MONALISA for stochastic simulations of Petri net models of biochemical systems

Mathematical modeling of the molecular switch of TNFR1-mediated signaling pathways applying Petri net formalism and in silico knockout analysis

The paper describes a mathematical model of the molecular switches of cell survival, apoptosis, and necroptosis in cellular signaling pathways initiated by tumor necrosis factor 1. Based on experimental findings in the literature, we constructed a Petri net model based on detailed molecular reactions of the molecular players, protein complexes, post-translational modifications, and cross talk. The model comprises 118 biochemical entities, 130 reactions, and 299 edges. We verified the model by evaluating invariant properties of the system at steady state and by in silico knockout analysis. Applying Petri net analysis techniques, we found 279 pathways, which describe signal flows from receptor activation to cellular response, representing the combinatorial diversity of functional pathways.120 pathways steered the cell to survival, whereas 58 and 35 pathways led to apoptosis and necroptosis, respectively. For 65 pathways, the triggered response was not deterministic and led to multiple possible outcomes. We investigated the in silico knockout behavior and identified important checkpoints of the TNFR1 signaling pathway in terms of ubiquitination within complex I and the gene expression dependent on NF-κB, which controls the caspase activity in complex II and apoptosis induction. Despite not knowing enough kinetic data of sufficient quality, we estimated system’s dynamics using a discrete, semi-quantitative Petri net model.

It is still a challenge to develop mechanistic models for big molecular systems without the knowledge of enough kinetic parameters of sufficient quality. At the same time, more qualitative and semi-quantitative data have been produced in increasing numbers, e.g., by new high-throughput technologies. This has generated demands for new concepts at appropriate abstraction levels. The Petri net formalism enables the integration of qualitative as well as quantitative data and provides algorithms and methods for model verification and model simulation. Moreover, Petri nets exhibit a clear and coherent visualization. Here, we modeled the molecular switches between cell survival, apoptosis, and necroptosis induced by tumor necrosis factor 1. We were interested not only in an exhaustive exploration of all possible signaling pathways, but also in finding the system’s checkpoints. Our Petri net model comprises 118 biochemical entities, 130 reactions, and 299 edges. We found 279 pathways that describe signal flows from receptor activation to cellular response.120 pathways steered the cell to survival, whereas 58 and 35 pathways led to apoptosis and necroptosis, respectively. For 65 pathways, the triggered response was not deterministic, leading to multiple possible outcomes. We applied in silico knockout analyses to the Petri net model and could identify important checkpoints of the tumor necrosis factor 1 signaling pathway.

Petri Net modelling approach for analysing the behaviour of [inline-formula removed] and Ca2+ signalling pathways in arrhythmogenic right ventricular cardiomyopathy

Arrhythmogenic right ventricular cardiomyopathy (ARVC) is an inherited heart muscle disease that may result in arrhythmia, heart failure and sudden death. The hallmark pathological findings are progressive myocyte loss and fibro fatty replacement, with a predilection for the right ventricle. This study focuses on the adipose tissue formation in cardiomyocyte by considering the signal transduction pathways including Wnt/[inline-formula removed]-catenin and Wnt/Ca2+ regulation system. These pathways are modelled and analysed using stochastic petri nets (SPN) in order to increase our comprehension of ARVC and in turn its treatment regimen. The Wnt/[inline-formula removed]-catenin model predicts that the dysregulation or absence of Wnt signalling, inhibition of dishevelled and elevation of glycogen synthase kinase 3 along with casein kinase I are key cytotoxic events resulting in apoptosis. Moreover, the Wnt/Ca2+ SPN model demonstrates that the Bcl2 gene inhibited by c-Jun N-terminal kinase protein in the event of endoplasmic reticulum stress due to action potential and increased amount of intracellular Ca2+ which recovers the Ca2+ homeostasis by phospholipase C, this event positively regulates the Bcl2 to suppress the mitochondrial apoptosis which causes ARVC.

