Team:ETH Zurich/Modeling/Parameters

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<table border="6" align="center">
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{{:Team:ETH Zurich/Templates/SectionStart}}
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= Modeling - Parameters =
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'''Of course, our models do not work without parameters, and in our case, there are quite a lot of them. In order to keep track of all of their respective values and units, we gathered them in a series of tables on this page.'''
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{{:Team:ETH Zurich/Templates/SectionEnd}}
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{{:Team:ETH Zurich/Templates/SectionStart}}
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<tr align="center">
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= Single-Cell Model =
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<td> <b>Parameter</b> </td><td> <b>Description</b> </td><td> <b>Value</b></td><td> <b>Reference</b></td></tr>
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a. - assumption
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{|style="margin: 1em auto 1em auto; width: 80%;" class="wikitable sortable"
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!Parameter
 +
!Description
 +
!Value
 +
!Reference
 +
|-
 +
|α<sub>TetR</sub>
 +
|TetR max. production rate
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|3.93 μM/min, updated to 1 μM/min
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|[[Team:ETH_Zurich/Modeling/References#Ref5|[5]]]
 +
|-
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|α<sub>C</sub>
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|CI max. production rate
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|1 μM/min
 +
|[[Team:ETH_Zurich/Modeling/References#Ref1|[1]]]
 +
|-
 +
|α<sub>L1</sub>
 +
|LacI max. production rate
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|1 μM/min
 +
|[[Team:ETH_Zurich/Modeling/References#Ref1|[1]]]
 +
|-
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|α<sub>L2</sub>
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|LacI<sub>M1</sub> max. production rate
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|1 μM/min
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|[[Team:ETH_Zurich/Modeling/References#Ref1|[1]]]
 +
|-
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|α<sub>G</sub>
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|GFP max. production rate
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|2 μM/min
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|[[Team:ETH_Zurich/Modeling/References#Ref1|[1]]]
 +
|-
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|α<sub>LuxI</sub>
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|LuxI max. production rate
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|1 μM/min
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|[[Team:ETH_Zurich/Modeling/References#Ref1|[1]]]
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|-
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|k<sub>s1</sub>
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|AHL<sub>i</sub> production rate
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|0.01 1/min
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|[[Team:ETH_Zurich/Modeling/References#Ref2|[2]]]
 +
|-
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|ρ<sub>R</sub>
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|LuxR-AHL dimerization rate
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|0.5 1/(μM<sup>3</sup>*min)
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|[[Team:ETH_Zurich/Modeling/References#Ref1|[1]]]
 +
|-
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|α<sub>RFP</sub>
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|RFP max. production rate
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|1 μM/min
 +
|a.
 +
|-
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|β<sub>AcA</sub>
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|Acetaldehyde repression coefficient
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|7.124 μM
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|[[Team:ETH_Zurich/Modeling/References#Ref5|[5]]]
 +
|-
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|β<sub>T</sub>
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|TetR repression coefficient
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|0.01 μM, updated to 0.1 μM/min
 +
|a.
 +
|-
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|β<sub>C</sub>
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|CI repression coefficient
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|0.008 μM
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|[[Team:ETH_Zurich/Modeling/References#Ref1|[1]]]
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|-
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|β<sub>L</sub>
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|LacI repression coefficient
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|0.8 μM
