states. We used MMseqs2- based clustering (Steinegger & Söding, 2017) at 30% se- quence identity to remove redundant ensembles. Our final curated dataset comprised 219 ensembles, with an average of 18 conformational states per structure.
Foldability An important metric in inverse folding is the foldability, which measures whether the predicted structure for generated sequence matches the original structure. We used Chai-1 (Chai Discovery, 2024) without MSA infor- mation to predict structures for the sequences generated by both ADFLIP and LigandMPNN. We assessed structural similarity to the reference structure from the PDB using RMSD and TM-score metrics (Mukherjee & Zhang, 2009), alongside the confidence scores from the structure predic- tion (pLDDT). We define generated sequence foldable if its predicted structure achieves a TM-score matching or exceeding 0.5 when compared to its reference structure. Our evaluation spanned all protein complexes in the test dataset with fewer than 5 ligands.
We again assessed performance using perplexity and se- quence recovery rate, comparing the use of a single structure from the ensemble with the use of the entire ensemble for sequence generation. For sequence generation with single structure, we selected the structure that exhibits the most extensive interactions with the non-protein elements from the ensemble.
As shown in Table 2, both ADFLIP and LigandMPNN
Sequence recovery As shown in Table 3, incorporating multiple conformational states improved sequence recovery rates: 8.6% for small molecule interactions and 5.8% for
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All-atom inverse protein folding through discrete flow matching
Table 3. Recovery rate performance of NMR dataset.
Table 5. Ligand binding affinity guided results
Metric/ / Model
Ligand
Nucleotide
Metal Ion
Model
Affinity gain Foldability
Perplexity +
ADFLIP (Unguided) 41.9%
100%
LIGANDMPNN
7.82
9.37
3.27
ADFLIP (Guided)
58.1%
91.4%
ADFLIP(SINGLE)
7.34
8.71
3.12
ADFLIP(MULTIPLEE)
5.58
6.91
2.69
Recovery Rate (%) 1
incorporating DSMBind predictions in the flow matching process, we aimed to guide the generation process towards sequences that are predicted to have higher binding affinity for their target ligands.
LIGANDMPNN
40.58
32.63
64.82
ADFLIP(SINGLE)
41.48
34.48
65.44
ADFLIP(MUULTIPLE)
50.08
40.33
68.01
We tested our guidance- based approach using the subset of 210 protein-ligande complexes from the test set described in Section 4.1 that contain a single ligand. First, we used DSMBind to establish baseline binding affinities for the wild-type sequences. We then set our generation target to achieve a 10% improvement over the wild-type binding affinities. For each structure, we generated 10 different sequences and evaluated their predicted binding affinities using DSMBind. To assess the effectiveness of our guidance approach, we compared guided and unguided sequences generated by ADFLIP.
Table 4. Numerical comparison between generated sequence struc- ture and the native structure for NMR dataset. Single indicates se- quence generation using an individual conformational state, while Multiple indicates sequence generation using the complete ensem- ble of NMR conformational states.
Model
RMSD (A)
TM-score
PLDDT
Foldability
LIGANDMPNN
8.34
0.68
78.4
84.5%
ADFLIP (Single)
9.10
0.67
79.5
81.7%
ADFLIP (Multiple)
0.69
80.19
82.5%
nucleotide interactions. These improvements were achieved using the same model, without fine-tuning, demonstrating ADFLIP's inherent ability to integrate information from multiple structural states during sequence generation. For metal ion interactions, we observed more modest improve- ment of 2.6% in sequence recovery. This is likely because metal- sites in proteins typically maintain relatively stable conformations, even in the dynamic protein ensem- bles captured by NMR (which was also reflected in the higher overall recovery rates for metal-binding proteins in the NMR test set).
We evaluated the effectiveness of our approach using two metries: (1) affinity gain whether the generated se- quence's 's predicted binding affinity exceeds that of the wild- type sequence and (2) foldability whether the generated sequence's 's predicted structure maintains structural similar- ity to the input backbone, i.e. with TM-score 2 0.5.
As shown in Table 5, our guidance- based approach signif- icantly improves the success rate of generating sequenees with enhanced binding affinity from 41.9% 58. 1%, while maintaining foldability above 90%. However, note that by using fixed protein backbone structure, and limited side chain sampling, the ability of DSMBind to achieve better binding affinity is currently limited. Refinement of the backbone structure in our method may yield further improvements in the future.
Foldability We assessed the foldability of the generated sequences by predicting their structures using Chai-l. We compared the predicted structure with the structure from the original NMR ensemble that had the lowest RMSD with the predicted structure. Although generating sequences for dynamic protein complexes remains difficult (as evidenced by high RMSDs, low TM-scores, low PLDDT scores and low foldabilities), using ensemble information in ADFLIP reduces the average RMSD from 9.11 to 7.61 Á compared to using single structure (see Table 4).
5. Discussion
The ultimate goal of protein design is to create proteins with improved or new functionalities compared to those existing in nature. Because protein functionality is typically cou- pled to conformational change, and it often involves a wide range of chemistry, the design of new protein functional- ity will need to consider both all-atom structures and the requirement of single sequence to adopt multiple confor- mations. ADFLIP represents step in this direction. Its all-atom model improves sequence recovery rates compared to current state-of-the oftte-of-thearr art for protein complexes with lig- ands, nucleotides, or metal ions. Leveraging the flexibility of discrete flow matching, ADFLIP also allows incorpo-
4.3. Guidance by binding affinity
We assessed guidance- based sequence generation in AD- FLIP by incorporating DSMBind (Jin et al., 2024) predic- tions of ligand binding affinity. DSMBind is an unsuper- vised, deep saaringg-bsse predictor of binding affinity that takes as input the complex structure (including side chain information), protein sequences, and ligand information. By
8

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All-atom inverse protein folding through discrete flow matching
rating multiple conformational states in the sequence gen- eration process, as demonstrated for structure ensembles determined by NMR. Moreover, the flow matching process allows steering sequence generation towards desired prop- erties through training-free guidance sampling, as demon- strated by the design of higher affinity ligand binders using DSMBIND (Jin et al., 2024) as a plug-in regressor.
