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.     

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.     

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/.     

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.     

Bridging the gap: linking molecular simulations and systemic descriptions of cellular compartments

Metabolic processes in biological cells are commonly either characterized at the level of individual enzymes and metabolites or at the network level. Often these two paradigms are considered as mutually exclusive because concepts from neither side are suited to describe the complete range of scales. Additionally, when modeling metabolic or regulatory cellular systems, often a large fraction of the required kinetic parameters are unknown. This even applies to such simple and extensively studied systems like the photosynthetic apparatus of purple bacteria. Using the chromatophore vesicles of Rhodobacter sphaeroides as a model system, we show that a consistent kinetic model emerges when fitting the dynamics of a molecular stochastic simulation to a set of time dependent experiments even though about two thirds of the kinetic parameters in this system are not known from experiment. Those kinetic parameters that were previously known all came out in the expected range. The simulation model was built from independent protein units composed of elementary reactions processing single metabolites. This pools-and-proteins approach naturally compiles the wealth of available molecular biological data into a systemic model and can easily be extended to describe other systems by adding new protein or nucleic acid types. The automated parameter optimization, performed with an evolutionary algorithm, reveals the sensitivity of the model to the value of each parameter and the relative importances of the experiments used. Such an analysis identifies the crucial system parameters and guides the setup of new experiments that would add most knowledge for a systemic understanding of cellular compartments. The successful combination of the molecular model and the systemic parametrization presented here on the example of the simple machinery for bacterial photosynthesis shows that it is actually possible to combine molecular and systemic modeling. This framework can now straightforwardly be applied to other currently less well characterized but biologically more relevant systems.     

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.     

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.     

Efficient modeling, simulation and coarse-graining of biological complexity with NFsim

Managing the overwhelming numbers of molecular states and interactions is a fundamental obstacle to building predictive models of biological systems. Here we introduce the Network-Free Stochastic Simulator (NFsim), a general-purpose modeling platform that overcomes the combinatorial nature of molecular interactions. Unlike standard simulators that represent molecular species as variables in equations, NFsim uses a biologically intuitive representation: objects with binding and modification sites acted on by reaction rules. During simulations, rules operate directly on molecular objects to produce exact stochastic results with performance that scales independently of the reaction network size. Reaction rates can be defined as arbitrary functions of molecular states to provide powerful coarse-graining capabilities, for example to merge Boolean and kinetic representations of biological networks. NFsim enables researchers to simulate many biological systems that were previously inaccessible to general-purpose software, as we illustrate with models of immune system signaling, microbial signaling, cytoskeletal assembly and oscillating gene expression.     

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.     

Space as the final frontier in stochastic simulations of biological systems

Recent technological and theoretical advances are only now allowing the simulation of detailed kinetic models of biological systems that reflect the stochastic movement and reactivity of individual molecules within cellular compartments. The behavior of many systems could not be properly understood without this level of resolution, opening up new perspectives of using computer simulations to accelerate biological research. We review the modeling methodology applied to stochastic spatial models, also to the attention of non-expert potential users. Modeling choices, current limitations and perspectives of improvement of current general-purpose modeling/simulation platforms for biological systems are discussed.     

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).     

Online model checking approach based parameter estimation to a neuronal fate decision simulation model in Caenorhabditis elegans with hybrid functional Petri net with extension

Mathematical modeling and simulation studies are playing an increasingly important role in helping researchers elucidate how living organisms function in cells. In systems biology, researchers typically tune many parameters manually to achieve simulation results that are consistent with biological knowledge. This severely limits the size and complexity of simulation models built. In order to break this limitation, we propose a computational framework to automatically estimate kinetic parameters for a given network structure. We utilized an online (on-the-fly) model checking technique (which saves resources compared to the offline approach), with a quantitative modeling and simulation architecture named hybrid functional Petri net with extension (HFPNe). We demonstrate the applicability of this framework by the analysis of the underlying model for the neuronal cell fate decision model (ASE fate model) in Caenorhabditis elegans. First, we built a quantitative ASE fate model containing 3327 components emulating nine genetic conditions. Then, using our developed efficient online model checker, MIRACH 1.0, together with parameter estimation, we ran 20-million simulation runs, and were able to locate 57 parameter sets for 23 parameters in the model that are consistent with 45 biological rules extracted from published biological articles without much manual intervention. To evaluate the robustness of these 57 parameter sets, we run another 20 million simulation runs using different magnitudes of noise. Our simulation results concluded that among these models, one model is the most reasonable and robust simulation model owing to the high stability against these stochastic noises. Our simulation results provide interesting biological findings which could be used for future wet-lab experiments.     

