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Team:ETH Zurich/modeling/parameters
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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> | ||
|- | |- | ||
| - | |K<sub>mLux</sub>|| | + | |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] |
|- | |- | ||
| - | |d<sub>LuxAHL</sub>||0.004 min<sup>-1</sup>|| | + | |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] |
|- | |- | ||
|d<sub>LuxR</sub>||0.0231 min<sup>-1</sup>||Degradation rate of LuxR||Literature <sup>[[Team:ETH_Zurich/project/references|[21]]]</sup> | |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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|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) | |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) | ||
|- | |- | ||
| - | |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) | + | |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) |
|- | |- | ||
|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) | |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) | ||
|- | |- | ||
| - | |K<sub>mLas</sub>||0. | + | |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] |
|- | |- | ||
| - | |d<sub>LasAHL</sub>||0.004 min<sup>-1</sup>||Degradation rate of LasAHL (30C12HSL)|| | + | |d<sub>LasAHL</sub>||0.004 min<sup>-1</sup>||Degradation rate of LasAHL (30C12HSL)||Estimated |
|- | |- | ||
|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) | |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>mRNAGFP</sub>||0.2773 min<sup>-1</sup>||Degradation rate of mRNA<sub>GFP</sub>||Literature <sup>[[Team:ETH_Zurich/project/references|[22]]]</sup> | |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> | ||
|- | |- | ||
| - | |d<sub>GFP</sub>||0.0049 min<sup>-1</sup>||Degradation rate of GFP||Fitted to experimental data | + | |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] |
|- | |- | ||
|k<sub>mRNALasI</sub>||5 nMmin<sup>-1</sup>||Production rate of mRNA<sub>LasI</sub>||Estimated | |k<sub>mRNALasI</sub>||5 nMmin<sup>-1</sup>||Production rate of mRNA<sub>LasI</sub>||Estimated | ||
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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> | |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> | ||
|- | |- | ||
| - | |D<sub>m</sub>||100 min<sup>-1</sup>||Diffusion rate of AHL through the membrane||Estimated from literature <sup>[[Team:ETH_Zurich/project/references|[27]]]</sup> | + | |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> |
| + | |- | ||
| + | |r||0.006 min<sup>-1</sup>||Growth rate of ''E. coli'' in our alginate beads|| | ||
| + | |- | ||
| + | |α||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] | ||
| + | |- | ||
| + | |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] | ||
|- | |- | ||
| - | | | + | |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> |
|- | |- | ||
| - | | | + | |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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We used the following tools for modelling and simulation: | We used the following tools for modelling and simulation: | ||
| - | * MATLAB version 8.3.0.532 (R2014a). Natick, Massachusetts: The MathWorks Inc., 2014. for deterministic model, curve fitting and parameter estimation. | + | * 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. |
* COMSOL Multiphysics software Version 4.4.0.248, COMSOL Ltd, 2014, for diffusion model and simulation. | * COMSOL Multiphysics software Version 4.4.0.248, COMSOL Ltd, 2014, for diffusion model and simulation. | ||
* MEIGO Toolbox for parameter estimation.<sup>[[Team:ETH_Zurich/project/references|[26]]]</sup> | * MEIGO Toolbox for parameter estimation.<sup>[[Team:ETH_Zurich/project/references|[26]]]</sup> | ||
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{{:Team:ETH Zurich/tpl/foot}} | {{:Team:ETH Zurich/tpl/foot}} | ||
Latest revision as of 03:39, 18 October 2014
Parameters and Tools
Parameters
No model is complete without parameters. Our exhaustive list of parameters are summarised in the table below.
