Model Mathematics

\frac{d}{d time} (ATP_cyt) = \frac{J_diff_ATP - (J_hyd + J_CKMM)}{V_cyt}

\frac{d}{d time} (ADP_cyt) = \frac{J_diff_ADP + J_hyd + J_CKMM}{V_cyt}

\frac{d}{d time} (PCr_cyt) = \frac{J_diff_PCr + J_CKMM}{V_cyt}

\frac{d}{d time} (Cr_cyt) = \frac{J_diff_Cr - J_CKMM}{V_cyt}

\frac{d}{d time} (Pi_cyt) = \frac{J_diff_Pi + J_hyd}{V_cyt}

\frac{d}{d time} (ATP_ims) = \frac{J_syn - (J_diff_ATP + J_CKMi)}{V_ims}

\frac{d}{d time} (ADP_ims) = \frac{J_CKMi - (J_syn + J_diff_ADP)}{V_ims}

\frac{d}{d time} (PCr_ims) = \frac{J_CKMi - J_diff_PCr}{V_ims}

\frac{d}{d time} (Cr_ims) = \frac{- (J_CKMi + J_diff_Cr)}{V_ims}

\frac{d}{d time} (Pi_ims) = \frac{- (J_syn + J_diff_Pi)}{V_ims}

J_CKMM = \frac{Vmax_MM_f \frac{ATP_cyt Cr_cyt}{Kia Kb} - (Vmax_MM_b \frac{ADP_cyt PCr_cyt}{Kic Kd})}{Den_MMCK} Den_MMCK = 1.0 + \frac{Cr_cyt}{Kib} + \frac{PCr_cyt}{Kid} + ATP_cyt (\frac{1.0}{Kia} + \frac{Cr_cyt}{Kia Kb}) + ADP_cyt (\frac{1.0}{Kic} + \frac{PCr_cyt}{Kid Kc} + \frac{Cr_cyt}{Kic KIb}) Kc = \frac{Kic Kd}{Kid} KIb = Kib

J_CKMi = \frac{Vmax_Mi_f \frac{ATP_ims Cr_ims}{Kia Kb} - (Vmax_Mi_b \frac{ADP_ims PCr_ims}{Kic Kd})}{Den_MiCK} Den_MiCK = 1.0 + \frac{Cr_ims}{Kib} + \frac{PCr_ims}{Kid} + ATP_ims (\frac{1.0}{Kia} + \frac{Cr_ims}{Kia Kb}) + ADP_ims (\frac{1.0}{Kic} + \frac{PCr_ims}{Kid Kc} + \frac{Cr_ims}{Kic KIb}) Kc = \frac{Kic Kd}{Kid} KIb = Kib

t_cycle_1 = \frac{60}{freq_1} t_cycle_2 = \frac{60}{freq_2} duration_1 = nb_of_cycles_1 t_cycle_1 ltime = \{\begin{matrix} time - (t_cycle_1 ⌊ \frac{time}{t_cycle_1} ⌋) if time ≦ duration_1 \\ time - duration_1 - (t_cycle_2 ⌊ \frac{time - duration_1}{t_cycle_2} ⌋) otherwise \end{matrix} t_cycle = \{\begin{matrix} t_cycle_1 if time ≦ duration_1 \\ t_cycle_2 otherwise \end{matrix} H_ATPmax = \{\begin{matrix} 6 J_hyd_basis_1 if time ≦ duration_1 \\ 6 J_hyd_basis_2 otherwise \end{matrix} J_hyd = \{\begin{matrix} \frac{H_ATPmax ltime}{t_cycle} 6 if ltime \geq 0 \land ltime < \frac{1}{6} t_cycle \\ H_ATPmax (1 - (6 (\frac{ltime}{t_cycle} - (\frac{1}{6})))) if ltime \geq \frac{1}{6} t_cycle \land ltime < \frac{1}{3} t_cycle \\ 0 if ltime \geq \frac{1}{3} t_cycle \land ltime < t_cycle \end{matrix}

J_syn = V_max_syn \frac{ADP_ims Pi_ims}{KPi KADP Den_syn} Den_syn = 1.0 + \frac{ADP_ims}{KADP} + \frac{Pi_ims}{KPi} + \frac{ADP_ims Pi_ims}{KADP KPi}

J_diff_ATP = PS_tot_ATP (ATP_ims - ATP_cyt)

J_diff_ADP = PS_tot_ADP (ADP_ims - ADP_cyt)

J_diff_PCr = PS_tot_PCr (PCr_ims - PCr_cyt)

J_diff_Cr = PS_tot_Cr (Cr_ims - Cr_cyt)

J_diff_Pi = PS_tot_Pi (Pi_ims - Pi_cyt)