Table 1.

Parameters values.

Parameter	Best fit	Confidence interval	Description
X0* (OD600)	0.064		Initial cell concentration
C* (OD600)	5.8828		Maximum bacterial concentration
B (t−1)	0.6384		Cell growth rate
M (t)	3.2823		Cell growth inflection time
kA ($\frac{O{D}_{490}}{t}$)	1, 561.68	1, 000−2, 000	AI-2 velocity production
km1 (OD600)	1.5793	0.8491−10	the cell growth at half of kA
Xδ** (OD600)	5.7953		Bacterial concentration at the stationary phase
kXA (t−1)	343.98	400−500	AI-2 uptake rate by PTS
km2 (OD600)	5.8205	4.4554−5.8211	Cell growth at half of kXA
kLA (β−gal·t−1)	0.0044	0.0001−0.0999	AI-2 uptake rate by LsrACDB proteins
km3 (OD600)	3.9128	0.001−10	Cell growth at half of kL
kL ($\frac{\beta -gal}{O{D}_{490}·t}$)	0.5825	0.1−5	Operon expression rate
kAL (${(O{D}_{490}·t)}^{-1}$)	0.0028	0.0001−1	lsrACDB genes expression rate
kR (t−1)	0.1037	0.001−5	lsrR gene expression rate
n1	2.9302	0.8096−10	Exponent for adjusting curves
n2	8.9542	2.0857−9	Exponent for adjusting curves
n3**	0.0017		Exponent for adjusting curves

The symbol ^* means that parameters were fixed according to data in Xavier and Bassler (2005a). Symbol ^** means that parameters were fixed based on the profile likelihood graphics. The confidence interval after 500 bootstrap repetitions was calculated within 2.5 and 97.5% quantiles, the confidence interval for parameters in Equation (1) were not calculated.