A graphical and computational modeling platform for biological pathways

A major endeavor of systems biology is the construction of graphical and computational models of biological pathways as a means to better understand their structure and function. Here, we present a protocol for a biologist-friendly graphical modeling scheme that facilitates the construction of detailed network diagrams, summarizing the components of a biological pathway (such as proteins and biochemicals) and illustrating how they interact. These diagrams can then be used to simulate activity flow through a pathway, thereby modeling its dynamic behavior. The protocol is divided into four sections: (i) assembly of network diagrams using the modified Edinburgh Pathway Notation (mEPN) scheme and yEd network editing software with pathway information obtained from published literature and databases of molecular interaction data; (ii) parameterization of the pathway model within yEd through the placement of 'tokens' on the basis of the known or imputed amount or activity of a component; (iii) model testing through visualization and quantitative analysis of the movement of tokens through the pathway, using the network analysis tool Graphia Professional and (iv) optimization of model parameterization and experimentation. This is the first modeling approach that combines a sophisticated notation scheme for depicting biological events at the molecular level with a Petri net-based flow simulation algorithm and a powerful visualization engine with which to observe the dynamics of the system being modeled. Unlike many mathematical approaches to modeling pathways, it does not require the construction of a series of equations or rate constants for model parameterization. Depending on a model's complexity and the availability of information, its construction can take days to months, and, with refinement, possibly years. However, once assembled and parameterized, a simulation run, even on a large model, typically takes only seconds. Models constructed using this approach provide a means of knowledge management, information exchange and, through the computation simulation of their dynamic activity, generation and testing of hypotheses, as well as prediction of a system's behavior when perturbed.

Petri net-based prediction of therapeutic targets that recover abnormally phosphorylated proteins in muscle atrophy

Background

Muscle atrophy, an involuntary loss of muscle mass, is involved in various diseases and sometimes leads to mortality. However, therapeutics for muscle atrophy thus far have had limited effects. Here, we present a new approach for therapeutic target prediction using Petri net simulation of the status of phosphorylation, with a reasonable assumption that the recovery of abnormally phosphorylated proteins can be a treatment for muscle atrophy.

Results

The Petri net model was employed to simulate phosphorylation status in three states, i.e. reference, atrophic and each gene-inhibited state based on the myocyte-specific phosphorylation network. Here, we newly devised a phosphorylation specific Petri net that involves two types of transitions (phosphorylation or de-phosphorylation) and two types of places (activation with or without phosphorylation). Before predicting therapeutic targets, the simulation results in reference and atrophic states were validated by Western blotting experiments detecting five marker proteins, i.e. RELA, SMAD2, SMAD3, FOXO1 and FOXO3. Finally, we determined 37 potential therapeutic targets whose inhibition recovers the phosphorylation status from an atrophic state as indicated by the five validated marker proteins. In the evaluation, we confirmed that the 37 potential targets were enriched for muscle atrophy-related terms such as actin and muscle contraction processes, and they were also significantly overlapping with the genes associated with muscle atrophy reported in the Comparative Toxicogenomics Database (p-value < 0.05). Furthermore, we noticed that they included several proteins that could not be characterized by the shortest path analysis. The three potential targets, i.e. BMPR1B, ROCK, and LEPR, were manually validated with the literature.

Conclusions

In this study, we suggest a new approach to predict potential therapeutic targets of muscle atrophy with an analysis of phosphorylation status simulated by Petri net. We generated a list of the potential therapeutic targets whose inhibition recovers abnormally phosphorylated proteins in an atrophic state. They were evaluated by various approaches, such as Western blotting, GO terms, literature, known muscle atrophy-related genes and shortest path analysis. We expect the new proposed strategy to provide an understanding of phosphorylation status in muscle atrophy and to provide assistance towards identifying new therapies.

Electronic supplementary material

The online version of this article (10.1186/s12918-018-0555-0) contains supplementary material, which is available to authorized users.

Manatee invariants reveal functional pathways in signaling networks

Background

Signal transduction pathways are important cellular processes to maintain the cell’s integrity. Their imbalance can cause severe pathologies. As signal transduction pathways feature complex regulations, they form intertwined networks. Mathematical models aim to capture their regulatory logic and allow an unbiased analysis of robustness and vulnerability of the signaling network. Pathway detection is yet a challenge for the analysis of signaling networks in the field of systems biology. A rigorous mathematical formalism is lacking to identify all possible signal flows in a network model.

Results

In this paper, we introduce the concept of Manatee invariants for the analysis of signal transduction networks. We present an algorithm for the characterization of the combinatorial diversity of signal flows, e.g., from signal reception to cellular response. We demonstrate the concept for a small model of the TNFR1-mediated NF- κB signaling pathway. Manatee invariants reveal all possible signal flows in the network. Further, we show the application of Manatee invariants for in silico knockout experiments. Here, we illustrate the biological relevance of the concept.

Conclusions

The proposed mathematical framework reveals the entire variety of signal flows in models of signaling systems, including cyclic regulations. Thereby, Manatee invariants allow for the analysis of robustness and vulnerability of signaling networks. The application to further analyses such as for in silico knockout was shown. The new framework of Manatee invariants contributes to an advanced examination of signaling systems.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0448-7) contains supplementary material, which is available to authorized users.