 +
|[[Team:ETH_Zurich/Modeling/References#Ref1|[1]]]
 +
|-
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|θ<sub>R</sub>
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|LuxR-AHL repression coefficient
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|0.01 μM
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|[[Team:ETH_Zurich/Modeling/References#Ref1|[1]]]
 +
|-
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|γ<sub>TetR</sub>
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|TetR degradation rate
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|0.0692 1/min
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|a.
 +
|-
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|γ<sub>C</sub>
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|CI degradation rate
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|0.0692 1/min
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|[[Team:ETH_Zurich/Modeling/References#Ref1|[1]]]
 +
|-
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|γ<sub>L</sub>
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|LacI degradation rate
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|0.0231 1/min
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|[[Team:ETH_Zurich/Modeling/References#Ref1|[1]]]
 +
|-
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|γ<sub>G</sub>
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|GFP degradation rate
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|0.0692 1/min
 +
|[[Team:ETH_Zurich/Modeling/References#Ref1|[1]]]
 +
|-
 +
|γ<sub>LuxI</sub>
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|LuxI degradation rate
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|0.0167 1/min
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|[[Team:ETH_Zurich/Modeling/References#Ref3|[3]]]
 +
|-
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|k<sub>s0</sub>
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|AHL<sub>i</sub> degradation rate
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|1 1/min
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|[[Team:ETH_Zurich/Modeling/References#Ref2|[2]]]
 +
|-
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|k<sub>se</sub>
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|AHL<sub>e</sub> degradation rate
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|1 1/min
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|[[Team:ETH_Zurich/Modeling/References#Ref2|[2]]]
 +
|-
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|γ<sub>R</sub>
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|LuxR-AHL degradation rate
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|0.0231 1/min
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|[[Team:ETH_Zurich/Modeling/References#Ref1|[1]]]
 +
|-
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|γ<sub>RFP</sub>
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|RFP degradation rate
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|0.0041 1/min
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|[[Team:ETH_Zurich/Modeling/References#Ref4|[4]]]
 +
|-
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|n<sub>1</sub>
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|LacI cooperativity coefficient
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|2
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|[[Team:ETH_Zurich/Modeling/References#Ref1|[1]]]
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|-
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|n<sub>2</sub>
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|CI cooperativity coefficient
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|2
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|[[Team:ETH_Zurich/Modeling/References#Ref1|[1]]]
 +
|-
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|n<sub>3</sub>
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|TetR cooperativity coefficient
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|2
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|[[Team:ETH_Zurich/Modeling/References#Ref2|[2]]]
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|-
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|n<sub>4</sub>
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|LuxR-AHL cooperativity coefficient
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|1
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|[[Team:ETH_Zurich/Modeling/References#Ref1|[1]]]
 +
|-
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|n<sub>5</sub>
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|AlcR-AcA cooperativity coefficient
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|1.352
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|[[Team:ETH_Zurich/Modeling/References#Ref5|[5]]]
 +
|-
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|n<sub>7</sub>
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|XylR cooperativity coefficient
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|5
 +
|[[Team:ETH_Zurich/Modeling/References#Ref5|[6]]]
 +
|-
 +
|η
 +
