Single-cell Growth Rate Variability in Balanced Exponential Growth

Exponential accumulation of cell size and highly expressed proteins is observed at the single-cell level in many bacterial species. While the exponential rates fluctuate from cycle to cycle, they remain stable on average over time and strongly correlated across different proteins and cell size. In this study, we investigate growth-rate variability at this state of balanced biosyn-thesis, and present a theoretical framework to explain its properties through the emergence of a high-dimensional collective dynamic attractor. This stable attractor arises from recurrent interactions among multiple cellular components, driving them to converge to the same expo-nential growth rate, thereby sustaining the balanced state. The convergence of growth rates induces a decay in instantaneous growth rate noise throughout the cell cycle, with a faster decay for higher average growth rates. Notably, our analysis identifies random deviations from symmetric division as the primary source of growth rate variability. The theory offers a coherent set of predictions for many observations, validated by extensive experimental single-cell data. The spontaneous emergence of homeostasis through dynamic interactions suggests that specific control mechanisms to compensate deviations from a target may not be necessary to maintain homeostasis in a balanced state.