Difference between revisions of "Team:ETH Zurich/Modeling/Parameters"

 
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<h1>Parameters</h1>
 
<h1>Parameters</h1>
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<h2>AHL module</h2>
 
<h2>AHL module</h2>
 
<h3>Single cell model</h3>
 
<h3>Single cell model</h3>
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<tr><td>\(\text{LuxR}_\text{tot}\)</td><td>0.0025 &mu;M</td><td>Total concentration of LuxR </td><td>estimated</td></tr>
 
<tr><td>\(\text{LuxR}_\text{tot}\)</td><td>0.0025 &mu;M</td><td>Total concentration of LuxR </td><td>estimated</td></tr>
 
<tr><td>\(a_\mathrm{LuxI}\)</td><td>1 &mu;M.min<SUP>-1</SUP></td><td>Maximal production rate of LuxI</td><td><a href="https://2015.igem.org/Team:ETH_Zurich/References#Basu2005">Basu, 2005</a></td></tr>
 
<tr><td>\(a_\mathrm{LuxI}\)</td><td>1 &mu;M.min<SUP>-1</SUP></td><td>Maximal production rate of LuxI</td><td><a href="https://2015.igem.org/Team:ETH_Zurich/References#Basu2005">Basu, 2005</a></td></tr>
−
<tr><td>\(k_\mathrm{leaky}\)</td><td>0.0005 &mu;M<SUP>-1</SUP></td><td>Leakiness of P<SUB>LuxR</SUB> promoter </td><td>estimated</td></tr>
+
<tr><td>\(a_\mathrm{LuxI,ribo}\)</td><td>0.1 &mu;M.min<SUP>-1</SUP></td><td>Maximal production rate of LuxI</td><td><a href="https://2014.igem.org/Team:ETH_Zurich">ETHZ 2014</a></td></tr>
−
<tr><td>\(K_\mathrm{a,LuxRAHL}\)</td><td>0.01 &mu;M</td><td>Activation coefficient of LuxRAHL </td><td>estimated</td></tr>
+
<tr><td>\(k_\mathrm{leaky}\)</td><td>0.0375 &mu;M<SUP>-1</SUP></td><td>Coefficient for leakiness dependency on LuxR concentration of P<SUB>LuxR</SUB> promoter </td><td><a href="https://2013.igem.org/Team:ETH_Zurich/Parameter"> ETHZ 2013 </a></td></tr>
−
<tr><td>\(d_\mathrm{LuxI}\)</td><td>0.0167 min<SUP>-1</SUP></td><td>Degradation rate of LuxI </td><td>estimated</td></tr>
+
<tr><td>\(K_\mathrm{a,LuxRAHL}\)</td><td>9.89 nM</td><td>Activation coefficient of LuxRAHL </td><td>Estimated from our <a href="https://2015.igem.org/Team:ETH_Zurich/Modeling/AHL_Module#_Dose_response_curves_and_apparent_K_M__values">own data </a></td></tr>
 +
<tr><td>\(K_\mathrm{LuxRAHL,ribo}\)</td><td>285 nM</td><td>Activation coefficient of LuxRAHL in case of a riboregulated LuxR responsive promoter </td><td><a href="https://2014.igem.org/Team:ETH_Zurich">ETHZ 2014</a></td></tr>
 +
<tr><td>\(L_\mathrm{lux,ribo}\)</td><td>0.01463  nM.min<SUP>-1</SUP></td><td>Leakiness after using riboswitch for P<SUB>lux</SUB> </td><td><a href="https://2014.igem.org/Team:ETH_Zurich">ETHZ 2014</a></td></tr>
 +
<tr><td>\(n_\mathrm{lux}\)</td><td>1.7</td><td>Hill coefficient for LuxRAHL activation </td><td><a href="https://2014.igem.org/Team:ETH_Zurich">ETHZ 2014</a></td></tr>
 +
<tr><td>\(d_\mathrm{LuxI}\)</td><td>0.0167 min<SUP>-1</SUP></td><td>Degradation rate of LuxI </td><td><a href="https://2010.igem.org/Team:MIT_tmodel">MIT 2010</a></td></tr>
 
<tr><td>\(a_\mathrm{AHL}\)</td><td>0.04 &mu;M.min<SUP>-1</SUP></td><td>Production rate of AHL </td><td><a href="https://2015.igem.org/Team:ETH_Zurich/References#Weber2013">Weber, 2013</a></td></tr>
 
