Team:Grenoble/Projet/Modelling/Parameters

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<div  class="blocbackground" id="Sensitivity">
<div  class="blocbackground" id="Sensitivity">
    <h2>Parameters sensitivity</h2>
    <h2>Parameters sensitivity</h2>
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    <p>In order to know if an error on the parameters would induce a completely different behaviour of our system,
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    <p>
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    we studied the sensitivity of our system to a change on the parameters.
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      In order to know if an error on the parameters would induce a completely different behaviour of our system,
 +
      we studied the sensitivity of our system to changes in the parameter values.
    </p>
    </p>
    <p>
    <p>
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    This study was performed by increasing or decreasing our parameters values by a range of percentages (from -66% to +300% for each parameter).
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      This study was performed by increasing or decreasing our parameters values by a range of percentages (from -66% to +300% for each parameter).
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    Then we studied the change on the output of our system, the ratio of IPTG over aTc that induces the coloration.
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      Then we studied the change on the output of our system, the ratio of IPTG over aTc that induces the coloration.
    </p>
    </p>
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    On the following figure one can see the influence on the output of our system (the ratio of IPTG over aTc on the interface)
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    <p>
-
    for several different aTc concentrations. For these concentrations the switch is still efficient, even though the resulting
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      On the following figure one can see the influence on the output of our system (the ratio of IPTG over aTc on the interface)
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    variation on the output will induce an error on our measure.
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      for several aTc concentrations. For these concentrations the switch is still efficient, even though the resulting
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      variation on the output will induce an error on our measure.
    </p>
    </p>
    <table class="nobordure">
    <table class="nobordure">
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    </table>
    </table>
     
     
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    <p>For low values of aTc concentration the error is too minor to perturb the mechanism of our system. If the error is  
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    <p>For low values of aTc concentration the error is too minor to perturb the mechanism of our system. However,
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    superior to -50% or +100% for parameters such as K<SUB>pLac - LacI</SUB> or K<SUB>pTet - TetR</SUB> however, it will
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    it becomes impossible to predict the system output if the error is superior to -50% or +100% for parameters such  
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    be impossible to predict the output. In such a case a characterization of the responsible parameter would be necessary.
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    as K<SUB>pLac - LacI</SUB> or K<SUB>pTet - TetR</SUB>. In such a case a characterization of the responsible  
 +
    parameter would be necessary.
    </p>
    </p>
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    <p>For higher values of aTc concentration however, the value of IPTG necessary for a switch is very high and errors on the
+
    <p>
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    parameters can cause the system not to switch for the chosen IPTG gradient. In this case, the IPTG maximal necessary value
+
    For higher aTc concentrations however, the level of IPTG at which the switch occurs is very high. Errors on the parameters
-
    for quantification would be too high for a living cell. The only problem being a decrease of the maximum value we can quantify.
+
    prevents the system to switch for the chosen IPTG gradient. In this case, the IPTG maximal necessary valuefor quantification
 +
    would be too high for a living cell. The only problem being a decrease of the maximum value we can quantify.
    </p>
    </p>
 +
    <center>
    <a href="https://static.igem.org/mediawiki/2011/0/01/Parameters_sensitivity3.png"><img src="https://static.igem.org/mediawiki/2011/0/01/Parameters_sensitivity3.png" class="centerwide"/></a>
    <a href="https://static.igem.org/mediawiki/2011/0/01/Parameters_sensitivity3.png"><img src="https://static.igem.org/mediawiki/2011/0/01/Parameters_sensitivity3.png" class="centerwide"/></a>
    <div class="legend"><strong>Figure 2: </strong>Parameters sensitivity for 6.2e-04 M of aTc</div>
    <div class="legend"><strong>Figure 2: </strong>Parameters sensitivity for 6.2e-04 M of aTc</div>
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    </center>
   
