Transcription of a

The scbA gene is transcribed into scbA mRNA (a).

Chemical equation

$O_{A} \rightarrow O_{A} + a$ (maximum transcription in the scenario where the activating complex $A-R_2$ does not exist) $O_{A}'-AR_{2} \rightarrow O_{A}'-AR_{2} + a$ (maximum transcription in the scenario where the activating complex $A-R_2$ exists) $O_{A}-R_{2} \rightarrow O_{A}-R_{2} + a$ (basal transcription)

Rate equation

$r= T_{A}\cdot [O_{A}]$ or $r= T_{A}\cdot [O_{A}'-AR_{2}]$ $r= T_{A_{basal}}\cdot [O_{A}-R_{2}]$

Parameters

The parameters of this reaction are the basal and maximum transcription rate of ScbA ($T_{A}$ and $T_{A_{basal}}$). These parameters are derived by the strength of the promoter ($\Omega_{A}$ and $\Omega_{A_{basal}}$) but also taking into account the transcriptional interference by the scbR promoter. In this model, we have assumed that the isolated promoter strength is equal to the number of transcripts produced per unit of time. Therefore, the parameters $\Omega_{A}$ and $\Omega_{A_{basal}}$ are assumed to be equal to the transcription rate constant of the isolated promoter. These parameter values were derived from published data on E.coli mRNA transcription rate and calculations based on genomic properties of Streptomyces coelicolor A3(2). Additionally, the firing rate (elongation initiation rate) constant ($k_{F}$) is needed. This parameter is also derived from literature and is sampled from the same distribution for both scbR and scbA promoters, but is then multiplied by a heterogeneity factor $\chi$ to calculate the final $k_{F_A}$ for the scbA promoter. The heterogeneity factor for each promoter is sampled from a xxx distribution.

Name	Value	Units	Value in previous GBL models	Remarks-Reference
$Omega_{A}$	$0.11-5.65$	$min^{-1}$	$0.45 s^{-1}$ (Range tested: $10^{-4}-10 s^{-1}$) (Bistability range: $0.44-0.5 s^{-1}$ and $0.0225-0.9 s^{-1}$)	In a recent publication by R.A. Cox, genomic properties and macromolecular compositions of Streptomyces coelicolor A3(2) and E.coli were reported, along with equations that connect these properties. For S. coelicolor, the polypeptide elongation rate $ε_{aa}$ is reported to be 3.17 amino acids s-1, from which the mRNA elongation rate can be calculated according to Cox from the equation $ε_{mRNA}= 3ε_{aa}$ (factor 3 reflects the number of nucleotides per codon), therefore $9.51$ nucleotides $\cdot s^{-1}$. As ScbA has 945 pb, the transcription rate constant can be calculated as per $T_{A}=\frac{945 bp/gene}{1.77 bp/s}=533.9 s/gene=8.89 min/gene$ $T_{A}=\frac{945 bp/gene}{9.51 bp/s}=99.37 s/gene=1.66 min/gene$, thus resulting in final values of $0.11 min^{-1}$ and $0.60 min^{-1}$. Cox et al. 2004 Cox et al. 2004 Additionally, Bremer et al. have reported an mRNA transcription rate of 55 noucleotides/s for E. coli, a value which is also shared by R.A. Cox, while Vogel et al. have published a range of mRNA transcription rates in the range of 28-89 noucleotides/s, depending on different growth rates of E. coli. By the same calculations, the corresponding transcription rate constants are $3.49 min^{-1}$ and $1.78-5.65 min^{-1}$. Bremer et al. 2004 Vogel et al. 2004
$k_{F}$	$18-33$	$min^{-1}$	N/A	Pai et al. reported a typical transcription initiation rate in QS systems to be $20 min^{-1}$. Pai et al. 2009 This value is also supported by Kennell et al. who calculated the transcription initiation rates from experimental data derived from in vitro experiments using E. coli. The results showed one initiation every 3.3 sec (therefore transcription rate $18.2 min^{-1}$). Kennell et al. 1977 Finally, Tadmor et al. reported a maximum transcription initiation rate of $33 min^{-1}$ in E. coli based on observational data. Tadmor et al. 2008

From the $k_{F_{A}}$ and the $\Omega_{A}$ and $\Omega_{A_{basal}}$ the basal and maximal occupancy ($\theta^o_{A_{basal}}$ and $\theta^o_{A}$) of the isolated scbA promoter can be calculated as per $\theta^o_{A_{basal}}=\frac{\Omega_{A_{basal}}}{k_{F_{A}}}$ and $\theta^o_{A}=\frac{\Omega_{A}}{k_{F_{A}}}$. Also, by employing the ratio of the bound vs. total promoter $\rho_{A}=\frac{[O_{A}-R_{2}]}{[O_{A}]+[O_{A}-R_{2}]}$, the effective occupancy of the isolated scbA promoter can be calculated as per $\theta^o_{eff_{A}}=\rho_{A}\cdot \theta^o_{A_{basal}}+ (1-\rho_{A})\cdot \theta^o_{A}$. Similarly, the effective occupancy of the isolated scbR promoter ($\theta^o_{eff_{A}}$)is calculated as described in theTranscription of r. Therefore, the promoter relative activity is equal to $\frac{P_A}{P^o_A}=\frac{1}{1+\frac{\theta^o_{eff_{R}}\cdot (1-\theta^o_{eff_{A}})}{(1-\theta^o_{eff_{R}})}}$ and the final basal and maximal transcription rate constants are calculated as per $T_{A_{basal}}=\frac{P_A}{P^o_A} \cdot \Omega_{A_{basal}}$ and $T_{A}=\frac{P_A}{P^o_A} \cdot \Omega_{A}$ respectively.

Parameters with uncertainty

When deciding how to describe the uncertainty for this parameter we must take into consideration that the reported values are either calculated or derived with approximation from experiments and from other macromolecular properties. Additionally, some of the values correspond to mRNA transcription rates of different bacteria species (E. coli). This means that there might be a notable difference between actual parameter values and the ones reported in literature. These facts influence the quantification of the parameter uncertainty and therefore the shape of the corresponding distributions. Therefore, by assigning the appropriate weights to the parameter values and using the method described here, the appropriate probability distributions were designed.

Therefore, although the weight of the distribution is put on the values calculated for S. coelicolor by setting $0.57 min^{-1}$ as the mode of the log-normal distribution for the $\Omega_{A}$, we wish to explore the full range of reported values. Thus, the confidence interval factor is set to $12.5$ and the range where 95.45% of the values are found is between $0.0457$ and $7.17$ $min^{-1}$.

With regards to the firing rate $k_F$, the reported values are within the range of $18-33 min^{-1}$ with the most probable values being $18-20 min^{-1}$. Since these values are reported as being the average rates (and $33 min^{-1}$ being the maximum), we will also sample lower values, so the final sampling range will be around the values $10-33 min^{-1}$. The mode of the distribution is set to $20.4 min^{-1}$ and the confidence interval factor is set to $1.74$. Therefore, the range where 95.45% of the values are found is between $12$ and $35.6$ $min^{-1}$.

The probability distributions for the parameters, adjusted accordingly in order to reflect the above values, are the following:

The location and scale parameters of the distribution are:

Parameter	μ	σ
$\Omega_{A}$	$0.35405$	$0.95491$
$k_{F}$	$3.0886$	$0.2686$