ElMasri 2008
Notes
Arsene ElMasri et al. 2008
Overview
| key | value |
|---|---|
| Modelled species/orgamism(s) | http://purl.obolibrary.org/obo/NCBITaxon_9606 |
| Model chemical(s) | http://purl.obolibrary.org/obo/CHEBI_190436 |
| Input route(s) | 2 (oral, inhalation) |
| Time resolution | h |
| Amounts unit | mol |
| Volume unit | dimensionless |
| Number of compartments | 8 |
| Number of species | 32 |
| Number of parameters | 78 (33 external / 45 internal) |
Diagram
Compartments
| id | name | unit | model qualifier |
|---|---|---|---|
| Lumen | Compartment of lumen | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00478 |
| Gut | Compartment of Gut | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00477 |
| Liver | Compartment of liver | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00558 |
| Lung | Compartment of lung | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00559 |
| Arterial | Compartment of arterial blood | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00552 |
| Venous | Compartment of venous blood | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00561 |
| Rest | Compartment of rest of the body | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00450 |
| Urine | Compartment of urine | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00556 |
Species
| id | name | unit | model qualifier |
|---|---|---|---|
| ALumen_As3 | Amount of As3+ in lumen | mol | not specified |
| ALumen_As5 | Amount of As5+ in lumen | mol | not specified |
| AGut_As3 | Amount of As3+ in gut | mol | http://purl.obolibrary.org/obo/PBPKO_00496 |
| AGut_As5 | Amount of As5+ in gut | mol | http://purl.obolibrary.org/obo/PBPKO_00496 |
| AGut_AsM5 | Amount of MMA5 in gut | mol | http://purl.obolibrary.org/obo/PBPKO_00496 |
| AGut_AsD5 | Amount of DMA5 in Gut | mol | http://purl.obolibrary.org/obo/PBPKO_00496 |
| AArterial_AsD5 | Amount of DMA5 in arterial blood | mol | http://purl.obolibrary.org/obo/PBPKO_00631 |
| ALiver_As3 | Amount of As3+ in liver | mol | http://purl.obolibrary.org/obo/PBPKO_00497 |
| ALiver_As5 | Amount of As5+ in liver | mol | http://purl.obolibrary.org/obo/PBPKO_00497 |
| ALiver_AsM3 | Amount of MMA3 in liver | mol | http://purl.obolibrary.org/obo/PBPKO_00497 |
| ALiver_AsM5 | Amount of MMA5 in liver | mol | http://purl.obolibrary.org/obo/PBPKO_00497 |
| ALiver_AsD3 | Amount of DMA3 in liver | mol | http://purl.obolibrary.org/obo/PBPKO_00497 |
| ALiver_AsD5 | Amount od DMA5 in liver | mol | http://purl.obolibrary.org/obo/PBPKO_00497 |
| ARest_As3 | Amount of As3+ in rest of the body | mol | http://purl.obolibrary.org/obo/PBPKO_00501 |
| ARest_As5 | Amount of As5+ in rest of the body | mol | http://purl.obolibrary.org/obo/PBPKO_00501 |
| ARest_AsM5 | Amount of MMA5 in rest of the body | mol | http://purl.obolibrary.org/obo/PBPKO_00501 |
| ARest_AsD5 | Amount of DMA5 in rest of the body | mol | http://purl.obolibrary.org/obo/PBPKO_00501 |
| AArterial_As3 | Amount of As3+ in arterial blood | mol | http://purl.obolibrary.org/obo/PBPKO_00631 |
| AArterial_As5 | Amount of As5+ in arterial blood | mol | http://purl.obolibrary.org/obo/PBPKO_00631 |
| AArterial_AsM5 | Amount of MMA5 in arterial blood | mol | http://purl.obolibrary.org/obo/PBPKO_00631 |
| AVenous_As3 | Amount of As3+ in venous blood | mol | http://purl.obolibrary.org/obo/PBPKO_00632 |
| AVenous_As5 | Amount of As5+ in venous blood | mol | http://purl.obolibrary.org/obo/PBPKO_00632 |