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All-atom inverse protein folding through discrete flow matching
A. Dataset
We follow the dataset generation process used in LigandMPNN, collecting protein assemblies from the Protein Data Bank (PDB) as of December 16, 2022, that were determined by X-ray crystallography or cryo-electron microscopy at resolution better than 3.5 Å and contain fewer than 6,000 residues. Residues introduced solely aid crystallisation (e.g.. ZMR, Z9D) were removed. Following the AlphaFold3 paper, such residues parsed as glycans. A full list of excluded crystallisation-aid residues and glycan residues is provided in Appendix D.
We cluster each protein chain at 30% sequence identity threshold using MMseqs2 (Steinegger & Söding, 2017). We hold out a non-overlapping subset of clusters corresponding to distinct interaction contexts: 317 protein- small molecule complexes, 74 protein-nucleote available in Appendix D. The resulting training dataset comprises 27,818 clusters. For both training and evaluation, we use the same PDB collection in the LigandMPNNN repository".
complexes, and 83 protein-metal ion complexes. The full list of held-out PDB entries
B. Purity Sampling
The following algorithm describes the adaptive time step sampling strategy used in ADFLIP. Starting from a fully masked sequence, the method employs denoising network fe to predict amino acid distributions. Unlike fixed-timestep approaches, this method adaptively selects high-confidence positions for sampling based on a purity threshold т. Only positions exceeding this threshold are updated at each step, allowing for progressive and focused refinement. A side chain packing network 9,, is then applied model side chains the newly sampled positions. The process iterates until all positions resolved, the model's confidence saturates, or the maximum number of iterations K is reached. If unresolved positions remain at the end, they are sampled in a final fallback step.
Algorithm 2 ADFLIP Adaptive Sampling Process
Input:
N protein backhone conformation and non-protein structures Ti, NN Initial sequence 5u (m, ...,
Initial side chains Xo =
Purity threshold т, maximum iterations
Denoising network fe, side chain packing network 9n Initialise 0, M positions still masked, while M 0 and 1 and & < K do
for 1 to N do
Compute p" ($1) = fols;, In, Xi) end for p(š1) = 1
N Σn (51)
Compute purity scores o; = max, p(s(1) j) for masked positions
I oi
(Positions to sample]
Sample 8 ~ p(x(') for E
for n = to do
Compute xi = g(s,, v.) for positions in I end for
M + M - [7| (Update mask count)
- L + I (L is sequence length)
A: < +11
end while
if k = K and M > 0 then
Let J= j 88 m (Remaining masked positions)
Sample 8)
(1) p(8 (3) for
end if
Return: Final sequence 81
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All-atom inverse protein folding through discrete flow matching
C. Training-free classifier Guidance Sampling
The following algorithm outlines the training-free classifier guidance sampling strategy used in ADFLIP. Starting from a fully masked sequence, the method uses denoising network fo to produce amino acid distributions p(8)) conditioned on the input structures, Unlike standard sampling-basee approaches, we do not sample a sequence from this distribution. Instead, we directly feed the probability distribution p(51) into regressor network h& to predict the target property value ý. The guidance signal is derived from the discrepancy between the predicted value and the desired target y. approximated as a pseudo-gradient - v., +, lly ølI?. which is used to reweight the sequence distribution. This guides the sampling process toward sequences more likely to yield the desired property. A side chain packing network In assigns side chains for each structure. Reverse-time sampling with a fixed time step At is performed iteratively (e.g., using Eq. 1) until the full sequence generated.
Algorithm 3 Training-free classifier Guidance Sampling Process Input:
N protein and non-protein structures (11,,.., 2NN Initial sequence so (m, (m......)) m)
Initial side chains Xo = /
Time step At
Denoising network Sa. side chain packing network In. regressor network he Target value y Initialise =0 0
while < 1 do
for 1 to N do
Compute p" (8:)= fnsst,
end for
p(81) N En (31) Compute y by p({1): ÿ = ho (p(s1))
Approximate plyss) 81) 2== -Ve1ly - 01
Sample $1 for 1 to N do
(})())
Compute xi g( F.,) end for
Compute RG (s: = E (s1))) (Boc) Sample S++Ar by Eq 1
1+( AL
end while
Return: Final sequence 81
D. PDB IDs and CCD codes
PDB IDs for the small molecule interaction benchmark 1A28, 182C, IDRY, IERG HELB, REPO, IKUR IGT KGIG, IGVW, 1GX8, HIST, IKAY IKDK.
IKVI, 118G,
INCL INFX, INHZ INLO, INNY, INWI. LONY, IPYN, IQBI, LQKT, IQNK, TRUP, ISQN, IVIN, EXD IXWS, LYCL IYQU, 1295, 1ZP8, BAYR 2807, 2841
2BAJ, 2BAK, 2ALL 2HSM 2CET 2628. 2H0T, 2HDP 2G34, 2HAH, ZIHO, ZIWX, 2120, 2134, 2341, 2J94, 2195, 2000, 20AX, 2016. 2011 PPAJ, 2PIG, 2PT2 2OOG ZHHP 2080 2QBS, 2QE4.
