Structural analysis of a Petri net model of oxidative stress in atherosclerosis

Atherosclerosis is a complex process of gathering sub-endothelial plaques decreasing lumen of the blood vessels. This disorder affects people of all ages, but its progression is asymptomatic for many years. It is regulated by many typical and atypical factors including the immune system response, a chronic kidney disease, a diet rich in lipids, a local inflammatory process and a local oxidative stress that is here one of the key factors. In this study, a Petri net model of atherosclerosis regulation is presented. This model includes also some information about stoichiometric relationships between its components and covers all mentioned factors. For the model, a structural analysis based on invariants was made and biological conclusions are presented. Since the model contains inhibitor arcs, a heuristic method for analysis of such cases is presented. This method can be used to extend the concept of feasible t-invariants.