Spatial-temporal modelling and analysis of bacterial colonies with phase variable genes

2015 Copyright is held by the owner/author(s). This article defines a novel spatial-temporal modelling and analysis methodology applied to a systems biology case study, namely phase variation patterning in bacterial colony growth. We employ coloured stochastic Petri nets to construct the model and run stochastic simulations to record the development of the circular colonies over time and space. The simulation output is visualised in 2D, and sector-like patterns are automatically detected and analysed. Space is modelled using 2.5 dimensions considering both a rectangular and circular geometry, and the effects of imposing different geometries on space are measured. We close by outlining an interpretation of the Petri net model in terms of finite difference approximations of partial differential equations (PDEs). One result is the derivation of the “best” nine-point diffusion model. Our multidimensional modelling and analysis approach is a precursor to potential future work on more complex multiscale modelling.EPSRC Research Grant EP I036168/1; German BMBF Research Grant 0315449H

Engineering a genetic circuit for Turing patterns in E. coli with a Synthetic Biology approach

Genetic circuits that can form spatial patterns have been a major topic of interest within Synthetic Biology. Turing patterns are self-organising spatial wave, spot or labyrinthine patterns that are formed in some reaction-diffusion circuits. The simplest Turing circuit involves a slow-diffusing activator and a fast-diffusing inhibitor, interacting to regulate their own and each other’s rates of production. An unambiguous implementation of Turing patterns with a genetic circuit is still lacking because of their exquisitely fine-tuned nature. This study aims to address this shortcoming and sets out to engineer a genetic circuit for Turing patterning in E. coli from first principles. Two genetic circuits were studied. Firstly, a phage circuit was designed according to the minimal self-activation, lateral inhibition Turing topology and involves a slow-diffusing M13 filamentous phage and a fast-diffusing 3OC6HSL quorum sensing signal. This circuit was abandoned because of the many complexities of phage biology, which were working against its successful implementation as a Turing generator. The focus was shifted to circuit ‘3954’, which was designed according to a more robust three-node topology and implemented with two small molecule diffusors; this could be done because the circuit allows for equal diffusivity of the two diffusing signals. All the components of circuit ‘3954’ were tested in reduced subcircuits and were shown to be functioning as expected. Growing bacterial colonies bearing the circuit were then visualised for pattern formation using confocal microscopy. Even though no Turing patterns were detected, the colonies consistently showed a centre-surround expression pattern of the fluorescence reporters, where GFP was expressed at the colony centre, whereas mCherry was predominantly expressed at the periphery. The obtained reaction-diffusion patterns are a good foundation for further tuning and exploration.Open Acces

Spatial Heterogeneity of Autoinducer Regulation Systems

Autoinducer signals enable coordinated behaviour of bacterial populations, a phenomenon originally described as quorum sensing. Autoinducer systems are often controlled by environmental substances as nutrients or secondary metabolites (signals) from neighbouring organisms. In cell aggregates and biofilms gradients of signals and environmental substances emerge. Mathematical modelling is used to analyse the functioning of the system. We find that the autoinducer regulation network generates spatially heterogeneous behaviour, up to a kind of multicellularity-like division of work, especially under nutrient-controlled conditions. A hybrid push/pull concept is proposed to explain the ecological function. The analysis allows to explain hitherto seemingly contradicting experimental findings

Challenges of biofilm control and utilization : lessons from mathematical modelling

Funding This work was supported by a scholarship grant from the School of Natural and Computing Sciences at the University of Aberdeen and the Faculty of Health Sciences at Curtin University.Peer reviewedPostprin

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

From The 2017 Network Tools and Applications in Biology (NETTAB) Workshop Palermo, Italy. 16–18 October 2017Background: 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.The open access fee has been covered by Brunel University Londo