Hemojuvelin-hepcidin axis modeled and analyzed using Petri nets

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)-PKCβ 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 (β 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 (β 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.

Control of Cholesterol Metabolism Using a Systems Approach

Simple Summary

Cholesterol is the main sterol in mammals that is essential for healthy cell functionining. It plays a key role in metabolic regulation and signaling, it is a precursor molecule of bile acids, oxysterols, and all steroid hormones. It also contributes to the structural makeup of the membranes. Its homeostasis is tightly controlled since it can harm the body if it is allowed to reach abnormal blood concentrations. One of the diseases associated with elevated cholesterol levels being the major cause of morbidities and mortalities worldwide, is atherosclerosis. In this study, we have developed a model of the cholesterol metabolism taking into account local inflammation and oxidative stress. The aim was to investigate the impact of the interplay of those processes and cholesterol metabolism disturbances on the atherosclerosis development and progression. We have also analyzed the effect of combining different classes of drugs targeting selected components of cholesterol metabolism.

Abstract

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.

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 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.

Petri net-based model of the human DNA base excision repair pathway

Cellular DNA is daily exposed to several damaging agents causing a plethora of DNA lesions. As a first aid to restore DNA integrity, several enzymes got specialized in damage recognition and lesion removal during the process called base excision repair (BER). A large number of DNA damage types and several different readers of nucleic acids lesions during BER pathway as well as two sub-pathways were considered in the definition of a model using the Petri net framework. The intuitive graphical representation in combination with precise mathematical analysis methods are the strong advantages of the Petri net-based representation of biological processes and make Petri nets a promising approach for modeling and analysis of human BER. The reported results provide new information that will aid efforts to characterize in silico knockouts as well as help to predict the sensitivity of the cell with inactivated repair proteins to different types of DNA damage. The results can also help in identifying the by-passing pathways that may lead to lack of pronounced phenotypes associated with mutations in some of the proteins. This knowledge is very useful when DNA damage-inducing drugs are introduced for cancer therapy, and lack of DNA repair is desirable for tumor cell death.

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.

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.

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.

Modelling and Simulation of Biochemical Processes Using Petri Nets

Systems composed of many components which interact with each other and lead to unpredictable global behaviour, are considered as complex systems. In a biological context, complex systems represent living systems composed of a large number of interacting elements. In order to study these systems, a precise mathematical modelling was typically used in this context. However, this modelling has limitations in the structural understanding and the behavioural study. In this sense, formal computational modelling is an approach that allows to model and to simulate dynamical properties of these particular systems. In this paper, we use Hybrid Functional Petri Net (HFPN), a Petri net extension dedicated to study and verify biopathways, to model and study the Methionine metabolic pathway. Methionine and its derivatives play significant roles in human bodies. We propose a set of simulations for the purpose of studying and analysing the Methionine pathway’s behaviour. Our simulation results have shown that several important abnormalities in this pathway are related to sever diseases such as Alzheimer’s disease, cardiovascular disease, cancers and others.

Petri net-based approach to modeling and analysis of selected aspects of the molecular regulation of angiogenesis

The functioning of both normal and pathological tissues depends on an adequate supply of oxygen through the blood vessels. A process called angiogenesis, in which new endothelial cells and smooth muscles interact with each other, forming new blood vessels either from the existing ones or from a primary vascular plexus, is particularly important and interesting, due to new therapeutic possibilities it offers. This is a multi-step and very complex process, so an accurate understanding of the underlying mechanisms is a significant task, especially in recent years, with the constantly increasing amount of new data that must be taken into account. A systems approach is necessary for these studies because it is not sufficient to analyze the properties of the building blocks separately and an analysis of the whole network of interactions is essential. This approach is based on building a mathematical model of the system, while the model is expressed in the formal language of a mathematical theory. Recently, the theory of Petri nets was shown to be especially promising for the modeling and analysis of biological phenomena. This analysis, based mainly on t-invariants, has led to a particularly important finding that a direct link (close connection) exist between transforming growth factor β1 (TGF-β1), endothelial nitric oxide synthase (eNOS), nitric oxide (NO), and hypoxia-inducible factor 1, the molecules that play a crucial roles during angiogenesis. We have shown that TGF-β1 may participate in the inhibition of angiogenesis through the upregulation of eNOS expression, which is responsible for catalyzing NO production. The results obtained in the previous studies, concerning the effects of NO on angiogenesis, have not been conclusive, and therefore, our study may contribute to a better understanding of this phenomenon.

Usefulness of serum interleukin-18 in predicting cardiovascular mortality in patients with chronic kidney disease--systems and clinical approach

The aim of this study was to check if serum interleukin-18 (IL-18) predicts 2-year cardiovascular mortality in patients at various stages of chronic kidney disease (CKD) and history of acute myocardial infarction (AMI) within the previous year. Diabetes mellitus was one of the key factors of exclusion. It was found that an increase in serum concentration of IL-18 above the cut-off point (1584.5 pg/mL) was characterized by 20.63-fold higher risk of cardiovascular deaths among studied patients. IL-18 serum concentration was found to be superior to the well-known cardiovascular risk parameters, like high sensitivity C-reactive protein (hsCRP), carotid intima media thickness (CIMT), glomerular filtration rate, albumins, ferritin, N-terminal prohormone of brain natriuretic peptide (NT-proBNP) in prognosis of cardiovascular mortality. The best predictive for IL-18 were 4 variables, such as CIMT, NT-proBNP, albumins and hsCRP, as they predicted its concentration at 89.5%. Concluding, IL-18 seems to be important indicator and predictor of cardiovascular death in two-year follow-up among non-diabetic patients suffering from CKD, with history of AMI in the previous year. The importance of IL-18 in the process of atherosclerotic plaque formation has been confirmed by systems analysis based on a formal model expressed in the language of Petri nets theory.