Dynamics-inspired Structure Hallucination for Protein-protein Interaction Modeling
Authors: Fang Wu
Stan Z. Li
Venue: Accepted by TMLR ()

Abstract: Protein-protein interaction (PPI) represents a central challenge within the biology field, and accurately predicting the consequences of mutations in this context is crucial for drug design and protein engineering. Deep learning (DL) has shown promise in forecasting the effects of such mutations but is hindered by two primary constraints. First, the structures of mutant proteins are often elusive to acquire. Secondly, PPI takes place dynamically, which is rarely integrated into the DL architecture design. To address these obstacles, we present a novel framework named Refine-PPI with two key enhancements. First, we introduce a structure refinement module trained by a mask mutation modeling (MMM) task on available wild-type structures, which is then transferred to hallucinate the inaccessible mutant structures. Second, we employ a new kind of geometric network, called the probability density cloud network (PDC-Net), to capture 3D dynamic variations and encode the atomic uncertainty associated with PPI. Comprehensive experiments on SKEMPI.v2 substantiate the superiority of Refine-PPI over all existing tools for predicting free energy change. These findings underscore the effectiveness of our hallucination strategy and the PDC module in addressing the absence of mutant protein structure and modeling geometric uncertainty.

Published in Transactions on Machine Learning Research (03/2025)
Dynamics-inspired Structure protein Interaction Modeling
Hallucination for Protein-
Fang Wu
fangund978ssansorrddee
Deportment of Computer Science Stanford University
Stan Z. Li
Stan. ZQ. wwwwwesttaae..eeeeeeeeee.... edu.ccr
School of Engineering Westlake University
Reviewed OpenReview: https: https:///penreeviau
openreview. net/ forum? id= GGHk5uk006
Abstract
Protein-protein interaction (PPI) represents central challenge within the biology field, and accurately predicting the consequences of mutations in this context is crucial for drug design and protein engineering. Deep learning (DL) has shown promise in forecasting the effects of such mutations but is hindered by two primary constraints. First, the structures of mutant proteins are often elusive to acquire. Secondly, PPI takes place dynamically, which is rarely integrated into the DT. architecture design. To address these obstacles, we present a novel framework named Refine-PPI with two key enhancements. First, we introduce structure refinement. module trained by mask mutation modeling (MMM) task on available wild-type structures, which is then transferred to produce the inaccessible mutant structures. Second, we employ new kind of geometric network, called the probability density cloud network (PDC-Net), to capture 3D dynamic variations and encode the atomic uncertainly associated with PPI. Comprehensive experiments on SKEMPLx2 substantiate the superiority Refine- PPI over existing tools for predicting free energy change. These findings underscore the offectiveness of our hallucination strategy and the PDC module addressing the absence of mutant protein structure and modeling geometric uncertainty.
1 Introduction
Protcins seldom act in isolation and typically engage in interactions with others to perform wide array of biological functions (Phizicky & Fields, 1995 Du et al., 2016 One illustrative instance involves antibod- ies, which belong to protein category within the immune system. They identify and attach to proteins found on pathogen surfaces and trigger immune responses by interacting with receptor proteins in immune cells (Lu et al.) 2018). Accordingly, it is crucial to devise approaches to modulate these interactions, and a prevalent strategy to introduce amino acid mutations at the interface (see Fig. However, the space of possible mutations vast, making impractical or prohibitive to conduct experimental tests on all viable modifications in a laboratory setting (Li et al. 2023 Thus, computational techniques are required to guide the recognition of desirable mutations by forecasting their mutational effects on binding strength, commonly measured by the change in binding free energy termed AAG.
The past decade has witnessed the great potential of deep learning (DL) techniques Rives et al. 2021
Min et al. 2022) in biological science, such as protein design (Tang et al.) 2024a b Wu et al. 2024b) a 2025), folding classification (Hermosilla al. (2200), model quality assessment (Wu et al. (023b). and function prediction (Gligorijević et al.) 2021).. These DL algorithms also surpass conventional approaches computing AAG and be roughly divided into biophysics- and statistics-based kinds. In particular, the

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Antigen
Mutations
Antibody
Geometric Deep Learning
Optimized A ntiboddy
Figure 1: Geometric deep learning is applied to optimize the antibody sequences and achieve desired prop- erties (e.g., better affinity and specificity).
former depends on sampling from energy functions and consequently faces trade-off between efficiency and accuracy (Schymkowitz et al. 2005 Leman et al. 2020 Meanwhile, statistical-baser moth are limited by the selection of descriptors and cannot take advantage of the growing availability of protein structures (Alford et al. 2017).
Despite DL's fruitful progress identifying AAG, their efficacy encounters various obstacles. First the absence of the mutant complex structure. Due to the long-standing consensus that protein function is intricately related to its structure, an emerging line seeks to encode protein structures using 3D-CNNs
GNNs (Jing et al. 2020 Satorras et al. 2021 Wu et al. 2021a 2023a 2021b), but typically relies experimental structures like Protein Data Bank (PDB). Their performance deteriorates significantly when fed low-quality or noisy protein structures (Huang et al. 2024). Regrettably, in antibody optimization, obtaining mutant structures is an insurmountable obstacle, and the exact conformational variations upon mutations are unknown. While groundbreaking approaches such as Alphafold (Jumper et al., 2021 and 2021 have brought a revolution in directly inferring protein structures from amino acid sequences, they struggle accuralely forecast the structure of antibody-antigen complexes compared to monomers (Ruffolo et al.
Alphafold-Multimne (Evans et al.]
2023 As alternative, some scientists turn to energy- -baeed protein
2019) to sample mutant structures, which show finite efficacy and dramatically increase overall computational time (Cai et al. 2023). The second limitation is the overlook of existing DL, on the fundamental thermodynamic principle. Proteins exhibit inherent dynamism, critical
folding tools like FoldX (Delgado et al.
for biological functions and therapeutic targeting (Miller & Phillips 2021 Wu et al. 2022a Wu & Li, 2023). Many real-world observations are not solely dependent on a single structure but influenced by the equilibrium distribution (Ganser et al. 2019). For example, inferring biomolecule functions involves assessing the probabilities associated with various structures to identify metastable states.
To overcome these barriers, introduce Refine-PPI (see Fig. 3) with two key innovations for the mutation effect pre- diction problem. First, we devise a masked mutation modeling (MMM) stralegy and propose to predict the mulant structure and A&G simultaneously. Refine-PPT combines the prediction of structure and the prediction of free energy change into joint training objective rather than relying external soft- ware to sample mutant structures. This offers several distinct advantages. On the one hand, the predicted mutant struc- ture exhibits significant differences from the wild-type struc-
0.5
Per-structure Spearman
Refine-PPI
0.4
FoldX
RDE-Net
MIF-Net
0.3
Rosetta
ture, providing crucial geometric information related to the change in binding free energy. On the other hand, MMM not only enables inference of the most likely equilibrium conforma- tion of the mutant structure but also encourages graph mani- fold learning with the denoising objective Godwin et al. (2021). Besides, AAG implicitly conveys extra information about the structural difference before and after the mutation. Collective training with AAG would promote the efficiency of structure prediction. Second, we introduce a new kind of geometric GNN callod PDC-Net to capture the flexibility and dynamics of conformations during the binding process. Specifically, each particle in complex is represented as probability density cloud (PDC) that illustrates the scale and strength of their motion throughout the interaction procedure. Then, an aligned
0.2 0.3
0.4 Per-structure Pearson
0.5
Figure 2: Performance Refine-PPI on SKEMPI.v2 compared to other energy- based or pretrained baselines.
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A.
Pooling
G
R
L
Wide-type (Given)
Shared Weights
AAG
E
G
x
Pooling
Mutant (Unknown)
Interface Residues
Equivariant Network
Hallucinated Structures
Predict A4G
B
M
LM
Complex Structures
Probability Density Cloud
PDC-Network
Figure 3: A. The overall pipeline of our Refine-PPI. The given wild-type structure and the masked mutant structure are subsequently fed into weight-shared equivariant neural networks. The masked region is recon- structed, and the mutation effect is predicted by comparing the features of two resulting complexes. B. The procedure of deep learning architecture. The particles in the complex are represented as probability density clouds (PDCs), where each atom moves according some goometric distributions instead of being immo- bile. Then, the natural parameters including mean, variance, and co-variance are updated and propagated throughout PDC-Network.
network is used to propagate the distributions of the equilibrium of molecular systems. A comprehensive evaluation in the SKEMPL.v2 dataset (Jankauskaité et al. 2019) proves that our Refine-PPI outperforms all present methodologies by a significant margin (see Fig. and it is promising to generate absent mulant structures via a multi-task training scheme.
