# Using persistent homology and dynamical distances to analyze protein binding

arXiv: https://arxiv.org/abs/1412.1394 · HTML: https://mlsanity.com/paper/1412.1394/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Dec 2014.

## Built on by (most cited first, 15 of 15)

- [Going beyond persistent homology using persistent homology](https://mlsanity.com/paper/2311.06152/) (2023)
- [The decomposition of the higher-order homology embedding constructed from the k-Laplacian](https://mlsanity.com/paper/2107.10970/) (2021)
- [Adaptive Topological Feature via Persistent Homology: Filtration Learning for Point Clouds](https://mlsanity.com/paper/2307.09259/) (2023)
- [Minimal Cycle Representatives in Persistent Homology using Linear Programming: an Empirical Study with User's Guide](https://mlsanity.com/paper/2105.07025/) (2021)
- [Topological Point Cloud Clustering](https://mlsanity.com/paper/2303.16716/) (2023)
- [Topology Applied to Machine Learning: From Global to Local](https://mlsanity.com/paper/2103.05796/) (2021)
- [Topological Causal Effects](https://mlsanity.com/paper/2603.02289/) (2026)
- [Reduction Algorithms for Persistence Diagrams of Networks: CoralTDA and PrunIT](https://mlsanity.com/paper/2211.13708/) (2022)
- [The Shape of Consumer Behavior: A Symbolic and Topological Analysis of Time Series](https://mlsanity.com/paper/2506.19759/) (2025)
- [k-Means Clustering for Persistent Homology](https://mlsanity.com/paper/2210.10003/) (2022)
- [Explaining the Power of Topological Data Analysis in Graph Machine Learning](https://mlsanity.com/paper/2401.04250/) (2024)
- [From augmented microscopy to the topological transformer: a new approach in cell image analysis for Alzheimer's research](https://mlsanity.com/paper/2108.01625/) (2021)
- [Mathematical Insights into Protein Architecture: Persistent Homology and Machine Learning Applied to the Flagellar Motor](https://mlsanity.com/paper/2504.16941/) (2025)
- [Measuring Dataset Diversity from a Geometric Perspective](https://mlsanity.com/paper/2602.09340/) (2026)
- [Selecting Interpretable Circular Coordinates from Data](https://mlsanity.com/paper/2607.08230/) (2026)

## Abstract (arXiv)

Persistent homology captures the evolution of topological features of a model as a parameter changes. The most commonly used summary statistics of persistent homology are the barcode and the persistence diagram. Another summary statistic, the persistence landscape, was recently introduced by Bubenik. It is a functional summary, so it is easy to calculate sample means and variances, and it is straightforward to construct various test statistics. Implementing a permutation test we detect conformational changes between closed and open forms of the maltose-binding protein, a large biomolecule consisting of 370 amino acid residues. Furthermore, persistence landscapes can be applied to machine learning methods. A hyperplane from a support vector machine shows the clear separation between the closed and open proteins conformations. Moreover, because our approach captures dynamical properties of the protein our results may help in identifying residues susceptible to ligand binding; we show that the majority of active site residues and allosteric pathway residues are located in the vicinity of the most persistent loop in the corresponding filtered Vietoris-Rips complex. This finding was not observed in the classical anisotropic network model.