Addressing data uncertainty of Caulobacter crescentus cell cycles using hybrid Petri nets with fuzzy kinetics

Studying and analysing the various phases and key proteins of cell cycles is essential for the understanding of cell development and differentiation. To this end, mechanistic models play an important role towards a system level understanding of the interactions between cell cycle components. Many quantitative models of cell cycles have been previously constructed using either stochastic or deterministic approaches. However, cell cycle models are inherently hybrid requiring the full and accurate interplay of the continuous system dynamics and their corresponding discrete events. Moreover, not all required experimental data are usually available when designing in-silico experiments for these scenarios. In this paper, we employ hybrid Petri nets to implement a hybrid model of the Caulobacter crescentus cell cycle. The model handles all required logics of cell cycles in a very elegant way. We then extend this model to support fuzzy kinetics for those parts where sufficient experimental data are not available and thus precise kinetic parameters cannot be estimated. With some of the kinetic parameters being set as fuzzy numbers, the model produces uncertain bands of outputs reflecting different possibilities of an output comprising most likely the correct one.