Modeled mitochondrial oxygen traces ($q=-Vd{c}_{{\mathrm{O}}_2}/dt$)

The following original model chooses piecewise constant oxygen consumption rates in a closed, well-mixed $2\mathrm{mL}$ suspension. It assumes no gas exchange, negligible addition volume, a corrected sensor and sufficient oxygen throughout. The curves are invented teaching examples, not measured traces, fitted data or a reconstruction of Figure 6.

Start at $c(0)=220\mu \mathrm{mol}{\mathrm{L}}^{-1}$. On successive one-minute intervals, choose positive slope magnitudes $5,25,5,25,6,32,1\mu \mathrm{mol}{\mathrm{L}}^{-1}\mathrm{mi}{\mathrm{n}}^{-1}$. Integration gives the endpoint concentrations $220,215,190,185,160,154,122,121\mu \mathrm{mol}{\mathrm{L}}^{-1}$. This is just the recurrence $c_{i+1}=c_i-r_i\Delta t$, with $\Delta t=1\min$; the step plot shows $r_i=-dc/dt$. The trace remains above zero by construction.

During the second ADP interval, the total consumption rate isWith a stipulated mitochondrial protein mass of $0.20\mathrm{mg}$, that is $250\mathrm{nmol}\mathrm{mi}{\mathrm{n}}^{-1}\mathrm{m}{\mathrm{g}}^{-1}$. Using a denominator twice as large would halve this reported rate without changing the raw oxygen trace. Comparisons therefore need both loading and the chosen denominator.

For a second bookkeeping check, the modeled post-antimycin A slope of $1\mu \mathrm{mol}{\mathrm{L}}^{-1}\mathrm{mi}{\mathrm{n}}^{-1}$ corresponds to $2\mathrm{nmol}\mathrm{mi}{\mathrm{n}}^{-1}$ background. If that background is additive and unchanged in earlier windows, subtraction gives $48$, $10$ and $62\mathrm{nmol}\mathrm{mi}{\mathrm{n}}^{-1}$ for excess ADP, oligomycin and FCCP, respectively. The oligomycin-sensitive difference is $48-10=38\mathrm{nmol}\mathrm{mi}{\mathrm{n}}^{-1}$. It is a difference in oxygen consumption under the chosen interventions, not an ATP production rate. Converting it into one requires additional coupling assumptions or an independent ATP measurement; the FCCP interval shows why slope alone cannot supply that conversion.

Across the whole seven-minute example, consumption is $V(c(0)-c(7))=198\mathrm{nmol}$, also the sum of the seven interval consumptions. This equality checks the rate-to-amount accounting independently of how the intervals are named. Actual records require attention to calibration, mixing transients, background stability and decreasing oxygen availability; a line that steepens or flattens alone does not identify the cause.