Table 1.
Model parameters and initial conditions
| Parameter | Value | Source | Meaning of the parameter |
| kins | 10-3 nM-1 s-1 | [36] | insulin binding to the receptor |
| kins1d | 4·10-4 s-1 | [36] | insulin dissociation from the receptor (I1, PM) |
| kins2d | 4·10-2 s-1 | [36] | insulin dissociation from the receptor (I2, PM) |
| kins1den | 1.925·10-3 s-1 | [49] | insulin dissociation from the receptor (I1, EN) |
| kins2den | 3.85·10-3 s-1 | [50] | insulin dissociation from the receptor (I2, EN) |
| kyd | 3.85·10-3 s-1 | [51] | receptor dephosphorylation (PM) |
| kyden | 7.22·10-3 s-1 | [52] | receptor dephosphorylation (EN) |
| kyp | 0.0231 s-1 | [52] | autophosphorylation of the receptor (I1 and I2) |
| intk1 | 5.5·10-4 s-1 | [34] | internalization of phosphorylated receptors |
| intk2 | 2·10-4 s-1 | [34] | internalization of unphosphorylated receptors |
| reck1 | 1.533·10-3 s-1 | [34] | recycling of receptors without insulin |
| k1ub | 0.35 s-1 | [46] | nonspecific insulin binding in the liver |
| k2ub | 0.2 s-1 | [46] | dissociation of nonspecifically bound insulin |
| pansec | 0.0016976 nM·s-1 | calc. | pancreatic insulin secretion |
| K pan | 0.5 nM | ass. | concentration of half-maximal insulin secretion |
| mliver | 0.05·mbody | [46] | mass of the liver |
| vp | 0.03375·10-3 l·g-1·mbody | [54] | plasma volume |
| ρliver | 1.051·103 g·l-1 | [53] | density of the liver |
| vhep | (mliver/ρliver)·0.78 | [45] | total hepatocyte volume |
| vd | 0.272·10-3 l·g-1·vhep·ρliver | [46] | volume of the space of Disse |
| mkidney | 2·0.85 g·mbody/(230 g) | [55] | mass of the kidney |
| K kidney | 0.0225·10-3 l·(s·g)-1·mkidney | [47] | clearance of the kidney |
Note that mbody (body weight in g), tin (injection time in s), nin and n*,in (amounts of injected unlabeled and labeled insulin in nmol) are also model parameters. We do not give values for them in this table as they depend on the analyzed scenario. Note that the model can be used for rats of arbitrary body weights as well as for different injection times and amounts of injected labeled and unlabeled insulin. Initial conditions are: Ins = 0.07, Ins* = 0, R = 31.619, IR = 0.430007, I2R = 0.000696311, Rp = 0.227528, IRp = 2.07275, I2Rp = 0.00363012, Ren = 4.88528, IRen = 0.145537, I2Ren = 0.000121295, Rpen = 0.122602, IRpen = 0.492464, I2Rpen = 0.000433466, Insub = 1.29948·10-6·mbody, Ins*,ub = 0. The unit of Insub and Ins*,ub is nmol, the unit of all other state variables is nM. ass.: assumption, calc.: calculation (see Additional file 4), EN: in endosomes, PM: at the plasma membrane, I1: one insulin molecule bound to the receptor, I2: two insulin molecules bound to the receptor.