| AVenous_AsM5 | Amount of MMA5 in venous blood | mol | http://purl.obolibrary.org/obo/PBPKO_00632 |
| AVenous_AsD5 | Amount of DMA5 in venous blood | mol | http://purl.obolibrary.org/obo/PBPKO_00632 |
| ALung_As3 | Amount of As3+ in lung | mol | http://purl.obolibrary.org/obo/PBPKO_00504 |
| ALung_As5 | Amount of As5+ in lung | mol | http://purl.obolibrary.org/obo/PBPKO_00504 |
| ALung_AsM3 | Amount of MMA3 in lung | mol | http://purl.obolibrary.org/obo/PBPKO_00504 |
| ALung_AsM5 | Amount of MMA5 in lung | mol | http://purl.obolibrary.org/obo/PBPKO_00504 |
| ALung_AsD3 | Amount of DMA3 in lung | mol | http://purl.obolibrary.org/obo/PBPKO_00504 |
| ALung_AsD5 | Amount of DMA5 in lung | mol | http://purl.obolibrary.org/obo/PBPKO_00504 |
| AUrine_AsM3 | Cumulative amount of MMA3 in urine | mol | http://purl.obolibrary.org/obo/PBPKO_00274 |
| AUrine_AsD3 | Cumulative amount of DMA3 in urine | mol | http://purl.obolibrary.org/obo/PBPKO_00274 |
Transfer equations
| id | from | to | equation |
|---|---|---|---|
| _J0 | ALumen_As3 | AGut_As3 | ALumen_As3 * Ka_As3 * Frac |
| _J1 | ALumen_As5 | AGut_As5 | ALumen_As5 * Ka_As5 * Frac |
| _J2 | AGut_As3 | ALiver_As3 | QGut * AGut_As3 / (VGut * PG_As3) |
| _J3 | AGut_As5 | ALiver_As5 | QGut * AGut_As5 / (VGut * PG_As5) |
| _J4 | AGut_AsM5 | ALiver_AsM5 | QGut * AGut_AsM5 / (VGut * PG_AsM) |
| _J5 | AGut_AsD5 | ALiver_AsD5 | QGut * AGut_AsD5 / (VGut * PG_AsD) |
| _J6 | AArterial_As3 | AGut_As3 | QGut * AArterial_As3 / VArt |
| _J7 | AArterial_As5 | AGut_As5 | QGut * AArterial_As5 / VArt |
| _J8 | AArterial_AsM5 | AGut_AsM5 | QGut * AArterial_AsM5 / VArt |
| _J9 | AArterial_AsD5 | AGut_AsD5 | QGut * AArterial_AsD5 / VArt |
| _J10 | AArterial_As3 | ALiver_As3 | QL * AArterial_As3 / VArt |
| _J11 | AArterial_As5 | ALiver_As5 | QL * AArterial_As5 / VArt |
| _J12 | ALiver_As3 | AVenous_As3 | (QL + QGut) * ALiver_As3 / (VL * PL_As3) |
| _J13 | ALiver_As5 | AVenous_As5 | (QL + QGut) * ALiver_As5 / (VL * PL_As5) |
| _J14 | AArterial_AsM5 | ALiver_AsM5 | QL * AArterial_AsM5 / VArt |
| _J15 | ALiver_AsM5 | AVenous_AsM5 | (QL + QGut) * ALiver_AsM5 / (VL * PL_AsM) |
| _J16 | AArterial_AsD5 | ALiver_AsD5 | QL * AArterial_AsD5 / VArt |
| _J17 | ALiver_AsD5 | AVenous_AsD5 | (QL + QGut) * ALiver_AsD5 / (VL * PL_AsD) |
| _J18 | ALiver_As3 | ALiver_As5 | ALiver_As3 * kox_As3 |
| _J19 | ALiver_As5 | ALiver_As3 | ALiver_As5 * kred_As5 |
| _J20 | ALiver_As3 | ALiver_AsM5 | V_As3_MMA * ALiver_As3 / VL / ((K_As3_MMA + ALiver_As3 / VL) * (1 + ALiver_AsM3 / VL / Kinh)) |
| _J21 | ALiver_As3 | ALiver_AsD5 | V_As3_DMA * ALiver_As3 / VL / (K_As3_DMA + ALiver_As3 / VL) |
| _J22 | ALiver_AsM3 | ALiver_AsM5 | kox_M3 * ALiver_AsM3 |
| _J23 | ALiver_AsM5 | ALiver_AsM3 | kred_M5 * ALiver_AsM5 |
| _J24 | ALiver_AsM3 | ALiver_AsD5 | V_M3_DMA * ALiver_AsM3 / VL / ((K_M3_DMA + ALiver_AsM3 / VL) * (1 + ALiver_As3 / VL / Kinh)) |
| _J25 | ALiver_AsD3 | ALiver_AsD5 | kox_D3 * ALiver_AsD3 |
| _J26 | ALiver_AsD5 | ALiver_AsD3 | kred_D5 * ALiver_AsD5 |
| _J27 | AArterial_As3 | ARest_As3 | QRest * AArterial_As3 / VArt |
| _J28 | AArterial_As5 | ARest_As5 | QRest * AArterial_As5 / VArt |
| _J29 | ARest_As3 | AVenous_As3 | QRest * ARest_As3 / (VRest * PRest_As3) |
| _J30 | ARest_As5 | AVenous_As5 | QRest * ARest_As5 / (VRest * PRest_As5) |
| _J31 | AArterial_AsM5 | ARest_AsM5 | QRest * AArterial_AsM5 / VArt |
