Kinetic PDE models of cell size control: size blow-up and evolution of growth rate

We derive kinetic equations for the distribution of cells in age, size, and added size after birth. These kinetic PDE models incorporate timer, sizer, and adder mechanisms of cell division. After properly constructing cell division rates, we show that an sizer-adder PDE model can lead to diverging cell sizes, particularly if the distribution of daughter cells immediately after birth is broad. The kinetic models are also extended to include growth rate correlation between successive generations. As the population evolves, so does the distribution of cellular growth rates. Representative numerical solutions to our PDEs will be presented.