Representing network reconstruction solutions with colored Petri nets

The reconstruction of biological networks from experimental time series data is one of the challenges in systems biology. Currently, most network reconstruction approaches usually yield one solution. In contrast, the (automatic) network reconstruction method proposed by Marwan et al. generates all possible minimal solutions fitting the given set of data, and thus reveals all alternative mechanisms to explain the biological phenomena under study. Although this is interesting and helpful, the generated solutions are usually too many and thus difficult to manage. In this paper, we propose the use of colored Petri nets to represent all possible solutions for a network reconstruction problem by encoding each solution as a color. Specifically, we present two folding (coloring) approaches for generating colored Petri net models for a given set of Petri net networks (solutions). To do this, we not only offer a compact representation of all solutions in one colored model for a given network reconstruction problem, but also facilitate the analysis of each solution by choosing its corresponding color. We also give an application of our coloring approaches by taking the phosphate regulatory network in enteric bacteria as example.