Binding of R2 to OA operator

The ScbR homo-dimer (R₂) binds to the ScbA gene operator (O_A) and represses its mRNA transcription.

Chemical equation

$O_{A} + 2R_{2} \rightleftharpoons O_{A}-R_{2}$

Rate equation

$r= \frac{k^{-}_{2}}{K_{d2}}\cdot [O_{A}]\cdot [R_{2}]^{2} - k^{-}_{2}\cdot [O_{A}-R_{2}]$

Parameters

The parameters of this reaction are the dissociation constant for binding of ScbR to O_A ($K_{d2}$) and the dissociation rate for binding of ScbR to O_A ($k^{-}_{2}$). ScbR is a member of the TetR family of repressors, named after the member of this group which is the most completely characterized, the TetR repressor protein. TetR binds to the operator tetO, repressing its own expression and that of the efflux determinant tetA in a similar way as ScbR binding to O_R and O_A and repressing its own expression and the expression of ScbA. Therefore parameter values were derived from published data on the TetR-tetO interaction and on tetR-like proteins binding to their corresponding operators.

Name	Value	Units	Value in previous GBL models	Remarks-Reference
$K_{d2}$	$0.005 - 5.8$	$nM$	$7.44 nM$ (Range tested: $10^{-5}-10 nM$) (Bistability range: $7.30-8.30 nM$)	An early publication based on stopped-flow measurements at various salt concentrations reports a KA of $2 \cdot 10^{11} M^{-1}$ , therefore a Kd ($\frac{1}{K_a}$) of $0.005 nM$. Kleinschmidt et al. 1988 Data derived from equilibrium SPR analysis of TetR-tetO interaction report a Ka of $5.6 \pm 2 nM^{-1}$, therefore a Kd ($\frac{1}{K_a}$) of $0.179 \pm 0.5 nM$. Kamionka et al. 2004 Additionally, a study on the TetR-like protein Rv3066 binding to the mmr operon in M. tuberculosis suggests a Kd of $4.4 \pm 0.3 nM$. Bolla et al. 2012 Finally, in vitro studies on TetR-like protein ActR in S. coelicolor suggest a Kd in the range of $0.1-5.8 nM$ Ahn et al. 2007
$k^{-}_{2}$	$0.09-0.85$	$min^{-1}$	N/A	According to the study by Kleinschmidt et al. mentioned above, the maximal association rate constant was $k_{a}= 3 \cdot 10^{8} M^{-1} s^{-1}$. By taking into account the equilibrium association constant reported above ($K_{A}=2 \cdot 10^{11} M^{-1}$), the dissociation rate constant can be calculated as per $k_{2}= \frac{k_a}{K_A}=\frac{3 \cdot 10^{8} M^{-1} s^{-1}}{2 \cdot 10^{11} M^{-1}}=0.0015 s^{-1}= 0.09 min^{-1}$. Kleinschmidt et al. 1988 Additionally, a study on a TetR-like protein (RolR) which binds to its operator rolO and blocks the transcription of rolHMD and of its own gene, in Corynebacterium glutamicum (Gram positive and GC content ~ 50-60% bacteria) reports the dissociation rates $1.41 \cdot 10^{-2} s^{-1} (0.846 min^{-1})$ and $7.34 \cdot 10^{-3}s^{-1} (0.44 min^{-1})$ measured by surface plasmon resonance (SPR). Li et al. 2012

Parameters with uncertainty

The most plausible parameter value for the $K_{d2}$ is decided to be $5 nM$ and the confidence interval $1.1$. This means that the mode of the PDF is 5 and the range where 95% of the values are found is between 4.55 and 5.5 nM.

In a similar way, the most plausible value for $k^{-}_{2}$ is $0.9 min^{-1}$ and the confidence interval $1.3$. This means that the mode of the PDF is 0.9 and the range where 95% of the values are found is between 0.6923 and 1.17 $min^{-1}$.

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

500px 500px

The location and scale parameters of the distributions are:

Parameter	μ	σ
$K_{d2}$	$1.6118$	$0.04834$
$k^{-}_{2}$	$-0.0878$	$0.1327$