ZOMG, JUWL, JUWO. /UW TVTA 2VHO ZVH6, IVEM 2VRJ, 2VW5, ZVWC, TWBY. 2WC3, ZWER ZWFC, ZWFQ, TWGJ, ZWIE BYYG JWYL IXAR 2XR8 2NDA 1XHT, 2XII 2X12, 2XI0.
2XIX, 2YTZ. ZYR0, 2YN1, ZYN2, ZYDW, ZYEK, ZYEL, ZYFE ZYPX, ZYGE,
2Y10, 2083, 3EAX. BEKR, 3 3FV2, SEYK. SGBA, SUBB, SOCS, SGCU, 3GY3, SHEK, 3125, SIOC, SIPH, 31W6, 3897,
IZMM, BACW, BACX, 3LPK, SLXK, 3M25,
3865,
3CKP SCOW, SCOY,
3N76, SNQU, SNYX, 20SX, JOSP, 3PWW.
BROC. STEN. SUNI, SUEI SHEV. SUEW, SUEX, 3VHA, TVHE, 3VHD, SIF SVVY, IVWI, 3VW2, TWHA, 3W76, TW75, 1ZC5, 37MO 377F, 4AAY, 4AJW 4A71, 4AGE 4AP7, 4860, 4R9K, ACTOL
ACGA, 4CMO. 4DAS, 4ESW. 4E60. 4E91L 4EAZ, 4EGK 4ERT, 4FCQ, 4FFS, 4FLP 4GISN SEENY, 4GU6, 4HGE AIGTT, 4KUYY 4K0Y, 4KAO AKCX, ALYW. 4MOR 4M12 4M13, AMUE 4NHB, ANWC.
ADOM, SEUS, 2007, 4L09, S008, 4PSZ, 4PMM, APOR AQEV, 4UEW, JOYY. 4RFM, 4RWJ, 4YTH 470K, 47AF, SAAD, SIEL. SIH9, SJOS, SKZZ, 5L22, SLLL SLNY, SLSG. SNEE, SNWI, SNYH, SOPS, S0QS, SQGP ST19, STPX, 5V82, SYPS, SYFT. 6C2R, SCIR, 6CPW, SIXIQ, 60EER GDYU, SONY, GELS. GELO, SELP. 6EY9, 6EYR, 6FIN, 6GE7, 6GP9, 6GFS, 6GHH, 6161, 6164, 6167, 6MDO, 6MHI, 6MH7, 6N7A, 6NKX, 6N09, 6NV9, 6OLX, 6Q17
SUYE, 4V01, 4WSR, 4W9L,
4WKN 4NAP, 4XIE. 4NIR 4Y 4YHK, 4YMB, 4YML, NYNB.
S126,, SDAH,
SDNT, SDLX, SDOC, STWWR, SE74,
SENG, SROP SEQY, SERI, SEXM, SEXN, SPOR, SFTO SFUT, SHOV, SEV, SEEV SI9K, SWZ
PDB IDs for the nucleotide interaction benchmark LADA, JAMP, JANA, IB0I, IBCI. LBCS, IDE2 IECS, IULO. HHLN LES, IPVL IQUM, ISFU, JUSE, IXPX.
IYUS, 2038, 2082, 2N19, 4E0P, ANID, 4WAL, SCM3, SLLAW, SMIT, SVCV, SW9S, SYBD, SBJV, 6DNW, 6FQR, 6GDR, 6KBS, OLFE, SLMJ, 60D4, 6WDZ, 6Y93, 7BCA, 700G, 7EL3, USA. 2JU3, 7KIL, 7KU, 7MTL. 7200, RDWM
2XDH, 2YPB, 22H3. 240, SADIL 38SU, 3HC3, 8073, SINA, SUXA, JLSK SMJD, AMVA, 3NTQ, 3VUK, JYWB, 3ZPS, 4BHM. 4BQA.
PDB IDs for the metal interaction benchmark IDWH, IF4M, IE8S, 1E72, IF3S, IFFE, WOR OLOKK IMSE, IMSE, IMOL IMXY. IMXZ IMYL, INKL IQUM,
ISGE, ITE1, LUSE, 28N2, 2CFN 25SC, 2N09, 2NQJ. 20L7. 2VXX, 2ZWN, 38VX, SCVS, 384N, SESL, 3PGG, 3HG39, 3HKN, 3HKT. 3192, SK7R, 3124, 317T, SMOP, 3MI9, 30TU, 3U92,
3U90, 3L99 SWON, 4NO), 1 4HLTT AIDE, AHU, 4111, 4112, 4NAZ, 4W18, AX68, SP55, SEGS, SHEZ, S141, SL70, SVDE 6A4X, OBULL OCYT, 6IYZ, OLKE, OLRD. OWIZ 6X75,
ZDNR, 7E34, 7KIL, 7N7G. 7STL. 757M, TWSE, 7WB2
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All-atom inverse protein folding through discrete flow matching
PDB IDs for the NMR benchmark
RVOH, SWLS. 8XST, 8XZI, 9ATN, 9CSE, 9GAG, 5K5G, 5185, SLSD. SMIG, SMBT, SMAD, SMPG, SMPL. SNBM, SNFR, SNKO, SNOC,
SNWM, SOB0, SOGU, SORS, SOWL SIMO, STMX, SUAK, SUSS, SU9B, SU8S, SVTO, SWASS SWYO, 5X29, SXIZ SKVEE SXZK, SYAM, 2NBY SZAL, S2UX. GBIG, ABTG. 6BAS, 6WAL GWLII, 6XTL, 6XOR, 6YSV, 6YPS, 6ZDB, 7ADO, 7ACT. 762B, 7CLV, 7CSQ. TDEE. 7DFE, 7JQ8, 7K35, 7K7F, 6CTB. 7LO1, 7MLA, 7NDI, 7OVC, THI 7KKU, 7QIL, 7QDE, TQRL 7086, 7QUL, TRNO, TRPM, 2MY2, 2MYJ, 2MZ1, 2MZC.
