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 ($k^{-}_{1}$). 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
$K_{d1}$	$0.005 - 5.8$	$nM$	$8.82 nM$ (Range tested: $10^{-5}-10 nM$)	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 $0.005 nM$. 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 $0.179 \pm 0.5 nM$. Additionally, a study on the TetR-like protein Rv3066 binding to the mmr operon in M. tuberculosis suggests a Kd of $4.4 \pm 0.3 nM$. Finally, in vitro studies on TetR-like protein ActR in S. coelicolor suggest a Kd in the range of $0.1-5.8 nM$
$k^{-}_{1}$	$0.6-1.2$	$min^{-1}$	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
$K_{d1}$	$1.5126$	$0.0926$
$k^{-}_{1}$	$-0.0878$	$0.1327$