Comparing Petri net-based models of biological systems using Holmes.

MOTIVATION: The first and necessary step in systems approach to study biological phenomena 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 article. 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. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

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.

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.

A Stochastic Petri Net-Based Model of the Involvement of Interleukin 18 in Atherosclerosis.

Interleukin 18 (IL-18) is a proinflammatory and proatherogenic cytokine with pleiotropic properties, which is involved in T and NK cell maturation and the synthesis of other inflammatory cytokines and cell adhesion molecules. It plays a significant role in orchestrating the cytokine cascade, accelerates atherosclerosis and influences plaque vulnerability. To investigate the influence of IL-18 cytokine on atherosclerosis development, a stochastic Petri net model was built and then analyzed. First, MCT-sets and t-clusters were generated, then knockout and simulation-based analysis was conducted. The application of systems approach that was used in this research enabled an in-depth analysis of the studied phenomenon. Our results gave us better insight into the studied phenomenon and allow revealing that activation of macrophages by the classical pathway and IL-18-MyD88 signaling axis is crucial for the modeled process.

A Role of Inflammation and Immunity in Essential Hypertension-Modeled and Analyzed Using Petri Nets.

Recent studies have shown that the innate and adaptive immune system, together with low-grade inflammation, may play an important role in essential hypertension. In this work, to verify the importance of selected factors for the development of essential hypertension, we created a Petri net-based model and analyzed it. The analysis was based mainly on t-invariants, knockouts of selected fragments of the net and its simulations. The blockade of the renin-angiotensin (RAA) system revealed that the most significant effect on the emergence of essential hypertension has RAA activation. This blockade affects: (1) the formation of angiotensin II, (2) inflammatory process (by influencing C-reactive protein (CRP)), (3) the initiation of blood coagulation, (4) bradykinin generation via the kallikrein-kinin system, (5) activation of lymphocytes in hypertension, (6) the participation of TNF alpha in the activation of the acute phase response, and (7) activation of NADPH oxidase-a key enzyme of oxidative stress. On the other hand, we found that the blockade of the activation of the RAA system may not eliminate hypertension that can occur due to disturbances associated with the osmotically independent binding of Na in the interstitium. Moreover, we revealed that inflammation alone is not enough to trigger primary hypertension, but it can coexist with it. We believe that our research may contribute to a better understanding of the pathology of hypertension. It can help identify potential subprocesses, which blocking will allow better control of essential hypertension.

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.

A Control-Theoretic Model of Atherosclerosis.

We propose a control-theoretic aggregate model of the progression of atherosclerosis plaque, a chronic inflammatory disease of the arterial wall, to study the basic features of this disease. In the model, we exploit the role of inflammation in the disease progression, and use statins-drugs commonly recommended in atherosclerosis-to control this progression. We use a logistic function to allow for constrained growth of plaque. In the model, both the patient's age and overall health impact the plaque growth and its sensitivity to statins. The model parameters are estimated using original data, or calibrated using published research as well as our own clinical and laboratory studies. We contend that our model helps to gauge the statins' impact on a patient's plaque thickness, hence the disease's progression and cardiovascular risk, without requiring artery scans.

Holmes: a graphical tool for development, simulation and analysis of Petri net based models of complex biological systems.

SUMMARY: Model development and its analysis is a fundamental step in systems biology. The theory of Petri nets offers a tool for such a task. Since the rapid development of computer science, a variety of tools for Petri nets emerged, offering various analytical algorithms. From this follows a problem of using different programs to analyse a single model. Many file formats and different representations of results make the analysis much harder. Especially for larger nets the ability to visualize the results in a proper form provides a huge help in the understanding of their significance. We present a new tool for Petri nets development and analysis called Holmes. Our program contains algorithms for model analysis based on different types of Petri nets, e.g. invariant generator, Maximum Common Transitions (MCT) sets and cluster modules, simulation algorithms or knockout analysis tools. A very important feature is the ability to visualize the results of almost all analytical modules. The integration of such modules into one graphical environment allows a researcher to fully devote his or her time to the model building and analysis. AVAILABILITY AND IMPLEMENTATION: Available at http://www.cs.put.poznan.pl/mradom/Holmes/holmes.html. CONTACT: piotr@cs.put.poznan.pl.

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.

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.

Hemojuvelin-hepcidin axis modeled and analyzed using Petri nets.

Systems biology approach to investigate biological phenomena seems to be very promising because it is capable to capture one of the fundamental properties of living organisms, i.e. their inherent complexity. It allows for analysis biological entities as complex systems of interacting objects. The first and necessary step of such an analysis is building a precise model of the studied biological system. This model is expressed in the language of some branch of mathematics, as for example, differential equations. During the last two decades the theory of Petri nets has appeared to be very well suited for building models of biological systems. The structure of these nets reflects the structure of interacting biological molecules and processes. Moreover, on one hand, Petri nets have intuitive graphical representation being very helpful in understanding the structure of the system and on the other hand, there is a lot of mathematical methods and software tools supporting an analysis of the properties of the nets. In this paper a Petri net based model of the hemojuvelin-hepcidin axis involved in the maintenance of the human body iron homeostasis is presented. The analysis based mainly on T-invariants of the model properties has been made and some biological conclusions have been drawn.

