General mechanism for concentration-based cell size control

Cells control their size to cope with noise during growth and division. Eukaryotic cells exhibiting "sizer" control (targeting a specific size before dividing) may rely on molecular concentration thresholds, but simple implementations of this strategy are not stable. We derive a general criterion for concentration-based sizer control and demonstrate it with a mechanistic model that resolves the instability by using multistage progression towards division. We show that if molecular dynamics in one stage satisfy the sizer criterion, then sizer control follows for the whole progression. We predict that perturbations to the molecular dynamics in non-sizer stages shift the size statistics without disrupting sizer control, consistent with recent experiments in fission yeast.