# Model Mathematics

### Component: F6P

$ddtime F6P = V_hk - V_pfk - V_pfk2$

### Component: F26P

$ddtime F26P = V_pfk2$

### Component: GAP

$ddtime GAP = 2.0 ⁢ V_pfk- V_pk$

### Component: PYR

$ddtimePYR=V_pk-V_op+V_ldh$

### Component: LAC

$ddtimeLAC=2.25⁢V_ldh+V_lac$

### Component: ATP

$ddtime ATP = 2.0 ⁢ V_pk + 15.0 ⁢ V_op + V_ck - V_hk + V_pfk + V_pfk2 + V_ATPase ⁢ 1 - dAMP_dATP -1$

### Component: PCr

$ddtime PCr =- V_ck$

### Component: V_hk

$V_hk = Vmax_hk ⁢ ATP ATP + Km_ATP_hk ⁢ 1 + F6P KI_F6P 4 -1$

### Component: V_pfk

$V_pfk = Vmax_pfk ⁢ F6P F6P + Km_F6P_pfk ⁢ ATP ATP + Km_ATP_pfk ⁢ F26P F26P + Km_F26P_pfk ⁢ ATP_inh ⁢ AMP_act$

### Component: V_pfk2

$V_pfk2=Vmaxf_pfk2⁢ATPATP+Km_ATP_pfk2⁢F6PF6P+Km_F6P_pfk2⁢AMP_pfk2-Vmaxr_pfk2⁢F26PF26P+Km_F26P_pfk2$

### Component: V_pk

$V_pk=Vmax_pk⁢GAPGAP+Km_GAP_pk⁢ADPADP+Km_ADP_pk⁢ATP_inh$

### Component: V_op

$V_op=Vmax_op⁢PYRPYR+Km_PYR_op⁢ADPADP+Km_ADP_op⁢11+0.1⁢ATPADP$

### Component: V_ldh

$V_ldh = kf_ldh ⁢ PYR - kr_ldh ⁢ LAC$

### Component: V_ck

$V_ck = kf_ck ⁢ PCr ⁢ ADP - kr_ck ⁢ Cr ⁢ ATP$

### Component: Cr

$Cr = PCrtot - PCr$

### Component: V_ATPase

$V_ATPase = Vmax_ATPase ⁢ ATP ATP + Km_ATP ⁢ 1 + v_stim$

### Component: V_lac

$V_lac = Vlac_0 ⁢ 1 + v_stim ⁢ K_LAC - K_LAC_eff ⁢ LAC$

$ADP = ATP 2 ⁢- Q_adk + u$$u = Q_adk 2 + 4 ⁢ Q_adk ⁢ ANP ATP - 1$

### Component: dAMP_dATP

$dAMP_dATP =- 1 + Q_adk 2 +- 0.5 ⁢ u + Q_adk ⁢ ANP ATP ⁢ u$

### Component: AMP

$AMP = ANP - ATP + ADP$

### Component: ATP_inh

$ATP_inh=1+nATP⁢ATPKI_ATP1+ATPKI_ATP4$

### Component: AMP_act

$AMP_act=1+AMPKa_AMP1+nAMP⁢AMPKa_AMP4$

### Component: v_stim

$v_stim=stim⁢v1_n+v2_n⁢time-tot_n_stim⁢ⅇ-time-to⁢unitpulseSBt_n_stim⁢unitpulseSB$$unitpulseSB = 1 if time ≥ to ∧ time ≦ to + tend 0 otherwise$

### Component: AMP_pfk2

$AMP_pfk2=AMPKamp_pfk2nh_amp1+AMPKamp_pfk2nh_amp$
Source
Derived from workspace Cloutier Wellstead 2009 at changeset ac493499b199.
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