When $a \ne 0$, there are two solutions to \(ax^2 + bx + c = 0\) and they are $$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.\leftrightarrow$$ List of chemical species:
Symbol | Description |
---|---|
$O_{T7}$ | T7 polymerase gene, controlled by LacO operon |
Constant | Value | Unit | Description |
---|---|---|---|
$$k_{sMR}$$ | $$24.67^{*}$$ | $$nM min^{-1}$$ | Transcription rate of LacI-mRNA, constitutive promoter |
$$\lambda_{MR}$$ | $$0.462$$ | $$min^{-1}$$ | Degradation rate of LacI-mRNA |
$$k_{sR}$$ | $$15$$ | $$min^{-1}$$ | Translation rate of LacI protein |
$$\lambda_{R}$$ | $$0.2$$ | $$min^{-1}$$ | Degradation rate of LacI protein |
$$k_{2R}$$ | $$50$$ | $$nM^{-1} min^{-1}$$ | Dimerization rate of LacI monomer |
$$k_{-2R}$$ | $$10^{-3}$$ | $$min^{-1}$$ | Dissociation rate of LacI dimer |
$$k_{rT7}$$ | $$960$$ | $$nM^{-1} min^{-1}$$ | Binding constant, LacI dimer and T7 LacO |
$$k_{-rT7}$$ | $$2.4$$ | $$min^{-1}$$ | Unbinding constant, LacI dimer and T7 LacO |
$$\lambda_{R2}$$ | $$0.2$$ | $$min^{-1}$$ | Degradation rate of LacI dimer |
$$k_{dr1}$$ | $$3\times10^{-7}$$ | $$nM^{-2}min^{-1}$$ | Rate constant of forming IPTG-LacI dimer |
$$k_{-dr1}$$ | $$12$$ | $$min^{-1}$$ | Rate constant of dissociating IPTG-LacI dimer |
$$k_{dr2}$$ | $$3\times10^{-7}$$ | $$nM^{-2}min^{-1}$$ | Rate constant, IPTG displacing LacI dimer from the T7 LacO |
$$k_{-dr2}$$ | $$4.8\times10^3$$ | $$min^{-1}$$ | Rate constant, IPTG-LacI binding to empty T7 LacO, releasing two IPTG molecules |
$$k_{rCre}$$ | $$960$$ | $$nM^{-1}min^{-1}$$ | Binding constant, LacI dimer and Cre LacO |
$$k_{-rCre}$$ | $$2.4$$ | $$min^{-1}$$ | Unbinding constant, LacI dimer and Cre LacO |
$$k_{dr3}$$ | $$3\times10^{-7}$$ | $$nM^{-2}min^{-1}$$ | Rate constant, IPTG displacing LacI dimer from the Cre LacO |
$$k_{-dr3}$$ | $$4.8\times10^3$$ | $$min^{-1}$$ | Rate constant, IPTG-LacI binding to empty Cre LacO, releasing two IPTG molecules |
$$\lambda_{I2R2}$$ | $$0.2$$ | $$min^{-1}$$ | Degradation rate of $IPTG_2-LacI_2$ |
$$k_{s0MT7}$$ | $$0.01$$ | $$min^{-1}$$ | Leaky transcription rate of T7 mRNA (LacI bound) |
$$k_{s1MT7}$$ | $$0.5$$ | $$min^{-1}$$ | Transcription rate of T7 mRNA (empty LacO) |
$$\lambda_{MT}$$ | $$0.462$$ | $$min^{-1}$$ | Degradation rate of T7 mRNA |
$$k_{sT7}$$ | $$30$$ | $$min^{-1}$$ | Translation rate of T7 protein |
$$\lambda_{T7}$$ | $$0.2$$ | $$min^{-1}$$ | Degradation rate of T7 protein |
$$k_{s0MCre}$$ | $$0.01$$ | $$min^{-1}$$ | Leaky transcription rate of Cre mRNA (LacI bound) |
$$k_{s1MCre}$$ | $$0.5$$ | $$min^{-1}$$ | Transcription rate of Cre mRNA (empty LacO) |
$$\lambda_{MCre}$$ | $$0.462$$ | $$min^{-1}$$ | Degradation rate of Cre mRNA |
$$k_{sCre}$$ | $$30$$ | $$min^{-1}$$ | Translation rate of Cre protein |
$$\lambda_{Cre}$$ | $$0.2$$ | $$min^{-1}$$ | Degradation rate of Cre protein |
![](https://static.igem.org/mediawiki/2017/d/d1/IGEM_Edinburgh_UG_Modeling_fig._2.png)