| _J32 | ARest_AsM5 | AVenous_AsM5 | QRest * ARest_AsM5 / (VRest * PRest_AsM) |
| _J33 | AArterial_AsD5 | ARest_AsD5 | QRest * AArterial_AsD5 / VArt |
| _J34 | ARest_AsD5 | AVenous_AsD5 | QRest * ARest_AsD5 / (VRest * PRest_AsD) |
| _J35 | AVenous_As3 | ALung_As3 | QLung * AVenous_As3 / VVen |
| _J36 | AVenous_As5 | ALiver_As5 | QLung * AVenous_As5 / VVen |
| _J37 | ALung_As3 | ALung_As5 | kox_As3 * ALung_As3 |
| _J38 | ALung_As5 | ALung_As3 | kred_As5 * ALung_As5 |
| _J39 | ALung_As3 | AArterial_As3 | QLung * ALung_As3 / (VLung * PLung_As3) |
| _J40 | ALung_As5 | AArterial_As5 | QLung * ALung_As5 / (VLung * PLung_As5) |
| _J41 | AVenous_AsM5 | ALung_AsM5 | QLung * AVenous_AsM5 / VVen |
| _J42 | ALung_AsM5 | ALung_AsM3 | kred_M5 * ALung_AsM5 |
| _J43 | ALung_AsM3 | ALung_AsM5 | kox_M3 * ALung_AsM3 |
| _J44 | ALung_AsM5 | AArterial_AsM5 | QLung * ALung_AsM5 / (VLung * PLung_AsM) |
| _J45 | AVenous_AsD5 | ALung_AsD5 | QLung * AVenous_AsD5 / VVen |
| _J46 | ALung_AsD5 | ALung_AsD3 | kred_D5 * ALung_AsD5 |
| _J47 | ALung_AsD3 | ALung_AsD5 | kox_D3 * ALung_AsD3 |
| _J48 | ALung_AsD5 | AArterial_AsD5 | QLung * ALung_AsD5 / (VLung * PLung_AsD) |
| _J49 | ALiver_AsM3 | AUrine_AsM3 | Kurine_MMA * (ALiver_AsM3 / PL_AsM) |
| _J50 | ALiver_AsD3 | AUrine_AsD3 | Kurine_DMA * (ALiver_AsD3 / PL_AsD) |
| _J51 | ALung_AsM3 | AUrine_AsM3 | Kurine_MMA * ALung_AsM3 / PLung_AsM |
| _J52 | ALung_AsD3 | AUrine_AsD3 | Kurine_DMA * ALung_AsD3 / PLung_AsD |
ODEs
\(\frac{d[\mathtt{ALumen-As3}]}{dt} = - \mathit{ALumen_{As3}}\cdot \mathit{Ka_{As3}}\cdot \mathit{Frac}\)
\(\frac{d[\mathtt{ALumen-As5}]}{dt} = - \mathit{ALumen_{As5}}\cdot \mathit{Ka_{As5}}\cdot \mathit{Frac}\)
\(\frac{d[\mathtt{AGut-As3}]}{dt} = \mathit{ALumen_{As3}}\cdot \mathit{Ka_{As3}}\cdot \mathit{Frac} - \frac{\mathit{QGut}\cdot \mathit{AGut_{As3}}}{\mathit{VGut}\cdot \mathit{PG_{As3}}} + \frac{\mathit{QGut}\cdot \mathit{AArterial_{As3}}}{\mathit{VArt}}\)
\(\frac{d[\mathtt{AGut-As5}]}{dt} = \mathit{ALumen_{As5}}\cdot \mathit{Ka_{As5}}\cdot \mathit{Frac} - \frac{\mathit{QGut}\cdot \mathit{AGut_{As5}}}{\mathit{VGut}\cdot \mathit{PG_{As5}}} + \frac{\mathit{QGut}\cdot \mathit{AArterial_{As5}}}{\mathit{VArt}}\)
\(\frac{d[\mathtt{AGut-AsM5}]}{dt} = - \frac{\mathit{QGut}\cdot \mathit{AGut_{AsM5}}}{\mathit{VGut}\cdot \mathit{PG_{AsM}}} + \frac{\mathit{QGut}\cdot \mathit{AArterial_{AsM5}}}{\mathit{VArt}}\)
\(\frac{d[\mathtt{AGut-AsD5}]}{dt} = - \frac{\mathit{QGut}\cdot \mathit{AGut_{AsD5}}}{\mathit{VGut}\cdot \mathit{PG_{AsD}}} + \frac{\mathit{QGut}\cdot \mathit{AArterial_{AsD5}}}{\mathit{VArt}}\)
\(\frac{d[\mathtt{AArterial-AsD5}]}{dt} = - \frac{\mathit{QGut}\cdot \mathit{AArterial_{AsD5}}}{\mathit{VArt}} - \frac{\mathit{QL}\cdot \mathit{AArterial_{AsD5}}}{\mathit{VArt}} - \frac{\mathit{QRest}\cdot \mathit{AArterial_{AsD5}}}{\mathit{VArt}} + \frac{\mathit{QLung}\cdot \mathit{ALung_{AsD5}}}{\mathit{VLung}\cdot \mathit{PLung_{AsD}}}\)
\(\frac{d[\mathtt{ALiver-As3}]}{dt} = \frac{\mathit{QGut}\cdot \mathit{AGut_{As3}}}{\mathit{VGut}\cdot \mathit{PG_{As3}}} + \frac{\mathit{QL}\cdot \mathit{AArterial_{As3}}}{\mathit{VArt}} - \frac{(\mathit{QL}+\mathit{QGut})\cdot \mathit{ALiver_{As3}}}{\mathit{VL}\cdot \mathit{PL_{As3}}} - \mathit{ALiver_{As3}}\cdot \mathit{kox_{As3}} + \mathit{ALiver_{As5}}\cdot \mathit{kred_{As5}} - \frac{\frac{\mathit{V\_As3\_MMA}\cdot \mathit{ALiver_{As3}}}{\mathit{VL}}}{(\mathit{K\_As3\_MMA}+\frac{\mathit{ALiver_{As3}}}{\mathit{VL}})\cdot (1+\frac{\frac{\mathit{ALiver_{AsM3}}}{\mathit{VL}}}{\mathit{Kinh}})} - \frac{\frac{\mathit{V\_As3\_DMA}\cdot \mathit{ALiver_{As3}}}{\mathit{VL}}}{\mathit{K\_As3\_DMA}+\frac{\mathit{ALiver_{As3}}}{\mathit{VL}}}\)
