Model To Predict Fluoresce Intensity and Wavelengths Given Parameters
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.
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.
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:
$$ y = 100.2 x ^{1.43154} $$
Proof
When constructing our proteins with our current method, there were 3 vectors we could order from
Therefore any combination is equal to sgRNA vector chances of 1 in 64
Times order 1 in 6
Types of brick used Times brick in 1 in 102
Therefore 102 x 6 x 64, any combination has the probability of 1 in 39168
Randomness comes from the fact the system relies on Brownian Motion, a random process to create these combinations.
However, in order for a movement to fall under Brownian Motion, it must fulfill a condition where the process must have continuous paths. This is not true as once the structures begin to form, the paths stop (they do not collide off each other elastically, but rather, combine.) Furthermore, there would be no transposition once it's in the bacterium otherwise it would become biased towards options that put less metabolic stress on the bacterium.
This is a limitation on the system which could be solved by using metabolites, which are random as shown by
this paper.
