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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 the biochemical pathways in the Lung Ranger, we used a variety of mathematical tools to create algorithms and simulations.This allowed us to accelerate the development and testing of various hypotheses.
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 our engineered PQS system.
Results
Sigmoidal Expression of mCherry in PQS System
When our PQS system was induced with synthetic PQS, no mCherry was expressed. We attempted to use mathematical modelling 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.
Fig 1. shows how the concentration of mCherry increases over time. The general trend is that the rate of expression of mCherry is proportional to PQS signal strength. Most striking is the rapid switch from low expression to high expression as the signal is increased.
When the gradients of mCherry were plotted against PQS concentration, Fig 2, the result was a sigmoidal curve with sharp transition located between signal values of 0.1µM and 1µM. Below this, expression was effectively zero, and above it, expression was uniformly high.
These results suggest that the levels of synthetic PQS investigated in our engineered pathway were too low and that the ten fold increases used in the experiments would yield no measurable change in mCherry expression provided the signal level was below the threshold predicted by the model. To investigate this further we went on to carry out stochastic simulations of the system.
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