\(\frac{d[\mathtt{ALiver-As5}]}{dt} = \frac{\mathit{QGut}\cdot \mathit{AGut_{As5}}}{\mathit{VGut}\cdot \mathit{PG_{As5}}} + \frac{\mathit{QL}\cdot \mathit{AArterial_{As5}}}{\mathit{VArt}} - \frac{(\mathit{QL}+\mathit{QGut})\cdot \mathit{ALiver_{As5}}}{\mathit{VL}\cdot \mathit{PL_{As5}}} + \mathit{ALiver_{As3}}\cdot \mathit{kox_{As3}} - \mathit{ALiver_{As5}}\cdot \mathit{kred_{As5}} + \frac{\mathit{QLung}\cdot \mathit{AVenous_{As5}}}{\mathit{VVen}}\)
\(\frac{d[\mathtt{ALiver-AsM3}]}{dt} = - \mathit{kox_{M3}}\cdot \mathit{ALiver_{AsM3}} + \mathit{kred_{M5}}\cdot \mathit{ALiver_{AsM5}} - \frac{\frac{\mathit{V\_M3\_DMA}\cdot \mathit{ALiver_{AsM3}}}{\mathit{VL}}}{(\mathit{K\_M3\_DMA}+\frac{\mathit{ALiver_{AsM3}}}{\mathit{VL}})\cdot (1+\frac{\frac{\mathit{ALiver_{As3}}}{\mathit{VL}}}{\mathit{Kinh}})} - \mathit{Kurine_{MMA}}\cdot \frac{\mathit{ALiver_{AsM3}}}{\mathit{PL_{AsM}}}\)
\(\frac{d[\mathtt{ALiver-AsM5}]}{dt} = \frac{\mathit{QGut}\cdot \mathit{AGut_{AsM5}}}{\mathit{VGut}\cdot \mathit{PG_{AsM}}} + \frac{\mathit{QL}\cdot \mathit{AArterial_{AsM5}}}{\mathit{VArt}} - \frac{(\mathit{QL}+\mathit{QGut})\cdot \mathit{ALiver_{AsM5}}}{\mathit{VL}\cdot \mathit{PL_{AsM}}} + \frac{\frac{\mathit{V\_As3\_MMA}\cdot \mathit{ALiver_{As3}}}{\mathit{VL}}}{(\mathit{K\_As3\_MMA}+\frac{\mathit{ALiver_{As3}}}{\mathit{VL}})\cdot (1+\frac{\frac{\mathit{ALiver_{AsM3}}}{\mathit{VL}}}{\mathit{Kinh}})} + \mathit{kox_{M3}}\cdot \mathit{ALiver_{AsM3}} - \mathit{kred_{M5}}\cdot \mathit{ALiver_{AsM5}}\)
\(\frac{d[\mathtt{ALiver-AsD3}]}{dt} = - \mathit{kox_{D3}}\cdot \mathit{ALiver_{AsD3}} + \mathit{kred_{D5}}\cdot \mathit{ALiver_{AsD5}} - \mathit{Kurine_{DMA}}\cdot \frac{\mathit{ALiver_{AsD3}}}{\mathit{PL_{AsD}}}\)
\(\frac{d[\mathtt{ALiver-AsD5}]}{dt} = \frac{\mathit{QGut}\cdot \mathit{AGut_{AsD5}}}{\mathit{VGut}\cdot \mathit{PG_{AsD}}} + \frac{\mathit{QL}\cdot \mathit{AArterial_{AsD5}}}{\mathit{VArt}} - \frac{(\mathit{QL}+\mathit{QGut})\cdot \mathit{ALiver_{AsD5}}}{\mathit{VL}\cdot \mathit{PL_{AsD}}} + \frac{\frac{\mathit{V\_As3\_DMA}\cdot \mathit{ALiver_{As3}}}{\mathit{VL}}}{\mathit{K\_As3\_DMA}+\frac{\mathit{ALiver_{As3}}}{\mathit{VL}}} + \frac{\frac{\mathit{V\_M3\_DMA}\cdot \mathit{ALiver_{AsM3}}}{\mathit{VL}}}{(\mathit{K\_M3\_DMA}+\frac{\mathit{ALiver_{AsM3}}}{\mathit{VL}})\cdot (1+\frac{\frac{\mathit{ALiver_{As3}}}{\mathit{VL}}}{\mathit{Kinh}})} + \mathit{kox_{D3}}\cdot \mathit{ALiver_{AsD3}} - \mathit{kred_{D5}}\cdot \mathit{ALiver_{AsD5}}\)
\(\frac{d[\mathtt{ARest-As3}]}{dt} = \frac{\mathit{QRest}\cdot \mathit{AArterial_{As3}}}{\mathit{VArt}} - \frac{\mathit{QRest}\cdot \mathit{ARest_{As3}}}{\mathit{VRest}\cdot \mathit{PRest_{As3}}}\)
\(\frac{d[\mathtt{ARest-As5}]}{dt} = \frac{\mathit{QRest}\cdot \mathit{AArterial_{As5}}}{\mathit{VArt}} - \frac{\mathit{QRest}\cdot \mathit{ARest_{As5}}}{\mathit{VRest}\cdot \mathit{PRest_{As5}}}\)
\(\frac{d[\mathtt{ARest-AsM5}]}{dt} = \frac{\mathit{QRest}\cdot \mathit{AArterial_{AsM5}}}{\mathit{VArt}} - \frac{\mathit{QRest}\cdot \mathit{ARest_{AsM5}}}{\mathit{VRest}\cdot \mathit{PRest_{AsM}}}\)
\(\frac{d[\mathtt{ARest-AsD5}]}{dt} = \frac{\mathit{QRest}\cdot \mathit{AArterial_{AsD5}}}{\mathit{VArt}} - \frac{\mathit{QRest}\cdot \mathit{ARest_{AsD5}}}{\mathit{VRest}\cdot \mathit{PRest_{AsD}}}\)
