Persistent topology for cryo-EM data analysis

TL;DR

This paper introduces persistent homology as a tool for analyzing cryo-EM data, enabling noise removal and structure identification by tracking topological features during denoising, and demonstrating its utility in model selection.

Contribution

The work applies persistent homology to cryo-EM data analysis, providing a novel topological denoising method and a strategy for resolving ill-posed inverse problems in structure determination.

Findings

Persistent homology visualizes separation of signal and noise topological features.

Geometric flows preserve structural topological fingerprints while reducing noise.

Topological analysis favors the third tubulin model over others based on data comparison.

Abstract

In this work, we introduce persistent homology for the analysis of cryo-electron microscopy (cryo-EM) density maps. We identify the topological fingerprint or topological signature of noise, which is widespread in cryo-EM data. For low signal to noise ratio (SNR) volumetric data, intrinsic topological features of biomolecular structures are indistinguishable from noise. To remove noise, we employ geometric flows which are found to preserve the intrinsic topological fingerprints of cryo-EM structures and diminish the topological signature of noise. In particular, persistent homology enables us to visualize the gradual separation of the topological fingerprints of cryo-EM structures from those of noise during the denoising process, which gives rise to a practical procedure for prescribing a noise threshold to extract cryo-EM structure information from noise contaminated data after certain iterations of the geometric flow equation. To further demonstrate the utility of persistent homology for cryo-EM data analysis, we consider a microtubule intermediate structure (EMD-1129). Three helix models, an alpha-tubulin monomer model, an alpha- and beta-tubulin model, and an alpha- and beta-tubulin dimer model, are constructed to fit the cryo-EM data. The least square fitting leads to similarly high correlation coefficients, which indicates that structure determination via optimization is an ill-posed inverse problem. By a comparison of the topological fingerprints of the original data and those of three models, we found that the third model is topologically favored. The present work offers persistent homology based new strategies for topological denoising and for resolving ill-posed inverse problems.