Effective Potential for Cellular Size Control

For various species of biological cells, experimental observations indicate the existence of universal distributions of the cellular size, scaling relations between the cell-size moments and simple rules for the cell-size control. We address a class of models for the control of cell division, and present the steady state distributions. By introducing concepts such as effective force and potential, we are able to address the appearance of scaling collapse of different distributions and the connection between various moments of the cell-size. Our approach allows us to derive strict bounds which a potential cell-size control scenario must meet in order to yield a steady state distribution. The so-called "adder" model for cell-size control exhibits the weakest control that still enables the existence of stable size distribution, a fact that might explain the relative "popularity" of this scenario for different cells.