Algorithms for evaluation of minimal cut sets

Objective: We propose away to enhance the evaluation of minimal cut sets (MCSs) in biological systems modeled by Petri nets, by providing criteria and methodology for determining their optimality in disabling specific processes without affecting critical system components. Methods: This study concerns Petri nets to model biological systems and utilizes two primary approaches for MCS evaluation. First is the analyzing impact on t-invariants to identify structural dependencies. Second is assessing the impact on potentially starved transitions caused by the inactivity of specific MCSs. This approach deal with net dynamics. These methodologies aim to offer practical tools for assessing the quality and effectiveness of MCSs. Results: The proposed methodologies were applied to two case studies. In the first case, a cholesterol metabolism network was analyzed to investigate how local inflammation and oxidative stress, in conjunction with cholesterol imbalances, influence the progression of atherosclerosis. The MCSs were ranked, with the top sets presented, focusing on those that disabled the fewest number of t-invariants. In the second case, a carbohydrate metabolism disorder model was examined to understand its impact on atherosclerosis progression. The analysis aimed to identify MCSs that could inhibit the atherosclerosis process by targeting specific transitions. Both studies utilized the Holmes software for calculations, demonstrating the effectiveness of the proposed evaluation methodologies in ranking MCSs for practical biological applications. Conclusion: The algorithms proposed in this paper offer an analytical approach for evaluating the quality of MCSs in biological systems. By providing criteria for MCS optimality, these approaches have potential to enhance the utility of MCS analysis in systems biology, aiding in the understanding and manipulation of complex biological networks. Algorithm are implemented within Holmes software, an open-source project available at https://github. com/bszawulak/HolmesPN.