Length, Area or Volume? How the cell's definition of its size affects size fluctuations

How single-celled organisms achieve size homeostasis during growth and division is an important question. To divide at the correct size, cells must be able to estimate their own size. A cell can have its rate-limiting growth in different dimensions, e.g. length, area or volume (which differ only by factors of cell radius for the cylindrical cells considered here). Similarly, the cell can also estimate its size in any of these dimensions. It is of considerable biological interest to determine which dimension is used for which purpose. Here, we explore how different choices affect fluctuations in cell size at division. We address this by analyzing a phenomenological, stochastic model for coupled growth and size estimation. The cell stops growing and divides when the estimator reaches a threshold value. In the simplest case, in which rate-limiting growth and size estimation occur along the same dimension, this dimension should have the smallest relative variance at division; fluctuations in the cylinder radius can only increase the variances of the other dimensions. Things become more complicated when the dimensions for rate-limiting growth and estimation are different, as current evidence suggests is the case for E. coli. We then predict that either dimension can have the smallest relative variance, depending on the magnitude of the estimation noise.