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Team:Marburg:Safety:Modelling
From 2014.igem.org
Modelling cellular behaviour and robustness of the SURFkiller
In order to predict the behaviour of our SURFkiller, we created a model of our system. For this we used MATLAB software environment. The aim was to simulate cellular protein synthesis in different situations, and based on this information predict the robustness of the SURFkiller. Modelling was based on the following parameters:
| Parameter | Description |
|---|---|
| [mx] | mRNA concentration |
| α0,x | Maximum transcription rate |
| βx | Protein synthesis rate |
| δmx | mRNA degradation rate |
| δp | Standard dilution rate of the protein due to cell division |
| δR | Degradation rate of TetR due to LVA tag |
| Κx | Dissociation (Equilibrium) constant |
| nx | Hill coefficient |
| [Χ] | Protein concentration |
The mathematical equations we based our model on are given as:
a) Production of Antiholin
b) Production of Holin
c) Production of TetR
d) Production of the ribosome-hibernation factor YvyD
e) Production of the ribosomal protein RpL5
Challenging different SURFkiller scenarios in silico
To understand behaviour and robustness of SURFkiller in our model, we simulated several scenarios which would pose a challenge for the SURF killer. The efficient system would perform its function under virtually any conditions, and do it in in shortest possible time period.
Scenario 1: A SURFkiller-equipped GMO leaves the lab
The organism leaves the lab environment. Concentration of the IPTG anti-repressor quickly drops to minimal levels, as a consequence of the degradation and diffusion through the cell membrane. In this case the critical variable is the concentration of the L5 essential ribosomal protein. The results are shown in graphs below.
At the time point T=200 min, the mRNA concentration sharply drops, production of the L5 protein stops, and its concentration in the cells starts to decrease. If we assume that a cell needs around 2000 functional ribosomes in order to survive the cell death occurs at latest when the level of the L5 protein drops below 2000 nM. A concentration of 2000 nM in the volume of a cell, which is about 1 fL, equals about 2000 molecules. From our simulation we can see that the current number of ribosomes is below the critical number of 2000 at latest 60 minutes after the cell leaves the lab environment even if we assume that every L5 molecule leads to the formation of a functional ribosome.
Case 2: Mutations compromising modular functions of the SURFkiller
The efficiency of a kill-switch can be compromised with mutation that may occur on one of the promoters used in the system. SURF killer is designed to remain robust even in these situations, incorporating a secondary toxin-antitoxin system (Holin-Antiholin) that balances promoter function in our system. In this case we simulated a situation where one of the LacI promoters gets constitutive. L5 protein is always produced in this case, and doesn't cause death of the cell. However, since the toxin is also under control of the same promoter it also gets produced.
As the organism leaves the lab environment, levels of antitoxin production start to sink, widening the gap between the levels of toxin and antitoxin in the organism. The critical concentration of toxin in the cell, in the case of T4 Holin, is around 1000-3000 molecules. Since number of free Holin molecules dictates death of the cell, we concentrate on the difference between toxin and antitoxin levels in the cell. Even if we take the worst case, where 3000 free T4 Holin molecules are needed, our model shows that the cell lysis will occur at latest 30 minutes after it leaves the lab environment.
A variation of this scenario could be when a mutation occurs after the bacteria leave the lab but before they die due to the lack of L5.
Figure legend:????
The mutation occurs at the T=250 min in the simulation depicted in graphs above, and we can see how the concentration of both L5 protein and T4 Holin rebounds after the initial drop caused by the bacteria leaving the lab. Antiholin production is not affected by this mutation, as it is located on another module in the system. Regardless of the mutation, Holin-induced cell lysis still occurs at latest 30 minutes after the mutation. Otherwise, cell dies from the lack of the L5 protein, as in the first case.
Scenario 3: Rpl5 is lost from SURFkiller
For our third scenario we decided to test the unlikely case where the L5 encoding gene is removed from the operon under control of the Lac-promoter, for instance by the means of homologous recombination. It is then possible that the levels of the L5 protein will be high enough in the cell while the difference between Holin and Antiholin is kept low, even if it escapes the lab. The third security layer of our SURF killer is designed for this case, and activated if all other security measures get compromised.
Outside of the lab environment TetR protein translation stops, and its concentration starts to sink, as shown with the red line in the graph above. As its concentration sinks below the threshold level (around 20 molecules), it is unable to repress the constitutive promoter and the yvyD gene gets expressed starting synthesis of the protein, shown in blue. As YvyD levels rise, they dimerize more and more ribosomes, which in the end result in a cell death. The short period of YvyD production at the beginning is due to the fact that level of TetR protein starts below 20 molecules at the very beginning of the simulation.
Sensitivity of the simulation on the parameters used
In order to make sure that our simulation adequately describes real-world scenarios we ran a calculation on how our results depend on different choice of parameters, primarily transcription rates of mRNA and translation rates of proteins. Choice and calculation of these parameters is one of the most challenging tasks in modelling process, so this simulation sheds light on how would our SURF killer function, even with non-optimal parameters.
As we can see from the graphs above, if we vary the standard translation rate of 2.3 min-1 there is comparatively small change in the time needed for the cell death to occur. If the translation rate is below 0.6 the cells cannot survive even under lab conditions because the steady state number of ribosomes is below 2000. Similar is applicable to variations in transcription rate. If the assumed transcription rate of 10 nM/min doubles, the expected survival time of the cell is around 25 minutes longer.
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