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

A Graphical and Computational Modelling 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

Mechanistic exploration of ligand binding to ETB receptor embedded in different membrane environments

Endothelin B (ETB) receptor belongs to a GPCR family, and it consists of seven transmembrane helices connected by three extracellular and intracellular loops. ETB receptor’s main function is vasodilation, thus the receptor is involved in diseases affecting the vasculature. Therefore, ETB targeting drugs have been a major topic in drug discovery and design. Several drugs have been developed, with two of them being bosentan and K-8794. Bosentan is an antagonist targeting both ETA and ETB receptors, while K-8794 is bosentan’s high affinity analog (150 nM) targeting selectively to ETB receptor. In this current investigation, the main goal was to explore and understand the mechanistic basis of bosentan and K-8794 binding to ETB receptor embedded in POPC, DPPC, POPE and DMPC membrane environments. To achieve this, a series of long-range molecular dynamics (MD) simulations were carried out. The trajectories from the simulation outputs were analysed for the receptor’s structural stability (RMSD, RMSF, Rg, H-bond). Moreover, essential dynamics analysis based on principal component analysis (PCA), binding free energy (BFE) estimation based on MM/GBSA approach, and dihedral angle analysis for the hotspot residues were carried out. According to the RMSD analysis revealed that all the systems have reached the equilibrium state during the last 200 ns of the MD simulations. The RMSF investigation reported that the most fluctuating regions of the receptor were the extracellular and intracellular loops. The Rg analysis showed that the ligand-receptor complexes maintained their overall compactness in most of the membrane environments. The H-bond analysis suggested that the ETB receptor residues Lys182, Lys273, and Arg343 formed relevant H-bond interactions with the two ligands and the ETB receptor. The PCA analysis showed that the ligand-ETB complexes were highly flexible by forming several conformations; however, the two ligands were restraining the receptor by disallowing any drastic helical movement. The BFE estimation revealed the most energy contributing (hotspot) residues – Lys182 and Trp336 for both bosentan and K-8794-ETB complexes. The dihedral angle analysis showed that both hotspot residues maintained similar conformation for all of the ligand-bound ETB complexes embedded in the four membrane environments

Coupling of Petri Net Models of the Mycobacterial Infection Process and Innate Immune Response

Algorithms and the Foundations of Software technologyComputer Systems, Imagery and Medi

Computational modelling of mycobacterium infection and innate immune response in zebrafish

In this thesis we provided a comprehensive overview on the steps that are involved in the modeling process and simulation of biological phenomena; from the choice of the method to the validation of the results. We gradually implemented a model with which we would be able to study the complex interplay of the components involved in the Mycobacterium marinum infection process and innate immune response in zebrafish embryos. In itself this process is a model for deeper understanding of tuberculosis infection in humans using zebrafish as model organism. Each chapter is a building block in the modeling process, which gradually forms a model that can represent cause-and-effect among these components involved in the biological behavior.Computer Systems, Imagery and Medi

A Review of Mathematical Models for the Formation of\ud Vascular Networks

Mainly two mechanisms are involved in the formation of blood vasculature: vasculogenesis and angiogenesis. The former consists of the formation of a capillary-like network from either a dispersed or a monolayered population of endothelial cells, reproducible also in vitro by specific experimental assays. The latter consists of the sprouting of new vessels from an existing capillary or post-capillary venule. Similar phenomena are also involved in the formation of the lymphatic system through a process generally called lymphangiogenesis.\ud \ud A number of mathematical approaches have analysed these phenomena. This paper reviews the different modelling procedures, with a special emphasis on their ability to reproduce the biological system and to predict measured quantities which describe the overall processes. A comparison between the different methods is also made, highlighting their specific features