Biological oscillations without genetic oscillator or external forcing

Abstract

Oscillators play a crucial role in biological systems, enabling complex behaviors such as cell division and circadian cycles. As a result, researchers have been studying both natural and synthetic genetic oscillators. Interestingly, oscillating cellular behaviors are often linked to biological oscillators. In a previous study (1), we discovered sustained oscillations related to phenotypic switching in different cellular systems and gene circuits, without any external forcing. These oscillations were associated with the induction of slow-growing phenotypes. In this paper, we aim to understand when and why such phenotypic instabilities can arise, leading to oscillations in cell populations. To achieve this, we developed a simple mathematical model of a stress phenotype and solved it analytically to determine the range of operating conditions in continuous culture for which the gene expression should not reach a stable equilibrium. This range of conditions is expected to exhibit an unstable biological behavior, which we verified in Bacillus subtilis cultures. Our findings demonstrate that oscillations can occur in the absence of genetic oscillators or external forcing, departing from the classical Monod model. While we explain this phenomenon for the stress response in continuous culture, it is likely that similar unexpected behavior can occur in any long-term culture where there is environmental feedback connecting the inducer and the cellular system considered.