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.     

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.     

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.     

Iron-Hepcidin Dysmetabolism,Anemia and Renal Hypoxia,Inflammation and Fibrosis in the Remnant Kidney Rat Model

Anemia is a common complication of chronic kidney disease (CKD) that develops early and its severity increases as renal function declines. It is mainly due to a reduced production of erythropoietin (EPO) by the kidneys; however, there are evidences that iron metabolism disturbances increase as CKD progresses. Our aim was to study the mechanisms underlying the development of anemia of CKD, as well as renal damage, in the remnant kidney rat model of CKD induced by 5/6 nephrectomy. This model of CKD presented a sustained degree of renal dysfunction, with mild and advanced glomerular and tubulointerstitial lesions. Anemia developed 3 weeks after nephrectomy and persisted throughout the protocol. The remnant kidney was still able to produce EPO and the liver showed an increased EPO gene expression. In spite of the increased EPO blood levels, anemia persisted and was linked to low serum iron and transferrin levels, while serum interleukin (IL)-6 and high sensitivity C-reactive protein (hs-CRP) levels showed the absence of systemic inflammation. The increased expression of duodenal ferroportin favours iron absorption; however, serum iron is reduced which might be due to iron leakage through advanced kidney lesions, as showed by tubular iron accumulation. Our data suggest that the persistence of anemia may result from disturbances in iron metabolism and by an altered activity/function of EPO as a result of kidney cell damage and a local inflammatory milieu, as showed by the increased gene expression of different inflammatory proteins in the remnant kidney. In addition, this anemia and the associated kidney hypoxia favour the development of fibrosis, angiogenesis and inflammation that may underlie a resistance to EPO stimuli and reduced iron availability. These findings might contribute to open new windows to identify putative therapeutic targets for this condition, as well as for recombinant human EPO (rHuEPO) resistance, which occurs in a considerable percentage of CKD patients.     

Hepcidin mRNA levels in mouse liver respond to inhibition of erythropoiesis

Hepcidin, a key regulator of iron metabolism, decreases intestinal absorption of iron and its release from macrophages. Iron, anemia, hypoxia, and inflammation were reported to influence hepcidin expression. To investigate regulation of the expression of hepcidin and other iron-related genes, we manipulated erythropoietic activity in mice. Erythropoiesis was inhibited by irradiation or posttransfusion polycythemia and stimulated by phenylhydrazine administration and erythropoietin. Gene expression of hepcidin and other iron-related genes (hemojuvelin, DMT1, ferroportin, transferrin receptors, ferritin) in the liver was measured by the real-time polymerase chain reaction. Hepcidin expression increased despite severe anemia when hematopoiesis was inhibited by irradiation. Suppression of erythropoiesis by posttransfusion polycythemia or irradiation also increased hepcidin mRNA levels. Compensated hemolysis induced by repeated phenylhydrazine administration did not change hepcidin expression. The decrease caused by exogenous erythropoeitin was blocked by postirradiation bone marrow suppression. The hemolysis and anemia decrease hepcidin expression only when erythropoiesis is functional; on the other hand, if erythropoiesis is blocked, even severe anemia does not lead to a decrease of hepcidin expression, which is indeed increased. We propose that hepcidin is exclusively sensitive to iron utilization for erythropoiesis and hepatocyte iron balance, and these changes are not sensed by other genes involved in the control of iron metabolism in the liver.     

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.     

Application of Petri net theory for modelling and validation of the sucrose breakdown pathway in the potato tuber

MOTIVATION: Because of the complexity of metabolic networks and their regulation, formal modelling is a useful method to improve the understanding of these systems. An essential step in network modelling is to validate the network model. Petri net theory provides algorithms and methods, which can be applied directly to metabolic network modelling and analysis in order to validate the model. The metabolism between sucrose and starch in the potato tuber is of great research interest. Even if the metabolism is one of the best studied in sink organs, it is not yet fully understood. RESULTS: We provide an approach for model validation of metabolic networks using Petri net theory, which we demonstrate for the sucrose breakdown pathway in the potato tuber. We start with hierarchical modelling of the metabolic network as a Petri net and continue with the analysis of qualitative properties of the network. The results characterize the net structure and give insights into the complex net behaviour.     

Scrutinizing the mechanisms underlying the induction of anemia of inflammation through GPI-mediated modulation of macrophage activation in a model of African trypanosomiasis

In animal trypanosomiasis the severity of infection is reflected by the degree of anemia which resembles anemia of inflammation, involving a skewed iron homeostasis leading to iron accumulation within the reticuloendothelial system. Myeloid cells (M cells) have been implicated in the induction and maintenance of this type of anemia and modulation of M cells through the main trypanosome-derived glycosylphosphatidylinositol (GPI)-anchor could attenuate both anemia and trypano-susceptibility in Trypanosoma brucei-infected mice. Herein the GPI-based treatment, allowing a straightforward comparison between trypanotolerance and susceptibility in T. brucei-infected C57Bl/6 mice, was further adopted to scrutinize mechanisms/pathways underlying trypanosome-elicited anemia. Hereby, the following interlinkable observations were made in GPI-based treated (GBT) T. brucei-infected mice: (i) a reduced inflammatory cytokine production and increased IL-10 production associated with alleviation of anemia and restoration of serum iron levels, (ii) a shift in increased liver expression of iron storage towards iron export genes, (iii) increased erythropoiesis in the bone marrow and extramedullar sites (spleen) probably reflecting a normalized iron homeostasis and availability. Collectively, our results demonstrate that reprogramming macrophages towards an anti-inflammatory state alleviates anemia of inflammation by normalizing iron homeostasis and restoring erythropoiesis.     

