Periodic forcing of microbial cultures: a model for induction synchrony

Periodic environmental shifts have been used to induce synchrony in many different microbial populations. In this article, the induction synchrony phenomenon is analyzed using an age distribution model in which the age at which the cells divide is subjected to periodic forcing. It is found that synchrony will occur whenever the period of the forcing lies in the interval between the youngest and the oldest division age that occur in the population during the forcing. The analysis also predicts that under certain conditions it should be possible to obtain a multimodal synchrony in which cells in the population are distributed among a set of discrete, synchronized cell lines. The behavior of the age distribution when the conditions for synchrony are not satisfied is briefly explored. It is found that the age distribution model is able to exhibit a very rich spectrum of possible dynamic behavior. Many of the phenomena observed can be thought of in terms that are familiar from nonlinear analysis, such as stable and unstable limit cycles, period doubling, halving, and chaos. The richness of dynamic behavior opens the possibility that environmental shifts or periodic forcing could be used as a powerful tool in discriminating models of microbial kinetics and cell cycle control.