Shape-dependent bounds on cell growth rates

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I consider how cell shape and environmental geometry affect the rate of nutrient capture and the consequent maximum growth rate of a cell, focusing on rod-like species like E.coli. Simple modeling immediately implies that it is the elongated profiles of such cells that allows for them to grow -- as observed -- at exponential rates in nutrient-rich media. Growth is strongly suppressed when nutrient capture is diffusion-limited: In three dimensions, the length is bounded by L t¹/², and in lower dimensions growth is algebraic. Similar bounds are easily obtained for other cell geometries, groups of cells, etc. Fits of experimental growth curves to such bounds can be used to estimate various quantities of interest, including generalized metabolic rates.