Single-cell Growth Rate Variability in Balanced Exponential Growth

Abstract

Exponential accumulation of cell size and highly expressed proteins is observed in many bacterial species at the single cell level. Exponential rates exhibit cycle-by-cycle fluctuations and correlation across components - different proteins and cell size. In such balanced growth, homeostasis of all variables is maintained simultaneously. In this study, we examine the phenomenological features of growth-rate variability and present a theoretical framework to explain them and the emergence of multi-variable homeostasis. Our findings suggest that homeostasis results from the emergence of a high-dimensional dynamic attractor supporting balanced exponential growth. The stability of this attractor leads to a decay in instantaneous growth rate noise throughout the cell cycle, aligning with empirical findings. We also correctly predict that cells with higher growth rates experience a faster decay in growth rate noise. Surprisingly, our analysis identifies noise generated by uneven cell division as the primary source of variability in growth rates. The theory offers a clear explanation for many observations, validated against extensive single-cell data. The emergence of homeostasis spontaneously from dynamic interactions suggests that specific control mechanisms correcting deviations from a target may be unnecessary.