Gilbert_Sandoval
Notes
Human AFB1 PBK (Gilbert-Sandoval): Stomach → SI1→…→SI7 → Colon; absorption from each SI box to Liver Liver perfusion-limited + Hill metabolism (to AFQ1, AFBO on venous conc) Blood ↔ Rest; 10 once-daily oral boluses; mass balance
Overview
| key | value |
|---|---|
| Modelled species/orgamism(s) | http://purl.obolibrary.org/obo/NCBITaxon_9606 |
| Model chemical(s) | http://purl.obolibrary.org/obo/CHEBI_2504 |
| Input route(s) | no routes detected |
| Time resolution | h |
| Amounts unit | ng |
| Volume unit | L |
| Number of compartments | 13 |
| Number of species | 15 |
| Number of parameters | 46 (18 external / 28 internal) |
Diagram
Compartments
| id | name | unit | model qualifier |
|---|---|---|---|
| Stomach | Stomach compartment | L | http://purl.obolibrary.org/obo/PBPKO_00566 |
| SI1 | Small intestine compartment | L | http://purl.obolibrary.org/obo/PBPKO_00472 |
| SI2 | Small intestine compartment | L | http://purl.obolibrary.org/obo/PBPKO_00472 |
| SI3 | Small intestine compartment | L | http://purl.obolibrary.org/obo/PBPKO_00472 |
| SI4 | Small intestine compartment | L | http://purl.obolibrary.org/obo/PBPKO_00472 |
| SI5 | Small intestine compartment | L | http://purl.obolibrary.org/obo/PBPKO_00472 |
| SI6 | Small intestine compartment | L | http://purl.obolibrary.org/obo/PBPKO_00472 |
| SI7 | Small intestine compartment | L | http://purl.obolibrary.org/obo/PBPKO_00472 |
| Colon | Colon compartment | L | not specified |
| 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 |
| Feces | Feces compartment | L | http://purl.obolibrary.org/obo/PBPKO_00555 |
Species
| id | name | unit | model qualifier |
|---|---|---|---|
| ASt | Amount in stomach | ng | not specified |
| ASI1 | Amount in small intestine | ng | not specified |
| ASI2 | Amount in small intestine | ng | not specified |
| ASI3 | Amount in small intestine | ng | not specified |
| ASI4 | Amount in small intestine | ng | not specified |
| ASI5 | Amount in small intestine | ng | not specified |
| ASI6 | Amount in small intestine | ng | not specified |
| ASI7 | Amount in small intestine | ng | not specified |
| AColon | Amount in colon | ng | not specified |
| AFeaces | Amount in feces | ng | http://purl.obolibrary.org/obo/PBPKO_00273 |
| 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 |
| ALiverMet1 | Amount in liver (metabolised) | ng | not specified |
| ALiverMet2 | Amount in liver (metabolised) | ng | not specified |
Transfer equations
| id | from | to | equation |
|---|---|---|---|
| _J0 | ASt | ASI1 | ksto * ASt |
| _J1 | ASI1 | ASI2 | kt * ASI1 |
| _J2 | ASI2 | ASI3 | kt * ASI2 |
| _J3 | ASI3 | ASI4 | kt * ASI3 |
