Analysis of signalling pathways using the prism model checker

We describe a new modelling and analysis approach for signal transduction networks in the presence of incomplete data. We illustrate the approach with an example, the RKIP inhibited ERK pathway [1]. Our models are based on high level descriptions of continuous time Markov chains: reactions are modelled as synchronous processes and concentrations are modelled by discrete, abstract quantities. The main advantage of our approach is that using a (continuous time) stochastic logic and the PRISM model checker, we can perform quantitative analysis of queries such as if a concentration reaches a certain level, will it remain at that level thereafter? We also perform standard simulations and compare our results with a traditional ordinary differential equation model. An interesting result is that for the example pathway, only a small number of discrete data values is required to render the simulations practically indistinguishable

SIMULATION AND ANALYSIS OF PENTOSE PHOSPHATE PATHWAY IN PLASMODIUM FALCIPARUM USING COLORED PETRI NETS MODEL

Plasmodium falciparum is a protozoan parasite and the deadliest of five human malaria species which is responsible for the majority of malaria related deaths in humans. The erythrocytes’ stage of Plasmodium falciparum depend on Pentose Pathway as an alternative source of energy and it releases electrons used in protecting the Plasmodium falciparum from its host. Colored Petri Net has been recognized as one of the important models in modelling and analyzing biological pathways. It is an accurate qualitative and quantitative modelling tool for modeling complex biological systems. In this work, the modeling of the pentose phosphate pathway in Plasmodium falciparum is presented using the Petri Net Markup Language (PNML). The Colored Petri Net (CPN) models based on the Petri Net representation and the conservation and kinetic equations were used to examine the dynamic behavior of the metabolic pathway. The usefulness of Petri Nets is demonstrated for the quantitative analysis of the pathway. We obtained data from Biocyc database. The constructed model was viewed through the Colored Petri Net Tool (CPN tool 4.0). Specific drug targets called the essential reactions within the pathway were identified, listed and proposed. These essential reactions would alter the functioning of the pathway which would affect the energy and protection needs of the parasite therefore leading to the death of the parasite in the human red blood cell

Petri Net modelling approach for analysing the behaviour of Wnt/[inline-formula removed] -catenin and Wnt/Ca 2+ 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

Application of Petri net based analysis techniques to signal transduction pathways

BACKGROUND: Signal transduction pathways are usually modelled using classical quantitative methods, which are based on ordinary differential equations (ODEs). However, some difficulties are inherent in this approach. On the one hand, the kinetic parameters involved are often unknown and have to be estimated. With increasing size and complexity of signal transduction pathways, the estimation of missing kinetic data is not possible. On the other hand, ODEs based models do not support any explicit insights into possible (signal-) flows within the network. Moreover, a huge amount of qualitative data is available due to high-throughput techniques. In order to get information on the systems behaviour, qualitative analysis techniques have been developed. Applications of the known qualitative analysis methods concern mainly metabolic networks. Petri net theory provides a variety of established analysis techniques, which are also applicable to signal transduction models. In this context special properties have to be considered and new dedicated techniques have to be designed. METHODS: We apply Petri net theory to model and analyse signal transduction pathways first qualitatively before continuing with quantitative analyses. This paper demonstrates how to build systematically a discrete model, which reflects provably the qualitative biological behaviour without any knowledge of kinetic parameters. The mating pheromone response pathway in Saccharomyces cerevisiae serves as case study. RESULTS: We propose an approach for model validation of signal transduction pathways based on the network structure only. For this purpose, we introduce the new notion of feasible t-invariants, which represent minimal self-contained subnets being active under a given input situation. Each of these subnets stands for a signal flow in the system. We define maximal common transition sets (MCT-sets), which can be used for t-invariant examination and net decomposition into smallest biologically meaningful functional units. CONCLUSION: The paper demonstrates how Petri net analysis techniques can promote a deeper understanding of signal transduction pathways. The new concepts of feasible t-invariants and MCT-sets have been proven to be useful for model validation and the interpretation of the biological system behaviour. Whereas MCT-sets provide a decomposition of the net into disjunctive subnets, feasible t-invariants describe subnets, which generally overlap. This work contributes to qualitative modelling and to the analysis of large biological networks by their fully automatic decomposition into biologically meaningful modules

Heparan Sulfate Induces Necroptosis in Murine Cardiomyocytes: A Medical-In silico Approach Combining In vitro Experiments and Machine Learning.