<tr><td>\(a_\mathrm{AHL}\)</td><td>0.04 &mu;M.min<SUP>-1</SUP></td><td>Production rate of AHL </td><td><a href="https://2015.igem.org/Team:ETH_Zurich/References#Weber2013">Weber, 2013</a></td></tr>
 
<tr><td>\(d_\mathrm{AHL}\)</td><td>0.01 min<SUP>-1</SUP></td><td>Degradation rate of AHL</td><td><a href="https://2015.igem.org/Team:ETH_Zurich/References#Basu2005">Basu, 2005</a></td></tr>
 
<tr><td>\(d_\mathrm{AHL}\)</td><td>0.01 min<SUP>-1</SUP></td><td>Degradation rate of AHL</td><td><a href="https://2015.igem.org/Team:ETH_Zurich/References#Basu2005">Basu, 2005</a></td></tr>
−
<tr><td>\(v_\mathrm{AiiA}\)</td><td>\(k_\mathrm{cat} \cdot C_\mathrm{AiiA} \)</td><td>Maximal conversion rate of AiiA </td><td></td></tr>
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<tr><td>\(v_\mathrm{AiiA}\)</td><td>\(k_\mathrm{cat} \cdot C_\mathrm{AiiA} \)</td><td>Maximal conversion rate of AiiA </td><td>calculated</td></tr>
−
<tr><td>\(k_\mathrm{cat}\)</td><td>1.63 10<SUP>3</SUP>min<SUP>-1</SUP></td><td>Turnover number of AiiA </td><td><a href="https://2015.igem.org/Team:ETH_Zurich/References#Wang2004">Wang, 2004</a></td></tr>
+
<tr><td>\(k_\mathrm{cat}\)</td><td>1.63&times;10<SUP>3</SUP>min<SUP>-1</SUP></td><td>Turnover number of AiiA </td><td><a href="https://2015.igem.org/Team:ETH_Zurich/References#Wang2004">Wang, 2004</a></td></tr>
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<tr><td>\(C_\mathrm{AiiA}\)</td><td>0.05 &mu;M</td><td>Concentration of AiiA </td><td></td></tr>
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<tr><td>\(C_\mathrm{AiiA}\)</td><td>varied</td><td>Concentration of AiiA </td><td>estimated</td></tr>
−
<tr><td>\(K_\mathrm{M,AiiA}\)</td><td>2.95 10<SUP>3</SUP> &mu;M</td><td> of AiiA </td><td><a href="https://2015.igem.org/Team:ETH_Zurich/References#Wang2004">Wang, 2004</a></td></tr>
+
<tr><td>\(K_\mathrm{M,AiiA}\)</td><td>2.95&times;10<SUP>3</SUP> &mu;M</td><td> Half-maximal rate substrate concentration of AiiA </td><td><a href="https://2015.igem.org/Team:ETH_Zurich/References#Wang2004">Wang, 2004</a></td></tr>
 
<tr><td>\(a_\mathrm{GFP}\)</td><td>2 &mu;M.min<SUP>-1</SUP></td><td>Maximal production rate of GFP </td><td><a href="https://2015.igem.org/Team:ETH_Zurich/References#Basu2005">Basu, 2005</a></td></tr>
 
<tr><td>\(a_\mathrm{GFP}\)</td><td>2 &mu;M.min<SUP>-1</SUP></td><td>Maximal production rate of GFP </td><td><a href="https://2015.igem.org/Team:ETH_Zurich/References#Basu2005">Basu, 2005</a></td></tr>
−
<tr><td>\(d_\mathrm{GFP}\)</td><td>0.01 min<SUP>-1</SUP></td><td>Degradation rate of GFP </td><td>estimated</td></tr>
+
<tr><td>\(d_\mathrm{GFP}\)</td><td>0.01 min<SUP>-1</SUP></td><td>Degradation rate of GFP </td><td>estimated from doubling time of <i>E. coli</i></td></tr>
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<h3>Compartment model</h3>
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<tr> <th>Name </th> <th>Value</th><th>Description </th><th>References/Estimation </th> </tr>
 +
<tr> <td>\(N_{d}\) </td> <td>150</td><td>Number of <i> E. coli </i> in the doughnut </td><td>Maximal number of <i>E. coli </i> that would fit on the surface </td> </tr>
 +
<tr> <td>\(N_{b,max}\) </td> <td>12798</td><td>Maximum number of <i> E. coli </i> in the bulk </td><td>Considering the maximal OD is 2</td> </tr>
 +
<tr> <td>\(V_{cell,d}\) </td> <td>6 &mu;m<SUP>3</SUP></td><td>Volume around an <i> E. coli </i> in the doughnut </td><td>estimated</td> </tr>
 +
<tr> <td>\(V_{cell,b,worst}\) </td> <td>78 &mu;m<SUP>3</SUP></td><td>Volume around an <i> E. coli </i> in the bulk</td><td>Worst case, estimated from \(N_{b,max}\) </td> </tr>
 +
<tr> <td>\(V_{cell,b,norm}\) </td> <td>1000 &mu;m<SUP>3</SUP></td><td>Volume around an <i> E. coli </i> in the bulk</td><td>Normal case</td> </tr>
 