| Parameter | Value | Description | Reference |
|---|---|---|---|
| αLuxR | 0.005 μMmin-1 | Production rate of LuxR | Literature [20] |
| kRLux | 0.1 nM-1min-1 | Rate of formation of RLux from LuxAHL and LuxR | Literature [19] |
| k-RLux | 10 min-1 | Dissociation rate of RLux | Literature [19] |
| KmLux | 10 nM | Lumped parameter for the Lux system | Fitted to experimental data |
| dLuxAHL | 0.004 min-1 | External degradation rate of LuxAHL (30C6HSL) | Fitted to experimental data |
| dLuxR | 0.0231 min-1 | Degradation rate of LuxR | Literature [21] |
| dRLux | 0.0231 min-1 | Degradation rate of RLux | Literature [20] |
| dmRNABxb1 | 0.2773 min-1 | Degradation rate of mRNABxb1 | Literature [22] |
| dBxb1 | 0.01 min-1 | Degradation rate of Bxb1 | Assumed |
| LPLux | 0.01463 nMmin-1 | Leakiness after using riboswitch for Plux | Fitted to experimental data |
| KmRNABxb1 | 5 nMmin-1 | Rate of transcription of Bxb1 | Estimated |
| kBxb1 | 0.1 min-1 | Rate of formation of Bxb1 | Assumed |
| αLasR | 0.005 μMmin-1 | Production rate of LasR | Literature [20](Assumed to be the same as Lux system) |
| kRLas | 0.1 nM-1min-1 | Rate of formation of RLas from LasAHL and LasR | Literature [19] (Assumed to be the same as Lux system) |
| k-RLas | 10 min-1 | Dissociation rate of RLas | Literature [19](Assumed to be the same as Lux system) |
| KmLas | 0.45 nM | Lumped parameter for the Las system | Fitted to experimental data |
| dLasAHL | 0.004 min-1 | Degradation rate of LasAHL (30C12HSL) | Estimated |
| dLasR | 0.0231 min-1 | Degradation rate of LasR | Literature [21] (Assumed to be the same as Lux system) |
| dRLas | 0.0231 min-1 | Degradation rate of RLas | Literature [20] (Assumed to be the same as
Lux system) |
| dmRNAϕc31 | 0.2773 min-1 | Degradation rate of mRNAϕc31 | Literature [22] |
| dϕc31 | 0.01 min-1 | Degradation rate of ϕC31 | Assumed |
| LPLas | 0.02461 nMmin-1 | Leakiness after using riboswitch for Plas | Fitted to experimental data |
| KmRNAϕc31 | 5 nMmin-1 | Rate of transcription of ϕc31 | Estimated |
| kϕc31 | 0.1 min-1 | Rate of formation of ϕc31 | Assumed |
| kDBxb1 | 1 nM-1min-1 | Dimerization rate of Bxb1 | Fitted |
| k-DBxb1 | 10-6 min-1 | Dissociation rate of DBxb1 | Fitted |
| kSABxb1 | 1 nM-1min-1 | Rate of formation of SABxb1 from DBxb1 and SIBxb1 | Fitted |
| k-SABxb1 | 10-6 min-1 | Dissociation rate of SABxb1 | Fitted |
| dDBxb1 | 0.02 min-1 | Degradation rate of DBxb1 | Assumed |
| kDϕc31 | 1 nM-1min-1 | Dimerization rate of ϕc31 | Fitted |
| k-Dϕc31 | 10-6 min-1 | Rate of dissociation of Dϕc31 | Fitted |
| kSAϕc31 | 1 nM-1min-1 | Rate of formation of SAϕc31 from Dϕc31 and SIϕc31 | Fitted |
| k-SAϕc31 | 10-6 min-1 | Rate of dissociation of SAϕc31 | Fitted |
| dDϕc31 | 0.02 min-1 | Degradation rate of Dϕc31 | Assumed |
| kToffBxb1 | 0.1 nM-2min-1 | Rate of flipping of Ton,i to ToffBxb1 | Assumed |
| k-ToffBxb1 | 0.1 nM-2min-1 | Rate of flipping of ToffBxb1 to Ton,f | Assumed |
| kToffϕc31 | 0.1 nM-2min-1 | Rate of flipping of Ton,i to Toffϕc31 | Assumed |
| k-Toffϕc31 | 0.1 nM-2min-1 | Rate of flipping of Toffϕc31 to Ton,f | Assumed |
| kmRNAGFP | 5 nMmin-1 | Production rate of mRNAGFP | Estimated |
| kGFP | 1 min-1 | Rate of formation of folded GFP | Estimated |
| dmRNAGFP | 0.2773 min-1 | Degradation rate of mRNAGFP | Literature [22] |
| dGFP | 0.0049 min-1 | Degradation rate of GFP | Fitted to experimental data |
| kmRNALasI | 5 nMmin-1 | Production rate of mRNALasI | Estimated |
| kLasI | 20 min-1 | Rate of formation of LasI | Estimated |
| dmRNALasI | 0.2773 min-1 | Degradation rate of mRNALasI | Literature [22] |
| dLasI | 0.0167 min-1 | Degradation rate of LasI | Literature [21] |
| kLasAHL | 0.04 min-1 | Production rate of LasAHL (30C12HSL) from the LasI | Literature [19] |
| θ | 0.01 μM | Km value for the production of mRNAGFP and mRNALasI | Literature [20] (approximation) |
| DAHLext | 4.9 10-6 cm2/s | Diffusion coefficient of extracellular AHL in liquid | Literature [27] |
| Dm | 100 min-1 | Diffusion rate of AHL through the membrane | Estimated from literature [27] |
| r | 0.006 min-1 | Growth rate of E. coli in our alginate beads | |
| α | 100 min-1 | Ratio of E. coli volume to the volume of one bead | V E. coli from literature [28], bead volume from experimental setup |
| N0 | 107 cells | Initial number of cells per bead | Experimental setup |
| Nm | 8 107 cells | Maximum number of cells per bead | Estimated from literature [29] |
| Cbeads | 1 | Correction factor (a priori) for diffusion of LuxAHL in alginate beads | Estimated from literature [30] |
Tools
We used the following tools for modelling and simulation:
- 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.
- COMSOL Multiphysics software Version 4.4.0.248, COMSOL Ltd, 2014, for diffusion model and simulation.
- MEIGO Toolbox for parameter estimation.[26]
