Mukherjee
Notes
Mukherjee, D., et al. (2014) Human PBK for oral absorption (Mukherjee 2014 core): GI (GI→Fast/Slow; Slow→Colon; Fast→Gut) Perfusion-limited: Gut ↔ Blood, Liver ↔ Blood, Rest ↔ Blood Parent metabolism in liver (1st order by default, MM optional)
Overview
| key | value |
|---|---|
| Modelled species/orgamism(s) | http://purl.obolibrary.org/obo/NCBITaxon_9606 |
| Model chemical(s) | http://purl.obolibrary.org/obo/CHEBI_10106 |
| Input route(s) | 1 (oral) |
| Time resolution | h |
| Amounts unit | ng |
| Volume unit | L |
| Number of compartments | 12 |
| Number of species | 16 |
| Number of parameters | 51 (23 external / 28 internal) |
Diagram
Compartments
| id | name | unit | model qualifier |
|---|---|---|---|
| GILumen | GI lumen compartment | L | http://purl.obolibrary.org/obo/PBPKO_00478 |
| Fast | Fast GI lumen compartment | L | http://purl.obolibrary.org/obo/PBPKO_00478 |
| Slow | Slow GI lumen compartment | L | http://purl.obolibrary.org/obo/PBPKO_00478 |
| Colon | Colon compartment | L | not specified |
| Gut | Gut compartment | L | http://purl.obolibrary.org/obo/PBPKO_00477 |
| Liver | Liver compartment | L | http://purl.obolibrary.org/obo/PBPKO_00558 |
| Blood | Blood compartment | L | http://purl.obolibrary.org/obo/PBPKO_00464 |
| Rest | Rest of body compartment | L | http://purl.obolibrary.org/obo/PBPKO_00450 |
| Bile | Bile (pseudo) compartment | L | not specified |
| Feces | Feces compartment | L | http://purl.obolibrary.org/obo/PBPKO_00555 |
| Stomach | Stomach compartment | L | http://purl.obolibrary.org/obo/PBPKO_00566 |
| Spleen | Spleen compartment | L | http://purl.obolibrary.org/obo/PBPKO_00492 |
Species
| id | name | unit | model qualifier |
|---|---|---|---|
| AGILumen | Amount in GI lumen | ng | not specified |
| AFast | Amount in fast GI lumen | ng | not specified |
| ASlow | Amount in slow GI lumen | ng | not specified |
| AColon | Amount in colon | ng | not specified |
| AGut | Amount in gut | ng | http://purl.obolibrary.org/obo/PBPKO_00496 |
| ALiver | Amount in liver | ng | http://purl.obolibrary.org/obo/PBPKO_00497 |
| ABlood | Amount in blood | ng | http://purl.obolibrary.org/obo/PBPKO_00623 |
| ARest | Amount in rest of body | ng | http://purl.obolibrary.org/obo/PBPKO_00501 |
| ASt | Amount in stomach | ng | not specified |
| ASpleen | Amount in spleen | ng | not specified |
| ABile | Amount in Bile (may be removed) | ng | not specified |
| AFeces | Amount in feces | ng | http://purl.obolibrary.org/obo/PBPKO_00273 |
| ALiverMet1 | Amount of metabolite in liver | ng | not specified |
| ALiverMet2 | Amount of metabolite in liver | ng | not specified |
| ALiverMet3 | Amount of metabolite in liver | ng | not specified |
| ALiverMet4 | Amount of metabolite in liver | ng | not specified |
Transfer equations
| id | from | to | equation |
|---|---|---|---|
| _J0 | AGILumen | AFast | ktFL * AGILumen |
| _J1 | AGILumen | ASlow | ktSL * AGILumen |
| _J2 | ASlow | AColon | kt * ASlow |
