Generalized Protein Pocket Generation with Prior-Informed Flow Matching
Authors: ZAIXI ZHANG
Marinka Zitnik
Qi Liu
Venue: NeurIPS 2024 spotlight (2024)
Keywords: Protein-ligand interaction
Protein pocket design
Generative Models
Molecules
Structure-based Drug Design
Primary area: machine_learning_for_other_sciences_and_fields
TL;DR: PocketFlow is a flow matching model for protein pocket generation that uses protein-ligand interaction priors to improve generation quality.

Abstract: Designing ligand-binding proteins, such as enzymes and biosensors, is essential in bioengineering and protein biology. One critical step in this process involves designing protein pockets, the protein interface binding with the ligand. Current approaches to pocket generation often suffer from time-intensive physical computations or template-based methods, as well as compromised generation quality due to the overlooking of domain knowledge. To tackle these challenges, we propose PocketFlow, a generative model that incorporates protein-ligand interaction priors based on flow matching. During training, PocketFlow learns to model key types of protein-ligand interactions, such as hydrogen bonds. In the sampling, PocketFlow leverages multi-granularity guidance (overall binding affinity and interaction geometry constraints) to facilitate generating high-affinity and valid pockets. Extensive experiments show that PocketFlow outperforms baselines on multiple benchmarks, e.g., achieving an average improvement of 1.29 in Vina Score and 0.05 in scRMSD. Moreover, modeling interactions make PocketFlow a generalized generative model across multiple ligand modalities, including small molecules, peptides, and RNA.

Generalized Protein Pocket Generation with Prior-Informed Flow Matching
Zaixi Zhang Marinka Zitnik
Liu
1: School of Computer Science and Technology. University of Science and Technology of China
2:State Key Laboratory Cognitive Intelligence, Hefei, Anhui, China
3:Harvard University
zaixi @ mail www..udu.c..c.... marinka hasshaavardd.ed gilliul@ustc..euuu... ustc.edu.cn
Abstract
Designing ligand-binding proteins, such enzymes and biosensors, is essential in bioengineering and protein biology. One critical step in this process involves designing protein pockets, the protein interface binding with the ligand. Current approaches to pocket generation often suffer from time-intensive physical compu- tations template-based methods, well as compromised generation quality due to the overlooking of domain knowledge. To tackle these challenges, we propose PocketFlow. generative model that incorporates protein-ligand ligand interaction priors based on flow matching. During training, PocketFlow learns to model key types of protein-ligamt interactions, such hydrogen bonds. In the sampling, PocketFlow leverages multi- caalti-gaaularity guidance (overall binding affinity and interaction geom- etry constraints) to facilitate generating high-affinity and valid pockets. Extensive experiments show that PocketFlow outperforms baselines on multiple benchmarks, e.g., achieving an average improvement of 1.29 Vina Score and 0.05 in scRMSD. Moreover, modeling interactions make PocketFlow generalized generative model across multiple ligand modalities, including small molecules, peptides, and RNA.
Introduction
Proteins are the fundamental building blocks of living organisms, often interacting with ligands (e.g.. small molecules, nucleic acids, and peptides) to execute their functions. Recently, computational methods have played critical roles designing functional proteins binding with ligands with broad applications in bio- bio-engineering and therapeutics [76] 52
g 58). For example. Polizzi methods design de novo proteins binding with the drug apixaban [5]; Ych et al.. 83 use deep learning methods to generate efficient light-emitting enzyme luciferases with selective substrate catalysis capabilities. To design such ggaadd-iiddngg proteins, an essential step is to design protein pockets, the protein interface interacting with binding ligands [68] 39 12 28 However, the complexity of gygand-proteil interactions, the variability of protein sidechains, and sequence-structure relationships pose great challenges for pocket design
50
51 67
al., (65) leverage template-mateet
25
51
48
Traditional methods for pocket design mainly focus on physies modeling or template-matching 12
28
65 19 62]. However, the involved physical energy calculation or substructure enumeration could be quite time-consuming. Recent advancements in pocket design have benefited lot from deep learning- based approaches [73 92 83,
47 [11, [88.. However, these innovative approaches often overlook essential domain knowledge, such as the pootein-ligand interactions and the geometric constraints governing them. Though they can efficiently generate many candidates, further screening/optimization required to get valid and high-affinity pockets. Moreover, most methods are restricted to small molecule ligands, omitting other important ligand types such as nucleic acids [ and peptides (53
Marinka Zitnik and Qi Liu are the corresponding authors.
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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To tackle the aforementioned challenges, we propose PocketFlow, protein-ligand interaction prior- informed flow matching model for protein pocket generation. Firstly, we define conditional flows for diverse data modalities in the protein-ligand complex including backbone frames, sidechain torsions, and residue/interaction types. We choose flow matching as the generative framework because of its efficiency and flexibility [3 (7). Furthermore, PocketFlow explicitly learns the dominant protein-ligand interaction types including hydrogen bonds [35], salt bridges [24), hydrophobic interactions [6]]. and π л stacking [36). which are crucial for strong binding stability and affinity of pootein-ligande pairs 22.. In the sampling process, binding affinity and interaction geometry guidance are adopted to encourage generating pockets with high affinity and validity. Specifically, we leverage a lightweight binding affinity predictor to predict the affinity of the generated complex and apply distance and angle constraints to promote desirable motein-ligane interactions. To circumvent the non-differentiability issues associated with residue type sampling, we employ novel sidechain ensemble method for interaction geometry calculations. Extensive experiments show that PocketFlow provides a generalized framework for high-quality protein pocket generation across various ligand modalities (small molecules, RNA, peptides, etc..). The code is provided at Our main contributions are summarized as:
https: //gi //tgt/bb..t.ttt.//g cww/coo/aaaaao
Our study broadens the scope of protein pocket generation tasks to include various ligand modalities such as small molecules, nucleic acids, and peptides.
Generalized tasks:
Novel method: PocketFlow combines the recent progress of flow-matching- based generative models and physical/chemical interaction priors (affinity guidance and interaction geometry guidance) to generate protein pockets with enhanced affinity and structural validity.
PocketFlow outperforms existing methods on various benchmarks of pocket generation, producing an average improvement of 1.29 in Vina score and 0.05 in scRMSD. Further interaction analysis highlights the model's ability to foster benefi- cial protein-ligand interactions, e.g., an average of 4.12 hydrogen bonds, while markedly reducing steric clashes (an average of 1.21 in generated pockets v.s. 4.59 in the test set).
Strong performance:
2
Related Works
2.1
Generative Models for Protein Generation
Recent advancements in deep generative models have significantly advanced the field of de novo protein structure generation, enabling researchers to create proteins with specific desired properties
94 91). For example, RFDiffusion [8] employs denoising diffusion proba- 33 in conjunction with RosFold 7 for de nove protein structure generation. achieved notable success by generating proteins validated in wet lab experiments. Chroma [37] leverages similar diffusion process with efficient neural architecture for molecular systems that enables long-range reasoning with sub-quadratic scaling. It also demonstrates strong capabilities to satisfy constraints including symmetries, substructure, shape, semantics, and simple natural- language prompts. Recently, models leveraging flow matching frameworks have shown promising results protein generation [86]
81
37
86
13
bilistic models
[3]. For example, FoldFlow [33 proposed series of www-matching-based generative models for protein backbones with improved training stability and efficiency than diffusion- models. FrameFlow [84] 885 further shows sampling efficiency and achieves success on motif-scaffolding tasks with flow matching. However, these protein gener- ation methods are not directly applicable to protein pocket generation that requires protein-ligand interaction modeling.
13
85
40
2.2 Protein Pocket Generation
Protein pockets are the protein interface where the ligand binds to the protein and pocket design is a critical task for bioengineering [68] 39
28 Traditional methods for pocket design focus on physics modeling or pepplattemaaccing 12
12
62 93.. For example, PocketOptimizer [62] predicts mutations in protein pockets to increase binding affinity based on physical energy calculation, which may bring a large time burden. The recent progress in protein pocket design has
For instance, FAIR [92 co-designs pocket structures and sequences using a two-stage coarse-to- fine refinement approach. RFDiffusion All-Atom [8 extends RFDiffusion for joint modeling of protein and ligand structure to generate
been facilitated by deep generative models 73 92
93 48

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grsand-binding protein and further leverages Proeem/PPNN@TLLLgaddMPPPP for sequence design. However, deep-learning methods lacking physical/chemical prior guidance may be less accurate and generalizable. In PocketFlow, we aim to design prior-guided pocket generative models.
3 Preliminaries
3.1
Notations and Problem Formulation
(a)
(b)
Forward Process
Ligand
One PocketFlow
Interaction Type 2011
Alem gill
Rocidus ape di
Co
Cr
type: Liaine
Affinity Protctrr [v(k))]
Weighted Bun
Interaction Geometry Guidance
Farm oriontationn
00
Hydrogen bridges
Hydrophobic
stacking
((G))
Computc Gradiont
Cappottin g!
Figure 1: (a) Parameterization of pooein-llignde complex. (b) Illustration of PocketFlow forward process. The affinity and interaction geometry guidance are proposed to improve affinity and structural validity. The red/blue lines denote the unconditionaalguiiaan paths respectively.
Notations. As shown in Figure a)), model protein-ligand complex C (P, g consisting of protein P and ligand 9 (small molecule as an example). Protein P is composed of a sequence of residues (amino acids) with residue types denoted (+ E R220 Consistent with [92] [87]. the protein pocket R P is defined as the subset of residues closest to the ligand atoms under threshold 8 (c.g.. 3.5 Å). In residue, the backbone structure (consisting of Ca. N, C, O) is parameterized with C. position (+) E R and frame orientation matrix (a) E SO(3) following 443 84 The sidechain
is parameterized with maximal 4 torsion angles x = {xx1 x x²2xx " E [0, 2T) Given these key parameters, the full atom protein structure can be derived with the ideal frame coordinates and the sidechain bond length/angles 43 The protein-ligant interaction type for each residue is marked as (10) E IR (Hydrogen bond, Salt bridge, Hydrophobic, ग-ग stacking, no interaction). A pocket with Nr residues can be compactly represented as R = (c(1) ( O , ((),, 7(0) }(, As for the ligand, use generalized atom-level representation that accommodates various modalities including small molecules, peptides, and RNA. The atom types and bonding information between atoms are given and PocketFlow predicts the N₁ ligand atom coordinates (also denoted as (i) for conciseness).
Problem Formulation. PocketFlow co-designs residue types and 3D structures of the protein pocket conditioned on the ligand (could be small molecules, nucleic acids, peptides, etc.) and protein scaffold (the other parts of protein besides the pocket region, i.e., P R). The ligand structure G is also predicted. Formally, PocketFlow aims to learn conditional generative model ps (R, GIP \ R).
3.2 Preliminaries on Flow Matching
Flow matching (FM) [77] is a simulation-free method for learning continuous normalizing flows (CNFs) [8] that generates data by integrating an ordinary differential equation (ODE) over learned vector field. Here, we first give an overview of Riemannian flow matching [17]. On a manifold M,
the CNF ())+) M - M is defined by integrating along time-dependent vector field (z) E T. where T.M denotes the tangent space of the manifold at æ AM: a (x)) u. (v)((x)), vo(x)
a, E [0, 1]. The flow transforms simple distribution Po towards the data distribution Pl. In FM,
the target is learn neural network vo (z, that approximates ue(x), while the vanilla regression
loss: CFM (B) E.-.s(o. (a)) (o t) - uz (2) is hard to compute in practice. Here, 2/00 1]
is the uniform distribution between 0 and and
[1 is the norm induced by the Riemannian
3

