Team:ETH Zurich/modeling/parameters

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==Parameters==
No model is complete without parameters. Our exhaustive list of parameters are summarised in the table below.  
No model is complete without parameters. Our exhaustive list of parameters are summarised in the table below.  
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|k<sub>-RLux</sub>||10 min<sup>-1</sup>||Dissociation rate of RLux ||Literature <sup>[[Team:ETH_Zurich/project/references|[19]]]</sup>
|k<sub>-RLux</sub>||10 min<sup>-1</sup>||Dissociation rate of RLux ||Literature <sup>[[Team:ETH_Zurich/project/references|[19]]]</sup>
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|-
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|K<sub>mLux</sub>||0.0124nM||Lumped parameter for the Lux system||Fitted: [https://2014.igem.org/Team:ETH_Zurich/modeling/qs QS module]
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|K<sub>mLux</sub>||10 nM||Lumped parameter for the Lux system|| [https://2014.igem.org/Team:ETH_Zurich/modeling/qs#Parameters Fitted to experimental data]
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|-
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|d<sub>LuxAHL</sub>||0.004 min<sup>-1</sup>||Degradation rate of LuxAHL (30C6HSL)||Estimated
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|d<sub>LuxAHL</sub>||0.004 min<sup>-1</sup>||External degradation rate of LuxAHL (30C6HSL)||[https://2014.igem.org/Team:ETH_Zurich/modeling/qs#Degradation Fitted to experimental data]
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|-
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|d<sub>LuxR</sub>||0.0231 min<sup>-1</sup>||Degradation rate of LuxR||Literature <sup>[[Team:ETH_Zurich/project/references|[20]]]</sup>
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|d<sub>LuxR</sub>||0.0231 min<sup>-1</sup>||Degradation rate of LuxR||Literature <sup>[[Team:ETH_Zurich/project/references|[21]]]</sup>
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|-
|d<sub>RLux</sub>||0.0231 min<sup>-1</sup>||Degradation rate of RLux||Literature <sup>[[Team:ETH_Zurich/project/references|[20]]]</sup>
|d<sub>RLux</sub>||0.0231 min<sup>-1</sup>||Degradation rate of RLux||Literature <sup>[[Team:ETH_Zurich/project/references|[20]]]</sup>
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|-
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|d<sub>mRNABxb1</sub>||0.2773 min<sup>-1</sup>||Degradation rate of mRNA<sub>Bxb1</sub>||Literature <sup>[[Team:ETH_Zurich/project/references|[22]]]</sup>
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|-
|d<sub>Bxb1</sub>||0.01 min<sup>-1</sup>||Degradation rate of Bxb1||Assumed
|d<sub>Bxb1</sub>||0.01 min<sup>-1</sup>||Degradation rate of Bxb1||Assumed
|-
|-
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|L<sub>PLux</sub>||0.01463 nMmin<sup>-1</sup>||Leakiness after using riboswitch for PLux||Fitted: [https://2014.igem.org/Team:ETH_Zurich/modeling/qs QS module]
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|L<sub>PLux</sub>||0.01463 nMmin<sup>-1</sup>||Leakiness after using riboswitch for P<sub>lux</sub>||[https://2014.igem.org/Team:ETH_Zurich/modeling/qs Fitted to experimental data]
|-
|-
|K<sub>mRNABxb1</sub>||5 nMmin<sup>-1</sup>||Rate of transcription of Bxb1||Estimated
|K<sub>mRNABxb1</sub>||5 nMmin<sup>-1</sup>||Rate of transcription of Bxb1||Estimated
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|k<sub>Bxb1</sub>||1 min<sup>-1</sup>||Rate of formation of Bxb1||Estimated
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|k<sub>Bxb1</sub>||0.1 min<sup>-1</sup>||Rate of formation of Bxb1||Assumed
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|α<sub>LasR</sub>||0.005 μMmin<sup>-1</sup>||Production rate of LasR||Literature <sup>[[Team:ETH_Zurich/project/references|[20]]]</sup>
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|α<sub>LasR</sub>||0.005 μMmin<sup>-1</sup>||Production rate of LasR||Literature <sup>[[Team:ETH_Zurich/project/references|[20]]]</sup>(Assumed to be the same as Lux system)