\(\frac{d[\mathtt{AArterial-As3}]}{dt} = - \frac{\mathit{QGut}\cdot \mathit{AArterial_{As3}}}{\mathit{VArt}} - \frac{\mathit{QL}\cdot \mathit{AArterial_{As3}}}{\mathit{VArt}} - \frac{\mathit{QRest}\cdot \mathit{AArterial_{As3}}}{\mathit{VArt}} + \frac{\mathit{QLung}\cdot \mathit{ALung_{As3}}}{\mathit{VLung}\cdot \mathit{PLung_{As3}}}\)
\(\frac{d[\mathtt{AArterial-As5}]}{dt} = - \frac{\mathit{QGut}\cdot \mathit{AArterial_{As5}}}{\mathit{VArt}} - \frac{\mathit{QL}\cdot \mathit{AArterial_{As5}}}{\mathit{VArt}} - \frac{\mathit{QRest}\cdot \mathit{AArterial_{As5}}}{\mathit{VArt}} + \frac{\mathit{QLung}\cdot \mathit{ALung_{As5}}}{\mathit{VLung}\cdot \mathit{PLung_{As5}}}\)
\(\frac{d[\mathtt{AArterial-AsM5}]}{dt} = - \frac{\mathit{QGut}\cdot \mathit{AArterial_{AsM5}}}{\mathit{VArt}} - \frac{\mathit{QL}\cdot \mathit{AArterial_{AsM5}}}{\mathit{VArt}} - \frac{\mathit{QRest}\cdot \mathit{AArterial_{AsM5}}}{\mathit{VArt}} + \frac{\mathit{QLung}\cdot \mathit{ALung_{AsM5}}}{\mathit{VLung}\cdot \mathit{PLung_{AsM}}}\)
\(\frac{d[\mathtt{AVenous-As3}]}{dt} = \frac{(\mathit{QL}+\mathit{QGut})\cdot \mathit{ALiver_{As3}}}{\mathit{VL}\cdot \mathit{PL_{As3}}} + \frac{\mathit{QRest}\cdot \mathit{ARest_{As3}}}{\mathit{VRest}\cdot \mathit{PRest_{As3}}} - \frac{\mathit{QLung}\cdot \mathit{AVenous_{As3}}}{\mathit{VVen}}\)
\(\frac{d[\mathtt{AVenous-As5}]}{dt} = \frac{(\mathit{QL}+\mathit{QGut})\cdot \mathit{ALiver_{As5}}}{\mathit{VL}\cdot \mathit{PL_{As5}}} + \frac{\mathit{QRest}\cdot \mathit{ARest_{As5}}}{\mathit{VRest}\cdot \mathit{PRest_{As5}}} - \frac{\mathit{QLung}\cdot \mathit{AVenous_{As5}}}{\mathit{VVen}}\)
\(\frac{d[\mathtt{AVenous-AsM5}]}{dt} = \frac{(\mathit{QL}+\mathit{QGut})\cdot \mathit{ALiver_{AsM5}}}{\mathit{VL}\cdot \mathit{PL_{AsM}}} + \frac{\mathit{QRest}\cdot \mathit{ARest_{AsM5}}}{\mathit{VRest}\cdot \mathit{PRest_{AsM}}} - \frac{\mathit{QLung}\cdot \mathit{AVenous_{AsM5}}}{\mathit{VVen}}\)
\(\frac{d[\mathtt{AVenous-AsD5}]}{dt} = \frac{(\mathit{QL}+\mathit{QGut})\cdot \mathit{ALiver_{AsD5}}}{\mathit{VL}\cdot \mathit{PL_{AsD}}} + \frac{\mathit{QRest}\cdot \mathit{ARest_{AsD5}}}{\mathit{VRest}\cdot \mathit{PRest_{AsD}}} - \frac{\mathit{QLung}\cdot \mathit{AVenous_{AsD5}}}{\mathit{VVen}}\)
\(\frac{d[\mathtt{ALung-As3}]}{dt} = \frac{\mathit{QLung}\cdot \mathit{AVenous_{As3}}}{\mathit{VVen}} - \mathit{kox_{As3}}\cdot \mathit{ALung_{As3}} + \mathit{kred_{As5}}\cdot \mathit{ALung_{As5}} - \frac{\mathit{QLung}\cdot \mathit{ALung_{As3}}}{\mathit{VLung}\cdot \mathit{PLung_{As3}}}\)
\(\frac{d[\mathtt{ALung-As5}]}{dt} = \mathit{kox_{As3}}\cdot \mathit{ALung_{As3}} - \mathit{kred_{As5}}\cdot \mathit{ALung_{As5}} - \frac{\mathit{QLung}\cdot \mathit{ALung_{As5}}}{\mathit{VLung}\cdot \mathit{PLung_{As5}}}\)
\(\frac{d[\mathtt{ALung-AsM3}]}{dt} = \mathit{kred_{M5}}\cdot \mathit{ALung_{AsM5}} - \mathit{kox_{M3}}\cdot \mathit{ALung_{AsM3}} - \frac{\mathit{Kurine_{MMA}}\cdot \mathit{ALung_{AsM3}}}{\mathit{PLung_{AsM}}}\)
\(\frac{d[\mathtt{ALung-AsM5}]}{dt} = \frac{\mathit{QLung}\cdot \mathit{AVenous_{AsM5}}}{\mathit{VVen}} - \mathit{kred_{M5}}\cdot \mathit{ALung_{AsM5}} + \mathit{kox_{M3}}\cdot \mathit{ALung_{AsM3}} - \frac{\mathit{QLung}\cdot \mathit{ALung_{AsM5}}}{\mathit{VLung}\cdot \mathit{PLung_{AsM}}}\)
\(\frac{d[\mathtt{ALung-AsD3}]}{dt} = \mathit{kred_{D5}}\cdot \mathit{ALung_{AsD5}} - \mathit{kox_{D3}}\cdot \mathit{ALung_{AsD3}} - \frac{\mathit{Kurine_{DMA}}\cdot \mathit{ALung_{AsD3}}}{\mathit{PLung_{AsD}}}\)
