Semi-quantitative modelling of biological
       systems with extended Fuzzy Petri nets

                        Jure Bordon, Miha Moškon, Miha Mraz

                                 University of Ljubljana,
                      Faculty of Computer and Information science,
                                        Slovenia,
                              jure.bordon@fri.uni-lj.si



       Abstract. State of the art approaches for modelling biological systems
       can be classified as qualitative or quantitative. Qualitative models are
       relatively simple and require only basic knowledge of the system, but
       may only be used to get a rough image about the system’s dynamics.
       On the other hand, quantitative models are able to mimic accurate dy-
       namical properties of observed system, but require accurate kinetic data,
       which is often lacking. Existing fuzzy Petri net approaches only consider
       qualitative modelling. We propose a new, semi-quantitative approach
       based on fuzzy logic and extended Petri nets (PNs). Fuzzy logic allows
       us to linguistically describe biological processes, even if kinetic data are
       unknown. We present the details of fuzzification, defuzzification and the
       definition of IF-THEN rules on a model of degradation from a repres-
       silator. We demonstrate how our approach circumvents the problem of
       missing kinetic parameters and how it can be used to augment existing
       quantitative methods such as models based on ordinary differential equa-
       tions. By using fuzzy logic we were able to obtain comparable results to
       those of existing methods while using only rough estimation of kinetic
       parameter values, showing our method can be used for sufficient system
       analysis that helps with designing a novel biological system even when
       accurate kinetic data are unknown.

       Keywords: biological switching systems, modelling biological systems,
       fuzzy logic, Petri nets, Fuzzy Petri nets




G. Balbo and M. Heiner (Eds.): BioPPN 2013, a satellite event of PETRI NETS 2013,
CEUR Workshop Proceedings Vol. 988, 2013.