Team:ETH Zurich/modeling/whole

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=== Ideal case ===
=== Ideal case ===
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[[File:ETHZ_IdealCase.png|center|700px|thumb|'''Figure 3''' The four cases for the whole cell under ideal conditions. On [https://2014.igem.org/Team:ETH_Zurich/project/overview#Implementation_in_E._coli our project overview], you can see  see in action how the circuit responds to different inputs.]]
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[[File:ETHZ_IdealCase.png|center|800px|thumb|'''Figure 2''' The four cases for the whole cell under ideal conditions. On [https://2014.igem.org/Team:ETH_Zurich/project/overview#Implementation_in_E._coli our project overview], you can see  see in action how the circuit responds to different inputs.]]
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Under ideal conditions, there is no leakiness or cross-talk. The figure shows the production of GFP as a function of four different combinations of inputs in an ideal whole cell. No GFP is produced when there is no LasAHL and LuxAHL or when both are present. GFP is produced only when one of the input AHLs are present, thus emulating an XOR system. In the case with 0.5 nM of LuxAHL and no LasAHL as input, the rate of production of GFP reduces after six hours. This could be attributed to the delayed production of LasAHL from LasI. In the case with only LasAHL as input, there is a positive feedback of LasAHL.
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Under ideal conditions, there is no leakiness or cross-talk. The Figure 2 shows the production of GFP as a function of four different combinations of inputs in an ideal whole cell. No GFP is produced when there is no LasAHL and LuxAHL or when both are present. GFP is produced only when one of the input AHLs are present, thus emulating an XOR system. In the case with 0.5 nM of LuxAHL and no LasAHL as input, the rate of production of GFP reduces after six hours. This could be attributed to the delayed production of LasAHL from LasI. In the case with only LasAHL as input, there is a positive feedback of LasAHL.
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[[File:ETHZ_00TerminatorwithLeakiness.png|center|600px|thumb|'''Figure 4''' The dynamics of flipping of the terminators when the cell receives 0.5 nM LuxAHL and 0 nM of LasAHL and produces GFP and LasI]]
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[[File:ETHZ_00TerminatorwithLeakiness.png|center|600px|thumb|'''Figure 3''' The dynamics of flipping of the terminators when the cell receives 0.5 nM LuxAHL and 0 nM of LasAHL and produces GFP and LasI]]
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[[File:ETHZ_XORWholeCell.png|center|500px|thumb|'''Figure 5''' Predicted XOR behaviour for the whole cell model without leakiness]]
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[[File:ETHZ_XORWholeCell.png|center|500px|thumb|'''Figure 4''' Predicted XOR behaviour for the whole cell model without leakiness]]
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[[File:ETHZ_Leakiness.png|center|800px|thumb|'''Figure 6''' The four cases for the whole cell with basal leakiness]]
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[[File:ETHZ_Leakiness.png|center|800px|thumb|'''Figure 5''' The four cases for the whole cell with basal leakiness]]
From our experimental data, we observed some basal leakiness for P<sub>Lux</sub> and P<sub>Las</sub> even after using riboregulators. From the model we see that, this small basal leakiness is amplified downstream. The basal leakiness results in production of integrases which further act on the XOR module and cause the switching of the terminator. Thus, there is GFP and LasI produced, and the LasI produced further catalyses the production of more LasAHL. Thus, we observe some GFP even without inputs.   
From our experimental data, we observed some basal leakiness for P<sub>Lux</sub> and P<sub>Las</sub> even after using riboregulators. From the model we see that, this small basal leakiness is amplified downstream. The basal leakiness results in production of integrases which further act on the XOR module and cause the switching of the terminator. Thus, there is GFP and LasI produced, and the LasI produced further catalyses the production of more LasAHL. Thus, we observe some GFP even without inputs.   
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<!--[[File:ETHZ_00TerminatorwithLeakiness.png|center|500px|thumb|'''Figure 7''' No inputs and only basal leakiness]]-->
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<!--[[File:ETHZ_00TerminatorwithLeakiness.png|center|500px|thumb|'''Figure 6''' No inputs and only basal leakiness]]-->
<!--The figure above summarizes the predicted effect of basal leakiness on the flipping of the terminator. The basal leakiness results in production of Bxb1 and ΦC31 which result in flipping of the terminator. In this case, since the cell produces LasI there is increased production of LasAHL. The LasAHL produced induces the production of ΦC31 which further causes flipping of all terminators flanked by the ΦC31 sites. Thus, by 200 minutes almost all ΦC31 sites are inactive and the cell will stay ON. -->
