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Team:Glasgow/Modeling
From 2014.igem.org
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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
Figure 1: Basic Run and Tumble
In order to simplify the model, we made a number of assumptions. These are:
- Tumbling is instantaneous
- Chemotaxic gradient is not a factor and so the run time has an element of randomness
- An E.coil cell can be represented as a sphere
- Speed is constant (20μms-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, which will induce directionality in the motion.
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.
Figure 2: Bacterial movement with no chemotaxic gradient
Figure 3:Alteration of bacterial random walk with chemotaxic gradient present
Based on the previous research, we decided on some distributions for our models' random parameters.
Tumble Angle
- Normal Distribution
- Mean: 68 degrees
- Standard Deviation: 36 degrees
- Exponential Distribution
- Mean: 1 second
Figure 5: Giff displaying path of 10 bacteria
Figure 4: a 100 step Random Walk Simulation
This is the result of a MATLAB simulation using the angle and run time distributions stated above. The gif shows the path of 10 different bacterium, and how they move out from a central point. Each makes 300 steps (so please note than the graphs are not directly comparable. Rather, they should display the randomness of the motion). Roughly, the gif is 10x faster than normal movement (assuming the mean run time is 1 second).
The simulation we'd created did, of course, have a significant element of randomness. Below is an example of a run that provided us with a random (but strangely familiar) bacterial path.
Figure 6: "Random 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 |
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