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Team:Glasgow/Modeling
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Revision as of 15:38, 6 August 2014
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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:
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.
These is the result of a MATLAB simulation using the angle and run time distributions. Of course, every run was entirely random. The gif shows the path of 10 different bacterium, all spreading out from a central point. The timing of this is roughly x10 faster than real life.
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 20ms-1.Given angle, speed and time, new x and y coordinates are calculated and plotted. This process is repeated for any number of steps to show the theoretical path of a bacterium.
These is the result of a MATLAB simulation using the angle and run time distributions. Of course, every run was entirely random. The gif shows the path of 10 different bacterium, all spreading out from a central point. The timing of this is roughly x10 faster than real life.
And here's random walk run that happened to look like a dog.