<!--The figure above summarizes the predicted effect of basal leakiness on the flipping of the terminator. The basal leakiness results in production of Bxb1 and ΦC31 which result in flipping of the terminator. In this case, since the cell produces LasI there is increased production of LasAHL. The LasAHL produced induces the production of ΦC31 which further causes flipping of all terminators flanked by the ΦC31 sites. Thus, by 200 minutes almost all ΦC31 sites are inactive and the cell will stay ON. -->
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[[File:ETHZ_XORWholeCellwithLeakiness.png|center|800px|thumb|'''Figure 8''' Predicted XOR behaviour for the whole cell model with leakiness]]
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[[File:ETHZ_XORWholeCellwithLeakiness.png|center|800px|thumb|'''Figure 6''' Predicted XOR behaviour for the whole cell model with leakiness]].
=== With Leakiness and Crosstalk ===  
=== With Leakiness and Crosstalk ===  
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We modelled cross-talk by fitting Hill-functions to experimental data.  For each quorum sensing module, there are two levels of [https://2014.igem.org/Team:ETH_Zurich/expresults cross-talk]. At the first level, we could have any of the two AHLs binding to a given regulator thus activating the promoter while at the second level there is cross talk between regulators and their respective native promoters. Thus, for activation of a given promoter, we can have four Hill functions corresponding to the combinations of inducer and regulator interactions. Since, we are using two quorum sensing modules activating two different promoters, we have eight Hill functions.  
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We modelled cross-talk by fitting Hill-functions to experimental data.  For each quorum sensing module, there are two levels of [https://2014.igem.org/Team:ETH_Zurich/expresults cross-talk]. At the first level, we could have any of the two AHLs binding to a given regulator thus activating the promoter while at the second level there is cross talk between regulators and their respective native promoters. Thus, for activation of a given promoter, we can have four Hill functions corresponding to the combinations of inducer and regulator interactions. Since we are using two quorum sensing modules activating two different promoters, we have eight Hill functions.  
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Since, all the measurements were in terms of fluorescence, the V<sub>max</sub> for each Hill function was also in terms of fluorescence. In order to observe the effect of cross-talk we normalized the V<sub>max</sub> of non native interactions (in Lux system, P<sub>Lux</sub> being activated by LasAHL-LuxR, LasAHL-LasR or LuxAHL-LasR complexes) with the V<sub>max</sub> of the native interaction (LuxR binding to LuxAHL and activating P<sub>Lux</sub>). These ratios acted as weights for the effect of a non-native interaction on the promoter.  
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As all the measurements were in terms of fluorescence, the V<sub>max</sub> for each Hill function was also in terms of fluorescence. In order to observe the effect of cross-talk we normalized the V<sub>max</sub> of non native interactions (in Lux system, P<sub>Lux</sub> being activated by LasAHL-LuxR, LasAHL-LasR or LuxAHL-LasR complexes) with the V<sub>max</sub> of the native interaction (LuxR binding to LuxAHL and activating P<sub>Lux</sub>). These ratios acted as weights for the effect of a non-native interaction on the promoter.  
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For an ideal whole cell model, it was necessary  to have no or minimum leakiness and cross-talk. However, in reality this was not the case. Although we were able to reduce leakiness significantly using riboregulators, we still had the issue of cross-talk. However,
 
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[[File:ETHZ_DynamicsWithCrossTalk.png|center|800px|thumb|'''Figure 7''' The four cases for the whole cell with basal leakiness and cross-talk]]
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For an ideal whole cell model, it was necessary  to have no or minimum leakiness and cross-talk. However, in reality this was not the case. Although we were able to reduce leakiness significantly using riboregulators, we still had the issue of cross-talk. However, we observe that the system acts as an XOR gate till about 300 mins even with cross talk.
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In Figure 7 we observe the four cases with both cross-talk and leakiness.
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[[File:ETHZ_WikiXORCTDiffLeakiness.png|center|500px|thumb|'''Figure 8''' The four cases for the whole cell with basal leakiness and cross-talk]]
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Figure 8, shows the predicted XOR gate performance by a single cell model with basal leakiness and cross talk for different concentrations of LasAHL and LuxAHL at the end of 270 min. The system turns OFF when the input concentration of either AHLs is greater than 100 nM due to the effect of cross-talk.

Latest revision as of 02:39, 18 October 2014

iGEM ETH Zurich 2014