Key Therapeutic Targets to Treat Hyperglycemia-Induced Atherosclerosis Analyzed Using a Petri Net-Based Model.

Chronic superphysiological glucose concentration is a hallmark of diabetes mellitus (DM) and a cause of damage to many types of cells. Atherosclerosis coexists with glucose metabolism disturbances, constituting a significant problem and exacerbating its complications. Atherosclerosis in DM is accelerated, so it is vital to slow its progression. However, from the complex network of interdependencies, molecules, and processes involved, choosing which ones should be inhibited without blocking the pathways crucial for the organism's functioning is challenging. To conduct this type of analysis, in silicotesting comes in handy. In our study, to identify sites in the network that need to be blocked to have an inhibitory effect on atherosclerosis in hyperglycemia, which is toxic for the human organism, we created a model using Petri net theory and performed analyses. We have found that blocking isoforms of protein kinase C (PKC)-PKCß and PKCγ-in diabetic patients can contribute to the inhibition of atherosclerosis progression. In addition, we have discovered that aldose reductase inhibition can slow down atherosclerosis progression, and this has been shown to reduce PKC (ß and γ) expression in DM. It has also been observed that diminishing oxidative stress through the inhibitory effect on the AGE-RAGE axis may be a promising therapeutic approach in treating hyperglycemia-induced atherosclerosis. Moreover, the blockade of NADPH oxidase, the key enzyme responsible for the formation of reactive oxygen species (ROS) in blood vessels, only moderately slowed down atherosclerosis development. However, unlike aldose reductase blockade, or direct PKC (ß and γ), the increased production of mitochondrial ROS associated with mitochondrial dysfunction effectively stopped after NADPH oxidase blockade. The results obtained may constitute the basis for further in-depth research.

Dietary Habits and Lifestyle, Including Cardiovascular Risk among Vegetarians and Omnivores during the COVID-19 Pandemic in the Polish Population.

Background: This study assessed how two food groups­omnivores (OMN) and vegetarians (VEGE)­differ in lifestyle changes, including dietary habits during the COVID-19 pandemic. Materials: A total of 861 persons participated in the survey and were divided into two groups: persons following a mixed diet (n = 489) and vegetarians, including vegans (n = 372). The mean age shows no significant differences. Methods: An online survey was conducted on the Polish population during the COVID-19 pandemic. Data was collected using social media; the survey was intended for adults and included separate sheets for different diets (OMN vs. VEGE). Results: The results in both groups were similar regarding the burden of premature diseases. Most respondents (~90%) did not indicate cardiovascular disease abnormalities. In the OMN group, overweight and obesity occurred more often, and the OMN group also showed a higher percentage of people reporting weight gain (OMN 42.7% vs. VEGE 35.9%). The results disclosed the VEGE group significantly more frequently chose products, i.e., vegetables (p = 0.029), legumes (p < 0.001), and dairy products or their plant substitutes (p = 0.002), compared to the OMN group. Conclusions: The VEGE group revealed the most regularities in dietary habits during the pandemic.

Is It Feasible to Predict Cardiovascular Risk among Healthy Vegans, Lacto-/Ovo-Vegetarians, Pescatarians, and Omnivores under Forty?

Guidelines for cardiovascular (CV) risk assessment among young adults are uncertain. Researchers are still looking for new tools for earlier diagnosis of cardiovascular diseases (CVD), the leading cause of mortality in the modern world. This study aimed to assess whether CV risk estimation is possible in groups of healthy individuals under the age of 40 on different dietary patterns (vegans-VEGAN (n = 48), lacto-/ovo-vegetarians-VEGE (n = 49), pescatarians-PESCA (n = 23), and omnivores-OMN (n = 35)) during the pandemic period. Four metrics containing selected risk classifiers were created, and participants were assessed using them. Groups including meat consumption showed increased CV risk predictions in the metrics assessment. The next analyzes showed statistically significant relationships between the results from the created metrics and selected non-basic biomarkers for ApoA1 (OMN group, p = 0.028), IL-6 (PESCA group, p = 0.048), HCY (VEGAN group, p = 0.05), and hsCRP (OMN + PESCA groups, p = 0.025). We found that predicting CV risk among healthy people under 40 adhering to different dietary patterns, taking into account basic and non-basic laboratory assessments and created metrics, is challenging but feasible. Furthermore, the OMN group appeared to be at the highest risk of increased CV risk in the future, while risk tended to be the lowest in the VEGAN group.

Graphlets in comparison of Petri net-based models of biological systems.

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.

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.

The Mutual Contribution of 3-NT, IL-18, Albumin, and Phosphate Foreshadows Death of Hemodialyzed Patients in a 2-Year Follow-Up.

Patients with chronic kidney disease (CKD), especially those who are hemodialyzed (HD), are at significantly high risk of contracting cardiovascular disease and having increased mortality. This study aimed to find potential death predictors, the measurement of which may reflect increased mortality in HD patients, and then combine the most promising ones in frames of a simple death risk assessment model. For this purpose, HD patients (n=71) with acute myocardial infarction in the last year (HD group) and healthy people (control group) as a comparative group (n=32) were included in the study. Various laboratory determinations and non-invasive cardiovascular tests were performed. Next, patients were followed for two years, and data on cardiovascular (CV) deaths were collected. On this basis, two HD groups were formed: patients who survived (HD-A, n=51) and patients who died (HD-D, n=20). To model HD mortality, 21 out of 90 potential variables collected or calculated from the raw data were selected. The best explanatory power (95.5%) was reached by a general linear model with four variables: interleukin 18, 3-nitrotyrosine, albumin, and phosphate. The interplay between immuno-inflammatory processes, nitrosative and oxidative stress, malnutrition, and calcium-phosphate disorders has been indicated to be essential in predicting CV-related mortality in studied HD patients. ClinicalTrials.gov Identifier: NCT05214872.

Chronic Kidney Disease as a Cardiovascular Disorder-Tonometry Data Analyses.

Tonometry is commonly used to provide efficient and good diagnostics for cardiovascular disease (CVD). There are many advantages of this method, including low cost, non-invasiveness and little time to perform. In this study, the effort was undertaken to check whether tonometry data hides valuable information associated with different stages of chronic kidney disease (CKD) and end-stage renal disease (ESRD) treatment. For this purpose, six groups containing patients at different stages of CKD following different ways of dialysis treatment, as well as patients without CKD but with CVD and healthy volunteers were assessed. It was revealed that each of the studied groups had a unique profile. Only the type of dialysis was indistinguishable a from tonometric perspective (hemodialysis vs. peritoneal dialysis). Several techniques were used to build profiles that independently gave the same outcome: analysis of variance, network correlation structure analysis, multinomial logistic regression, and discrimination analysis. Moreover, to evaluate the classification potential of the discriminatory model, all mentioned techniques were later compared and treated as feature selection methods. Although the results are promising, it could be difficult to express differences as simple mathematical relations. This study shows that artificial intelligence can differentiate between different stages of CKD and patients without CKD. Potential future machine learning models will be able to determine kidney health with high accuracy and thereby classify patients. ClinicalTrials.gov Identifier: NCT05214872.

Nutritional Status and Habits among People on Vegan, Lacto/Ovo-Vegetarian, Pescatarian and Traditional Diets.

Background: This study assessed the possible dependencies between nutritional habits and body composition among subjects with different dietary habits. Materials: A total of 196 healthy (aged 18−50 yrs) participants were enrolled in the study and divided into 4 groups according to their diet: vegans-VEGAN (n = 53), lacto/ovo-vegetarians­VEGE (n = 52), pescatarians-PESCA (n = 28), and omnivores-OMN (n = 43). Methods: The Food Frequency Questionnaire (FFQ) was used, and body composition was assessed on the In-Body120 analyzer. Results: Our result revealed in OMN + PESCA groups a higher average consumption frequency of sweets (p = 0.024), cheese/plant cheese (p < 0.001), eggs and egg dishes/egg substitutes (p < 0.001), butter, margarine/plant margarine (p < 0.001), cream /plant cream (p = 0.018), wine and cocktails (p = 0.028), vodka (p = 0.039) and lower of natural cottage cheese/tofu/tempeh (p < 0.001), vegetable oils (p = 0.036), legumes (p < 0.001) and nuts and seeds(p < 0.001) compared to the VEGAN + VEGE groups. The body composition analysis showed significant differences in skeletal muscle mass (SMM) (p = 0.019) and the content of minerals (p = 0.048) between groups. VEGAN disclosed the lowest average values of body fat mass (BFM), percentage body fat (PBF), and visceral adipose tissue (VAT) than other studied groups. Conclusions: The body composition analysis showed mean values within normal ranges in all of the groups, but some average results of OMN, PESCA, and VEGE compared to VEGAN were not highly satisfactory (in addition to eating behavior outcomes).

Control of Cholesterol Metabolism Using a Systems Approach.

Cholesterol is an essential component of mammalian cells and is involved in many fundamental physiological processes; hence, its homeostasis in the body is tightly controlled, and any disturbance has serious consequences. Disruption of the cellular metabolism of cholesterol, accompanied by inflammation and oxidative stress, promotes the formation of atherosclerotic plaques and, consequently, is one of the leading causes of death in the Western world. Therefore, new drugs to regulate disturbed cholesterol metabolism are used and developed, which help to control cholesterol homeostasis but still do not entirely cure atherosclerosis. In this study, a Petri net-based model of human cholesterol metabolism affected by a local inflammation and oxidative stress, has been created and analyzed. The use of knockout of selected pathways allowed us to observe and study the effect of various combinations of commonly used drugs on atherosclerosis. The analysis results led to the conclusion that combination therapy, targeting multiple pathways, may be a fundamental concept in the development of more effective strategies for the treatment and prevention of atherosclerosis.