Multiple timescales in bacterial growth homeostasis

In balanced exponential growth, bacterial cells maintain the stability of multiple properties simultaneously: cell size, growth rate, cycle time and more. These are not independent but strongly coupled variables; it is not a-priori clear which are under direct regulation and which are stabilized as a by-product of interactions. Here, we address this problem by separating different timescales in bacterial single-cell dynamics. Disentangling homeostatic set-points from fluctuations around them, we find that some properties have flexible set-points that highly sensitive to environment - defining "sloppy" variables, while other set-points are buffered and held tightly controlled - "stiff" variables. These control variables are combinations of sloppy ones that compensate one another over long times, creating a hierarchical buffering that protects them from environmental perturbations. This is manifested geometrically as a control manifold in the space of growth and division variables, whose in-plane directions span sloppy variables, while out-of-plane deviations are highly constrained. Cell size is found to be a sloppy variable, which is coupled to growth and division only on the short, single-cycle timescale. Our results show that cellular homeostasis involves multi-level regulation operating on multiple timescales. More generally, our work offers a data-driven approach for identifying control variables in a multi-dimensional system that can be applicable also in other contexts.