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|k<sub>RLas</sub>||0.1 nM<sup>-1</sup>min<sup>-1</sup>|| Rate of formation of RLas from LasAHL and LasR||Literature <sup>[[Team:ETH_Zurich/project/references|[19]]]</sup>
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|k<sub>RLas</sub>||0.1 nM<sup>-1</sup>min<sup>-1</sup>|| Rate of formation of RLas from LasAHL and LasR||Literature <sup>[[Team:ETH_Zurich/project/references|[19]]]</sup> (Assumed to be the same as Lux system)
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|k<sub>-RLas</sub>||10 min<sup>-1</sup>||Dissociation rate of RLas ||Literature  <sup>[[Team:ETH_Zurich/project/references|[19]]]</sup>
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|k<sub>-RLas</sub>||10 min<sup>-1</sup>||Dissociation rate of RLas ||Literature  <sup>[[Team:ETH_Zurich/project/references|[19]]]</sup>(Assumed to be the same as Lux system)
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|-
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|K<sub>mLas</sub>||0.1145 nM||Lumped parameter for the Las system ||Fitted: [https://2014.igem.org/Team:ETH_Zurich/modeling/qs QS module]
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|K<sub>mLas</sub>||0.45 nM||Lumped parameter for the Las system ||[https://2014.igem.org/Team:ETH_Zurich/modeling/qs Fitted to experimental data]
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|-
|d<sub>LasAHL</sub>||0.004 min<sup>-1</sup>||Degradation rate of LasAHL (30C12HSL)||Estimated
|d<sub>LasAHL</sub>||0.004 min<sup>-1</sup>||Degradation rate of LasAHL (30C12HSL)||Estimated
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|-
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|d<sub>LasR</sub>||0.0231 min<sup>-1</sup>||Degradation rate of LasR||Literature <sup>[[Team:ETH_Zurich/project/references|[19]]]</sup> (Assumed to be the same for Lux system)
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|d<sub>LasR</sub>||0.0231 min<sup>-1</sup>||Degradation rate of LasR||Literature <sup>[[Team:ETH_Zurich/project/references|[21]]]</sup> (Assumed to be the same as Lux system)
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|-
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|d<sub>RLas</sub>||0.0231 min<sup>-1</sup>||Degradation rate of RLas||Literature <sup>[[Team:ETH_Zurich/project/references|[19]]]</sup> (Assumed to be the same for Lux system)
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|d<sub>RLas</sub>||0.0231 min<sup>-1</sup>||Degradation rate of RLas||Literature <sup>[[Team:ETH_Zurich/project/references|[20]]]</sup> (Assumed to be the same as
 +
Lux system)
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|-
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|d<sub>mRNAϕc31</sub>||0.2773 min<sup>-1</sup>||Degradation rate of mRNA<sub>ϕc31</sub>||Literature <sup>[[Team:ETH_Zurich/project/references|[22]]]</sup>
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|-
|d<sub>ϕc31</sub>||0.01 min<sup>-1</sup>||Degradation rate of ϕC31||Assumed
|d<sub>ϕc31</sub>||0.01 min<sup>-1</sup>||Degradation rate of ϕC31||Assumed
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|L<sub>PLas</sub>||0.02461 nMmin<sup>-1</sup>||Leakiness after using riboswitch for PLas||Fitted: [https://2014.igem.org/Team:ETH_Zurich/modeling/qs QS module]
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|L<sub>PLas</sub>||0.02461 nMmin<sup>-1</sup>||Leakiness after using riboswitch for P<sub>las</sub>||[https://2014.igem.org/Team:ETH_Zurich/modeling/qs Fitted to experimental data]
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|-
|K<sub>mRNAϕc31</sub>||5 nMmin<sup>-1</sup>||Rate of transcription of ϕc31||Estimated
|K<sub>mRNAϕc31</sub>||5 nMmin<sup>-1</sup>||Rate of transcription of ϕc31||Estimated
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|k<sub>ϕc31</sub>||0.1 min<sup>-1</sup>||Rate of formation of ϕc31||Estimated
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|k<sub>ϕc31</sub>||0.1 min<sup>-1</sup>||Rate of formation of ϕc31||Assumed
