Institute of Computing Science, Poznan University of Technology, Piotrowo 2, Poznan 60-965, Poland.
Institute of Computing Science, Poznan University of Technology, Piotrowo 2, Poznan 60-965, Poland.
Biosystems. 2022 Dec;222:104793. doi: 10.1016/j.biosystems.2022.104793. Epub 2022 Oct 20.
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.
METHODS & RESULTS: 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.
在过去的二十年中，系统生物学得到了迅猛的发展。系统方法的基础是被分析系统的形式模型。它可以用某些数学分支的语言创建，最近基于 Petri 网的生物模型似乎特别有前途，因为它们具有很强的表现力。对这类模型进行分析的方法之一是基于转移不变量。它们对应于一些不会改变所建模生物系统状态的子过程。在这种分析过程中，出现了研究过渡子集的需求，这导致了有趣的组合问题——这些问题在理论和实践中都得到了考虑。
考虑了两个反发生问题。这些问题涉及一组转移，它们既不是任何 t-不变支持集的子集，也不是来自这些支持集集合的任何 t-不变支持集的子集。它们以形式化的方式定义，分析了它们的计算复杂性，并为其中一个问题提供了精确算法。
对复杂生物现象进行全面分析具有挑战性。找到不影响属于整个研究生物系统的子过程的基本过程，对于完整理解这样的模型可能是必要的，而这要归功于所提出的算法。
