Davis 2017 model
The Davis 2017 model is a mechanistic description of the photosynthetic electron transport chain and the thylakoid proton motive force (pmf), resolving the pmf into its two thermodynamically distinct components: the transmembrane electric field (Δψ) and the lumen pH gradient. Its central result is that the Δψ component, rather than lumen acidification, drives elevated PSII charge recombination, which produces singlet oxygen and subsequent PSII photodamage.
Electron transport runs from PSII through the plastoquinone pool, cytochrome b6f, plastocyanin, PSI and ferredoxin to NADPH, while counter-ion fluxes (KEA3 K⁺/H⁺ antiport, VKC K⁺ channel) partition the pmf between Δψ and the pH gradient, and non-photochemical quenching is captured through PsbS protonation and the xanthophyll cycle.
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Generated LaTeX Code
\begin{align*}
\frac{d QA\_red}{dt} &= - QA\_red \cdot k\_recomb \cdot {10}^{7 + 16.666666666666668 \cdot Dpsi - 1 \cdot pH\_lumen} \\
& + PPFD \cdot PhiPSII - PQ \cdot QA\_red \cdot k\_QA \\
& + \frac{PQH\_2 \cdot QA \cdot k\_QA}{Keq\_QA} \\
\frac{d PQH\_2}{dt} &= 0.5 \cdot PQ \cdot QA\_red \cdot k\_QA \\
& - 0.5 \cdot \frac{PQH\_2 \cdot QA \cdot k\_QA}{Keq\_QA} \\
& - 0.5 \cdot \frac{PC\_ox \cdot PQH\_2 \cdot Vmax\_b6f \cdot c\_b6f \cdot (1 - \frac{1}{1 + {10}^{pH\_lumen - pKa\_reg}})}{PQ + PQH\_2} - PC\_red \cdot Vmax\_b6f \cdot c\_b6f \cdot {10}^{7 + 16.666666666666668 \cdot Em\_PQH2\_pH7 + 16.666666666666668 \cdot pmf - 1 \cdot pH\_lumen - 16.666666666666668 \cdot Em\_PC\_pH7} \cdot (1 - \frac{1}{1 + {10}^{pH\_lumen - pKa\_reg}}) \cdot (1 - \frac{PQH\_2}{PQ + PQH\_2}) \\
\frac{d pH\_lumen}{dt} &= \frac{lumen\_protons\_per\_turnover}{b\_H} \cdot QA\_red \cdot k\_recomb \cdot {10}^{7 + 16.666666666666668 \cdot Dpsi - 1 \cdot pH\_lumen} \\
& - \frac{lumen\_protons\_per\_turnover}{b\_H} \cdot PPFD \cdot PhiPSII \\
& - \frac{2 \cdot lumen\_protons\_per\_turnover}{b\_H} \cdot \frac{PC\_ox \cdot PQH\_2 \cdot Vmax\_b6f \cdot c\_b6f \cdot (1 - \frac{1}{1 + {10}^{pH\_lumen - pKa\_reg}})}{PQ + PQH\_2} - PC\_red \cdot Vmax\_b6f \cdot c\_b6f \cdot {10}^{7 + 16.666666666666668 \cdot Em\_PQH2\_pH7 + 16.666666666666668 \cdot pmf - 1 \cdot pH\_lumen - 16.666666666666668 \cdot Em\_PC\_pH7} \cdot (1 - \frac{1}{1 + {10}^{pH\_lumen - pKa\_reg}}) \cdot (1 - \frac{PQH\_2}{PQ + PQH\_2}) \\
& + \frac{lumen\_protons\_per\_turnover \cdot n}{b\_H} \cdot ATP\_synthase\_driving\_force \cdot Vmax\_ATPsynth \\
& + \frac{lumen\_protons\_per\_turnover}{b\_H} \cdot k\_KEA3 \cdot (H\_lumen \cdot K\_st - H\_stroma \cdot K\_lu) \\
\frac{d Dpsi}{dt} &= - volt\_per\_charge \cdot QA\_red \cdot k\_recomb \cdot {10}^{7 + 16.666666666666668 \cdot Dpsi - 1 \cdot pH\_lumen} \\
& + volt\_per\_charge \cdot PPFD \cdot PhiPSII \\
& + volt\_per\_charge \cdot \frac{PC\_ox \cdot PQH\_2 \cdot Vmax\_b6f \cdot c\_b6f \cdot (1 - \frac{1}{1 + {10}^{pH\_lumen - pKa\_reg}})}{PQ + PQH\_2} - PC\_red \cdot Vmax\_b6f \cdot c\_b6f \cdot {10}^{7 + 16.666666666666668 \cdot Em\_PQH2\_pH7 + 16.666666666666668 \cdot pmf - 1 \cdot pH\_lumen - 16.666666666666668 \cdot Em\_PC\_pH7} \cdot (1 - \frac{1}{1 + {10}^{pH\_lumen - pKa\_reg}}) \cdot (1 - \frac{PQH\_2}{PQ + PQH\_2}) \\
& + volt\_per\_charge \cdot Fd\_ox \cdot P700\_red \cdot PPFD \cdot PSI\_antenna\_size \\
& - n \cdot volt\_per\_charge \cdot ATP\_synthase\_driving\_force \cdot Vmax\_ATPsynth \\
& - volt\_per\_charge \cdot k\_KEA3 \cdot (H\_lumen \cdot K\_st - H\_stroma \cdot K\_lu) \\
& - volt\_per\_charge \cdot 0.5 \cdot P\_K \cdot (Dpsi - \frac{0.06 \cdot \ln(\frac{K\_st}{K\_lu})}{\ln(10)}) \cdot (K\_lu + K\_st) \\
\frac{d K\_lu}{dt} &= lumen\_protons\_per\_turnover \cdot k\_KEA3 \cdot (H\_lumen \cdot K\_st - H\_stroma \cdot K\_lu) \\
& - lumen\_protons\_per\_turnover \cdot 0.5 \cdot P\_K \cdot (Dpsi - \frac{0.06 \cdot \ln(\frac{K\_st}{K\_lu})}{\ln(10)}) \cdot (K\_lu + K\_st) \\
\frac{d PC\_ox}{dt} &= - \frac{PC\_ox \cdot PQH\_2 \cdot Vmax\_b6f \cdot c\_b6f \cdot (1 - \frac{1}{1 + {10}^{pH\_lumen - pKa\_reg}})}{PQ + PQH\_2} - PC\_red \cdot Vmax\_b6f \cdot c\_b6f \cdot {10}^{7 + 16.666666666666668 \cdot Em\_PQH2\_pH7 + 16.666666666666668 \cdot pmf - 1 \cdot pH\_lumen - 16.666666666666668 \cdot Em\_PC\_pH7} \cdot (1 - \frac{1}{1 + {10}^{pH\_lumen - pKa\_reg}}) \cdot (1 - \frac{PQH\_2}{PQ + PQH\_2}) \\
& + P700\_ox \cdot PC\_red \cdot k\_PCtoP700 \\
\frac{d Zx}{dt} &= - Zx \cdot k\_EZ \\
& + \frac{1 \cdot Vmax\_VDE \cdot Vx}{1 + {10}^{nh\_VDE \cdot (pH\_lumen - pKa\_VDE)}} \\
\frac{d singO2}{dt} &= phi\_1O2 \cdot phi\_triplet \cdot QA\_red \cdot k\_recomb \cdot {10}^{7 + 16.666666666666668 \cdot Dpsi - 1 \cdot pH\_lumen} \\
\frac{d P700\_ox}{dt} &= Fd\_ox \cdot P700\_red \cdot PPFD \cdot PSI\_antenna\_size \\
& - P700\_ox \cdot PC\_red \cdot k\_PCtoP700 \\
\frac{d Fd\_red}{dt} &= Fd\_ox \cdot P700\_red \cdot PPFD \cdot PSI\_antenna\_size \\
& - Fd\_red \cdot NADP\_st \cdot k\_FdtoNADP \\
\frac{d NADPH\_st}{dt} &= 0.5 \cdot Fd\_red \cdot NADP\_st \cdot k\_FdtoNADP \\
& - NADPH\_st \cdot k\_CBB \\
\frac{d LEF}{dt} &= Fd\_red \cdot NADP\_st \cdot k\_FdtoNADP \\
\frac{d ATP\_made}{dt} &= ATP\_synthase\_driving\_force \cdot Vmax\_ATPsynth
\end{align*}Fit to data
Fit settings
| Setting | Value |
|---|---|
| Fit backend | |
| Function evaluations per progress update | |
| Maximum total function evaluations | |
| Stop once residual norm reaches |
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Every bar shares one fixed step budget. Drag a divider to move a cutoff, drag a bar's top edge (or focus it and use the arrow keys) to change its share — the final stage isn't draggable, it always gets whatever's left. Double-click a bar or use its + to split it, use a divider's × (or Delete/Backspace while it's focused) to remove it.
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t=0 t=100
| Stage | Data cutoff | Iteration budget |
|---|---|---|
| 1 (final) | full data | 1000 iterations (runs to convergence within this) |
Data
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| Parameter | Fit | Log-space | Initial guess / fixed value | Fitted value |
|---|---|---|---|---|
| PPFD | — | |||
| k_recomb | — | |||
| phi_triplet | — | |||
| phi_1O2 | — | |||
| sigma0_II | — | |||
| c_b6f | — | |||
| pKa_reg | — | |||
| Em_PC_pH7 | — | |||
| Em_PQH2_pH7 | — | |||
| Vmax_b6f | — | |||
| pKa_PsbS | — | |||
| NPQ_max | — | |||
| pH_stroma | — | |||
| PSI_antenna_size | — | |||
| k_QA | — | |||
| Keq_QA | — | |||
| k_PCtoP700 | — | |||
| k_FdtoNADP | — | |||
| K_st | — | |||
| k_KEA3 | — | |||
| P_K | — | |||
| lumen_protons_per_turnover | — | |||
| n | — | |||
| DeltaGATP | — | |||
| Vmax_ATPsynth | — | |||
| b_H | — | |||
| volt_per_charge | — | |||
| k_EZ | — | |||
| nh_VDE | — | |||
| pKa_VDE | — | |||
| Vmax_VDE | — | |||
| QA_total | — | |||
| PQ_tot | — | |||
| P700_total | — | |||
| PC_tot | — | |||
| Fd_tot | — | |||
| NADP_tot | — | |||
| Xanthophyll_tot | — | |||
| k_CBB | — |
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