2 Preliminary and Background
Definition and Notations. A protein-protein complex multi-chain protein structure, separated into two groups. Each group contains at least protein chain and each chain consists of several amino acids. The wild-type complex is represented as 3D graph GT, constituted of a ligand G.V and receptor GWT. G is composed of a batch of nodes V and edges E. V represents residues or atoms at different resolutions, and Us E V has several intrinsic attributes such as the initial -i-ddmensionn roto-translational invariant features h, E R (e.g., atom or amino acid types, and electronegativity) and coordinates x; E R3 determines the connectivity between these particles and is divided into internal edges within each component as &g and ER and external edges between counterparts εLR- We assume residues in the entire complex and consistent rosidue numbers (i.e., WWT MMT n). We select four backbone atoms (N, Ca. C, O) and additional C3 to represent each amino acid.
Problem Statement. The mutation effect prediction is approximate the ground-truth function that maps from the wild-type structure GWT and mutant information (i.e., where and how some residues mutate from one type a; (ACDFFCHIKIMMPPQRSTWWYY to the other at) to AAG.
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3 Method
Overview. Refine-PPI (see Fig. 3 has three constituents parameterized by P,O,T, respectively. The backbone module h.(.) encodes the input 3D complex structure, the structure refinement module fa(.) geneates the unseen mutant structure, and the predictor (-(.) estimates the final AAG. The whole pipeline is described below. To begin with, the wild-type structure GWT and a well-initialized mutant structure GMT (the initialization details will be clucidated later) are fed into hp(()) to gain their corresponding features ZWT E TR and ZMT Raxy, respectively. Then, the imperfect mutant structure GMT along with its first-round representation ZMT forwarded into fo(.) for several cycles and acquires the ultimate structure GMT with more robust coordinates &MT,, Subsequently, the predicted mulant structure GATT is encoded by hp()) again, and can retrieve its second-round updated representation Z R=x*,, As last, pooling layer and g-(.) are appended to aggregate graph-level representations of both wild-type and mutation-type noted as H HT E R and HMT E R based on ZWI and Z and output the predicted free energy change ÿ-
Mask Mutation Modeling. As GMT is hard to attain, we rely on the accessible GWT to train fo(.) to restore the fragmentary structures. To this end, introduce mask mutation modeling (MMM) task, which requires fo).) to reconstruct corrupted wild-type structures GWT, Here, consider dungle-mutation circumstance for better illustration where the m-th residue mutates from am to d'm. Then, a (1 rr)-ength segment around this mutation site is masked, denoled as Vmni = {u: ( which starts from the (m - l)- th residue and ends at the (m + r)-th residue. We aim to recover the structure of this masked region {x SxWT m+r
Ji=m-I given GWT, its representation, and the native amino acid type am. The entire process is fo NMMT,WT. GWT, (m)) - (xWT)) wTy m+r Jimmr""
Intuitively, how to corrupt GMT is significant, because the same corruption mechanism will be imposed to procure the incipient mutant structure GMT during inference, serving as a starting point to deduce the final predicted structure GMT. Here, we investigate two strategies to initialize coordinates of the masked regions Vmnut Firstly, we borrow ideas from denoising-basee molecular pretraining methods (Godwin al.] 2021] Feng et al.] 2023) and independently add a random Gaussian noise of zero mcan N/(0, a) to the original coordinates as XT = xXWT +e, where determines the scale of the noisy deviation. This denoising objective is equivalent to learning special force field (aidi et al. 2022).
In addition, we introduce a more challenging mode to corrupt GM and hypothesize that the mutant regions m Vmmut are completely unknown. To be specific, we initialize the coordinates the masked regions (xWT) Jimm-t according to the even distribution between the residue right before the region (namely, Um-t-1) and the residue right after the region (namely, Um-r-1). Notably, residues immediately preceding or following the region can be missing, in which case we extend the existing side in reverse to initialize Vmuc. (sce Fig. 6 The overall process is written as follows:
Xm-1-1 (i - m + +1+11 1) Xm+rt1 X 11-1
if 3um -1-1, Um+r+1
[-r+2
8; Xm (m + +r +++ 1 i) (Xmtr+2 xmtrt1),
if if -1-1-1111- 30 m0 D0m+r+1,
(1)
Xm-1-1 + (1 (i- m + 1 (Xm-t-1 Xm-1-2),
Noteworthily, both initialization strategies can be easily extended to multiple mutations.
After that, the corrupted wild-type structure gWT is sent sequentially to hp(.) and fa(-) to restore the coordinates of the mutant regions masked, resulting in xWT As coordination data usually contains noise, take the cue from MEAN (Kong al. (022) and adopt the Huber loss (Huber) 1992) instead of the common RMSD loss to avoid numerical instability. The loss function is defined by comparing to the actual X;:
Lrefine
Σ VE
Inmber (Ri,x;). X:).
(2)
V
AAG Prediction. We impose the same strategy in MMM initialize GMT based on GWT, Then given the mutant information a'y, we utilize weight-shared h.()) and weight-shared fo(-) to acquire the unknown
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m+r mutant structure as p (xMr) -=-- gMr 0,p) is worth noting that the resulting x xW does not
carry gradients with no backpropagation at this phase. Later, we leverage GWT and GMT to extract their corresponding representations Z and Z separately. zwr and ZMr are then delivered to gr()) to acquire the predicted change in free energy G. Supervision is realized by the sum of two losses as L = ((x ([xWT)mtr mtr J=m-+ ( [x=T) ji=m-1). where À is the balance hyperparameter. The whole paradigm illustrated in pscudo-code is put in Algorithm
CaaG (y. () + >Cretiee
Algorithm The workflow of our Refine-PPI.
Input: wild-type structure gWT, mutant site and amino acid types am and a'i backbone module hp: refinement model fe, head predictor Øri number of recycles k, the real free energy change y, loss weight À GOT, G GMM <- Equation (gWT)
Initialize structures
# Training-only
for t = 0, l.... k do
Z, + hp (g.
x 5 fo (g.TT WWT, WT am)
end for
Lrefine f- Equation
( WT .x W
> The MMM loss
for = 0, ...,,..... k
do ho (G
ZMT No grad.
x
No grad.
So (GMT Z. X a(m))
end for
Z ZWT MT ho (gWT). .hp (T
2 - 9r (Z Z Z
LAAG + RMSE( y)
The AAG loss
# Backpropagation
P. 0,0,T LDAG XLrefine
3.1 Probability Density Cloud Network
Kinetics in Molecules. Cutting-edge architectures extend networks to Euclidean and non-Euclidean domains, encompassing manifolds, meshes, or strings. As molecules can be naturally represented as graphs, graph approaches become dominant in molecular modeling {Schütt et al. 2018 Fuchs et al.) 2020 Liao &
Smidt )022). Beyond addressing GNNs' inherent limitations (Wu et al. 2022b). they incorporate geometric principles like symmetry through equivariance and invariance. However, previous approaches were primarily designed for static and stable molecules characterized by deterministic and uncertainty-fiee structures. Here,
propose to integrate dynamics into geometric GNNs.
Probability Density Cloud. Atoms are never at rest, even at extremely low temperatures Clerk- Maxwell 1873). and exhibit translational, rotational, or vibrational motion. In quantum mechanisms, elec- trons do not follow well-defined paths like planets around the Sun in classical physics but exist at specific energy levels and are described by wave functions, the mathematical functions on the probability of finding an cloctron in various locations around the nucleus (Schumakor 1986). Physicists commonly envision an electron or other quantum particle by depicting their probability distribution around specific region of space within an atom molecule, where the shape and size of orbitals depend the quantum numbers.
