Team:Glasgow/Modeling

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Section 1: Modelling of Bacteria Random Walk
Firstly, we created a very basic 2D model of a flagella propelled bacterium. This was heavily based on the “random walk” model we mentioned previously, only we introduced a small degree of order, based on a more extensive and all-encompassing model created by Dillon, Fauci and Gaver in 1995.(link to paper?)DOI: 10.1006/jtbi.1995.0251

In order to simplify the model, we made a number of assumptions. These are:

• Tumbling is instantaneous
• Chemotaxic gradient is not a factor
• An E.coil cell can be represented as a sphere
• Speed is constant (20ms^-1)

The movement of a bacteria through a medium is described thus:
1. The bacteria is moving at a random angle at a certain speed.
2. After a certain time (the “run” time), the bacteria reorientates itself (the “tumble”),
and sets off at a different angle. This run time can be influenced by the chemotaxic gradient,
if present.

The images below describe how the run times are influenced: if the bacteria is on a path towards the "food", it is unlikely to change direction.

Based on the previous research, we decided that the tumble angle would be picked each time from a normal distribution, having a mean of 68 degrees and a standard deviation of 36. This angle would be either added or subtracted from the previous position. The speed was set at a constant 20us-1 (chemotaxis was not a factor). Given angle, speed, and time, new x and y coordinates are calculated, and a line plotted to show the path. This process could be repeated for any number of steps to show the theoretical path of a bacterium.

This is the result of a MATLAB simulation using the angle and run time distributions stated above. Of course, every run was entirely random. The gif shows the path of 10 different bacterium, and how they move out from a central point. Each makes 300 steps. Roughly, the gif is 10x faster than normal movement (assuming the mean run time is 1 second).

And here's random walk run that happened to look like a dog.

Having obtained a reasonable working model of a bacteria's natural movement, we could now investigate the effect of the buoyancy provided by the gas vesicles we'd be introducing. With this information, we could make informed decisions about the direction of the project.

Intro

Bacterial Buoyancy