Interleukin 18 (IL-18) is one of the pro-inflammatory cytokines expressed by macrophages, suggesting that it plays important physiological and immunological functions, among the others: stimulation of natural killers (NKs) and T cells to interferon gamma (IFN- $\gamma$ ) synthesis. IL-18 was originally identified as interferon gamma inducing factor and now it is recognized as multifunctional cytokine, which has a role in regulation of innate and adaptive immune responses. Therefore, in order to investigate IL-18 contribution to the immuno-inflammatory processes underlying atherosclerosis, a systems approach has been used in our studies. For this purpose, a model of the studied phenomenon, including selected pathways, based on the Petri-net theory, has been created and then analyzed. Two pathways of IL-18 synthesis have been distinguished: caspase 1-dependent pathway and caspase 1-independent pathway. The analysis based on t-invariants allowed for determining interesting dependencies between IL-18 and different types of macrophages: M1 are involved in positive regulation of IL-18, while M2 are involved in negative regulation of IL-18. Moreover, the obtained results showed that IL-18 is produced more often via caspase 1-independent pathway than caspase 1-dependent pathway. Furthermore, we found that this last pathway may be associated with caspase 8 action.

Intracellular processes are cascades of biochemical reactions, triggered in response to various types of stimuli. Mathematical models describing their dynamics have become increasingly popular in recent years, as tools supporting experimental work in analysis of pathways and regulatory networks. Not only do they provide insights into general properties of these systems, but also help in specific tasks, such as search for drug molecular targets or treatment protocols. Different tools and methods are used to model complex biological systems. In this work, we focus on ordinary differential equations (ODEs) and Petri nets. We consider specific methods of analysis of such models, i.e., sensitivity analysis (SA) and significance analysis. So far, they have been applied separately, with different goals. In this paper, we show that they can complement each other, combining the sensitivity of ODE models and the significance analysis of Petri nets. The former is used to find parameters, whose change results in the greatest quantitative and qualitative changes in the model response, while the latter is a structural analysis and allows indicating the most important subprocesses in terms of information flow in Petri net. Ultimately, both methods facilitate finding the essential processes in a given signaling pathway or regulatory network and may be used to support medical therapy development. In the paper, the use of dual modeling is illustrated with an example of ATM/p53/NF- $$\kappa$$κ B pathway. Each method was applied to analyze this system, resulting in finding different subsets of important processes that might be prospective targets for changing this system behavior. While some of the processes were indicated in each of the approaches, others were found by one method only and would be missed if only that method was applied. This leads to the conclusion about the complementarity of the methods under investigation. The dual modeling approach of comprehensive structural and parametric analysis yields results that would not be possible if these two modeling approaches were applied separately. The combined approach, proposed in this paper, facilitates finding not only key processes, with which significant parameters are associated, but also significant modules, corresponding to subsystems of regulatory networks. The results provide broader insight into therapy targets in diseases in which the natural control of intracellular processes is disturbed, leading to the development of more effective therapies in medicine.

Many factors, such as endothelial dysfunction, inflammation and hemostatic disturbances, affect formation and progression of atherosclerotic plaque. In our study, we have focused on hemostatic disturbances with particular emphasis on the extrinsic pathways of coagulation. Thrombin is a main enzyme of coagulation and it is engaged in many different subprocesses. It leads to activation of factors of the coagulation cascade, transition of fibrinogen to fibrin monomer, endothelial damage, inflammation, activation of platelets and proliferation. In our study, selected aspects of disorders in prothrombotic states influenced by cigarette smoke have been modeled and analyzed. Tobacco-induced increased tissue factor, which is associated with less plasminogen activator and increased plasminogen activator-1 inhibitor, has been included in the presented model. These disorders together with accompanying inflammatory state are closely related to thrombus formation and cardiovascular disease promotion. The proposed model has been built using Petri nets and the analysis has been based mainly on t-invariants. Using the Petri net theory to model and analyze the investigated phenomena allows to better understand them by revealing some interesting dependencies in the studied biological system. It explains how tobacco smoke affects the analyzed processes and how harmful these effects are.