Inspired by this phenomenon, we portray particles as PDC showing regions with higher probability of finding them. X; are assumed to follow Gaussian as N(u,, Σ.). E R3 is the place where node i is most likely to be located, and Σ, E æ3x3 an isotropic (or spherical) covariance matrix signifying the independence upon the coordinate system. Given this premise, we can derive many invariant gcometries that emphasize molecular structural information. The primary variable is the distance d, = ||x; x11 As x; and Xj are are statistically independent, their difference follows a normal distribution as x; Xj
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N (1: Mgj - + mn) Lemons 2003 and its squared norm denoted di exhibits generalized chi-squared distribution (.) with set of natural parameters, comprising (1, - Híj 2, Ez). The mean and variance of (2), denoted as pday and day: arc:
Idd; = tr (E; Ej) + 11 myll
(3)
od, - 2tr 2tr +2) 40m (2, (1j);
where tr(.) calculates the trace of matrix. Furthermore, distributions of other geometric variables can also be induced. Let Xab be the directed vector from X, to X5, and consider triangle nodes (i,j, k), the angle distribution Xxzy can be characterized as the distribution of arccos |x xx,-,|||xxxx]| (x)
PDC-Net. Our PDC idea can be generalized to any geometric architecture and here we select EGNN (Satorras et al.) 2021 as backbone. Our PDC-Net no longer accepts deterministic geometrics dis and Xi, but lakes distributions Saz and fx, as ingredients. Its 1-th layer, named PDC-L, takes the set (1)* i=="" edge information & = {E ELR), and geometric feature distri-
of node embeddings h
input, and outputs a transformation on h(t-1) and u(++1), Concisely, h (1+1), ((+1)) = PDC-T. hh") 101) E), which is defined as follows:
butions w11)
(u.0 (1) (1) n
i=1
mj-i Φe (h. (1)
h Had.
) h (1+1) =oh
(1)
(1) h
Σ
m
(4)
5
14 ui
(1+1)
(1)
Σ
u - -1 (m(m)))))
(1)
(5)
[iiil
(EN(()
(1+1)) Σ + [W(1 x
Σ JEV(()
(D)) + + Q (m,-s),
(6)
where de: On. Uus 6, are the edge, node, mean, and variance operations respectively that are commonly approximated by Multilayer Perceptrons (MLPs). It is worth noting that the mean position of each particle, denoted pe is updated through a weighted sum of all relative differences (μ, 14;-88 15) 1y) Meanwhile, the variance Σ; is updated by a weighted sum of all additions (E, + Ej)ejen()- These stralegies align with the calculation of the mean and variance of the difference between two normal random variables. We also provide another type of mechanism to update the variance and observe slight improvement in Appendix(B.2) Regarding the initialization of Σ, we explore three different approaches, and details are elucidated in the Moreover, PDC-Net maintains the equivariance property, and the proof can be found in
Appendix 4.4.1
Appendix D
4 Results
4.1
Experimental Setups
Data Evaluation is carried out in SKEMPLv2 (Jankauskaité et al. 2019 It contains data on changes in the thermodynamic parameters and kinetic rate constants after mutation for structurally resolved PPIs. The latest version contains manually curated binding data for 7,085 mutations. The dataset is split into folds by structure, each containing unique protein complexes that do not appear in other folds. Two folds are used for train and validation, and the remaining fold is used for test. This yields 3 different sets of parameters and ensures that every data point in SKEMPLv2 is tested once. The pretraining data is derived from PDB- REDO, a database that contains refined X-ray structures in PDB. The protein chains are clustered based on 50% sequence identily, leading to 38,413 chain clusters, which are randomly divided into the training, validation, and test sets by 95%/0.5% 4.5% respectively.
Baselines and Metrics. We evaluate PDC-Net against various categories of techniques. The initial kind encompasses conventional empirical energy functions such Rossetta Cartesian AAG Park et al. (2016):
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Table 1: Evaluation of AAG prediction on the SKEMPLv2 dataset.
Per-Structure
Overall RMSE
Method
Pretrain
Pearson Spearman
Pearson
Spearman
MAE
AUROC
Energy Function-based
Rosetta
0.3284
0.2988
0.3113
0.3468
1.6173
1.1311
0.6562
FoldX
0.3789
0,3693
0.3120
0.4071
1.9080
1.3089
0.6582
Supervised-basse
DDGPred
x
0.3750
0.34007
0.6580
0.4687
1.4998
1.0821
0.6992
End-to-End
0.3873
0.3587
0.6373
0.4882
1.6198
1.1761
0.7172
Sequence- based
ESM-1v
0.0073
-0.0118
0.1921
0.1572
1.9609
1.3683
0.5414
PSSM
0.0826
0,0822
0.0159
0.0666
1.9978
1.3895
0.5260
MSA Transf.
0.1031
0.0868
0.1173
0.1313
1.9835
1.3816
0.5768
Tranception
0.1348
0. 0.1236
0.1141
0.1402
2.0382
1.3883
0.5885
Unsupervised or Semi-supervised-ble based
B- factor
0.2042
0.1686
0.2390
0,2625
2.0411
1.4402
0.6044
ESM-IF
0.2241
0.2019
0.3194
0,2806
1.8860
1.2857
0.5899
MIF-Alogit
0.1585
0.1166
0.2918
0.2192
1.9092
1.3301
0.5749
MIF-Net.
0.3965
0.3509
0.6523
0.5134
1.5932
1.1469
0.7329
RDE-Linear
0.2903
0.2632
0.4185
0.3514
1.7832
1.2159
0.6059
RDE-Net.
0.4448
0.4010
0.6447
0.5584
1.5799
1.1123
0.7454
DiffA ffinity
0.4220
0.3970
0.6690
0.5560
1.5350
1.0930
0.7440
PPIFormer
0.4281
0.3995
0.6450
0.5304
1.6420
1.1186
0.7380
Refine-PPP
0.4475
0.4102
0.6584
0.5394
1.5556
1.0946
0.7517
Refine-PPI
0.4561
0.4374
0.6592
0.5608
1.5643
1.1093
0.7542
methodologies, exemplified by ESM-1v Meier et al. (2021). PSSM, MSA Transformer Rao al. (2021), and Trancep- tion Notin et al. (2022). The third category includes end-to-end learning models such as DDGPred Shan ct al. (2022) and another End-to-End model that adopts Graph Transformer (GT) Luo et al. (2023)
Alford et al. (2017) and FoldX. The second grouping comprises aoqueecceevolutioo...
the encoder architecture, but employs MLP to directly forecast AAG. The fourth grouping encompasses musuperviead/emisspprrrri semi-supervised learning approaches, consisting of ESM-IF Hsu et al. (022)) and MIF Yang ett al. (202)). They pretrain networks on structural data and then employ the pretrained representations to prodict AAG. MIF also utilizes GT as an encoder for comparative purposes with two variations: MIF- Alogit uses the disparity in log-probabilities of amino acid types to atlain AAG, and MIF-Network predicts AAG based on acquired representations. Besides, B-factors is the network that anticipates the B-factor of residues and incorporates the projected B-factor in lien of entropy for AAG prodiction. Lastly, Rotamer Density Estimator (RDE) Luo et al. 20023 uses flow-based generative model to estimate the probability distribution of rotamers and uses entropy to measure flexibility with two variants containing RDE-Linear and RDE-Network. DiffAffinity (Liu et al.) (2224) utilizes a Riemannian diffusson model to learn the generative process of side-chain conformations. PPIFormer (Bushuiev et al. 2023 is pretrained on a newly collected non-redundant. 3D PPT interface dataset PPTRef through the mask language modeling (MLM) tochnique. More details are in the Appendix A
Five metrics used: Pearson and Spearman correlation coefficients, minimized RMSE, minimized MAE (mean absolute error), and AUROC (area under the receiver operating characteristic). Calculating AUROC involves classifying mutations according to the direction of their AAG values. In practical scenarios, the correlation observed within a specific protein complex attracts heightened interest. To account for this, we arrange mutations according to their associated structures. Groups with fewer than 10 mutation data points are excluded. Subsoquently, correlation calculations are performed for cach structure independently, leading two additional metrics: the average per-structure Pearson and Spcarman correlation coefficients. Other details in the Appendix A

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A.
R
Ovarall SKEMPI.22
Single-mutation Subset
Mult-mutation Subset
1.5
10
Speaman: 5668/
Spearman: 0 5338
Speerman 0 5839
Prodicted ANG
Poarson: 0 6588
Pearson: 0.5687:
Pearson: 0.6307
Emera AMG
1.0
-10
-10
0
10
-10
0
10
-10
10
Experimental 44G
Experimental AAG
Experimental AÁG
0.0
Emrr of Wice-type Structura Recovery
0.5
1.0
1.5
Figure 4: A. Visualization of correlations between experimental AAG and predicted AAG. D. A selected example of the interface of a predicted mulant structure. B. The scalter plot shows that the recovery error of the wild-type structure has a positive relation with the error of AAG prediction.
4.2 Comparison with Existing Tools on Mutant Effect Prediction
Tab. 1 documents the results, and performance on subsets of single-mutation and multi-mutation is in Tab. 2 and Tab. 3. It can be seen that our Refine-PPi model is better or more compelitive all regression metrics. Precisely, it achieves the highest per-structure Spearman and Pearson's correlations, which are considered as our primary metrics because the correlation of one specific protein complex is the most important.
