Quorum Sensing

Menten approach (seeEq. 3c, for s and Box1). The equations for

the intracellular and the extracellular C8HSL are formed similar to

those for 3OC6HSL. They found that the system may possess up to

21 different stationary levels; however, the actual number of sta-

tionary levels depends on the given external AIs concentrations; in

any case many of these stationary states will be unstable and there-

fore not experimentally observable.

The last model we will present in this section is a model for the

one QS system of Pseudomonas putida IsoF. The QS signal

1

0.1

a

b

0.01

0.001

0.0001

1e-05

123456

time (hours)

QSM concentration (

μM)

78910

1

0.8

0.6

0.4

0.2

0

time (hours)

fraction of up-regulated cells (N

/Nu

)T

0 2 4 6 8 10121416

Fig. 3(a) Numerical results from [4], fitting model to the experimental data. (b) Predicted evolution of the up-
regulated cell fraction (up-regulated cells divided by total number of cellsNu/NT). Reproduced with permission

Differential Equations to Study Quorum Sensing 261