Computational modelling has often been sought to solve and predict biological phenomena, and it has notably been applied to bacterial behaviour simulation. As it is now, almost all iGEM teams use bacteria to engineer their bio-bricks and to make each year even more wonderful projects for the iGEM community. However, we also all have to keep in mind the safety issues, and confine our bacteria properly to avoid letting them spread in the laboratory.

How could we estimate a risk of contamination?

It was while considering this matter that the iGEM Bordeaux Team developed a simulation model aiming to :

• estimate the number of bacteria that could proliferate on a lab bench.
• see what percentage of these bacteria were able to maintain their plasmid.

This work will be developed in different sections. We will first justify our approach of the simulation, then describe our model and explain bacterial growth and plasmid transmission. We will finally make an assessment of our model, explain our approach to validate it and give our perspectives for this project.

1. Multi-agent modelling

The definition

In informatics, a multi-agent system aims to represent intelligent agents which interact with one another and with a specific environment. In our case, our agents are bacteria, dispersed randomly on a grid (our environment). The bacteria are submitted to successive actions such as growth or division, and have specific attributes such as a an individual cell mass, or more importantly a plasmid. Our model aims to provide friendly users with information about bacterial growth. If you wish to evaluate a risk of contamination, or to experiment with parameters to characterise bacterial plasmid transfer or plasmid maintenance, you are welcome to test it out!

Why have we chosen this model?

As stated before, our modelling choice was to implement a multi-agent systems. Multi-agent modelling is frequently used to model biological phenomena. It stands out against continuous mathematical modelling, which is often used for predictions at a population level[1].
Multi-agent modelling offers different advantages :

• Stochasticity : contrary to mathematical deterministic equations, it is much easier to induce randomness in multi-agents models.
• Heterogeneity within a population.
• Interaction between the different agents

2. Overview

Our programming choices

Our main concern in this project was the rapidity of the simulation. Indeed, bacteria can quickly develop, and our processor may have to face a horde of ever-growing agents. Hence, we chose to implement our simulation in C++.

Our program's dependencies are detailed in the software section.

Creating the agents and environment

Initially, an empty lattice is created, containing n number of squares. This number is determined by the height and length of the lattice provided by the user, and set by default at 1000x1000. A square is identified by its id in the lattice and can contain bacteria. If there is more than one bacterium, the bacteria are piled up in the square, with of course a limit to the piling,also set by the user.

The bacterial agents are then created, and randomly set in different squares. Each bacterial cell possesses certain characteristics such as a mass, a volume, an identifier of the square the cell is in etc.

3. How does it work?

Bacterial growth

This model can de divided into two main parts : the growth of the bacterial population and the transmission and maintenance of plasmids in the population.

For the growth of our bacterium agents, we tried two different implementations. The first one is an adaptation of bacterial growth implemented for the first time in Bacsim [2] and based on Donachie and Robison model for cell division. The second is adapted from the Indisim methodology [3] for bacterial growth simulation.

Plasmid loss

Bacterial plasmids are extra-chromosomal genetic elements that can be transferred from one bacterium to another. We chose with this model to implement the horizontal and vertical transfer of genes between these bacteria.

The vertical transfer of genes is the transmission of a plasmid from a cell to its daughter cell after division. During the division, it is assumed that the daughter bacterium can fail to receive the plasmid with a given probability p : this phenomenon is known as segregative loss. As the probability is directly taken from data from the scientific press [4], and as its source doesn't take into account the copy number of plasmid, we also chose not to.

Horizontal gene transfer, also known as conjugation is the direct transfer of genetic material between two bacterium located near each other. Conjugation happens for each plasmid-bearing cell at each time-step. If there is a plasmid free cell in a neighbour square, conjugation can occurs at a rate also taken from press to fit experimental data. It is also considered as an instantaneous event, thus being a simplification of the real process.

We also consider plasmid cost for a bacterium. Indeed, when there is no antibiotic in the environment, plasmid-free bacteria have an advantage over plasmid-bearing ones.

4. Assessment

Our actual version

Our actual version implements in a simple way bacterial growth and plasmid transmission and loss. A graphical interface allows the user to set different parameters and to run a simulation which outputs a figure plotting the number of bacteria as a function of time (as you can see below):

Furthermore, we also tried to put to the test the data given by the simulation. We used for that experimental data [5] of different densities of donor bacteria and recipients on agar slides at stationnary phase in function of initial cell densities.

Unfortunately, the figures obtained were not conclusive. We did not obtain similar curves between simulation and experimental data. This could be due to two main facts :

• first, the simulation time chosen (10 hours ) was not important enough to see likeness between the two sets of data.
• second, we set our bacteria into two states ( donors or recipients ) and didn't take into account the « transconjugant » state.

A bacterium becomes a transconjugant when it acquires a plasmid. Its properties are then different from a donor bacterium.

Prospects

As for now, we created a simple multi-agent model for bacterial growth and interactions. This model can be used as a base to more specific simulations on those subjects. Nevertheless, if we could continue this project we would tackle a few issues, such as :

• Create a transconjugant state and its repercussions.
• Create a plasmid agent with its own properties, that would allow to test more specific cases.
• Optimize the memory allocation to obtain results more quickly.

We hope that this project can help future Igem teams to develop bacterial simulation models! If one of you fellow igemer end up on this page (and if you are interested by this project), you are welcome to contact us!

Our code can be found on github, and installation instructions on the software section.

We would also like to thanks fellow iGEM teams for helping us on our model, and providing us with the 3D illustrations! You can find their wikis below :

Thank you iGEM Insa-Lyon, iGEM Aix-Marseille and iGEM Toulouse!