Mathematical Insights into Protein Architecture: Persistent Homology and Machine Learning Applied to the Flagellar Motor

We present a machine learning approach that leverages persistent homology to classify bacterial flagellar motors into two functional states: rotated and stalled. By embedding protein structural data into a topological framework, we extract multiscale features from filtered simplicial complexes constructed over atomic coordinates. These topological invariants, specifically persistence diagrams and barcodes, capture critical geometric and connectivity patterns that correlate with motor function. The extracted features are vectorized and integrated into a machine learning pipeline that includes dimensionality reduction and supervised classification. Applied to a curated dataset of experimentally characterized flagellar motors from diverse bacterial species, our model demonstrates high classification accuracy and robustness to structural variation. This approach highlights the power of topological data analysis in revealing functionally relevant patterns beyond the reach of traditional geometric descriptors, offering a novel computational tool for protein function prediction.