Effect of Size Variability, Filamentation and Division Dynamics on Escherichia coli Allometry

The cell surface area (SA) increase with volume (V) for cells is determined by growth and regulation of size and shape. Most studies of the rod-shaped model bacterium Escherichia coli have focussed on the phenomenology or molecular mechanisms governing such scaling. Here, we proceed to examine the role of population statistics and cell division dynamics in such scaling by a combination of microscopy, image analysis and statistical simulations. We find that while cells sampled from mid-log cultures follow a 2/3 exponent, similar to geometric (Platonic) solids, drug induced filamentous cells have higher exponent values. Modulating the growth rate to change the proportion of filamentous cells, we find SA-V scales with an exponent > 2/3, exceeding that predicted by the geometric scaling law. However, since increasing growth rates alter the mean and spread of population cell size distributions, we use statistical modeling to disambiguate between the effect of the mean size and variability. Simulating (i) increasing mean cell length with a constant standard deviation (s.d.) and (ii) a constant mean length with increasing s.d. results in scaling exponents that exceed the 2/3 geometric law, when population variability is included. In order to overcome possible effects of statistical sampling of unsynchronized cell populations, we virtually synchronized the estimation of SA-V scaling from single cell growth experiments. We find the exponent depends on the stage with the maximal cell length heterogeneity and scaling exponent observed during the intermediate period between birth (B) and division (D) stages. These results point to a need to consider population statistics and a role for cell growth and division when estimating SA-V scaling of bacterial cells.