Searching for significant reactions and subprocesses in models of biological systems based on Petri nets.

The primary aim of this research was to propose algorithms enabling the identification of significant reactions and subprocesses within models of biological systems constructed using classical Petri nets. These solutions allow to performance of two analysis methods: an importance analysis for identifying individual reactions critical to the functioning of the model and an occurrence analysis for finding essential subprocesses. To demonstrate the utility of these methods, analyses of an example model have been performed. In this case, it was a model related to the DNA damage response mechanism. It is worth noting that the proposed analyses can be applied to any biological phenomenon represented using the Petri net formalism. The presented analysis methods represent an extension of classical Petri net-based analyses. Their utility lies in their potential to enhance our comprehension of the biological phenomena under investigation. Furthermore, they can lead to the development of more effective medical therapies, as they can aid in the identification of potential molecular targets for drugs.

On anti-occurrence of subsets of transitions in Petri net-based models of complex biological systems.

BACKGROUND AND OBJECTIVE: 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. CONCLUSIONS: 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.

Interrelations between Iron and Vitamin A-Studied Using Systems Approach.

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.

Petri nets and ODEs as complementary methods for comprehensive analysis on an example of the ATM-p53-NF-[Formula: see text]B signaling pathways.

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-[Formula: see text]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.

Learning vector quantization as an interpretable classifier for the detection of SARS-CoV-2 types based on their RNA sequences.

We present an approach to discriminate SARS-CoV-2 virus types based on their RNA sequence descriptions avoiding a sequence alignment. For that purpose, sequences are preprocessed by feature extraction and the resulting feature vectors are analyzed by prototype-based classification to remain interpretable. In particular, we propose to use variants of learning vector quantization (LVQ) based on dissimilarity measures for RNA sequence data. The respective matrix LVQ provides additional knowledge about the classification decisions like discriminant feature correlations and, additionally, can be equipped with easy to realize reject options for uncertain data. Those options provide self-controlled evidence, i.e., the model refuses to make a classification decision if the model evidence for the presented data is not sufficient. This model is first trained using a GISAID dataset with given virus types detected according to the molecular differences in coronavirus populations by phylogenetic tree clustering. In a second step, we apply the trained model to another but unlabeled SARS-CoV-2 virus dataset. For these data, we can either assign a virus type to the sequences or reject atypical samples. Those rejected sequences allow to speculate about new virus types with respect to nucleotide base mutations in the viral sequences. Moreover, this rejection analysis improves model robustness. Last but not least, the presented approach has lower computational complexity compared to methods based on (multiple) sequence alignment. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s00521-021-06018-2.

The Crosstalk between SARS-CoV-2 Infection and the RAA System in Essential Hypertension-Analyses Using Systems Approach.

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.

ABG Assistant-Towards an Understanding of Complex Acid-Base Disorders.

The ability to diagnose acid-base imbalances correctly is essential for physicians and other healthcare workers. Despite its importance, it is often considered too complex and confusing. Although most people dealing with arterial blood gases (ABGs) do not usually have problems with acid-base disorder assessment, such an analysis is also carried out by other healthcare workers for whom this can be a challenging task. Many aspects may be problematic, partly due to multiple data analysis methods and no definitive statement on which one is better. According to our survey, the correctness of arterial blood gas analysis is unsatisfactory, especially in mixed disorders, which do not always manifest an obvious set of symptoms. Therefore, ABG parameters can be used as an established biomarker panel, which is considered to be a powerful tool for personalized medicine. Moreover, using different approaches to analyze acid-base disorders can lead to varying diagnoses in some cases. Because of these problems, we developed a mobile application that can spot diagnostic differences by taking into account physiological and chemical approaches, including their variants, with a corrected anion gap. The proposed application is characterized by a high percentage of correct analyses and can be an essential aid for diagnosing acid-base disturbances.

Virxicon: a lexicon of viral sequences.

MOTIVATION: Viruses are the most abundant biological entities and constitute a large reservoir of genetic diversity. In recent years, knowledge about them has increased significantly as a result of dynamic development in life sciences and rapid technological progress. This knowledge is scattered across various data repositories, making a comprehensive analysis of viral data difficult. RESULTS: In response to the need for gathering a comprehensive knowledge of viruses and viral sequences, we developed Virxicon, a lexicon of all experimentally acquired sequences for RNA and DNA viruses. The ability to quickly obtain data for entire viral groups, searching sequences by levels of taxonomic hierarchy-according to the Baltimore classification and ICTV taxonomy-and tracking the distribution of viral data and its growth over time are unique features of our database compared to the other tools. AVAILABILITYAND IMPLEMENTATION: Virxicon is a publicly available resource, updated weekly. It has an intuitive web interface and can be freely accessed at http://virxicon.cs.put.poznan.pl/.

Systems Approach to Study Associations between OxLDL and Abdominal Aortic Aneurysms.

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.

Selected Aspects of Tobacco-Induced Prothrombotic State, Inflammation and Oxidative Stress: Modeled and Analyzed Using Petri Nets.

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.

Theoretical Studies on the Engagement of Interleukin 18 in the Immuno-Inflammatory Processes Underlying Atherosclerosis.

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- γ ) 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.