Physical limits on size precision in single-celled microorganisms

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% in a constant environment. To investigate the origins of this precision, we study the fundamental physical limits on setting a size in single cells. We model stochastic growth dynamics and use a first-passage formalism wherein the cell decides to stop growing based on an internal, noisy estimate of its size. When growth and measurement noise are white and uncorrelated, we find that a Kalman filter which minimizes the dynamical estimator error also approximately minimizes the division size variance. We analyze published data and find that E. coli displays long correlation times in its growth rate, while S. pombe displays short correlation times. For S. pombe, simple estimates of white noise in estimator dynamics place our model prediction below the experimental 10% level, suggesting that long correlation times in the estimator noise limit S. pombe's ability to measure its size. In light of this finding, we discuss the relationship between an optimal dynamical filter corrupted by correlated measurement noise and the size variance predicted by our first-passage formalism.