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      Some aspects of the anemia of chronic disorders modeled and analyzed by petri net based approach

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          Abstract

          Anemia of chronic disorders is a very important phenomenon and iron is a crucial factor of this complex process. To better understand this process and its influence on some other factors we have built a mathematical model of the human body iron homeostasis, which possibly most exactly would reflect the metabolism of iron in the case of anemia and inflammation. The model has been formulated in the language of Petri net theory, which allows for its simulation and precise analysis. The obtained results of the analysis of the model’s behavior, concerning the influence of anemia and inflammation on the transferrin receptors, and hepcidin concentration changes are the valuable complements to the knowledge following from clinical research. This analysis is one of the first attempts to investigate properties and behavior of a not fully understood biological system on a basis of its Petri net based model.

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          Most cited references 37

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          Application of Petri net based analysis techniques to signal transduction pathways

          Background Signal transduction pathways are usually modelled using classical quantitative methods, which are based on ordinary differential equations (ODEs). However, some difficulties are inherent in this approach. On the one hand, the kinetic parameters involved are often unknown and have to be estimated. With increasing size and complexity of signal transduction pathways, the estimation of missing kinetic data is not possible. On the other hand, ODEs based models do not support any explicit insights into possible (signal-) flows within the network. Moreover, a huge amount of qualitative data is available due to high-throughput techniques. In order to get information on the systems behaviour, qualitative analysis techniques have been developed. Applications of the known qualitative analysis methods concern mainly metabolic networks. Petri net theory provides a variety of established analysis techniques, which are also applicable to signal transduction models. In this context special properties have to be considered and new dedicated techniques have to be designed. Methods We apply Petri net theory to model and analyse signal transduction pathways first qualitatively before continuing with quantitative analyses. This paper demonstrates how to build systematically a discrete model, which reflects provably the qualitative biological behaviour without any knowledge of kinetic parameters. The mating pheromone response pathway in Saccharomyces cerevisiae serves as case study. Results We propose an approach for model validation of signal transduction pathways based on the network structure only. For this purpose, we introduce the new notion of feasible t-invariants, which represent minimal self-contained subnets being active under a given input situation. Each of these subnets stands for a signal flow in the system. We define maximal common transition sets (MCT-sets), which can be used for t-invariant examination and net decomposition into smallest biologically meaningful functional units. Conclusion The paper demonstrates how Petri net analysis techniques can promote a deeper understanding of signal transduction pathways. The new concepts of feasible t-invariants and MCT-sets have been proven to be useful for model validation and the interpretation of the biological system behaviour. Whereas MCT-sets provide a decomposition of the net into disjunctive subnets, feasible t-invariants describe subnets, which generally overlap. This work contributes to qualitative modelling and to the analysis of large biological networks by their fully automatic decomposition into biologically meaningful modules.
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            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.
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              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.
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                Author and article information

                Contributors
                +48-61-8546590 , +48-61-8546599 , doforman@ump.edu.pl
                Journal
                Bioprocess Biosyst Eng
                Bioprocess and Biosystems Engineering
                Springer-Verlag (Berlin/Heidelberg )
                1615-7591
                1615-7605
                8 January 2011
                8 January 2011
                June 2011
                : 34
                : 5
                : 581-595
                Affiliations
                [1 ]Department of Clinical Biochemistry, Poznań University of Medical Sciences, Grunwaldzka 6, 60-780 Poznań, Poland
                [2 ]Institute of Computing Science, Poznań University of Technology, Piotrowo 2, 60-965 Poznań, Poland
                [3 ]Institute of Bioorganic Chemistry, Polish Academy of Sciences, Noskowskiego 12/14, 61-704 Poznań, Poland
                Article
                507
                10.1007/s00449-010-0507-6
                3092940
                21221653
                © The Author(s) 2011
                Categories
                Original Paper
                Custom metadata
                © Springer-Verlag 2011

                Biomedical engineering

                inflammation, modeling, petri net theory, iron, hepcidin

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