Limits on cellular size precision

Cells divide at a reproducible final size, even though growth and signaling dynamics are noisy. Experiments have shown that unicellular organisms' division size typically varies by about 10%-20% in a constant environment. To understand what sets this level of precision, we model stochastic growth dynamics and use a first-passage formalism wherein the cell decides to stop growing based on a noisy estimate of its own size. Our calculations suggest a tradeoff between growth noise and estimator noise, tuned by the estimator’s response time. While a faster response provides the cell with more independent measurements of its size, decreasing error in its size estimate, increasing the gain further also amplifies noise, eventually leading to a noisier estimate. We find that, when growth noise is sufficiently large, division size variance is minimized for nonzero negative feedback; conversely, when estimator noise is comparatively larger, division size variance is minimized when there is no negative feedback. For a class of activator accumulation models, these two limits of negative feedback correspond to sizer and adder correlations, respectively. To further investigate these ideas, we apply our modeling approach to published data on cell size and FtsZ expression dynamics in the bacterium E. coli. We account for experimental measurement noise and discuss the relative contributions of growth noise and expression noise to the division size precision of E. coli.