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Revision as of 20:51, 7 October 2014
Modeling
Maths.. maths is fun!
Modeling and Analysis of Signaling Pathways
Introduction
The models for each system were developed using three different approaches. 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.
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 2 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 3, 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.
Stochastic confirms “switch” behaviour
