Binding of A-R2 to OA' operator

The ScbA-ScbR complex (AR₂) binds to the alternative ScbA gene operator (O_A') and activates its maximum mRNA transcription.

Chemical equation

$O_{A}' + AR_{2} \rightleftharpoons O_{A}'-AR_{2}$

Rate equation

$r= \frac{k^{-}_{5}}{K_{d5}}\cdot [O_{A}']\cdot [AR_{2}] - k^{-}_{5}\cdot [O_{A}'-AR_{2}]$

Parameters

The parameters of this reaction are the dissociation constant for binding of ScbA-ScbR to O_A' ($K_{d5}$) and the dissociation rate for binding of ScbA-ScbR to O_A' ($k^{-}_{5}$).

Name	Value	Units	Origin	Remarks
$K_{d5}$	$0.1 - 5.6$	$nM$	TetR-tetO interaction and TetR-like Rv3066 from M. tuberculosis	The values were chosen by assuming that the interaction would be within the same range of strength as the ScbR-OA (without the complex).
$k^{-}_{5}$	$0.6-1.2$	$min^{-1}$	SPR of a TetR-like protein (RolR) on a Gram and GC content ~ 50-60% from Corynebacterium glutamicum

Parameters with uncertainty

The most plausible parameter value for the $K_{d5}$ 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 $k^{-}_{5}$ 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:

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The location and scale parameters of the distributions are:

Parameter	μ	σ
$K_{d5}$	$1.6118$	$0.04834$
$k^{-}_{5}$	$-0.0878$	$0.1327$