IGEM:IMPERIAL/2009/M1/Modelling/M1 1/detailed

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<ul> <li class="menu_header"><img src="http://2009.igem.org/wiki/images/c/c1/II09_Thumb_m1.png" width="15%" align="left"> Module 1: Protein production</li> <li><a href="http://openwetware.org/wiki/IGEM:IMPERIAL/2009/M1"> Overview</a></li> <li><a href="http://openwetware.org/wiki/IGEM:IMPERIAL/2009/M1/Genetic"> Genetic circuit</a></li> <li><a href="http://openwetware.org/wiki/IGEM:IMPERIAL/2009/M1/Results"> Results</a></li> <li><a href="http://openwetware.org/wiki/IGEM:IMPERIAL/2009/M1/Modelling"> Modelling</a></li> </ul>

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In the absence of IPTG:

Equation 1: Equation describing the rate of transcription of LacI MRNA (M_LacI):

k_mlacI is the transcription rate of M_lacI (a measure of promoter strength) and d_mlacI is the degradation rate. At steady state [math]\displaystyle{ \frac{d[M_{lacI}]}{dt} = 0 }[/math] so [math]\displaystyle{ M_{lacI} =\frac{k_{mlacI}}{d_{mlacI}} }[/math]

Equation 2: Equation describing the rate of translation of LacI protein (P_lacI)

At steady state [math]\displaystyle{ P_{lacI}= \frac{k_{mlac} k_{plac}}{d_{mlac} d_{plac}} }[/math] , where k_plac is the translation rate of lacI protein and d_placI is the degradation rate of P_lacI.

Equations 3 and 4 describe the transcription and translation of the protein of interest P_out.

Equation 3: Transcription of P_out Unlike in the previous case, the output promoter is inducible. In the absence of further information, we model the effect of LacI on transcription/ POPS activity with a Hill function, which represses when amounts are above the threshold K, and activates when P_lacI amounts fall below threshold. Such assumption can be revised in the light of contradicting experimental data.

At steady state: [math]\displaystyle{ Mout=\frac{k_{mout}}{d_{mout}}[k_{leak}+(1-k_{leak})\frac {K^n}{K^n+P_{lacI}^n }] }[/math] where k_leak is the lac promoter leakiness factor, K is the switching threshold of P_lacI} concentration needed to repress, n is the hill exponent k_mout is the transcription rate of Mout and d_mout is the degradation rate.

Equation 4: Equation describing the rate of translation of protein of interest P_out:

At steady state [math]\displaystyle{ P_{out} = \frac{k_{pout}}{d_{pout}}M_{out} }[/math] so [math]\displaystyle{ P_{out}= \frac{k_{mout}k_{pout}}{d_{mout}d_{pout}}[k_{leak}+(1-k_{leak})\frac {K^n}{K^n+P_{lacI}^n }] }[/math] which relates to the initial prediction that when the Lac promoter is weak and there is not enough P_lacI , we don’t get sufficient repression of production of our protein of interest. When levels of P_lacI go below the repression threshold, we get a “bump” in production.

When IPTG is introduced

When IPTG is added into the system, LacI can bind to it, forming an intermediate complex [IPTG-LacI]:

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IGEM:IMPERIAL/2009/M1/Modelling/M1 1/detailed

In the absence of IPTG:

When IPTG is introduced

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