Physical-aware model accuracy estimation for protein complex using deep learning method

“With the significant progress made by AlphaFold2 [1] in single-chain structure prediction, the prediction of structures for protein multimers has become the focus of research in the field.”

“With the significant progress made by AlphaFold2 [1] in single-chain structure prediction, the prediction of structures for protein multimers has become the focus of research in the field.”

“In this study, we designed a fusion network architecture, where each part is drawn from an equivariant graph neural network (EGNN) [20] coupled with invariant point attention (IPA) [1] and a ResNet network [39] with attention mechanism.”

“Thereby, we use the high-dimensional embedding of protein structure of backbone atoms in ESM-IF1 [34] (1* L *512) and the high-dimensional embedding of sequence in ESM2 [35] (1* L *1280) to establish the connection between evolutionary conservation information and structural accuracy.”

“AlphaFold-Multimer uses the Evoformer module to encode multiple sequence alignment and template information to reflect evolutionary information and decodes the structural coordinates and quality scores in the Structure module [2].”

“Each residual block contains three 2D convolutional layers with different dilation rates, normalization layers and GELU activation function [40].”

“In addition, Rosetta energy [36 – 38] features are also an important part of the input features, using the one-body-terms, the two-body energy terms and the presence of backbone-to-backbone hydrogen bonds features.”

“Inspired by concepts of atom-atom and atom-solvent contact areas, given the strong correlation between surface areas and physical interactions [19], it is reasonable to assume that the orientation characteristics of the contact surface may contain the crucial information of the native structure…”

“The network Adam optimizer [43] with a learning rate of 0.01 is used, which decays at a rate of 0.05 %.”

“The smaller the distance between the two, the greater the interaction force (such as van der Waals force) [48,49].”

“Specifically, we use Pearson[45] and Spearman [46] metrics to measure the correlation between the predicted lDDT score of interface residues and the true lDDT, focusing on evaluating the accuracy of the methods in ranking the models.”

“The calculation formula of lDDT is as follows [21]: lDDT i = p 1 + p 2 + p 3 + p 4 4 p 0 (9) where Dij represents the distance between residue i and residue j in the reference structure, dij represents the distance between residue i and residue j in the prediction model.”

“The smaller the distance between the two, the greater the interaction force (such as van der Waals force) [48,49].”

“These features are firstly input into the fully connected layer [40] to generate a 1* L *128 protein complex embedding, which is combined with the coordinates of complex model and input into the EGNN network coupled with IPA module.”

“ROC (AUC) [45] is used to evaluate the ability of the method to distinguish between high-quality and low-quality models.”

“These representations are fed into an equivalent graph neural network (EGNN) [20] coupled with the invariant point attention mechanism (IPA) [1] and a ResNet network to predict the per-residue accuracy estimation for protein multimers.”

“In existing literature, most protein complex EMA methods use a distance threshold, such as 5 Å or 8 Å, between specific atoms (e.g., C β and C α ) to define the concept of contact[22,23].”

“Thereby, we use the high-dimensional embedding of protein structure of backbone atoms in ESM-IF1 [34] (1* L *512) and the high-dimensional embedding of sequence in ESM2 [35] (1* L *1280) to establish the connection between evolutionary conservation information and structural accuracy.”

“The voxelization features project the protein structure into voxelized grids to describe the local structural information of residues [26,27] while USR [13,28 – 31] can quickly capture the topological information of protein structures by using three sets of interatomic distances.”

“The voxelization features project the protein structure into voxelized grids to describe the local structural information of residues [26,27] while USR [13,28 – 31] can quickly capture the topological information of protein structures by using three sets of interatomic distances.”

“Specifically, we use Pearson [43] and Spearman [44] metrics to measure the correlation between the predicted lDDT score of interface residues and the true lDDT, focusing on evaluating the accuracy of the methods in ranking the models.”

“It is worth noting that VoroIF-GNN predicts the contact area accuracy for the complex interface by building a graph to represent the local contact and solvent surface based on Voronoi tessellation [12,17,18].”

“Since the structure of protein complexes is the key to understanding its function, methods such as AlphaFold-Multimer [2], DMFold-Multimer [3], AFsample [4], trRosettaX2 [5], and the recently released AlphaFold3[6] have been actively developed to predict the structure of multimers.”

“The smaller the distance between the two, the greater the interaction force (such as van der Waals force) [48,49].”

“Large Language Models (LLM) capture the evolutionary conservation information of proteins and have been widely used in protein structure prediction, design and function research [32].”

“For any contact pair formed by atoms a i and a j , the contact area can be calculated by using the triangulation algorithm [24] and Voronota software (version: 1.27.3834) [12].”