</table>
 
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−
 
 
<h2>Lactate module</h2>
 
<h2>Lactate module</h2>
−
<h3>Single cell model</h3>
 
−
<h4>Assumptions</h4>
 
 
<table>
 
<table>
−
<tr> <th>Name </th> <th>Description </th><th>Minimum Value</th><th>Maximum Value</th><th>References/Estimation </th> </tr>
+
<tr> <th>Name </th> <th>Description </th><th>Value</th><th>References/Estimation </th> </tr>
−
<tr> <td>\(\text{B}\)</td> <td> \(\frac{Lac_\mathrm{ini}^2}{K_\mathrm{d,DLL}}\) </td><td> 0.000001</td> <td> 4</td>  <td></td> </tr>
+
<tr> <td>\(K_{\mathrm{A,Lact}}\)</td> <td> Lumped parameter for the lactate sensor </td><td>175 &mu;M</td><td>Based on the <a href="https://2015.igem.org/Team:ETH_Zurich/Modeling/Experiments_Model">characterization</a> of the promoters. </td> </tr>
−
<tr> <td>\(\text{Lac}_{\text{ini}}\)</td> <td> Initial concentration of lactate in the medium </td><td> 0.1 &mu;M</td> <td> 2 &mu;M</td>  <td>Low concentration of lactate in the medium</td> </tr>
+
<tr> <td>\( a_\mathrm{LacI}\)</td> <td> Maximal production rate of LacI</td> <td>1 &mu;M.min<SUP>-1</SUP> </td> <td><a href="https://2015.igem.org/Team:ETH_Zurich/References#Basu2005">Basu, 2005</a></td> </tr>
−
<tr> <td>\(K_\mathrm{d,DLL}\)</td> <td> Dissociation constant between the dimer of Lldr and Lactate</td><td>10 &mu;M<SUP>2</SUP> </td> <td>10000 &mu;M<SUP>2</SUP></td> <td> </td> </tr>
+
<tr> <td>\( d_\mathrm{LacI}\)</td> <td> Degradation rate of LacI</td> <td>0.0231 min<SUP>-1</SUP> </td> <td><a href="https://2015.igem.org/Team:ETH_Zurich/References#Basu2005">Basu, 2005</a></td> </tr>
−
<tr> <td>\(\alpha\)</td> <td> Multiplication factor between the initial concentration of Lactate and Production of normal cells</td><td>1 </td> <td>150</td> <td>estimated </td> </tr>
+
<tr> <td>\(  K_\mathrm{R,LacI}\)</td> <td>Repression coefficient of LacI</td><td>0.8 &mu;M </td> <td><a href="https://2015.igem.org/Team:ETH_Zurich/References#Basu2005">Basu, 2005</a></td> </tr>
−
<tr> <td>\(F_\mathrm{C}\)</td> <td> Fold change between Lactate production by cancer and normal cells</td><td>2 </td> <td>4</td> <td>estimated </td> </tr>
+
<tr> <td>\(  n_1\)</td> <td>Hill coefficient of LldR</td><td>1.7</td> <td>estimated</td> </tr>
−
<tr> <td>\(a_1\)</td> <td> \(\frac{a_\mathrm{LacI}}{d_\mathrm{LacI}\cdot K_{RLacI}}\)</td><td>0.05 </td> <td>1000</td> <td></td> </tr>
+
<tr> <td>\(  n_2\)</td> <td>Hill coefficient of LacI</td><td>1.7</td> <td>estimated</td> </tr>
−
<tr> <td>\( a_\mathrm{LacI}\)</td> <td> Maximal production rate of LacI</td><td>0.05 &mu;M.min<SUP>-1</SUP> </td> <td>1 &mu;M.min<SUP>-1</SUP> </td> <td><a href="https://2015.igem.org/Team:ETH_Zurich/References#Basu2005">Basu, 2005</a></td> </tr>
+
−
<tr> <td>\( d_\mathrm{LacI}\)</td> <td> Degradation rate of LacI</td><td>0.01 min<SUP>-1</SUP> </td> <td>0.1 min<SUP>-1</SUP> </td> <td><a href="https://2015.igem.org/Team:ETH_Zurich/References#Basu2005">Basu, 2005</a></td> </tr>
+
−
<tr> <td>\(  K_\mathrm{R,LacI}\)</td> <td>Repression coefficient of LacI</td><td>0.1 &mu;M </td> <td>10 &mu;M </td> <td><a href="https://2015.igem.org/Team:ETH_Zurich/References#Basu2005">Basu, 2005</a></td> </tr>
+
−
<tr> <td>\( \gamma_1\)</td> <td> \( \frac{L_\mathrm{2tot}}{K_\mathrm{R,L}}\)</td><td>5 </td> <td>10000</td> <td>estimated </td> </tr>
+
−
<tr> <td>\(  L_\mathrm{2tot}\)</td> <td> Total concentration of LldR dimer  </td><td>0.5 &mu;M</td> <td>10 &mu;M</td> <td>estimated from paxdb</td> </tr>
+
−
<tr> <td>\(  K_\mathrm{R,L}\)</td> <td> Repression coefficient of LldR</td><td>0.001 &mu;M</td> <td>0.1 &mu;M</td> <td>estimated</td> </tr>
+
−
<tr> <td>\(  \gamma_2\)</td> <td> \(\frac{IPTG_{tot}}{K_{IL}}\)</td><td>0</td> <td>500</td> <td>estimated</td> </tr>
+
−
<tr> <td>\(  \frac{a_1}{\gamma_2+1}\)</td> <td></td><td>0.001</td> <td>1000</td> <td>estimated</td> </tr>
+
−
<tr> <td>\(  n_1\)</td> <td>Hill coefficient of LldR</td><td>0.5</td> <td>2.5</td> <td>estimated</td> </tr>
+
−
<tr> <td>\(  n_2\)</td> <td>Hill coefficient of LacI</td><td>1.5</td> <td>2.5</td> <td>estimated</td> </tr>
+
 
