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Team:Glasgow/Modeling Part2 align=
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Section 2: Bacteria and Buoyancy
With the main focus of our project being the gas vesicles, we decided to model the effect that they would have on the
bacterium's path.
The net force on the bacterium should be positive for floatation to occur. This force is composed of three components:
The buoyancy force, the force due to gravity and Stokes drag force. They are applied thus:
With some preliminary calculations, we decided that the movement would be essentially linear – while there is an acceleration phase at the beginning while the forces are unbalanced, the time it takes to reach a constant terminal velocity is negligible compared to the time for which we're observing the system.
One of the problems with this model is finding the E. Coli mass that will be replaced by the vesicles – we need this in order to find the final density. This was estimated by replacing a given volume (5, 10, 15 etc), with an equivalent (lower density) volume of gas vesicle.
We would use the density and the assumptions above to calculate a new density for the bacteria. This is put into the terminal velocity equation:
The following graphs show the effect of gas vesicles on the upwards speed of E. Coli, over 24 hours.
Click here to edit this page
bacterium's path.
The net force on the bacterium should be positive for floatation to occur. This force is composed of three components:
The buoyancy force, the force due to gravity and Stokes drag force. They are applied thus:
Normally, a bacterium's density is greater than water (E.Coli is about 1100kg/m^3, compared to water's 998kg/m^3
at 20 degrees Celcius). The presence of gas vesicles replaces some of the mass of the cell with lighter gas,
thus reducing the density.
As with the random walk model, we'll state our assumptions up here.
- The density of a gas vacoule would be 250kg/m3, a value obtained by Walsby in his study of the cyanobacteria anabaea flos-aquae
- It is believed that the bacteria will increase in volume as a result of gas vesicle production. We'll roughly estimate this to be half the % of total volume the vesicles will fill.
- Again, we assume the bacteria is a sphere.
With some preliminary calculations, we decided that the movement would be essentially linear – while there is an acceleration phase at the beginning while the forces are unbalanced, the time it takes to reach a constant terminal velocity is negligible compared to the time for which we're observing the system.
One of the problems with this model is finding the E. Coli mass that will be replaced by the vesicles – we need this in order to find the final density. This was estimated by replacing a given volume (5, 10, 15 etc), with an equivalent (lower density) volume of gas vesicle.
We would use the density and the assumptions above to calculate a new density for the bacteria. This is put into the terminal velocity equation:
The following graphs show the effect of gas vesicles on the upwards speed of E. Coli, over 24 hours.
Click here to edit this page
