Binding of R2 to OR operator

The ScbR homo-dimer (R₂) binds to its own gene operator (O_R) and represses its mRNA transcription.

Chemical equation

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

Rate equation

$r= \frac{k^{-}_{1}}{K_{d1}}\cdot [O_{R}]\cdot [R_{2}]^{2} - k^{-}_{1}\cdot [O_{R}-R_{2}]$

Parameters

The parameters of this reaction are the dissociation constant for binding of ScbR to O_R ($K_{d1}$) and the dissociation rate for binding of ScbR to O_R ($k^{-}_{1}$).

Name	Value	Units	Value in previous GBL models	Remarks-Reference
$K_{d1}$	$0.1 - 5.6$	$nM$	$8.82 nM$ (Range tested: $10^{-5}-10 nM$)	TetR-tetO interaction and TetR-like Rv3066 from M. tuberculosis Repressor protein TetR binds to the operator tetO, repressing its own expression and that of the efflux determinant tetA. Similar structure and activity as ScbR binding to OR
$k^{-}_{1}$	$0.6-1.2$	$min^{-1}$	N/A	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 $K_{d1}$ is decided to be $4.5 nM$ and the confidence interval $1.2$. This means that the mode of the PDF is 4.5 and the range where 95% of the values are found is between 3.75 and 5.4 nM.

In a similar way, the most plausible value for $k^{-}_{1}$ 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
$K_{d1}$	$1.5126$	$0.0926$
$k^{-}_{1}$	$-0.0878$	$0.1327$