|Diffusion rate across the cell membrane
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|2
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|[[Team:ETH_Zurich/Modeling/References#Ref2|[2]]]
 +
|-
 +
|η<sub>ext</sub>
 +
|Average diffusion rate for all cells
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|1
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|[[Team:ETH_Zurich/Modeling/References#Ref2|[2]]]
 +
|-
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|N
 +
|Number of cells
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|1
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|a.
 +
|-
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|a<sub>XylR</sub>
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|XylR max. production rate
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|95.5 μM/min
 +
|[[Team:ETH_Zurich/Modeling/References#Ref7|[6]]]
 +
|-
 +
|γ<sub>XylRi</sub>
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|XylRi degradation rate
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|0.03553 1/min
 +
|[[Team:ETH_Zurich/Modeling/References#Ref7|[6]]]
 +
|-
 +
|γ<sub>XylRa</sub>
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|XylRa degradation rate
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|0.04527 1/min
 +
|[[Team:ETH_Zurich/Modeling/References#Ref7|[6]]]
 +
|-
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|K<sub>XylR</sub>
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|XylR activation coefficient
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|1.419*10-3 μM
 +
|[[Team:ETH_Zurich/Modeling/References#Ref6|[6]]]
 +
|-
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|r<sub>XylR</sub>
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|XylRi oligomerization constant
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|0.04315e-3 1/(μM*min)
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|[[Team:ETH_Zurich/Modeling/References#Ref6|[6]]]
 +
|-
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|r<sub>RXylR</sub>
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|XylRa dissociation constant
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|0.1301e-3 1/(μM*min)
 +
|[[Team:ETH_Zurich/Modeling/References#Ref6|[6]]]
 +
|}
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{{:Team:ETH Zurich/Templates/SectionEnd}}
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{{:Team:ETH Zurich/Templates/SectionStart}}
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<tr align="center">
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= Diffusion Model =
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<td> α<sub>TetR</sub> </td><td>TetR production rate</td><td>3.93 μM/min</td><td>[5]</td></tr>
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{|style="margin: 1em auto 1em auto; width: 80%;" class="wikitable sortable"
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!Parameter
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!Description
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!Value
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!Reference
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|-
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|z<sub>end</sub>
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|Microfluidics channel length
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|5 cm
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|[[Team:ETH_Zurich/Modeling/Microfluidics#Cell Density|Choice in diffusion model]]
 +
|-
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|R<sub>Channel</sub>
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|Microfluidics channel radius
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|1 mm
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|[[Team:ETH_Zurich/Modeling/Microfluidics#Cell Density|Choice in diffusion model]]
 +
|-
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|V<sub>eColi</sub>
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|''E. coli'' average volume
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|2 μm<sup>3</sup>
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|[[Team:ETH_Zurich/Modeling/References#Ref13|[13]]] [[Team:ETH_Zurich/Modeling/References#Ref14|[14]]]
 +
|-
 +
|cd<sub>OD600, undiluted</sub>
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|''E. coli'' Cell Density at OD<sub>600</sub> = 1
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|1e9 1/ml
 +
|[[Team:ETH_Zurich/Modeling/References#Ref13|[13]]] [[Team:ETH_Zurich/Modeling/References#Ref16|[16]]]
 +
|-
 +
|c<sub>Dilution</sub>
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|Dilution of cell culture in microfludics channel
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|1/8
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|[[Team:ETH_Zurich/Modeling/Microfluidics#Cell Density|Choice in diffusion model]]
 +
|-
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|style="white-space: nowrap;"|cdRel<sub>OD600, undiluted</sub>
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|Relative ''E. coli'' Cell Density at OD<sub>600</sub> = 1, undiluted