Multiple point mutations are often required for successful affinity maturation (Sulea et al., 2018). and Refine-PPI outperforms DDGPred and RDE-Net by large margin in the multi-mutation subset. This stems from the fact that RDE-Net and DDGPred perceive the mutant structures the same as the wild-type and consequently are not aware of the structural distinction. On the contrary, the mutant structures with multiple mutations should be more different than those with single mutations, and it becomes more crucial to detect the variant after the mutation. Refine-PPI anticipates the structural transformation due to mutation and can connect. the structural change with AAG. Notably, Refine-PPI trained from scratch has already outpassed pretrained methods such as RDE-Net, MIF-Net, and ESM-IF, which enjoy the unsupervised benefits in PDB-REDO. This further verifies the great success of Refine-PPI.
4.3 Zero-shot Mutant Effect Prediction
To evaluate the effectiveness of Refine-PPI in zero-shot mutant effect prediction, we conducted extensive experiments the ProteinGym benchmark (Notin et al. 2024). To obtain structural data, utilized AlphaFold-2 to predict the three-dimensional structures of wild-type protein sequences. A notable limita- tion of Refine-PPI is that it provides mutant structure predictions without directly outputting the prob- ability distribution over amino acid lypes. To address this, we integrated ESM-IF with Refine-PPI to compute final mutant effect scores by coupling structural insights with senuence-based predictions. We compared Refino-PPI against a comprchensive range of state-of-tho-art models, including soquencc-basod models, alignment-based models, inverse folding models, and ensemble approaches. The results, summarized in Table 4 highlight the performance of zero-shot mutant effect prediction on ProteinGym. Key findings reveal that Refine-PPI outperforms all existing inverse folding methods, achieving the highest Spearman correlation of 0.411. This represents a 4.5% improvement in rank correlation over the vanilla ESM-IF, sur- passing even the best-performing sequence-based method, VESPA. These results underscore the robustness of the MMM and the innovative PDC--et architecture, which together enhance the predictive capabilities of Refine- The superior performance of Refine-PPI demonstrates capability to integrate structural and sequence-level insights effectively, providing a significant advancement in the field of zero-shot mutant effect prediction.
4.4 Correlation between Variance and Atomic Uncertainty
PDC posits that atoms adhere to Gaussian and derives geometric attributes such as distance and angles as distributions, where Σ determines the magnitude of 3D atomic uncertainty. Here, we justify the correspon- dence between E and positional uncertainty. Notably, experimentally observing and documenting particle
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Table 2: Evaluation of AAG prediction on the
subset of the SKEMPIv2 dataset.
Per-Structure
Overall RMSE
Method
Pretrain
Pearson
Spearman
Pearson
Spearman
MAE
AUROC
Energy Funetion-based
Rosetta
0.1915
0,0836
0.1991
0.2303
2.6581
2.0246
0.6207
FoldX
0.3908
0.3640
0.3560
0.3511
1.5576
1.0713
0.6178
Supervised-basee based
DDGPred
x
0.3912
0.3896
0.5938
0.5150
2.1813
1.6699
0.7590
End-to-End
X
0.4178
0.4034
0.5858
0.4944
2.1971
1.7087
0.7532
Sesee
ESM-1v
-0.0599
-0.1284
0.1923
0.1749
2.7586
2.1193
0.5415
PSSM
-0.0174
-0.0504
-0.1126
-0,0458
2.7937
2.1499
0.4442
MSA Transf.
-0.0097
-0.0000
0.0067
0.0030
2.8115
2.1591
0.4870
Tranception
-0.0688
-0.0120
-0.0185
-0.0184
2.9280
2.2359
0.4874
Unsupervised or
based
B-factor
0.2078
0.1850
0.2009
0.2445
2.6557
2.0186
0.5876
ESM-IF
0.2016
0.1491
0.3260
0.3353
2.6446
1.9555
0.6373
MIF-Alogit
0.1053
0.0783
0.3358
0.2886
2.5361
1.8967
0.6066
MIF-Net.
0.3968
0.3789
0.6139
0.5370
2.1399
1.6422
0.7735
RDE-Linear
0.1763
0.2056
0.4583
0.4247
2.4460
1.8128
0.6573
RDE-Net.
0.4233
0.3926
0,6288
0.5900
2.0980
1.5747
0.7749
DifEAffinity
0.4140
0.3877
0.6500
0.6020
2.0510
1.5400
0.78/0
PPIFormer
0.3985
0.3925
0.6405
0.5946
2.1407
1.5753
0893
Refine- PPI
0.4474
0.4134
0.6307
0.5839
2.0939
1.5894
0.7831
Refine-PPI
X
0.4558
0.4289
0.6458
0.6091
2.0601
1.554
0.8064
uncertainty within macromolccules, such as proteins, is challenging. All data PDB or SKEMPI.2 are deterministic and uncertainty-free conformations. As a solution, resort to molecular dynamics (MD) simulations to simulate atomic motions. Notably, MD approximates atomic motions by Newtonian physics and can capture the sequential behavior of molecules in full atomic details at very fine temporal resolution. We run short-time MD for all complexes in SKEMPI.22 and calculate the Root Mcan Square Fluctuation (RMSF) alongside the entire trajectory, which numerically indicates positional differences between entire structures over time. It calculates individual residue flexibility, or how much a particular residue fluctuates during a simulation.
4.4.1 Initialization of Variance
We investigate three mechanisms to initialize Σ. First and naively, we turn all Σ; into an identity matrix I. Second, we leverage RMSF as the initial Σ. Third, we adopt a learnable strategy to initialize E, where an embedding layer maps each category of twenty residue types to their corresponding E. Their perfor- mance is listed in Tab. [] where the mean and standard deviation are documented for three runs. It can be found that MD-based initialization achicves the best Spearman (0.4287), outweighing the learnable one (0.4102) and the identity matrix (0.4043), emphasizing the efficacy of incorporating simulated uncertainty into the PDC module. This implies that simulated uncertainty the optimal choice for this variance, and learned variance idcally should move towards this simulated uncortainty. However, since MD simulations are time-consuming and costly, it is prohibited to implement MD during the inference stage each time. As a consequence, we use the learnable sort in Refine-PPI for subsequent experiments.
Table 5: Performance of different initialization methods for the coordinate variance Σ (without pretraining)
Per-Structure
Method
Pearson
Spearman
Identity Matrix
0.4422 + 0.0033
0.4043 + 0.0018
MD Simulations
0.4522 0.0036
0.4287 + 0.0015
Learnable Σ
0.4475 = 0.0034
0.4102 0.0017
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Table Evaluation of AAG prediction on the single-mutatinn subset of the SKEMPIv2 dataset.
Per-Structure
Overall RMSE
Method
Pretrain
Pearson
Spearman
Pearson
Spearman
MAE
AUROC
Energy Function-based
Rosetta
0.3284
0.2988
0.3113
0.3468
1.6173
1.1311
0.6562
FoldX
0.3908
0,3640
0.3560
0.3511
1.5576
1.0713
0.6478
seervvsedd-ased
DDGPred
x
0.3711
0.3-127
0.6515
0.4390
1.3285
0.9618
0.6858
End-to-End
0.3818
0.3426
0.6605
0.4594
1.3148
0.9569
0.7019
Sequence- based
ESM-1v
0.0422
0.0273
0.1914
0.1572
1.7226
1.1917
0.5492
PSSM
0.1215
0.1229
0.1224
0.0997
1.7420
1.2055
0.5659
MSA Transf.
0.1415
0.1293
0.1755
0.1749
1.7294
1.1942
0.5917
Tranception
0.1912
0.1816
0.1871
0.1987
1.7455
1.1708
0.6089
Unsupervised or Semmi-uperrised--aee based
B- factor
0.1884
0.1661
0.1748
0,2054
1.7242
1.1889
0.6100
ESM-IF
0.2308
0.2090
0.2957
0,2866
1.6728
1.1372
0.6051
MIF-Alogit
0.1616
0.1231
0.2548
0.1927
1.6928
1.1671
0.5630
MIF-Net.
0.3952
0.3479
0.6667
0.4802
1.3052
0.9411
0.7175
RDE-Linear
0.3192
0.2837
0.3796
0.3394
1.5997
1.0805
0.6027
RDE-Net.