\(\frac{d[\mathtt{ALung-AsD5}]}{dt} = \frac{\mathit{QLung}\cdot \mathit{AVenous_{AsD5}}}{\mathit{VVen}} - \mathit{kred_{D5}}\cdot \mathit{ALung_{AsD5}} + \mathit{kox_{D3}}\cdot \mathit{ALung_{AsD3}} - \frac{\mathit{QLung}\cdot \mathit{ALung_{AsD5}}}{\mathit{VLung}\cdot \mathit{PLung_{AsD}}}\)
\(\frac{d[\mathtt{AUrine-AsM3}]}{dt} = \mathit{Kurine_{MMA}}\cdot \frac{\mathit{ALiver_{AsM3}}}{\mathit{PL_{AsM}}} + \frac{\mathit{Kurine_{MMA}}\cdot \mathit{ALung_{AsM3}}}{\mathit{PLung_{AsM}}}\)
\(\frac{d[\mathtt{AUrine-AsD3}]}{dt} = \mathit{Kurine_{DMA}}\cdot \frac{\mathit{ALiver_{AsD3}}}{\mathit{PL_{AsD}}} + \frac{\mathit{Kurine_{DMA}}\cdot \mathit{ALung_{AsD3}}}{\mathit{PLung_{AsD}}}\)
Assignment rules
| variable | assignment |
|---|---|
| VRest | BW - 0.76 - VGut - VL - VLung - VB |
| CLumen_As3 | ALumen_As3 / Lumen |
| CLumen_As5 | ALumen_As5 / Lumen |
| CGut_As3 | AGut_As3 / Gut |
| CGut_As5 | AGut_As5 / Gut |
| CGut_AsM5 | AGut_AsM5 / Gut |
| CGut_AsD5 | AGut_AsD5 / Gut |
| CLiver_As3 | ALiver_As3 / Liver |
| CLiver_As5 | ALiver_As5 / Liver |
| CLiver_AsM3 | ALiver_AsM3 / Liver |
| CLiver_AsM5 | ALiver_AsM5 / Liver |
| CLiver_AsD3 | ALiver_AsD3 / Liver |
| CLiver_AsD5 | ALiver_AsD5 / Liver |
| CRest_As3 | ARest_As3 / Rest |
| CRest_As5 | ARest_As5 / Rest |
| CRest_AsM5 | ARest_AsM5 / Rest |
| CRest_AsD5 | ARest_AsD5 / Rest |
| CArterial_As3 | AArterial_As3 / Arterial |
| CArterial_As5 | AArterial_As5 / Arterial |
| CArterial_AsM5 | AArterial_AsM5 / Arterial |
| CArterial_AsD5 | AArterial_AsD5 / Arterial |
| CVenous_As3 | AVenous_As3 / Venous |
| CVenous_As5 | AVenous_As5 / Venous |
| CVenous_AsM5 | AVenous_AsM5 / Venous |
| CVenous_AsD5 | AVenous_AsD5 / Venous |
| CLung_As3 | ALung_As3 / Lung |
| CLung_As5 | ALung_As5 / Lung |
| CLung_AsM3 | ALung_AsM3 / Lung |
| CLung_AsM5 | ALung_AsM5 / Lung |
| CLung_AsD3 | ALung_AsD3 / Lung |
| CLung_AsD5 | ALung_AsD5 / Lung |
| Ka_As3 | 0.004 * 60 |
| Ka_As5 | 0.003 * 60 |
| QGut | 1 * 60 |
| VArt | VB / 2 |
| QL | 0.31 * 60 |
| kred_M5 | 0.008 * 60 |
| V_M3_DMA | 6.6e-7 * 60 |
| kred_D5 | 0.004 * 60 |
| QRest | QLung - QGut - QL |
| QLung | 5.2 * 60 |
| VVen | VB / 2 |
| Kurine_MMA | 0.3 * 60 |
| Kurine_DMA | 0.13 * 60 |
| Kurine_As | 0.07 * 60 |
Initial assignments
| variable | assignment |
|---|---|
| Gut | VGut |
| Liver | VL |
| Lung | VLung |
| Arterial | VArt |
| Venous | VVen |
| Rest | VRest |
| kred_As5 | 0.003 * 60 |
| V_As3_MMA | 5.3e-7 * 60 |
| V_As3_DMA | 2e-6 * 60 |
Parameters
| id | name | unit | model qualifier |
|---|---|---|---|
| VRest | Volume of rest of the body | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00105 |
| BW | Bodyweight | kg | http://purl.obolibrary.org/obo/PBPKO_00008 |
| VGut | Volume of gut | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00524 |
| VL | Volume of liver | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00077 |
| VLung | Volume of lung | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00097 |
| VB | Volume of blood | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00108 |
| CLumen_As3 | Concentration of As3+ in lumen | mol/L | not specified |
| CLumen_As5 | Concentration of As5+ in lumen | mol/L | not specified |
| CGut_As3 | Concentration of As3+ in gut | mol/L | http://purl.obolibrary.org/obo/PBPKO_00538 |
