Constructing biological pathway models with hybrid functional Petri nets

In many research projects on modeling and analyzing biological pathways, the Petri net has been recognized as a promising method for representing biological pathways. From the pioneering works by Reddy et al., 1993, and Hofest?dt, 1994, that model metabolic pathways by traditional Petri net, several enhanced Petri nets such as colored Petri net, stochastic Petri net, and hybrid Petri net have been used for modeling biological phenomena. Recently, Matsuno et al., 2003b, introduced the hybrid functional Petri net (HFPN) in order to give a more intuitive and natural modeling method for biological pathways than these existing Petri nets. Although the paper demonstrates the effectiveness of HFPN with two examples of gene regulation mechanism for circadian rhythms and apoptosis signaling pathway, there has been no detailed explanation about the method of HFPN construction for these examples. The purpose of this paper is to describe method to construct biological pathways with the HFPN step-by-step. The method is demonstrated by the well-known glycolytic pathway controlled by the lac operon gene regulatory mechanism.     

Modeling of Cell-to-Cell Communication Processes with Petri Nets Using the Example of Quorum Sensing

The understanding of the molecular mechanism of cell-to-cell communication is fundamental for system biology. Up to now, the main objectives of bioinformatics have been reconstruction, modeling and analysis of metabolic, regulatory and signaling processes, based on data generated from high-throughput technologies. Cell-to-cell communication or quorum sensing (QS), the use of small molecule signals to coordinate complex patterns of behavior in bacteria, has been the focus of many reports over the past decade. Based on the quorum sensing process of the organism Aliivibrio salmonicida, we aim at developing a functional Petri net, which will allow modeling and simulating cell-to-cell communication processes. Using a new editor-controlled information system called VANESA (http://vanesa.sf.net), we present how to combine different fields of studies such as life-science, database consulting, modeling, visualization and simulation for a semi-automatic reconstruction of the complex signaling quorum sensing network. We show how cell-to-cell communication processes and information-flow within a cell and across cell colonies can be modeled using VANESA and how those models can be simulated with Petri net network structures in a sophisticated way.     

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.     

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.     

BioNetSim: a Petri net-based modeling tool for simulations of biochemical processes

BioNetSim, a Petri net-based software for modeling and simulating biochemistry processes, is developed, whose design and implement are presented in this paper, including logic construction, real-time access to KEGG (Kyoto Encyclopedia of Genes and Genomes), and BioModel database. Furthermore, glycolysis is simulated as an example of its application. BioNetSim is a helpful tool for researchers to download data, model biological network, and simulate complicated biochemistry processes. Gene regulatory networks, metabolic pathways, signaling pathways, and kinetics of cell interaction are all available in BioNetSim, which makes modeling more efficient and effective. Similar to other Petri net-based softwares, BioNetSim does well in graphic application and mathematic construction. Moreover, it shows several powerful predominances. (1) It creates models in database. (2) It realizes the real-time access to KEGG and BioModel and transfers data to Petri net. (3) It provides qualitative analysis, such as computation of constants. (4) It generates graphs for tracing the concentration of every molecule during the simulation processes.     

Petri net modeling of high-order genetic systems using grammatical evolution

Understanding how DNA sequence variations impact human health through a hierarchy of biochemical and physiological systems is expected to improve the diagnosis, prevention, and treatment of common, complex human diseases. We have previously developed a hierarchical dynamic systems approach based on Petri nets for generating biochemical network models that are consistent with genetic models of disease susceptibility. This modeling approach uses an evolutionary computation approach called grammatical evolution as a search strategy for optimal Petri net models. We have previously demonstrated that this approach routinely identifies biochemical network models that are consistent with a variety of genetic models in which disease susceptibility is determined by nonlinear interactions between two DNA sequence variations. In the present study, we evaluate whether the Petri net approach is capable of identifying biochemical networks that are consistent with disease susceptibility due to higher order nonlinear interactions between three DNA sequence variations. The results indicate that our model-building approach is capable of routinely identifying good, but not perfect, Petri net models. Ideas for improving the algorithm for this high-dimensional problem are presented.     

