Team:Bielefeld-Germany/Project/Model

From 2010.igem.org

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Construct Maps

Model of BBa_K389015

Fig. 1: Main construct of acetosyringone inducible luciferase expression system containing constitutive expression of the two component receptor system (virA+virG).

Model of BBa_K389016

Fig. 2: Control construct of acetosyringone inducible RFP read out system.

Model of BBa_K389014

Fig. 3: Screening construct of acetosyringone inducible kanamycin resistance read out system.

Fitting the data

As seen in the fig. 1 - 3 the models for the application of the used VirA/G signaling system is quite complex. Due to the fact that there were no further details to interactions between the components of this receptor system in the literature, which are helpful for modelling, and a determination of these parameters would be too time-consuming we decided to fit the vir promoter activity to different concentrations of the natural inducer of the VirA/G signaling system, acetosyringone. As the promoter activity is not directly accessible we decided to measure it by using a reporter gene.

Promoter activity is normally measured in polymerases per second (PoPS). To correlate the concentration of a reporter gene with PoPS a synthesis rate for the reporter gene has to be measured to see how many molecules are produced by one cell in a certain time (Canton and Labno, 2004). This relation can be described as


Bielefeld Produktbildung.jpg
(1)


with the amount of product P, the cell count X and the specific production rate of product molecules per cell and time qP. To determine the PoPS exactly from the specific production rate there is more information needed like the decay of the reporter molecule, the stability of the reporter gene mRNA, the effectivity of the reporter gene's RBS and many more. So we assumed that these parameters do not change in the time of our measurement. In addition we assumed after Canton and Labno, 2004 that


Bielefeld RFUpropP.jpg
(2)


and


Bielefeld ODpropX.jpg
(3)


so the specific production rate can be approximated by the equation (4):


Bielefeld specific production rate.jpg
.
(4)


As the reporter gene accumulates exponentially during the exponential growth phase the amount of product at every time of the cultivation can be described with a fit of the form


Bielefeld Expfit.jpg
(5)


so the specific production rate of each taken sample can be calculated with the derivation of this fit function and eq. (4). In fig. 4 such a fit is shown.


Fig. 4: Exponential fit on the measured RFU plotted against cultivation time of a cultivation of BBa_K389016 in Escherichia coli DB3.1 in LB medium with 10 mg ml-1 chloramphenicol and 150 µM acetosyringone.


The specific production rates qP of all samples of all cultivations made with a specific inductor concentration c are averaged and normalized against the specific production rate of the uninduced system qP,0:


Bielefeld QPN.jpg
(6)


This normalized specific production rate we calculated is commensurate to relative promotor units (RPU) which is commensurate to PoPS (polymerase per seconds) (Canton and Labno, 2004; Pasotti et al., 2009):


Bielefeld QPNRPUPoPS.jpg
(7)


After calculating the qP,n of mRFP in the presence of different concentrations of the inducer acetosyringone a transfer function is determined. Nelson et al. (2002) suggest using a dose response function and fitting it with a logistical equation for the data analysis of receptor systems. So the data was fitted with a function of the form


Bielefeld Doseresponse fit.jpg
(8)


with the Hill coefficient p, the bottom asymptote A1, the top asymptote A2 and the switch point log(x0). Figure 5 shows the measured normalized specific production rates qP,n (eq. 6) plotted against the logarithm of the concentration of the inductor acetosyringone in µM. The fit has an R2 = 0.99.


Figure 5: Transfer function for the part BBa_K389016 (R2 = 0.99).


With this function it is possible to describe the factor ɸI the PoPS of the vir promoter rises in an induced VirA/G signaling system compared to the basal transcription of the promoter depending from the concentration of inducer acetosyringone c added to the medium:

Bielefeld Finale formel.jpg
.
(9)