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|0.001
 +
|[[Team:ETH_Zurich/Modeling/Microfluidics#Cell Density|Derived from V<sub>eColi</sub>, cd<sub>OD600, undiluted</sub>]]
 +
|-
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|cdRel<sub>OD600, diluted</sub>
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|Relative ''E. coli'' Cell Density at OD<sub>600</sub> = 1, diluted
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|0.000125
 +
|[[Team:ETH_Zurich/Modeling/Microfluidics#Cell Density|Derived from cdRel<sub>OD600, undiluted</sub>, c<sub>Dilution</sub>]]
 +
|-
 +
|C<sub>Agarose</sub>
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|Scaling coefficient for diffusion of small molecules in agarose instead of water
 +
|0.9
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|a.
 +
|-
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|D<sub>AcAl</sub>
 +
|Acetaldehyde Diffusion Constant
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|1.23e-5 cm<sup>2</sup>/s
 +
|[[Team:ETH_Zurich/Modeling/References#Ref8|[8]]]
 +
|-
 +
|m<sub>AcAl</sub>
 +
|Acetaldehyde Molecular Weight
 +
|44.05316 u
 +
|[[Team:ETH_Zurich/Modeling/References#Ref8|[8]]]
 +
|-
 +
|K<sub>cat,AcAl</sub>
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|Specific enzyme activity of acetaldehyde dehydrogenase in ''E. coli''
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|14.1 μmol/(min*mg)
 +
|[[Team:ETH_Zurich/Modeling/References#Ref10|[10]]] [[Team:ETH_Zurich/Modeling/References#Ref11|[11]]]
 +
|-
 +
|[E]<sup>T</sup>
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|Mean acetaldehyde dehydrogenase enzyme concentration in ''E. coli''
 +
|1.6659 kg/m<sup>3</sup>
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|[[Team:ETH_Zurich/Modeling/Microfluidics#Estimation of vmax.2CAcAl|Estimation from cell extract]], [[Team:ETH_Zurich/Modeling/References#Ref11|[11]]]
 +
|-
 +
|v<sub>max,AcAl</sub>
 +
|Maximum reaction rate for acetaldehyde dehydrogenase degrading acetaldehyde
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|0.02349 M/min
 +
|[[Team:ETH_Zurich/Modeling/Microfluidics#Estimation of vmax.2CAcAl|Estimation from cell extract]], [[Team:ETH_Zurich/Modeling/References#Ref11|[11]]]
 +
|-
 +
|K<sub>M,AcAl</sub>
 +
|Michaelis-Menten constant for acetaldehyde dehydrogenase degrading acetaldehyde
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|10 μM
 +
|[[Team:ETH_Zurich/Modeling/References#Ref10|[10]]] [[Team:ETH_Zurich/Modeling/References#Ref11|[11]]]
 +
|-
 +
|m<sub>ADH</sub>
 +
|Molecular mass of acetaldehyde dehydrogenase
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|33442 u
 +
|[[Team:ETH_Zurich/Modeling/References#Ref12|[12]]]
 +
|-
 +
|n<sub>ADH</sub>
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|Mean number of acetaldehyde dehydrogenase protein molecules per ''E. coli'' cell
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|style="white-space: nowrap;"|28512.2, rounded to 30000
 +
|[[Team:ETH_Zurich/Modeling/Microfluidics#Estimation of vmax.2CAcAl|Estimation from cell extract]], [[Team:ETH_Zurich/Modeling/References#Ref11|[11]]]
 +
|-
 +
|[ADH]<sub>Extract</sub>
 +
|acetaldehyde dehydrogenase concentration in ''E. coli'' cell extract
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|19 mg/ml
 +
|[[Team:ETH_Zurich/Modeling/References#Ref11|[11]]]
 +
|-
 +
|dil<sub>Extract</sub>
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|''E. coli'' cell extract dilution
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|1/12
 +
|[[Team:ETH_Zurich/Modeling/References#Ref11|[11]]]
 +
|}
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<tr align="center">
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{{:Team:ETH Zurich/Templates/SectionEnd}}
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<td> α<sub>C</sub> </td><td>CI production rate</td><td>1 μM/min</td><td>[1]</td></tr>
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{{:Team:ETH Zurich/Templates/SectionStart}}
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= Combined Model =
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</table>
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{|style="margin: 1em auto 1em auto; width: 80%;" class="wikitable sortable"
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!Parameter
 +
!Description
 +
!Value
 +
!Reference
 +
|-
 +
|D<sub>AHL</sub>
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|AHL Diffusion Constant
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|4.9e-6 cm<sup>2</sup>/s
 +
|[[Team:ETH_Zurich/Modeling/References#Ref9|[9]]]
 +
|-
 +
|m<sub>AHL</sub>
 +
|AHL Molecular Weight
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|297.38990 u
 +
|[[Team:ETH_Zurich/Modeling/References#Ref15|[15]]]
 +
|-
 +
|γ<sub>AHL,ext</sub>
 +
|AHL cell-external degradation
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|8.0225e-006/s
 +
|Derived from 1 day half-life at pH 7 [[Team:ETH_Zurich/Modeling/References#Ref7|[7]]]
 +
|}
 +
{{:Team:ETH Zurich/Templates/SectionEnd}}
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{{:Team:ETH Zurich/Templates/HeaderNewEnd}}

