# Model Mathematics

### Component: ATbl

$ddtime ATbl = Qb ⁢ CTbf - CTblf + Qp ⁢ CTpf - CTbl + Ql ⁢ CTlf - CTbl + Qt ⁢ 1.0 - ts ⁢ CTtv - CTblf + k2T$

$ddtime ADbl = Qbt ⁢ CDbf - CDblf + Qp ⁢ CDpf - CDblf + Ql ⁢ CDlf - CDbl$

### Component: CT_A

$ddtime CT_A = kTA_on ⁢ CTblf ⁢ CAf - kTA_off ⁢ CT_A$

### Component: CD_A

$ddtime CD_A = kDA_on ⁢ CDblf ⁢ CAf - kDA_off ⁢ CD_A$

### Component: CTblf

$CTblf = CTbl - CT_A$

### Component: CDblf

$CDblf = CDbl - CD_A$

### Component: CAf

$CAf = CA - CT_A + CD_A$

### Component: ATl

$ddtime ATl = Ql ⁢ CTbl - CTlf - Vmax1 ⁢ CTlf km5alpha + CTlf + k1T ⁢ ATl PTl$

$ddtime ADl = Ql ⁢ CDbl - CDlf - Vmax1 ⁢ CTlf km5alpha + CTlf + k1D ⁢ ADl PDl$

### Component: CTlf

$CTlf = CTl PTl$

### Component: CDlf

$CDlf = CDl PDl$

### Component: ATif

$ddtime ATif = Qt ⁢ 1.0 - ts ⁢ CTblf - CTif PTif + mu ⁢ CTst PTst - CTif + k1T ⁢ CLH$