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LHO, ULE. UEA, VIM, VIL VGL, VIL. VEN. VIE.
14


Reviews:
[{"review_id": "bhSpzXQ8IS", "reviewer": "Reviewer_kagU", "summary": "This paper introduces ADFLIP, a model for inverse protein folding designed for complex biomolecular systems. By by incorporating all-atom structural context (including protein backbone, non-protein components like ligands and metal ions, and progressively predicted side chains) and handling dynamic protein complexes with multiple structural states.", "questions": "", "limitations": "", "rating": 1, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "## Clarification on \"All-Atom\" Structure in ADFLIP\nPerhaps we had not explained clearly enough what we mean by ‘all-atom’.   This interpretation of “all-atom” was introduced previously with RoseTTAFold-all atom[1].\nIn this context, all-atom refers not only to including the full set of protein atoms (backbone and side chains) but also to incorporating non-protein biological components such as ligands, ions, and nucleotides. Most inverse folding methods—including PiFold, ProteinMPNN, and others—limit their input representation to backbone atoms (typically N, C, O).\n\nBy contrast, our method, ADFLIP, is designed to operate on full biological assemblies that may include a broader set of atoms from diverse molecules beyond proteins. This enables modeling protein-ligand, protein-RNA, or protein-ion interactions in a generalizable manner. Therefore, our all-atom terminology emphasizes the inclusion of all relevant atomic context in biomolecular complexes—not just the geometric features derived from protein atoms—enabling applications in more complex and realistic biological environments. \nWe will revise the introduction and related work to more clearly explain this distinction.\n\n## Novelty and Technical Contributions of ADFLIP\nWhile previous works such as UniIF have explored inverse folding in all-atom settings, the objectives differ. UniIF is designed as a general framework for modeling all biological structures, including proteins, RNAs, and small molecules, rather than focusing specifically on protein design. In contrast, ADFlip is specific for protein design tasks, particularly for proteins that interact with ligands, nucleotides, and other biomolecules. Our work introduces several novel contributions:\n1. Generative Modeling with Discrete Flow Matching:\nADFLIP is, to our knowledge, the first inverse folding framework that applies *discrete flow matching* to protein sequence design, taking into account protein complex context. This is particularly advantageous when handling input structures with high uncertainty, which are common when flexible ligands or RNA components are present, where traditional autoregressive models struggle. Our experiments demonstrate that ADFLIP outperforms autoregressive baselines on both single-structure and multi-structure inputs.\n2. Training-Free Classifier Guidance for Conditional Generation:\nWe propose a novel, training-free classifier-guidance approach for conditional generation with flow matching. Existing guidance techniques often require retraining regressors or classifiers to accept noisy intermediate inputs $ s_t $. Instead, we use a pre-trained classifier/regressor  (e.g., AlphaFold) that operates on clean inputs $ s_1$, and approximate $ p(y | s_t)$ by taking the expectation over $ p(s_1 | s_t) $, as described in Eq. (line 308). This allows us to plug in any pretrained predictor *without* retraining, enabling flexible and efficient conditional design.\n3. Support for Multiple Structural States:\nADFLIP supports input ensembles with multiple structural conformations, capturing dynamic aspects of protein complexes. This is crucial for modeling biological systems where a single static structure may be insufficient.\nIn summary, ADFLIP introduces a general-purpose, generative approach to inverse folding in full biological assemblies by (1) leveraging a broader all-atom context, (2) introducing discrete flow matching for improved sample quality and uncertainty modeling, and (3) enabling flexible, training-free guidance using pretrained models.\nWe hope this response clarifies the distinctiveness of ADFLIP and addresses your concerns. We thank you for your valuable feedback, which will help in improving our manuscript.\n\n[1]Krishna, Rohith, et al. \"Generalized biomolecular modeling and design with RoseTTAFold All-Atom.\" Science 384.6693 (2024): eadl2528.", "claims_and_evidence": "The paper heavily emphasizes \"all-atom\" in the title and abstract, implying it's a novel and crucial advantage. However, the meaning of \"all-atom\" in the context of ADFLIP and its distinctiveness from other methods are not clearly and convincingly established. PiFold and other GNN-based methods do use geometric features constructed from all atoms (backbone atoms) to represent protein structure. The geometric features (distances, angles, etc.) inherently rely on the coordinates of all atoms. Therefore, simply stating \"all-atom\" as an advantage is misleading because it's not a feature unique to ADFLIP compared to modern GNN-based methods. The input is more expressive, it should be distinct from inverse folding problem based on backbone atoms.", "methods_and_evaluation_criteria": "The proposed methods in ADFLIP, particularly discrete flow matching, all-atom context awareness, GNN architecture, and ensemble handling, are make sense for the problem of inverse protein folding in complex biomolecular systems. However, I fail to recognize the key technical innovations.", "theoretical_claims": "N/A", "experimental_designs_or_analyses": "The central claim regarding \"all-atom\" as a unique and clearly defined advantage is weakly supported and potentially misleading due to the lack of clear definition, lack of isolation of the \"all-atom\" effect, and potentially inaccurate characterization of baselines.", "relation_to_broader_scientific_literature": "It is related to inverse folding problem, which is an important area in molecular biology.", "essential_references_not_discussed": "The problem setting can be solved by the method proposed by UniIF [1] published in NeurIPS 2024.\n\n[1] Gao, Zhangyang, et al. \"Uniif: Unified molecule inverse folding.