Difference between revisions of "Team:KU Leuven/Modeling/Internal/Ultra/Test"

2.1 Cell A

The designed circuit in Cell A is under control of a temperature sensitive cI repressor. Upon raising the temperature, the circuit is activated and production of LuxR and LuxI initiates. LuxI will consectively produce AHL, which binds with LuxR to activate the production of Leucine and Ag43. We can extract the following ODE's from this circuit:
${\alpha}$:transcription term, ${\beta}$:translation term, ${d}$:degradation term, ${D}$:diffusion term ${K_d}$:dissociation constant, ${n}$:hill coefficient, ${L}$:leak term $$\frac{{\large d} m_{cI}}{d t} = \alpha_1 {\cdot} cI_{gene} - d_{mCI} {\cdot} m_{cI}$$ $$\frac{{\large d}{cI}}{d t} = \beta_{cI} {\cdot} {cI} -2 {\cdot} {k_{cI,dim}} {\cdot} {cI}^2 + 2 {\cdot}{k_{-cI,dim}}{\cdot} {[cI]_2} - d_{cI} {\cdot} {cI}$$ $$\frac{{\large d}{[cI]_2}}{d t}= k_{cI,dim} {\cdot} {cI}^2 - {k_{-cI,dim}}{\cdot} {[cI]_2} $$ $$\frac{{\large d} m_{LuxI}}{d t} = (L_{lambda} + {\frac{\alpha_{lambda}}{1 + ({\frac{[cI]_2}{K_{d1}}})^{n_{cI}}}}) {\cdot} LuxI_{gene} - d_{mLuxI} {\cdot} m_{LuxI} $$ $$\frac{{\large d} m_{LuxR}}{d t} = (L_{lambda} + {\frac{\alpha_{lambda}}{1 + ({\frac{[cI]_2}{K_{d1}}})^{n_{cI}}}}) {\cdot} LuxR_{gene} - d_{mLuxR} {\cdot} m_{LuxR} $$ $$\frac{{\large d} LuxI}{d t} = \beta_{LuxI} {\cdot} {m_{LuxI}} - d_{LuxI} {\cdot}{LuxI} $$ $$\frac{{\large d} LuxR}{d t} = \beta_{LuxR} {\cdot} {m_{LuxR}} -k_{lux,as} {\cdot}{LuxR}{\cdot}{AHL_{in}} + k_{lux,dis}{\cdot}{[LuxR/AHL]} - d_{LuxR} {\cdot}{LuxR} $$ $$\frac{{\large d} AHL_{in}}{d t} = {k_{luxI}} {\cdot} {luxI} - k_{lux,as} {\cdot}{luxR}{\cdot}{AHL_{in}} + k_{lux,dis}{\cdot}{[luxR/AHL]}+ ( {D_{IN,AHL}} {\cdot} {AHL_{out}} - {D_{OUT,AHL}} {\cdot} {AHL_{in}} ) - d_{AHL,in} {\cdot} {AHL_{in}}$$ $$\frac{{\large d} AHL_{out}}{d t} = ( {D_{OUT,AHL}} {\cdot} {AHL_{in}} - {D_{IN,AHL}}{\cdot}{AHL_{out}} ) -d_{AHL,out}{\cdot}{AHL_{out}}$$ $$\frac{{\large d} [luxR/AHL]}{d t} = k_{lux,as} {\cdot}{luxR}{\cdot}{AHL_{in}} - k_{lux,dis}{\cdot}{[luxR/AHL]} - 2 {\cdot} k_{lux,dim} {\cdot}{[luxR/AHL]^2} + 2 {\cdot}{k_{-lux,dim}}{\cdot}{[luxR/AHL]_{2}}$$ $$\frac{{\large d} [luxR/AHL]_{2}}{d t} = k_{lux,dim} {\cdot}{[luxR/AHL]^2} - k_{- lux,dim} {[luxR/AHL]} $$ $$\frac{{\large d} m_{ilvE}}{d t} = (L_{lux} + \frac{\alpha_{lux}}{1+(\frac{K_{d2}}{[luxR/AHL]_{2}})^{n_{lux}}} ) {\cdot} ilvE_{gene} - d_{milvE} {\cdot} {m_{ilvE}} $$ $$\frac{{\large d} m_{Ag43}}{d t} = (L_{lux} + \frac{\alpha_{lux}}{1+(\frac{K_{d2}}{luxR/AHL]_{2}})^{n_{lux}}} ) {\cdot} Ag43_{gene} - d_{mAg43} {\cdot} {m_{Ag43}} $$ $$\frac{{\large d} Transaminase B}{d t} = \beta_{TB} {\cdot} {m_{ilvE}} - d_{TB} {\cdot} {Transaminase B} $$ $$\frac{{\large d} Leucine_{out}}{d t} = (D_{OUT,Leu} {\cdot}{leucine_{in}} - D_{IN,Leu} {\cdot}{leucine_{out}}) - d_{Leu,out} {\cdot} {Leucine_{out}} $$ $$\frac{{\large d} Ag43}{d t} = \beta_{Ag43} {\cdot} {m_{Ag43}} - d_{Ag43} {\cdot} {Ag43} $$ We visualize these ODE's in Simbiology which results in the following diagram:

