On anti-occurrence of subsets of transitions in Petri net-based models of complex biological systems

• Published in: BioSystems Vol. 222; p. 104793
• Main Authors: Gutowska, Kaja, Formanowicz, Piotr
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.12.2022
• Subjects: Biological systems; Computational complexity; Exact algorithm; Petri nets; Sets of transitions; Sets of transitions; Exact algorithm; Petri nets; Computational complexity; Biological systems
• ISSN: 0303-2647; 1872-8324; 1872-8324
• DOI: 10.1016/j.biosystems.2022.104793

In the last two decades there can be observed a rapid development of systems biology. The basis of systems methods is a formal model of an analyzed system. It can be created in a language of some branch of mathematics and recently Petri net-based biological models seem to be especially promising since they have a great expressive power. One of the methods of analysis of such models is based on transition invariants. They correspond to some subprocesses which do not change a state of the modeled biological system. During such analysis, a need arose to study the subsets of transitions, what leads to interesting combinatorial problems — which have been considered in theory and practice. Two problems of anti-occurrence were considered. These problems concern a set of transitions which is not a subset of any of t-invariant supports or is not a subset of t-invariant supports from some collection of such supports. They are defined in a formal way, their computational complexity is analyzed and an exact algorithm is provided for one of them. A comprehensive analysis of complex biological phenomena is challenging. Finding elementary processes that do not affect subprocesses belonging to the entire studied biological system may be necessary for a complete understanding of such a model and it is possible thanks to the proposed algorithm. •The computational complexity of anti-occurrence problems in Petri net-based models.•Exact algorithm for anti-occurrence sets finding.•Relations between t-invariants as a key stage in an analysis of the biological models.•Elementary processes not affecting subprocesses belonging to the studied system.•A comprehensive analysis of complex biological phenomena based on transitions subsets.