Combined Chemotaxis, Lysis and Glue Deposition Model

Introduction

In order to examine how the system as a whole behaves it is necessary to combine the results of modelling the gene regulatory network with a macroscopic model of interacting E. Coli cells. This was done by estimating that quorum sensing becomes activated when the density of bacteria around the source of chemoattractant goes above a critical value. The radius within which quorum sensing is activated varies over time, and depends on how many bacteria there are. We combine the lysis time calculated from our stochastic simulations with this model so that this amount of time after quorum sensing is activated the bacteria lyse and deposit glue.

Results

In the simulation we assume the bacteria to be distributed throughout the pipeline so that they continually arrive at the breach by chemotaxis. Due to a lack of computing power, we performed a scaled simulation by having quorum sensing activate for a lower density of bacteria than in reality. The graph below shows the number of alive bacteria at the site of the breach:

As you can see in the above graph the number of bacteria increases initially as bacteria arrive from the surrounding area. It eventually reaches an equilibrium value as the rate of bacteria lysing equals the rate of arriving bacteria.

As the bacteria number reaches an equilibrium the effective radius within which the bacteria quorum sense also reaches an equilibrium, as illustrated below at point 3.

The above graph and diagram show the progression of the quorum sensing region as bacteria continue to arrive. As there is a constant rate of lysing bacteria, there is a linear increase in glue concentration at the breach, as illustrated below:

The increase in glue concentration does not stop, as we have not modelled the eventual sealing of the hole. Once the hole is sealed the chemoattractant gradient would dissipate, along with the signalling molecule IPTG. Eventually the genes for lysis and glue production would no longer be activated and the glue concentration would stop increasing.

Conclusion

This model shows, assuming that the gene regulatory network behaves as expected, that the E. Coli would chemotax, activate and deposit glue. Actual experiments would need to be done with lysing cells that actually deposit glue, and if the glue seals the hole. As the glue production does not stop until the IPTG is gone, it can be assumed that the hole would actually be sealed, the size of the glue plug is however uncertain.

Guide to Program

The program can be accessed on the downloads tab in the modelling section. Here is a short description of some of the components of the program, so that future modellers can develop it easier.

initial_cell_number -- Calculates the initial cell number in the observed radius from the initial density

initial_cell_prop -- Calculates the initial properties associated withn each bacteria such as distance from fracture.

movement -- Every iteration the movement module calculates the trajectory of each bacteria based on the run and tumble movement and whether the cell is moving up the chemotactic gradient.

radii_function -- Calculates the 'effective radius' of the simulation.

sort -- Contains a sorting routine to order the radii for othwer modules

quorum_sensing -- Determines whether a specific cell has quorum sensed based on a calculation of the surronding cell density.

inner_dynamics -- Provides the concentrations of different proteins within the cell in response to the external stimulants.

cell_increase -- Calculates the increase in cells from the outside environment in each iteration from chemotaxis.

increase_cell_prop -- Calculates the properties associated with cells entering the 'observed radius'

cell_decrease -- Calculates the number of cells lysing.

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References

[1] A.B. Goryachev, D.J. Toh, T. Lee. “Systems analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants”. BioSystems 83 (2006) 178–187

[2] Michail Stamatakis and Nikos V. Manttaris. “Comparison of Deterministic and Stochastic Models of the lac Operon Genetic Network” Biophysical Journal Volume 96 February 2009 887-906 887

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