---

metric Instead, it is tractable to define conditional vector field uz and obtain the conditional FM objective: LCFM(0) 11.0//0.11. (ar)) ).P (1,,,)) t) (2(2))))] g. It has been proved that
VoCrMs (0) VoLCFM (0) [57 17.. the inference, ODE solvers are applied solve the ODE,
e.g., 11 = ODESolve vo, 0, 1) where is the initialized data and 21 is the generated data.
PocketFlow
PocketFlow is an interaction prior-informed flow-matching model for pocket design. In this section, we first define PocketFlow for different components in the protein-ligand complex (backbone Sec.
sidechain in Sec. 4.2 and residuc/interaction types in Sec 4.3) Then we show the prior-informed
traiiing and sampling in Sec. and
4.1 PocketFlow on SE(3)
As introduced in Sec. 3.1 each residue frame can be parameterized by a rigid transformation
T = (x(*) ( within SE(3) space. The backbone with N, residues can thus be described by a set of transformations [T ..... [[) belonging to SE(3) and constitutes a product space. The following deduction focuses on a single frame but can be generalized to the whole protein backbone. The C. coordinates (+)) are initialized with linear interpolation and extrapolation based the coordinates of neighboring scaffold residues following [92]. The prior distribution of O is chosen as the uniform distribution on (O(3). Following previous works 17 84], the conditional flow for (+)) and O defined ,r (1 =))² (8) + tax and 0 exp ( (t (oogo." (O(*)) respectively, which are geodesic paths in RR and SO(3). The exponential map expo, can be computed using Rodrigues' formula and the logarithmic map logo, is similarly easy to compute with its Lie algebra
so(3) 84 The loss function of PocketFlow on SE(3) is the summation of the two losses below:
N.+N,
(oo Be.ps
N +
1
N
(ar
11
(8)
(6) + a
2
(1)
Nr
log (0
Cori (.0m000))m000000000000... N,
Σ
(0
1-t
SO(3)
where we additionally consider N2 ligand atom coordinates in (o), for which we use Gaussian distribution at the center of ligand mass as the prior distribution.
4.2 PocketFlow on Torus
As described Sec. 3.1
sidechain conformation of each residue can be represented as maximally
four torsion angles x (3) {x"1 x²2 x3 xx1) E [0, 2m) In a pocket with N, residues, the
#1)
sidechain torsion angles form a hypertorus T TIN." which is the quotient space RAIN, /2 with the equivalence relation: X (x'..... ..N.)
,NN.))
(x" + 2 2=,..., ANN.) ~ (x' ....... x 4N, + 2xx
41 90]
Following [42], the prior distribution is chosen
uniform distribution over T We regard the torsion angles as mutually independent and use interpolation paths as: X = (1 - t)xo + f(x1 - Xo)
where Xi (xi Xo + T) mod (2T) + Xo. The loss for the torsion angles is defined as:
Nr
(x Lior (0) = EEr, (xpp
1
2 (xi
(x)
xi + +x6
(3)
N
4.3 PocketFlow on Residue Types and Interaction Types
Each residue is assigned probability vector with 20 dimensions: c(t) E 20 The prior distribution is set as the uniform distribution and the conditional flow is defined as the Euclidean interpolation between co and C₁ (one hot vector indicating residue type). C is probability vector because its
summation over all types equals 1. We leverage the cross-entropy loss CE(s,) following [53 73 16):
N.
Lres
CB
+ (1 - 1) (c (c) 1), ()),
(4)

---

which measures the difference between the true probability and the inferred one 2/0 t)ng (6) (c()) t). We also note the recent progress of the sequential flow matching methods which can be seamlessly integrated into PocketFlow and are left for future works.
=
c.
+
74 [6
It has been shown that modeling Protein-ligand interactions explicitly in biomolecular generative models can effectively enhance the generalizability [89 (97]. We used the protein-ligand interaction profiler (PLIP) [69] to detect and annotate the protein-ligand interactions for each residue by analyzing their binding structure. Following 197]. 4 dominant interactions are considered including salt bridges, π-д stacking, hydrogen bonds, and hydrophobie interactions. For simplicity, a residue has more than one interaction, we take the one with the highest rank, which considers both the contribution to the binding affinity and the frequencies (see Appendix,
B Similar to residue types, interactions i=1' Besides the interaction types, we also consider an unknown/none type. Similar to Equ. 4 have the interaction loss:
are modeled as category data: = {T() N=
Nr. CE
Linter = -ew.kr...ppcchhheo0lhp..l.l.
+ (1-0))))
(5)
4.4 Model Training
Network Architecture. To design the binding protein pocket R = (c(0) x:()) 100'x(0
7())
ii=1 we utilize an architecture modified from the FrameDiff [86] which incorporates Invariant Point Attention (IPA) from AF2 43) to encode spatial features combined with transformer layers [79 to encode sequence-level features. To achieve unified representation both protein residues and ligand atoms, we follow the approach used in RoseTTAFold All-Atom [49] where each ligand atom is treated as an individual residue. Initial representations are based on atom element type embeddings, and the frame orientations are set as identity matrices. To further model the covalent bonding information (single bond, double bond, triple bond, or aromatic bond), we also add the bond embeddings to the 2D track. We use additional MLPs based on the residue embeddings to predict the residue types, interaction types, and sidechain torsion angles. Instead of directly predicting the vector field, we let the model predict the final structure at t= 1 and interpolate obtain the vector field. More details introduced in the Appendix. C
and update the binding ligand coordinates {
Overall Training Loss. The overall training loss of PocketFlow is the summation Equ. П
4 and 5 To fully utilize the protein-ligand context information, we use the whole protein-ligand complex structure at 1, i.e., C, = P. U.G Gr as the inputs of (o(-)))
Equivariance. Following (84, (3). we perform all training and sampling within the zero center of mass (CoM) subspace by subtracting the CoM of the scaffold from the initialized structure. PocketFlow has the ideal SE(3)
property of geometric generative models:
Theorem Denote the trass-tttnnooooaatoon as Ty. PocketFlow pe (R, G P R.) SE(3) equivari- ant i.e, Po(T,RR [TT (P) R)) P& GIP \ R), where R denotes the designed pocket, G is the binding ligand, and P R is the protein scaffold.
The main idea is that the SE(3)-invariant prior and -Eu))--quivariant neural network lead to an Squiivaqu generative process of PocketFlow. We give the full proof in the Appendix. D
4.5 Pocket Sampling with Prior Guidance
To improve the binding affinity and structural validity of the generated protein pocket, we proposed a novel domain-knonn knowledge-guider guided sampling scheme. Generally, we use classifier-guider sampling 233 and consider overall binding affinity guidance and interaction geometry guidance. To encourage the generated protein-ligane complex to satisfy a specific condition y. we apply the Bayes rule [3] 30
Vc, log p(C, y) = Vc, l(g)(C.)) + Vc, log log((,)).),
(6)
where Ve, log p(C.) is the unconditional vector field (c, t) and Ve, log (oy(()) is the guidance term to constrain the generated complex in a specific condition y.
Binding Affinity Guidance. To generate protein pockets with higher binding affinity to the target ligand, we train a separate lightweight affinity predictor for guidance (More details of the predictor in Appendix. E.I) Specifically, the data points in the training set are annotated I if their affinity is
5

---

higher than the average score of the dataset, otherwise 0 [66]. Because the intermediate structure is noisy, we take the expected structure at & = 1, i.e., Ci (C,) from the model output and feed it into the predictor. Then we have the classifier-guie guideed velocity field üg (C,, t):
Ög (C2 t) = to (C2, 1) - vVe, po = (C,),
(7)
where we add scaling factor 7 > 0 that controls the gradient strength. pe is the affinity predictor and Ub E {0, 1 is the binary label of binding affinity.
Interaction Geometry Guidance. Inspired by 89]. we considered 4 dominant non-covalent inter- action types in PocketFlow, including salt bridges, т-т stacking, hydrogen bonds, and hydrophobic interactions. The local geometries need to satisfy a series of distance/angle constraints form strong interactions [69]. For example, for hydrogen bonds, the distances between donor and acceptor atoms need to be less than 4.1 À and larger than 2 Á to reduce steric clashes [35]. The following inequality is a necessary condition for residues in (C₁) with predicted interaction label I as hydrogen bond:
(z(()) x²(5)
min
min
S Lmaxx
iE (A) JEg
where Liin and Imax distance constraints; with predicted hydrogen bonds. With little abuse of notations, (9) and x denote the candidate atom coordinates in the residue and ligand respectively. The distance guidance can be derived as:
A(k)
libond denote the k-th residue in the set of residues
Antoonal
( Gimax (0, -1 m + Ea max (0, - -
Vc.
where ((*) = min LEA : || |/x0(0) - 2010112 and Eı, E2 > O are constant coefficients that control
the strength of guidance. The detailed deduction is included in the Appendix. E.2 Besides the distance constraint, the hydrogen bond needs to satisfy the acceptor/donor angle constraint [69], e.g.,
the donor/acceptor angle needs be larger than 100%, The angle guidance is presented follows:
AAhdonal
Ve...
max(0, ammin (()),,
(10)
where di()) max
se (lt) Jeg hangle(x (())) and hangle(-,-) calculates the acceptor/donor
angle in Figure. Es O is the guidance coefficient. The guidance for the other interactions is discussed in Appendix.
E We note that the residue type/side chain structure of the pocket is not
determined during the sampling. Directly sampling from the residue type distribution makes the model not differentiable 38 We propose the Sidechain Ensemble for the interaction geometry calculation, i.e., the weighted sum of geometric guidance with respect to residue types (Figure. (6)
Sampling. With the initialized data, the sampling process is the integration of the ODE dC, (o t) from / = 0 to ( = with Euler solver [14]. 7, E2, and &a are set as in the default setting. To apply the guidance, we use úp which is vo plus guidance terms (Equ.
de
and 10
X Xi+A: reg
(8)
X
(8) + 60 (x (1) .))a))
(11)
2 At 2 + (x) ,t)at;
(6)
O = 0.00 exp (O)( .t)At)
(12)
( S+ = norm (c.) + oo(c :)At):
1/ norm ( + 00 (1 .))+):
(13)
where At is the time step; ua(:; 1) denotes the subcomponent of the vector field for different variables. norm(-) means normalizing the vector to probability vector such that the summation is 1, and reg(-)
means regularizing the torsion angles by reg(T) = (r + T) mod (2T)) ( π.
5
Experiments
5.1 Experimental Settings
Datasets.
Following previous works 29 71 92 we consider two widely used protein-small molecule
binding datasets for experimental evaluations: CrossDocked dataset (27 generated through cross- docking and is split with mmseqs2 [75 30% sequence identity, leading to train/val/test set of

