Modular and Hierarchical Modelling Concept for Large Biological Petri Nets Applied to Nociception (original) (raw)
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The construction of monolithic pathway models, as well as their coupling, curation and the integration of new data is arduous and inconvenient. The modular Petri net modeling concept we present here shows one way to manage these difficulties. In our concept, proteins are represented as functional units by Petri net submodels with a defined structure and connection interface, called modules. Each module integrates all publicly available information about its intramolecular changes and interactions with other molecules. Hence, a module corresponds to an interactive review written in a formalized language. This allows to intuitively understand the functionality of a protein. Modules of interacting proteins communicate through matching subnets, which renders the automatic generation of molecular networks possible. Here, we demonstrate the applicability and advantages of our concept on pain signaling. The molecular mechanisms involved in pain signaling are complex and poorly understood. To enhance our understanding of the mechanisms and to get an impression of the functional interactions among the involved pathways, we systematically build a model from modules of pain-relevant proteins. We also offer a prospect of a platform to organize approved cu-rated modules in order to generate molecular networks. Hopefully, our concept helps bridging the gap between experimental bioscientists and theoretically oriented systems biologists.
Petri Net Modeling via a Modular and Hierarchical Approach Applied to Nociception
We describe signal transduction of nociceptive mechanisms involved in chronic pain by a qualitative Petri net model. More precisely , we investigate signaling in the peripheral terminals of dorsal root ganglion (DRG) neurons. It is a first approach to integrate the current neurobiological and clinical knowledge about nociception on the molecular level from literature in a model describing all the interactions between the involved molecules. Due to the large expected total size of the model under development, we employed a hierarchical and modular approach. In our entire noci-ceptive network, each biological entity like a receptor, enzyme, macro-molecular complex etc. is represented by a self-contained and functional autonomous Petri net, a module. Analysis of the Petri net modules and simulation studies ensure the fulfillment of criteria important for biological Petri nets and the ability to represent the modeled biological function.
Modeling and Analysis of the Molecular Basis of Pain in Sensory Neurons
PLOS One, 2009
Intracellular calcium dynamics are critical to cellular functions like pain transmission. Extracellular ATP plays an important role in modulating intracellular calcium levels by interacting with the P2 family of surface receptors. In this study, we developed a mechanistic mathematical model of ATP-induced P2 mediated calcium signaling in archetype sensory neurons. The model architecture, which described 90 species connected by 162 interactions, was formulated by aggregating disparate molecular modules from literature. Unlike previous models, only mass action kinetics were used to describe the rate of molecular interactions. Thus, the majority of the 252 unknown model parameters were either association, dissociation or catalytic rate constants. Model parameters were estimated from nine independent data sets taken from multiple laboratories. The training data consisted of both dynamic and steady-state measurements. However, because of the complexity of the calcium network, we were unable to estimate unique model parameters. Instead, we estimated a family or ensemble of probable parameter sets using a multi-objective thermal ensemble method. Each member of the ensemble met an error criterion and was located along or near the optimal trade-off surface between the individual training data sets. The model quantitatively reproduced experimental measurements from dorsal root ganglion neurons as a function of extracellular ATP forcing. Hypothesized architecture linking phosphoinositide regulation with P2X receptor activity explained the inhibition of P2X-mediated current flow by activated metabotropic P2Y receptors. Sensitivity analysis using individual and the whole system outputs suggested which molecular subsystems were most important following P2 activation. Taken together, modeling and analysis of ATP-induced P2 mediated calcium signaling generated qualitative insight into the critical interactions controlling ATP induced calcium dynamics. Understanding these critical interactions may prove useful for the design of the next generation of molecular pain management strategies.
A module-based approach to biomodel engineering with Petri nets.