| _J3 | AFast | AGut | kabsFL * AFast |
| _J4 | ASlow | AGut | kabsSL * ASlow |
| _J5 | AColon | AFeces | kfe * AColon |
| _J6 | ABlood | AGut | QG * CBlood |
| _J7 | AGut | ALiver | QG * CGut / PG |
| _J8 | ABlood | ALiver | QLhep * CBlood |
| _J9 | ALiver | ABlood | QL * CLiver / PL |
| _J10 | ABlood | ARest | QRest * CBlood |
| _J11 | ARest | ABlood | QRest * CRest / PRest |
| _J12 | ALiver | ALiverMet1 | CLintLMet1 * CLiver |
| _J13 | ALiver | ALiverMet2 | CLintLMet2 * CLiver |
| _J14 | ALiver | ALiverMet3 | CLintLMet3 * CLiver |
| _J15 | ALiver | ALiverMet4 | CLintLMet4 * CLiver |
| _J16 | ALiver | ABile | QBile * kbiliary * CLiver |
| _J17 | ABile | AGILumen | QBile * CBile |
| _J18 | ABlood | ASt | QSt * CBlood |
| _J19 | ASt | ALiver | QSt * CStomach / PStomach |
| _J20 | ABlood | ASpleen | QSpleen * CBlood |
| _J21 | ASpleen | ALiver | QSpleen * CSpleen / PSpleen |
ODEs
\(\frac{d[\mathtt{AGILumen}]}{dt} = - \mathit{ktFL}\cdot \mathit{AGILumen} - \mathit{ktSL}\cdot \mathit{AGILumen} + \mathit{QBile}\cdot \mathit{CBile}\)
\(\frac{d[\mathtt{AFast}]}{dt} = \mathit{ktFL}\cdot \mathit{AGILumen} - \mathit{kabsFL}\cdot \mathit{AFast}\)
\(\frac{d[\mathtt{ASlow}]}{dt} = \mathit{ktSL}\cdot \mathit{AGILumen} - \mathit{kt}\cdot \mathit{ASlow} - \mathit{kabsSL}\cdot \mathit{ASlow}\)
\(\frac{d[\mathtt{AColon}]}{dt} = \mathit{kt}\cdot \mathit{ASlow} - \mathit{kfe}\cdot \mathit{AColon}\)
\(\frac{d[\mathtt{AGut}]}{dt} = \mathit{kabsFL}\cdot \mathit{AFast} + \mathit{kabsSL}\cdot \mathit{ASlow} + \mathit{QG}\cdot \mathit{CBlood} - \frac{\mathit{QG}\cdot \mathit{CGut}}{\mathit{PG}}\)
\(\frac{d[\mathtt{ALiver}]}{dt} = \frac{\mathit{QG}\cdot \mathit{CGut}}{\mathit{PG}} + \mathit{QLhep}\cdot \mathit{CBlood} - \frac{\mathit{QL}\cdot \mathit{CLiver}}{\mathit{PL}} - \mathit{CLintLMet1}\cdot \mathit{CLiver} - \mathit{CLintLMet2}\cdot \mathit{CLiver} - \mathit{CLintLMet3}\cdot \mathit{CLiver} - \mathit{CLintLMet4}\cdot \mathit{CLiver} - \mathit{QBile}\cdot \mathit{kbiliary}\cdot \mathit{CLiver} + \frac{\mathit{QSt}\cdot \mathit{CStomach}}{\mathit{PStomach}} + \frac{\mathit{QSpleen}\cdot \mathit{CSpleen}}{\mathit{PSpleen}}\)
\(\frac{d[\mathtt{ABlood}]}{dt} = - \mathit{QG}\cdot \mathit{CBlood} - \mathit{QLhep}\cdot \mathit{CBlood} + \frac{\mathit{QL}\cdot \mathit{CLiver}}{\mathit{PL}} - \mathit{QRest}\cdot \mathit{CBlood} + \frac{\mathit{QRest}\cdot \mathit{CRest}}{\mathit{PRest}} - \mathit{QSt}\cdot \mathit{CBlood} - \mathit{QSpleen}\cdot \mathit{CBlood}\)
\(\frac{d[\mathtt{ARest}]}{dt} = \mathit{QRest}\cdot \mathit{CBlood} - \frac{\mathit{QRest}\cdot \mathit{CRest}}{\mathit{PRest}}\)
\(\frac{d[\mathtt{ASt}]}{dt} = \mathit{QSt}\cdot \mathit{CBlood} - \frac{\mathit{QSt}\cdot \mathit{CStomach}}{\mathit{PStomach}}\)
\(\frac{d[\mathtt{ASpleen}]}{dt} = \mathit{QSpleen}\cdot \mathit{CBlood} - \frac{\mathit{QSpleen}\cdot \mathit{CSpleen}}{\mathit{PSpleen}}\)
\(\frac{d[\mathtt{ABile}]}{dt} = \mathit{QBile}\cdot \mathit{kbiliary}\cdot \mathit{CLiver} - \mathit{QBile}\cdot \mathit{CBile}\)
