Single cell model

Motivation:

The last decades have been marked by a high technological development in the field of computation. This has allowed synthetic biology to use modeling tools to predict behaviors and thus make more efficient the construction of genetic circuits.

We have used these tools to model two of our constructs: pFadBA_34_RFP and pFadBA_34_luxR_plux_32_RFP.

Regarding the model for pFadBA_34_RFP:

To analyze the response of pFadBA promoter to palmitic acid (PA) presence, we have used the RFP reporter protein to obtain fluorescence measurements. The issue of those experiments was that the PA has effects in the fluorescence over a concentration of 1mM, which generates a lot of noise. Because of this, we could not obtain experimentally the complete transfer function of this construct.

Nevertheless, we have made parameter optimization with weighted non-linear regression functions in order to obtain the curve that fitted the best our less noisy data. With this, we were able to estimate the whole transfer function of our construct.

Regarding the model for pFadba_34_luxR_plux_32_RFP:

In this case, even if we had the same problem that with pFadBA, since luxR/plux amplifies considerably the signal, we could obtain the whole curve with acceptable noise levels. Here, we also adapted our parameters to obtain a model that reflects the best the behaviour of the construct.

pFadBA model was created to complement and refine the experimental data, in contrast to pFadba_34_luxR_plux_32_RFP whose model was created for a different aim.The pFadba_34_luxR_plux_32_RFP system response is dependent on an eternal inducer: lactone. Having a model that predicts how much lactone is necessary for the modulation we want will facilitate its use in the future.

The ODE for the pFadBA_34_RFP and pFadba_34_luxR_plux_32_RFP systems are given below:

$$ X_{FadR}= [FadR]\left(\frac{Kd_2^{n_1}}{[FA]^{n_1}+Kd_1^{n_1}}\right) $$ $$ \frac{d[RFP]}{dt}=\alpha_{RFP} [RFP] \left(\frac{Kd_5^{n_5}}{Kd_5^{n_5}+X_{FadR}^{n_5}}\right) - \gamma_{RFP} [RFP] $$ $$ \frac{d[luxR]}{dt}=\alpha_{luxR} [luxR] \left(\frac{Kd_2^{n_2}}{Kd_2^{n_2}+X_{FadR}^{n_2}}\right) - \gamma_{luxR} [luxR] $$ $$ luxR_{AHL} = [luxR] \left(\frac{[AHL]^{n_3}}{[AHL]^{n_3}+Kd_3^{n_3}}\right) $$ $$ \frac{d[RFP]}{dt} = \alpha_{RFP} \left(\frac{[luxR_{AHL}]^{n_4}}{Kd_4^{n_4}+[luxR_{AHL}]^{n_4}}\right) - \gamma_{RFP} [RFP] $$Both sets of experimental data were convoluted in order to obtain a general deterministic model for pFadBA promoter.

pfadBA_34_RFP experimental fitting to the model.

pFadBA_34_luxR_plux_RFP experimental fitting of the model.

Conclusions:

We can say that with these models we have obtained a consistent way to predict and analyze the pFadBA promoter behaviour.

Parameters:

Parameter | Value | Reference |
---|---|---|

$Kd_1$ |
1200 $\mu$M | Data Fitted |

$Kd_2$ | 0.13 $\mu$M | iGEM Taida 2012 |

$\alpha_{luxR}$ | 0.000325 $\mu$M/min | Data Fitted |

$\gamma_{luxR}$ | 0.0231 $min^{-1}$ | iGEM Zurich ETH 2014 |

$n_1$ | 3 | iGEM Taida 2012 |

$n_2$ | 2 | iGEM Taida 2012 |

$\alpha_{RFP}$ | 3.5 | Data Fitted |

$\gamma_{RFP}$ | 0.0041 $min{-1}$ | Data Fitted |

$Kd_3$ |
0.0001892 nM | Literature |

$Kd_4$ | 0.015 nM | Literature |

$n_3$ | 2 | Literature |

$n_4$ | 1 | Literature |

[FadR] | 0.16 $\mu$M | Assumption |