Phenomenological and molecular-level Petri net modeling and simulation of long-term potentiation

Petri net-based modeling methods have been used in many research projects to represent biological systems. Among these, the hybrid functional Petri net (HFPN) was developed especially for biological modeling in order to provide biologists with a more intuitive Petri net-based method. In the literature, HFPNs are used to represent kinetic models at the molecular level. We present two models of long-term potentiation previously represented by differential equations which we have transformed into HFPN models: a phenomenological synapse model and a molecular-level model of the CaMKII regulation pathway. Through simulation, we obtained results similar to those of previous studies using these models. Our results open the way to a new type of modeling for systems biology where HFPNs are used to combine different levels of abstraction within one model. This approach can be useful in fully modeling a system at the molecular level when kinetic data is missing or when a full study of a system at the molecular level it is not within the scope of the research.     

Neural system modeling and simulation using Hybrid Functional Petri Net

The Petri net formalism has been proved to be powerful in biological modeling. It not only boasts of a most intuitive graphical presentation but also combines the methods of classical systems biology with the discrete modeling technique. Hybrid Functional Petri Net (HFPN) was proposed specially for biological system modeling. An array of well-constructed biological models using HFPN yielded very interesting results. In this paper, we propose a method to represent neural system behavior, where biochemistry and electrical chemistry are both included using the Petri net formalism. We built a model for the adrenergic system using HFPN and employed quantitative analysis. Our simulation results match the biological data well, showing that the model is very effective. Predictions made on our model further manifest the modeling power of HFPN and improve the understanding of the adrenergic system. The file of our model and more results with their analysis are available in our supplementary material.     

Quantitative Petri net model of gene regulated metabolic networks in the cell

A method to exploit hybrid Petri nets (HPN) for quantitatively modeling and simulating gene regulated metabolic networks is demonstrated. A global kinetic modeling strategy and Petri net modeling algorithm are applied to perform the bioprocess functioning and model analysis. With the model, the interrelations between pathway analysis and metabolic control mechanism are outlined. Diagrammatical results of the dynamics of metabolites are simulated and observed by implementing a HPN tool, Visual Object Net ++. An explanation of the observed behavior of the urea cycle is proposed to indicate possibilities for metabolic engineering and medical care. Finally, the perspective of Petri nets on modeling and simulation of metabolic networks is discussed.     

Modeling and simulation of molecular biology systems using petri nets: modeling goals of various approaches

Petri nets are a discrete event simulation approach developed for system representation, in particular for their concurrency and synchronization properties. Various extensions to the original theory of Petri nets have been used for modeling molecular biology systems and metabolic networks. These extensions are stochastic, colored, hybrid and functional. This paper carries out an initial review of the various modeling approaches based on Petri net found in the literature, and of the biological systems that have been successfully modeled with these approaches. Moreover, the modeling goals and possibilities of qualitative analysis and system simulation of each approach are discussed.     

An integrated pathway system modeling of Saccharomyces cerevisiae HOG pathway: a Petri net based approach

Biochemical networks comprise many diverse components and interactions between them. It has intracellular signaling, metabolic and gene regulatory pathways which are highly integrated and whose responses are elicited by extracellular actions. Previous modeling techniques mostly consider each pathway independently without focusing on the interrelation of these which actually functions as a single system. In this paper, we propose an approach of modeling an integrated pathway using an event-driven modeling tool, i.e., Petri nets (PNs). PNs have the ability to simulate the dynamics of the system with high levels of accuracy. The integrated set of signaling, regulatory and metabolic reactions involved in Saccharomyces cerevisiae’s HOG pathway has been collected from the literature. The kinetic parameter values have been used for transition firings. The dynamics of the system has been simulated and the concentrations of major biological species over time have been observed. The phenotypic characteristics of the integrated system have been investigated under two conditions, viz., under the absence and presence of osmotic pressure. The results have been validated favorably with the existing experimental results. We have also compared our study with the study of idFBA (Lee et al., PLoS Comput Biol 4:e1000–e1086, 2008) and pointed out the differences between both studies. We have simulated and monitored concentrations of multiple biological entities over time and also incorporated feedback inhibition by Ptp2 which has not been included in the idFBA study. We have concluded that our study is the first to the best of our knowledge to model signaling, metabolic and regulatory events in an integrated form through PN model framework. This study is useful in computational simulation of system dynamics for integrated pathways as there are growing evidences that the malfunctioning of the interplay among these pathways is associated with disease.     

Modelling and simulation of signal transductions in an apoptosis pathway by using timed Petri nets

This paper first presents basic Petri net components representing molecular interactions and mechanisms of signalling pathways, and introduces a method to construct a Petri net model of a signalling pathway with these components. Then a simulation method of determining the delay time of transitions, by using timed Petri nets — i.e. the time taken in firing of each transition — is proposed based on some simple principles that the number of tokens flowed into a place is equivalent to the number of tokens flowed out. Finally, the availability of proposed method is confirmed by observing signalling transductions in biological pathways through simulation experiments of the apoptosis signalling pathways as an example.     

