Reconstructing the single-cell-level behavior of a toggle switch from population-level measurements

Single-cell-level behaviors of cells are typically inferred from ensemble measurements. However, such inferences implicitly assume a biological version of ergodicity: the percentage of cells in a state is identical to the probability to find a cell in that state. While the ergodicity does not always hold, it has been rarely tested. Here, we reveal that the ergodicity does not necessarily hold even for simple toggle switches and that apparent stabilities of the switches are due to a balance between single-cell-level biased stabilities and growth rates differences. Therefore, verification of the ergodicity and reconstructing single-cell-level behaviors are crucial for understanding intracellular systems.