Persistent Sheaf Laplacian Analysis of Protein Stability and Solubility Changes upon Mutation

TL;DR

The paper tackles predicting mutation-induced changes in protein stability ($\Delta\Delta G$) and solubility with interpretable models that encode heterogeneous physicochemical interactions. It introduces SheafLapNet, a topological deep learning framework built on the Persistent Sheaf Laplacian (PSL) that fuses PSL-derived features, auxiliary descriptors, and evolutionary embeddings from the ESM-2 transformer. The method achieves state-of-the-art performance on stability benchmarks ($S2648$, $S350$) and solubility benchmarks (PON-Sol2), with improvements in $PCC$ and $RMSE$ for stability and higher $CPR$ and $GC^2$ for solubility, while providing mechanistic interpretability through PSL spectra. These results demonstrate that incorporating heterogeneous, topology-informed representations improves generalization and interpretability in predicting mutation effects, with potential impact on disease understanding and precision medicine.

Abstract

Genetic mutations frequently disrupt protein structure, stability, and solubility, acting as primary drivers for a wide spectrum of diseases. Despite the critical importance of these molecular alterations, existing computational models often lack interpretability, and fail to integrate essential physicochemical interaction. To overcome these limitations, we propose SheafLapNet, a unified predictive framework grounded in the mathematical theory of Topological Deep Learning (TDL) and Persistent Sheaf Laplacian (PSL). Unlike standard Topological Data Analysis (TDA) tools such as persistent homology, which are often insensitive to heterogeneous information, PSL explicitly encodes specific physical and chemical information such as partial charges directly into the topological analysis. SheafLapNet synergizes these sheaf-theoretic invariants with advanced protein transformer features and auxiliary physical descriptors to capture intrinsic molecular interactions in a multiscale and mechanistic manner. To validate our framework, we employ rigorous benchmarks for both regression and classification tasks. For stability prediction, we utilize the comprehensive S2648 and S350 datasets. For solubility prediction, we employ the PON-Sol2 dataset, which provides annotations for increased, decreased, or neutral solubility changes. By integrating these multi-perspective features, SheafLapNet achieves state-of-the-art performance across these diverse benchmarks, demonstrating that sheaf-theoretic modeling significantly enhances both interpretability and generalizability in predicting mutation-induced structural and functional changes.

Figures (7)

• Figure 1: Illustration of the Persistent Sheaf Laplacian (PSL) neural network (SheafLapNet) workflow. The framework predicts mutation-induced stability and solubility changes by integrating multi-scale protein representations. For each input protein structure, the feature generation pipeline extracts three distinct components: (1) sequence-based embeddings derived from pretrained protein Transformer models, (2) topological features computed via the PSL framework, and (3) auxiliary physicochemical features. These three sets of features are concatenated to form the input of the neural network for the prediction task.
• Figure 2: Illustration of model performance in protein stability changes upon mutation. (a). 5-fold cross-validation performance of SheafLapNet for S2648 dataset compared to existing state-of-the-art models cang2017topologynetquan2016strumworth2011sdm. (b). Blind test performance of SheafLapNet for S350 dataset compared to existing state-of-the-art models cang2017topologynetquan2016strumworth2011sdmcapriotti2005mutant2. (c). Comparison of experimental protein stability changes with predicted ones from SheafLapNet for S2648 dataset. (d). Comparison of experimental protein stability changes with predicted ones from SheafLapNet for S350 dataset.
• Figure 3: Illustration of model performance in protein stability changes upon mutation in the S2648 dataset. (a). Residue-residue matrix comparing the averaged experimental and predicted mutation-induced stability changes $\Delta\Delta G$ for the whole dataset of 2648 mutations, where X indicates no mutation samples. (b). Model performance across different mutation types based on residue physicochemical properties. (c): Model performance across different structural regions defined by the relative accessible solvent area (rASA). (d): Structural shift on protein (PDB ID: 1ARR) of the Q39G mutation from interior to surface region. (e): Model performance stratified by four mutation region types, with cell annotations indicating the sample count per category.
• Figure 4: Illustration of model performance in classifying mutation-induced protein solubility changes. Light blue denotes Accuracy (CPR), dark blue denotes Normalized Accuracy, light green denotes Generalized Squared Correlation (GC$^2$), and dark green denotes Normalized GC$^2$. (a) Performance from 10-fold cross-validation on the PON-Sol2 dataset, comparing SheafLapNet against existing models yang2021ponwee2024integration. For existing PON-Sol2 models yang2021pon, RFE refers to recursive feature elimination, and all refers to the use of all features. (b) Independent blind test results on the PON-Sol2 dataset, comparing SheafLapNet against state-of-the-art models yang2021ponyang2016ponwee2024integration. (c) Model accuracy from 10-fold cross-validation stratified by physicochemical mutation groups. (d) Model accuracy from 10-fold cross-validation analyzed by specific amino acid substitution types, where X denotes samples with no mutation.
• Figure 5: Illustration of persistent sheaf Laplacians. (a): a filtration process of the Rips complex from a point cloud data. (b): the persistent multiplicity of zero eigenvalues from the sheaf Laplacian matrices in 0-D and 1-D dimensions. (c): the minimal value of non-zero eigenvalues from the zero-dimensional and one-dimensional sheaf Laplacian matrices.