| CGut_As5 | Concentration of As5+ in gut | mol/L | http://purl.obolibrary.org/obo/PBPKO_00538 |
| CGut_AsM5 | Concentration of MMA5 in gut | mol/L | http://purl.obolibrary.org/obo/PBPKO_00538 |
| CGut_AsD5 | Concentration of DMA5 in gut | mol/L | http://purl.obolibrary.org/obo/PBPKO_00538 |
| CLiver_As3 | Concentration of As3+ in liver | mol/L | http://purl.obolibrary.org/obo/PBPKO_00539 |
| CLiver_As5 | Concentration of As5+ in liver | mol/L | http://purl.obolibrary.org/obo/PBPKO_00539 |
| CLiver_AsM3 | Concentration of MMA3 in liver | mol/L | http://purl.obolibrary.org/obo/PBPKO_00539 |
| CLiver_AsM5 | Concentration of MMA5 in liver | mol/L | http://purl.obolibrary.org/obo/PBPKO_00539 |
| CLiver_AsD3 | Concentration of DMA3 in liver | mol/L | http://purl.obolibrary.org/obo/PBPKO_00539 |
| CLiver_AsD5 | Concentration of DMA5 in liver | mol/L | http://purl.obolibrary.org/obo/PBPKO_00539 |
| CRest_As3 | Concentration of As3+ in the rest of the body | mol/L | http://purl.obolibrary.org/obo/PBPKO_00548 |
| CRest_As5 | Concentration of As5+ in the rest of the body | mol/L | http://purl.obolibrary.org/obo/PBPKO_00548 |
| CRest_AsM5 | Concentration of MMA5 in the rest of the body | mol/L | http://purl.obolibrary.org/obo/PBPKO_00548 |
| CRest_AsD5 | Concentration of DMA5 in the rest of the body | mol/L | http://purl.obolibrary.org/obo/PBPKO_00548 |
| CArterial_As3 | Concentration of As3+ in arterial blood | mol/L | not specified |
| CArterial_As5 | Concentration of As5+ in arterial blood | mol/L | not specified |
| CArterial_AsM5 | Concentration of MMA5 in arterial blood | mol/L | not specified |
| CArterial_AsD5 | Concentration of DMA5 in arterial blood | mol/L | not specified |
| CVenous_As3 | Concentration of As3+ in venous blood | mol/L | not specified |
| CVenous_As5 | Concentration of As5+ in venous blood | mol/L | not specified |
| CVenous_AsM5 | Concentration of MMA5 in venous blood | mol/L | not specified |
| CVenous_AsD5 | Concentration of DMA5 in venous blood | mol/L | not specified |
| CLung_As3 | Concentration of As3+ in lung | mol/L | http://purl.obolibrary.org/obo/PBPKO_00543 |
| CLung_As5 | Concentration of As5+ in lung | mol/L | http://purl.obolibrary.org/obo/PBPKO_00543 |
| CLung_AsM3 | Concentration of MMA3 in lung | mol/L | http://purl.obolibrary.org/obo/PBPKO_00543 |
| CLung_AsM5 | Concentration of MMA5 in lung | mol/L | http://purl.obolibrary.org/obo/PBPKO_00543 |
| CLung_AsD3 | Concentration of DMA3 in lung | mol/L | http://purl.obolibrary.org/obo/PBPKO_00543 |
| CLung_AsD5 | Concentration of DMA5 in lung | mol/L | http://purl.obolibrary.org/obo/PBPKO_00543 |
| Ka_As3 | Oral absorption of As3+ | /h | http://purl.obolibrary.org/obo/PBPKO_00141 |
| Frac | Fraction of absorption | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00263 |
| Ka_As5 | Oral absorption of As5+ | /h | http://purl.obolibrary.org/obo/PBPKO_00141 |
| QGut | Blood-flow to gut | L/h | http://purl.obolibrary.org/obo/PBPKO_00531 |
| PG_As3 | Partition coefficient Gut / Plasma of As3+ | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00572 |
| PG_As5 | Partition coefficient Gut / Plasma of As5+ | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00572 |
| PG_AsM | Partition coefficient Gut / Plasma of MMA | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00572 |
| PG_AsD | Partition coefficient Gut / Plasma of DMA | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00572 |
