A mathematical model to investigate quorum sensing regulation and its heterogeneity in Pseudomonas syringae on leaves

• In the present study, a mathematical model has been developed to examine the production of small diffusible signalling molecules by the plant-pathogenic bacterium Pseudomonas syringae pv. syringae, the causative agent of brown spot disease of bean and frost damage to a variety of plants.
• The mathematical modelling in the present study has indicated that the QS activation (autoinduction) of QS diffusible signal in Pss on plants is heterogeneous and is influenced by environmental factors such as water availability on the leaf surface.
• The findings of the present study have enabled a better understanding of the behaviour of bacterial pathogens and have provided a basis to develop control strategies of plant disease.
• This work is the first one to demonstrate the use of mathematical modelling to understand QS of Pss on leaves. The model is generic enough to be applied to other QS systems, especially other AHL-based systems, such as those that human pathogens use.

Pseudomonas syringae is a plant-pathogen which, through the signalling system quorum sensing (QS), controls virulence. In this paper, we use the integral of a non-negative stochastic process to study the QS state of the bacterial colonies it forms when living on leaf surfaces.We investigate the extent to which factors such as water availability and diffusional losses of QS signalling molecules (autoinducers) would affect QS across colonies. Our results support that QS activation is indeed a good indicator of diffusional limitation, as QS is enhanced when diffusion of autoinducers signal decreases (either as a result of water availability or loss by diffusion).Using further experimental data, we explore heterogeneity of QS activation of this bacterium (colonies do not become homogeneously activated) when growing in this natural habitat. We extend our model to test a hypothesis regarding the initial QS potential of the cells. We are able to conclude that stochastic growth and uneven nutrient availability of the leaf surface may contribute only partially to the heterogeneity observed. We discuss the possible (evolutionary) explanations of this strategy.