Trondheim iGEM 2013

Modelling of the Pm/Xyls Promotor system

The Pm/Xyls promotor system is a positive regulator system where the regulator molcule, Xyls, is constitutivly produced. When Xyls binds to the inducer, m-toluic acid, this complex is able to bind to the Pm promoter(see figure 1). Binding to the promoter facilitates binding of RNA polymerase (RNAp) making it active (RNApa). This enables the production of mRNA in (1) elongation step, and (2) translation. The mRNA will be translated into the recombinant protein, or in our case, RFP. Over time mRNA and RFP will be degraded to some extent.

Figure: Overview of how the Pm/Xyls Promotor system funtions. Production of recombinant protein is dependent on access to the inducer m-toluic acid.

The reaction equations in the Pm/Xyls promotor system are listed below. The degradation of mRNA and RFP will inhibit an exponential growth in their production, and after some time the levels of mRNA and RFP will stabilize around a steady state.

A deterministic simulation of the system was run on Cain software with the parameters as viewed in figure 2. Only the number/consentration of the inducer was varieted. A .zip file with all of the modeling files can be downloaded here.The csv files are named according to the number of inducer that was applied in the deterministic simulation. Stochastic analysis of the system, also using the Cain software, shows that fluctuations are much larger when the inducer level is low. This is to be expected, since stochastic effects are known to be important in many cases where molecule numbers become small (much less than 100). The overall (and average)results of the stochastic simulations agreed with the deterministic ones, and for simplicity we only show the deterministic data.

Figure 2: Overview of parameters applied in the Cain program

The labels of the species (reaction molecules) are as follow: XLS = Xyls, inducer = m-toluic acid, XLSinducer = complex of XylS and m-toluic acid, DNA = plasmic DNA, XDNA = Binding of XLSinducer to the DNA, RNAp = RNA polymerase, RNApa = active RNA polymerase, E = elongation, RFP = fluorescent protein.


Varies starter concentration of inducer (0, 0.06, 0.3, 0.6, 1.2 and 6 µM) gave the result as indicated in figure 3 and the table below.

Figure 3: Different concentrations of inducer (0 to 6 uM) was applyed in the deterministic simulations, yeilding different amounts of RFP.

Start consentration (µM) of inducer Molecules of inducer Consentration (µM) of RFP (steady state) Molcules of RFP (steady state)
0 0 0 0
0.06 100 0.51 850
0.3 500 0.63 1050
0.6 1000 0.66 1100
1.2 2000 0.68 1135
6.0 10 000 0.71 1180

As the levels of inducer increases, the steady state of the protein product increases up until it reaches 1200 molcules. An huge increase in inducer over 10 000 molecules will not give a RFP steady state of over 1200. The steady state is determined by the rates K4, K5, D1 and D2. During the model building and working with analysis of the model (both deterministic and stochastic), we noticed that the system would easily enter saturation: The levels of the inducer were irrelevant to the steady state levels of the RFP. Only when the following conditions are met: K1 « K11 and K2 « K22, we will find a tunable response of the system with varying inducer levels. When these requirements are not met, the system will not dependent on the level of inducer as the system early will be saturated. The reason for this is that there is a limited number of sites in the available DNA for binding with the active inducer, so that elongation and translation can take place. When these sites are fully occupied, further increases of inducer levels will have no effect. While the Xyls system typically is in a high-copy plasmid, the number (~30-50) of binding sites is a very small number compared to the concentrations of inducer and xyls molecules.