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

Abstract

Background 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. Results 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. Conclusions 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. Electronic supplementary material The online version of this article (10.1186/s12859-019-2690-z) contains supplementary material, which is available to authorized users.

From Epidemic to Pandemic Modelling

“…Going beyond visual inspection, the order and height of peaks can be ascertained computationally from the traces. More generally, many behavioural properties of interest can be expressed using linear temporal logic and analysed in practice via simulative model checking (Donaldson and Gilbert, 2008;Gilbert et al, 2019), which is specifically useful for exploring larger models by the use of property libraries, see Section 3 and Figure 10.…”

“…The use of colour enables us to encode matrices, where colours (natural numbers) represent indices; multidimensional matrices can be represented by appropriate colour tuples. Previously we have used this approach to encode one, two and three dimensional Cartesian space where coordinates were represented as tuples over the entire matrix (Gilbert et al, 2013), for example, modelling diffusion and cell movement in biological systems: planar cell polarity in the Drosophila wing (Gao et al, 2013), phase variation in bacterial colonies (Pârvu et al, 2015), bacterial quorum sensing (Gilbert et al, 2019) and intra-cellular calcium dynamics (Ismail et al, 2020).…”

From Epidemic to Pandemic Modelling

“…The use of colour enables us to encode matrices, where colours (natural numbers) represent indices; multidimensional matrices can be represented by appropriate colour tuples. Previously we have used this approach to encode one, two and three dimensional Cartesian space where coordinates were represented as tuples over the entire matrix [GHLS13], for example modelling diffusion and cell movement in biological systems: planar cell polarity in the Drosophila wing [GGH + 13], phase variation in bacterial colonies [PGH + 15], bacterial quorum sensing [GHGC19] and intra-cellular calcium dynamics [IHAH20].…”

Hybrid modelling of biological systems: current progress and future prospects

“…the gene regulation (e.g. activation or deactivation of genes) [ 5 ], the birth and death of species and the crossing of concentration thresholds of some species, all of which cause state switching [ 6 ]. For such biological phenomena, hybrid models that integrate discrete with continuous or stochastic with deterministic methods could be more appropriate.…”