Computational Analysis of the Mutual Constraints between Single-Cell Growth and Division Control Models

Three models of division control are proposed to achieve cell size homeostasis: sizer, timer, and adder. However, few published studies of division control take into account the dynamics of single-cell growth and most assume that single-cell growth is exponential. Here, computational simulations considering exponential, linear, and bilinear growth models are performed. These simulations confirm that a timer division control model alone cannot lead to size homeostasis if the single-cell growth model is exponential. Furthermore, timer and adder division control models cannot be distinguished if the single-cell growth model is linear. Models of division control cannot be easily differentiated by analysis of average cell behavior because the birth sizes of the majority of cells are close to the population average. However, the differences between division control models are amplified in outlier cells whose birth size is far from the average. A method is introduced for vector field analysis of the speed of convergence of outlier lineages toward the steady-state birth size, which can help to distinguish between division control models and single-cell growth models.