Modeling and Analyzing Biological Systems Using Colored Hierarchical Petri Nets Illustrated by C. Elegans Vulval Development

Colored Petri nets allow compact, parameterizable and scalable representations of large-scale biological models by encoding, e.g., species as colored tokens, and offer a variety of analysis techniques, e.g., structural analysis, simulation and model checking to analyze biological models. However, so far colored Petri nets have not been widely used and well explored in systems biology. In this paper, we aim to present a systematic approach to modeling and analyzing complex biological systems using colored Petri nets in order to help biologists to easily use them. We first describe a framework comprising a family of related colored Petri nets: Colored qualitative Petri net (QPN^c), colored stochastic Petri net (SPN^c) and colored continuous Petri net (CPN^c). They share structure, but are specialized by their kinetic information. Based on this framework, we present our colored Petri net approach to modeling and analyzing complex biological systems. First a biological system is modeled as a hierarchical QPN^C model, animated and analyzed by structural analysis; then it is converted into a SPN^C or CPN^c model, to be further analyzed using stochastic or continuous simulation, and simulative or numerical model checking. We demonstrate this approach using a nontrivial example, Caenorhabditis elegans vulval development.