\(\frac{d[\mathtt{AFeces}]}{dt} = \mathit{kfe}\cdot \mathit{AColon}\)
\(\frac{d[\mathtt{ALiverMet1}]}{dt} = \mathit{CLintLMet1}\cdot \mathit{CLiver}\)
\(\frac{d[\mathtt{ALiverMet2}]}{dt} = \mathit{CLintLMet2}\cdot \mathit{CLiver}\)
\(\frac{d[\mathtt{ALiverMet3}]}{dt} = \mathit{CLintLMet3}\cdot \mathit{CLiver}\)
\(\frac{d[\mathtt{ALiverMet4}]}{dt} = \mathit{CLintLMet4}\cdot \mathit{CLiver}\)
Assignment rules
| variable | assignment |
|---|---|
| Gut | VG |
| Liver | VL |
| Blood | VB |
| Rest | VRest |
| Bile | VBile |
| Stomach | VSt |
| Spleen | VSpleen |
| VL | VLc * BW |
| VB | VBc * BW |
| VG | VGc * BW |
| VRest | 0.84 * BW - VL - VB - VG - VSt - VSpleen |
| QC | 15 * pow(BW, 0.74) |
| QL | QLc * QC |
| QG | QGc * QC |
| QRest | QC - (QL + QG + QSt + QSpleen) |
| QLhep | QL - QSt - QG - QSpleen |
| ktFL | 20 * 60 |
| ktSL | 0.05 * 60 |
| kt | 3.45 * 60 |
| kabsFL | 15.45 * 60 |
| kfe | 0.0034 * 60 |
| kbiliary | 0.0585 * 60 |
| VLkg | VLc * 1000 |
| CLintLMet1 | CLintLMet1C * VLkg * BW * 60 / 1000 |
| CLintLMet2 | CLintLMet2C * VLkg * BW * 60 / 1000 |
| CLintLMet3 | CLintLMet3C * VLkg * BW * 60 / 1000 |
| CLintLMet4C | 5 * pow(10, -6) |
| CLintLMet4 | CLintLMet4C * VLkg * BW * 60 / 1000 |
| CGut | AGut / Gut |
| CLiver | ALiver / Liver |
| CBlood | ABlood / Blood |
| CRest | ARest / Rest |
| CStomach | ASt / Stomach |
| CSpleen | ASpleen / Spleen |
| CBile | ABile / Bile |
Initial assignments
| variable | assignment |
|---|---|
| CLintLMet1C | 4.776 * pow(10, -3) |
| CLintLMet2C | 2.36 * pow(10, -2) |
| CLintLMet3C | 7.057 * pow(10, -3) |
Parameters
| id | name | unit | model qualifier |
|---|---|---|---|
| BW | Bodyweight | kg | http://purl.obolibrary.org/obo/PBPKO_00008 |
| VLc | Volume fraction of liver | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00078 |
| VBc | Volume fraction of blood | dimensionless | not specified |
| VGc | Volume fraction of gut | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00509 |
| VL | Volume of liver | L | http://purl.obolibrary.org/obo/PBPKO_00077 |
| VB | Volume of blood | L | http://purl.obolibrary.org/obo/PBPKO_00108 |
| VG | Volume of gut | L | http://purl.obolibrary.org/obo/PBPKO_00524 |
| VSt | Volume of stomach | L | http://purl.obolibrary.org/obo/PBPKO_00067 |
| VSpleen | Volume of spleen | L | http://purl.obolibrary.org/obo/PBPKO_00095 |
| VBile | Volume of bile | L | not specified |
| VRest | Volume of rest of body | L | http://purl.obolibrary.org/obo/PBPKO_00105 |
| QC | Cardiac output | L/h | http://purl.obolibrary.org/obo/PBPKO_00013 |
| QLc | Cardiac output fraction to liver | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00025 |
| QGc | Cardiac output fraction to gut | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00513 |
| QL | Cardiac output to liver | L/h | http://purl.obolibrary.org/obo/PBPKO_00024 |
| QG | Cardiac output to gut | L/h | http://purl.obolibrary.org/obo/PBPKO_00531 |
