Intracellular processes are cascades of biochemical reactions, triggered in response to various types of stimuli. Mathematical models describing their dynamics have become increasingly popular in recent years, as tools supporting experimental work in analysis of pathways and regulatory networks. Not only do they provide insights into general properties of these systems, but also help in specific tasks, such as search for drug molecular targets or treatment protocols. Different tools and methods are used to model complex biological systems. In this work, we focus on ordinary differential equations (ODEs) and Petri nets. We consider specific methods of analysis of such models, i.e., sensitivity analysis (SA) and significance analysis. So far, they have been applied separately, with different goals. In this paper, we show that they can complement each other, combining the sensitivity of ODE models and the significance analysis of Petri nets. The former is used to find parameters, whose change results in the greatest quantitative and qualitative changes in the model response, while the latter is a structural analysis and allows indicating the most important subprocesses in terms of information flow in Petri net. Ultimately, both methods facilitate finding the essential processes in a given signaling pathway or regulatory network and may be used to support medical therapy development. In the paper, the use of dual modeling is illustrated with an example of ATM/p53/NF-$$\kappa$$ κ B pathway. Each method was applied to analyze this system, resulting in finding different subsets of important processes that might be prospective targets for changing this system behavior. While some of the processes were indicated in each of the approaches, others were found by one method only and would be missed if only that method was applied. This leads to the conclusion about the complementarity of the methods under investigation. The dual modeling approach of comprehensive structural and parametric analysis yields results that would not be possible if these two modeling approaches were applied separately. The combined approach, proposed in this paper, facilitates finding not only key processes, with which significant parameters are associated, but also significant modules, corresponding to subsystems of regulatory networks. The results provide broader insight into therapy targets in diseases in which the natural control of intracellular processes is disturbed, leading to the development of more effective therapies in medicine.

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Regulation of gene expression is one of the most important problems analyzed in systems biology. It involves, among other, interactions of mRNA with miRNA - a small (21-25 nt) single–stranded non–coding RNA molecule. Its main function is post-transcriptional regulation of gene expression leading to gene silencing. It is achieved either by inhibition of translation or by degradation of mRNA. The detailed mechanisms employed include inhibition of attaching the 60s ribosomal subunit, premature ribosome drop-off or inhibition of protein elongation process, cleavage of mRNA or destabilization of mRNA. Another mechanism of regulation of gene expression involves reactive oxygen species (ROS - radical and non-radical oxygen species formed by the partial reduction of oxygen) which, being released from mitochondrium cytochrome C and inducing DNA damage, induce the apoptosis pathway. ROS level can be regulated by antioxidant systems existing in a cell. This paper presents analysis of a model of gene regulation based on these molecules, in which Petri net is used to find the key reactions and, subsequently, an ODE-based model is used to verify these conclusions.