\" Advances in Neural Information Processing Systems 37 (2024): 135843-135860.", "other_strengths_and_weaknesses": "This paper is well-organized and clearly-written. But the problem setting is quite simple. It seems to extend the traditional inverse folding into protein complex scenarios.", "other_comments_or_suggestions": "N/A", "questions_for_authors": "Could you please clearly define what \"all-atom\" specifically means in the context of ADFLIP and how your approach to \"all-atom\" context is fundamentally different and uniquely advantageous compared to how baseline methods utilize all-atom geometric information? Simply considering non-protein components and side-chain prediction doesn't seem to be a fundamentally different \"all-atom\" concept.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "cpX4nt1Gn0", "reviewer": "Reviewer_1WvW", "summary": "This paper proposed a new method, namely ADFLIP, a generative model for inverse protein folding that designs sequences based on all-atom structural contexts. It is designed to handle complexes with non-protein components and dynamic structures using ensemble sampling. ADFLIP progressively incorporates side-chain context and leverages classifier guidance sampling for sequence optimization. The authors showed experimental results on a dataset curated from PDB.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**How does ADFlip perform on protein only dataset such as CATH**\n\nThank you for the suggestion. We retrained ADFlip on the CATH 4.2 dataset and evaluated its performance based on sequence recovery rate. The results are summarized below:\n\n| Method        | Sequence RR (%) |\n|---------------|-----------------------------|\n| ProteinMPNN   | 45.96                       |\n| PiFold        | 51.66                       |\n| **ADFlip**    | **52.13**                   |\n\n**How does other inverse folding model perform on all-atom dataset**\n\nThank you for the suggestion. Due to time constraints during the first review period, we are still working on additional evaluations. We aim to include results for other inverse folding models on the all-atom dataset in the second-round discussion and the revised manuscript.", "claims_and_evidence": "- The main claim of this paper is supported by evidence of experimental results.\n\n- The results are shown for only one dataset of inverse folding. I understand this dataset used here is more aligned with the claim, however, the question naturally comes to mind how this method would perform compared to other method in the more widely used in inverse folding datasets such as CATH 4.2 and CATH 4.3.\n\n- The comparison is shown against PiFold, ProteinMPNN, and LigandFold. However, there are other more recent methods that significantly outperform PiFold and ProteinMPNN on other dataset such as CATH 4.2, CATH 4.3, TS50, TS500, etc. Some examples include LM-Design (Zheng et al. 2023), DPLM (Wang et al. 2024), AIDO.Protein (Ning et al. 2024), and so on. Although none of these methods use use all-atom structural context or the ligands, I would how ADFLIP would perform against those methods in their evaluation dataset as well as the most traditional ones.", "methods_and_evaluation_criteria": "- The method is sound and properly described.\n\n- The evaluation criteria is also sound. However, there is some gap in the evaluation on more widely used dataset and against more recent methods.", "theoretical_claims": "- The authors provided clear mathematical derivation of their proposed approach\n\n- The demonstration algorithms are also sound and properly explained.", "experimental_designs_or_analyses": "- The experimental design and analyses are valid. \n\n- I appreciate how the authors not only showed the recovery rate and perplexity, but also foldabity as well as related metrics such as TM-score, pLDDT, and RMSD.", "relation_to_broader_scientific_literature": "The key contribution of this paper is related to proteomics research as well as machine learning research with such biological data. Their provided method has good use-case in applications such as drug design and discovering therapeutics.", "essential_references_not_discussed": "N/A", "other_strengths_and_weaknesses": "N/A", "other_comments_or_suggestions": "N/A", "questions_for_authors": "N/A", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "hTxGzjEJPO", "reviewer": "Reviewer_BnUA", "summary": "A method named ADFLIP is proposed for inverse folding in all-atom structural contexts, e.g., containing ligand, nucleotide, and metal ions. The method is based on conditional discrete flow matching and a hierarchical GNN architecture. Additionally, it incorporates amino acid sidechains predicted by an external model as context and is able to perform training-free classifier guidance. Experimental results show improved performance over a re-trained version of LigandMPNN for diverse recovery metrics. The authors also show increased affinity gain measured in silico when an external model, DSMBind, is used for guidance.\n\n## update after rebuttal\n\nAfter the rebuttal, the authors addressed some of my concerns and I have raised my score.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**1.Related Work**\n\nThank you for pointing this out. We mentioned the paper by Yi et al. [1] in the introduction, but agree it should also be included in the related work. We will rewrite the related work section and discuss the discrete diffusion method for inverse protein folding from Yi et al and also another diffusion model [2][3]. This will help clarify how our work connects to previous studies.\n\n[1]Yi, Kai, et al. \"Graph denoising diffusion for inverse protein folding.\" Advances in Neural Information Processing Systems 36 (2023): 10238-10257.\n\n[2]Wang, Xinyou, et al. \"Diffusion language models are versatile protein learners.\" arXiv preprint arXiv:2402.18567 (2024).\n\n[3]Wang, Xinyou, et al. \"Dplm-2: A multimodal diffusion protein language model.\" arXiv preprint arXiv:2410.13782 (2024).\n\n\n**2.Methodology Explanation for Flow Matching**\n\nThank you for this suggestion. It is correct that, in our framework, discrete flow matching generates the distribution $p(s_t​)$ at each timestep. However, unlike continuous flow models, where the denoiser predicts noise, the denoiser of discrete flow matching directly predicts data (e.g., sequence tokens).