Degradation of C

The SCB protein (C) degrades.

Chemical equation

$C\rightarrow \varnothing$

Rate equation

$r= d_{C}\cdot[C]$

Parameters

The parameter of this reaction is the degradation rate of C ($d_{C}$). The parameter values were derived from measurements and estimations of autoinducer degradation rates from other bacteria (AHL, PAI2).

Name	Value	Units	Value in previous GBL models	Remarks-Reference
$d_{C}$	$7.68 \cdot 10^{-5}- 2 \cdot 10^{-2}$	$min^{-1}$	$6.7 \cdot 10^{-5} s^{-1}$ $(0.00402 min^{-1})$ Range tested: $0-2 \cdot 10^{-4} s^{-1}$ ($0-0.012 min^{-1}$) Bistability range: $0-0.0085 s^{-1}$ ($0-0.51 min^{-1}$) and $6.7 \cdot 10^{-6}$ $-6.7 \cdot 10^{-3} s^{-1}$ ($0.000402$ $-0.402 min^{-1}$)	Chen et al. empirically calculated the degradation rate of the autoinducer PAI2 in Pseudomonas aeruginosa cultures and reported a best-fit degradation constant of $0.195 h^{-1} (0.00325 min^{-1})$. Chen et al. 2005 Additionally, the degradation rates of the quorum sensing autoinducer AHL have been measured in vitro by Kaufmann et al. and the reported rates for different AHLs are between $1.28 \cdot 10^{-6}-3.07 \cdot 10^{-5} s^{-1}$ $(7.68 \cdot 10^{-5}-1.84 \cdot 10^{-3} min^{-1})$. Weber et al. also reported that the degradation rate of AHL in vivo has been estimated, and is within the range $5 \cdot 10^{-3}-2 \cdot 10^{-2} min^{-1}$. Kaufmann et al. 2005 Weber et al. 2011 With regards to SCBs in particular, according to a review by E. Takano these molecules are very stable and can be still detected after more than 12h into stationary phase. E. Takano 2006 Therefore, we can assume that the degradation rate of SCB is slower than the ones reported for other autoinducers and will not exceed the value $2 \cdot 10^{-2} min^{-1}$.

Parameters with uncertainty

When deciding how to describe the uncertainty for this parameter we must take into consideration that the reported values are either calculated or estimated based on in vitro and in vivo experiments in different bacteria species. Additionally, the values correspond to various autoinducers but not to SCBs. This means that there might be a notable difference between actual parameter values and the ones reported in literature. However, from the published information we can safely assume that SCBs are very stable molecules and their degradation rate will not exceed the maximum rate published for the other autoinducers. These facts influence the quantification of the parameter uncertainty and therefore the shape of the corresponding distribution. By assigning the appropriate weights to the parameter values and using the method described here, the appropriate probability distribution was designed.

Thus, the weight of the distribution is put to $0.0032 min^{-1}$ which is set as the mode of the log-normal distribution for the $d_{C}$ and the Spread is $5.1$, so the range where 68.27% of the values are found is between $6 \cdot 10^{-4}$ and $0.016 min^{-1}$. Thus, it will be possible to also explore potentially slower degradation rates.

The probability distribution for the parameter, adjusted accordingly in order to reflect the above values, is the following:

The values retrieved from literature and their weights are indicated by the blue dashed lines, and the uncertainty for each value is indicated using a default value of 10% error (orange lines).

The parameter information of the distribution is:

Parameter	Mode	Spread	μ	σ
$d_{C}$	$0.0032$	$5.1$	$-4.6234$	$1.0539$