Learning Petri net models of non-linear gene interactions

Understanding how an individual's genetic make-up influences their risk of disease is a problem of paramount importance. Although machine-learning techniques are able to uncover the relationships between genotype and disease, the problem of automatically building the best biochemical model or "explanation" of the relationship has received less attention. In this paper, I describe a method based on random hill climbing that automatically builds Petri net models of non-linear (or multi-factorial) disease-causing gene-gene interactions. Petri nets are a suitable formalism for this problem, because they are used to model concurrent, dynamic processes analogous to biochemical reaction networks. I show that this method is routinely able to identify perfect Petri net models for three disease-causing gene-gene interactions recently reported in the literature.     

A structured approach for the engineering of biochemical network models, illustrated for signalling pathways

Quantitative models of biochemical networks (signal transduction cascades, metabolic pathways, gene regulatory circuits) are a central component of modern systems biology. Building and managing these complex models is a major challenge that can benefit from the application of formal methods adopted from theoretical computing science. Here we provide a general introduction to the field of formal modelling, which emphasizes the intuitive biochemical basis of the modelling process, but is also accessible for an audience with a background in computing science and/or model engineering. We show how signal transduction cascades can be modelled in a modular fashion, using both a qualitative approach--qualitative Petri nets, and quantitative approaches--continuous Petri nets and ordinary differential equations (ODEs). We review the major elementary building blocks of a cellular signalling model, discuss which critical design decisions have to be made during model building, and present a number of novel computational tools that can help to explore alternative modular models in an easy and intuitive manner. These tools, which are based on Petri net theory, offer convenient ways of composing hierarchical ODE models, and permit a qualitative analysis of their behaviour. We illustrate the central concepts using signal transduction as our main example. The ultimate aim is to introduce a general approach that provides the foundations for a structured formal engineering of large-scale models of biochemical networks.     

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.     

A Petri net approach to the study of persistence in chemical reaction networks

Persistence is the property, for differential equations in R(n), that solutions starting in the positive orthant do not approach the boundary of the orthant. For chemical reactions and population models, this translates into the non-extinction property: provided that every species is present at the start of the reaction, no species will tend to be eliminated in the course of the reaction. This paper provides checkable conditions for persistence of chemical species in reaction networks, using concepts and tools from Petri net theory, and verifies these conditions on various systems which arise in the modeling of cell signaling pathways.     

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.     

Predictive modeling of signaling crosstalk during C. elegans vulval development

Caenorhabditis elegans vulval development provides an important paradigm for studying the process of cell fate determination and pattern formation during animal development. Although many genes controlling vulval cell fate specification have been identified, how they orchestrate themselves to generate a robust and invariant pattern of cell fates is not yet completely understood. Here, we have developed a dynamic computational model incorporating the current mechanistic understanding of gene interactions during this patterning process. A key feature of our model is the inclusion of multiple modes of crosstalk between the epidermal growth factor receptor (EGFR) and LIN-12/Notch signaling pathways, which together determine the fates of the six vulval precursor cells (VPCs). Computational analysis, using the model-checking technique, provides new biological insights into the regulatory network governing VPC fate specification and predicts novel negative feedback loops. In addition, our analysis shows that most mutations affecting vulval development lead to stable fate patterns in spite of variations in synchronicity between VPCs. Computational searches for the basis of this robustness show that a sequential activation of the EGFR-mediated inductive signaling and LIN-12 / Notch-mediated lateral signaling pathways is key to achieve a stable cell fate pattern. We demonstrate experimentally a time-delay between the activation of the inductive and lateral signaling pathways in wild-type animals and the loss of sequential signaling in mutants showing unstable fate patterns; thus, validating two key predictions provided by our modeling work. The insights gained by our modeling study further substantiate the usefulness of executing and analyzing mechanistic models to investigate complex biological behaviors.     

A survey on methods for modeling and analyzing integrated biological networks

Understanding how cellular systems build up integrated responses to their dynamically changing environment is one of the open questions in Systems Biology. Despite their intertwinement, signaling networks, gene regulation and metabolism have been frequently modeled independently in the context of well-defined subsystems. For this purpose, several mathematical formalisms have been developed according to the features of each particular network under study. Nonetheless, a deeper understanding of cellular behavior requires the integration of these various systems into a model capable of capturing how they operate as an ensemble. With the recent advances in the "omics" technologies, more data is becoming available and, thus, recent efforts have been driven toward this integrated modeling approach. We herein review and discuss methodological frameworks currently available for modeling and analyzing integrated biological networks, in particular metabolic, gene regulatory and signaling networks. These include network-based methods and Chemical Organization Theory, Flux-Balance Analysis and its extensions, logical discrete modeling, Petri Nets, traditional kinetic modeling, Hybrid Systems and stochastic models. Comparisons are also established regarding data requirements, scalability with network size and computational burden. The methods are illustrated with successful case studies in large-scale genome models and in particular subsystems of various organisms.     