0.4687
0.4333
0.6421
0.5271
1.3333
0.9392
0.7367
DiffA ffinity
0.4290
0.4090
0.6720
0.5230
1.2880
0.9230
0.7330
PPIFormer
0.4192
0.3796
0.6287
0.4772
1.4232
0.9562
0.7213
Refine-PPP
0.4474
0,4134
0.6667
0.5338
1. 1,2963
0.9179
0.7431
Refine-PPI
0.4701
0.4459
0.6658
0.5153
1.2978
0.9287
0.7481
4.4.2 Analysis of Learned Uncertainty
Visualization of Learned Variance. We randomly pick four PDBs and visualize the learned variance, that is, the mag- nitude of ||2 in Fig. 5 Pictures show that particles at the interface have a smaller variation than those at protein edges. This aligus with the biological concept that atoms in the bind- ing surface are less volatile than atoms in other parts of the complex. This phenomenon confirms that PDC-Net has adap- tively comprehended the magnitude and strength of entities' motion during PPTs.
WT 2QJA
WT 5F4E
WT 3MZG
WT AUWQ
Quantitative Analysis. We also quantitatively investigated the correlation between the learned variance and the ground truth uncortainty. A detailed comparison, classified by residucs at and not at the interface, is Tab. D Notably, the ground truth RMSF at the interface significantly smaller than that observed elsewhere. At the same time, the learned Σ, exhibits parallel pattern, where || at the interface is much smaller. This analysis further substantiates that the learned variance corresponds to atomic uncertainty.
DREP
GRUN
Figure 5: Visualization of learned uncer- tainty. A darker color corresponds to a more flexible protein segment.
4.4.3 Performance of Uncertainty Prediction with MD Simulations
To further verify the efficacy of our PDC-Net to capture the atomic uncertainty, we propose a more straight- forward task, where DL models are required to directly predict the simulated uncortainty (i.e., RMSF). On the one hand, we adopt PDC-EGNN and directly enforce the learnable variance correspond to the sim- ulated uncertainly. The loss term is therefore set MSF( ||2 RMSF). On the other hand, we leverage
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Table 4: Performer of zero-shot substitution on the DMS benchmark. We report the corrected average of Spearman's rank correlation, AUC, MCC, NDCG@10% and top 10% recall between model scores and experimental measurements the ProteinGym substitution benchmark.
Model Name Model Type
Spearman
AUC
MCC
NDCG
Recall
Site-Independent
0.359
0.696
0.286
0.747
0.201
WaveNet
0.373
0.707
0.294
0.761
0.203
EVmutation
0.395
0.716
0.305
0.777
0.222
Alignment-
DeepSequence
0.419
0.729
0.328
0.776
0.226
EVE
0.439
0.741
0.342
0.783
0.230
GEMME
0.455
0.749
0.352
0.777
0.211
UniRep
0.190
0.605
0.147
0.647
0.139
CARP (640M)
0.368
0.701
0.285
0.748
0.208
ESM-1b
0.394
0.719
0.311
0.747
0.203
ESM-2 (15B)
Sequence- based
0.401
0.720
0.314
0.759
0.208
RITA XL
0.372
0.707
0.293
0.751
0.193
ESM-Iv
0.407
0.723
0.320
0.749
0.211
ProGen2 XL
0.391
0.717
0.306
0.767
0.199
VESPA
0.436
0.742
0.346
0.775
0.201
UniRep evotuned
0.347
0.693
0.274
0.739
0.181
MSA Transformer
0.434
0.738
0.340
0.779
0.224
Hybrid Ensemble
Tranception L
0.434
0.739
0.341
0.779
0.220
TranceptEVE
0.456
0.751
0.356
0.786
0.230
ESM-IF1
0.422
0.730
0.331
0.748
0.223
MIF-ST
0.401
0.718
0.311
0.766
0.226
Inverse Folding
ProteinMPNN
0.258
0.639
0.196
0.713
0.186
Refine-PPI
0.441
0.746
0.343
0.769
0.229
Table 6: Performance of different position variance update methods without pretraining.
Interface
Non-Interface
Overall
RMSF
0.4945 0.6072
0.9735 0.8940
0.8271
0.7745
some advanced geometric networks and require them to output RMSF based on the residue feature of the final layer. The loss is written as MSE(MLP(h(4) RMSF), where MLP is the abbreviation of the multi- layer perceptron. A group baselines are selected for thorough comparison, including SchNet (Schütt et al. 2018), GVP-GNN (Jing et al. 2020), SF(3) Transformer (Fuchs et al. 2020). SphereNet (Liu al. [021] TorchMD-Net (Thölke & De Fabritiis 2021), and EquiFormer (Liao & Smidt 2022). We run three random seeds and report the mean and standard deviation of these three runs in Tab. The experiments show that the PDC module achieves the best performance in understanding the atomic uncertainty and significantly improves the ability of EGNN to forecast RMSF. This phenomenon illustrates that our design of Σ can be a good choice to represent and encode atomic uncertainty in the 3D space.
To summarize, though our loss term primarily influences output positions without directly enforcing the net- work to capture uncortainty information, extensive experiments demonstrate that the thcoretical foundation of our PDC-module design closely connects the concept of atomic uncertainty with the variance of positional distributions Σ.
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Published in Transactions on Machine Learning Research (03/2025)
Table 7: Performance on the uncertainty prediction task.
Model
MSE
SchNet
0.5214 + 0.038
GVP-GNN
0.2807 + 0.025
STr3))Trans.
0.3462 + 0.035
EGNN
0.2609 = 0.026
TorchMD-Net
0,2011 = 0.013
SphereNet
0.1688 = 0.021
EquiFormer
0.1659 = 0.022
PDC-EGNN
0.1381 0.020
4.5 Discussion of Refine-PPP
Ablation Studies. We also conduct additional experiments to investigate the contributions of cach component of our Refine-PPI and the results are displayed in Tab. 9 It can be concluded that the introduction of co-training of the structure refinement and the AAG' prediction greatly contributes to the promotion of all metrics, culminating an increase 11.8% and 15.6% per-structure Pearson's and Spearman correla- tions. Additionally, PDC-Net also brings obvious benefits such as lower MAE and a higher AUORC. In Tab. g we report the performance of two initialization strategies to corrupt the masked region. The easy mode (denoising-bate based) is slightly outpassed by the hard one (surrounding--ased))
Table 8: Performance of different coordi- nate initialization strategies for MMM.
Per-Structure Pearson
Method
Spearman
Easy
0.4417
0.4060
Hard
0.4475
0.4102
Table 9: Ablation study Refine-PII without pretraining, where we choose the backbone ho (t.e., Graph Transformer) as the foundation model for comparison (f.e., No. 1).
Per-Structure
Overall RMSE
No.
MMM
PDC-Net
Pearson Spearman
Pearson
Spearman
MAE
AUROC
X
X
0.3708
0.3353
0.6210
0.4907
1.6199
1.1933
0.7225
2
V
X
0.4145
0.3875
0.6571
0.5553
1.5580
1.1025
0.7460
/
0.4475
0.4102
0.6584
0.5394
1.5556
1.0946
0.7517
Visualization of Results. We envision the scatter plot of experimental and predicted AAG and also draw the relation between the error of wild-type structure recovery and the error of AAG estimation in Fig. It can be found that, generally, a small error of wild-type structure reconstruction leads to a more accurate AAG prediction. This indicates that these two tasks are closely related to each other. In addition, we provide a case study of 16 seed complexes with different numbers of mutations that are well predicted by our Refine-PPI in Fig. It can be discovered that Refine-PPI can realize pretty high Spearman of 0.7 even when there more than three mutations. In addition, we visualize three predicted mutant structures in the Appendix C
5 Conclusion
This work proposes new framework named Refine-PPI to predict the mutation effect. Given that mutant structures are always absent, we introduce an additional structure refinement module to recover the masked regions around the mutations. This module is trained simultaneously via mask geometric modeling. In addition, we notice that protein-proted interactions are a dynamic process, but few prior studies have considered this charactoristic in a deep learning design. To bridge the gap, we present a probability density cloud (PDC)-Network capture the dynamics in atomic resolution. Our results highlight the necessity adopt more robust. mutant structure and consider dynamics for molecular modeling.