</table>
 
</table>
 
<h2>Reaction-diffusion model</h2>
 
<h2>Reaction-diffusion model</h2>
 
<table>
 
<table>
−
<tr> <th>Name </th> <th>Description </th><th>Minimum Value</th><th>Maximum Value</th><th>References/Estimation </th> </tr>
+
<tr><th>Name </th><th>Description </th><th>Value</th><th>References/Estimation </th> </tr>
−
<tr><td>\(D_\text{AHL,agar}\)</td><td>Diffusion coefficient of AHL in agar</td><td>\(3.0\times 10^{-10} m^2/s\)</td><td><a href="https://2015.igem.org/Team:ETH_Zurich/References#Trovato2014">Trovato, 2014</a></td>
+
<tr><td>\(D_{aq,AHL}\)</td><td>Diffusion coefficient of AHL through water</td><td>4.9&times;10<sup>-6</sup>cm<sup>2</sup>/s</td><td>ETHZ 2014</td></tr>
 +
<tr><td>\(D_{m,AHL}\)</td><td>Diffusion coefficient of AHL through a cell membrane</td><td>4.629&times;10<sup>-16</sup> m<sup>2</sup>/s</td><td><a href="https://2015.igem.org/Team:ETH_Zurich/References#Kaplan1985">Kaplan, <i>et al.</i>, 1985</a></td></tr>
 +
<tr><td>\(R_\text{Jurkat}\)</td><td>Radius of a Jurkat cell</td><td>5.75 &mu;m</td><td><a href="http://bionumbers.hms.harvard.edu/">BioNumbers</a></td></tr>
 +
<tr><td>\(R_\textit{E. coli}\)</td><td>Short-side radius of an <i>E. coli</i> cell</td><td>0.5 &mu;m</td><td><a href="http://bionumbers.hms.harvard.edu/">BioNumbers</a></td></tr>
 +
<tr><td>\(k_\text{int;Lact}\)</td><td>Lactate import rate by LldP</td><td>0.008666/s</td><td><a href="https://2015.igem.org/Team:ETH_Zurich/References#Dong1993">Dong, <i>et al.</i>, 1993</a></td></tr>
 +
<tr><td>\(t_\text{dub}\)</td><td><i>E. coli</i> doubling time</td><td>30 min</td><td><a href="http://bionumbers.hms.harvard.edu/">BioNumbers</a></td></tr>
 