2012
Based on Petri nets as formal language for biomodel engineering, we describe the general concept of a modular modelling approach that considers the functional coupling of modules representing components of the genome, the transcriptome, and the proteome in the form of an executable model. The composable, metadata-containing Petri net modules are organized in a database with version control and accessible through a web interface. The effects of genes and their mutated alleles on downstream components are modelled by gene modules coupled to protein modules through RNA modules by specific interfaces designed for the automatic, database-assisted composition. Automatically assembled models may integrate forward and reverse engineered modules and consider cell type-specific gene expression patterns. Prospects for automatic model generation including its application to systems biology , synthetic biology, and to functional genomics are discussed. 1 INTRODUCTION Since the One Gene – One Protein Hypothesis has originally been proposed by George Beadle and Edward Tatum (Beadle and Tatum 1941) we have learned that the building blocks of life, the genes, the RNAs, the proteins, and the metabolites all together form a complex network of regulatory interactions. This network is robust, adaptive, and to some extent self-healing, as it includes multiple regulatory feedback loops composed of interacting proteins that often involve other types of biomolecules (Figure 1A). The early view that the flow of information within a cell occurs from the genes to the proteins has been revisited by many exciting discoveries that have been made during the past decades. We meanwhile appreciate that in reality the flow of information, in terms of regulatory interactions, occurs back and forth between the components of the different classes of biomolecules (DNA, RNA, proteins, small molecules). We also understand that there is extensive information processing mediated by the network of interacting proteins and that many proteins seem to be just made for fulfilling these computational tasks. Many qualitative models on molecular mechanisms as well as the corresponding computational (kinetic) models exclusively focus on protein-protein interactions. When working with such models one should keep in mind that the considered networks are not necessarily hard-wired but may change. Alterations in the wiring due to components that may be added, deleted, or modified may be brought about by changes in the pattern of expressed genes. The gene expression pattern in general is responsive to environmental (experimental) conditions, it may depend on the considered cell type, or even on the history of an individual cell and impact stimulus sensing and responses (see (Otomo et al. 1989) for example). Changes in gene expression patterns can be central to regulatory processes. For a given process, the importance of gene regulation may differ from species to species. In fission yeast for example , the cell cycle is regulated mainly through protein-protein interactions. In mammalian cells, the proteins regulating the cell cycle are similar. However, regulation in addition affects changes in the gene expression altering the concentration of proteins involved in cell cycle regulation (Lodish et al. 1996). For technical reasons, (high-throughput) experimental techniques often reveal information restricted to one class of biomolecule at a time (the genome, the transcriptome, the proteome, the metabolome etc.) or to one type of molecular interaction (e.g. protein-protein or protein-DNA interactions). For a true systems level understanding which systems biology aims at, we have to integrate these data to
A Hybrid Petri Net Model of the Akt-Wnt-mTOR-p70S6K Signalling Network in Neurons
Fundamenta Informaticae, 2018
Signalling networks in the mammalian cell are complex systems. Their dynamic properties can often be explained by the interaction of regulatory network motifs. Computational modelling is instrumental in explaining how these systems function. To accomplish this task in this paper, we combine hybrid Petri net modelling and simulation, which produce the individual trajectories of protein concentrations and enable structural analysis of the reaction network. In the end, we generate dynamic graphs to get a system view of the signalling network dynamics. We use this methodology on the regulatory network of the proteins mTOR and p70S6K. In neuronal synaptic plasticity, prolonged activation of these proteins is needed to support an increased protein synthesis. However, biologists wonder how two brief calcium influxes of 1 second each can lead to this long activation downstream. With our computational approach and a new model of the Akt-Wnt-mTOR-p70S6K network, we explore the current biological hypothesis for the response of mTOR: the crosstalk between the Akt and Wnt pathways. Simulation results indicate instead that a feedforward motif between Akt, GSK3 and TSC2 acts as a coincidence detector. From the simulation results, we can also make two predictions that can be tested experimentally and indicate where a molecular regulatory mechanism seems to be missing to completely explain the activity in the signalling network.
