= Cell culture passage accounting
{title2=$N_{\mathrm{seed}}=fN_{\mathrm{harvest}}$}
In an original constructed example, seed $300\,000$ <biological cells> in $6\,\mathrm{mL}$ of <cell culture medium>. Suppose the recoverable count becomes $1\,200\,000$ before the next <subculture>. Transfer a well-mixed quarter of that harvest into a new vessel and bring its final <volume (thermodynamics)> to $6\,\mathrm{mL}$. Assume complete recovery, no loss during transfer and no division during handling. The selected portion contains
$$
N_{\mathrm{seed}}=\frac14(1\,200\,000)=300\,000,\qquad c_{\mathrm{seed}}=\frac{300\,000}{6\,\mathrm{mL}}=50\,000\,\mathrm{mL}^{-1}.
$$
The other $900\,000$ <biological cells> remain outside the tracked vessel. The lower count after transfer is selection of a portion, not evidence of death. Adding fresh <cell culture medium> lowers the <number density> further without changing the selected count.
\Image[/cell-culture-passage-and-doubling-accounting.png]
{title=One <subculture> transfer can follow two <cell line population doublings>}
{description=Original constructed count ledger, not an observed <HeLa> growth curve. Each growth interval multiplies the recoverable count by four; each transfer retains one quarter. The tracked lineage gains four net <cell line population doublings> across two intervals although both seed counts are $300\,000$. Boxes describe whole cultured populations, not persistent individual <biological cells>.}
If the next interval again changes $300\,000$ to $1\,200\,000$, the two growth intervals contribute $2+2=4$ net <cell line population doublings>. At the second harvest there has been just one intervening passage. Another quarter-transfer would add another passage without adding a growth interval. Thus neither passage number nor the <logarithm> of the final count divided by the very first seed count records all growth when portions are removed.
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