Team:UNOTT/Modelling

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
  • Are Our Constructions Random?

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




    • Are our constructions random

      When constructing our proteins with our current method, there were 3 vectors we could order from
      $$ \textrm{sgRNA plasmid} \left\{\begin{matrix} 1 & 2 & 3\\ 1 & 1 & 1\\ 1 & 2 & 3 \end{matrix}\right. $$ $$ \textrm{etc.} \therefore \textrm{there are 64 variations of arrangement} $$ $$ \therefore \textrm{1 / 64 chance of each variation, which is randomly constructed} $$ $$ \textrm{Order of Plasmid Bricks} \begin{Bmatrix} 1 & 2 & 3 \\ 2 & 1 & 3 \\ 3 & 2 & 1 \\ 3 & 1 & 2 \\ 2 & 3 & 1 \\ 1 & 3 & 2 \\ \end{Bmatrix} $$
      Types of brick used
      • 1 in 12 promoters per brick
      • 1 in 3 terminators per brick
      • 1 in 3 fluorescent per brick
      • 1 in 102 proteins per brick
      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.