Biopathways representation and simulation on hybrid functional Petri net

The following two matters should be resolved in order for biosimulation tools to be accepted by users in biology/medicine: (1) remove issues which are irrelevant to biological importance, and (2) allow users to represent biopathways intuitively and understand/manage easily the details of representation and simulation mechanism. From these criteria, we firstly define a novel notion of Petri net called Hybrid Functional Petri Net (HFPN). Then, we introduce a software tool, Genomic Object Net, for representing and simulating biopathways, which we have developed by employing the architecture of HFPN. In order to show the usefulness of Genomic Object Net for representing and simulating biopathways, we show two HFPN representations of gene regulation mechanisms of Drosophila melanogaster (fruit fly) circadian rhythm and apoptosis induced by Fas ligand. The simulation results of these biopathways are also correlated with biological observations. The software is available to academic users from http://www.GenomicObject.Net/.     

基于Petri网的基因调控网络建模与分析

如何有效描述与分析复杂的基因调控网络(GRN)是生物学家研究基因表达调控机制的关键步骤.现有大部分方法在建模过程中忽略了生物中广泛存在的协同作用,模型预测结果与实际生物行为之间存在误差.基于混合函数Petri网(HFPN)理论提出了一种对基因调控网络进行定量分析的新方法.首先简要介绍GRN与HFPN的基础理论,然后为HFPN引入两类新元素:逻辑库所与逻辑变迁,描述基因调控网络的逻辑规则以及转录因子间的协同作用,最后构建海胆endo16基因调控网络的Petri网模型,并预测模型在不同位点发生突变时的基因表达水平变化.分析结果与文献实验数据相一致,验证了方法的正确性.     

Colored Petri net modeling and simulation of signal transduction pathways

Presented herein is a methodology for quantitatively analyzing the complex signaling network by resorting to colored Petri nets (CPN). The mathematical as well as Petri net models for two basic reaction types were established, followed by the extension to a large signal transduction system stimulated by epidermal growth factor (EGF) in an application study. The CPN models based on the Petri net representation and the conservation and kinetic equations were used to examine the dynamic behavior of the EGF signaling pathway. The usefulness of Petri nets is demonstrated for the quantitative analysis of the signal transduction pathway. Moreover, the trade-offs between modeling capability and simulation efficiency of this pathway are explored, suggesting that the Petri net model can be invaluable in the initial stage of building a dynamic model.     

Structural modeling and analysis of signaling pathways based on Petri nets

The purpose of this paper is to discuss how to model and analyze signaling pathways by using Petri net. Firstly, we propose a modeling method based on Petri net by paying attention to the molecular interactions and mechanisms. Then, we introduce a new notion "activation transduction component" in order to describe an enzymic activation process of reactions in signaling pathways and shows its correspondence to a so-called elementary T-invariant in the Petri net models. Further, we design an algorithm to effectively find basic enzymic activation processes by obtaining a series of elementary T-invariants in the Petri net models. Finally, we demonstrate how our method is practically used in modeling and analyzing signaling pathway mediated by thrombopoietin as an example.     

Algebraic properties of automata associated to Petri nets and applications to computation in biological systems

Biochemical and genetic regulatory networks are often modeled by Petri nets. We study the algebraic structure of the computations carried out by Petri nets from the viewpoint of algebraic automata theory. Petri nets comprise a formalized graphical modeling language, often used to describe computation occurring within biochemical and genetic regulatory networks, but the semantics may be interpreted in different ways in the realm of automata. Therefore, there are several different ways to turn a Petri net into a state-transition automaton. Here, we systematically investigate different conversion methods and describe cases where they may yield radically different algebraic structures. We focus on the existence of group components of the corresponding transformation semigroups, as these reflect symmetries of the computation occurring within the biological system under study. Results are illustrated by applications to the Petri net modelling of intermediary metabolism. Petri nets with inhibition are shown to be computationally rich, regardless of the particular interpretation method. Along these lines we provide a mathematical argument suggesting a reason for the apparent all-pervasiveness of inhibitory connections in living systems.     

Model validation of biological pathways using Petri nets--demonstrated for apoptosis

This paper demonstrates the first steps of a new integrating methodology to develop and analyse models of biological pathways in a systematic manner using well established Petri net technologies. The whole approach comprises step-wise modelling, animation, model validation as well as qualitative and quantitative analysis for behaviour prediction. In this paper, the first phase is addressed how to develop and validate a qualitative model, which might be extended afterwards to a quantitative model. The example used in this paper is devoted to apoptosis, the genetically programmed cell death. Apoptosis is an essential part of normal physiology for most metazoan species. Disturbances in the apoptotic process could lead to several diseases. The signal transduction pathway of apoptosis includes highly complex mechanisms to control and execute programmed cell death. This paper explains how to model and validate this pathway using qualitative Petri nets. The results provide a mathematically unique and valid model enabling the confirmation of known properties as well as new insights in this pathway.     

