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Semi-quantitative Modelling of Gene Regulatory Processes with Unknown Parameter Values Using Fuzzy Logic and Petri Nets

Bordon J., Moškon M., Zimic N., Mraz M.

Fundamenta Informaticae

2018

Vol. 160, nr 1/2

81--100

Petri nets are a well-established modelling framework in life sciences and have been widely applied to systems and synthetic biology in recent years. With the various extensions they serve as graphical and simulation interface for both qualitative and quantitative modelling approaches. In terms of quantitative approaches, Stochastic and Continuous Petri nets are extensively used for modelling biological system’s dynamics if underlying kinetic data are known. However, these are often only vaguely defined or even missing. In this paper we present a fuzzy approach, which can be used to model biological processes with unknown kinetic data in order to still obtain quantitatively relevant simulation results. We define fuzzy firing rate functions, which can be used in Continuous Petri nets and are able to describe different processes that govern the dynamics of gene expression networks. They can be used in combination with the conventional firing rate functions and applied only in the parts of the system for which the kinetic data are missing. The case study of the proposed approach is performed on models of a hypothetical repressilator and Neurospora circadian rhythm.