\nIn our implementation, a trained denoiser first estimates $p(s_1)$, and then $p(s_t)$ is computed by taking an expectation over this estimate, as shown in Equation (line 137) and Algorithm 1. \n\nIn the revised manuscript, we will add clearer descriptions, expanded mathematical formulations, and improved illustrations to explain the conditional discrete flow matching process more intuitively.\n\n**3.Classifier Guidance**\n\nOur classifier-guidance approach shares a similar objective with Chroma and RFdiffusion in that we aim to condition generation on an external property $y$, estimated via $p(y∣s_t)$. However, there is a key difference in how this is achieved.\nChroma and RFdiffusion use continuous diffusion models and typically require training a separate classifier or regressor (y = f(s_t)) directly on noisy intermediate states, $s_t$. In contrast, our method uses a training-free guidance strategy: we leverage a pre-trained classifier or regressor that operates on clean data $s_1​$, such as AlphaFold.\nWe estimate $p(y∣s_1)$ from this clean output and then derive $p(y∣s_t)$ by taking the expectation over s1∼p(s_1∣s_t), as described in Equation (line 307). This approach avoids the need to retrain an external model and enables seamless integration of existing structure-based predictors.\n\n**4.Methodology Clarification: Does removing sidechains at masked positions bias decoding toward early samples, and is there an ablation study on this effect?**\n\t\nThank you for this insightful comment. We conducted an ablation study on the parameter $\\tau$ for purity sampling, which controls how much side-chain information is preserved for masked positions during the denoising process. A smaller $\\tau$ value retains more side-chain atoms, providing richer structural context to the denoiser. Conversely, a higher $\\tau$ results in fewer sampled residues and less side-chain information.\n| $\\tau$ | Interaction Recovery Rate | Std. Dev. |\n|------------------------------------|-------------------------------|-----------|\n| 0.3                                | 0.602                         | 0.1399    |\n| 0.5                                | 0.603                         | 0.1411    |\n| 0.7                                | 0.588                         | 0.1457    |\n| 0.9                                | 0.568                         | 0.1459    |\n\n**5. Need for Ablation Studies for sidechain**\n\nWe conducted an ablation study to assess the impact of incorporating predicted side-chain atoms into the denoiser's input. The results are summarized below:\n| Model               | Ligand (%)        | Nucleotide (%)    | Metal Ion (%)     |\n|---------------------|-------------------|-------------------|-------------------|\n| ADFLIP w/ sidechain | 62.19 ± 13.60     | 50.21 ± 13.52     | 75.79 ± 18.18     |\n| ADFLIP w/o sidechain| 61.43 ± 16.20     | 49.74 ± 13.32     | 75.92 ± 16.52     |\n\nWhile the inclusion of side-chain information leads to moderate improvements in sequence recovery, we believe its primary value lies in enhancing biological fidelity rather than optimizing this metric alone. In many downstream tasks—such as enzyme design or protein–ligand interaction modeling—minor torsional differences in side chains can lead to substantial functional changes (e.g., in binding affinity or catalytic activity). Therefore, even small gains in sequence recovery reflect a more meaningful structural signal that allows the model to better capture fine-grained biophysical nuances. We will discuss this in more detail in the revised manuscript.\n\n**6.(Conditional Flow Matching Formulation) Additional information about the conditional and the formulation from Campbell et al would be helpful for readers.**\n\nWe agree, and will add more detail about Conditional Flow Matching in the revised manuscript.", "claims_and_evidence": "The claims made in the manuscript are supported by clear evidence.", "methods_and_evaluation_criteria": "The evaluation criteria make sense for the problem investigated.", "theoretical_claims": "The theoretical claims seem correct. Additional information about the conditional discrete flow matching formulation in (Campbell et al, 2024) would help to verify the claims in the manuscript.", "experimental_designs_or_analyses": "The experimental designs and analyses seem valid. Re-training LigandMPNN for the proposed cluster might affect the fairness of evaluation depending on the rigorousness of the checkpoint chosen for evaluation.", "relation_to_broader_scientific_literature": "The key contributions of the manuscript are related to:\n\n1. Proposing a conditional flow matching framework for all-atom protein sequence design.\n2. Incorporate partial side-chains using a pre-trained model during the sequence reconstruction process.", "essential_references_not_discussed": "References for Inverse Folding such as [REF1] using discrete diffusion are missing.\n[REF1] Yi, Kai, et al. \"Graph denoising diffusion for inverse protein folding.\" Advances in Neural Information Processing Systems 36 (2023): 10238-10257.", "other_strengths_and_weaknesses": "Strengths:\n2. A discrete flow matching framework is proposed for all-atom protein sequence design. As the denoiser network, the authors combine residue-wise and atom-wise features obtained by a GNN, and a transformer-based architecture is used for decoding.\n3. The authors propose the use of an external network to sample sidechains during the sequence decoding process to provide additional information in all-atom contexts when decoding.\n1. The proposed method is able to handle multiple conformations, and the adaptive sampling proposed by the authors might be useful for other inverse folding algorithms.\n\nWeaknesses:\n1. The manuscript would improve with additional information and clarification about the methodology. \n2. Additional ablation studies regarding sequences generated by the model and how different components affect the overall performance seem needed.