Transition to Quorum Sensing in an Agrobacterium Population: A Stochastic Model

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Abstract
Understanding of the intracellular molecular machinery that is responsible for the complex collective behavior of multicellular populations is an exigent problem of modern biology. Quorum sensing, which allows bacteria to activate genetic programs cooperatively, provides an instructive and tractable example illuminating the causal relationships between the molecular organization of gene networks and the complex phenotypes they control. In this work we—to our knowledge for the first time—present a detailed model of the population-wide transition to quorum sensing using the example of Agrobacterium tumefaciens. We construct a model describing the Ti plasmid quorum-sensing gene network and demonstrate that it behaves as an “on–off” gene expression switch that is robust to molecular noise and that activates the plasmid conjugation program in response to the increase in autoinducer concentration. This intracellular model is then incorporated into an agent-based stochastic population model that also describes bacterial motion, cell division, and chemical communication. Simulating the transition to quorum sensing in a liquid medium and biofilm, we explain the experimentally observed gradual manifestation of the quorum-sensing phenotype by showing that the transition of individual model cells into the “on” state is spread stochastically over a broad range of autoinducer concentrations. At the same time, the population-averaged values of critical autoinducer concentration and the threshold population density are shown to be robust to variability between individual cells, predictable and specific to particular growth conditions. Our modeling approach connects intracellular and population scales of the quorum-sensing phenomenon and provides plausible answers to the long-standing questions regarding the ecological and evolutionary significance of the phenomenon. Thus, we demonstrate that the transition to quorum sensing requires a much higher threshold cell density in liquid medium than in biofilm, and on this basis we hypothesize that in Agrobacterium quorum sensing serves as the detector of biofilm formation. Understanding the interplay between the extracellular environment and intracellular decision circuitry of a cell is important but is an arduous goal to achieve since many interacting factors, difficult to measure and control in experiment, are involved. The authors address this problem by means of computational modeling using the example of a bacterial population that cooperatively switches on a common gene expression program if a certain critical population density is achieved. They developed a detailed model of the intracellular control network and demonstrated that it can operate as an “on–off” gene expression switch that is sensitive to environmental control and yet highly robust to intracellular molecular noise. The population-wide transition is further modeled using a novel method in which each bacterium is given a unique copy of an intracellular network. This approach, which allows monitoring of both the dynamics of individual cells and population behavior, provides an explanation for the gradual appearance of the transition to the “on” state that has been observed in experiments, and quantitatively predicts the critical value of the population density at which this transition occurs. Unexpectedly, a comparison of the cell densities required for the transition in different environmental conditions brought about a hypothesis regarding the previously elusive ecological and evolutionary function of this cooperative phenomenon.