### Component: ATst

$ddtime ATst = mu ⁢ CTif - CTst PTst$

### Component: CTtv

$CTtv = CTif PTif$

### Component: ATp

$ddtime ATp = Qp ⁢ CTbl - CTpf - Vmax0 ⁢ CTpf km5alpha + CTpf$

$ddtime ADp = Qp ⁢ CDbl - CDpf - Vmax0 ⁢ CTpf km5alpha + CTpf$

### Component: CT_R

$ddtime CT_R = kTR_on ⁢ CTpf ⁢ CRf - kTR_off ⁢ CT_R$

### Component: CD_R

$ddtime CD_R = kDR_on ⁢ CDpf ⁢ CRf - kDR_off ⁢ CD_R$

### Component: CDT

$ddtime CDT = kDT_on ⁢ CD_R ⁢ CT_R - kDT_off ⁢ CDT$

### Component: CDD

$ddtime CDD = kDD_on ⁢ CD_R 2.0 - kDD_off ⁢ CDD$

### Component: CTT

$ddtime CTT = kTT_on ⁢ CT_R 2.0 - kTT_off ⁢ CTT$

### Component: CDD5a

$ddtime CDD5a = kDNA_onDD5a ⁢ CDD ⁢ CDNA5af - kDNA_offDD5a ⁢ CDD5a$

### Component: CDDcd

$ddtime CDDcd = kDNA_onDDcd ⁢ CDD ⁢ CDNAcdf - kDNA_offDDcd ⁢ CDDcd$

### Component: CDDsec

$ddtime CDDsec = kDNA_onDDsec ⁢ CDD ⁢ CDNAsecf - kDNA_offDDsec ⁢ CDDsec$

### Component: CDDcp

$ddtime CDDcp = kDNA_onDDcp ⁢ CDD ⁢ CDNAcpf - kDNA_offDDcp ⁢ CDDcp$

### Component: CDT5a

$ddtime CDT5a = kDNA_onDT5a ⁢ CDT ⁢ CDNA5af - kDNA_offDT5a ⁢ CDT5a$

### Component: CDTcd

$ddtime CDTcd = kDNA_onDTcd ⁢ CDT ⁢ CDNAcdf - kDNA_offDTcd ⁢ CDTcd$

### Component: CDTsec

$ddtime CDTsec = kDNA_onDTsec ⁢ CDT ⁢ CDNAsecf - kDNA_offDTsec ⁢ CDTsec$

### Component: CDTcp

$ddtime CDTcp = kDNA_onDTcp ⁢ CDT ⁢ CDNAcpf - kDNA_offDTcp ⁢ CDTcp$

### Component: CTT5a

$ddtime CTT5a = kDNA_onTT5a ⁢ CTT ⁢ CDNA5af - kDNA_offTT5a ⁢ CTT5a$

### Component: CTTcd

$ddtime CTTcd = kDNA_onTTcd ⁢ CTT ⁢ CDNAcdf - kDNA_offTTcd ⁢ CTTcd$

### Component: CTTsec

$ddtime CTTsec = kDNA_onTTsec ⁢ CTT ⁢ CDNAsecf - kDNA_offTTsec ⁢ CTTsec$

### Component: CTTcp

$ddtime CTTcp = kDNA_onTTcp ⁢ CTT ⁢ CDNAcpf - kDNA_offTTcp ⁢ CTTcp$

### Component: CTpf

$CTpf = CTp - CT_R + 2.0 ⁢ CTT + CDT + T 1.0 + NTp T = CTTsec + CDTsec + CTT5a + CDT5a + CTTcd + CDTcd + CTTcp + CDTcp$

### Component: CDpf

$CDpf = CDp - CD_R + 2.0 ⁢ CDD + CDT + D 1.0 + NDp D = CDDsec + CDTsec + CDD5a + CDT5a + CDDcd + CDTcd + CDDcp + CDTcp$

### Component: CRf

$CRf = CR - CT_R + CD_R + 2.0 ⁢ CTT + CDD + CDT + 2.0 ⁢ CDNAcdf + CDNAsecf + CDNAcpf + CDNA5af$

### Component: CDNAcdf

$CDNAcdf = CDNAcd - CTTcd + CDDcd + CDTcd$

### Component: CDNAsecf

$CDNAsecf = CDNAsec - CTTsec + CDDsec + CDTsec$

### Component: CDNA5af

$CDNA5af = CDNA5a - CTT5a + CDD5a + CDT5a$

### Component: CDNAcpf

$CDNAcpf = CDNAcp - CTTcp + CDDcp + CDTcp$

### Component: DNAocp

$DNAocp = CTTcp + CDDcp + CDTcp CDNAcp$

### Component: DNAosec

$DNAosec = CTTsec + CDDsec + CDTsec CDNAsec$

### Component: DNAocd

$DNAocd = CTTcd + CDDcd + CDTcd CDNAcd$

### Component: DNAo5a

$DNAo5a = CTT5a + CDD5a + CDT5a CDNA5a$

### Component: ATb

$ddtime ATb = Qb ⁢ CTblf - CTb PTb$

$ddtime ADb = Qbt ⁢ CDblf - CDb PDb$

### Component: ALH

$A =- kLH1 ⁢ alpha_T ⁢ CTblf + alpha_D ⁢ CDblf + kLH2 B = kLH3 ddtime ALH = A - kLH4 ⁢ ALH if A > B B - kLH4 ⁢ ALH otherwise$

### Component: AR

$ddtime AR = k1R - keR ⁢ CRf$

### Component: CR

$CR = AR Vp$

### Component: Qp

$Qp = kQp ⁢ Vpc Vpc = VPC1 + VPC2$

### Component: Vmax

$Vmax = k5a ⁢ DNAo5a$

### Component: VPC1

$ddtime VPC1 = VPC1 VPC1b ⁢ kcpl ⁢ DNAocp - kcd1 ⁢ 1.0 - DNAocd ⁢ VPC1$

### Component: VPL1

$ddtime VPL1 = VPC1 VPC1b ⁢ ksec ⁢ DNAosec - kflo ⁢ VPL1$

### Component: Vp

$Vp = VPC1 + VPC2 + VPL1 + VPL2$

### Component: model_parameters

$Qb = Qc - Qp + Qt + Ql Qbt = Qc - Qp + Ql CTbf = CTb PTb CDbf = CDb PDb$
Source
Derived from workspace Potter, Zager, Barton, 2006 at changeset 941e8c510816.
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