Model Mathematics

\frac{d}{d time} (ATP) = \frac{J_ATP - (V_hyd + V_MMCK)}{V_cyt}

\frac{d}{d time} (ADP) = \frac{J_ADP + V_hyd + V_MMCK}{V_cyt}

\frac{d}{d time} (PCr) = \frac{J_PCr + V_MMCK}{V_cyt}

\frac{d}{d time} (Cr) = \frac{J_Cr - V_MMCK}{V_cyt}

\frac{d}{d time} (Pi) = \frac{J_Pi + V_hyd}{V_cyt}

\frac{d}{d time} (ATP_i) = \frac{- (J_ATP + V_syn + V_MiCK)}{V_ims}

\frac{d}{d time} (ADP_i) = \frac{V_syn + V_MiCK - J_ADP}{V_ims}

\frac{d}{d time} (PCr_i) = \frac{V_MiCK - J_PCr}{V_ims}

\frac{d}{d time} (Cr_i) = \frac{- (V_MiCK + J_Cr)}{V_ims}

\frac{d}{d time} (Pi_i) = \frac{V_syn - J_Pi}{V_ims}

V_MMCK = \frac{Vf \frac{ATP Cr}{Kia Kb} - (Vb \frac{ADP PCr}{Kic Kd})}{Den_MMCK} Den_MMCK = 1.0 + \frac{Cr}{Kib} + \frac{PCr}{Kid} + ATP (\frac{1.0}{Kia} + \frac{Cr}{Kia Kb}) + ADP (\frac{1.0}{Kic} + \frac{PCr}{Kid Kc} + \frac{Cr}{Kic KIb}) Kc = \frac{Kic Kd}{Kid} KIb = Kib

V_MiCK = \frac{Vf \frac{ATP_i Cr_i}{Kia Kb} - (Vb \frac{ADP_i PCr_i}{Kic Kd})}{Den_MiCK} Den_MiCK = 1.0 + \frac{Cr_i}{Kib} + \frac{PCr_i}{Kid} + ATP_i (\frac{1.0}{Kia} + \frac{Cr_i}{Kia Kb}) + ADP_i (\frac{1.0}{Kic} + \frac{PCr_i}{Kid Kc} + \frac{Cr_i}{Kic KIb}) Kc = \frac{Kic Kd}{Kid} KIb = Kib

V_syn = V_syn_max \frac{ADP_i Pi_i}{KPi KADP Den_syn} Den_syn = 1.0 + \frac{ADP_i}{KADP} + \frac{Pi_i}{KPi} + \frac{ADP_i Pi_i}{KADP KPi}

J_ATP = R_ATP (ATP_i - ATP)

J_ADP = R_ADP (ADP_i - ADP)

J_PCr = R_PCr (PCr_i - PCr)

J_Cr = R_Cr (Cr_i - Cr)

J_Pi = R_Pi (Pi_i - Pi)