Motility Data Acquisition
Using manual tracking we hope to acquire sufficient data to obtain B. Subtilis motility properties such as run velocity, run duration, tumbling angle and tumbling duration. This is done by first tracking cells and obtaining coordinate points, and from these points extracting out the above mentioned motility characteristics. The next phase would be to study the statistical distribution of these various properties, and compare them to our own statistical models of B.Subtilis motility. Our approach to collecting motility data is shown in the figure below:
Approach to Motility Data Collection
Materials
We will be using the Zeiss Axiovert 200 inverted microscope with a fully motorised stage, controlled by Improvision Volocity acquisition software. This system offers a full incubation chamber with temperature and CO2 control, a large range of filter sets from UV to farred and a highly sensitive 1300x1000 pixel camera for fast lowlight imaging. Video images are captured into memory by the system at a basal video frame rate of 16.3Hz. This can be further increased by performing binning.
Method
It was concluded from the validation of tracking software that manual tracking provides for the most reliable form of tracking. We intend to use manual tracking to track B.Subtilis and extract twodimensional coordinate data points which is described by the trajectory of the cells.
Data Extraction
We will input coordinate points obtained into algorithms to extract motility properties such as run velocity, run duration, tumbling angle and tumbling duration. Errors associated with our data extraction algorithm will also be assessed using synthetic videos. Once motility data extraction is complete, we may go on to model the motility of B.Subtilis.
Algorithm Error Analysis
Synthetic data was used as an input to assess the errors associated with our algorithm used to extract run velocity, run duration, tumbling angle and tumbling duration from twodimensional coordinate data. The data extracted from the algorithm used is then fitted with models used to construct the bacteria's trajectory. Errors associated with the model's parameters are then determined.
The following assumptions were made:
 During tumbling the bacteria's displacement and hence velocity is zero.
 Bacteria's run velocity is averaged between periods when tumbling takes place.
Synthetic trajectory was constructed using the following parameters:
 Run Velocity: Normal Distribution, μ=55, σ=2
 Run Duration: Exponential Distribution, λ = 1.
 Tumbling Angle: von Mises Distribution, a=0, k=1.
 Tumbling Duration: Exponential Distribution, λ = 10.
Posterior (μ,σ) for run velocity
 Posterior λ for run duration
 Posterior λ for tumbling duration




(μ,σ) at Maximum Posterior = (54.5879,3.2300) Mean of μ = 54.5711, Std of μ = 0.3743. Mean of σ = 3.2950, Std of σ = 0.2695
 λ at Maximum Posterior = 0.5460 Mean of λ = 0.5539, Std of λ = 0.0644.
 λ at Maximum Posterior = 6.9800 Mean of λ = 7.0791, Std of λ = 0.8229.

Errors at Maximum Posterior Δμ = 0.749%, Δσ = 61.5%
 Error at Maximum Posterior Δλ = 45.4%
 Error at Maximum Posterior Δλ = 30.2%

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