piotr@cs.put.poznan.pl.

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.

Motivation The first and necessary step in systems approach to study biological phenomana is building a formal model. One of the possibilities is to construct a model based on Petri nets. They have an intuitive graphical representation on one hand, and on the other, can be analyzed using formal mathematical methods. Finding homologies or conserved processes playing important roles in various biological systems can be done by comparing models. The ones expressed as Petri nets are especially well-suited for such a comparison, but there is a lack of software tools for this task. Results To resolve this problem, a new analytical tool has been implemented in Holmes application and described in this paper. It offers four different comparison methods, i.e., the ones based on t-invariants, decomposition, graphlets and branching vertices. Availability and implementation Available at http://www.cs.put.poznan.pl/mradom/Holmes/holmes.html

Capability to compare biological models is a crucial step needed in an analysis of complex organisms. Petri nets as a popular modelling technique, needs a possibility to determine the degree of structural similarities (e.g., comparison of metabolic or signaling pathways). However, existing comparison methods use matching invariants approach for establishing a degree of similarity, and because of that are vulnerable to the state explosion problem which may appear during calculation of a minimal invariants set. Its occurrence will block usage of existing methods. To find an alternative for this situation, we decided to adapt and tests in a Petri net environment a method based on finding a distribution of graphlets. First, we focused on adapting the original graphlets for notation of bipartite, directed graphs. As a result, 151 new graphlets with 592 orbits were created. The next step focused on evaluating a performance of the popular Graphlet Degree Distribution Agreement (GDDA) metric in the new environment. To do that, we decided to use randomly generated networks that share typical characteristics of biological models represented in Petri nets. Our results confirmed the usefulness of graphlets and GDDA in Petri net comparison and discovered its limitations.