Antisense interaction between r and a

The full length mRNA of scbR (r) binds to the full length mRNA of scbA (a) and form a complex which prevents further translation of both mRNAs.

Chemical equation

$a + r \rightleftharpoons r-a$

Rate equation

Failed to parse (Cannot store math image on filesystem.): r= K_{ar}\cdot [r]\cdot [a]-K_{-ar} \cdot [a-r]

Parameters

The parameters of this reaction is the binding and unbinding rate constant for the interaction of scbR mRNA with scbA mRNA ($K_{ar}$) and (Failed to parse (Cannot store math image on filesystem.): K_{-ar} ).

Name	Value	Units	Value in previous GBL models	Remarks-Reference
$K_{ar}$	$0.16-8.24$	Failed to parse (Cannot store math image on filesystem.): nM^{-1} \cdot min^{-1}	Failed to parse (Cannot store math image on filesystem.): 0.001 nM^{-1} \cdot s^{-1} (Bistability range: Failed to parse (Cannot store math image on filesystem.): 6.5 \cdot 10^{-4}-0.16 nM^{-1} \cdot s^{-1} )	In a recent publication by R.A. Cox, genomic properties and macromolecular compositions of Streptomyces coelicolor A3(2) and E.coli were reported, along with equations that connect these properties. For S. coelicolor, the polypeptide elongation rate $ε_{aa}$ is reported to be in the range between 0.59 and 3.17 amino acids s-1, from which the mRNA elongation rate can be calculated according to Cox from the equation $ε_{mRNA}= 3ε_{aa}$ (factor 3 reflects the number of nucleotides per codon), therefore $1.77$ $9.51$ nucleotides $\cdot s^{-1}$. As ScbR has 648 pb, the transcription rate constant can be calculated as per $T_{R}=\frac{648 bp/gene}{1.77 bp/s}=366.1 s/gene=6.1 min/gene$ and $T_{R}=\frac{648 bp/gene}{9.51 bp/s}=68.14 s/gene=1.14 min/gene$, thus resulting in final values of $0.16$ and $0.88 min^{-1}$. Cox et al. 2004 Cox et al. 2004

Name	Value	Units	Origin	Remarks
$K_{ar}$	Failed to parse (Cannot store math image on filesystem.): 0.06-0.18	Failed to parse (Cannot store math image on filesystem.): nM^{-1} \cdot min^{-1}	measurements of antisense mRNA interactions	For the range of values the possibility that high GC contents may affect the constants is taken into account
Failed to parse (Cannot store math image on filesystem.): K_{-ar}	Failed to parse (Cannot store math image on filesystem.): 0.006-6	$min^{-1}$

Parameters with uncertainty

The most plausible parameter value for the $K_{ar}$ is decided to be Failed to parse (Cannot store math image on filesystem.): 0.1 and the confidence interval Failed to parse (Cannot store math image on filesystem.): 1.5 . This means that the mode of the PDF is 0.1 and the range where 95% of the values are found is between 0.067 and 0.15.

Similarly, the most plausible parameter value for the Failed to parse (Cannot store math image on filesystem.): K_{-ar} is decided to be Failed to parse (Cannot store math image on filesystem.): 0.6 and the confidence interval Failed to parse (Cannot store math image on filesystem.): 0.1 . This means that the mode of the PDF is 0.6 and the range where 95% of the values are found is between 0.06 and 6.

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 distribution are:

Parameter	μ	σ
$K_{ar}$	Failed to parse (Cannot store math image on filesystem.): -2.2618	Failed to parse (Cannot store math image on filesystem.): 0.2020
Failed to parse (Cannot store math image on filesystem.): K_{-ar}	$0.3043$	$0.9028$