“The CASP15 results show that most successful prediction methods for protein multimers used modifications of the standard AlphaFold, including extensive sampling through variations on MSA construction, the use of multiple seeds, an increased number of recycles and extensive network dropout [7].”

“Inspired by the concepts of atom-atom and atom-solvent contact area [12,16 – 18], we use residue-level contact areas and contact surface-based orientation features to represent the strength of physical interactions between protein surface regions and their surrounding solvents, which may provide a…”

“In existing literature, most protein complex EMA methods use a distance threshold, such as 5 Å or 8 Å, between specific atoms (e.g., C β and C α ) to define the concept of contact[22,23].”

“In addition, Rosetta energy [36 – 38] features are also an important part of the input features, using the one-body-terms, the two-body energy terms and the presence of backbone-to-backbone hydrogen bonds features.”

“It is worth noting that VoroIF-GNN predicts the contact area accuracy for the complex interface by building a graph to represent the local contact and solvent surface based on Voronoi tessellation [12,17,18].”

“The voxelization features project the protein structure into voxelized grids to describe the local structural information of residues [26,27] while USR [13,28 – 31] can quickly capture the topological information of protein structures by using three sets of interatomic distances.”

“Specifically, the cross-entropy loss function is used to evaluate the estogram map loss; the binary cross entropy loss function is used to evaluate the mask map loss; the root mean square deviation[44] is used to evaluate the coordinate loss and residue-wise plDDT score loss.”

“Since the structure of protein complexes is the key to understanding its function, methods such as AlphaFold-Multimer [2], DMFold-Multimer [3], AFsample [4], trRosettaX2 [5], and the recently released AlphaFold3[6] have been actively developed to predict the structure of multimers.”

“On average, the evaluation accuracy of core residues is 24.79 %, 29.33 % higher than that of surface and interface residues, respectively (Table S4).”

“Multi-model methods require multiple models as input and then evaluate the quality of the models using structural alignments and strategies, such as MULTICOM_qa [9], ModFOLDdock [10] and VoroIF-jury [11].”

“Inspired by the concepts of atom-atom and atom-solvent contact area [12,16 – 18], we use residue-level contact areas and contact surface-based orientation features to represent the strength of physical interactions between protein surface regions and their surrounding solvents, which may provide a…”

“Since the structure of protein complexes is the key to understanding its function, methods such as AlphaFold-Multimer [2], DMFold-Multimer [3], AFsample [4], trRosettaX2 [5], and the recently released AlphaFold3[6] have been actively developed to predict the structure of multimers.”

“In existing literature, most protein complex EMA methods use a distance threshold, such as 5 Å or 8 Å, between specific atoms (e.g., C β and C α ) to define the concept of contact[22,23].”

“Not surprisingly, estimation of model accuracy (EMA) of multimeric structures has recently received much attention in the field and has been introduced into CASP15 as a new prediction category [8].”

“Experimental results demonstrate that our method outperforms state-of-the-art EMA methods, including DeepUMQA3, ModFOLDdockR, ModFOLDdockS, VoroIF, Venclovas, FoldEver, ModFOLDdock and Manifold on 30 protein complex targets in CASP15.”

“Multi-model methods require multiple models as input and then evaluate the quality of the models using structural alignments and strategies, such as MULTICOM_qa [9], ModFOLDdock [10] and VoroIF-jury [11].”

“The voxelization features project the protein structure into voxelized grids to describe the local structural information of residues [26,27] while USR [13,28 – 31] can quickly capture the topological information of protein structures by using three sets of interatomic distances.”

“Single-model methods require only a single protein complex structure as input, and do not require additional information to predict model quality, such as VoroIF-GNN [12], DeepUMQA3 [13], et.al.”

“However, it is challenging for the above methods to characterize the solvent effects of the surrounding environment of the protein surface, which is a crucial driver for the protein folding problem [15] and protein-protein interactions [16].”

“Single-model methods 24–28 provide a fully autonomous solution for evaluating protein model accuracy by employing statistical potential-based scoring systems or machine learning frameworks.”

“…enzymatic functions that combines structure and sequence-derived information [16], physics-aware approach for evaluation of protein complex models [17], improvements to the prediction of structures for chimeric proteins using windowed multiple sequence alignments [18], and improvements to the…”

“Voronoi partitioning allows for the precise calculation of per-atom contact areas and local solvent-accessible surface area (SASA), effectively approximating hydrophobic effects and van der Waals interactions, as demonstrated by VoroIF-GNN [23] and DeepUMQA-PA [24].”

“…encoding and does not explicitly include physicochemical interaction features such as contact surfaces, orientation-specific interactions, or solvent accessibility, all of which have been shown to improve protein model quality assessment methods like DeepUMQA-PA and EquiRank [ 27 , 28 ].”