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Some aspects of modeling and analysis of complex biological systems using time Petri nets

Olszak J., Radom M., Formanowicz P.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2018

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Vol. 66, nr 1

67--78

EN

Models of complex biological systems can be built using different types of Petri nets. Qualitative nets, for example, can be successfully used to obtain a model of such a system and on its basis a structure-based analysis can be performed. Time is an important factor influencing a whole biological system behaviour and in many cases it should be considered during building a model of such a system. In this paper various types of time Petri nets have been described and methods for studying corresponding models have been discussed. In particular, an algorithm using time parameters to enhance t-invariants based analysis is proposed. This algorithm allows for calculation of the minimal and maximal numbers of tokens (respectively, for an optimistic and pessimistic case) in particular places necessary to assure that all transitions from a given t-invariant support will be able to fire. Additionally, to address the problem of the proper assignment of time values to transitions, the known methods for calculation and evaluation of such time parameters based on the net structure have also been discussed.

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The study of the influence of micro-environmental signals on macrophage differentiation using a quantitative Petri net based model

Rżosińska K., Formanowicz D., Formanowicz P.

Archives of Control Sciences

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2017

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Vol. 27, no. 2

331--349

EN

The complexity of many biological processes, which, thanks to the development of many fields of science, becomes for us more and more obvious, makes these processes extremely interesting for further analysis. In this paper a quantitative model of the process of macrophage differentiation, which is essential for many phenomena occurring in the human body, is proposed and analyzed. The model is expressed in the language of Petri net theory on the basis of one of the three hypotheses concerning macrophage differentiation existing in the literature. The performed analysis allowed to find an importance of individual factors in the studied phenomenon.

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The effect of cigarette smoking on endothelial damage and atherosclerosis development – modeled and analyzed using Petri nets

Chmielewska K., Formanowicz D., Formanowicz P.

Archives of Control Sciences

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2017

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Vol. 27, no. 2

211--228

EN

Atherosclerosis as one of the crucial causes of cardiovascular diseases (CVD) is the leading reason of death worldwide. One of the contributing factors to this phenomenon is endothelial dysfunction, which is associated with the impact of various agents and their interactions. Tobacco smoke is one of the well known factors here. For better understanding of its significance a model of its impact on atherosclerotic plaque formation has been proposed. The model contains selected aspects of the influence of tobacco smoke, dual function of nitric oxide (NO) (influence of various mechanisms on NO bioavailability), oxidative stress which promotes low density lipoproteins oxidation, macrophages significance and other mechanisms leading to an aggravation of the endothelial disturbances. The model has been built using Petri nets theory and the analysis has been based on t-invariants. This approach allowed to confirm the important role of inflammation and oxidative stress in atherosclerosis development and moreover it has shown the considerable influence of the cigarette smoke.

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A Petri net based model of oxidative stress in atherosclerosis

Formanowicz D., Kozak A., Formanowicz P.

Foundations of Computing and Decision Sciences

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2012

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Vol. 37, No. 2

59--78

EN

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.