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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!Parameter!!Value!!Description!!Reference
!Parameter!!Value!!Description!!Reference
|-
|-
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|α<sub>LuxR</sub>||60 nMmin<sup>-1</sup>||Production rate of LuxR||Estimated
+
|α<sub>LuxR</sub>||0.005 μMmin<sup>-1</sup>||Production rate of LuxR||Literature <sup>[[Team:ETH_Zurich/project/references|[20]]]</sup>
|-
|-
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|k<sub>RLux</sub>||0.1 nM<sup>-1</sup>min<sup>-1</sup>|| Rate of formation of RLux from 30C6HSL and LuxR||Weber
+
|k<sub>RLux</sub>||0.1 nM<sup>-1</sup>min<sup>-1</sup>|| Rate of formation of RLux from LuxAHL and LuxR||Literature <sup>[[Team:ETH_Zurich/project/references|[19]]]</sup>
|-
|-
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|k<sub>-RLux</sub>||10 min<sup>-1</sup>||Dissociation rate of RLux ||Weber
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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>
|-
|-
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|k<sub>DRLux</sub>||0.05 nM<sup>-1</sup>min<sup>-1</sup>||Dimerization rate of RLux ||Weber
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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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|k<sub>-DRLux</sub>||1 min<sup>-1</sup>||Dissociation rate of DRLux ||Weber
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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]
|-
|-
-
|K<sub>dPLux</sub>||0.007652 nM||Dissociation rate constant for DRLux-PLux ||Fitted
+
|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>30C6HSL</sub>||0.004 min<sup>-1</sup>||Degradation rate of 30C6HSL||Estimated/Fitted
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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>
|-
|-
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|d<sub>LuxR</sub>||0.0174 min<sup>-1</sup>||Degradation rate of LuxR||Weber
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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>
-
|-
+
-
|d<sub>RLux</sub>||0.0174 min<sup>-1</sup>||Degradation rate of RLux||Weber
+
-
|-
+
-
|d<sub>DRLux</sub>||0.0231 min<sup>-1</sup>||Degradation rate of DRLux||Weber
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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>||0.04458 nM<sup>-1</sup>min<sup>-1</sup>||Leakiness after using riboswitch for PLux||Fitted
+
|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]
|-
|-
-
|α<sub>LasR</sub>||60 nMmin<sup>-1</sup>||Production rate of LasR||Estimated
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|K<sub>mRNABxb1</sub>||5 nMmin<sup>-1</sup>||Rate of transcription of Bxb1||Estimated
|-
|-
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|k<sub>RLas</sub>||0.1 nM<sup>-1</sup>min<sup>-1</sup>|| Rate of formation of RLas from 30C12HSL and LasR||Weber
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|k<sub>Bxb1</sub>||0.1 min<sup>-1</sup>||Rate of formation of Bxb1||Assumed
|-
|-
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|k<sub>-RLas</sub>||10 min<sup>-1</sup>||Dissociation rate of RLas ||Weber
+
|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>DRLas</sub>||0.05 nM<sup>-1</sup>min<sup>-1</sup>||Dimerization rate of RLas ||Weber
+
|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>-DRLas</sub>||1 min<sup>-1</sup>||Dissociation rate of DRLas ||Weber
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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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|K<sub>dPLas</sub>||1.3672 nM||Dissociation rate constant for DRLas-PLas ||Fitted
+
|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>30C12HSL</sub>||0.004 min<sup>-1</sup>||Degradation rate of 30C12HSL||Estimated/Fitted
+
|d<sub>LasAHL</sub>||0.004 min<sup>-1</sup>||Degradation rate of LasAHL (30C12HSL)||Estimated
|-
|-
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|d<sub>LasR</sub>||0.0174 min<sup>-1</sup>||Degradation rate of LasR||Weber
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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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|d<sub>RLas</sub>||0.0174 min<sup>-1</sup>||Degradation rate of RLas||Weber
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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)
|-
|-
-
|d<sub>DRLas</sub>||0.0231 min<sup>-1</sup>||Degradation rate of DRLas||Weber
+
|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>
|-
|-
|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>PLux</sub>||0.02461 nM<sup>-1</sup>min<sup>-1</sup>||Leakiness after using riboswitch for PLas||Fitted
+
|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]
|-
|-
-
|k<sub>DBxb1</sub>||1 nM<sup>-1</sup>min<sup>-1</sup>||Dimerization rate of Bxb1||Fitted
+
|K<sub>mRNAϕc31</sub>||5 nMmin<sup>-1</sup>||Rate of transcription of ϕc31||Estimated
|-
|-
-
|k<sub>-DBxb1</sub>||10<sup>-4</sup> min<sup>-1</sup>||Dissociation rate of DBxb1||Fitted
+