IET Systems Biology, 2008
Assembly of quantitative models of large complex networks brings about several challenges. One of them is combinatorial complexity, where relatively few signaling molecules can combine to form thousands or millions of distinct chemical species. A receptor that has several separate phosphorylation sites can exist in hundreds of different states, many of which must be accounted for individually when simulating the time course of signaling. When assembly of protein complexes is being included, the number of distinct molecular species can easily increase by a few orders of magnitude. Validation, visualization, and understanding the network can become intractable. Another challenge appears when the modeler needs to recast or grow a model. Keeping track of changes and adding new elements present a significant difficulty. We describe an approach to solve these challenges within the Virtual Cell (VCell). Using (i) automatic extraction from pathway databases of model components, and (ii) rules of interactions that serve as reaction network generators, we provide a way for semi-automatic generation of quantitative mathematical models that also facilitates the reuse of model elements.
2000
Assembly of quantitative models of large complex networks brings about several challenges. One of them is combinatorial complexity, where relatively few signaling molecules can combine to form thousands or millions of distinct chemical species. A receptor that has several separate phosphorylation sites can exist in hundreds of different states, many of which must be accounted for individually when simulating the
Modularization of biochemical networks based on classification of Petri net t-invariants
BMC Bioinformatics, 2008
Background: Structural analysis of biochemical networks is a growing field in bioinformatics and systems biology. The availability of an increasing amount of biological data from molecular biological networks promises a deeper understanding but confronts researchers with the problem of combinatorial explosion. The amount of qualitative network data is growing much faster than the amount of quantitative data, such as enzyme kinetics. In many cases it is even impossible to measure quantitative data because of limitations of experimental methods, or for ethical reasons. Thus, a huge amount of qualitative data, such as interaction data, is available, but it was not sufficiently used for modeling purposes, until now. New approaches have been developed, but the complexity of data often limits the application of many of the methods. Biochemical Petri nets make it possible to explore static and dynamic qualitative system properties. One Petri net approach is model validation based on the computation of the system's invariant properties, focusing on t-invariants. T-invariants correspond to subnetworks, which describe the basic system behavior.
A Petri-Net-Based Framework for Biomodel Engineering
Modeling and Simulation in Science, Engineering and Technology, 2014
Petri nets provide a unifying and versatile framework for the synthesis and engineering of computational models of biochemical reaction networks and of gene regulatory networks. Starting with the basic definitions, we provide an introduction into the different classes of Petri nets that reinterpret a Petri net graph as a qualitative, stochastic, continuous, or hybrid model. Static and dynamic analysis in addition to simulative model checking provide a rich choice of methods for the analysis of the structure and dynamic behavior of Petri net models. Coloring of Petri nets of all classes is powerful for multiscale modeling and for the representation of location and space in reaction networks since it combines the concept of Petri nets with the computational mightiness of a programming language. In the context of the Petri net framework, we provide two most recently developed approaches to biomodel engineering, the database-assisted automatic composition and modification of Petri nets with the help of reusable, metadata-containing modules, and the automatic reconstruction of networks based on time series data sets. With all these features the framework provides multiple options for biomodel engineering in the context of systems and synthetic biology.
An Open Petri Net Implementation of Gene Regulatory Networks
arXiv: Molecular Networks, 2019
Gene regulatory network (GRN) plays a central role in system biology and genomics. It provides a promising way to model and study complex biological processes. Several computational methods have been developed for the construction and analysis of GRN. In particular, Petri net and its variants were introduced for GRN years ago. On the other hand, Petri net theory itself has been rapidly advanced recently. Especially noteworthy is the combination or treatment of Petri net with the mathematical framework of category theory (categorization), which endows Petri net with the power of abstraction and composability. Open Petri net is a state-of-art implementation of such "categorized" Petri nets. Applying open Petri net to GRN may potentially facilitate the modeling of large scale GRNs. In this manuscript, we took a shallow step towards that direction.