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Polymorphic Cycle Basis in a Sequence of Graphs to Analyze the Structural Evolution of a Molecular Dynamic Trajectory

Authors Ylène Aboulfath , Dominique Barth, Thierry Mautor, Dimitri Watel , Marc-Antoine Weisser

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Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Applied computing → Chemistry
  • Theory of computation → Theory and algorithms for application domains
Keywords
  • Graph theory
  • Cycle basis
  • Molecular analysis

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Abstract

Molecular dynamics analysis is a fundamental topic in chemistry, in particular the study of the formation and dissolution of hydrogen bonds over time. The dynamics of these bonds create and break cycles which are crucial to the structure of the molecules. The challenge in cycle analysis is twofold: there is an exponential number of cycles, and some cycles are very close.
We introduce a graph-based approach using minimum cycle bases to assist in molecular dynamics analysis. Given a set of graphs representing a molecule trajectory, we determine, for each graph, a minimum cycle basis and construct a graph of cycles which represents the cycles of minimum bases and their interactions. Then, we aggregate all information from these graphs of cycles into a polygraph. Each vertex of the polygraph represents a class of cycles appearing in different minimum bases and playing equivalent roles in the trajectory.
This paper introduces our approach, establishes the complexity of associated problems, and suggests an implementation. Simulations are conducted on both real and generated data to evaluate the performance of our approach.

Cite As Get BibTex

Ylène Aboulfath, Dominique Barth, Thierry Mautor, Dimitri Watel, and Marc-Antoine Weisser. Polymorphic Cycle Basis in a Sequence of Graphs to Analyze the Structural Evolution of a Molecular Dynamic Trajectory. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 1:1-1:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SEA.2025.1

Author Details

Ylène Aboulfath
  • DAVID lab, Université de Versailles Saint-Quentin/Université Paris-Saclay, France
Dominique Barth
  • DAVID lab, Université de Versailles Saint-Quentin/Université Paris-Saclay, France
Thierry Mautor
  • DAVID lab, Université de Versailles Saint-Quentin/Université Paris-Saclay, France
Dimitri Watel
  • SAMOVAR lab, Evry, France
  • Ecole Nationale Superieur d'Informatique pour l'Industrie et l'Entreprise, Evry, France
Marc-Antoine Weisser
  • LISN, CentraleSupélec, Université Paris-Saclay, France

References

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