| _J4 | ASI4 | ASI5 | kt * ASI4 |
| _J5 | ASI5 | ASI6 | kt * ASI5 |
| _J6 | ASI6 | ASI7 | kt * ASI6 |
| _J7 | ASI7 | AColon | kt * ASI7 |
| _J8 | ASI1 | ALiver | kabsSI1 * CSI1 |
| _J9 | ASI2 | ALiver | kabsSI2 * CSI2 |
| _J10 | ASI3 | ALiver | kabsSI3 * CSI3 |
| _J11 | ASI4 | ALiver | kabsSI4 * CSI4 |
| _J12 | ASI5 | ALiver | kabsSI5 * CSI5 |
| _J13 | ASI6 | ALiver | kabsSI6 * CSI6 |
| _J14 | ASI7 | ALiver | kabsSI7 * CSI7 |
| _J15 | AColon | AFeaces | kfe * AColon |
| _J16 | ABlood | ALiver | QL * CBlood |
| _J17 | ALiver | ABlood | QL * CLiver / PL |
| _J18 | ABlood | ARest | QRest * CBlood |
| _J19 | ARest | ABlood | QRest * CRest / PRest |
| _J20 | ALiver | ALiverMet1 | VmaxMet1 * pow(CLiver / PL, nMet1) / (pow(S50Met1, nMet1) + pow(CLiver / PL, nMet1)) |
| _J21 | ALiver | ALiverMet2 | VmaxMet2 * pow(CLiver / PL, nMet2) / (pow(S50Met2, nMet2) + pow(CLiver / PL, nMet2)) |
ODEs
\(\frac{d[\mathtt{ASt}]}{dt} = - \mathit{ksto}\cdot \mathit{ASt}\)
\(\frac{d[\mathtt{ASI1}]}{dt} = \mathit{ksto}\cdot \mathit{ASt} - \mathit{kt}\cdot \mathit{ASI1} - \mathit{kabsSI1}\cdot \mathit{CSI1}\)
\(\frac{d[\mathtt{ASI2}]}{dt} = \mathit{kt}\cdot \mathit{ASI1} - \mathit{kt}\cdot \mathit{ASI2} - \mathit{kabsSI2}\cdot \mathit{CSI2}\)
\(\frac{d[\mathtt{ASI3}]}{dt} = \mathit{kt}\cdot \mathit{ASI2} - \mathit{kt}\cdot \mathit{ASI3} - \mathit{kabsSI3}\cdot \mathit{CSI3}\)
\(\frac{d[\mathtt{ASI4}]}{dt} = \mathit{kt}\cdot \mathit{ASI3} - \mathit{kt}\cdot \mathit{ASI4} - \mathit{kabsSI4}\cdot \mathit{CSI4}\)
\(\frac{d[\mathtt{ASI5}]}{dt} = \mathit{kt}\cdot \mathit{ASI4} - \mathit{kt}\cdot \mathit{ASI5} - \mathit{kabsSI5}\cdot \mathit{CSI5}\)
\(\frac{d[\mathtt{ASI6}]}{dt} = \mathit{kt}\cdot \mathit{ASI5} - \mathit{kt}\cdot \mathit{ASI6} - \mathit{kabsSI6}\cdot \mathit{CSI6}\)
\(\frac{d[\mathtt{ASI7}]}{dt} = \mathit{kt}\cdot \mathit{ASI6} - \mathit{kt}\cdot \mathit{ASI7} - \mathit{kabsSI7}\cdot \mathit{CSI7}\)
\(\frac{d[\mathtt{AColon}]}{dt} = \mathit{kt}\cdot \mathit{ASI7} - \mathit{kfe}\cdot \mathit{AColon}\)
\(\frac{d[\mathtt{AFeaces}]}{dt} = \mathit{kfe}\cdot \mathit{AColon}\)
\(\frac{d[\mathtt{ALiver}]}{dt} = \mathit{kabsSI1}\cdot \mathit{CSI1} + \mathit{kabsSI2}\cdot \mathit{CSI2} + \mathit{kabsSI3}\cdot \mathit{CSI3} + \mathit{kabsSI4}\cdot \mathit{CSI4} + \mathit{kabsSI5}\cdot \mathit{CSI5} + \mathit{kabsSI6}\cdot \mathit{CSI6} + \mathit{kabsSI7}\cdot \mathit{CSI7} + \mathit{QL}\cdot \mathit{CBlood} - \frac{\mathit{QL}\cdot \mathit{CLiver}}{\mathit{PL}} - \frac{\mathit{VmaxMet1}\cdot {\left(\frac{\mathit{CLiver}}{\mathit{PL}}\right)}^{\mathit{nMet1}}}{{\mathit{S50Met1}}^{\mathit{nMet1}}+{\left(\frac{\mathit{CLiver}}{\mathit{PL}}\right)}^{\mathit{nMet1}}} - \frac{\mathit{VmaxMet2}\cdot {\left(\frac{\mathit{CLiver}}{\mathit{PL}}\right)}^{\mathit{nMet2}}}{{\mathit{S50Met2}}^{\mathit{nMet2}}+{\left(\frac{\mathit{CLiver}}{\mathit{PL}}\right)}^{\mathit{nMet2}}}\)