\n3. The methodology for the guidance by binding affinity using the fixed input structure and DSMBind is arguable, even though it shows the ability of the proposed method for guided generation.", "other_comments_or_suggestions": "1. (Line 97) Typo: “Saport”\n2. (Line 77-78) The word “here” appears twice.\n3. The equation numbering appears to be wrong throughout the manuscript. \n4. Algorithm 1 appears before Fig. 1 in the text. Might need to re-arrange the order.\n5. (Line 413) Typo: “DSMBIND”", "questions_for_authors": "1. (Related Work) The reviewer suggests re-writing the Related Work section. Additionally, references for Inverse Folding like [REF1] using discrete diffusion are missing.\n[REF1] Yi, Kai, et al. \"Graph denoising diffusion for inverse protein folding.\" Advances in Neural Information Processing Systems 36 (2023): 10238-10257.\n2. (Methodology Explanation) Figures 1/2 and the methodology section writing do not give enough information for the reader to understand the steps of the conditional flow matching methodology. Specifically, from my understanding, the flow matching is generating the distribution s_t at each timestep, more information or illustrations regarding this process seems needed. \n3. (Classifier Guidance) Does the training-free classifier guidance methodology work in a similar fashion to potential in other generative protein models like Chroma and RFDiffusion? What are the differences between these approaches and your flow matching-based approach?\n4. (Methodology Clarification) Removing the side chains for masked positions might still influence the decoding toward sequences that were sampled at the beginning of the denoising process. Do the authors discuss or have an experiment to test this factor or how it influences the generation? An ablation study would help the effect of using the sidechain context.\n5. (Need for Ablation Studies) What is the influence on the results of adding the sidechains? What is the influence on the results of using only the GNN architecture with a sequence decoder, in this case, is your architecture similar to the current LigandMPNN formulation?\n6. (Conditional Flow Matching Formulation) Additional information about the conditional and the formulation from Campbell et al would be helpful for readers.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "b9uSrj7wGn", "reviewer": "Reviewer_dLqF", "summary": "All-atom Discrete Flow Matching Inverse Protein Folding (ADFLIP) is a generative model for designing protein sequences conditioned on full atomic structures. Unlike existing inverse folding methods, ADFLIP progressively incorporates predicted side chains during sequence generation. Additionally, ADFLIP employs training-free classifier guidance to optimize sequences using pre-trained models. Evaluations on protein-ligand, nucleotide, and metal ion complexes, show that ADFLIP achieves state-of-the-art performance in both single-structure and multi-structure inverse folding tasks, highlighting its potential for all-atom protein design.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**1.What is more impactful, the architecture introduced or the discrete flow matching? A lot of attention to the architecture is provided and it clearly is beneficial but deeper ablations as to what degree does the underlying generative framework and architecture play a role would strengthen the contribution.**\n\nThank you for your comment. Both the multi-scale GNN architecture and the discrete flow matching framework play important and complementary roles in ADFLIP.\nThe flow matching framework provides a flexible generative backbone that allows for integrating diverse sources of information—such as multiple structural states and external guidance signals. As shown in Table 4, this enables improved generation performance under dynamic structural contexts.\nOn the other hand, the multi-scale architecture dynamically captures both atom-level and residue-level information, enabling the model to reason over partial side-chain context during sampling. To assess its effect, we conducted an ablation study:\n| **Model**              | **Ligand (%)**     | **Nucleotide (%)** | **Metal Ion (%)**  |\n|------------------------|--------------------|---------------------|---------------------|\n| ADFLIP w/ sidechain    | 62.19 ± 13.60       | 50.21 ± 13.52       | 75.79 ± 18.18       |\n| ADFLIP w/o sidechain   | 61.43 ± 16.20       | 49.74 ± 13.32       | 75.92 ± 16.52       |\n\nWhile the numerical gains in recovery rate are moderate, we believe the use of side-chain information has significant implications for downstream applications of inverse folding, such as enzyme design or protein–ligand interaction modeling—because the chemical interactions with small-molecule ligands or substrates are typically through the protein side chains, and where even minor torsional differences in side chains can result in substantial functional changes. We will point out this advantage of our all-atom approach more explicitly in the revised version.\n\n**What are the mean/std or distributions of the sequence recoveries?**\nWe have computed the mean and standard deviation of the sequence recovery rates for LigandMPNN and ADFLIP as below. We will also include the distribution in the revised manuscript.\n| Method     | Ligand (%)        | Nucleotide (%)    | Metal Ion (%)     |\n|------------|-------------------|-------------------|-------------------|\n| LigandMPNN | 57.96 ± 11.77     | 46.14 ± 12.13     | 69.31 ± 17.46     |\n| ADFLIP     | 62.19 ± 13.60     | 50.21 ± 13.52     | 75.79 ± 18.18     |\n\n\n\n**What happens when you do not use purity sampling wrt the benchmarks?**\nWe performed an ablation study to evaluate the impact of purity sampling on performance across benchmarks. Specifically, we varied the purity threshold and compared it to a fixed-step denoising strategy.\nPurity Sampling (variable threshold):\n| Threshold | Average Non-Protein RR | Std Dev |\n|-----------|------------------------|---------|\n| 0.3       | 0.602                 | 0.1399  |\n| 0.5       | 0.603                 | 0.1411  |\n| 0.7       | 0.588                 | 0.1457  |\n| 0.9       | 0.568                 | 0.1459  |\n\nFixed-Step Sampling:\n| Denoise Steps | Average Non-Protein RR | Std Dev |\n|---------------|------------------------|---------|\n| 2             | 0.565                 | 0.1313  |\n| 5             | 0.592                 | 0.1350  |\n| 10            | 0.593                 | 0.1361  |\n\nWe will add these new results as supplementary data to the revised manuscript.