Matuszyńska 2016 PhD model

\begin{align*}
  \frac{d atp}{dt} &= kf\_atp\_synthase \cdot (adp - \frac{atp}{keq\_atp\_synthase}) \\
  & - atp \cdot kf\_ex\_atp \\ 
  \frac{d pq\_ox}{dt} &= \max(- kcat\_b6f, kcat\_b6f \cdot (pq\_red \cdot {pc\_ox}^{2} - \frac{pq\_ox \cdot {pc\_red}^{2}}{keq\_b6f})) \\
  & - kf\_cyclic\_electron\_flow \cdot pq\_ox \cdot {fd\_red}^{2} \\
  & - kf\_ndh \cdot pq\_ox - 0.5 \cdot ps2states \cdot k2 \\
  & + O2\_lumen \cdot kPTOX \cdot pq\_red \\ 
  \frac{d pc\_ox}{dt} &= - 2 \cdot \max(- kcat\_b6f, kcat\_b6f \cdot (pq\_red \cdot {pc\_ox}^{2} - \frac{pq\_ox \cdot {pc\_red}^{2}}{keq\_b6f})) \\
  & + A1 \cdot PPFD \cdot (1 - PSII\_cross\_section) \\ 
  \frac{d fd\_ox}{dt} &= 2 \cdot kf\_cyclic\_electron\_flow \cdot pq\_ox \cdot {fd\_red}^{2} \\
  & + 2 \cdot \frac{vmax\_fnr \cdot (\frac{nadp \cdot {\frac{fd\_red}{km\_fnr\_fd\_red}}^{2}}{km\_fnr\_nadp} - \frac{nadph \cdot {\frac{fd\_ox}{km\_fnr\_fd\_red}}^{2}}{keq\_fnr \cdot km\_fnr\_nadp})}{-1 + (1 + \frac{nadp}{km\_fnr\_nadp}) \cdot (1 + {\frac{fd\_red}{km\_fnr\_fd\_red}}^{2} + \frac{fd\_red}{km\_fnr\_fd\_red}) + (1 + \frac{nadph}{km\_fnr\_nadp}) \cdot (1 + {\frac{fd\_ox}{km\_fnr\_fd\_red}}^{2} + \frac{fd\_ox}{km\_fnr\_fd\_red})} \\
  & - A1 \cdot PPFD \cdot (1 - PSII\_cross\_section) \\ 
  \frac{d protons\_lumen}{dt} &= - \frac{HPR}{bH} \cdot kf\_atp\_synthase \cdot (adp - \frac{atp}{keq\_atp\_synthase}) \\
  & + \frac{4}{bH} \cdot \max(- kcat\_b6f, kcat\_b6f \cdot (pq\_red \cdot {pc\_ox}^{2} - \frac{pq\_ox \cdot {pc\_red}^{2}}{keq\_b6f})) \\
  & + \frac{2}{bH} \cdot 0.5 \cdot ps2states \cdot k2 \\
  & - \frac{1}{bH} \cdot kf\_proton\_leak \cdot (protons\_lumen - 4000 \cdot {10}^{- pH}) \\ 
  \frac{d lhc}{dt} &= - \frac{1 \cdot kStt7 \cdot lhc}{1 + {\frac{pq\_ox}{PQ\_tot \cdot km\_lhc\_state\_transition\_12}}^{n\_ST}} \\
  & + kPph1 \cdot lhc\_prot \\ 
  \frac{d psbs\_de}{dt} &= - \frac{kf\_lhc\_protonation \cdot psbs\_de \cdot {protons\_lumen}^{kh\_lhc\_protonation}}{{protons\_lumen}^{kh\_lhc\_protonation} + {4000 \cdot {10}^{- ksat\_lhc\_protonation}}^{kh\_lhc\_protonation}} \\
  & + kf\_lhc\_deprotonation \cdot psbs\_pr \\ 
  \frac{d vx}{dt} &= - \frac{kf\_violaxanthin\_deepoxidase \cdot vx \cdot {protons\_lumen}^{kh\_violaxanthin\_deepoxidase}}{{protons\_lumen}^{kh\_violaxanthin\_deepoxidase} + {4000 \cdot {10}^{- ksat\_violaxanthin\_deepoxidase}}^{kh\_violaxanthin\_deepoxidase}} \\
  & + kf\_zeaxanthin\_epoxidase \cdot zx
\end{align*}