Ontology based standardization of Petri net modeling for signaling pathways

Taking account of the great availability of Petri nets in modeling and analyzing large complicated signaling networks, semantics of Petri nets is in need of systematization for the purpose of consistency and reusability of the models. This paper reports on standardization of units of Petri nets on the basis of an ontology that gives an intrinsic definition to the process of signaling in signaling pathways.     

Simulation of a Petri net-based Model of the Terpenoid Biosynthesis Pathway

Background  

The development and simulation of dynamic models of terpenoid biosynthesis has yielded a systems perspective that provides new insights into how the structure of this biochemical pathway affects compound synthesis. These insights may eventually help identify reactions that could be experimentally manipulated to amplify terpenoid production. In this study, a dynamic model of the terpenoid biosynthesis pathway was constructed based on the Hybrid Functional Petri Net (HFPN) technique. This technique is a fusion of three other extended Petri net techniques, namely Hybrid Petri Net (HPN), Dynamic Petri Net (HDN) and Functional Petri Net (FPN).     

181 Integrative analysis of gene expression and protein–protein interaction networks in Glioblastoma

Glioblastoma multiforme (GBM) is the most malignant of all the brain tumors with very low median survival time of one year, as per Central Brain Tumor Registry of the USA, 2001. Efforts are ongoing to understand this disease pathogenesis in complete details. Global gene expression changes in GBM pathogenesis have been studied by several groups using microarray technology (e.g. Carro et al., 2010). One of the many approaches to ‘understand the control mechanisms underlying the observed changes in the activity of a biological process’ (Cline et al., 2007) is integration of gene expression and protein–protein interactions (PPI) datasets. Among several examples, aberrant activation of Wnt/β-catenin signaling pathway as well as sonic hedgehog (SHH) signaling pathway is reported in GBMs (Klaus & Birchmeier, 2008). Further, these two pathways are also involved in proliferation and clonogenicity of glioma cancer stem cells (Li et al., 2009), which are thought to play a role in glioma initiation, proliferation, and invasion, and are one of the important points of intervention. Hedgehog–Gli1 signaling is also found to regulate the expression of stemness genes. In this paper, analyses of the relationship between the significant differential expression of these and other genes and the connectivity as well as topological features of a PPI network would be discussed. This way, genes potentially overlooked when relying solely on expression profiles may be identified which can be biologically relevant as possible drug target/s or disease biomarker/s.     

Topological analysis of metabolic networks based on Petri net theory

Petri net concepts provide additional tools for the modelling of metabolic networks. Here, the similarities between the counterparts in traditional biochemical modelling and Petri net theory are discussed. For example the stoichiometry matrix of a metabolic network corresponds to the incidence matrix of the Petri net. The flux modes and conservation relations have the T-invariants, respectively, P-invariants as counterparts. We reveal the biological meaning of some notions specific to the Petri net framework (traps, siphons, deadlocks, liveness). We focus on the topological analysis rather than on the analysis of the dynamic behaviour. The treatment of external metabolites is discussed. Some simple theoretical examples are presented for illustration. Also the Petri nets corresponding to some biochemical networks are built to support our results. For example, the role of triose phosphate isomerase (TPI) in Trypanosoma brucei metabolism is evaluated by detecting siphons and traps. All Petri net properties treated in this contribution are exemplified on a system extracted from nucleotide metabolism.     

Fuzzy Stochastic Petri Nets for Modeling Biological Systems with Uncertain Kinetic Parameters

Stochastic Petri nets (SPNs) have been widely used to model randomness which is an inherent feature of biological systems. However, for many biological systems, some kinetic parameters may be uncertain due to incomplete, vague or missing kinetic data (often called fuzzy uncertainty), or naturally vary, e.g., between different individuals, experimental conditions, etc. (often called variability), which has prevented a wider application of SPNs that require accurate parameters. Considering the strength of fuzzy sets to deal with uncertain information, we apply a specific type of stochastic Petri nets, fuzzy stochastic Petri nets (FSPNs), to model and analyze biological systems with uncertain kinetic parameters. FSPNs combine SPNs and fuzzy sets, thereby taking into account both randomness and fuzziness of biological systems. For a biological system, SPNs model the randomness, while fuzzy sets model kinetic parameters with fuzzy uncertainty or variability by associating each parameter with a fuzzy number instead of a crisp real value. We introduce a simulation-based analysis method for FSPNs to explore the uncertainties of outputs resulting from the uncertainties associated with input parameters, which works equally well for bounded and unbounded models. We illustrate our approach using a yeast polarization model having an infinite state space, which shows the appropriateness of FSPNs in combination with simulation-based analysis for modeling and analyzing biological systems with uncertain information.