| VArt | Volume of arterial blood | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00121 |
| QL | Blood-flow to liver | L/h | http://purl.obolibrary.org/obo/PBPKO_00024 |
| PL_As3 | Partition coefficient Liver / Plasma of As3+ | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00577 |
| PL_As5 | Partition coefficient Liver / Plasma of As5+ | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00577 |
| PL_AsM | Partition coefficient Liver / Plasma of MMA | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00577 |
| PL_AsD | Partition coefficient Liver / Plasma of DMA | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00577 |
| kox_As3 | Oxydation factor of As3+ | /h | not specified |
| kred_As5 | Reduction factor of As5+ | /h | not specified |
| V_As3_MMA | Maximum metabolism from As3+ to MMA | mol/h | http://purl.obolibrary.org/obo/PBPKO_00613 |
| K_As3_MMA | Michaelis-Menten binding constant from As3+ to MMA | mol/L | http://biomodels.net/SBO/SBO_0000027 |
| Kinh | Non-competitive inhibition constant | mol/L | http://purl.obolibrary.org/obo/PBPKO_00222 |
| V_As3_DMA | Maximum metabolism from As3+ to DMA | mol/h | http://purl.obolibrary.org/obo/PBPKO_00613 |
| K_As3_DMA | Michaelis-Menten binding constant from As3+ to DMA | mol/L | http://biomodels.net/SBO/SBO_0000027 |
| kox_M3 | Oxydation factor of MMA3 to MM5 | dimensionless | not specified |
| kred_M5 | Reduction factor of MMA5 to MM3 | /h | not specified |
| V_M3_DMA | Maximum metabolism from MMA3 to DMA | mol/h | http://purl.obolibrary.org/obo/PBPKO_00613 |
| K_M3_DMA | Michaelis-Menten binding from MMA3 to DMA | mol/L | http://biomodels.net/SBO/SBO_0000027 |
| kox_D3 | Oxydation factor of DMA3 to DMA5 | dimensionless | not specified |
| kred_D5 | Reduction factor of DMA5 to DMA3 | /h | not specified |
| QRest | Blood-flow to the rest of the body | L/h | http://purl.obolibrary.org/obo/PBPKO_00050 |
| PRest_As3 | Partition coefficient Restbody / Plasma of As3+ | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00585 |
| PRest_As5 | Partition coefficient Restbody / Plasma of As5+ | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00585 |
| PRest_AsM | Partition coefficient Restbody / Plasma of MMA | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00585 |
| PRest_AsD | Partition coefficient Restbody / Plasma of DMA | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00585 |
| QLung | Blood-flow to lung - Cardiac output | L/h | http://purl.obolibrary.org/obo/PBPKO_00013 |
| VVen | Volume of venous blood | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00122 |
| PLung_As3 | Partition coefficient Lung / Plasma of As3+ | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00579 |
| PLung_As5 | Partition coefficient Lung / Plasma of As5+ | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00579 |
| PLung_AsM | Partition coefficient Lung / Plasma of MMA | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00579 |
| PLung_AsD | Partition coefficient Lung / Plasma of DMA | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00579 |
| Kurine_MMA | Urinal excretion factor of MMA | /h | http://purl.obolibrary.org/obo/PBPKO_00534 |
| Kurine_DMA | Urinal excretion factor of DMA | /h | http://purl.obolibrary.org/obo/PBPKO_00534 |
| Age | not specified | y | http://purl.obolibrary.org/obo/PBPKO_00521 |
| Kurine_As | Urinal excretion factor of iAs | /h | http://purl.obolibrary.org/obo/PBPKO_00534 |