Diffusion of C and Ce

The SCB1 protein (C) diffuses from each cell to the environment and back.

Chemical equation

$C \underset{r \cdot D}{\stackrel{D}{\rightleftharpoons}} C_{e}$

Rate equation

The rate equation is different for the two reactions in order to express the dynamics of the cell density in the environment. Therefore, an additional term $r= V_{cell,tot}/V_{ext}$ is added in the rate of diffusion from the external environment to the cell. This term represents the additional propensity given to the diffusion of extracellular SCB1 by the accumulation of cells in the environment and the consequent increase of cell density. The two rate laws are therefore formed as follows:

$r_{out}= D \cdot ([C_{e}]-[C])$ $r_{in}= r \cdot D \cdot([C]-[C_{e}])$

Further information on the coefficient $r$ and the dynamics of cell growth and division is provided here.

Parameters

The parameter of this reaction is the diffusion rate of C ($D$).

Name	Value	Units	Origin	Remarks
$D$	$0.1-24$	$min^{-1}$	Diffusion rates of autoinducers in Agrobacterium tumefaciens (AAI) and Vibrio fischeri (AHL)

Parameters with uncertainty

The most plausible parameter value for the $D$ is decided to be Failed to parse (Cannot store math image on filesystem.): 10 min^{-1} and the confidence interval $2$. This means that the mode of the PDF is 10 and the range where 95% of the values are found is between Failed to parse (Cannot store math image on filesystem.): 5 and $20 min^{-1}$.

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

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The location and scale parameters of the distribution are:

Parameter	μ	σ
$d_{C}$	Failed to parse (Cannot store math image on filesystem.): 2.4152	$0.3356$