# Model Mathematics

### Component: PYR

$ddtimePYR=V_GLYC-V_LDH+V_PDH+V_ALS$

### Component: ACP

$ddtimeACP=V_PTA-V_ACK$

### Component: ACAL

$ddtimeACAL=V_ACALDH-V_ADH$

### Component: ACLAC

$ddtimeACLAC=0.5⁢V_ALS-V_ALDC+V_NEALC$

### Component: ACET

$ddtimeACET=V_ALDC+V_NEALC-V_ACETDH+V_ACETEFF$

### Component: ATP

$ddtimeATP=V_GLYC+V_ACK-V_ATPase$

$ADP=A_tot-ATP$

$ddtimeNADH=V_GLYC+V_PDH-V_LDH+V_ACALDH+V_ADH+V_ACETDH+V_NOX$

$NAD=NAD_tot-NADH$

### Component: ACCOA

$ddtimeACCOA=V_PDH-V_ACALDH+V_PTA$

### Component: COA

$COA=C_tot-ACCOA$

### Component: V_GLYC

$V_GLYC=V_GLYC_tempifV_GLYC_temp≥0V_GLYC_tempotherwiseV_GLYC_temp=V_GLYC_max⁢GLCKm_GLC⁢NADKm_NAD⁢ADPKm_ADP1+GLCKm_GLC+PYRKm_PYR⁢1+NADKm_NAD+NADHKm_NADH⁢1+ADPKm_ADP+ATPKm_ATP$

### Component: V_LDH

$V_LDH=V_LDH_tempifV_LDH_temp≥0V_LDH_tempotherwiseV_LDH_temp=V_LDH_maxKm_PYR⁢Km_NADH⁢PYR⁢NADH-LAC⁢NADKeq1+PYRKm_PYR+LACKm_LAC⁢1+NADHKm_NADH+NADKm_NAD$

### Component: V_PDH

$V_PDH=V_PDH_tempifV_PDH_temp≥0V_PDH_tempotherwiseV_PDH_temp=V_PDH_max1+Ki⁢NADHNAD⁢PYRKm_PYR⁢NADKm_NAD⁢COAKm_COA1+PYRKm_PYR⁢1+NADKm_NAD+NADHKm_NADH⁢1+COAKm_COA+ACCOAKm_ACCOA$

### Component: V_PTA

$V_PTA=V_PTA_tempifV_PTA_temp≥0V_PTA_tempotherwiseV_PTA_temp=V_PTA_maxKi_ACCOA⁢Km_P⁢ACCOA⁢P-ACP⁢COAKeq1+ACCOAKi_ACCOA+PKi_P+ACPKi_ACP+COAKi_COA+ACCOA⁢PKi_ACCOA⁢Km_P+ACP⁢COAKm_ACP⁢Ki_COA$

### Component: V_ACK

$V_ACK=V_ACK_tempifV_ACK_temp≥0V_ACK_tempotherwiseV_ACK_temp=V_ACK_maxKm_ADP⁢Km_ACP⁢ACP⁢ADP-AC⁢ATPKeq1+ACPKm_ACP+ACKm_AC⁢1+ADPKm_ADP+ATPKm_ATP$

### Component: V_ACALDH

$V_ACALDH=V_ACALDH_tempifV_ACALDH_temp≥0V_ACALDH_tempotherwiseV_ACALDH_temp=V_ACALDH_maxKm_ACCOA⁢Km_NADH⁢ACCOA⁢NADH-NAD⁢COA⁢ACALKeq1+NADKm_NAD+NADHKm_NADH⁢1+ACCOAKm_ACCOA+COAKm_COA⁢1+ACALKm_ACAL$

$V_ADH=V_ADH_tempifV_ADH_temp≥0V_ADH_tempotherwiseV_ADH_temp=V_ADH_maxKm_ACAL⁢Km_NADH⁢ACAL⁢NADH-ETOH⁢NADKeq1+NADKm_NAD+NADHKm_NADH⁢1+ACALKm_ACAL+ETOHKm_ETOH$

### Component: V_ALS

$V_ALS=V_ALS_tempifV_ALS_temp≥0V_ALS_tempotherwiseV_ALS_temp=V_ALS_max⁢PYRKm_PYR⁢1-ACLACPYR⁢Keq⁢PYRKm_PYR+ACLACKm_ACLACN-11+PYRKm_PYR+ACLACKm_ACLACN$

### Component: V_ALDC

$V_ALDC=V_ALDC_tempifV_ALDC_temp≥0V_ALDC_tempotherwiseV_ALDC_temp=V_ALDC_max⁢ACLACKm_ACLAC1+ACLACKm_ACLAC+ACETKm_ACET$

### Component: V_ACETEFF

$V_ACETEFF=V_ACETEFF_tempifV_ACETEFF_temp≥0V_ACETEFF_tempotherwiseV_ACETEFF_temp=V_ACETEFF_max⁢ACETKm_ACET1+ACETKm_ACET$

### Component: V_ACETDH

$V_ACETDH=V_ACETDH_tempifV_ACETDH_temp≥0V_ACETDH_tempotherwiseV_ACETDH_temp=V_ACETDH_maxKm_ACET⁢Km_NADH⁢ACET⁢NADH-BUT⁢NADKeq1+ACETKm_ACET+BUTKm_BUT⁢1+NADHKm_NADH+NADKm_NAD$

### Component: V_ATPase

$V_ATPase=V_ATPase_tempifV_ATPase_temp≥0V_ATPase_tempotherwiseV_ATPase_temp=V_ATPase_max⁢ATPADPNKm_ATPN+ATPADPN$

### Component: V_NOX

$V_NOX=V_NOX_tempifV_NOX_temp≥0V_NOX_tempotherwiseV_NOX_temp=V_NOX_max⁢NADH⁢OKm_NADH⁢Km_O1+NADHKm_NADH+NADKm_NAD⁢1+OKm_O$

### Component: V_NEALC

$V_NEALC=k⁢ACLAC$
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