# Team:Bielefeld-Germany/Project/Model

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== Fitting the data == | == 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. | + | 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 ([http://partsregistry.org/Part:BBa_F2620:Experience/Endy/Data_analysis | + | 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 ([http://partsregistry.org/Part:BBa_F2620:Experience/Endy/Data_analysis Canton and Labno, 2004]). This relation can be described as |

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- | with the amount of product P, the cell count X and the specific production rate of product molecules per cell and time q<sub>P</sub>. 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 [http://partsregistry.org/Part:BBa_F2620:Experience/Endy/Data_analysis | + | with the amount of product P, the cell count X and the specific production rate of product molecules per cell and time q<sub>P</sub>. 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 [http://partsregistry.org/Part:BBa_F2620:Experience/Endy/Data_analysis Canton and Labno, 2004] that |

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+ | [[Image:Bielefeld_RFUpropP.jpg|100px|center]] <div align="right">(2)</div> | ||

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+ | and | ||

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+ | [[Image:Bielefeld_ODpropX.jpg|80px|center]] <div align="right">(3)</div> | ||

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

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+ | [[Image:Bielefeld_specific_production_rate.jpg|150px|center]]. <div align="right">(4)</div> | ||

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+ | 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 | ||

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+ | [[Image:Bielefeld_Expfit.jpg|100px|center]] <div align="right">(5)</div> | ||

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+ | 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. | ||

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+ | [[Image:Bielefeld_ExpFit_auf_RFU.jpg|500px|thumb|center|'''Fig. 4: Exponential fit on the measured RFU plotted against cultivation time of a cultivation of <partinfo>K389016</partinfo> in ''Escherichia coli'' DB3.1 in LB medium with 10 mg ml<sup>-1</sup> chloramphenicol and 150 µM acetosyringone. ''']] | ||

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+ | The specific production rates q<sub>P</sub> 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 q<sub>P,0</sub>: | ||

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+ | [[Image:Bielefeld_QPN.jpg|100px|center]] <div align="right">(6)</div> | ||

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+ | This normalized specific production rate we calculated is commensurate to relative promotor units (RPU) which is commensurate to PoPS (polymerase per seconds) ([http://partsregistry.org/Part:BBa_F2620:Experience/Endy/Data_analysis Canton and Labno, 2004]; [http://partsregistry.org/Part:BBa_J23101:Experience Pasotti ''et al.'', 2009]): | ||

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+ | [[Image:Bielefeld_QPNRPUPoPS.jpg|150px|center]] <div align="right">(7)</div> | ||

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+ | After calculating the q<sub>P,n</sub> of mRFP in the presence of different concentrations of the inducer acetosyringone a transfer function is determined. [http://www.nature.com/nature/journal/v416/n6877/abs/nature726.html 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 | ||

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+ | [[Image:Bielefeld_Doseresponse_fit.jpg|175px|center]] <div align="right">(8)</div> | ||

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+ | with the Hill coefficient p, the bottom asymptote A1, the top asymptote A2 and the switch point log(x<sub>0</sub>). Figure 5 shows the measured normalized specific production rates q<sub>P,n</sub> (eq. 6) plotted against the logarithm of the concentration of the inductor acetosyringone in µM. The fit has an R<sup>2</sup> = 0.99. | ||

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+ | [[Image:Bielefeld_Final_RFP_fit.jpg|600px|thumb|center|'''Figure 5: Transfer function for the part <partinfo>K389016</partinfo> (R<sup>2</sup> = 0.99).''']] | ||

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+ | With this function it is possible to describe the factor ɸ<sub>I</sub> 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: | ||

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+ | [[Image:Bielefeld_Finale_formel.jpg|250px|center]]. <div align="right">(9)</div> |

## Latest revision as of 21:51, 27 October 2010

# Construct Maps

## Model of BBa_K389015

## Model of BBa_K389016

## Model of BBa_K389014

## 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

with the amount of product P, the cell count X and the specific production rate of product molecules per cell and time q_{P}. 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

and

so the specific production rate can be approximated by the equation (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

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.

The specific production rates q_{P} 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 q_{P,0}:

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):

After calculating the q_{P,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

with the Hill coefficient p, the bottom asymptote A1, the top asymptote A2 and the switch point log(x_{0}). Figure 5 shows the measured normalized specific production rates q_{P,n} (eq. 6) plotted against the logarithm of the concentration of the inductor acetosyringone in µM. The fit has an R^{2} = 0.99.

With this function it is possible to describe the factor ɸ_{I} 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: