Cell line population doublings ($d={\log }_2(N_1/N_0)$)

For positive recoverable counts $N_0,N_1$ bracketing one growth interval, define its net cell line population doublings byThe formula counts how many factors of two produce the observed net factor. For exactly two divisions per original biological cell, with all daughters recovered, $N_1=2^2{N}_0$, giving $d=2$. Death or loss of biological cells makes this a net estimate of division.^[ref]

Under constant-rate exponential growth, $N(t)=N_0{e}^{rt}$, a growth interval of duration $\Delta t$ givesFor the constructed fourfold increase over $48\mathrm{h}$, $d=2$ and the model doubling time is $24\mathrm{h}$. The proof follows by taking the natural logarithm and solving $e^{r{t}_2}=2$. This is a fitted property of that interval and model: it is not a universal HeLa doubling time, nor the interval between two divisions of each individual biological cell. Across successive growth intervals, add their $d$ values; keep transfer losses separate as in cell culture passage accounting.