Modeling the Metabolism of Arabidopsis thaliana: Application of Network Decomposition and Network Reduction in the Context of Petri Nets

Motivation:Arabidopsis thaliana is a well-established model system for the analysis of the basic physiological and metabolic pathways of plants. Nevertheless, the system is not yet fully understood, although many mechanisms are described, and information for many processes exists. However, the combination and interpretation of the large amount of biological data remain a big challenge, not only because data sets for metabolic paths are still incomplete. Moreover, they are often inconsistent, because they are coming from different experiments of various scales, regarding, for example, accuracy and/or significance. Here, theoretical modeling is powerful to formulate hypotheses for pathways and the dynamics of the metabolism, even if the biological data are incomplete. To develop reliable mathematical models they have to be proven for consistency. This is still a challenging task because many verification techniques fail already for middle-sized models. Consequently, new methods, like decomposition methods or reduction approaches, are developed to circumvent this problem. Methods: We present a new semi-quantitative mathematical model of the metabolism of Arabidopsis thaliana. We used the Petri net formalism to express the complex reaction system in a mathematically unique manner. To verify the model for correctness and consistency we applied concepts of network decomposition and network reduction such as transition invariants, common transition pairs, and invariant transition pairs. Results: We formulated the core metabolism of Arabidopsis thaliana based on recent knowledge from literature, including the Calvin cycle, glycolysis and citric acid cycle, glyoxylate cycle, urea cycle, sucrose synthesis, and the starch metabolism. By applying network decomposition and reduction techniques at steady-state conditions, we suggest a straightforward mathematical modeling process. We demonstrate that potential steady-state pathways exist, which provide the fixed carbon to nearly all parts of the network, especially to the citric acid cycle. There is a close cooperation of important metabolic pathways, e.g., the de novo synthesis of uridine-5-monophosphate, the γ-aminobutyric acid shunt, and the urea cycle. The presented approach extends the established methods for a feasible interpretation of biological network models, in particular of large and complex models.

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.

Modelling the Structure and Dynamics of Biological Pathways

There is a need for formalised diagrams that both summarise current biological pathway knowledge and support modelling approaches that explain and predict their behaviour. Here, we present a new, freely available modelling framework that includes a biologist-friendly pathway modelling language (mEPN), a simple but sophisticated method to support model parameterisation using available biological information; a stochastic flow algorithm that simulates the dynamics of pathway activity; and a 3-D visualisation engine that aids understanding of the complexities of a system’s dynamics. We present example pathway models that illustrate of the power of approach to depict a diverse range of systems.

This Community Page presents a biologist-friendly method for compiling detailed graphical models of biological pathways from the literature, including their subsequent parameterization for use in dynamic simulations of their activity.

Quasi-Steady-State Analysis based on Structural Modules and Timed Petri Net Predict System's Dynamics: The Life Cycle of the Insulin Receptor

The insulin-dependent activation and recycling of the insulin receptor play an essential role in the regulation of the energy metabolism, leading to a special interest for pharmaceutical applications. Thus, the recycling of the insulin receptor has been intensively investigated, experimentally as well as theoretically. We developed a time-resolved, discrete model to describe stochastic dynamics and study the approximation of non-linear dynamics in the context of timed Petri nets. Additionally, using a graph-theoretical approach, we analyzed the structure of the regulatory system and demonstrated the close interrelation of structural network properties with the kinetic behavior. The transition invariants decomposed the model into overlapping subnetworks of various sizes, which represent basic functional modules. Moreover, we computed the quasi-steady states of these subnetworks and demonstrated that they are fundamental to understand the dynamic behavior of the system. The Petri net approach confirms the experimental results of insulin-stimulated degradation of the insulin receptor, which represents a common feature of insulin-resistant, hyperinsulinaemic states.

Systems Medicine: The Application of Systems Biology Approaches for Modern Medical Research and Drug Development

The exponential development of highly advanced scientific and medical research technologies throughout the past 30 years has arrived to the point where the high number of characterized molecular agents related to pathogenesis cannot be readily integrated or processed by conventional analytical approaches. Indeed, the realization that several moieties are signatures of disease has partly led to the increment of complex diseases being characterized. Scientists and clinicians can now investigate and analyse any individual dysregulations occurring within the genomic, transcriptomic, miRnomic, proteomic, and metabolomic levels thanks to currently available advanced technologies. However, there are drawbacks within this scientific brave new age in that only isolated molecular levels are individually investigated for their influence in affecting any particular health condition. Since their conception in 1992, systems biology/medicine focuses mainly on the perturbations of overall pathway kinetics for the consequent onset and/or deterioration of the investigated condition/s. Systems medicine approaches can therefore be employed for shedding light in multiple research scenarios, ultimately leading to the practical result of uncovering novel dynamic interaction networks that are critical for influencing the course of medical conditions. Consequently, systems medicine also serves to identify clinically important molecular targets for diagnostic and therapeutic measures against such a condition.