Binding of R2 to A

The ScbR homo-dimer (R₂) forms a complex with ScbA (A).

Chemical equation

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

Rate equation

$r= \frac{k^{-}_{3}}{K_{d3}}\cdot [A]\cdot [R_{2}] - k^{-}_{3}\cdot [A-R_{2}]$

Parameters

[NOTE TO MARC: I think the parameter values for the k3 are too arbitrary (see explanation below). Is there any way to choose more reliable ones?]

The parameters of this reaction are the dissociation constant for binding of ScbR to ScbA ($K_{d3}$) and the dissociation rate for binding of ScbR to ScbA ($k^{-}_{3}$). Since no evidence of the existence of the ScbA-ScbR complex has been found so far, our belief is that the interaction between the two proteins should be an unstable/ transient. The values of such complexes according to the literature , lie in the millimolar or micromolar scale.

Ozbabacan et al.(2011)

Parameter	Value	Units	Origin	Remarks
$K_{d3}$	$10^{-6} - 10^{-9}$	$nM$	Comparison of strong vs weak protein-protein interactions	The range of values correspond to weak protein interactions. $ΔG^{o}$ interactions of different proteins were investigated by calculating the $K_{eq}$ by using the Van't Hoff equation $\ln K_{eq} = - \frac{{\Delta H^\ominus}}{RT}+ \frac{{\Delta S^\ominus }}{R}.$
$k^{-}_{3}$	$1.1 \cdot 10^{4}- 4.356 \cdot 10^{6}$	$min^{-1}$	From various mechanisms of protein-protein interaction it was deduced that the $K_{a}$ of the reaction should be less than $6.6 \cdot 10^{9} M^{-1}s^{-1}$. Therefore the range of $K_{a}$ is $1 nM^{-1}min^{-1} - 396 nM^{-1}min^{-1}$. Therefore the range of the $k^{-}_{3}$ values is calculated as per $k^{-}_{3}=K_{d3} \cdot K_{a}$, where the value for $K_{d3}$ is assumed to be the most plausible $K_{d3}$ value within the reported range.

Parameters with uncertainty

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

The most plausible parameter value for the $K_{d3}$ is decided to be $10^{3} nM$ and the confidence interval $10$. This means that the mode of the PDF is $1.1 \cdot 10^{4}$ and the range where 95% of the values are found is between $1.1 \cdot 10^{3}$ and $1.1 \cdot 10^{5}$ nM.

In a similar way, the most plausible value for $k^{-}_{3}$ is $6.6\cdot 10^{5} min^{-1}$ and the confidence interval 6. This means that the mode of the PDF is $6.6\cdot 10^{5}$ and the range where 95% of the values are found is between $1.1\cdot 10^{5}$ and $3.96\cdot 10^{6}$ $min^{-1}$.

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
$K_{d3}$	$10.1208$	$0.90284$
$k^{-}_{3}$	$13.9575$	$0.74669$