= Citric acid cycle first-turn carbon tracing
Net <stoichiometry> does not identify individual <chemical atoms>. In the ordinary forward <citric acid cycle>, neither entering <acetyl group> <carbon> is released in that same first turn: both released <carbon dioxide> <carbon> <chemical atoms> came from the starting <oxaloacetate>. The entering <carbon> remains in regenerated intermediates.<The Citric Acid Cycle (Boston University lecture slides)>[The Citric Acid Cycle, slide numbered 4, Origin of C-Atoms in CO2: entering acetyl carbons retained and released carbons from starting oxaloacetate]{ref}
Consider a chosen ideal first-turn experiment, with negligible natural <carbon-13> abundance and no exchange, side pathways, repeated turns or <isotope> effects. Supply $10\,\mathrm{\mu mol}$ of initially unlabelled <oxaloacetate> and $10\,\mathrm{\mu mol}$ of <acetyl-CoA>, of which $6\,\mathrm{\mu mol}$ has both <acetyl group> <carbon> positions labelled with <carbon-13>. The other $4\,\mathrm{\mu mol}$ has neither position labelled. The label refers only to the <acetyl group>, not to <coenzyme A>.
The input contains $2\times6=12\,\mathrm{\mu mol}$ of labelled <carbon> <chemical atoms>. The $10\,\mathrm{\mu mol}$ of <citrate> initially formed contains $60\,\mathrm{\mu mol}$ of <carbon> <chemical atoms>, so its labelled-<carbon> fraction is $12/60=20\%$. After exactly one forward traversal per starting <oxaloacetate>, the $20\,\mathrm{\mu mol}$ of released <carbon dioxide> has zero label, while the regenerated $10\,\mathrm{\mu mol}$ of <oxaloacetate> contains all $12\,\mathrm{\mu mol}$ of labelled <carbon> <chemical atoms> among $40\,\mathrm{\mu mol}$ total: $30\%$.
\Image[/citric-acid-cycle-first-turn-label-ledger.png]
{title=First-turn <carbon-13> accounting distinguishes net <stoichiometry> from <chemical atom> identity}
{description=Original ideal calculation, not historical or measured <isotope> data. Stacked bars show the <amount of substance> of <carbon> <chemical atoms>, not amounts of whole <molecules>. The first two bars are alternative stages; the last two are simultaneous outputs whose totals sum to the preceding <citrate> bar. <Carbon-13> is restricted initially to the incoming <acetyl groups>; natural abundance and side pathways are excluded.}
The conservation check is $60=20+40$ for total <carbon> and $12=0+12$ for label. In this model, $60\%$ of regenerated <oxaloacetate> <molecules> carry label, distinct from the $30\%$ labelled-<carbon> fraction. The regenerated <oxaloacetate> is the same <chemical species> and the same <amount of substance> as the initial acceptor pool, but its <chemical atom> identities have changed. Saying that the cycle oxidizes an <acetyl group> to two <carbon dioxide> is a net ledger, not a claim that those exact two incoming <chemical atoms> immediately leave. Later-turn label release requires positional tracking and mixing assumptions; the first-turn balance alone does not determine it.
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