Latest revision as of 13:36, 28 October 2011

Can you feel the smoke tonight?
 

Contents

Modeling - Parameters

Of course, our models do not work without parameters, and in our case, there are quite a lot of them. In order to keep track of all of their respective values and units, we gathered them in a series of tables on this page.

Single-Cell Model

a. - assumption

Parameter Description Value Reference
αTetR TetR max. production rate 3.93 μM/min, updated to 1 μM/min [5]
αC CI max. production rate 1 μM/min [1]
αL1 LacI max. production rate 1 μM/min [1]
αL2 LacIM1 max. production rate 1 μM/min [1]
αG GFP max. production rate 2 μM/min [1]
αLuxI LuxI max. production rate 1 μM/min [1]
ks1 AHLi production rate 0.01 1/min [2]
ρR LuxR-AHL dimerization rate 0.5 1/(μM3*min) [1]
αRFP RFP max. production rate 1 μM/min a.
βAcA Acetaldehyde repression coefficient 7.124 μM [5]
βT TetR repression coefficient 0.01 μM, updated to 0.1 μM/min a.
βC CI repression coefficient 0.008 μM [1]
βL LacI repression coefficient 0.8 μM [1]
θR LuxR-AHL repression coefficient 0.01 μM [1]
γTetR TetR degradation rate 0.0692 1/min a.
γC CI degradation rate 0.0692 1/min [1]
γL LacI degradation rate 0.0231 1/min [1]
γG GFP degradation rate 0.0692 1/min [1]
γLuxI LuxI degradation rate 0.0167 1/min [3]
ks0 AHLi degradation rate 1 1/min [2]
kse AHLe degradation rate 1 1/min [2]
γR LuxR-AHL degradation rate 0.0231 1/min [1]
γRFP RFP degradation rate 0.0041 1/min [4]
n1 LacI cooperativity coefficient 2 [1]
n2 CI cooperativity coefficient 2 [1]
n3 TetR cooperativity coefficient 2 [2]
n4 LuxR-AHL cooperativity coefficient 1 [1]
n5 AlcR-AcA cooperativity coefficient 1.352 [5]
n7 XylR cooperativity coefficient 5 [6]
η Diffusion rate across the cell membrane 2 [2]
ηext Average diffusion rate for all cells 1 [2]
N Number of cells 1 a.
aXylR XylR max. production rate 95.5 μM/min [6]
γXylRi XylRi degradation rate 0.03553 1/min [6]
γXylRa XylRa degradation rate 0.04527 1/min [6]
KXylR XylR activation coefficient 1.419*10-3 μM [6]
rXylR XylRi oligomerization constant 0.04315e-3 1/(μM*min) [6]
rRXylR XylRa dissociation constant 0.1301e-3 1/(μM*min) [6]


Diffusion Model

Parameter Description Value Reference
zend Microfluidics channel length 5 cm Choice in diffusion model
RChannel Microfluidics channel radius 1 mm Choice in diffusion model
VeColi E. coli average volume 2 μm3 [13] [14]
cdOD600, undiluted E. coli Cell Density at OD600 = 1 1e9 1/ml [13] [16]
cDilution Dilution of cell culture in microfludics channel 1/8 Choice in diffusion model
cdRelOD600, undiluted Relative E. coli Cell Density at OD600 = 1, undiluted 0.001 Derived from VeColi, cdOD600, undiluted
cdRelOD600, diluted Relative E. coli Cell Density at OD600 = 1, diluted 0.000125 Derived from cdRelOD600, undiluted, cDilution
CAgarose Scaling coefficient for diffusion of small molecules in agarose instead of water 0.9 a.
DAcAl Acetaldehyde Diffusion Constant 1.23e-5 cm2/s [8]
mAcAl Acetaldehyde Molecular Weight 44.05316 u [8]
Kcat,AcAl Specific enzyme activity of acetaldehyde dehydrogenase in E. coli 14.1 μmol/(min*mg) [10] [11]
[E]T Mean acetaldehyde dehydrogenase enzyme concentration in E. coli 1.6659 kg/m3 Estimation from cell extract, [11]
vmax,AcAl Maximum reaction rate for acetaldehyde dehydrogenase degrading acetaldehyde 0.02349 M/min Estimation from cell extract, [11]
KM,AcAl Michaelis-Menten constant for acetaldehyde dehydrogenase degrading acetaldehyde 10 μM [10] [11]
mADH Molecular mass of acetaldehyde dehydrogenase 33442 u [12]
nADH Mean number of acetaldehyde dehydrogenase protein molecules per E. coli cell 28512.2, rounded to 30000 Estimation from cell extract, [11]
[ADH]Extract acetaldehyde dehydrogenase concentration in E. coli cell extract 19 mg/ml [11]
dilExtract E. coli cell extract dilution 1/12 [11]


Combined Model

Parameter Description Value Reference
DAHL AHL Diffusion Constant 4.9e-6 cm2/s [9]
mAHL AHL Molecular Weight 297.38990 u [15]
γAHL,ext AHL cell-external degradation 8.0225e-006/s Derived from 1 day half-life at pH 7 [7]


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