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

Abstract

This paper 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. The simulation output is visualised 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.

Keywords: Coloured stochastic Petri nets; Partial differential equations; Ordinary differential equations; Spatial-temporal modelling; Systems Biology; Pattern analysis; Multidimensional; BioModel Engineering.

Simulation output visualisation

Illustrative model simulations are visualised below considering circular (left) and rectangular (right) geometries.

Models

The computational models described in the paper are made available here.

Analysis tools

The analysis tools were implemented in C++ and are employed to automatically detect and analyse sector-like patterns in bacterial colonies with phase variable genes.

Requirements for executing scripts

The GNU parallel package needs to be installed on your machine in order for (some of) the Bash scripts to execute properly; see the GNU parallel website for more details regarding the package and/or how to download and install it.

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Binaries

A Linux (x64) compiled version of the tools and simple usage examples are made available here.

VirtualBox image

For non-Linux users a preconfigured Ubuntu mini 12.04 image for VirtualBox (Download VirtualBox) containing the Linux (x64) compiled version of the tools and simple usage examples is made available here. In order to keep the size of the image at a minimum a non-GUI based version of Ubuntu was installed. Thus the GUI-enabled version of the tools will not be executable without additional configuration. The login credentials (username/password) are user/password (not "very" safe I must agree) and all tools are stored in the /home/user/tools folder.

Remark: More details about the tools and usage instructions are provided in the README file (see "tools" folder).

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