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6 Limitations and Future Work
Despite the success of Refine-PII in estimating the mutation effect, there is still room left for improvement. (1) First, Refine-PPI keeps most of the complex stable and merely restores region around the mulant sile. It is possible that the entire complex can be significantly different upon mutation. Therefore, a promising future direction would be to enlarge the mask region. (2) Furthermore, previous studics demonstrate the benefit of structural pretraining to dramatically expand the representation space of DL models. We expect to implement MMM with more experimental structures other than PDB (e.g., Alphafold-Datiee Database and transfer the knowledge to predict free energy change. (3) Last but not least, side chains are critical to the specificity and affinity of PPIs. Accurate modeling of side chains is essential for predicting how mutations might alter binding free energy and interaction dynamics. Several recent studies (Tuu et al. 2023 Liu et al. 2024) attempt to model the change of side chains upon mutations via diffusion or flow generative approaches. By focusing solely on the backbone and omitting explicit side-chain modeling, the current framework may overlook subtle but critical contributions residue side chains to PPIs, especially in cases where mutations involve side-chain changes that disrupt or create interactions at the interface. This choice prioritizes capturing structural flexibility and uncertainly at the global level, which aligns well with our aim of modeling dynamic interactions. However, omitting explicit side-chain modeling is limitation in scenarios where fine-grained side-chain interactions dominate the mutation effect. To address this limitation, propose several future directions, such as integrating side-chain ficxibility into PDC-Net and refining mutant structures at the fine-grained side-chain level.
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Traian Sulca, Greg Hussack, Shannon Ryan, Jamshid Tanha, and Enrico O Purisima. Application of assisted design of antibody and protein therapeuties (adapt) improves efficacy of a clostridium difficile toxin a single-domain antibody. Scientifie reports, 8(1):2260, 2018.
Xiangru Tang, Howard Dai, Elizabeth Knight, Fang Wu, Yunyang Li, Tianxiao Li, and Mark Gerstein. A survey of generative ai for de novo drug design: new frontiers in molecule and protein generation. arXiv preprint trx::22402.000 08703, 2024a.
Xiangru Tang, Xinwu Ye, Fang Wu, Daniel Shao, Yin Fang, Siming Chen, Dong Xu, and Mark Gerstein. Be- design: A biochemistry-awant framework for highly accurate inverse protein folding. bioRriu, pp. 1024-10, 2024b.
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Fang Wu, Qiang Zhang, Dragomir Radev, Jiyu Cui, Wen Zhang, Huabin Xing, Ningyu Zhang, and Huajun Chen. 3d-traasffommr: Molecular representation with transformer in 3d space. 2021a.
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Published in Transactions on Machine Learning Research (03/2025)
A Experimental Details
We implement all experiments on 4 A100 GPUs, each with 80G memory. Refine-PPI is trained with an Adam optimizer without weight docay and with 81 = 0.9 and 52 = 0.999. A ReduceLROnPlateau scheduler is employed to automatically adjust the learning rate with a patience of 10 epochs and minimum learning rate of 1.e- 6. The batch size is set to 64 and an initial learning rate of 1.e 1e-4. 4. The maximum iterations are 50K and the validation frequency is 1K iterations. The node dimension is 128, and no dropout is conducted. As for the structure refinement, the recycle number is set as 3, and the balance weight is tuned as 1.0. We performed a grid search to find the optimal length of the masked region and found that | = r = 5 is a good choice. However, different initializations require different optimal hyperparamcters, and typically we can mask longer regions for denoising- based MMM. The pretraining follows a similar training scheme with a batch size of 32. During pretraining, the data loader randomly selects a cluster and then randomly chooses chain from the cluster to ensure balanced sampling. Since no mutant residue exists in PDB-REDO, we randomly select a seed residue from the chosen chain and adopt the same MMM stralegy.
As for the specific model architecture, the backbone module htp()) can take the form of any conventional geometric neural network (e.g., GVP-GNN, EGNN, SE(3)-Tranffommer Graph Transformer). Here, we adopt a one-layer Graph Transformer (Luo et al. 2023 to extract general representations of proteins. The refinement module fo(-) needs to output both updated features and coordinates, and therefore we use PDC- EGNN as fo) in our experiments. Lastly, the head predictor gr (.) is a simple linear layer that accepts the concatenation of representations of both wide and mutation types and forecasts the change in free energy. The total model size of our Refine-PPI is approximately 6M.
A.1 Baselines Implementations
Baselines that require training and calibration using the SKEMPLv2 dataset (DDGPred, End-to-End, B- factor, MIF-Alogit, MIF-Network, RDE-Linear, and RDE-Net) are trained independently using the 3 differ- ent splits of the dataset as described in Section 4.1 This is to ensure that every data point in the SKEMPL.v2 dataset is tested once. Below are descriptions of the implementation of the baseline methods, which follow the same scheme as Luo et al. (2023) and Bushuiev et al. (0023).
Rosetta Allord et al. 2017 Leman et al. 20200: The Rosetta version is 2021.16, and the scoring function is rcf2015_ cart. Every protein structure in the SKEMPLv2 dataset is first preprocessed using the relax application. The mutant structure is built by cartesian ddg. The binding free energies of both wild-type and mutant structures are predicted by interface_eneee AAG is calculated by subtracting the binding energy of the wild-type structure from the binding energy of the mutant.
BooG_sspprated/dee dSASAx100). Finally, the binding
2019) Structures are first relaxed by the RepairPDB command. Mutant structures are built with the Build command based on the repaired structure. The change in binding free energy AAG is calculated by subtracting the wild-type energy from the mutant energy.
FoldX (Delgado et al.
ESM-1v Meier et al. 2021]: We use the implementation provided in the ESM open-source repository. Protein language models can only predict the effect of mutations for single protein sequences. Therefore, the cases where mutations occur in multiple sequences are ignored. The sequence of the mutated protein chain extracted from the SEQRES entry the PDB file. A masked marginal mode is used to score both wild-type and mutant sequences and use their difference an estimate of AAG.
PSSM MSAs are constructed from the Uniref90 database for chains with mutation annotations in the SKEMPI.22 dataset. Jackhmmer version 3.3.1 is used following the setting in Meier et al. (2021). The MSAS are filtered using HHfflter with coverage 75 and sequence identity 90. This HHffitter parameter is reported to have the best performance for MSA Transformer according to Meier et al. (2021). Position- specific scoring matrices (PSSM) is calculated and the change in probability is used as a prediction of AAG.
MSA Transformer (Rao et al.] 2021]: We use the implementation provided in the ESM open-source repository. We input the MSAs constructed during the evaluation of the PSSM to the MSA Transformer.
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We used the mask- marginal mode to score both wild-type and mutant sequences and use their difference the prediction of AAG.
Tranception (Notin et al. 2022; : We use the implementation provided in the Tranception open-source
repository. We predict mutation effects using the large model checkpoint. Previously built MSAs (not filtered by HHfilter) are used for inference-time retrieval.
DDGPred (Shan et al. 2022 We use the implementation that follows the paper by Shan et al. (2022) Since this model requires predicted side-chain structures of the mutant, use mutant structures packed during our evaluation of Rosetta to train the model and run prediction.
The end-to-end model shares the same encoder architecture as RDE (Lo et al. 2023). The difference that in the RDE normalizing flows follow the encoder to model rotamer distributions, but in the end-to-end model, the embeddings are directly fed to an ML.P predict AAG.
End-to-Ende
B-factor: This model predicts per-atom b-factors for proteins. It has the same encoder archilecture RDE (Luo al.) 2023). The encoder is followed by an MLP that predicts vector for each amino acid, where each dimension is the predicted b-factor of different atoms in the amino acid. The amino acid-level b- factor is calculated by averaging the atom-level b-factors. The predicted b-factors are used as a measurement of conformational flexibility. They are used to predict AAG using the linear model same as RDF-Linear [uo
et al.
2023
ESM-IF (Hsu al. 2022): : ESM-IF can score protein sequences using the logelikelihood. The scoring
function implemented in the ESM repository. We enable the -multichain backbone flag to let the model see the whole protcin-protein complex. We subtract the log-likelihood of the wild-type from the mutant to predict AAG.
MIF Architecture: The masked inverse folding (MIF) network uses the same encoder architecture as RDE [uo et al., 2023). Following the encoder is a per-amino-acid 20-category classifier that predicts the lype masked amnno acids. We use the same PDB-REDO train-lest split to train the model. At training time, we randomly crop a patch consisting of 128 residues and randomly mask 10% amino acids. The model learns to recover the type of masked amino acids with the standard cross entropy loss.
MIF-Alogit: To score mutations, we first mask the lype of mulated amino acids. Then, use the log probability of the amino acid type as the score. Analogously, we have the score of the wild-type bound ligand, wild-type bound receptor, wild-type unbound ligand, unbound receptor, mutated bound ligand, mutated bound receptor, and mutated unbound ligand. Therefore, we use the identical linear model to RDF-Linear (Tuo et al. 2023) to predict AAG from the scores.