2.1 Cell B

We can repeat this assignment for Cell B: $$\frac{{\large d} m_{cI}}{d t} = \alpha_1 {\cdot} cI_{gene} - d_1 {\cdot} m_{cI}$$ $$\frac{{\large d}{cI}}{d t} = \beta_1 {\cdot} {cI} -2 {\cdot} {k_{cI,dim}} {\cdot} {cI}^2 + 2 {\cdot}{k_{-cI,dim}}{\cdot} {[cI]_2} - d_{cI} {\cdot} {cI}$$ $$\frac{{\large d}{[cI]_2}}{d t}= k_{cI,dim} {\cdot} {cI}^2 - {k_{-cI,dim}}{\cdot} {[cI]_2} $$ $$\frac{{\large d} m_{luxR}}{d t} = (L_{lambda} + {\frac{\alpha_{lambda}}{1 + ({\frac{cI}{K_{d1}}})^{n_{cI}}}}) {\cdot} luxR_{gene} - d_{mluxR} {\cdot} m_{luxR} $$ $$\frac{{\large d} luxR}{d t} = \beta_{luxR} {\cdot} {m_{luxR}} - d_{luxR} {\cdot}{luxR} $$ $$\frac{{\large d} AHL_{in}}{d t} = ( {D_{IN,AHL}} {\cdot} {AHL_{out}} - {D_{OUT,AHL}} {\cdot} {AHL_{in}} ) - k_{lux,as}{\cdot}{luxR}{\cdot}{AHL_{in}} + k_{lux,dis}{\cdot}{[luxR/AHL]} - d_{AHL,in} {\cdot} {AHL_{in}} $$ $$\frac{{\large d} AHL_{out}}{d t} = ( {D_{OUT,AHL}} {\cdot} {AHL_{in}} - {D_{IN,AHL}}{\cdot}{AHL_{out}} ) -d_{AHL,out}{\cdot}{AHL_{out}} $$ $$\frac{{\large d} [luxR/AHL]}{d t} = k_{lux,as} {\cdot}{luxR}{\cdot}{AHL_{in}} - k_{lux,dis}{\cdot}{[luxR/AHL]} - 2 {\cdot} k_{lux,dim} {\cdot}{[luxR/AHL]^2} + 2 {\cdot}{[luxR/AHL]_{2}} $$ $$\frac{{\large d} [luxR/AHL]_{2}}{d t} = k_{lux,dim} {\cdot}{[luxR/AHL]^2} - k_{- lux,dim} {[luxR/AHL]} $$ $$\frac{{\large d} m_{CheZ}}{d t} = (L_{lux} + \frac{\alpha_{lux}}{1+(\frac{K_{d2}}{[luxR/AHL]_{2}})^{n_{lux}}} ) {\cdot} CheZ_{gene} - d_{mCheZ} {\cdot} {m_{CheZ}} $$ $$\frac{{\large d} m_{PenI}}{d t} = (L_{lux} + \frac{\alpha_{lux}}{1+(\frac{K_{d2}}{luxR/AHL]_{2}})^{n_{lux}}} ) {\cdot} PenI_{gene} - d_{mPenI} {\cdot} {m_{PenI}} $$ $$\frac{{\large d} CheZ}{d t} = \beta_{CheZ} {\cdot} {m_{CheZ}} - d_{CheZ} {\cdot} {CheZ} $$ $$\frac{{\large d} PenI}{d t} = \beta_{PenI} {\cdot} {m_{PenI}} - d_{PenI} {\cdot} {PenI} $$ $$\frac{{\large d} m_{RFP}}{d t} = (L_{Pen} + {\frac{\alpha_{Pen}}{1 + ({\frac{PenI}{K_{d3}}})^{n_{Pen}}}}) {\cdot} RFP_{gene} - d_{mRFP} {\cdot} m_{RFP} $$ $$\frac{{\large d} RFP}{d t} = \beta_{RFP} {\cdot}{m_{RFP}} - d_{RFP} {\cdot}{RFP} $$ We visualize these ODE's in the Simbiology toolbox. This gives us the following diagrams:

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X. Parameters

[1] Temporal Patterns Generated by Salmonella typhimurium, D. E. Woodward, R. Tyson, M. R. Myerscough, J. D. Murray, E. 0.Budrene,l and H. C.Berg , Biophysical Journal Volume 68 May 1995 2181-2189

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