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.     

Systems biology of death receptor networks: live and let die

The extrinsic apoptotic pathway is initiated by death receptor activation. Death receptor activation leads to the formation of death receptor signaling platforms, resulting in the demolition of the cell. Despite the fact that death receptor-mediated apoptosis has been studied to a high level of detail, its quantitative regulation until recently has been poorly understood. This situation has dramatically changed in the last years. Creation of mathematical models of death receptor signaling led to an enormous progress in the quantitative understanding of the network regulation and provided fascinating insights into the mechanisms of apoptosis control. In the following sections, the models of the death receptor signaling and their biological implications will be addressed. Central attention will be given to the models of CD95/Fas/APO-1, an exemplified member of the death receptor signaling pathways. The CD95 death-inducing signaling complex (DISC) and regulation of CD95 DISC activity by its key inhibitor c-FLIP, have been vigorously investigated by modeling approaches, and therefore will be the major topic here. Furthermore, the non-linear dynamics of the DISC, positive feedback loops and bistability as well as stoichiometric switches in extrinsic apoptosis will be discussed. Collectively, this review gives a comprehensive view how the mathematical modeling supported by quantitative experimental approaches has provided a new understanding of the death receptor signaling network.     

Electronic data sources for kinetic models of cell signaling

Functional understanding of signaling pathways requires detailed information about the constituent molecules and their interactions. Simulations of signaling pathways therefore build upon a great deal of data from various sources. We first survey electronic data resources for cell signaling modeling and then based on the type of data representation the data sources are broadly classified into five groups. None of the data sources surveyed provide all required data in a ready-to-be-modeled fashion. We then put forward a "wish list" for the desired attributes for an ideal modeling centric database. Finally, we close with perspectives on how electronic data sources for cell signaling modeling have developed. We suggest that future directions in such data sources are largely model-driven and are hinged on interoperability of data sources.     

The signaling petri net-based simulator: a non-parametric strategy for characterizing the dynamics of cell-specific signaling networks

Reconstructing cellular signaling networks and understanding how they work are major endeavors in cell biology. The scale and complexity of these networks, however, render their analysis using experimental biology approaches alone very challenging. As a result, computational methods have been developed and combined with experimental biology approaches, producing powerful tools for the analysis of these networks. These computational methods mostly fall on either end of a spectrum of model parameterization. On one end is a class of structural network analysis methods; these typically use the network connectivity alone to generate hypotheses about global properties. On the other end is a class of dynamic network analysis methods; these use, in addition to the connectivity, kinetic parameters of the biochemical reactions to predict the network's dynamic behavior. These predictions provide detailed insights into the properties that determine aspects of the network's structure and behavior. However, the difficulty of obtaining numerical values of kinetic parameters is widely recognized to limit the applicability of this latter class of methods. Several researchers have observed that the connectivity of a network alone can provide significant insights into its dynamics. Motivated by this fundamental observation, we present the signaling Petri net, a non-parametric model of cellular signaling networks, and the signaling Petri net-based simulator, a Petri net execution strategy for characterizing the dynamics of signal flow through a signaling network using token distribution and sampling. The result is a very fast method, which can analyze large-scale networks, and provide insights into the trends of molecules' activity-levels in response to an external stimulus, based solely on the network's connectivity. We have implemented the signaling Petri net-based simulator in the PathwayOracle toolkit, which is publicly available at http://bioinfo.cs.rice.edu/pathwayoracle. Using this method, we studied a MAPK1,2 and AKT signaling network downstream from EGFR in two breast tumor cell lines. We analyzed, both experimentally and computationally, the activity level of several molecules in response to a targeted manipulation of TSC2 and mTOR-Raptor. The results from our method agreed with experimental results in greater than 90% of the cases considered, and in those where they did not agree, our approach provided valuable insights into discrepancies between known network connectivities and experimental observations.