An automated approach to translate a biological process from ODEs into graphical hybrid functional Petri Nets

The study of biological systems is growing rapidly, and can be considered as an intrinsic task in biological research, and a prerequisite for diagnosing diseases and drug development. The integration of biological studies with computer technologies led to noticeable developments in biology with the appearance of many powerful modeling and simulation techniques and tools. The help of computers in biology resulted in deeper knowledge about complex biological systems and biopathways behaviors. Among modeling tools, the Petri Net formalism plays an important role. Petri Net is a powerful computerized and graphical modeling technique originally developed by Carl Adam Petri in 1960 to model discrete event systems. With its various extensions, Petri Nets find applications in many other fields including Biology. The extension known under the name Hybrid Functional Petri Net (HFPN) was developed specifically to model biological systems. Traditionally, biological processes are captured as systems of ordinary differential equations (ODEs). However, HFPNs offer a much more elegant and versatile approach to represent these processes more accurately. In fact, HFPNs allow to capture phenomena which are impossible to capture with ODES, while being more intuitive and easy to understand and model with. In this work we propose an approach to translate a system of ODEs representing a biological process into a HFPN. The resulting HFPN, not only preserves the semantics of the original model, but is also more humanly readable thanks to the use of a novel technique to connect its components in a smart way. To validate our approach, we implemented it as an extension to the tool Real Time Studio (an integrated environment for modeling, simulation and automatic verification of real-time systems), and compared our simulation results with those obtained by simulating systems of ODEs using MATLAB.