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

Network Modeling and Control of Dynamic Disease Pathways, Review and Perspectives

Dynamic disease pathways are a combination of complex dynamical processes among bio-molecules in a cell that leads to diseases. Network modeling of disease pathways considers disease-related bio-molecules (e.g. DNA, RNA, transcription factors, enzymes, proteins, and metabolites) and their interaction (e.g. DNA methylation, histone modification, alternative splicing, and protein modification) to study disease progression and predict therapeutic responses. These bio-molecules and their interactions are the basic elements in the study of the misregulation in the disease-related gene expression that lead to abnormal cellular responses. Gene regulatory networks, cell signaling networks, and metabolic networks are the three major types of intracellular networks for the study of the cellular responses elicited from extracellular signals. The disease-related cellular responses can be prevented or regulated by designing control strategies to manipulate these extracellular or other intracellular signals. The paper reviews the regulatory mechanisms, the dynamic models, and the control strategies for each intracellular network. The applications, limitations and the prospective for modeling and control are also discussed.

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.

Mathematical Modeling Support for Lung Cancer Therapy-A Short Review

The paper presents a review of models that can be used to describe dynamics of lung cancer growth and its response to treatment at both cell population and intracellular processes levels. To address the latter, models of signaling pathways associated with cellular responses to treatment are overviewed. First, treatment options for lung cancer are discussed, and main signaling pathways and regulatory networks are briefly reviewed. Then, approaches used to model specific therapies are discussed. Following that, models of intracellular processes that are crucial in responses to therapies are presented. The paper is concluded with a discussion of the applicability of the presented approaches in the context of lung cancer.

Mathematical modeling of regulatory networks of intracellular processes - Aims and selected methods

Regulatory networks structure and signaling pathways dynamics are uncovered in time- and resource consuming experimental work. However, it is increasingly supported by modeling, analytical and computational techniques as well as discrete mathematics and artificial intelligence applied to to extract knowledge from existing databases. This review is focused on mathematical modeling used to analyze dynamics and robustness of these networks. This paper presents a review of selected modeling methods that facilitate advances in molecular biology.

Holistic View on the Structure of Immune Response: Petri Net Model

The simulation of immune response is a challenging task because quantitative data are scarce. Quantitative theoretical models either focus on specific cell-cell interactions or have to make assumptions about parameters. The broad variation of, e.g., the dimensions and abundance between lymph nodes as well as between individual patients hampers conclusive quantitative modeling. No theoretical model has been established representing a consensus on the set of major cellular processes involved in the immune response. In this paper, we apply the Petri net formalism to construct a semi-quantitative mathematical model of the lymph nodes. The model covers the major cellular processes of immune response and fulfills the formal requirements of Petri net models. The intention is to develop a model taking into account the viewpoints of experienced pathologists and computer scientists in the field of systems biology. In order to verify formal requirements, we discuss invariant properties and apply the asynchronous firing rule of a place/transition net. Twenty-five transition invariants cover the model, and each is assigned to a functional mode of the immune response. In simulations, the Petri net model describes the dynamic modes of the immune response, its adaption to antigens, and its loss of memory.

Merits and Demerits of ODE Modeling of Physicochemical Systems for Numerical Simulations

In comparison with the first-principles calculations mostly using partial differential equations (PDEs), numerical simulations with modeling by ordinary differential equations (ODEs) are sometimes superior in that they are computationally more economical and that important factors are more easily traced. However, a demerit of ODE modeling is the need of model validation through comparison with experimental data or results of the first-principles calculations. In the present review, examples of ODE modeling are reviewed such as sonochemical reactions inside a cavitation bubble, oriented attachment of nanocrystals, dynamic response of flexoelectric polarization, ultrasound-assisted sintering, and dynamics of a gas parcel in a thermoacoustic engine.

Clinical Phenotypes of Cardiovascular and Heart Failure Diseases Can Be Reversed? The Holistic Principle of Systems Biology in Multifaceted Heart Diseases

Recent advances in cardiology and biological sciences have improved quality of life in patients with complex cardiovascular diseases (CVDs) or heart failure (HF). Regardless of medical progress, complex cardiac diseases continue to have a prolonged clinical course with high morbidity and mortality. Interventional coronary techniques together with drug therapy improve quality and future prospects of life, but do not reverse the course of the atherosclerotic process that remains relentlessly progressive. The probability of CVDs and HF phenotypes to reverse can be supported by the advances made on the medical holistic principle of systems biology (SB) and on artificial intelligence (AI). Studies on clinical phenotypes reversal should be based on the research performed in large populations of patients following gathering and analyzing large amounts of relative data that embrace the concept of complexity. To decipher the complexity conundrum, a multiomics approach is needed with network analysis of the biological data. Only by understanding the complexity of chronic heart diseases and explaining the interrelationship between different interconnected biological networks can the probability for clinical phenotypes reversal be increased.