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Table 1: Evaluation of different models on mall-moleeuue- protein pocket design. We report the average and standard deviation values across three independent runs. We highlight the best two results with bold text and underlined text, respectively.
CrokeDocked (C)
Binding MOAD SLR
Model
(AR
Vina
AAR
Vina
Test set
0.65
-7.016
0.67
-8.076
DEPACT
31.52::3.265 26%
0,73=0000
-6.632:0.16 18
35,30:22. 19%
0.77=0.08
-7.571=0.15
dyMEAN
38.71+22.169
0.79:00.09
6.855540.06
41.22:4 1.0%%
0.80+0.12 12
-7.675=0.09
FAIR
40.16::1.1%%
0.75
-7.015=00.12
43.68::0.92%
0.72:40.04
-7.930=00115
REDiffusionAA
50.85::: .85%
0.68+0.00
-7.012:40.09
49.09 2,49%
0.70=00044
-8.020=0.11
PocketFlow
12.19=1.344% %
0.67=00.04
0..236:10166
54.30=1.705% %
0.68:20033
-9,370=0.24
w/o Guide
50.94441.333
0.65+0004
-7.37540.10
1.543.
0.64
8.380=00.1
w/o Geo Guide
49,80#1.4100
0.68=0.03
-8.120=0.14
1.,49%1.533%
0.71
-9.17=0.22
w/o Gen & Aff Guide
48.50 1.66%
0.71 0.006
-7.13540.13
49.71 ..68%
0.69
8.241
w/o Inter Learning
1.27%
0.66
-7.968:10.15
$2.25 1.74%
0.68
-..031
Reference (INJE)
Designed (INJE)
Reference [2PQL]
Designed (2PQL)
Pocket Swep Hl BICHAAADHH
Porkett Seg: RICISADGHY Vinia Scorec-
Pocket Seq: FINHVDFM Vina Scone:
Pociset Seep LIVIVOFM Vina Score: -0.06
Vina Scoree-66.. -6.53
Figure 2: Case studies of mmall-molecule-inddiie designed structures/sequenees of two protein pockets from the CrossDocked (PDB ID: INJE) and Binding MOAD (PDB ID: 2PQL) datasets respectively.
protein pocket design. We show the reference and
100k/100/100 complexes. Binding MOAD dataset [3 contains experimentally determined protein- small molecule complexes and is split based the proteins' enzyme commission number (}) resulting in 40k protein-small molecule pairs for training, 100 pairs for validation, and 100 pairs for testing. To test the generalizability of PocketFlow other ligand modalities, we further consider PPDßench (3) which contains 133 non-redundant complexes of protein-peptides and PDBBind RNA 88), which contains 56 protein-RNA pairs by filtering the PDBBind nucleic acid subset. More details of data preprocessing are included in the Appendix. A Considering the distance ranges of protein-ligee ligand interactions [60). we redesign all the protein residues that contain atoms within 3.5 Å of any binding ligand atoms, i.e., the pocket area. The number of designed residues is set the same as the reference pocket. We sample 100 pockets for each complex in the test set for evaluation.
Baselines and Implementation. PocketFlow is compared with four state-of-the-ar representative baseline methods. DEPACT [19] is a template-mates
method [88] for pocket design by searching and grafting residues. dyMEAN 47 and FAIR [92] are deep-learning methods based on equivariant translation and iterative refinement. RFDiffusionAA (48) is the latest version of RFDiffusion [81], which can directly generate protein pocket structures conditioned the peuuenccestructure co-design scheme in dyMEAN and FAIR, the residue types and sidechain structures in RFDiffusionAA determined with LigandMPNN (22 in post-hoc manner.
the ligand. Different from
For experiments on PPDBench and PDBBind RNA, we pretrain PocketFlow and baseline models on the combination of the CrossDocked and Binding MOAD dataset, in which we carefully eliminate all complexes with the same PDB IDs to avoid potential data leakage. Then we represent the peptide and RNA similar to small molecules (atom coordinates/tpps and covalent bonds) and input to PocketFlow for sampling without fine-tuning. For simplicity, the structure of peptide/RNA is set fixed. All the baselines are run the same Tesla A100 GPU.
Performance Metrics. We employ the following metrics to comprehensively evaluate the validity of the generated pocket sequence and structure. Amino Acid Recovery (AAR) is defined as the overlapping ratio between the predicted and ground truth residue types. In bioengineering, mutating too many residues may lead to instability or failure to fold [4] Therefore, larger AAR is more favor- able. scRMSD refers to self-consistency Root Mean Squared Deviation between the generated and the predicted pocket's 's backbone atoms to reflect structural validity. Following established pipelines
7

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Table 2: Evaluation of different approaches on the peptide and RNA datasets. DEPACT is not reported here because it is specially designed for small molecules. dyMEAN, FAIR, and PocketFlow are pretrained on protein-small molecule datasets and we use the checkpoint of RFDiffusionAA [
PPDBench
PDBBind AAG
Model
AAR (T)
(J
(LG
AAR
(ERMSD
Test
0.64
0.59
dyMEAN
26.29:t:105%%
0.71::0.05
-0,23::0.04
25,90 1.2%%
0.71=00.04
-0.18:0.003
FAIR
32.53++0.89%
0.86-20.04
0.054+0.07
24.90=00.229
0.80+0005
0.134-0.05
RFDiffusionAA
46.85:
0.65::0.06
00.6::0.05
44.69=1.9095
0.65
0045::0.007
PocketFlow
48.19::1.34% %
0.67::0.04
-1.06::.004
14.34:11.14%
0.69=0.01
40.7::10.07
w/o Aff Guide
18.7
0.70=0.02
-0.47 10
42.15= 1.56%
0.68==0.04
-0,35:20.11
Geo Guide
47.30-+-1.94%
0.72++0.05
00.9640.088
41.734+2.35%
0.77-+0.09
10.65+0.15
w/o Geo & Aff Guide
44.63+t1.799
0.78=00.55
-0.01
29.70+1.2249
0.78=0.06
-0,26:00.08
w/o Inter Learning
36.41 +1 1.38%
0.74+00.0
-0.34:+0.05
36.27 1.47%
0.82-+0.13
0,23++0.06
Reference (INQ7)
Designed (1NQ7)
Reference (SDNO)
Designed (SDND)
Pocket Seq: K2JPE
Pocket Seq: KOLME
Pocket Seq: NRYKTYND
Pocket Seg: ORYKTYDO
22G: 1.50
A56: 0.75
Figure Case studies of peptide/RNA-binne and designed structures/sequences of two protein pockets from PPDBench (PDB ID: INQ7) and PDBBind RNA (PDB ID: 5DNO) datasets respectively. The ligand structures (orange) are set fixed.
protein pocket design. We show the reference
for each generated protein structure, eight sequences are firstly derived by ProteinMPNN and the folded structures with ESMFold (56). report the minimum scRMSD for the predicted structures. To measure the binding affinity for protein-small molecule pairs, we calculate Vina Score with AutoDock Vina (78 following 664 92]. For protein-peptide and protein-RNA pairs, we calculate Rosetta AAG [5) and Rosetta-Viene RNP-AAG <4] respectively that measure the binding affinity change. The unit kcal/mol and a lower Vina score/AAG indicates higher affinity.
77
21
5.2 Smalll-moleutt--inding Pocket Design
Table shows the results of different methods on the CrossDocked and Binding MOAD dataset for small-molecule-bnnniie pocket design. We can observe that PocketFlow overperforms baseline models with a clear margin on AAR, scRMSD, and Vina scores, demonstrating the strong ability of PocketFlow to design pockets with high validity and affinity. The average improvements over the RFDiffusionAA on AAR, scRMSD, and Vina Score are 3.3%, 0.05, and 1.29 respectively. PocketFlow also predicts more aligned sidechain angles with ground truth as evidenced in Table. [ Compared with baselines, PocketFlow enjoys the advantage of powerful flow-matching architecture and effective physical/chemical prior guidance. Different from the post-hoc manner of deriving sequences in RFDiffusionAA [8], the co-design scheme also encourages sequence-structure consistency. We also compare the generation efficiency of different models in Figure. 7 Considering the pocket quality improvement brought by PocketFlow, the time overhead is acceptable.
We also perform ablation studies Table. [ where w/o Aff Guide, w/o Geo Guide, and w/o Geo & Aff Guide indicate generating pockets without Affinity Guidance, Interaction Geometry Guidance, and all Guidance respectively. In w/o Inter Learning, we retrain a model without learning interaction types and generate pockets without Interaction Geometry Guidance as well. We can observe that the Affinity and Geometry Guidance indeed play critical roles enhancing binding affinity and structural validity. For example, the Vina score drops to -7.135 without guidance from -8.236 on the CrossDocked dataset. We also note Affinity Guidance may have slight side effects on scRMSD and we need to balance the strength of unconditional and guidance terms (more results in Appendix. F.