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.     

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.     

Logic modeling and the ridiculome under the rug

Logic-derived modeling has been used to map biological networks and to study arbitrary functional interactions, and fine-grained kinetic modeling can accurately predict the detailed behavior of well-characterized molecular systems; at present, however, neither approach comes close to unraveling the full complexity of a cell. The current data revolution offers significant promises and challenges to both approaches - and could bring them together as it has spurred the development of new methods and tools that may help to bridge the many gaps between data, models, and mechanistic understanding.Have you used logic modeling in your research? It would not be surprising if many biologists would answer no to this hypothetical question. And it would not be true. In high school biology we already became familiar with cartoon diagrams that illustrate basic mechanisms of the molecular machinery operating inside cells. These are nothing else but simple logic models. If receptor and ligand are present, then receptor-ligand complexes form; if a receptor-ligand complex exists, then an enzyme gets activated; if the enzyme is active, then a second messenger is being produced; and so on. Such chains of causality are the essence of logic models (Figure 1a). Arbitrary events and mechanisms are abstracted; relationships are simplified and usually involve just two possible conditions and three possible consequences. The presence or absence of one or more molecule, activity, or function, [some icons in the cartoon] will determine whether another one of them will be produced (created, up-regulated, stimulated) [a 'positive' link] or destroyed (degraded, down-regulated, inhibited) [a 'negative' link], or be unaffected [there is no link]. The icons and links often do not follow a standardized format, but when we look at such a cartoon diagram, we believe that we 'understand' how the system works. Because our brain is easily able to process these relationships, these diagrams allow us to answer two fundamental types of questions related to the system: why (are certain things happening)? What if (we make some changes)?     

Multi-scale lung modeling

Multi-scale modeling of biological systems has recently become fashionable due to the growing power of digital computers as well as to the growing realization that integrative systems behavior is as important to life as is the genome. While it is true that the behavior of a living organism must ultimately be traceable to all its components and their myriad interactions, attempting to codify this in its entirety in a model misses the insights gained from understanding how collections of system components at one level of scale conspire to produce qualitatively different behavior at higher levels. The essence of multi-scale modeling thus lies not in the inclusion of every conceivable biological detail, but rather in the judicious selection of emergent phenomena appropriate to the level of scale being modeled. These principles are exemplified in recent computational models of the lung. Airways responsiveness, for example, is an organ-level manifestation of events that begin at the molecular level within airway smooth muscle cells, yet it is not necessary to invoke all these molecular events to accurately describe the contraction dynamics of a cell, nor is it necessary to invoke all phenomena observable at the level of the cell to account for the changes in overall lung function that occur following methacholine challenge. Similarly, the regulation of pulmonary vascular tone has complex origins within the individual smooth muscle cells that line the blood vessels but, again, many of the fine details of cell behavior average out at the level of the organ to produce an effect on pulmonary vascular pressure that can be described in much simpler terms. The art of multi-scale lung modeling thus reduces not to being limitlessly inclusive, but rather to knowing what biological details to leave out.     

A unified modeling of Kanban systems using petri nets

The success of some Just In Time (JIT) systems has led to a growing interest in Kanban systems, which provide a way to implement a JIT control policy. Much work has recently been devoted to this problem, and especially many models have been developed to evaluate the performance of such systems. In this article, we focus our attention of these existing models. Each author uses his/her own representation, which is not formal in most cases, and so it is often difficult to understand the proposed model and to compare it with others. In this article, we show that Petri nets are well suited to provide a unified modeling of Kanban systems. We first propose a basic model, then show that most models encountered in the literature can easily be represented by a Petri net model. Once such a formal model is obtained, it can then be used to analyze the behavior of the system, both qualitatively and quantitatively. Some preliminary results pertaining to the quantitative analysis are presented at the end of the article.     

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.