A delay model for quorum sensing of Pseudomonas putida

The bacterial strain Pseudomonas putida IsoF, isolated from a tomato rhizosphere, possesses a quorum sensing regulation system, which allows the bacteria to recognise aspects of their environment or to communicate with each other by the so-called autoinducer molecules. In an experimental study, the time series of the autoinducer production did not show the expected behaviour, as it was observed for other bacterial species by indirect measurements. The modelling approach introduced here allows an explanation of the behaviour, supporting the hypothesis of the existence of a further (not yet detected) enzyme, which degrades the autoinducer into an inactive form. Especially the properties of the considered delay differential system allow for the description of the time series. For example the appearance of a first small maximum in the initial phase can be explained by a delay differential equation.