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Methods
Clash
HB (1)
Salt (1)
Hydro (1)
x-
Test set
4.59
3.89
0.26
5.89
0.32
DEPACT
6.72
3.10
0.14
5.70
0.16
dyMEAN
4.65
3.07
0.17
5.85
0.20
FAIR
4.90
3.30
0.18
5,47
0.15
RFDiffusionAA
3.58
3.76
0.22
5.65
0.31
PocketFlow 1.21
4.12
0.27
6.03
0.28
Table 3: Interaction analysis of the generated protein pockets on the CrossDocked dataset. We measure the average number of steric clashes (Clash), hydrogen bonds (HB), salt bridges (Salt), hydrophobic interactions (Hydro), and π- stacking (æ лτ) per protein-ligand complex. More results on the variants of PocketFlow are included in Appendix F
5.3 Generalization to Other Ligand Domains
Besides small molecules, binding protein with other ligand modalities such as peptides and nucleic acids play critical roles in biomedicine [82] However, the available dataset size compared with small molecules prottcin complexes is quite limited (c.g., ~ 100 in PPDBench v.s. over 100k in CrossDocked). Here, we explore whether the pretrained PocketFlow on the combination of CrossDocked and Binding MOAD can generalize to peptide and RNA-binding pocket design in Table. 2 The peptide and RNA ligands represented molecules (atoms and covalent bonds) to fit into the pretrained models. We have observed that PocketFlow achieves performance comparable to the state-of-the-ane art baseline, RFDiffusionAA. with prior guidance significantly enhancing its generalizability. Our hypothesis is that the protein-ligand interactions and fundamental physical laws learned by PocketFlow are applicable universally across various biomolecular domains [89] (97]. By
explicitly incorporating physical and chemical priors into the generative model, PocketFlow not only aligns with these universal principles but also gains marked advantage of generalizability.
5.4 Interaction Analysis and Case Studies
We adopt PLIP (69 and posecheck [31] to detect the protein-ligand interactions in the generated pockets. In Table. we show the average number of steric clashes, hydrogen bond donors, acceptors, and hydrophobic interactions (without redocking). We observe that PocketFlow with fewer clashes and more favorable interactions. For example, the average steric clashes for RFDiffusionAA and PocketFlow are 3.58 and 1.21 respectively. The average number of Hydrogen Bonds for RFDiffusionAA and PocketFlow are 3.76 and 4.12 respectively. These improvements can be attributed to the model's affinity/geometry guidance and its enhanced modeling of pocket/ligand flexibility, both which promote the formation of advantageous moteinn-liaane interactions while minimizing clashes. Some interaction types such the reference, which may be due to the low frequency of these interactions in the dataset.
generate pockets
stacking in PocketFlow
little less than
Figure. 2 and show examples of the generated pockets for small molecules, peptides, and RNA. PocketFlow recovers most residue types and changes several key residues to achieve higher binding affinity. The overall structure of the pocket, including the sidechains, is generally well-maintained.
5.5 Limitations and Broader Impacts
While PocketFlow is a powerful generative method for pocket generation, we find the following limitations for further improvement. First, PocketFlow is only trained on protein-small molecule datasets in the paper. In the future, incorporating protein pooein-peptides/nullld acids/metal datasets, even the generated data from AlphaFold3 2 would be promising directions. Second, the integration of pretrained protein language models PocketFlow's performance. Additionally, wet lab experiments to verify PocketFlow's efficacy are planned. Potential negative impacts may include the misuse of PocketFlow for creating harmful biomolecules 332. Rigorous oversight and screening access to the model should be considered.
55 and structure models [96] could significantly enhance
Conclusion
In this paper, we proposed PocketFlow, protein-ligand interaction prior-informed flow matching model for protein pocket generation. We define multimodal flow matching for protein backbone

---

frames, sidechain torsion angles, and residue/interaction types to appropriately represent the protein- ligand complex. The binding affinity and interaction geometry guidance effectively improve the validity and affinity of the generated pockets. Moreover, PocketFlow offers unified framework covering small-molecule, nucleic acids, and eeptides-bindigg protein pocket generation.
7
Acknowledgements
This research was supported by grants from the National Natural Science Foundation of China (Grant No. 62332095) and the Fundamental Research Funds for the Central Universities.
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A Dataset Preprocessing
We consider two widely used datasets for benchmark evaluation: CrossDocked dataset [27 contains
22.5 million protein-molecule pairs generated through cross-docking. Following previous works we filter out data points with binding pose RMSD greater than Å. leading to refined subset with around 180k data points. For data splitting, we use mmseqs2 [75] to cluster data at 30% sequence identity, and randomly draw 100k protein-ligand structure pairs for training and 100 pairs from the remaining clusters for testing and validation, respectively; Binding MOAD dataset [34 contains around 41k experimentally determined protein-ligand complexes. Following previous work 77 we keep pockets with valid and moderately 'drug-like' ligands with QED score 2 0.3. We further filter the dataset discard molecules containing atom types E {C, N, O, B, Br, CI, P. I, F) as well as binding pockets with non-standard amino acids. Then, we randomly sample and split the filtered dataset based on the Enzyme Commission Number (EC Number) do not contain proteins from the same EC Number main class. Finally, we have 40k protein-ligand ligand pairs for training, 100 pairs for validation, and 100 pairs for testing. For all the benchmark tasks in this paper, PocketFlow and all the other baseline methods are trained with the same data split for fair comparison.
[59 64 92
ensure different sets
To test the generalizability of PocketFlow to other ligand modalities, we further consider PPDBench B1. which contains 133 non-redundant complexes of protein-peptides and PDBBind RNA (80), which contains 56 protein-RNA pairs by filtering the PDBBind nucleic acid subset with RNA sequence lengths longer than 5 and less than 15.
B Considered Protein-ligand Interactions
Table 4: Key geometric constraints to define protein-ligant interactions distances in Angström.
69
Angles in degree and
Variable
Value
Description
Ref.
INTER_ WNTER_DIST_ITT DIST_MIN MIN
2.0
Min. distance avoid steric clashes
31
4.0 Á
Max. distance of carbon atoms for hydrophobic interaction
69
HBOND DWSTDIITMAAA MAX
WROND_DIST_IAE
4.1
Max. distance between acceptor and donor hydrogens bonds
HBOND_DOK SOON_ANGLE_WN
100%
Min. angle at the hydrogen bond donor (X-D...A)
35
HBOND_ACCS LACCACCAAEL_MTT
100%
Min. angle at the hydrogen bond acceptor .)
35
PISTACK DITTACKDIIST___A _IS___MSSXAAX MAX
7.5 Á
Max. distance between ring centers for stacking
PISTACK_ANG ANV_DEV
30"
Max. deviation from optimum angle for stacking
69
DESTACK_DFFSET__CC PISTACK DFFSET MAX
2.0 Á
Max. offset between aromatic ring centers for stacking
69
AALTBRIDGE_DIST.MAA
5.5 Á
Distance between two centers of charges in salt bridges
10
we considered dominant non-covalent interaction types in PocketFlow, including salt bridges, π-ग stacking, hydrogen bonds, and hydrophobic interactions (ranked based on their contribution to affinity and reversed frequency). The frequency statistics are listed in Table
Following 97
Salt bridges [0), which are electrostatic interactions between oppositely charged cen- ters, are often considered among the strongest interactions in protein structures and other biomolecular complexes. They can significantly contribute to stability and binding affinity due to their strong electrostatic nature. To form salt bridges, two centers of opposite charges need to be below distance of SALTBRIDGE DIST MAX.
Hydrogen bonds 35 oceur between a hydrogen atom covalently bonded to more elec- tronegative atom (like oxygen or nitrogen) and another electronegative atom. Their strength is less than that of salt bridges but significant in biological contexts.
A hydrogen bond is established between hydrogen bond donor and acceptor (OpenBabel 63 is used to detect hydrogen bond donor/acceptor). The distance between the donor and acceptor needs to be less than HBOND DIST _MAX. The donor and acceptor angle needs to BROND_DON
larger than HBOND DON_ ANGLE MIN and HBOND ACC_ BOCC_ANGL___P MIN respectively. Since PloketFlow only considers heavy atoms (no hydrogen atoms), consider the geometry
16

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of hydrogen bonds without protonation 35 (see Figure, -.. For simplicity, we do not differentiate donor/acceptor in the interaction geometry guidance.
क- stacking [69 involve the stacking of aromatic rings (like those found in phenylalanine, tyrosine, tryptophan) due to favorable van der Waals forces and sometimes electrostatic interactions, म-ズ stacking is crucial in the structure of nucleic acids and proteins, especially in the active sites of many enzymes, although they are generally weaker than hydrogen bonds and salt bridges.
To form л-ズ stacking, we first need two aromatic rings (OpenBabel 63 is used to detect aromatic rings). The distance between the two ring centers needs to be below "ISTACK_DIST _AX. The angle between two normal vectors of ring planes needs to be below PISTACK ANG -_DVV Additionally, each ring center projected onto the opposite ring plane. The distance between the other ring center and the projected point (i.e., the offset) has be less than PISTACK OFFSET MAX. Figure. shows the illustration.
Hydrophobic Interactions [1]] caused by the tendency of hydrophobic side chains to avoid contact with water, leading them to aggregate. While these are not strong interactions their own, they play crucial role in the folding and stability of proteins by driving the burial of nonpolar groups away from the aqueous environment, thereby contributing significantly the overall stability. To form hydrophobic interactions, the atom distance needs to be less than HYDROPH HYDROPH_DIST.
X1
Distance
Donor Angle
Acceptor Angle
X2
Figure 4: Schematic representation of the geometry of hydrogen bond (without protonation). D and denote the hydrogen bond donor and acceptor respectively. XI and X2 are the neighboring atoms of donor and acceptor. The hydrogen bond distance as well as donor/acceptor angles are illustrated.
π-π Stacking Angle
Normal Vector
Distance
Projection
offset
Figure 5: Schematic representation of the geometry of я- stacking. To form stacking, need two aromatic rings. The distance of ring centers, the angle between normal vectors, and the projection offset of the ring centers need satisfy set of geometry constraints.
C Model Details
In PocketFlow, we adopt neural network architecture modified from the FrameDiff 86). This architecture consists of Invariant Point Attention from AlphaFold2 [43] and transformer blocks
17

