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Revision as of 13:12, 28 August 2017

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It was decided that the central aim for the modeling would be to write a simulation for the wet lab to use to show what they can expect during the construction of the bacteria. The parameters that were decided for the model would be the protein concentrations and wavelength of the lasers that would enter the culture.

Download our source code from our gitHub page

Assuming the gene expression was unregulated and the gene is always on, the constitutive gene expression model was used to guide the model.

$$ sfGFP \underset{Transcriptin}{\rightarrow} mRNA \underset{Translation}{\rightarrow} sfGFP $$ $$ mRNA \underset{Degradation}{\rightarrow} \oslash $$ $$ sfGFP \underset{Degradation}{\rightarrow} \oslash $$

Using the Law of Mass Action, this model can be described as:

$$ mRNA = k_{1} -d _{1 } mRNA $$ $$ Protein = k_{2} \cdot mRNA - d_{2} \cdot Protein $$

Using this, we can calculate the concentration of proteins we can expect over time. This was useful because it allowed us to see how much protein was made which were emitting the light so we could make an accurate prediction of how much intensity there was at a certain amount of time.

Using Shemrock's online fluorescence graph maker, I generated the expected Absorption and Emission wavelengths that are taken in and produced by sfGFP (green), mRFP (red) and ECFP (blue) proteins. This was done through the web app on the website.

This graph tells us the emitted light is expected to be at a higher wavelength than when absorbed. This must be considered in the model as there is overlap between emitted and absorbed wavelengths so some emitted light may be absorbed and re-emitted at a higher wavelength.

This model is important as it guides us when using wavelengths as parameters so we know which wavelengths to use, especially when trying to create a specific color

To calculate our Protein concentration at any given time when using CRISPR, the expanded mRNA and Protein concentration models from the Constitutive Gene Expression Model were used and an element of repression was added to the model as we were using CRISPR as a repressor.

$$ Gene \overset{Repressor}{\rightarrow} mRNA \rightarrow Protein $$ $$ mRNA \underset{Degradation}{\rightarrow} \oslash $$ $$ sfGFP \underset{Degradation}{\rightarrow} \oslash $$

This change can be applied using the Law of Mass Action:

$$ m = k_{1} \cdot \frac{k^{n}}{k^{n} + R^{n}}- d_{1}m $$ $$ p = k_{2} m - d_{2}p $$

Where...

m = mRNA concentration
p = Protein concentration
R = Repressor
k1 = Max Transcription Rate
k = Repression Coefficient
n = Hill Coefficient (number of repressors that need to cooperatively bind the promoter to trigger the inhibition of gene expression)
R = Repressor
d1 = mRNA degradation rate
d2 = Protein degradation rate

When visually modeled using Python:

In order to calculate sample constants before the lab results were in, we looked into literature from lab results of similar studies. This data underwent non linear interpolation where the data was graphed first and as the graph resembled a:

$$ y = k x ^ {n} $$

Fitting where after applying regression, it was found the graph followed a fit of:

$$ y = 100.2 x ^{1.43154} $$