| QSpleen | Cardiac output to spleen | L/h | http://purl.obolibrary.org/obo/PBPKO_00042 |
| QSt | Cardiac output to stomach | L/h | http://purl.obolibrary.org/obo/PBPKO_00014 |
| QRest | Cardiac output to rest of body | L/h | http://purl.obolibrary.org/obo/PBPKO_00050 |
| QBile | Cardiac output to Bile | L/h | not specified |
| QLhep | arterial hepatic blood flow | L/h | not specified |
| PL | Partition coefficient blood-liver | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00577 |
| PRest | Partition coefficient blood- rest body | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00585 |
| PG | Partition coefficient blood-gut | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00572 |
| PStomach | Partition coefficient blood- stomach | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00590 |
| PSpleen | Partition coefficient blood- spleen | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00589 |
| ktFL | Transfer kinetic constant GI lumen to fast lumen | /h | not specified |
| ktSL | Transfer kinetic constant GI lumen to slow lumen | /h | not specified |
| kt | Kinetic constant slow lumen to colon | /h | not specified |
| kabsFL | Kinetic constant fast lumen to gut | /h | not specified |
| kabsSL | Kinetic constant slow lumen to gut | /h | not specified |
| kfe | Kinetic constant colon to feces | /h | not specified |
| kbiliary | Kinetic constant biliary excretion (liver to bile) | /h | not specified |
| VmaxGZEA | Vmax gut metabolism | not specified | http://biomodels.net/SBO/SBO_0000027 |
| KmGZEA | Km gut metabolism | not specified | http://biomodels.net/SBO/SBO_0000027 |
| VLkg | Volume fraction of liver convert to kg | g/kg | http://purl.obolibrary.org/obo/PBPKO_00078 |
| CLintLMet1C | Vmax/Km for reaction ZEA -> ZEAGLU | not specified | not specified |
| CLintLMet1 | Vmax/Km for reaction ZEA -> ZEAGLU | L/h | not specified |
| CLintLMet2C | Vmax/Km for reaction ZEA -> a-ZOL | not specified | not specified |
| CLintLMet2 | Vmax/Km for reaction ZEA -> a-ZOL | L/h | not specified |
| CLintLMet3C | Vmax/Km for reaction ZEA -> b-ZOL | not specified | not specified |
| CLintLMet3 | Vmax/Km for reaction ZEA -> b-ZOL | L/h | not specified |
| CLintLMet4C | Vmax/Km for reaction ZEA -> ZAN | not specified | not specified |
| CLintLMet4 | Vmax/Km for reaction ZEA -> ZAN | L/h | not specified |
| CGut | Concentration in gut | not specified | http://purl.obolibrary.org/obo/PBPKO_00538 |
| CLiver | Concentration in liver | not specified | http://purl.obolibrary.org/obo/PBPKO_00539 |
| CBlood | Concentration in blood | not specified | http://purl.obolibrary.org/obo/PBPKO_00301 |
| CRest | Concentration in rest of body | not specified | http://purl.obolibrary.org/obo/PBPKO_00548 |
| CStomach | Concentration in stomach | not specified | not specified |
| CSpleen | Concentration in spleen | not specified | not specified |
| CBile | Concentration in bile | not specified | not specified |