Difference between revisions of "Team:UNOTT/Modelling"

Revision as of 13:52, 3 September 2017

Modeling

The central aim for the modeling would be to write a simulation for the wet lab to aid construction of the bacteria.

Download our source code from our gitHub page

Constitutive Gene Expression
Absorption and Emission Wavelengths
Gene Transcription Regulation by Repressors (CRISPR)
Relationship between Max Fluorescence and Protein Concentration
MISSION: CONTROL PLASMID TRANSFORMATION

General Constitutive Gene Expression

Constitutive Gene Expression For Protein and mRNA Expression over Time

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.

Absorption and Emission Wavelengths From Given Concentrations of sfGFP, mRFP & ECFP

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

Gene Transcription Regulation by Repressors (CRISPR) - Concentration over Time

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:

Relationship between Max Fluorescence and Protein Concentration

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:

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

MISSION: CONTROL PLASMID TRANSFORMATION

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