Spatial quorum sensing modelling using coloured hybrid Petri nets and simulative model checking

Quorum sensing drives biofilm formation in bacteria in order to ensure that biofilm formation only occurs when colonies are of a sufficient size and density. This spatial behaviour is achieved by the broadcast communication of an autoinducer in a diffusion scenario. This is of interest, for example, when considering the role of gut microbiota in gut health. This behaviour occurs within the context of the four phases of bacterial growth, specifically in the exponential stage (phase 2) for autoinducer production and the stationary stage (phase 3) for biofilm formation.

We have used coloured hybrid Petri nets to step-wise develop a flexible computational model for E.coli biofilm formation driven by Autoinducer 2 (AI-2) which is easy to configure for different notions of space. The model describes the essential components of gene transcription, signal transduction, extra and intra cellular transport, as well as the two-phase nature of the system. We build on a previously published non-spatial stochastic Petri net model of AI-2 production, keeping the assumptions of a limited nutritional environment, and our spatial hybrid Petri net model of biofilm formation, first presented at the NETTAB 2017 workshop. First we consider the two models separately without space, and then combined, and finally we add space. We describe in detail our step-wise model development and validation. Our simulation results support the expected behaviour that biofilm formation is increased in areas of higher bacterial colony size and density. Our analysis techniques include behaviour checking based on linear time temporal logic.

The advantages of our modelling and analysis approach are the description of quorum sensing and associated biofilm formation over two phases of bacterial growth, taking into account bacterial spatial distribution using a flexible and easy to maintain computational model. All computational results are reproducible.