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779. In this section, we use superseripts to refer to the network layer and subscripts to indexes or variables. In the network, each residue/ligand atom is represented by one embedding and a frame T E (3)... For the ligand atoms, the orientation matrix of frame is set as identity matrices. Overall, at the E-th layer of the network, h" = _hg...., h E IR RNDD, are all the node embeddings where 16 is the embedding for the i-th node and N = N₂ + N2 is the total number of nodes; T = -T [T,,..,, Tx E (F(3) is the frames of every node at the f-th layer; z' E R xDD are edge embeddings with et, being the embedding of the edge between residues and j. In the following paragraphs, we introduce the details of feature initialization, node/edge update, backbone update, and residue type/interaction type/sidechain torsion angle predictions.
R
Feature initialization. Following [86], node embeddings are initialized with residue indices and timestep while edge embeddings additionally get relative sequence distances. Initial embeddings at layer O for residues i. are obtained with MLP and sinusoidal embeddings d(.) [79] over the
features. Following (86), we additionally include colficondiiinnng of predicted Ca displacements.
Let 2 be the Co coordinates predicted during self-conditioning. 50% of the time set ā 0. The binned displacement of two Ca is given as,
Nun
disp,y
Σ 1 <+).
(14)
where di...., d d are linspace(O, 20) equally spaced bins between 0 and 20 angstroms. In our experiments we set Noins 22. The initial embeddings can be expressed as
h (o(),, o(t)), ER.
(15)
2 MLP(O ((j), o(j o(j i), - @(!), ((disp,,)), where Da, D2 are node and edge embedding dimensions. For the initialization of C. coordinates, we use the interpolation and extrapolation strategy of FAIR [92].
ER
(16)
Node update. The process of node update shown below. Invariant Point Attention (IPA) is from
43 No weight sharing is performed across layers. We use the vanilla Transformer from 79 We
use Multi-Layer Perceptrons (MIP) with Linear layers, ReI.U activation, and LayerNorm 6 after
the final layer.
hipa LayerNorm(PPA(h1, "A =',TT)+h's
hipa E IR Nx Dr.
(17)
haki Linear(ho), hakip Nx
(18)
hi = concat(Huipa. hakip); hin E IR Nx Dai))
(19)
hiruss (ransformer(han)) harans E TR NDDx
(20)
haa Linear(harand ) he, hoa E N
(21)
h f+1 MLP(hoa), het1 E NxD,
(22)
Edge update. Each edge is updated with a MLP over the current edge and source and target node embeddings. In the first line, node embeddings are first projected down to half the dimension.
h E-1 down Linear(h 111)),
h E+1 down
E
NDD,/2
(23)
z/j concat( ch (t
he11 doon..g 2.y),
2/1 E Nx(D...)
(24)
(+1
LayerNormMMLP((2)
e+1 E NXNxD.
(25)
Backbone update. Our frame updates follow the BackboneUpdate algorithm in AlphaFold2 We write the algorithm here with our notation,
43
(b,, Ci de, x update = innear(h:))
(26)
(ai, bi, Cs dz) = (1, b, Ci, di) + 63 +c?
c dd?
(27)
af + 13 o7 - d3
2b,0; 20,d;
2b,d; + 24,0;
pupdatt
2b,c, + 2a,d
d b + c - d3
2c,d, 2a,b;
(28)
2b,d, 20.4
2c,d, + 2a,b;
a - b9 of + de
18

---

Tuipdate (Riiddue
224
updute)
(29)
T To T.uplalle
(30)
where b;. Ct. d2 E R. update converted into valid rotation matrix in Equ. 28 Following [84 8T] we use the planar geometry of the backbone to impute the oxygen atoms. Note that we only update the pocket and ligand nodes in PocketFlow while setting the scaffold nodes fixed.
24 E ER.
Equ. 27 constructs a normalized quaternion which is then
Residue/Interaction Type and Torsion angle Prediction. We predict the residuc/interaction types and sidechain torsion angles based on node embeddings.
he MLP(h"), h1 MLP(h"), hx - -LPPh)(("))
(31)
c c Noftmax(Lineall) (he + h)))), softmax(Linear(h; + h))),
(32)
X = Linear(hx + h mmdd2m
(33)
where I e RR,, and [0, 2TT44N In PocketFlow, the number of network blocks is set to the number of transformer layers within each block set to 4, and the number of hidden channels used in the IPA caleulation is set to 16. The node embedding size D; and the edge embedding size D2 are set as 128. We removed skip connections and psi-angle prediction. For model training, we Adam 45] optimizer with learning rate 0.0001, $1 0.9, B2 0.999. We train Tesla A100 GPU for 20 epochs. In the sampling process, the total number steps T is set as 50.
D Proof of Equivariance
Theorem 1. Denote the SErnsfrranoooonaiio as T, LocketFLow po po (R) is SE(3) equivari- iee, (o [T (P R)) pe (R, 9IP / \ R), where R denotes the designed pocket, G the binding ligand, and P R is the protein scaffold.
Proof. The main idea is that the SE(3)-invarinae prior and SE(3) SE(3)-qqivvariant neural network lead to an Squiiaaqnn generative process of PocketFlow. By subtracting the CoM the scaffold from the initialized structure, obtain an SE(3)-invariant prior distribution similar [86 (9) Moreover, the neural network for structure update as shown in Appendix C is SE(3)-equivariant Formally, the two conditions guarantee invariant likelihood (R.,. 91 subscripts to denote the time steps from f = 0 to to 1):
|P R) are as follows (we
Invariant Prior:
P(Ro, Go, P R) p(T, Go, P R)),
(34)
Equivariant Transition: po Ge G. RR)
(R P(R)),
(35)
We can obtain the conclusion follows:
T-1
(R, R)) = P(I,(Ro:: So. Go.P. P\ R)) II
po P P R))
==0
= = p(Ro, So. P R)
T II ( Sssts P\ R))
==0
-s |(Ro, Go, P R)
II
pe
(1 Casc P R)
==0
= Po R).
where T the total number of steps. We apply the invariant prior and equivariant transition conditions in the derivation.
D
19

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E
Classifier-guided Flow Matching
Here, we present the Bayesian approach to guide the flow matching with the affinity predictor. The key insight comes from connecting flow matching to diffusion models to which affinity guidance can be applied. Sampling data point from the prior distribution po. we have the following ordinary differential equation (ODE) [72] that pushes it to data distribution:
dC, = v(C,,t)dtt [IG.,)) 2 20(t) = dt,
(36)
where V log (CC,) is the score function, /(C,,t) 1) and g(t) are the drift and diffusion coefficients respectively. We modify Equ. t6 to be conditioned on the affinity label (vs = 1) followed by an application of Bayes rule,
((C,,) V = 11/
=1} de
de.-
(37)
S(C,,)) () _0(0) (V (og): + V Vlogpi(os = 1[C,)) de
(38)
1 ( = ||c)) dl,
(C.,))
(39)
where the first term is the unconditional vector field and the second term is the affinity guidance term. In practice, we do not directly predict the affinity label based on C, because the intermediate structure is noisy. We use the following transformation:
Pt 1(C,) = f plus = 1[C.)((C & plu; = (C,))
(40)
where či (C,) is the expected denoised protein- ligand complex structure based on C. Details of the affinity predictor is introduced in the Appendix. E.1 We need to choose g()) such that matches the learned probability path. Previous works [20 86 showed g(()² - in the Euclidean setting. For simplicity, set g() as constant and observe good performance in experiments.
E.1 Binding Affinity Predictor
In PocketFlow, we leverage a binding affinity predictor pe po (vb (C,)) to guide the denoising process, where 2s E {0, 1} is the binary label of binding affinity and Ć, (C.) is the expected protein-ligand structure at ( = 1. Following [66] 29), we leverage 3-layer EGNN 77) with the node initialized embeddings and residue/ligand atom coordinates from Appendix C Specifically, we take the C,
coordinates for the residues and ligand atom coordinates and construct K-NN graphs (k set as 9). Let
hū and zf be denote the node representations and coordinates at the f- layer. The (E (f++) +) th layer is computed as follows:
he+1 h
Σ Su M, M,,,,e JEN
(41)
6+1 22
2 +
Σ
(42)
JEN
where d', = 11 2=5l represents the Euclidean distance between node i and node j at the f-th layer, N denotes the K-NN neighbors, and eij indicates the direction of pressage-passingg including from protein to protein, from protein to ligand, from ligand to protein, and from ligand to ligand. The functions fr. and fa are graph attention networks. Finally, we append an average pooling, one linear layer, and softmax operation at the end to predict the binary label of affinity.
To train the binding affinity predictor, we first annotate the data points in the corresponding training set: data points are annotated if their affinity is higher than the average score of the dataset, otherwise O. We train the predictor separately instead of joint training with flow matching because we find it can converge more quickly than the flow matching losses. We did not train the predictor on the intermediate structures as we find they are noisy and deteriorate the predictor and PocketFlow's overall performance. In experiments, we use the Adam optimizer and train for 10 epochs.
20

---

E.2 Geometry Guidance
Distance Guidance. For hydrogen bonds, the distances between donor and acceptor atoms need to be less than 1 Å and larger than Å to reduce steric clashes [35 The following inequality is necessary condition for residues in Ci with predicted interaction label as hydrogen bond:
min
min iE REen
x0(5)
S Imax:
(43)
where min and /max are distance constraints; A Abbond denote the k-th residue in the set of pocket residues with predicted hydrogen bonds. With little abuse of notations, az(1) and 2;() denote the
atom coordinates in the residue and ligand respectively. We use the following derivations to obtain the guidance term for the distance constraints:
Vc, log P( (m1mmn S
min (A)
||x(1 2.10)12 S mmxx Asbondd)
(44)
iEA
[Anbanal
Ve,
log P(lmin
min WEG
||x110 -z(00112 Imax
(45)
km
[Aboond
Vc, min
(()) Jeo [1x(1) - xx10)/2 S -lmia) P(min, leA Jeg |x x0.0/22 S lmax))
P(lmin min iE ||x:(0 x(1i S (max)
k=
(46)
LAnional
Σ VVe. P(
min |z - x.10112 S mmxx + 22 P(
min (k)
||x
x011122 1 -lmin)
(E)
JGG
(k)
ie iE
(47)
AAndonal
Vc.ll
min
|x 200112 112 S mmax) Velell
min
[xx x011 -imin)>
WhonajEE jEG
(48)
where E
1/V Plnin, heo ((x(()
2000
(max) and &2
1/P(- (01-minn;ali ( (0) -000 ||2 < -minn). Due the discontinuity of the indicator function II(-) that is incompatible with the gradient,
apply & max(0, y) as surrogate of I[l < {) in the above equation. Although & and &a are dependent on C., we find setting them as constant still works well in experiments. With these approximations, we can derive guidance term for
hydrogen bond distance constraints:
(Anbonal
E max (0,d(t) (mmax) + Ea max (0, - -dw))]
Vc
(49)
where d(k) min (t))
abb jeg ||x(0) - x x000) Such distance guidance terms for hydrophobic
interactions, salt bridges, and π stackings similar. The difference is to replace Axtond with Abydro Asalt: and Ar that denotes the residue sets with corresponding interactions. We modify the functions in plip for the ease of detecting interaction atom pair candidates. practice, Ve, takes gradients with each component in C,, including Xt, 22, Ot, Ct and I,-
Angle Guidance. Besides the distance constraint, the hydrogen bond needs satisfy the accep- tor/donor angle constraint [69] e.g., the donor/acceptor angle needs to be larger than 100", hangle(-,-)
Phapss//gtthbb.om/ppaaamiiiii
21

