Topological Analysis of Molecular Dynamics Simulations using the Euler Characteristic

Alexander Smith, Spencer Runde, Alex K. Chew, Atharva S. Kelkar, Utkarsh Maheshwari, Reid C. Van Lehn, Victor M. Zavala

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Molecular dynamics (MD) simulations are used in diverse scientific and engineering fields such as drug discovery, materials design, separations, biological systems, and reaction engineering. These simulations generate highly complex data sets that capture the 3D spatial positions, dynamics, and interactions of thousands of molecules. Analyzing MD data sets is key for understanding and predicting emergent phenomena and in identifying key drivers and tuning design knobs of such phenomena. In this work, we show that the Euler characteristic (EC) provides an effective topological descriptor that facilitates MD analysis. The EC is a versatile, low-dimensional, and easy-to-interpret descriptor that can be used to reduce, analyze, and quantify complex data objects that are represented as graphs/networks, manifolds/functions, and point clouds. Specifically, we show that the EC is an informative descriptor that can be used for machine learning and data analysis tasks such as classification, visualization, and regression. We demonstrate the benefits of the proposed approach through case studies that aim to understand and predict the hydrophobicity of self-assembled monolayers and the reactivity of complex solvent environments.

Original languageEnglish (US)
Pages (from-to)1553-1567
Number of pages15
JournalJournal of Chemical Theory and Computation
Issue number5
StatePublished - Mar 14 2023
Externally publishedYes

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© 2023 American Chemical Society.

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