Cell size and shape regulation of E. coli determines surface area scaling with volume

The scaling of surface area and volume of cells has widespread consequences for cell physiology, growth and adaptation. While the surface area increases with volume as SA ~ V{gamma} the scaling exponent for proportional growth maintaining the shape and aspect is {gamma} ~ 2/3 or 0.66. However most well-studied cellular systems deviate from this standard exponent. At the same time, a mechanism that could predict the biological or physical basis of these scaling relations remains unclear. Here, we quantify the surface area scaling with volume of Escherichia coli cells with varying growth rates and under different conditions and find the scaling exponent varies from {gamma} ~ 0.7 to 0.9. A model of uncorrelated statistical variation of cell lengths and widths can reproduce the exponent observed in experiment. Average values of length and width on the other hand results in an impression of ideal geometric scaling, as reported in some studies. Experimental data however suggests that E. coli cell width is strongly correlated with length and a model of saturation best explains the observations. We hypothesize this model of cell size and shape regulation could serve the function of optimizing flux of nutrients, within the constraints of the cell division machinery.