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Latest revision as of 03:41, 19 September 2015

"What I cannot create I do not understand."
- Richard Feynmann

Parameters

AHL module

Single cell model

Name ValueDescription References/Estimation
\(K_{d,\text{LuxRAHL}}\)100 nMDissociation constant between luxR and AHLWeber, 2013
\(\text{LuxR}_\text{tot}\)0.0025 μMTotal concentration of LuxR estimated
\(a_\mathrm{LuxI}\)1 μM.min-1Maximal production rate of LuxIBasu, 2005
\(a_\mathrm{LuxI,ribo}\)0.1 μM.min-1Maximal production rate of LuxIETHZ 2014
\(k_\mathrm{leaky}\)0.0375 μM-1Coefficient for leakiness dependency on LuxR concentration of PLuxR promoter ETHZ 2013
\(K_\mathrm{a,LuxRAHL}\)9.89 nMActivation coefficient of LuxRAHL Estimated from our own data
\(K_\mathrm{LuxRAHL,ribo}\)285 nMActivation coefficient of LuxRAHL in case of a riboregulated LuxR responsive promoter ETHZ 2014
\(L_\mathrm{lux,ribo}\)0.01463 nM.min-1Leakiness after using riboswitch for Plux ETHZ 2014
\(n_\mathrm{lux}\)1.7Hill coefficient for LuxRAHL activation ETHZ 2014
\(d_\mathrm{LuxI}\)0.0167 min-1Degradation rate of LuxI MIT 2010
\(a_\mathrm{AHL}\)0.04 μM.min-1Production rate of AHL Weber, 2013
\(d_\mathrm{AHL}\)0.01 min-1Degradation rate of AHLBasu, 2005
\(v_\mathrm{AiiA}\)\(k_\mathrm{cat} \cdot C_\mathrm{AiiA} \)Maximal conversion rate of AiiA calculated
\(k_\mathrm{cat}\)1.63×103min-1Turnover number of AiiA Wang, 2004
\(C_\mathrm{AiiA}\)variedConcentration of AiiA estimated
\(K_\mathrm{M,AiiA}\)2.95×103 μM Half-maximal rate substrate concentration of AiiA Wang, 2004
\(a_\mathrm{GFP}\)2 μM.min-1Maximal production rate of GFP Basu, 2005
\(d_\mathrm{GFP}\)0.01 min-1Degradation rate of GFP estimated from doubling time of E. coli

Compartment model

Name ValueDescription References/Estimation
\(N_{d}\) 150Number of E. coli in the doughnut Maximal number of E. coli that would fit on the surface
\(N_{b,max}\) 12798Maximum number of E. coli in the bulk Considering the maximal OD is 2
\(V_{cell,d}\) 6 μm3Volume around an E. coli in the doughnut estimated
\(V_{cell,b,worst}\) 78 μm3Volume around an E. coli in the bulkWorst case, estimated from \(N_{b,max}\)
\(V_{cell,b,norm}\) 1000 μm3Volume around an E. coli in the bulkNormal case

Lactate module

Name Description ValueReferences/Estimation
\(K_{\mathrm{A,Lact}}\) Lumped parameter for the lactate sensor 175 μMBased on the characterization of the promoters.
\( a_\mathrm{LacI}\) Maximal production rate of LacI 1 μM.min-1 Basu, 2005
\( d_\mathrm{LacI}\) Degradation rate of LacI 0.0231 min-1 Basu, 2005
\( K_\mathrm{R,LacI}\) Repression coefficient of LacI0.8 μM Basu, 2005
\( n_1\) Hill coefficient of LldR1.7 estimated
\( n_2\) Hill coefficient of LacI1.7 estimated

Reaction-diffusion model

Name Description ValueReferences/Estimation
\(D_{aq,AHL}\)Diffusion coefficient of AHL through water4.9×10-6cm2/sETHZ 2014
\(D_{m,AHL}\)Diffusion coefficient of AHL through a cell membrane4.629×10-16 m2/sKaplan, et al., 1985
\(R_\text{Jurkat}\)Radius of a Jurkat cell5.75 μmBioNumbers
\(R_\textit{E. coli}\)Short-side radius of an E. coli cell0.5 μmBioNumbers
\(k_\text{int;Lact}\)Lactate import rate by LldP0.008666/sDong, et al., 1993
\(t_\text{dub}\)E. coli doubling time30 minBioNumbers