This is similar to RDE-Network (Luo et al., 2023). The difference that use the pre-trained encoder of MIF rather than the encoder of RDE. We also freeze the MIF encoder we aim to utilize the unsupervised representations.
MIF-Network:
DiffAffinity: We leverage its official weights at hhttss///githiii www..//urreaaath///ifffffainiaan for pre- diction of mutant effects. DiffAffinity is distinguished from prior efforts that have predominantly focused on generating protein backbone structures.
PPIFormer: We use EquiFormer as the backbone and pretrain it on PPIRef. Then the effects of mutations are predicted via the log odds ratio.
A.2 Visualization of Coordinate Initialization in MMM
To better clarify the initialization of our MMM, we show the process of two different mechanisms (i.e., the easy denoising-based and the hard surrounding-based one) in Fig. G
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Published in Transactions on Machine Learning Research (03/2025)
Linear Intespolation
Row Position
Extension
Noised Position
Denoising-based
Surrounding- based
Figure 6: The illustration of coordinate initialization in the MMM task.
B
Additional Results
B.1
Performance on Subsets and Case Studies
For better comparison of our Refine-PPP PPI and other baselines, we make a bar plot on per-structure Pearson's 's and Spearman correlations in Fig. 7 We also explicitly document the evaluation results of different methods on the multi-mutation and single-mutation subsets of the SKEMPLv2 dataset in Tab. 2 and Tab, 3 It can found that with pretraining on PDB-REDO, Refine-PPI achieves the best per-structure metrics on both and single-mutation subsets. This indicates that Refine-PPI more effective tool to screen and select mutant proteins for desired properties.
Spearman Pearson
Per Perr-Struture Correlations
0.4
0.3
0.2
0.1
0.0
ESM-1v
PSSM
MAS Transf.
franception
Rosetta
FoldX
DDGPred
End-to-End End
B-factor
ESM-IF
MIF Alogit
MIF-Net
RDE-Linear RDE-Net
Refine-PPi
Figure 7: Per-structure Spearman and Pearson correlations of different baseline methods and Refine-PPL.
B.2 Position Variance Update in PDC-EGNN
Notably, the way to update the variance of the positions of different atoms is not unique. Here, offer another kind of approach to renew the variance in the layer of PDC-EGNN.
2
x I((1)) 1+ [W(1]
(1+
Σ JEN())
(m)mn))))
Σ JEN(1)
By (m)
(7)
[(OI
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Published in Transactions on Machine Learning Research (03/2025)
where we leverage the same 6μ instead of new do. Besides, we distribute and square the x; terms because X; xj is not independent of x,. Noticeably, this Equation / does not damage the equivariance property of our model. Experiments show that this form of position variance computation performs slightly better in the mutant effect prediction task (see Tab. 10 with a per-structure Spearman 0.4490.
Table 10: Performance of different position variance update methods (without pretraining).
Per-Structure
Method
Pearson
Spearman
Equ.
0.4475
0.4102
Equ.
0.4490
0.4153
C Visualization of Predicted Structures
Here we provide some instances of mutant structures predicted by our Refine-PPI in Fig. Since the ground truth mutant structures are inaccessible, we leave it for future work examine their accuracy.
D Proof of Equivariance
Equivariance is an important characteristic, and here, we demonstrate that PDC-Net strictly follows this rule of principle. More formally, for any translation vector g R2 and for any orthogonal matrix Q e Raaa the model should satisfy:
h ht+1) {ou! + " 2(""0)"" i=1
PDC-L h (o.,(qn + + 2.QTT i=1 ..]
(8)
We will analyze how the Iranslation and rotation of input coordinates propagate through our model. We start by assuming that ho is invariant to the E(n) transformations on the coordinate distributions v. other words, information on the absolute position or oricntation of od not encoded in h Then, the distance between two particles is invariant to translations, rotations, and reflections. This because, for the mean of distance Pdd,
of the isotropic matrix and |1Q (1) have tr (QTE, E Σ,Q) tr (E, Ej) due to the characteristic (1) - T (1)
g (Qu)) + g)ll = 11Q (1) Qu
(1)
(1) 112 = (n 14 T
( (1
11 (1) || (1) 11 11.. Meanwhile, for the variance of distance Odzy we have [Qm4 + -- (Qp, + 9)] T + QT,+ 1Qu, + g- (Qp, + 9)] = (14-14 T (Σ, + E,) Q(4-
(4)) = (1, (11)) (E. + E,) -1y). Consequently, the output my-ri will also be invariant as the edge operation (.) becomes invariant.
Afterward, the equations of our model that update the mean and variance of coordinates x are E(n) equiv- ariant well. In the following, we prove their equivariance by showing that E(n) transformation of the input leads to the same transformation of the output. Notice that mj-ii is already invariant proven above, Notably, the translation has no impact over the variance of coordinates x Thus, we want to show:
Qu (1+1) (++1) +g= Qu +g+
Σ
(Qp! @ - -[- + o)) o (m
WOI
JEN()
(9)
QT Q Q 1 @ Q+ W(
Σ
( Q Q TT 0//00) de (my-vi)
(1)
JEN()
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Published in Transactions on Machine Learning Research (03/2025)
Sampler
Semples
35t5 Samples
SONY Sumples
MAZ: 393
MAC Szear: 6.336
MAZ: 523
MAC: Scear: 0.703
Speer 2,075
2pear-2.755 2775
Eals prnc diAAWs
cal preet deraiteot
ASD IKCa mm66
085 110
A601/031 BiCttro
Soed 1C3Y 15 Samples
Seed ALSE Samples
Seed 500 Samples
Seed 3841 Semples
mm
1mm
1m4
mae
mut
Pwar: G.BL 6.852
Pear: 0.25
Peat: 0.71
Pear: 0
ralo 2010 (NCm1000)
SAfS prid (12m11040
(L427
0.290
Oaalmmcl
Ocstinell
licatbrol
Seed Samples
Samples
Sumples
Samples
muz
muz
mur
MM MAC: 3333
M6S:
Eal5 prnt decanss
Spear: 0.333
MAD: 2564
AAG prost dezaimeh
Spaan. 7,67
AAGS ares ieaitech
MAC: 2.37
0.255
A": 0.000
AB5 (mc3
AMt Incarmo
A6t//eal BoctNre0
Sued LC25 1.5 Samples
Seed 2MT Semplec
Sued 4PTV Samples
Soud 2C30 Semple
1im
1m
1
mur
mar
2mz
mat.
MAD: A/7
AXc loce mro
Pear: 8.701
WE::
6,702
Fear:
Spur:
0,832
Smmut
mit
MSE:: 0,500
1.0
24
ASG imo)))
Ocalirect
ASG real Iscalhroo
Figure 8: Prediction plots of 16 seed PDBs that are made by Refine-PPI. Four rows correspond to different numbers of mutations, where the gray belt represents acceptable prediction errors. It can be found that Refine-PPI can perform well in all circumstances containing onc, two, or more mutations.
Its derivation is as follows.
Qu +g+ W((I
1
Σ JEN(()
(Qu!) + -(Qu + +g])
0₂ (m)-ss)
Qu (1) g+ + Q
1
Σ
11) -14" (m
[Nii]
jEN())
(10)
Q M [(11]
Σ
(4 !1) (4/" on (m,-ii) +
JEN(
Qui
(1+1) + +

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Published in Transactions on Machine Learning Research (03/2025)
Seed: IA4Y Mut: HBBA
Seed: 4K71
Seed: SUFQ
Mut: MA418V
Mut: QC27R
Figure 9: Examples of predicted structures of mutation-type.
Q D Q Q+
Σ
1 Q
(o
d (m--xx)
jEN(1)
- Wiii jEN(1)
Σ
(>.)) + + 6o (mz-x)
(11)
- = - (1+1)) Q.