---

calculates the acceptor/donor angle in Figure. A
Vc, log P((amia
max VE NEAh
hangle(a o0)) , k 1: [Abondd) })
(50)
Anhondl
V.
log P(amin
max iEA Ree
hangle(< 2()))
(51)
k=1
Antondl
Ve, P(amiu I max Ve Abmm jeg
hangle (x,))()
(52)
P(amin S max, max:eA (k)
Abbnadie hangle( ax(1))
TEA
k=1
Ve, P(amin I Anbonal
max EEA hdond JEG
hangle(x (z)))
(53)
where E3 = 1/P(( I max
AbonaJE@ jeg hangle( (0) x)))) The final guidance term is:
(1)
Abbbond
V
max(0, Ommn ()()),
amin
(54)
(8)) where (A) max &E A JeG hangle( (1) (l)) The angle constraint is similar for the stacking and the final guidance term is:
V C.
max (0, (k) Ormas)
(55)
(K) where Ox
min (EA Jeeg piangle(x:0) 5)) and piangle( -) calculates the stacking angle
Figure. All the operations and calculations used in geometry guidance are made differentiable
and can be plugged into the sampling process of PocketFlow.
Figure 6: Superposition of 20 residue-type sidechains. When calculating the geometry guidance, use the expected sidechain conformations with respect to the estimated residue type probability a(0 to avoid the non-differentiabiiiyy issue of residue type sampling.
Sidechain Ensemble. PocketFlow takes the co-design scheme, where the residue type/side chain structure of the pocket determined during sampling. Directly sampling from the residue type distribution makes the model not differentiable [38] We propose use the sidechain ensemble for
interaction geometry calculation, i.e., the weighted sum geometric guidance with respect to
residue types. For example, for Equ. 54 we have:
AAnoonal 20
Ea Vc,
2L [r]]
max O'min ((()),
(56)
where 2( (n] denote the n-th residue type probability and (K) calculates the angle with the n-th type residue side chain.
22

---

DEPACT OYEEAN
Average nuntiim isS
RS DifhuconnAA
web Guide
w0 (in Caudd
With Inter Leaening
30"
Figure 7: Average Generation time for 100 pockets by different models CrossDocked (the error bars show the standard deviations over different runs).
0.520
0.70
C.72
0.510
0.00
-0.2
0.60
(a)
(b)
(c)
Figure 8: The influence of Affinity Guidance Strength 7 the pocket metrics.
More Results
Here, we show additional results on efficiency analysis (Figure. hyperparameter analysis of ? (Figure. and ablation studies on the interaction analysis (Table. 6
Figure. shows that the PocketFlow is much more efficient than stat-of-the-arr diffusion- models such as RFDiffusionAA. Considering the high quality of the generated pockets, the slight time overhead over models based on iterative refinement (c.g., dyMEAN and FAIR) is acceptable. We find that Affinity and Interaction Geometry Guidance do not add much overhead to the generation process. Therefore, these prior guidance are efficient tools for pocket optimization.
In Figure. we explore the impact of Affinity Guidance Strength (?) on various generation metrics. As y is scaled up, the Vina Score significantly improves and quickly stabilizes; AAR initially increases before gradually decreasing; scRMSD, on the other hand, increases with higher These observations appropriate 7 effectively balance the guidance and unconditional terms. While Affinity Guidance promotes the generation of high-affinity pockets, an excessively high y can result in less valid pocket sequences structures. In the default configuration, is set to 1.
underscore the importance of selecting
To evaluate the validity of the generated sidechain structure, compute the Mean Absolute Error (MAE) of sidechain angles (degrees) following (90] in Table. 5 We mainly compare PocketFlow with RFDiffusionAA LiggndMINNN 22 the recovered residues. In the table, report the average MAE and can observe that PocketFlow achieves better performance generating valid sidechain structures.
Method
X1
X2
X3
X4
RFDiffusionAA
21.56
27.92
48.76
52.88
PocketFlow
19.40
26.22
44.57
50.10
Table 5: The MAE of RFDiffusiooAA + LigandMPNN and PocketFlow on sidechain torsion angles(degrees).
23

---

In Table. 6 we supplement further results of interaction analysis (Table. 3 in the main paper). We can observe that the guidance terms effectively improve the number of favorable interactions while reducing steric clashes, which lay the foundation for generating high-affinity pockets.
Methods Pocket-llww w/o Aff' Guide
Clash (1)
HB (1)
Salt (1)
Hydro (1)
x-T (1)
1.21
4.12
0.27
6.03
0.28
2,58
3.84
0.25
5.84
0.27
w/o Geo Guide
3.27
3.96
0.24
5.90
0.27
w/o Geo & Aff Guide
3.56
3.68
0.23
5.73
0.26
w/o Inter Learning
3.34
3.74
0.22
5.80
0.26
Table 6: Ablation studies on the interaction analysis. The best results are bolded and the runner-up is underlined.
24

