# Model Mathematics

### Component: ATP_cyt

$ddtimeATP_cyt=J_diff_ATP-J_hyd+J_CKMMV_cyt$

$ddtimeADP_cyt=J_diff_ADP+J_hyd+J_CKMMV_cyt$

### Component: PCr_cyt

$ddtimePCr_cyt=J_diff_PCr+J_CKMMV_cyt$

### Component: Cr_cyt

$ddtimeCr_cyt=J_diff_Cr-J_CKMMV_cyt$

### Component: Pi_cyt

$ddtimePi_cyt=J_diff_Pi+J_hydV_cyt$

### Component: ATP_ims

$ddtimeATP_ims=J_syn-J_diff_ATP+J_CKMiV_ims$

$ddtimeADP_ims=J_CKMi-J_syn+J_diff_ADPV_ims$

### Component: PCr_ims

$ddtimePCr_ims=J_CKMi-J_diff_PCrV_ims$

### Component: Cr_ims

$ddtimeCr_ims=-J_CKMi+J_diff_CrV_ims$

### Component: Pi_ims

$ddtimePi_ims=-J_syn+J_diff_PiV_ims$

### Component: J_CKMM

$J_CKMM = Vmax_MM_f ⁢ ATP_cyt ⁢ Cr_cyt Kia ⁢ Kb - Vmax_MM_b ⁢ ADP_cyt ⁢ PCr_cyt Kic ⁢ Kd Den_MMCK Den_MMCK = 1.0 + Cr_cyt Kib + PCr_cyt Kid + ATP_cyt ⁢ 1.0 Kia + Cr_cyt Kia ⁢ Kb + ADP_cyt ⁢ 1.0 Kic + PCr_cyt Kid ⁢ Kc + Cr_cyt Kic ⁢ KIb Kc = Kic ⁢ Kd Kid KIb = Kib$

### Component: J_CKMi

$J_CKMi = Vmax_Mi_f ⁢ ATP_ims ⁢ Cr_ims Kia ⁢ Kb - Vmax_Mi_b ⁢ ADP_ims ⁢ PCr_ims Kic ⁢ Kd Den_MiCK Den_MiCK = 1.0 + Cr_ims Kib + PCr_ims Kid + ATP_ims ⁢ 1.0 Kia + Cr_ims Kia ⁢ Kb + ADP_ims ⁢ 1.0 Kic + PCr_ims Kid ⁢ Kc + Cr_ims Kic ⁢ KIb Kc = Kic ⁢ Kd Kid KIb = Kib$

### Component: J_hyd

$t_cycle_1=60freq_1t_cycle_2=60freq_2duration_1=nb_of_cycles_1⁢t_cycle_1ltime=time-t_cycle_1⁢⌊timet_cycle_1⌋iftime≦duration_1time-duration_1-t_cycle_2⁢⌊time-duration_1t_cycle_2⌋otherwiset_cycle=t_cycle_1iftime≦duration_1t_cycle_2otherwiseH_ATPmax=6⁢J_hyd_basis_1iftime≦duration_16⁢J_hyd_basis_2otherwiseJ_hyd=H_ATPmax⁢ltimet_cycle⁢6ifltime≥0∧ltime<16⁢t_cycleH_ATPmax⁢1-6⁢ltimet_cycle-16ifltime≥16⁢t_cycle∧ltime<13⁢t_cycle0ifltime≥13⁢t_cycle∧ltime

### Component: J_syn

$J_syn = V_max_syn ⁢ ADP_ims ⁢ Pi_ims KPi ⁢ KADP ⁢ Den_syn Den_syn = 1.0 + ADP_ims KADP + Pi_ims KPi + ADP_ims ⁢ Pi_ims KADP ⁢ KPi$

### Component: J_diff_ATP

$J_diff_ATP = PS_tot_ATP ⁢ ATP_ims - ATP_cyt$

$J_diff_ADP = PS_tot_ADP ⁢ ADP_ims - ADP_cyt$

### Component: J_diff_PCr

$J_diff_PCr = PS_tot_PCr ⁢ PCr_ims - PCr_cyt$

### Component: J_diff_Cr

$J_diff_Cr = PS_tot_Cr ⁢ Cr_ims - Cr_cyt$

### Component: J_diff_Pi

$J_diff_Pi = PS_tot_Pi ⁢ Pi_ims - Pi_cyt$

### Component: fractional_volumes

Source
Derived from workspace Vanbeek, 2007 at changeset cc4f46e1303a.
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