Next Article in Journal
Experiments of Ultrasonic Positioning System with Symmetrical Array Used in Jiangmen Underground Neutrino Observatory
Next Article in Special Issue
A Novel TOPSIS Framework for Multi-Criteria Decision Making with Random Hypergraphs: Enhancing Decision Processes
Previous Article in Journal
Towards Discriminative Class-Aware Domain Alignment via Coding Rate Reduction for Unsupervised Adversarial Domain Adaptation
Previous Article in Special Issue
Extending Ramsey Numbers for Connected Graphs of Size 3
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Symmetry
Volume 16
Issue 9
10.3390/sym16091217
symmetry-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Partial Imaginary Transition State (ITS) Graphs: A Formal Framework for Research and Analysis of Atom-to-Atom Maps of Unbalanced Chemical Reactions and Their Completions

by
Marcos E. González Laffitte
1,2,*,
Klaus Weinbauer
1,3,
Tieu-Long Phan
1,4,
Nora Beier
1,
Nico Domschke
1,
Christoph Flamm
5,
Thomas Gatter
1,2,
Daniel Merkle
4,6 and
Peter F. Stadler
1,2,5,7,8,9,10,*
1
Bioinformatics Group, Department of Computer Science & Interdisciplinary Center for Bioinformatics, Leipzig University, Härtelstraße 16-18, D-04107 Leipzig, Germany
2
Center for Scalable Data Analytics and Artificial Intelligence (ScaDS.AI), Leipzig University, D-04103 Leipzig, Germany
3
Machine Learning Research Unit, TU Wien Informatics, Erzherzog-Johann-Platz 1 (FB02), A-1040 Wien, Austria
4
Department of Mathematics and Computer Science University of Southern Denmark DK-5230 Odense, Denmark
5
Department of Theoretical Chemistry, University of Vienna, Währingerstraße 17, A-1090 Vienna, Austria
6
Algorithmic Cheminformatics Group, Faculty of Technology, Bielefeld University, 33615 Bielefeld, Germany
7
Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, D-04103 Leipzig, Germany
8
Center for Non-Coding RNA in Technology and Health, University of Copenhagen, DK-1870 Fredriksberg, Denmark
9
Facultad de Ciencias, Universidad Nacional de Colombia, Sede Bogotá, Bogotá CO-111321, Colombia
10
Santa Fe Institute, 1399 Hyde Park Rd., Santa Fe, NM 87501, USA
*
Authors to whom correspondence should be addressed.
Symmetry 2024, 16(9), 1217; https://doi.org/10.3390/sym16091217
Submission received: 30 July 2024 / Revised: 28 August 2024 / Accepted: 5 September 2024 / Published: 16 September 2024
(This article belongs to the Special Issue Symmetry in Graph Algorithms and Graph Theory III)
Browse Figures
Versions Notes

Abstract

Atom-to-atom maps (AAMs) are bijections that establish the correspondence of reactant and product atoms across chemical reactions. They capture crucial features of the reaction mechanism and thus play a central role in modeling chemistry at the level of graph transformations. AAMs are equivalent to so-called “imaginary transition state” (ITS) graphs, making it possible to reduce tasks such as the computational comparison of AAMs to testing graph isomorphisms. In many application scenarios, nonetheless, only partial information is available, i.e., only partial maps or, equivalently, only subgraphs of the ITS graphs, are known. Here, we investigate whether and how, and to what extent, such partial chemical data can be completed and compared. The focus of this contribution is entirely on the development of a solid mathematical foundation for the analysis of partial AAMs and their associated partial ITS graphs.
Keywords: chemical graphs; cheminformatics; chemical reaction mechanisms; atom-to-atom maps; imaginary transition state; condensed graph of the reaction; (sub)graph isomorphism; (chemical) graph alignment; rebalancing of reactions; tautomerization reactions; hydrogen atom mapping chemical graphs; cheminformatics; chemical reaction mechanisms; atom-to-atom maps; imaginary transition state; condensed graph of the reaction; (sub)graph isomorphism; (chemical) graph alignment; rebalancing of reactions; tautomerization reactions; hydrogen atom mapping

Share and Cite

MDPI and ACS Style

González Laffitte, M.E.; Weinbauer, K.; Phan, T.-L.; Beier, N.; Domschke, N.; Flamm, C.; Gatter, T.; Merkle, D.; Stadler, P.F. Partial Imaginary Transition State (ITS) Graphs: A Formal Framework for Research and Analysis of Atom-to-Atom Maps of Unbalanced Chemical Reactions and Their Completions. Symmetry 2024, 16, 1217. https://doi.org/10.3390/sym16091217

AMA Style

González Laffitte ME, Weinbauer K, Phan T-L, Beier N, Domschke N, Flamm C, Gatter T, Merkle D, Stadler PF. Partial Imaginary Transition State (ITS) Graphs: A Formal Framework for Research and Analysis of Atom-to-Atom Maps of Unbalanced Chemical Reactions and Their Completions. Symmetry. 2024; 16(9):1217. https://doi.org/10.3390/sym16091217

Chicago/Turabian Style

González Laffitte, Marcos E., Klaus Weinbauer, Tieu-Long Phan, Nora Beier, Nico Domschke, Christoph Flamm, Thomas Gatter, Daniel Merkle, and Peter F. Stadler. 2024. "Partial Imaginary Transition State (ITS) Graphs: A Formal Framework for Research and Analysis of Atom-to-Atom Maps of Unbalanced Chemical Reactions and Their Completions" Symmetry 16, no. 9: 1217. https://doi.org/10.3390/sym16091217

APA Style

González Laffitte, M. E., Weinbauer, K., Phan, T.-L., Beier, N., Domschke, N., Flamm, C., Gatter, T., Merkle, D., & Stadler, P. F. (2024). Partial Imaginary Transition State (ITS) Graphs: A Formal Framework for Research and Analysis of Atom-to-Atom Maps of Unbalanced Chemical Reactions and Their Completions. Symmetry, 16(9), 1217. https://doi.org/10.3390/sym16091217

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop