Li 2021 model
The Li 2021 model is a kinetic model of photosynthesis centred on ion fluxes across the thylakoid membrane and their effect on the proton motive force (pmf). Built upon the Davis 2017 model, it gives a detailed account of the pmf-generating reactions — water splitting at photosystem II and plastoquinone oxidation at cytochrome b6f — while representing other steps with minimal complexity.
It adds two potassium and two chloride transport pathways to the thylakoid membrane and was validated against wild-type behaviour and several knockout mutants (VCCN1, CLCE, KEA3), making it a tool to dissect how ion fluxes regulate photosynthetic electron transport and photoprotection.
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\begin{align*}
\frac{d QA\_red}{dt} &= - QA\_red \cdot k\_recomb \cdot {10}^{7 + 16.666666666666668 \cdot Dpsi - 1 \cdot pH\_lumen} \\
& + PhiPSII \cdot light\_per\_L \cdot sigma0\_II \\
& - 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}) \\
& + 0.5 \cdot Fd\_red \cdot PQ \cdot k\_NDH1 - Fd\_ox \cdot PQH\_2 \cdot k\_NDH1 \cdot {10}^{-7 + 1 \cdot pH\_st + 16.666666666666668 \cdot Em\_Fd + 33.333333333333336 \cdot pmf - 16.666666666666668 \cdot Em\_PQH2\_pH7} \\
& + 0.5 \cdot \frac{PQ \cdot Vmax\_PGR \cdot {Fd\_red}^{4}}{(0.00010000000000000002 + {Fd\_red}^{4}) \cdot (PQ + PQH\_2)} \\
\frac{d pH\_lumen}{dt} &= \frac{ipt\_lu}{b\_H} \cdot QA\_red \cdot k\_recomb \cdot {10}^{7 + 16.666666666666668 \cdot Dpsi - 1 \cdot pH\_lumen} \\
& - \frac{ipt\_lu}{b\_H} \cdot PhiPSII \cdot light\_per\_L \cdot sigma0\_II \\
& - \frac{2 \cdot ipt\_lu}{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{2 \cdot ipt\_lu}{b\_H} \cdot Fd\_red \cdot PQ \cdot k\_NDH1 - Fd\_ox \cdot PQH\_2 \cdot k\_NDH1 \cdot {10}^{-7 + 1 \cdot pH\_st + 16.666666666666668 \cdot Em\_Fd + 33.333333333333336 \cdot pmf - 16.666666666666668 \cdot Em\_PQH2\_pH7} \\
& + \frac{ipt\_lu}{b\_H} \cdot k\_KEA3 \cdot pH\_act \cdot qL\_act \cdot (H\_lumen \cdot K\_st - H\_st \cdot K\_lu) \\
& + \frac{ipt\_lu}{b\_H} \cdot 0.25 \cdot k\_ClCe \cdot (Cl\_lu + Cl\_st) \cdot (H\_lumen + H\_st) \cdot (pmf + 2 \cdot driving\_force\_Cl) \\
& + \frac{ipt\_lu}{b\_H} \cdot H\_lumen \cdot k\_leak \cdot pmf \\
& + \frac{ipt\_lu}{b\_H} \cdot \begin{cases}HPR \cdot Vmax\_ATPsynth \cdot (1 - \frac{1}{1 + {10}^{-5.1000000000000005 + 25 \cdot pmf}}) \cdot (0.8 - \frac{1.0793299047744327e-9 \cdot {time}^{4}}{1 + 1.349162380968041e-9 \cdot {time}^{4}}) + HPR \cdot Vmax\_ATPsynth \cdot (1 - \frac{1}{1 + {10}^{-3.3000000000000003 + 25 \cdot pmf}}) \cdot (0.2 + \frac{1.0793299047744327e-9 \cdot {time}^{4}}{1 + 1.349162380968041e-9 \cdot {time}^{4}}) & light\_per\_L > 0 \\ 0 & \text{else}\end{cases} \\
\frac{d Dpsi}{dt} &= - vpc \cdot QA\_red \cdot k\_recomb \cdot {10}^{7 + 16.666666666666668 \cdot Dpsi - 1 \cdot pH\_lumen} \\
& + vpc \cdot PhiPSII \cdot light\_per\_L \cdot sigma0\_II \\
& + vpc \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}) \\
& + 2 \cdot vpc \cdot Fd\_red \cdot PQ \cdot k\_NDH1 - Fd\_ox \cdot PQH\_2 \cdot k\_NDH1 \cdot {10}^{-7 + 1 \cdot pH\_st + 16.666666666666668 \cdot Em\_Fd + 33.333333333333336 \cdot pmf - 16.666666666666668 \cdot Em\_PQH2\_pH7} \\
& + vpc \cdot Fd\_ox \cdot Y0 \cdot light\_per\_L \cdot sigma0\_I \\
& - vpc \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) \\
& - vpc \cdot 0.5 \cdot k\_VCCN1 \cdot (Cl\_lu + Cl\_st) \cdot (332 \cdot {driving\_force\_Cl}^{3} + 3.6 \cdot driving\_force\_Cl + 30.8 \cdot {driving\_force\_Cl}^{2}) \\
& - 3 \cdot vpc \cdot 0.25 \cdot k\_ClCe \cdot (Cl\_lu + Cl\_st) \cdot (H\_lumen + H\_st) \cdot (pmf + 2 \cdot driving\_force\_Cl) \\
& - vpc \cdot H\_lumen \cdot k\_leak \cdot pmf \\
& - vpc \cdot \begin{cases}HPR \cdot Vmax\_ATPsynth \cdot (1 - \frac{1}{1 + {10}^{-5.1000000000000005 + 25 \cdot pmf}}) \cdot (0.8 - \frac{1.0793299047744327e-9 \cdot {time}^{4}}{1 + 1.349162380968041e-9 \cdot {time}^{4}}) + HPR \cdot Vmax\_ATPsynth \cdot (1 - \frac{1}{1 + {10}^{-3.3000000000000003 + 25 \cdot pmf}}) \cdot (0.2 + \frac{1.0793299047744327e-9 \cdot {time}^{4}}{1 + 1.349162380968041e-9 \cdot {time}^{4}}) & light\_per\_L > 0 \\ 0 & \text{else}\end{cases} \\
\frac{d K\_lu}{dt} &= ipt\_lu \cdot k\_KEA3 \cdot pH\_act \cdot qL\_act \cdot (H\_lumen \cdot K\_st - H\_st \cdot K\_lu) \\
& - ipt\_lu \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}) \\
& + PC\_red \cdot Y2 \cdot k\_PCtoP700 \\
\frac{d Y2}{dt} &= Fd\_ox \cdot Y0 \cdot light\_per\_L \cdot sigma0\_I \\
& - PC\_red \cdot Y2 \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 Fd\_red}{dt} &= - Fd\_red \cdot PQ \cdot k\_NDH1 - Fd\_ox \cdot PQH\_2 \cdot k\_NDH1 \cdot {10}^{-7 + 1 \cdot pH\_st + 16.666666666666668 \cdot Em\_Fd + 33.333333333333336 \cdot pmf - 16.666666666666668 \cdot Em\_PQH2\_pH7} \\
& - \frac{PQ \cdot Vmax\_PGR \cdot {Fd\_red}^{4}}{(0.00010000000000000002 + {Fd\_red}^{4}) \cdot (PQ + PQH\_2)} \\
& + Fd\_ox \cdot Y0 \cdot light\_per\_L \cdot sigma0\_I \\
& - Fd\_red \cdot NADP\_st \cdot k\_FdtoNADP \\
& - \frac{0.00106 \cdot Fd\_red}{Fd\_ox + Fd\_red} \\
\frac{d NADPH\_st}{dt} &= 0.5 \cdot Fd\_red \cdot NADP\_st \cdot k\_FdtoNADP \\
& - 0.9712326548170112 \cdot kCBB \cdot (1 - e^{- 0.0016666666666666668 \cdot time}) \cdot (-0.22314355131420976 + \ln(\frac{NADPH\_st}{NADP\_st})) \\
\frac{d Cl\_lu}{dt} &= ipt\_lu \cdot 0.5 \cdot k\_VCCN1 \cdot (Cl\_lu + Cl\_st) \cdot (332 \cdot {driving\_force\_Cl}^{3} + 3.6 \cdot driving\_force\_Cl + 30.8 \cdot {driving\_force\_Cl}^{2}) \\
& + 2 \cdot ipt\_lu \cdot 0.25 \cdot k\_ClCe \cdot (Cl\_lu + Cl\_st) \cdot (H\_lumen + H\_st) \cdot (pmf + 2 \cdot driving\_force\_Cl) \\
\frac{d Cl\_st}{dt} &= - 0.1 \cdot ipt\_lu \cdot 0.5 \cdot k\_VCCN1 \cdot (Cl\_lu + Cl\_st) \cdot (332 \cdot {driving\_force\_Cl}^{3} + 3.6 \cdot driving\_force\_Cl + 30.8 \cdot {driving\_force\_Cl}^{2}) \\
& - 0.2 \cdot ipt\_lu \cdot 0.25 \cdot k\_ClCe \cdot (Cl\_lu + Cl\_st) \cdot (H\_lumen + H\_st) \cdot (pmf + 2 \cdot driving\_force\_Cl)
\end{align*}Edit analysis
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