Formation of homo-dimer R2

Two ScbR (R) proteins bind together to form an ScbR homo-dimer (R₂).

Chemical equation

$2R \rightleftharpoons R_{2}$

Rate equation

$r= \frac{k^{-}_{6}}{K_{d6}}\cdot [R]^{2} - k^{-}_{6}\cdot [R_{2}]$

Parameters

The parameters of this reaction are the dissociation constant for binding of one ScbR to another ($K_{d6}$) and the dissociation rate for binding of one ScbR to another ($k^{-}_{6}$).

Name	Value	Units	Value in previous GBL models	Remarks-Reference
$K_{d6}$	$35.3-114$	$nM$	N/A	Majka et al. published a study on dimerization of the initiator Protein DnaA of Streptomyces and on its mutants, where they report dissociation constants in the range $35.3-114 nM$. Majka et al. 2001 These values agree with Ozbabacan et al. who state that strong protein-protein interactions such as homodimerization have equilibrium dissociation constants $< 10^{-6} M$ and mostly in the nanomolar range.
$k^{-}_{6}$	$2.12-6.84$	$min^{-1}$	N/A	According to Northrup et al. the $k_{a}$ of protein-protein bond formations occur in the order of $10^{6} M^{-1}s^{-1}$. Northrup et al. 1992 Therefore, the range $0.5-5 \cdot 10^{6} M^{-1}s^{-1} (0.03-0.3 nM^{-1} min^{-1})$ is used to generate the probability distribution of $k_{on6}$. Afterwards, the log-normal distribution for the dissociation rate $k^{-}_{3}$ of the ScbR homo-dimer formation is derived from the distributions of $K_{d6}$ and $k_{on6}$.

Parameters with uncertainty

When deciding how to describe the uncertainty for this parameter we must take into consideration that the values reported in literature correspond to in vitro testing of different protein-protein interaction and dimerization reactions than ScbR, although they refer to another Streptomyces protein (DnaA). This means that there might be a difference between actual parameter values and the ones reported in literature. These facts influence the quantification of the parameter uncertainty and therefore the shape of the corresponding distributions.

More specifically, the weight of the sampling is kept at $30 nM$ (value that corresponds to the wild type protein homodimerization) which is set as the mode of the log-normal distribution for the $K_{d6}$. However, we wish to explore the full nanomolar scale when sampling for parameter values and therefore the confidence interval factor is set to $30$. In this way, the range where 95.45% of the values are found is between $1$ and $900 nM$.

Similarly, since the two parameters are interconnected, the mode of the log-normal distribution for the $k^{-}_{6}$ is set to $2 min^{-1}$ and the confidence interval factor is $30$. This means that the range where 95.45% of the values are found is between $0.067$ and $60$ $min^{-1}$.

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
$K_{d6}$	$4.8018$	$1.1835$
$k^{-}_{6}$	$2.094$	$1.1835$