\(\frac{d[\mathtt{ABlood}]}{dt} = - \mathit{QL}\cdot \mathit{CBlood} + \frac{\mathit{QL}\cdot \mathit{CLiver}}{\mathit{PL}} - \mathit{QRest}\cdot \mathit{CBlood} + \frac{\mathit{QRest}\cdot \mathit{CRest}}{\mathit{PRest}}\)
\(\frac{d[\mathtt{ARest}]}{dt} = \mathit{QRest}\cdot \mathit{CBlood} - \frac{\mathit{QRest}\cdot \mathit{CRest}}{\mathit{PRest}}\)
\(\frac{d[\mathtt{ALiverMet1}]}{dt} = \frac{\mathit{VmaxMet1}\cdot {\left(\frac{\mathit{CLiver}}{\mathit{PL}}\right)}^{\mathit{nMet1}}}{{\mathit{S50Met1}}^{\mathit{nMet1}}+{\left(\frac{\mathit{CLiver}}{\mathit{PL}}\right)}^{\mathit{nMet1}}}\)
\(\frac{d[\mathtt{ALiverMet2}]}{dt} = \frac{\mathit{VmaxMet2}\cdot {\left(\frac{\mathit{CLiver}}{\mathit{PL}}\right)}^{\mathit{nMet2}}}{{\mathit{S50Met2}}^{\mathit{nMet2}}+{\left(\frac{\mathit{CLiver}}{\mathit{PL}}\right)}^{\mathit{nMet2}}}\)
Assignment rules
| variable | assignment |
|---|---|
| VL | VLc * BW |
| VB | VBc * BW |
| VRest | 0.84 * BW - VL - VB |
| QC | 15 * pow(BW, 0.74) |
| QL | QLc * QC |
| QRest | QC - QL |
| kabsSI1 | kabs * VSI |
| kabsSI2 | kabs * VSI |
| kabsSI3 | kabs * VSI |
| kabsSI4 | kabs * VSI |
| kabsSI5 | kabs * VSI |
| kabsSI6 | kabs * VSI |
| kabsSI7 | kabs * VSI |
| VmaxMet1 | VmaxMet1c * 60 * MPL * VL |
| VmaxMet2 | VmaxMet2c * 60 * MPL * VL |
| CSt | ASt / Stomach |
| CSI1 | ASI1 / SI1 |
| CSI2 | ASI2 / SI2 |
| CSI3 | ASI3 / SI3 |
| CSI4 | ASI4 / SI4 |
| CSI5 | ASI5 / SI5 |
| CSI6 | ASI6 / SI6 |
| CSI7 | ASI7 / SI7 |
| CLiver | ALiver / Liver |
| CBlood | ABlood / Blood |
| CRest | ARest / Rest |
| MetLiver1 | VmaxMet1 * pow(CLiver / PL, nMet1) / (pow(S50Met1, nMet1) + pow(CLiver / PL, nMet1)) |
| MetLiver2 | VmaxMet2 * pow(CLiver / PL, nMet2) / (pow(S50Met2, nMet2) + pow(CLiver / PL, nMet2)) |
Initial assignments
| variable | assignment |
|---|---|
| SI1 | VSI |
| SI2 | VSI |
| SI3 | VSI |
| SI4 | VSI |
| SI5 | VSI |
| SI6 | VSI |
| SI7 | VSI |
| Liver | VL |
| Blood | VB |
| Rest | VRest |
| MPL | 39.46 * 1000 |
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 |
| VSI | Volume of small intestine | L | http://purl.obolibrary.org/obo/PBPKO_00071 |
| VL | Volume of liver | L | http://purl.obolibrary.org/obo/PBPKO_00077 |
| VB | Volume of blood | L | http://purl.obolibrary.org/obo/PBPKO_00108 |
| 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 |
| QL | Cardiac output to liver | L/h | http://purl.obolibrary.org/obo/PBPKO_00024 |
| QRest | Cardiac output to rest of body | L/h | http://purl.obolibrary.org/obo/PBPKO_00050 |
