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arXiv · 2610.33727

Multiscale Topology-Regulated Nonlinear Dynamics for Protein B-Factor Prediction and Single-Cell Type Classification

Zihan Wang·Mushal Zia·Xiaoqi Wei·Li Shen·Jian Jiang
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Abstract

Protein B-factor prediction and single-cell type classification are important for characterizing structural variability and cellular heterogeneity, with applications in biological function analysis and drug discovery. However, static geometric descriptors do not directly capture how multiscale connectivity shapes responses to local perturbations. Here, we introduce multiscale graph-coupled Burgers response learning (MGCBRL), a framework integrating algebraic topology and nonlinear dynamics to construct predictive biological representations. Specifically, a filtration converts protein coordinates or cellular principal component scores into weighted graphs at ten neighborhood scales. Independent unit impulses initiate node-specific responses governed by nonlinear Burgers dynamics. Statistical summaries or sampled source-node trajectories then encode the influence of structural neighborhoods on transient signal evolution. The simulated responses serve as computational probes rather than models of biological motion. For cross-protein prediction, multiscale response statistics are combined with spectral perturbation descriptors measuring changes in Laplacian spectra after node removal. For single-cell classification, principal component scores augment these features to retain explicit expression-space information, and the resulting descriptors support downstream supervised learning. Across 104 proteins and 13 single-cell datasets, MGCBRL achieved configuration-selected mean scores of 0.888 for within-protein Pearson correlation and 0.950 for transductive cell classification balanced accuracy, with leave-one-protein-out mean correlations of 0.496-0.558. Our framework provides a shared strategy for transforming multiscale biological connectivity into informative response descriptors, supporting predictive analysis of protein structures and transcriptomic profiles.

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Zihan Wang, Mushal Zia, Xiaoqi Wei, Li Shen, Jian Jiang. 2026-10-24. Multiscale Topology-Regulated Nonlinear Dynamics for Protein B-Factor Prediction and Single-Cell Type Classification. https://arxiv.org/abs/2610.33727

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