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|k<sub>DBxb1</sub>||1 nM<sup>-1</sup>min<sup>-1</sup>||Dimerization rate of Bxb1||Fitted: [https://2014.igem.org/Team:ETH_Zurich/modeling/int Integrase module]
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|k<sub>DBxb1</sub>||1 nM<sup>-1</sup>min<sup>-1</sup>||Dimerization rate of Bxb1||[https://2014.igem.org/Team:ETH_Zurich/modeling/int Fitted]
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|k<sub>-DBxb1</sub>||10<sup>-6</sup> min<sup>-1</sup>||Dissociation rate of DBxb1||Fitted: [https://2014.igem.org/Team:ETH_Zurich/modeling/int Integrase module]
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|k<sub>-DBxb1</sub>||10<sup>-6</sup> min<sup>-1</sup>||Dissociation rate of DBxb1|| [https://2014.igem.org/Team:ETH_Zurich/modeling/int Fitted]
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|-
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|k<sub>SABxb1</sub>||1 nM<sup>-1</sup>min<sup>-1</sup>||Rate of formation of SA<sub>Bxb1</sub> from DBxb1 and SI<sub>Bxb1</sub>||Fitted: [https://2014.igem.org/Team:ETH_Zurich/modeling/int Integrase module]
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|k<sub>SABxb1</sub>||1 nM<sup>-1</sup>min<sup>-1</sup>||Rate of formation of SA<sub>Bxb1</sub> from DBxb1 and SI<sub>Bxb1</sub>|| [https://2014.igem.org/Team:ETH_Zurich/modeling/int Fitted]
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|-
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|k<sub>-SABxb1</sub>||10<sup>-6</sup> min<sup>-1</sup>||Dissociation rate of SA<sub>Bxb1</sub>||Fitted: [https://2014.igem.org/Team:ETH_Zurich/modeling/int Integrase module]
+
|k<sub>-SABxb1</sub>||10<sup>-6</sup> min<sup>-1</sup>||Dissociation rate of SA<sub>Bxb1</sub>|| [https://2014.igem.org/Team:ETH_Zurich/modeling/int Fitted]
|-
|-
|d<sub>DBxb1</sub>||0.02 min<sup>-1</sup>||Degradation rate of DBxb1||Assumed
|d<sub>DBxb1</sub>||0.02 min<sup>-1</sup>||Degradation rate of DBxb1||Assumed
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|-
-
|k<sub>ϕc31</sub>||1 nM<sup>-1</sup>min<sup>-1</sup>||Dimerization rate of ϕc31||Fitted: [https://2014.igem.org/Team:ETH_Zurich/modeling/int Integrase module]
+
|k<sub>Dϕc31</sub>||1 nM<sup>-1</sup>min<sup>-1</sup>||Dimerization rate of ϕc31|| [https://2014.igem.org/Team:ETH_Zurich/modeling/int Fitted]
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|k<sub>-Dϕc31</sub>||10<sup>-6</sup> min<sup>-1</sup>||Rate of dissociation of Dϕc31||Fitted: [https://2014.igem.org/Team:ETH_Zurich/modeling/int Integrase module]
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|k<sub>-Dϕc31</sub>||10<sup>-6</sup> min<sup>-1</sup>||Rate of dissociation of Dϕc31|| [https://2014.igem.org/Team:ETH_Zurich/modeling/int Fitted]
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|-
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|k<sub>SAϕc31</sub>||1 nM<sup>-1</sup>min<sup>-1</sup>||Rate of formation of SA<sub>ϕc31</sub> from Dϕc31 and SI<sub>ϕc31</sub>||Fitted [https://2014.igem.org/Team:ETH_Zurich/modeling/int Integrase module]
+
|k<sub>SAϕc31</sub>||1 nM<sup>-1</sup>min<sup>-1</sup>||Rate of formation of SA<sub>ϕc31</sub> from Dϕc31 and SI<sub>ϕc31</sub>||[https://2014.igem.org/Team:ETH_Zurich/modeling/int Fitted]
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|-
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|k<sub>-SAϕc31</sub>||10<sup>-6</sup> min<sup>-1</sup>||Rate of dissociation of SA<sub>ϕc31</sub>||Fitted: [https://2014.igem.org/Team:ETH_Zurich/modeling/int Integrase module]
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|k<sub>-SAϕc31</sub>||10<sup>-6</sup> min<sup>-1</sup>||Rate of dissociation of SA<sub>ϕc31</sub>|| [https://2014.igem.org/Team:ETH_Zurich/modeling/int Fitted]
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|-
|d<sub>Dϕc31</sub>||0.02 min<sup>-1</sup>||Degradation rate of Dϕc31||Assumed
|d<sub>Dϕc31</sub>||0.02 min<sup>-1</sup>||Degradation rate of Dϕc31||Assumed
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|-