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G Baseline Implementation
is template-matching method that follows a two-step strategy for pocket design. Firstly, it searches the protein-ligand complexes in the template database with similar ligand fragments and constructs a cluster model (a set of pocket residues). The template databases are constructed based on the corresponding training datasets for fair comparisons. Secondly, it grafts the cluster model into the protein pocket with PACMatch. It works by placing residues from the cluster model on protein scaffolds by matching the atoms of residues with atoms of the protein scaffold. The backbone coordinates of the pocket residues are also modified in the process. The qualities of the generated pockets evaluated and ranked based top 100 designed pockets for evaluation. The output DEPACT+PACMatch is complete protein structures with redesigned pockets. In the paper, we only use DEPACT to represent the whole method of DEPACT+PACMalch for conciseness.
DEPACT [9]
statistical scoring function. We take the
RFDiffusionAA 48 is the latest version of RFDiffusion which combines a residue- based rep- resentation of amino acids and atomic representations of all other groups model protein-sme small molecules/mettls//nulll acids/covalent modification complexes. Starting from random distributions of amino acid residues surrounding target small molecules, RFDiffusionAA can directly generate the small molecule binding protein backbone. Furthermore, with LigandMPNN [22] the latest version of ProteinMPNN[[]] we can assign residue types and predict sidechain conformations considering the protein-ligante interactions. Experiments in RFDiffusionAA [48] show that the generated protein by RFDiffusionAA has better binding affinity than those obtained by RFDiffusion with auxiliary potential. We use the provided checkpoints of RFDiffusionAA for all the experiments since the training code is unavailable.
dyMEAN 47 is an and-to-end full-atom model for equivvaar antibody design given the epitope and the incomplete sequence of the antibody. Its previous version, MEAN [46], only considers the backbone atoms, while dyMEAN considers the complete atom structure and performs better on downstream tasks. Generally, dyMEAN co-designs antibody sequence and structure via a multi-round progressive full-shot refinement manner, which is more efficient than auto-regressive or diffusion- based approaches. An adaptive multi-channel equivariant encoder is used in dyMEAN, which can process protein residues of variable sizes when considering full atoms. To adapt dyMEAN to pocket design task, we replace the antigen with the target ligand molecule to provide the context information for pocket generation. We set the hidden size 128, the number of layers 3, and the number of iterations for decoding as 3.
FAIR 92 is our previous method for full atom pocket sequence sqquence-structure co-design. FAIR operates two steps, proceeding in a coarse-to-fine manner (backbone refinement to full atoms refinement, including side chains) for full-atom generation. In FAIR, residue types and atom coordinates are updated using a hierarchical graph transformer composed of residue-level and atom-level encoder. The number of layers for the atom and residue-level encoder are 6 and 2, respectively. Ko and K, are set as 24 and 8 respectively. The number of attention heads is set as 4; The hidden dimension is set as 128.
hhtpp://gitthubbc https////ghuuubooo////////////// PACMach
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Justification:
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Reviews:
[{"review_id": "ynC4WVAP9i", "reviewer": "Reviewer_gNH7", "summary": "The paper proposed PocketFlow, a generative model for designing protein pockets that bind with ligands. It aims to overcome limitations in existing methods by incorporating protein-ligand interaction priors and utilizing flow matching. PocketFlow is designed to handle multiple ligand modalities and demonstrates superior performance on various benchmarks.", "questions": "1. Why were these four types of interactions (hydrogen bond, salt bridge, hydrophobic, π-π stacking) chosen? Are there other interactions existing in protein-ligand binding that should be considered?\n2. Can the proposed method be extended to protein-ligand docking (fixing the pocket type and structure)?\n3. What is the efficiency of calculating different interaction types?\n4. Is there any metric to evaluate the correctness of the interactions generated?\n5. The original IPA relies on the rotational equivariance of frame orientation to achieve model’s invariance. However, the proposed method additionally treats the ligand atom as a residue and uses an invariant identity matrix to represent its orientation. Will the proposed IPA still output invariant embeddings?\n6. How are the guidance coefficients for different guidance mechanisms determined?\n7. Is RFDiffusionAA trained on the same dataset as the proposed model?", "limitations": "N/A", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The paper provides detailed methodology and includes anonymous code to reproduce the results.\n- The proposed method generalizes across various ligand modalities, including small molecules, peptides, and RNA.\n- The model outperforms existing methods on multiple benchmarks, demonstrating significant improvements in Vina scores and scRMSD.\n- The model explicitly models key protein-ligand interactions, enhancing binding stability and affinity.", "weaknesses": "- The method only considers interactions between protein and ligand, potentially neglecting interactions between protein sidechains within the pocket region.\n- For some residue types, there might be π instead of 2π symmetry in the sidechain structures, which the proposed method seems to simplify.\n- The use of flow matching and multiple guidance mechanisms could result in higher computational costs compared to simpler models.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for the constructive comments and appreciation!\n\n**Comment 1**: The method only considers interactions between protein and ligand, potentially neglecting interactions between protein sidechains within the pocket region.\n\n**Response 1**: Thanks for the insightful comment! In PocketFlow, we explicitly consider protein-ligand interactions as guidance terms because protein-ligand interactions mainly contribute to the protein-ligand binding affinity. They are also learned implicitly within our model architecture: the pairwise attentions capture inter-residue interactions and the supervision of the predicted sidechain torsion angles encourages forming valid and stable protein conformations. \n\nWe note that **PocketFlow has a flexible framework and can be generalized to model protein sidechain interactions with minor modifications**. For model simplicity and computational efficiency, we only consider the protein-ligand interactions in our current version of PocketFlow. We will include the above discussions in our revised paper.\n\n**Comment 2**: For some residue types, there might be π instead of 2π symmetry in the sidechain structures, which the proposed method seems to simplify.\n\n**Response 2**: Thanks for the constructive comments! Yes, we are aware some sidechain torsion angles are 180◦-rotation-symmetric, such that the predicted torsion angle χ and χ + π result in the same physical structure. Since only 4 of 39 possible sidechain torsion angles have such π symmetric properties, we did not consider them for simplicity in our preliminary version of PocketFlow. Following AlphaFold2 (supplementary 1.9.1), we can include such π symmetric constraints by providing the alternative ground truth torsion angle for training with minor modifications of the code. We will include the discussions and the implementation in our revised paper.\n\n**Comment 3**: The use of flow matching and multiple guidance mechanisms could result in higher computational costs compared to simpler models.\n\n**Response 3**: Thanks for the question! In Figure 7 of the submitted paper, we compare the average generation time of different models. Firstly, we observed that PocketFlow is much efficient than template-matching methods (DEPACT) and diffusion-based models (RFDiffuisonAA). The generation time is only larger than dyMEAN and FAIR. Considering the performance improvement brought by PocketFlow (1.29 in Vina Score and 0.05 in scRMSD), the additional overhead is acceptable. We also compare PocketFlow with its variants without guidance and observed that the guidance mechanisms are quite efficient and would not introduce much overhead. \n\n**Comment 4**: Why were these four types of interactions chosen? Are there other interactions existing in protein-ligand binding that should be considered?\n\n**Response 4**: In PocketFlow, the four types of interactions are chosen because they are the most frequently encountered and are crucial for strong binding stability and affinity. Previous works, e.g., KGDiff ([93] in the paper) also consider the four interactions and managed to improve binding affinity and generation quality. In Appendix. B, we described the details of the four dominant interactions. There are some other interactions in protein-ligand binding such as Van der Waals Forces and Metal Coordination. We did not consider them due to their weak contributions to binding affinity or low occurring frequency. Moreover, we only consider the four dominant interaction types for computation efficiency.\n\n**Comment 5**: Can PocketFlow be extended to protein-ligand docking (fixing the pocket type and structure)?\n\n**Response 5**: Yes, PocketFlow has a generalized and robust architecture that can be extended to protein-ligand docking by e.g., fixing the pocket type and structure. During the rebuttal period, we conducted preliminary experiments on adapting PocketFlow to the blind docking tasks. We conduct experiments on the PDBbind v2020 dataset and follow previous works such as DiffDock and FABind for the data preprocessing. For our testing phase, we utilized 363 complexes recorded after 2019. In the table below, we follow previous works and report the percentage of ligands RMSD below 2/5Å and the centroid distance below 2/5Å. We observe that even though PocketGen is not specially optimized for docking, it still achieves strong performance compared with state-of-the-art baselines. \n\n| Methods       | Ligand RMSD       |                 | Centroid Distance   |                 |  |\n|---------------|--------------------|-----------------|---------------------|-----------------|---------------------|\n|               | % Below 2Å | % Below 5Å |                 | % Below 2Å | % Below 5Å |                     |\n| QVINA-W       | 15.3     | 39.5     |                 | 25.7     | 39.5     | 49*                |\n| GNINA         | 12.5     | 37.0     |                 | 20.4     | 37.9     | 146                |\n| SMINA         | 13.5     | 39.1     |                 | 29.9     | 41.7     | 146*               |\n| GLIDE         | 19.6     | 32.2     |                 | 35.4     | 46.4     | 1405*              |\n| VINA          | 10.3     | 27.3     |                 | 20.4     | 37.3     | 205*               |\n| EQUiBind      | 3.4      | 43.8     |                 | 16.7     | 43.8     | **0.03**           |\n| TANKBind      | 4.3      | 44.8     |                 | **44.0**     | 70.8     | 0.87               |\n| E3Bind        | 4.5      | 34.3     |                 | 33.8     | 66.0     | 0.83               |\n| DiffDock     | **32.0**     | 48.3     |                 | 33.8     | 62.6     | 20.83              |\n| FABind        | 19.4     | *64.0*      |                 | 5.9      | **75.7**     | *0.12*                |\n| PocketFlow       | *30.2*     | **65.7**     |                 | *38.0*      | *71.3*    | 0.45               |\n\n- **Bold**: Best results\n- *Italic*: Second best", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "Peee6odITB", "reviewer": "Reviewer_gVL4", "summary": "The paper explores methods for generating protein pockets given a ligand using a flow matching generative approach. Unlike previous methods, the proposed approach integrates additional constraints into the flow matching learning process to guide the search for relevant pockets. Two types of constraints are considered: \n\n1. Affinity score prediction, which utilizes an oracle predictive model to guide the generation process.\n2. Geometric constraints, which ensure that the distances between atoms involved in specific types of bonds remain below certain thresholds.\n\nThe authors examine the effectiveness of these constraints, incorporating both domain knowledge and transferred knowledge from an affinity prediction model, in the generation of protein pockets. They benchmark their approach against state-of-the-art methods that do not use such constraints. The results demonstrate that the new pockets generated have improved RMSD and Vina scores.", "questions": "1. Could you please address the potential leakage between the dataset used for training the affinity predictor and the datasets used for assessing the pocket generation?\n2. Could you please clarify the impacts of HPO of the baselines and the proposed method in this work?", "limitations": "The authors have addressed relevant limitations of the work in the paper.", "rating": 7, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The concept of incorporating additional constraints into Flow Matching is interesting. While conditional flow matching exists, determining the appropriate constraints for pocket generation requires substantial domain knowledge and engineering effort to be effective. \n\nThe results are promising, as the authors conducted numerous experiments and comparisons with state-of-the-art methods. It is evident that considerable time was invested in gathering results from these methods. \n\nThe paper is well-written and enjoyable to read, even for those with limited knowledge of pocket generation problems.", "weaknesses": "I have a concern about the inclusion of the affinity oracle predictor, which was trained on separate datasets. The authors did not specify which dataset was used to train their predictor or address the potential for information leakage between the training dataset and the test set used for pocket finding. Since the predictor provides the flow matching with a prior on which pocket might be relevant for a given ligand, any leakage would give a clear advantage. I looked for more detailed information about the affinity predictor in the appendix but found none regarding the training dataset.\n\nI also question the novelty of the work in terms of its technical contribution to the machine learning community. While conditional flow matching itself is not new, the novel aspect of this work is the incorporation of additional domain constraints into the framework. Therefore, it is unlikely to be of significant interest to the machine learning research community from a methodological development perspective.\n\nAdditionally, since the authors retrained the baseline models with additional data, it is important that they report how hyperparameters were selected and tuned for these baselines.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for the valuable comments! Our replies are listed below:\n\n**Comment 1**: The authors did not specify which dataset was used to train their predictor or address the potential for information leakage between the training dataset and the test set used for pocket finding. \n\n**Response 1**: In the original submission lines 739-744, we described the dataset used to train the predictors: To train the binding affinity predictor, we first annotate the data points in the corresponding training set: data points are annotated 1 if their affinity is higher than the average score of the dataset, otherwise 0.\n\n**Therefore, no additional datasets are used and there is no data leakage risks**. In the revised paper, we will highlight the training dataset for the predictors and address the potential concerns. \n\n**Comment 2**: I also question the novelty of the work in terms of its technical contribution to the machine learning community. While conditional flow matching itself is not new, the novel aspect of this work is the incorporation of additional domain constraints into the framework. Therefore, it is unlikely to be of significant interest to the machine learning research community from a methodological development perspective.\n\n**Response 2**: Thanks for the comment! This paper is an application-driven paper and would firstly be of great interest to the growing AI for Science community. To well model the protein-ligand complex, we appropriately define **multi-modal flow matching process for different components**, including SE(3) flow matching for the protein backbone, torsional flow matching for sidechain torsion angles, and categorical flow matching for residue Types and interaction types. The incorporation of additional domain constraints into the framework is also not straightforward. For example, we novelly **formulate the complicated geometrical constraints (see Appendix. B) into guidance terms** for flow matching. To **tackle the non-differentiability of residue type sampling**, we propose the Sidechain Ensemble technique for the interaction geometry calculation. **We believe the above-mentioned techniques and practices will also inspire the machine learning research community.