\n[Will we add these to the revised manuscript?] Kai: Yes\n\n\n\n**How is classifier guidance implemented for the discrete flow models? A algorithm would be useful here.**\n\nThank you for this suggestion. We have included the training-free classifier guidance sampling algorithm below, which we will incorporate into the revised manuscript for clarity.\n### Algorithm: Training-Free Classifier Guidance Sampling\n\n**Input:**\n- $N$ protein and non-protein structures $\\{x_1, ..., x_N\\}$\n- Initial sequence $s_0 = (\\texttt{[MASK]}, ..., \\texttt{[MASK]})$\n- Initial sidechains $\\chi_0 = \\emptyset$\n- Time step $\\Delta t$\n- Denoising network $f_\\theta$, sidechain packing network $g_\\eta$, regressor network $h_\\phi$\n- Target property value $y$\n\n**Procedure:**\n1. Initialize $t = 0$\n2. **While** $t < 1$:\n   - **For** $n = 1$ to $N$:\n     - Compute $p^n(\\hat{s}_1) = f(s_t, x_n, \\chi_t)$\n   - Average over structures:  \n     $p(\\hat{s}_1) = \\frac{1}{N} \\sum_n p^n(\\hat{s}_1)$\n   - Compute predicted property:  \n     $\\hat{y} = h_\\phi(p(\\hat{s}_1))$\n   - Compute guidance respect to $s_1$:  \n       $$p(y \\mid \\hat{s}_1) \\approx -\\nabla||y - \\hat{y} ||^2$$\n   - Sample $s_1 \\sim p(\\hat{s}_1) \\cdot p(y | \\hat{s}_1)$\n   - **For** $n = 1$ to $N$:\n     - Compute sidechains:  \n       $\\chi^n_1 = g_\\eta(s_1, x_n)$\n   - Compute reward:  \n     $R_t(s_t, j) = E_{p_{1|t}(s_1|s_t)}[R_t(s_t, j|s_1)]$\n   - Sample $s_{t+\\Delta t}$ using Eq.1\n   - Update time: $t \\leftarrow t + \\Delta t$\n3. **Return**: Final sequence $s_1$", "claims_and_evidence": "As a primary comparison to LigandMPNN, ADFLIP demonstrates comprehensive evidence of its claims.", "methods_and_evaluation_criteria": "Inverse folding benchmarks and evaluations are clear but could use error bars. For example, in Table 1, for each complex structure, 10 sequences were sampled. Given the test set is not large it would be interesting to see the sequence recovery distribution or what is the per sample average and std delta of improvement over LigandMPNN rather than a single globular metric. \n\nGiven here ADFLIP and LigandMPNN are trained on the same data, the benchmarks are fair. It would also be important to add the results for the public LigandMPNN weights which could point to the importance of the training set filters.\n\n\nThe DSMBind-based guidance seems odd as it is a structure-based method. As a result, you generate nondiverse sequences that ideally fold to the same structure that improve the binding affinity. \n - Since ADFLIP cannot update the structure only when the model is incorrect in its sequence prediction, can it improve the binding affinity. \n - The benchmarks here also don't make sense, as why use TM-score rather than comparing the raw structure RMSD with Chai-1 for example, as done in prior evaluations. \n - Furthermore, the affinity gain, which is defined as whether the generated sequence’s predicted binding affinity exceeds that of the wild-type sequence, shows that in 42% of the time the generated sequences get worse than the reference's. \n\nOverall, the metrics are quite soft, and while an interesting approach, leaves more questions. Also a general a 10% improvement over the wild-type binding affinities may also be more difficult and not physically useful due to the exponetial relationship between concentration and affinity. Unclear how this 10% factors into the problem as currently written though.", "theoretical_claims": "No theoretical claims.\n\nThe hyperparmaters used to sample as well as the foundation for guidance and specifics are not provided.", "experimental_designs_or_analyses": "Yes non guided experiements are sound but could benefit from deeper analysis given the small test set.", "relation_to_broader_scientific_literature": "ADFLIP enables all-atom inverse folding with SOTA sequence recovery rates for protein complexes with ligands, nucleotides or metal ions. This is an important step for improving AI assisted protein design.", "essential_references_not_discussed": "Concurrent work so not expected to compare but FAMPNN [1] is worthwhile to discuss.\n\n[1] https://www.biorxiv.org/content/10.1101/2025.02.13.637498v1.full.pdf", "other_strengths_and_weaknesses": "The paper is missing key numerical details with regards to how the model was training, specific hyperparameters for training and generation. Key ablations like why use purity sampling and what happens when using standard DFM sampling are needed to bostler the need for the technical novelty.", "other_comments_or_suggestions": "nit: FLow in line 24", "questions_for_authors": "1. What is more impactful, the architecture introduced or the discrete flow matching? A lot of attention to the architecture is provided and it clearly is beneficial but deeper ablations as to what degree does the underlying generative framework and architecture play a role would strengthen the contribution.\n2. What are the mean/std or distributions of the sequence recoveries?\n3. What happens when you do not use purity sampling wrt the benchmarks?\n4. How is classifier guidance implemented for the discrete flow models? A algorithm would be useful here.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This paper presents a new generative model called ADFLIP for inverse protein folding based on all-atom structural contexts using discrete flow matching. ADFLIP progressively adds  predicted amino acid chains as structural context during sequence generation and allows pretrained models to guide the sequence generation process. Experimental results prove the effectiveness of the proposed approach over the current state-of-the-art approach LigandMPNN. 

The proposed approach is novel and shows very competitive performance over LigandMPNN. The AC hence believes the proposed approach makes a good contribution for the protein design community and vote for acceptance. The authors should address some of the limitations in the revised version (e.g., evaluating the model on more than one data sets, comparison with more recent approaches).
Decision: Accept (poster)