Model Mathematics

\frac{d}{d time} (C_6PG) = rG6PDH - (r6PGDH + mu C_6PG)

\frac{d}{d time} (C_Ru5P) = r6PGDH - (rR5PI + rRu5PE + mu C_Ru5P)

\frac{d}{d time} (C_R5P) = rR5PI - (rTKL1 + rRPPK + mu C_R5P)

\frac{d}{d time} (C_X5P) = rRu5PE - (rTKL1 + rTKL2 + mu C_X5P)

\frac{d}{d time} (C_S7P) = rTKL1 - (rTAL + mu C_S7P)

\frac{d}{d time} (C_E4P) = rTAL - (rTKL2 + rPKDA + mu C_E4P)

\frac{d}{d time} (C_G6P) = dC_G6P_dt dC_G6P_dt = \frac{44.1}{48 + 1 time + 0.45 {time}^{2}} + \frac{44.1 time}{(48 + 1 time + 0.45 {time}^{2}) (48 + 1 time + 0.45 {time}^{2})} (1 + 0.90 time)

\frac{d}{d time} (C_NADP) = \frac{-1.48}{9.17 + 16.1 time + 0.48 {time}^{2}} + \frac{1.48 time}{(9.17 + 16.1 time + 0.48 {time}^{2}) (9.17 + 16.1 time + 0.48 {time}^{2})} (16.1 + 0.96 time)

\frac{d}{d time} (C_NADPH) = \frac{0.516}{25.39 + 0.37 time + 0.5 {time}^{2}} - (\frac{0.516 time}{(25.39 + 0.37 time + 0.5 {time}^{2}) (25.39 + 0.37 time + 0.5 {time}^{2})} (0.37 + 1 time))

\frac{d}{d time} (C_MgATP) = \frac{29.83}{29.77 + 13.42 time + 0.05 {time}^{2}} - (\frac{29.83 time}{(29.77 + 13.42 time + 0.05 {time}^{2}) (29.77 + 13.42 time + 0.05 {time}^{2})} (13.42 + 0.1 time))

rG6PDH = rmax_G6PDH \frac{C_NADP}{(C_NADP + K_NADP_1 I_NADPH_1) I_MgATP_1} I_NADPH_1 = 1.0 + \frac{C_NADPH}{Ki_NADPH_1} I_MgATP_1 = 1.0 + \frac{C_MgATP}{Ki_MgATP_1}

r6PGDH = rmax_6PGDH \frac{C_NADP}{(C_NADP + K_NADP_2 I_NADPH_2) I_MgATP_2} I_NADPH_2 = 1.0 + \frac{C_NADPH}{Ki_NADPH_2} I_MgATP_2 = 1.0 + \frac{C_MgATP}{Ki_MgATP_2}

rR5PI = 1 rmax_R5PI C_Ru5P

rRu5PE = 1 rmax_Ru5PE C_Ru5P

rTKL1 = 1 rmax_TKL1 C_X5P C_R5P

rTAL = 1 rmax_TAL C_GAP C_S7P

rTKL2 = 1 rmax_TKL2 C_E4P C_X5P

rPKDA = 1 rmax_PKDA \frac{C_E4P}{C_E4P + K_PKDA}

rRPPK = 1 rmax_RPPK \frac{C_R5P}{C_R5P + K_RPPK}

rHK = qs

rPGI = qs - (rG6PDH + mu C_G6P + dC_G6P_dt)

qs = \{\begin{matrix} 0.131 if time < 0.0 \\ 0.546 otherwise \end{matrix}