  The rate at which individual bacterial cells grow depends on the
concentrations of cellular components such as ribosomes and proteins. These
concentrations continuously fluctuate over time and are inherited from mother
to daughter cells leading to correlations between the growth rates of cells
across generations. Division sizes of cells are also stochastic and correlated
across generations due to a phenomenon known as cell size regulation.
Fluctuations and correlations from both growth and division processes affect
the population dynamics of an exponentially growing culture. Here, we provide
analytic solutions for the population dynamics of cells with continuously
fluctuating growth rates coupled with a generic model of cell-size regulation.
We show that in balanced growth, the effects of growth and division processes
decouple; the population growth rate only depends on the single-cell growth
rate process, and the population cell size distribution only depends on the
model of division and cell size regulation. The population growth rate is
always higher than the average single-cell growth rate, and the difference
increases with growth rate variability and its correlation time. This
difference also sets the timescale for the population to reach its steady
state. We provide analytical solutions for oscillations in population growth
rate and traveling waves in size distribution during this approach to the
steady state.