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|k<sub>ToffBxb1</sub>||1 nM<sup>-2</sup>min<sup>-1</sup>||Rate of flipping of T<sub>on,i</sub> to T<sub>offBxb1</sub>||Assumed
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|k<sub>ToffBxb1</sub>||0.1 nM<sup>-2</sup>min<sup>-1</sup>||Rate of flipping of T<sub>on,i</sub> to T<sub>offBxb1</sub>||Assumed
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|-
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|k<sub>-ToffBxb1</sub>||1 nM<sup>-2</sup>min<sup>-1</sup>||Rate of flipping of T<sub>offBxb1</sub> to T<sub>on,f</sub>||Assumed
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|k<sub>-ToffBxb1</sub>||0.1 nM<sup>-2</sup>min<sup>-1</sup>||Rate of flipping of T<sub>offBxb1</sub> to T<sub>on,f</sub>||Assumed
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|-
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|k<sub>Toffϕc31</sub>||1 nM<sup>-2</sup>min<sup>-1</sup>||Rate of flipping of T<sub>on,i</sub> to T<sub>offϕc31</sub>||Assumed
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|k<sub>Toffϕc31</sub>||0.1 nM<sup>-2</sup>min<sup>-1</sup>||Rate of flipping of T<sub>on,i</sub> to T<sub>offϕc31</sub>||Assumed
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|k<sub>-Toffϕc31</sub>||1 nM<sup>-2</sup>min<sup>-1</sup>||Rate of flipping of T<sub>offϕc31</sub> to T<sub>on,f</sub>||Assumed
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|k<sub>-Toffϕc31</sub>||0.1 nM<sup>-2</sup>min<sup>-1</sup>||Rate of flipping of T<sub>offϕc31</sub> to T<sub>on,f</sub>||Assumed
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|k<sub>mRNAGFP</sub>||5 min<sup>-1</sup>||Production rate of mRNA<sub>GFP</sub>||Estimated
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|k<sub>mRNAGFP</sub>||5 nMmin<sup>-1</sup>||Production rate of mRNA<sub>GFP</sub>||Estimated
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|k<sub>GFP</sub>||1 min<sup>-1</sup>||Rate of formation of folded GFP||Estimated
|k<sub>GFP</sub>||1 min<sup>-1</sup>||Rate of formation of folded GFP||Estimated
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|k<sub>mRNALuxI</sub>||5 min<sup>-1</sup>||Production rate of mRNA<sub>LuxI</sub>||Estimated
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|d<sub>mRNAGFP</sub>||0.2773 min<sup>-1</sup>||Degradation rate of mRNA<sub>GFP</sub>||Literature <sup>[[Team:ETH_Zurich/project/references|[22]]]</sup>
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|k<sub>LuxI</sub>||1 min<sup>-1</sup>||Rate of formation of LuxI||Estimated
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|d<sub>GFP</sub>||0.0049 min<sup>-1</sup>||Degradation rate of GFP||[https://2014.igem.org/Team:ETH_Zurich/modeling/qs#Retrieving_degradation_rates Fitted to experimental data]
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|k<sub>mRNALasI</sub>||5 min<sup>-1</sup>||Production rate of mRNA<sub>LuxI</sub>||Estimated
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|k<sub>mRNALasI</sub>||5 nMmin<sup>-1</sup>||Production rate of mRNA<sub>LasI</sub>||Estimated
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|k<sub>LasI</sub>||1 min<sup>-1</sup>||Rate of formation of LuxI||Estimated
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|k<sub>LasI</sub>||20 min<sup>-1</sup>||Rate of formation of LasI||Estimated
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|d<sub>mRNAGFP</sub>||0.1386 min<sup>-1</sup>||Degradation rate of mRNA<sub>GFP</sub>||Literature <sup>[[Team:ETH_Zurich/project/references|[21]]]</sup>
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|d<sub>mRNALasI</sub>||0.2773 min<sup>-1</sup>||Degradation rate of mRNA<sub>LasI</sub>||Literature <sup>[[Team:ETH_Zurich/project/references|[22]]]</sup>
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|d<sub>GFP</sub>||0.0049 min<sup>-1</sup>||Degradation rate of GFP||Estimated
+
|d<sub>LasI</sub>||0.0167 min<sup>-1</sup>||Degradation rate of LasI||Literature <sup>[[Team:ETH_Zurich/project/references|[21]]]</sup>