Although abdominal aortic aneurysm (AAA) is a common vascular disease and is associated with high mortality, the full pathogenesis of AAA remains unknown to researchers. Abdominal aortic aneurysms and atherosclerosis are strongly related. Currently, it is more often suggested that development of AAA is not a result of atherosclerosis, however, individual factors can act independently or synergistically with atherosclerosis. One of such factors is low-density lipoprotein (LDL) and its oxidized form (oxLDL). It is known that oxLDL plays an important role in the pathogenesis of atherosclerosis, thus, we decided to examine oxLDL impact on the development of AAA by creating two models using Petri-nets. The first, full model, contains subprocess of LDL oxidation and all subprocesses in which it participates, while the second, reduced model, does not contain them. The analysis of such models can be based on t-invariants. They correspond to subprocesses which do not change the state of the modeled system. Moreover, the knockout analysis has been used to estimate how crucial a selected transition (representing elementary subprocess) is, based on the number of excluded subprocesses as a result of its knockout. The results of the analysis of our models show that oxLDL affects 55.84% of subprocesses related to AAA development, but the analysis of the nets based on knockouts and simulation has shown that the influence of oxLDL on enlargement and rupture of AAA is negligible.

A deficiency of vitamin A (VAD) and iron is the most common nutritional problem affecting people worldwide. Given the scale of the problem, the interactions between vitamin A and iron levels are widely studied. However, the exact mechanism of the impact of vitamin A on the regulation of iron metabolism remains unclear. An extremely significant issue becomes a better understanding of the nature of the studied biological phenomenon, which is possible by using a systems approach through developing and analyzing a mathematical model based on a Petri net. To study the considered system, the t-cluster analysis, the significance analysis, and the analysis of the average number of transition firings were performed. The used analyses have allowed distinguishing the most important mechanisms (both subprocesses and elementary processes) positively and negatively regulating an expression of hepcidin and allowed to distinguish elementary processes with a higher frequency of occurrence compared to others. The analysis also allowed to resolve doubts about the discrepancy in literature reports, where VAD leads to positive regulation of hepcidin expression or to negative regulation of hepcidin expression. The more detailed analyses have shown that VAD more frequently positively stimulates hepcidin expression and this mechanism is more significant than the mechanism inhibiting hepcidin expression indirectly by VAD.

The severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2), responsible for the coronavirus disease of 2019 (COVID-19) pandemic, has affected and continues to affect millions of people across the world. Patients with essential arterial hypertension and renal complications are at particular risk of the fatal course of this infection. In our study, we have modeled the selected processes in a patient with essential hypertension and chronic kidney disease (CKD) suffering from COVID-19, emphasizing the function of the renin-angiotensin-aldosterone (RAA) system. The model has been built in the language of Petri nets theory. Using the systems approach, we have analyzed how COVID-19 may affect the studied organism, and we have checked whether the administration of selected anti-hypertensive drugs (angiotensin-converting enzyme inhibitors (ACEIs) and/or angiotensin receptor blockers (ARBs)) may impact the severity of the infection. Besides, we have assessed whether these drugs effectively lower blood pressure in the case of SARS-CoV-2 infection affecting essential hypertensive patients. Our research has shown that neither the ACEIs nor the ARBs worsens the course infection. However, when assessing the treatment of hypertension in the active SARS-CoV-2 infection, we have observed that ARBs might not effectively reduce blood pressure; they may even have the slightly opposite effect. On the other hand, we have confirmed the effectiveness of arterial hypertension treatment in patients receiving ACEIs. Moreover, we have found that the simultaneous use of ARBs and ACEIs averages the effects of taking both drugs, thus leading to only a slight decrease in blood pressure. We are a way from suggesting that ARBs in all hypertensive patients with COVID-19 are ineffective, but we have shown that research in this area should still be continued.