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Revision as of 13:32, 6 September 2017
Modeling
During the plasmid constructions, the wet lab needed to know what to expect and we needed to be able to test every combination. Modeling allowed us to do this easily, within time the constraints and safely.
- Constitutive Gene Expression
- Absorption and Emission Wavelengths
- Gene Transcription Regulation by Repressors (CRISPR)
- Relationship between Max Fluorescence and Protein Concentration
- Are Our Constructions Random?
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Constitutive Gene Expression For Protein and mRNA Expression over Time
During discussions with wet-lab, we concluded that the gene expression would be unregulated and the gene would always be activated. After reading literature so see which model would satisfy these conditions, and it was found the constitutive gene expression model was suitable to guide the model.
The first step was to take the general model from literature and apply it in our scenario using the proteins (GFP, ECHP, RFP.)
$$ sfGFP \underset{Transcriptin}{\rightarrow} mRNA \underset{Translation}{\rightarrow} sfGFP $$ $$ mRNA \underset{Degradation}{\rightarrow} \oslash $$ $$ sfGFP \underset{Degradation}{\rightarrow} \oslash $$This tells us that the gene would undergo transcription to produce mRNA and the mRNA would undergo translation to become proteins which would be expressed and output fluorescence. At the same time, the concentration of protein and mRNA would undergo degradation and decrease to 0.
The second step would be to use the Law of Mass Action to add the degradation component for a more accurate concentration for protein and mRNA overtime. This model can be described as:
$$ mRNA = k_{1} -d _{1 } mRNA $$ $$ Protein = k_{2} \cdot mRNA - d_{2} \cdot Protein $$
This is important because we can use this model to calculate the concentration of proteins we can expect over time. This is useful as we can use this information to calculate the total emitted light spectra during the time period which is what we are looking for in our system. However, the constants and variables are individual for each protein and which means each protein would need it's own model to describe the behavior. These constants were found using literature (for GFP) and lab results (the rest.)
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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
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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} $$- 1 in 12 promoters per brick
- 1 in 3 terminators per brick
- 1 in 3 fluorescent per brick
- 1 in 102 proteins per brick