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|d<sub>LuxI</sub>||0.0167 min<sup>-1</sup>||Degradation rate of LuxI||Literature <sup>[[Team:ETH_Zurich/project/references|[21]]]</sup>  
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|k<sub>LasAHL</sub>||0.04 min<sup>-1</sup>||Production rate of LasAHL (30C12HSL) from the LasI||Literature <sup>[[Team:ETH_Zurich/project/references|[19]]]</sup>
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|d<sub>LasI</sub>||0.0167 min<sup>-1</sup>||Degradation rate of LasI||Literature <sup>[[Team:ETH_Zurich/project/references|[21]]]</sup>
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|θ||0.01 μM||K<sub>m</sub> value for the production of mRNA<sub>GFP</sub> and mRNA<sub>LasI</sub>||Literature <sup>[[Team:ETH_Zurich/project/references|[20]]]</sup> (approximation)
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|-
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|k<sub>LuxAHL</sub>||0.04 min<sup>-1</sup>||Production rate of LuxAHL (30C6HSL) from the LuxI||Literature  
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|D<sub>AHLext</sub>||4.9 10<sup>-6</sup> cm<sup>2</sup>/s||Diffusion coefficient of extracellular AHL in liquid||Literature <sup>[[Team:ETH_Zurich/project/references#Stewart|[27]]]</sup>
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|k<sub>LasAHL</sub>||0.04 min<sup>-1</sup>||Production rate of LasAHL (30C12HSL) from the LasI||Literature
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|D<sub>m</sub>||100 min<sup>-1</sup>||Diffusion rate of AHL through the membrane||[https://2014.igem.org/Team:ETH_Zurich/modeling/diffmodel#Estimation Estimated] from literature <sup>[[Team:ETH_Zurich/project/references|[27]]]</sup>
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|r||0.006 min<sup>-1</sup>||Growth rate of ''E. coli'' in our alginate beads||
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|&alpha;||100 min<sup>-1</sup>||Ratio of '' E. coli'' volume to the volume of one bead|| V<sub>'' E. coli''</sub> from literature <sup>[[Team:ETH_Zurich/project/references#Kaplan|[28]]]</sup>, bead volume from [https://2014.igem.org/Team:ETH_Zurich/expresults#Diffusion experimental setup]
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|-
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|N<sub>0</sub>||10<sup>7</sup> cells||Initial number of cells per bead|| [https://2014.igem.org/Team:ETH_Zurich/expresults#Diffusion Experimental setup]
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|-
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|N<sub>m</sub>||8 10<sup>7</sup> cells||Maximum number of cells per bead|| [https://2014.igem.org/Team:ETH_Zurich/modeling/diffmodel#Estimation Estimated] from literature <sup>[[Team:ETH_Zurich/project/references#Lars | [29]]]</sup>
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|-
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|C<sub>beads</sub>||1||Correction factor (a priori) for diffusion of LuxAHL in alginate beads|| [https://2014.igem.org/Team:ETH_Zurich/modeling/diffmodel#Estimation Estimated] from literature <sup>[[Team:ETH_Zurich/project/references#Cronenberg | [30]]]</sup>
|}
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==Tools==
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We used the following tools for modelling and simulation:
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* MATLAB version 8.3.0.532 (R2014a). Natick, Massachusetts: The MathWorks Inc., 2014. for deterministic model, curve fitting (function: fittype ; robustness option: LAR) and parameter estimation.
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* COMSOL Multiphysics software Version 4.4.0.248, COMSOL Ltd, 2014, for diffusion model and simulation.
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* MEIGO Toolbox for parameter estimation.<sup>[[Team:ETH_Zurich/project/references|[26]]]</sup>
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Latest revision as of 03:39, 18 October 2014

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