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Team:Dundee/Modeling
From 2014.igem.org
Modeling
Maths.. maths is fun!
Modeling and Analysis of Signaling Pathways
Introduction
In order to help analyze, construct and optimise these biological pathways in the Lung Ranger, we used mathematical modelling. In order to do this we:
-Used a variety of mathematical tools to create algorithms and simulations
-Developed and tested hypothesis with acceleration of results compared to the experiments.
Objectives
Our main target was to interact with the wet team to construct the Lung Ranger.
Methodology
As shown in figure 1 each of the approaches; ordinary differential equations (ODEs), stochastic simulation algorithm (SSA) and NetLogo, provided a different understanding of each system.
PQS
Objectives
We wanted to find a method of increasing the expression of mCherry in the PQS system.
Results
Sigmoidal Expression of mCherry in PQS System
When the PQS system was induced with synthetic PQS, no mCherry was expressed and so the wet team sought the advice of the dry team to find out why and how the situation could be resolved.
After constructing a series of ordinary differential equations (full derivation can be found in the appendix) we established the following relationship between PQS (Se) and mCherry:
Equation (1) was then analysed in MAPLE for varying PQS concentrations using the parameters in table 1.
Figure 1 shows how the concentration of mCherry increases over time. The general trend is that at low concentrations the rate of production of mCherry is slow and at high concentrations the production is fast.
When the gradients of d[mcherry]/dt were plotted against PQS concentration, Figure 2, the result was a sigmoidal curve. This implies that for PQS concentrations below 0.1𝜇M there should be low mCherry production and above 1𝜇M there should be high mCherry production.
We predict that the low expression could correlate to P.aeruginosa being in an acute planktonic state and the high expression to a chronic biofilm state.
Stochastic confirms “switch” behaviour
Once the PQS “switch” was found using the sigmoidal graphs for low and high production of mCherry, we were able to construct stochastic simulations in order to visualise this with regards to a single cell model. The simulations were able to show how varying the PQS signal would promote various level of mCherry expression over one cell cycle.
The stochastic mean in A seems low in comparison to the rest of the realisations which implies there were many reactions which didn’t express any mCherry. Figure 5 reveals that in 77% of the realisations for 0.02μM of PQS, no mCherry was produced. Increasing the PQS concentration by 10-fold, increases the number of reactions fired to 90%. For PQS concentrations greater than 2μM all the reactions fire in the given time frame.
What is interesting to note is that once the reactions have started they produce mCherry at the same rate, shown by the parallel realisations in figure 4. We can conclude that a rate limiting step in the system is the probability that the reaction for mCherry expression starts.
The stochastic results correlate with the deterministic results as the drastic change between low and high level production of mCherry remains between 0.2𝜇M and 2𝜇M as shown in table 2.
Increasing promoter numbers increases mCherry expression
Although we concluded from SSA that the firing of the mCherry promoter was a rate limiting step, we wanted to provide the wet team with more feedback on how to increase mCherry production. After testing several hypotheses it was found that increasing the number of promoters had the greatest impact on the expression of mCherry.
When the number of promoters were increased by 10-fold (30 to 300) there was a corresponding 10-fold increase in the “high” mCherry expression as shown in figure 7. We informed the wet team that increasing the number of promoters would significantly increase mCherry expression. However since its not possible to increase the number of promoters the wet team looked for a second system to detect P.aeruginosa.
Conclusions
BDSF
Objectives
Results
BCAM0228 phosphorylated by unknown compound
When the Burkholderia system was tested by the wet team, they found that even in the absence of BDSF, GFP was still expressed and needed our help for answers.
Before we could hypothesise why the system wasn’t working we had to gain an understanding of what should be happening.
Our deterministic model (figure 8) shows that in the absence of signal, no GFP is produced - the result the wet team were hoping to see. Conversely, when BDSF is present GFP is produced, shown in figure 9.
From our system of equations we know that the expression of GFP is dependant on the levels of BCAM0228[P]. We hypothesised that one of the ways our cell could be expressing GFP in the absence of signal was by having extra BCAM0228[P]. This suggests that an unknown compound is phosphorylating BCAM0228 in our cell.
When figure 10B is compared to figure 9B the overall expression is higher because BCAM0228 is being constitutively phosphorylated. We also infer that the presence of BDSF has very little effect on the expression of GFP. Therefore we can conclude the BDSF signal has no quantifiable effect on the production of GFP.
Conclusions
DSF
Objectives