**\n\n**Comment 3**: since the authors retrained the baseline models with additional data, it is important that they report how hyperparameters were selected and tuned for these baselines.\n\n**Response 3**: In Appendix. G Baseline Implementation, we described the details of running baseline methods. DEPACT is a template-matching method. **We used the recommended hyperparameters such as the weights of scoring functions from the original paper.** RFDiffusionAA is the state-of-the-art diffusion model for generalized biomolecular modeling and generation. **We use the provided checkpoints and the recommended hyperparameter setting from the paper** because the training code and data are not available. dyMEAN and FAIR are end-to-end deep generative models for protein sequence-structure codesign. **We performed a grid search over the key hyperparameters such as the number of layers and iterations based on the performance of validation datasets (Vina score).** Finally, we set the hidden size as 128, the number of layers as 3, and the number of iterations for decoding as 3 for dyMEAN. For FAIR, The number of layers for the atom and residue-level encoder are 6 and 2, respectively. Ka and Kr are set as 24 and 8 respectively. The number of attention heads is set as 4; The hidden dimension d is set as 128. \n\nWe will describe the selection/tuning of hyperparameters of baseline more clearly in the revised paper.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "vDG5VxQduX", "reviewer": "Reviewer_e3xX", "summary": "This paper studies the task of generalized ligand-binding protein pocket generation. To tackle the challenges of existing works, the authors proposed PocketFlow, a generative model that incorporates protein-ligand interaction priors based on flow matching. PocketFlow explicitly learns the protein-ligand interactions during training and leverages multi-granularity guidance to generate high-quality pockets during sampling. Experiments show that PocketFlow is a generalized generative model across various ligand modalities, including small molecules, peptides, and RNA.", "questions": "1. Why didn’t the authors apply discrete flow matching methods for residue/interaction type prediction, e.g., [1]?\n\n[1] Dirichlet flow matching with applications to dna sequence design, arXiv preprint arXiv:2402.05841, 2024", "limitations": "The authors discussed the limitations and broader impacts in Section 5.5.", "rating": 7, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper is well-written and easy to follow. The illustration of Figure 1 is attractive. The technical details and the code are provided for better reproducibility.\n2. PocketFlow represents the first few works to broaden the scope of pocket generation tasks to include various ligand modalities, such as small molecules, nucleic acids, and peptides. \n3. PocketFlow effectively combines the latest flow-matching models with prior knowledge (affinity guidance and interaction geometry guidance) to generate protein pockets with enhanced affinity and validity. \n4. The proposed algorithms overall sound valid to me. The tasks and evaluation metrics of peptide/RNA-binding pocket design are also well formulated. \n5. Experiments show that PocketFlow achieves an average improvement of 1.29 in Vina score and 0.05 in scRMSD. The authors also leverage PoseCheck to evaluate the protein-ligand interactions and steric clashes, which makes the evaluation comprehensive.", "weaknesses": "1. What is the time cost of PocketFlow and baseline methods in generating protein pockets? Would the prior knowledge-based guidance bring an extra burden to pocket generation?  \n2. In line 222, the authors mentioned sidechain ensemble for the interaction geometry calculation, which is too concise. The authors are recommended to elaborate more on this in the main pages. \n3. In Table 2, some metrics of PocketFlow are not the best and RFDiffusionAA has better results.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for the valuable comments and appreciation!\n\n**Comment 1**: What is the time cost of PocketFlow and baseline methods in generating protein pockets? Would the prior knowledge-based guidance bring an extra burden to pocket generation?\n\n**Response 1**: Thanks for the detailed question! In Figure 7 of the submitted paper, we compare the average generation time of different models. Firstly, we observed that PocketFlow is much more efficient than template-matching methods (DEPACT) and diffusion-based models (RFDiffuisonAA). The generation time is only larger than dyMEAN and FAIR which are based on equivariant translation. Considering the performance improvement brought by PocketFlow (1.29 in Vina Score and 0.05 in scRMSD), the additional overhead is acceptable. We also compared PocketFlow with its variants without guidance and observed that the guidance mechanisms are quite efficient and would not introduce much overhead. We will add more clear discussions in our revised paper. \n\n\n**Comment 2**: In line 222, the authors mentioned sidechain ensemble for the interaction geometry calculation, which is too concise. The authors are recommended to elaborate more on this in the main pages.\n\n**Response 2**: Thanks for the constructive suggestion! Due to the page limits, we include the detailed elaborations of sidechain ensemble technique in the appendix. PocketFlow takes the co-design scheme, where the residue type/side chain structure of the pocket is not determined during sampling. Directly sampling from the residue type distribution makes the model not differentiable. We propose to use the sidechain ensemble for the interaction geometry calculation, i.e., the weighted sum of geometric guidance with respect to residue types. We will put the detailed descriptions of sidechain ensemble in our final version.\n\n**Comment 3**: In Table 2, some metrics of PocketFlow are not the best and RFDiffusionAA has better results\n\n**Response 3**: Thanks for the detailed comments! We admit that RFDiffusionAA is indeed a strong baseline. In Table 2, we evaluate different methods on peptide/RNA-conditioned protein pocket generation to explore the generalization capability. The performance of PocketFlow is comparable to the state-of-the-art model RFDiffusionAA. Even though some results are not the best, PocketFlow achieves the second best. Such results are quite promising and show the potential of our multi-modality flow matching architecture and domain knowledge-based guidance. \nDuring rebuttal, we also tried enlarging the pertaining dataset (response 2 to reviewer bfsA) or leveraging SOTA discrete flow matching method (response 4) to improve the performance and achieved promising results.\nIn the future, we will keep updating our model and improve its performance.  \n\n**Comment 4**: Why didn’t the authors apply discrete flow matching methods for residue/interaction type prediction, e.g., [1]?\n\n[1] Dirichlet flow matching with applications to DNA sequence design, arXiv preprint arXiv:2402.05841, 2024\n\n**Response 4**: Thanks for mentioning the latest discrete flow matching methods, which inspires us a lot. Such discrete flow matching models are perpendicular to our work and can be seamlessly integrated into PocketFlow. During rebuttal, we performed additional experiments and observed promising results of incorporating the discrete flow matching model. We will include the new results with discrete flow matching model in our revised version.\n\n| Model         | CrossDocked           |                   |                  | Binding MOAD         |                   |                  |\n|---------------|-----------------------|-------------------|------------------|----------------------|-------------------|------------------|\n|               | AAR (↑)               | scRMSD (↓)        | Vina (↓)         | AAR (↑)              | scRMSD (↓)        | Vina (↓)         |\n| Test set      | -                     | 0.65              | -7.016           | -                    | 0.67              | -8.076           |\n| DEPACT        | 31.52±3.26%           | 0.73±0.06         | -6.632±0.18      | 35.30±2.19%          | 0.77±0.08         | -7.571±0.15      |\n| dyMEAN        | 38.71±2.16%           | 0.79±0.09         | -6.855±0.06      | 41.22±1.40%          | 0.80±0.12         | -7.675±0.09      |\n| FAIR          | 40.16±1.17%           | 0.75±0.03         | -7.015±0.12      | 43.68±0.92%          | 0.72±0.04         | -7.930±0.15      |\n| RFDiffusionAA | 50.85±1.85%           | 0.68±0.07         | -7.012±0.09      | 49.09±2.49%          | 0.70±0.04         | -8.020±0.11      |\n| PocketFlow    | *52.19±1.34%*       | *0.67±0.04*         | *-8.236±0.16*  | **54.30±1.70%**      | *0.68±0.03*         | **-9.370±0.24**  |\n| w/ discrete flow | **53.87±1.20%**           | **0.66±0.05**         | **-8.310±0.17**      | *53.39±1.65%*          | **0.65±0.03**         | *-9.267±0.31*      |\n\n- **Bold**: Best results\n- *Italic*: Second best", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "qLSj2EL1Xc", "reviewer": "Reviewer_bfsA", "summary": "In this paper, the authors proposed PocketFlow, a protein-ligand interaction prior-informed flow matching model for protein pocket generation. The flow matching for backbone frames, sidechain torsion angles, and residue/interaction types are appropriately defined. To enhance the structural validity and binding affinity of the generated pockets, the authors proposed to leverage affinity and geometry guidance in the sampling process. Extensive experiments show that PocketFlow provides a generalizable model for pocket generation covering various ligand modalities such as small molecules, nucleic acids, and peptides.", "questions": "Please see the Weaknesses.", "limitations": "The limitations and broader impacts are well discussed in Section 5.5 of the main paper.", "rating": 8, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "1. PocketFlow leverages domain knowledge including protein-ligand interactions and geometric constraints to enhance pocket generation quality, which is quite novel. \n2. PocketFlow extends the pocket generation task to broad ligand modalities such as small molecules, RNA, and peptides. Experiments show that the prior guidance can effectively improve the generalization capability. \n3. In experiments, the advantage of PocketFlow over state-of-the-art baselines such as RFDiffuisionAA is obvious, achieving an average improvement of 1.29 in Vina score and 0.05 in scRMSD in Table 1. \n4. The description of the PocketFlow algorithm is quite clear, and a preliminary version of code is provided for reproducibility. \n5. The authors conducted comprehensive ablation studies to show the contribution of affinity/geometry guidance and protein-ligand interaction learning.", "weaknesses": "1. The backbone model of PocketFlow is modified from existing work such as FrameDiff and is less novel.   \n2. In lines 252-253, the authors said PocketFlow is only pretrained on protein-small molecule datasets, i.e., CrossDocked and Binding MOAD. Is it possible to train PocketFlow on the combination of protein-small molecule/peptide/RNA datasets for better performance? \n3. In experiments on protein-peptide and RNA, PocketFlow represents peptide/RNA ligands as molecules. Could the frame representation for the protein residues also applied to peptide/RNA ligands?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for the constructive comments and appreciation!\n\n**Comment 1**: The backbone model of PocketFlow is modified from existing work such as FrameDiff and is less novel.\n\n**Response 1**: Thanks for the question! This paper is an application-driven paper and would be of great interest to the growing AI for Science community. To well model the protein-ligand complex, we appropriately define **multi-modal flow matching** process for different components, including SE(3) flow matching for the protein backbone, torsional flow matching for sidechain torsion angles, and categorical flow matching for residue Types and interaction types. The incorporation of additional domain constraints into the framework is also not straightforward. For example, we novelly **formulate the complicated geometrical constraints (see Appendix. B) into guidance terms** for flow matching. To **tackle the non-differentiability of residue type sampling**, we propose the Sidechain Ensemble technique for the interaction geometry calculation. We believe the above-mentioned techniques and practices will also inspire the machine learning research community.\n\n**Comment 2**: In lines 252-253, the authors said PocketFlow is only pretrained on protein-small molecule datasets, i.e., CrossDocked and Binding MOAD. Is it possible to train PocketFlow on the combination of protein-small molecule/peptide/RNA datasets for better performance?\n\n**Response 2**: Thanks for the detailed question! In Table 2, we explore whether the pretrained PocketFlow on the combination of CrossDocked and Binding MOAD can generalize to peptide and RNA-binding pocket design. In the rebuttal period, we further finetuned the pretrained model on protein-peptide/RNA datasets constructed following previous works [1-2]. The datasets are split based on peptide/RNA sequence similarity. In the following table, we report the latest results and observe that finetuning PocketFlow achieves better results across most of the metrics compared to the original ones in the submission. We will include the new experiments and discussions in our revised paper.\n\n| Model         | PPDBench              |                   |                  | PDBBind RNA          |                   |                  |\n|---------------|-----------------------|-------------------|------------------|----------------------|-------------------|------------------|\n|               | AAR (↑)               | scRMSD (↓)        | ΔΔG (↓)          | AAR (↑)              | scRMSD (↓)        | ΔΔG (↓)          |\n| Test set      | -                     | 0.64              | -                | -                    | 0.59              | -                |\n| dyMEAN        | 26.29±1.05%           | 0.71±0.05         | -0.23±0.04       | 25.90±1.22%          | 0.71±0.04         | -0.18±0.03       |\n| FAIR          | 32.53±0.89%           | 0.86±0.04         | 0.05±0.07        | 24.90±0.92%          | 0.80±0.05         | 0.13±0.05        |\n| RFDiffusionAA | *46.85±1.45%*           | **0.65±0.06**         | *-0.62±0.05*       | *44.69±1.90%*          | **0.65±0.03**         | *-0.45±0.07*       |\n| PocketFlow    | **48.54±1.37%**       | *0.67±0.03*        | **-1.15±0.07**   | **46.31±1.22%**      | *0.68±0.02*         | **-0.90±0.04**   |\n\n- **Bold**: Best results\n- *Italic*: Second best\n\n[1] Li J, Cheng C, Wu Z, et al. Full-Atom Peptide Design based on Multi-modal Flow Matching[J]. ICML, 2024.  \n[2] Nori D, Jin W. RNAFlow: RNA Structure & Sequence Design via Inverse Folding-Based Flow Matching[J]. ICML, 2024.\n\n**Comment 3**: In experiments on protein-peptide and RNA, PocketFlow represents peptide/RNA ligands as molecules. Could the frame representation for the protein residues also applied to peptide/RNA ligands?\n\n**Response 3**: Thanks for the insightful question! Yes, the peptide and RNA structures can also be modeled as frames and there are some recent reference papers such [1-3]. In PocketFlow, we represent peptide/RNA ligands as molecules for simplicity and explore the generalization capability of PocketFlow on other ligand domains. We will include the discussions of representation in our revised paper.\n\n[3] Anand R, Joshi C K, Morehead A, et al. RNA-FrameFlow for de novo 3D RNA Backbone Design[C]//ICML 2024 Workshop on Structured Probabilistic Inference {\\&} Generative Modeling.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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: The authors present a novel protein-ligand interaction prior flow-matching model for protein pocket generation. The approach defines flow matching for backbone frameworks, side-chain torsion angles, and residue/interaction types. To enhance the structural validity and binding affinity of generated pockets, the authors propose incorporating affinity and geometric guidance during the sampling process. Experimental results show that PocketFlow is a generalized generative model capable of handling a wide range of ligand types, including small molecules, peptides, and RNA, achieving SOTA performance.

The reviewers universally found this work interesting and timely, particularly given the growing ability to protein design. Despite some minor concerns, this is a strong paper that I recommend for acceptance to NeurIPS.
Decision: Accept (spotlight)