Limited by sensing - A minimal stochastic model of the lag-phase during diauxic growth

Many microbes when grown on a mixture of two carbon sources utilise first and exclusively the preferred sugar, before switching to the less preferred carbon source. This results in two distinct exponential growth phases, often interrupted by a lag-phase of reduced growth termed the lag-phase. While the lag-phase appears to be an evolved feature, it is not clear what drives its evolution, as it comes with a substantial up-front fitness penalty due to lost growth. In this article a minimal mathematical model based on a master-equation approach is proposed. This model can explain many empirically observed phenomena. It suggests that the lag-phase can be understood as a manifestation of the trade-off between switching speed and switching efficiency. Moreover, the model predicts heterogeneity of the population during the lag-phase. Finally, it is shown that the switch from one carbon source to another one is a sensing problem and the lag-phase is a manifestation of known fundamental limitations of biological sensors.