|k<sub>ϕc31</sub>||0.1 min<sup>-1</sup>||Rate of formation of ϕc31||Assumed
|-
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-
|k<sub>SABxb1</sub>||1 nM<sup>-1</sup>min<sup>-1</sup>||Rate of formation of SABxb1 from DBxb1 and SIBxb1||Fitted
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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>-SABxb1</sub>||10<sup>-4</sup> min<sup>-1</sup>||Dissociation rate of SABxb1||Fitted
+
|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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|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]
 +
|-
 +
|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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|-
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|k<sub>ϕc31</sub>||1 nM<sup>-1</sup>min<sup>-1</sup>||Dimerization rate of ϕc31||Fitted
+
|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>-4</sup> min<sup>-1</sup>||Rate of dissociation of Dϕc31||Fitted
+
|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]
|-
|-
-
|k<sub>SAϕc31</sub>||1 nM<sup>-1</sup>min<sup>-1</sup>||Rate of formation of SAϕc31 from Dϕc31 and SIϕc31||Fitted
+
|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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|k<sub>-SAϕc31</sub>||10<sup>-4</sup> min<sup>-1</sup>||Rate of dissociation of SAϕc31||Fitted
+
|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]
|-
|-
|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>||100 nM<sup>-2</sup>min<sup>-1</sup>||Rate of flipping of T<sub>on,i</sub> to T<sub>offBxb1</sub>||Assumed
+
|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>||100 nM<sup>-2</sup>min<sup>-1</sup>||Rate of flipping of T<sub>offBxb1</sub> to T<sub>on,f</sub>||Assumed
+
|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>||100 nM<sup>-2</sup>min<sup>-1</sup>||Rate of flipping of T<sub>on,i</sub> to T<sub>offϕc31</sub>||Assumed
+
|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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|-
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|k<sub>-Toffϕc31</sub>||100 nM<sup>-2</sup>min<sup>-1</sup>||Rate of flipping of T<sub>offϕc31</sub> to T<sub>on,f</sub>||Assumed
+
|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>GFP</sub>||10 min<sup>-1</sup>||Production rate of GFP||Assumed
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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>LuxI</sub>||10 min<sup>-1</sup>||Production rate of LuxI||Assumed
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|k<sub>GFP</sub>||1 min<sup>-1</sup>||Rate of formation of folded GFP||Estimated
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|k<sub>LasI</sub>||10 min<sup>-1</sup>||Production rate of LasI||Assumed
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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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|d<sub>GFP</sub>||0.0049 min<sup>-1</sup>||Degradation rate of GFP||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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|-
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|d<sub>LuxI</sub>||0.0167 min<sup>-1</sup>||Degradation rate of LuxI||Weber
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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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|d<sub>LasI</sub>||0.0167 min<sup>-1</sup>||Degradation rate of LasI||Weber
+
|k<sub>LasI</sub>||20 min<sup>-1</sup>||Rate of formation of LasI||Estimated
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|k<sub>30C6HSL</sub>||0.04 min<sup>-1</sup>||Production rate of 30C6HSL from the LuxI||Weber
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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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|k<sub>30C12HSL</sub>||0.04 min<sup>-1</sup>||Production rate of 30C12HSL from the LasI||Weber
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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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|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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|-
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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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|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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|-
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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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|-
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|r||0.006 min<sup>-1</sup>||Growth rate of ''E. coli'' in our alginate beads||
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|-
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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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|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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