Therefore, have proven that rotating and translating the mean and variance of x()) results in the same rolation and translation on the mean and variance of x (1+1)
Furthermore since the update of h only depend on my-i and h(") which as saw at the beginning of this proof, are E(n) invariant, therefore, h ((+1) will be invariant too. Thus, we conclude that a transformation
Qu, (1) g in pl (1) will result in the same transformation f (1+1) while h(+1) will remain invariant to it
that h((1), Qp::
( + Q 20 2] i=1 . is satisfied. ((+1) g, g x ( Q) -PDC-L h() (Qu
22


Reviews:
[{"review_id": "hffJ2ZZoNe", "reviewer": "Reviewer_DS9U", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n* The MMM objective is a simple yet effective idea that makes sense to me.\n\nWeaknesses:\n* The authors claim the method is performing \"Hallucination\" though it is very different. Hallucination refers to the technique of inverting a pre-trained image classification neural network by performing gradient descent through the logits in order to produce new images. For protein structures, hallucination refers to inverting a protein structure prediction neural network. Refine-PPI is claiming to perform hallucination though it is not doing any inversion.\n* It is odd that antibodies are used as the motivating example such as in figure 1 when no antibody experiments are done. SKEMPI is additionally not a trusted benchmark since the dataset is too small.\n* It is not properly explained which baselines (if any) are trained on SKEMPI whereas REFINE-PPI is trained on SKEMPI. This gives REFINE-PPI an unfair advantage and makes it unclear if the performance is coming from the algorithmic improvements.\n* Due to SKEMPI's limited dataset size, the authors use 3 cross fold validation. Yet no error bars are shown in the tables. The performance improvements also seem very marginal compared to methods like RDE-Net.\n* The claim of PDC-net capturing protein dynamics is unclear to me. First, the model does not model sidechains and backbone dynamics are likely difficult to model with short MD trajectories. Details of the MD trajectories are not included.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "Refine-PPI is a proposed method for predicted free energy changes in mutated protein structures. The paper proposes a new objective, mask mutation modeling (MMM), and a new neural network architecture to capture 3D dynamics and encode atomic uncertainty. The method is tested on SKEMPI v2 where they compare to baselines and show the method achieves competitive results. The results are then analyzed with ablations and attempting to measure the atomic uncertainty.", "claims_and_evidence_yn": "No", "claims_explanation": "", "audience_yn": "No", "audience_explanation": "", "requested_changes": "* Remove the claim that Refine-PPI is performing hallucination.\n* Show which baselines were trained on the same dataset as REFINE-PPI and answer if the same splits as the baselines was used.\n* Include details of the MD protocols.\n* How the means of the PDC-net are initialized?\n* What type of norm is $\\|\\Sigma_i\\|^2$ ?\n* How are the variances learned?\n* Include error bars across the folds in relevant tables.\n* Please explain why predicting RMSF is a good metric for predicting uncertainty.\n* Please explain the significance of the improvements with REFINE-PPI. Lot of the improvements seem to be on the order of O(0.01). Why is this a meaningful improvement?\n\nI would like to see the claims fixed and description of why a O(0.01) improvement in correlation is important to the reader.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "QTNCluK5vu", "reviewer": "Reviewer_avLi", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n1. The proposed Refine-PPI framework introduces a novel approach by incorporating a structure refinement module with mask mutation modeling, which effectively estimates mutation effects on protein-protein interactions.\n2. Refine-PPI uniquely captures the dynamic nature of PPIs, incorporating atomic uncertainty and dynamics into its modeling, providing more robust interpretations.\n3. PDC-Net maintains the SE(3)-equivariance, and the related proof has been provided.\n\nWeakness:\n1. Some experimental results show that the improvement is marginal. For example, in table 1, the improvement over the baseline RDE-net is limited.\n2. The hallucinated structures are not quantitiatively evaluated with a reasonable metric, making the results less comprehensive. Could the metric such as designability (widely used in evaluating protein backbone structure) be introduced here?\n3. Question: many baselines also use pretraining. Could the author explain the differences in terms of pretraining datasets used in more detail (if there are)? \n4.  Question: Could the predicted point cloud density be visualized and provide some intuitive interpretations?\n5. Some related works are missing and not sufficiently discussed, e.g., [1].\n\n \n\n[1] Liu, Shiwei, Tian Zhu, Milong Ren, Chungong Yu, Dongbo Bu, and Haicang Zhang. \"Predicting mutational effects on protein-protein binding via a side-chain diffusion probabilistic model.\" Advances in Neural Information Processing Systems 36 (2024).", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper presents a novel framework named Refine-PPI designed to estimate the mutation effects on protein-protein interactions (PPIs). The key contributions of this framework include the introduction of a structure refinement module, trained on mask mutation modeling (MMM) and structure refinement with $\\Delta \\Delta G$ prediction. This innovative approach addresses challenges related to the dynamic nature of PPIs and the difficulty of acquiring mutant protein structures.\nThe framework excels in outperforming existing methods in mutant effect prediction, as evidenced by its competitive or superior results in regression metrics across various datasets. Additionally, the integration of atomic uncertainty concepts is novel. This effort significantly promotes understanding and assessment of the effects of structural mutations, paving the way for enhanced PPI modeling.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "See the weaknesses above (especially about the evaluation).\n\nBeside, the presentation of the paper could be improved. Some typos exist. For example, \"pre-structure\" should be \"per-structure\" in Figure 2.\n\nSide chains are critical to protein-protein interaction, while these are not utilized in this work. The author could provide more disscusion about this.", "broader_impact_concerns": "No such concerns.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "IOF8H5Raz1", "reviewer": "Reviewer_ytG3", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "**Strengths**\n\n1. The introduction of dynamic modeling via PDC-Net and the MMM task adds significant value to PPI modeling, a core problem in biological/protein science.\n2. The proposed model aligns well with the dynamic and uncertain nature of biological systems, particularly in modeling molecular flexibility and uncertainty.\n\n**Weaknesses**\n\n1. (clarity and accessibility):\n    - The explanation of PDC-Net and its geometric formulation is dense and could be better contextualized / simplified. \n    - Limited details or no code provided on the PDC-Net may hinder reproducibility. \n\n2. While SKEMPI.v2 is a benchmark dataset, the evaluation could benefit from more diverse datasets to validate the general application of proposed components, including MMM and PDC-net.\n\n3. The paper assumes Gaussian distributions for atomic uncertainty without extensively justifying this choice or exploring alternative uncertainty models. (I am not disagreeing that Gaussian is not feasible, but it may require some derivation)", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper introduces **Refine-PPI**, a novel framework for modeling protein-protein interactions (PPI) with key innovations addressing the challenges in predicting mutation effects. The paper tackles two primary obstacles: the unavailability of mutant protein structures and the dynamic nature of PPI in the following ways:\n\n1.\t**Mask mutation modeling (MMM)** strategy for structure refinement, trained to hallucinate mutant structures.\n\n2.\t**Probability Density Cloud Network (PDC-Net)** to incorporate 3D dynamics and atomic uncertainty.\n\nEvaluated on the SKEMPI v2 dataset, the authors demonstrates the superior performance of refinePPI in predicting changes in binding free energy (ΔΔG) compared to existing methods.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "**Critical Revisions**\n\n1. (improved clarity): Provide additional details on the assumptions behind PDC-Net’s Gaussian modeling and initialization strategies. Simplify technical sections for broader accessibility. Is PDC-Net simply interpreting the latent/hidden variables of the network as parameters of gaussian? I cannot grasp the reason behind PDC-Net why it works better than vanilla equivariant GNN such as EGNN in section 3.1. Moreover, I do not quite understand the role and motivation of Section 3 - “Discussion” in page 5. \n2. The authors may consider testing Refine-PPI as well as PDC-net on datasets beyond SKEMPI.v2 to better demonstrate capabilities. Other mutation-related benchmark (such as ProteinGym) can be evaluated to enhance the solidness of the proposed method including MMM and PDC-Net.\n3. In Table 4, it seems the learnable covariance matrix achieved very marginal performance gain compared to identity matrix case, which seems the variance has to be initialized from some ground truth (simulation) data to be better. Under the gaussian distribution assumption for the uncertrainty, the $\\Sigma$ can be important for the core idea of the PDC-Net. I think it could benefit if the authors provide more experimental results demonstrating by visualization or something how the $\\Sigma$ changes from the initial state of training, which could help the readers understand how PDC-Net works over other vanilla GNN.\n\n**Additional Revisions**\n\n1. Use more intuitive diagrams and visualizations of PDC-Net operations, mutant structures, and uncertainty metrics. Figure 4 does not tell a clear illustration about PDC representation to me.\n2. Discuss potential applications in drug discovery and protein design, especially for antibodies or therapeutic proteins. Can the Refine-PPI or PDC-Net backbone can help solve specific problem or challenges relevant to the drug discovery yet prior methods fail to do? What are the potentials of proposed method in practice?", "broader_impact_concerns": "No broader impact concerns are noted.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: After the author rebuttal and paper revision, the majority of reviewers agree that this is a complete and good research paper that addresses a significant scientific problem with improved performance.
Decision: Accept (poster)