Adam Kozak

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

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.

Hemojuvelin-hepcidin axis modeled and analyzed using Petri nets

Systems biology approach to investigate biological phenomena seems to be very promising because it is capable to capture one of the fundamental properties of living organisms, i.e. their inherent complexity. It allows for analysis biological entities as complex systems of interacting objects. The first and necessary step of such an analysis is building a precise model of the studied biological system. This model is expressed in the language of some branch of mathematics, as for example, differential equations. During the last two decades the theory of Petri nets has appeared to be very well suited for building models of biological systems. The structure of these nets reflects the structure of interacting biological molecules and processes. Moreover, on one hand, Petri nets have intuitive graphical representation being very helpful in understanding the structure of the system and on the other hand, there is a lot of mathematical methods and software tools supporting an analysis of the properties of the nets. In this paper a Petri net based model of the hemojuvelin-hepcidin axis involved in the maintenance of the human body iron homeostasis is presented. The analysis based mainly on T-invariants of the model properties has been made and some biological conclusions have been drawn.

A Petri net based model of oxidative stress in atherosclerosis

Abstract. In this paper a Petri net based model of the process of oxidative stress in atherosclerosis is presented and analyzed. Model expressed in the language of Petri net theory have, on one hand, an intuitive graphical representation, and on the other hand their formal properties can be analyzed using rigorous mathematical methods. Moreover, the behavior of a net can be simulated what supports the process of model development and an interpretation of the results of the analysis. Both the analysis and the simulation can be supported by many freely available software tools. In the case of biological systems an analysis the t-invariants is especially important since they correspond to some elementary biological subprocesses. In this paper the results of such an analysis are presented. In particular, minimal t-invariants, MCT-sets and t-clusters are calculated, their biological meaning is determined and some biological conclusions are drawn.

Holmes: a graphical tool for development, simulation and analysis of Petri net based models of complex biological systems

Summary Model development and its analysis is a fundamental step in systems biology. The theory of Petri nets offers a tool for such a task. Since the rapid development of computer science, a variety of tools for Petri nets emerged, offering various analytical algorithms. From this follows a problem of using different programs to analyse a single model. Many file formats and different representations of results make the analysis much harder. Especially for larger nets the ability to visualize the results in a proper form provides a huge help in the understanding of their significance. We present a new tool for Petri nets development and analysis called Holmes. Our program contains algorithms for model analysis based on different types of Petri nets, e.g. invariant generator, Maximum Common Transitions (MCT) sets and cluster modules, simulation algorithms or knockout analysis tools. A very important feature is the ability to visualize the results of almost all analytical modules. The integration of such modules into one graphical environment allows a researcher to fully devote his or her time to the model building and analysis. Availability and implementation Available at http://www.cs.put.poznan.pl/mradom/Holmes/holmes.html. Contact piotr@cs.put.poznan.pl.

On a generalized model of labeled graphs

Labeled graphs have applications in algorithms for reconstructing chains that have been split into smaller parts. Chain reconstruction is a common problem in biochemistry and bioinformatics, particularly for sequencing DNA or peptide chains. Labeled graphs (in the sense defined in this paper) have also the important structural property which allows to reduce the Hamiltonian path problem to Eulerian path problem. This work introduces a model and properties of a class of base-labeled graphs that unify the properties of labeled and free-labeled graphs (Blazewicz et al., 1999) [1]. It describes the basic relationships between those classes and some of their applications. It also introduces lexical graphs which are the superclass of de Bruijn graphs. Lexical graphs keep many properties of de Bruijn graphs which have a wide area of applications e.g. in mathematics, electronics and computing sciences.

Structural analysis of a Petri net model of oxidative stress in atherosclerosis

Atherosclerosis is a complex process of gathering sub-endothelial plaques decreasing lumen of the blood vessels. This disorder affects people of all ages, but its progression is asymptomatic for many years. It is regulated by many typical and atypical factors including the immune system response, a chronic kidney disease, a diet rich in lipids, a local inflammatory process and a local oxidative stress that is here one of the key factors. In this study, a Petri net model of atherosclerosis regulation is presented. This model includes also some information about stoichiometric relationships between its components and covers all mentioned factors. For the model, a structural analysis based on invariants was made and biological conclusions are presented. Since the model contains inhibitor arcs, a heuristic method for analysis of such cases is presented. This method can be used to extend the concept of feasible t-invariants.