   
</div>
</div>

Revision as of 18:28, 28 October 2011

Grenoble 2011, Mercuro-Coli iGEM


Modelling - Parameters

Parameters

PDF file (detailed explanation on parameters and how we deduced them) for Toggle Switch
kplac pLac production rate 600 proteins/min [1]
kpTet pTet production rate 600 proteins/min [1]
kpMer pMer production rate 600 proteins/min [1]
δLacI LacI degradation rate 4.6E-2 min−1 PDF file
δTetR TetR degradation rate 4.6E-2 min−1 PDF file
δMerR MerR degradation rate 4.6E-2 min−1 PDF file
KpLac - LacI plac - LacI dissociation constant 5.45E-7 M Kyoto 10
KpMer - MerR pMer - MerR dissociation constant 1.00E-8 M [2]
KpTet - TerR pTet - TetR dissociation constant 5.00E-8 M [3]
KLacI - IPTG LacI - IPTG dissociation constant 2.96E-5 M [4]
KTetR - aTc aTc - TetR dissociation constant 1.5E-8 M [5]
KHg2+ - MerR Hg2+ - MerR dissociation constant 1E-7 M [2]
nplac plac cooperativity number 2,3 [4]
npMer pMer cooperativity number 2,5 [6]
npTet pTet cooperativity number 3 [7]

References

[1] Nature. 2000 Jan 20;403(6767):335-8. A synthetic oscillatory network of transcriptional regulators. Elowitz MB, Leibler S.

[2] Mol Gen Genet. 1999 Aug;262(1):154-62. Purification and characterization of MerR, the regulator of the broad-spectrum mercury resistance genes in Streptomyces lividans 1326. Rother D, Mattes R, Altenbuchner J.

[3] David Braun et al. Parameter estimation for two synthetic gene networks: A case study. IEEE 2005.

[4] Nature 403, 339-342 (20 January 2000) Construction of a genetic toggle switch in Escherichia coli. Timothy S. Gardner Charles R. Cantor & James J. Collins

[5] O. Scholz, P. Schubert, M. Kintrup and W. Hillen, Tet repressor induction without Mg2+, Biochemistry 39 (2000), pp. 10914–10920

[6] Ultrasensitivity and heavy-metal selectivity of the allosterically modulated MerR transcription complex. D M Ralston and T V O'Halloran

[7] Systems analysis of a quorum sensing network: design constraints imposed by the functional requirements, network topology and kinetic constants. Goryachev AB, Toh DJ, Lee T.

Parameters sensitivity

In order to know if an error on the parameters would induce a completely different behaviour of our system, we studied the sensitivity of our system to changes in the parameter values.

This study was performed by increasing or decreasing our parameters values by a range of percentages (from -66% to +300% for each parameter). Then we studied the change on the output of our system, the ratio of IPTG over aTc that induces the coloration.

On the following figure one can see the influence on the output of our system (the ratio of IPTG over aTc on the interface) for several aTc concentrations. For these concentrations the switch is still efficient, even though the resulting variation on the output will induce an error on our measure.

Figure 1: Parameters sensitivity for 2.8e-07 M of aTc

Note: On the next two figures the parameters are the following

1 kplac
2 Vcell
3 kpTet
4 KpLac - LacI
5 KpTet - TerR
6 KLacI - IPTG
7 KTetR - aTc
8 nplac
9 npTet
10 δTetR
11 δLacI
Figure 2: Parameters sensitivity for 6.3e-06 M of aTc

Variations from 1 to 13 :

1 -66%
2 -50%
3 -20%
4 -10%
5 -5%
6 +0%
7 +5%
8 +10%
9 +20%
10 +50%
11 +100%
11 +200%
11 +300%

For low values of aTc concentration the error is too minor to perturb the mechanism of our system. However, it becomes impossible to predict the system output if the error is superior to -50% or +100% for parameters such as KpLac - LacI or KpTet - TetR. In such a case a characterization of the responsible parameter would be necessary.

For higher aTc concentrations however, the level of IPTG at which the switch occurs is very high. Errors on the parameters prevents the system to switch for the chosen IPTG gradient. In this case, the IPTG maximal necessary valuefor quantification would be too high for a living cell. The only problem being a decrease of the maximum value we can quantify.

Figure 2: Parameters sensitivity for 6.2e-04 M of aTc
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