| 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 |
| ksto | stomach emptying rate | /h | not specified |
| kt | Transfer rate to next compartment within the intestines | /h | not specified |
| kfe | Excretion rate to feces | /h | http://purl.obolibrary.org/obo/PBPKO_00236 |
| kabs | Absorption rate in small intestine | /h | http://purl.obolibrary.org/obo/PBPKO_00142 |
| kabsSI1 | Absorption rate in small intestine | /h | http://purl.obolibrary.org/obo/PBPKO_00142 |
| kabsSI2 | Absorption rate in small intestine | /h | http://purl.obolibrary.org/obo/PBPKO_00142 |
| kabsSI3 | Absorption rate in small intestine | /h | http://purl.obolibrary.org/obo/PBPKO_00142 |
| kabsSI4 | Absorption rate in small intestine | /h | http://purl.obolibrary.org/obo/PBPKO_00142 |
| kabsSI5 | Absorption rate in small intestine | /h | http://purl.obolibrary.org/obo/PBPKO_00142 |
| kabsSI6 | Absorption rate in small intestine | /h | http://purl.obolibrary.org/obo/PBPKO_00142 |
| kabsSI7 | Absorption rate in small intestine | /h | http://purl.obolibrary.org/obo/PBPKO_00142 |
| MPL | {mg microsomal protein/kg liver} | mg/kg | not specified |
| VmaxMet1c | Vmax constant | not specified | http://biomodels.net/SBO/SBO_0000027 |
| VmaxMet2c | Vmax constant | not specified | http://biomodels.net/SBO/SBO_0000027 |
| nMet1 | Hill coefficient | dimensionless | not specified |
| nMet2 | Hill coefficient | dimensionless | not specified |
| S50Met1 | effective Hill S50 | umol/L | not specified |
| S50Met2 | effective Hill S50 | umol/L | not specified |
| VmaxMet1 | Vmax | not specified | http://biomodels.net/SBO/SBO_0000027 |
| VmaxMet2 | Vmax | not specified | http://biomodels.net/SBO/SBO_0000027 |
| CSt | Concentration in stomach | umol/L | not specified |
| CSI1 | Concentration in small intestine | umol/L | not specified |
| CSI2 | Concentration in small intestine | umol/L | not specified |
| CSI3 | Concentration in small intestine | umol/L | not specified |
| CSI4 | Concentration in small intestine | umol/L | not specified |
| CSI5 | Concentration in small intestine | umol/L | not specified |
| CSI6 | Concentration in small intestine | umol/L | not specified |
| CSI7 | Concentration in small intestine | umol/L | not specified |
| CLiver | Concentration in liver | umol/L | http://purl.obolibrary.org/obo/PBPKO_00539 |
| CBlood | Concentration in blood | umol/L | http://purl.obolibrary.org/obo/PBPKO_00301 |
| CRest | Concentration in rest of body | umol/L | http://purl.obolibrary.org/obo/PBPKO_00548 |
| MetLiver1 | Metabolite concentration | umol/L | not specified |
| MetLiver2 | Metabolite concentration | umol/L | not specified |