Hepcidin: a direct link between iron metabolism and immunity

Hepcidin, originally discovered in urine as a bactericidal peptide synthesized by hepatocytes was later proved to be a key regulator of iron metabolism at the whole body level, namely, in conditions of altered iron demand such as the increased or decreased total amount of body iron, inflammation, hypoxia and anemia. The major mechanism of hepcidin function seems to be the regulation of transmembrane iron transport. Hepcidin binds to its receptor, protein ferroportin, which serves as a transmembrane iron channel enabling iron efflux from cells. The hepcidin-ferroportin complex is then degraded in lysosomes and iron is locked inside the cells (mainly enterocytes, hepatocytes and macrophages). This leads to lowering of iron absorption in the intestine and to a decrease in serum iron concentration. Utilizing this mechanism, hepcidin regulates serum iron levels during inflammation, infection and possibly also in cancer. Under these conditions iron is shifted from circulation into cellular stores in hepatocytes and macrophages, making it less available for invading microorganisms and tumor cells. In anemia and hypoxia, hepcidin regulates the availability of iron for erythropoiesis. Hepcidin or hepcidin-related therapeutics could find a place in the treatment of various diseases such as hemochromatosis and anemia of chronic disease.     

Iron imports. IV. Hepcidin and regulation of body iron metabolism

Hepcidin, a small peptide synthesized in the liver, controls extracellular iron by regulating its intestinal absorption, placental transport, recycling by macrophages, and release from stores. Hepcidin inhibits the cellular efflux of iron by binding to and inducing the degradation of ferroportin, the sole iron exporter in iron-transporting cells. In turn, hepcidin synthesis is increased by iron loading and decreased by anemia and hypoxia. Hepcidin is markedly induced during inflammation, trapping iron in macrophages, decreasing plasma iron concentrations, and contributing to the anemia of inflammation. Hepcidin deficiency due to the dysregulation of its synthesis causes most known forms of hemochromatosis.     

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.     

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.     

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.     

Hepcidin研究进展

Hepcidin是肝脏特异性表达的一种小分子抗菌肽,是铁代谢的负调节激素。与炎症性贫血、遗传性血色沉着病等疾病的发病机制密切相关。证据显示,Hepcidin直接抑制肠上皮细胞铁吸收和诱导单核巨噬细胞铁滞留。同时,Hepcidin还具有广谱抗菌活性,与固有免疫密切相关。铁超载、感染、炎症及细胞因子可诱导Hepcidin表达,而贫血和缺氧则抑制其表达。Hepcidin的发现及其相关的铁离子运输机制的研究,将为铁离子吸收及分配的铁稳态调节和炎症性贫血、遗传性血色沉着病中的铁代谢障碍的分子机制探索开辟新的途径。本文就Hepcidin的分子特征、表达调控及生物学功能等方面研究进展进行综述。     

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.     

Role of Hepcidin in the Setting of Hypoferremia during Acute Inflammation

The anemia of chronic disease (also called anemia of inflammation) is an acquired disorder of iron homeostasis associated with infection, malignancy, organ failure, trauma, or other causes of inflammation. It is now widely accepted that induction of hepcidin expression in response to inflammation might explain the characteristic hypoferremia associated with this condition. To determine the role of hepcidin in acute inflammation and the regulation of its receptor, the iron exporter, ferroportin, wild-type, heterozygote and hepcidin knockout mice (Hepc−/−) were challenged with sublethal doses of lipopolysaccharide (LPS). Six hours after injection, ferroportin mRNA and protein levels were assessed in the duodenum and the spleen and plasma iron was determined. Our results demonstrate that hepcidin is crucial, though not the sole mediator of LPS-mediated acute hypoferremia, and also that hepcidin major contribution relies on decreased ferroportin protein levels found in the spleen. Furthermore, we establish that LPS-mediated repression of the membrane iron transporter DMT1 and oxidoreductase Dcytb in the duodenum is independent of hepcidin. Finally, our results in the hepc+/− mice indicate that elevated hepcidin gene expression is not a prerequisite for the setting of hypoferremia during early inflammatory response, and they highlight the intimate crosstalk between inflammatory and iron-responsive pathways for the control of hepcidin.     

Low red cell production may protect against severe anemia during a malaria infection—Insights from modeling

The malaria parasite causes lysis of red blood cells, resulting in anemia, a major cause of mortality and morbidity. Intuitively, one would expect the production of red blood cells to increase in order to compensate for this loss. However, it has been observed that this response is weaker than would be expected. Furthermore, iron supplementation for iron deficient children in malaria endemic regions can paradoxically adversely affect the clinical outcome of malaria infection. A possible explanation may lie in the preference that some malaria parasites show for infecting immature red blood cells (reticulocytes). In the presence of a parasite preference for immature red cells, a rise in red cell production can ‘fuel the fire’ of infection by increasing the availability of the parasite's preferred target cell.We present a mathematical model of red blood cell production and infection in order to explore this hypothesis. We assess the effect of varying the reticulocyte replacement rate and preference of the parasite for reticulocytes on four key outcome measures assessing anemia and parasitemia.For a given level of parasite preference for reticulocytes we uncover an optimal erythropoietic response which minimizes disease severity. Increasing red blood cell production much above this optimum confers no benefit to the patient, and in fact can increase the degree of anemia and parasitemia. These conclusions are consistent with epidemiological studies demonstrating that both iron deficiency and anemia are protective against severe malaria, whilst iron supplementation in malaria endemic regions is with an increased number of malaria related adverse effects. Thus, suppression of red blood cell production, rather than being an unfortunate side effect of inflammation, may be a host protective effect against severe malarial anemia.