Team:UNOTT/Modelling
MODELLING
Overview
Download our models and source code from our gitHub page
A major problem the project faced is that the comparison process of the fluorescence proteins wouldn't be possible to be investigated with all combinations as it would take too long.
To answer this problem, the team will attempt to model the fluorescence spectra over time expressed by the proteins given different. First, the type of gene expression would need to be identified and then, would be modified to considered the effects of inhibition and finally, be applied over time to see how much expression would occur at a certain time period. The team will use Mathematical modeling such as Ordinary Differential Equations because they are easy to convert into programming in order to build components for the simulation.
As a side project, the team will also investigate into whether our method is random and unique by investigating how many combinations we can make and whether we can accurately predict which combination will occur.
Constitutive Gene Expression For Protein and mRNA Expression over Time
Biological insight had told us we need a model with constant gene expression. Investigating models from literature 1 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.)
Figure 1 $$ sfGFP \underset{Transcriptin}{\rightarrow} mRNA \underset{Translation}{\rightarrow} sfGFP $$
The equation above describes the process of which the gene undergoes transcription to produce mRNA. The mRNA carries the genetic information copied from the DNA which codes for protein. The expression of protein, can therefore, be measured by the fluorescence which is the desired output of the system.
Figure 2 $$ mRNA \underset{Degradation}{\rightarrow} \oslash $$ $$ sfGFP \underset{Degradation}{\rightarrow} \oslash $$The two equations above state the same time, the concentration of protein and mRNA would undergo degradation which means the concentration would drop. However, since there is always protein and mRNA being created, over time, the creation and degradation keep the concentration constant. 2
We can apply Law of Mass Action combine both equations for the concentration of protein and mRNA over time. This model can be described as:
Figure 3 $$ mRNA = k_{1} -d _{1 } mRNA $$ $$ Protein = k_{2} \cdot mRNA - d_{2} \cdot Protein $$Where...
- mRNA is the concentration of mRNA
- Protein is the concentration of Protein
- k 1 is the constitutive transcription rate. This represents the number of mRNA molecules produced per gene, per unit of time.
- d 1 is the mRNA degradation rate
- k 2 is the translation rate. This represents the number of protein molecules produced per mRNA molecule, per unit of time.
- d 2 is the protein degradation rate.
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 parameters for each protein would need to be found. These constants were found using literature 3 (for GFP) and lab results (the rest.)
1 GB Stan, 20137. Modeling in Biology. London, the United Kingdom: Imperial College London. p, pp.59-65.
2 See Non-Inhibited conditions from Figure 5 Gene Transcription Regulation by Repressors (CRISPRi) - Concentration over Time
3 See Relationship between Max Fluorescence and Protein Concentration for more details
Gene Transcription Regulation by Repressors (CRISPRi) - Concentration over Time
The next step in developing our simulation was to calculate our protein concentration at any given time when using CRISPRi. Discussion with wet-lab revealed our method would be using CRISPRi as a repressor, which works by inhibiting the expression of one or more genes by binding to the promoter region 1 . The expanded mRNA and Protein concentration models from the Constitutive Gene Expression Model 2 were modified to include the element of repression from the CRISPRi inhibition.
$$ Gene \overset{Repressor}{\rightarrow} mRNA \rightarrow Protein $$ $$ mRNA \underset{Degradation}{\rightarrow} \oslash $$ $$ sfGFP \underset{Degradation}{\rightarrow} \oslash $$This change can be applied to the Law of Mass Action 3 :
$$ m = k_{1} \cdot \frac{k^{n}}{k^{n} + R^{n}}- d_{1}m $$ $$ p = k_{2} m - d_{2}p $$Where...
m is mRNA concentration, p is Protein concentration, R is Repressor, k1 is Max Transcription Rate, k is the Repression Coefficient, n is number of repressors that need to cooperatively bind the promoter to trigger the inhibition of gene expression (Hill Coefficient), R is Repressor, d1 is mRNA degradation rate, d2 is Protein degradation rate
The value for these constants and variables were taken from literature and calculating them 4 but later, adjusted to the lab results.
Figure 6
Figure 6 shows the structure which underwent CRISPRi inhibition are expected to produce lower concentration of the protein whose expression were are inhibiting. This is important as it means the team can calculate concentration of proteins which are inhibited and compare them to the control conditions as well as giving the correct concentration for the simulation.
Furthermore, by having a model which can calculate the protein concentration at any given time, we can deduce how much fluorescence is being emitted at that time period by the bacteria
4 See Relationship between Max Fluorescence and Protein Concentration
STEP 5: Freeze Drying & Revival
For Key. coli to work as intended and not deteriorate we need need to things to occur:
- The E. coli cells must be kept inactive so that nutrients is not depleted causing the transformed cells to die
- The E. coli cells must be able to be activated after inactivation to allow the fluorescent genes to be expressed to give the key its unique fluorescent code which will allow access to the appliance.
To accomplish this, we chose to freeze dry the cells within the key. This involved
STEP 6: CRISPRi & gRNA Efficiency
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