Life-threatening cardiomyopathy is a severe, but common, complication associated with severe trauma or sepsis. Several signaling pathways involved in apoptosis and necroptosis are linked to trauma- or sepsis-associated cardiomyopathy. However, the underling causative factors are still debatable. Heparan sulfate (HS) fragments belong to the class of danger/damage-associated molecular patterns liberated from endothelial-bound proteoglycans by heparanase during tissue injury associated with trauma or sepsis. We hypothesized that HS induces apoptosis or necroptosis in murine cardiomyocytes. By using a novel Medical-In silico approach that combines conventional cell culture experiments with machine learning algorithms, we aimed to reduce a significant part of the expensive and time-consuming cell culture experiments and data generation by using computational intelligence (refinement and replacement). Cardiomyocytes exposed to HS showed an activation of the intrinsic apoptosis signal pathway via cytochrome C and the activation of caspase 3 (both p < 0.001). Notably, the exposure of HS resulted in the induction of necroptosis by tumor necrosis factor α and receptor interaction protein 3 (p < 0.05; p < 0.01) and, hence, an increased level of necrotic cardiomyocytes. In conclusion, using this novel Medical-In silico approach, our data suggest (i) that HS induces necroptosis in cardiomyocytes by phosphorylation (activation) of receptor-interacting protein 3, (ii) that HS is a therapeutic target in trauma- or sepsis-associated cardiomyopathy, and (iii) indicate that this proof-of-concept is a first step toward simulating the extent of activated components in the pro-apoptotic pathway induced by HS with only a small data set gained from the in vitro experiments by using machine learning algorithms.This work was supported by an intramural grant to LM (START 46/16) and EZ (START 113/17). LM has received a grant by the Deutsche Forschungsgemeinschaft (DFG, MA 7082/1–1). We thank Dr Claycomb and his coworkers for providing the HL-1 cells and a detailed documentation. The Immunohistochemistry and Confocal Microscopy Unit, a core facility of the Interdisciplinary Center for Clinical Research (IZKF) Aachen, within the Faculty of Medicine at the RWTH Aachen University, supported this work

Modeling of the Glycolysis Pathway in Plasmodium falciparum using Petri Nets

Malaria is one of the deadly diseases, which affects a large number of the world’s population. The Plasmodium falciparum parasite during erythrocyte stages produces its energy mainly through anaerobic glycolysis, with pyruvate being converted into lactate. The glycolysis metabolism in P. falci-parum is one of the important metabolic pathways of the parasite because the parasite is entirely dependent on it for energy. Also, several glycolytic enzymes have been proposed as drug targets. Petri nets (PNs) have been recognized as one of the important models for representing biological pathways. In this work, we built a qualitative PN model for the glycolysis pathway in P. falciparum and analyzed the model for its structural and quantitative properties using PN theory. From PlasmoCyc files, a total of 11 reactions were extracted; 6 of these were reversible and 5 were irreversible. These reactions were catalyzed by a total number of 13 enzymes. We extracted some of the essential reactions in the pathway using PN model, which are the possible drug targets without which the pathway cannot function. This model also helps to improve the understanding of the biological processes within this pathway

Modelling Melanin Biosynthesis Pathway with Petri Nets

Melanin is a UV radiation-absorbing pigment that is responsible for variation in skin color. The melanin synthesis pathway is a series of chemical reactions that lead to the formation of melanin. By creating a mathematical model of the pathway, some questions can be answered: What are the relative quantities of the three different melanin produced given specific initial conditions? What are the factors responsible for an increase or decrease in a specific type of melanin produced? How do genetic defects lead to different kinds of albinism or hyperpigmentation disorders? How do skin-whitening products that target the pathway affect it? The paper develops a Petri Net model of the biological pathway to synthesise melanin in human skin. The Petri net model successfully simulated several pathway properties, and the results matched the experimental findings described in several papers. The model also simulated defects in the pathway that lead to different types of oculocutaneous albinism in humans. Hence, this paper shows that the easy to use Petri Nets could also be used to model complex biological processes.publishedVersio