Table 1.
Model initial conditions and parameters
| Species/constants | Value | Rationale |
| R for PAR2 | 5,000 µm−2 | Receptor density from this paper (Fig. 5) with overexpression. If the receptors were able to dissolve in cytosol, it would be 5 µM. |
| G (G protein) | 40 µm−2 | Number of free G protein at the PM |
| PLC | 10 µm−2 | Number of free PLC at the PM |
| PI | 140,000 µm−2 | Number of free PI at the PM |
| PIP | 3,600 µm−2 | Number free PIP at the PM |
| PIP2 | 5,000 µm−2 | Number of free PIP2 at the PM |
| IP3 | 0.015 µM | IP3 at cytosol before receptor activation: Steady-state balance from PLC and IP3ase |
| DAG at PM | 23 µm−2 | Number of DAG at the PM before receptor activation |
| Arrestin (cytosol) = Arrestin1 + Arrestin2 | 15 µM | β-Arrestin 1 (Arrestin1) and β-arrestin 2 (Arrestin2) have 7.5 µM, respectively, to leave proper amount β-arrestins in the cytosol after their binding to the PAR2 at the PM. We assumed that β-arrestin 1 has higher affinity to PAR2 compared with the β-arrestin 2. |
| PKC_cyto (PKC Cytosol) | 1 µM | The concentration was chosen to make reasonable fitting of DAG-bound PKC |
| GRK | 600 | Fixed value to similar to the peak value of PKC_DAG |
| Weighting_factor_PKC_DAG or Weighting_factor_GRK | 0.5 | Active PKC (PKC_DAG) gives the same contribution to phosphorylation of ligand bound receptor as GRK |
| kf_PKC_DAG | 0.02 µM−1*s−1 | Forward rate constant for binding of PKC and DAG |
| Kr_PKC_DAG | 0.06 s−1 | Reverse rate constant for dissociation of DAG from PKC, giving Kd = 3 µM |
| Ca2+ (cytosol) | 0.13 µM | Typical intracellular Ca2+ level is 0.1–0.2 µM |
| fold PIP2 | 3 | Making the size of the of the total PIP2 (bound plus free) three times the free pool |
| k_4K (basal) | 0.00078 s−1 | Fold PIP2 * 0.00026 s−1 |
| k_5K (basal) | 0.06 s−1 | Fold PIP2 * 0.02 s−1 |
| k_4K (stimulated) | 6* k_4K (basal) | To fit the recovery kinetics of PIP2 probe in Fig. 2 A |
| k_5K (stimulated) | 3* k_5K (basal) | To fit the recovery kinetics of PIP2 probe in Fig. 2 A and to explain the PIP2 hump, we added β-arrestin–dependent PIP5K activity only in Fig. 9 C |
| k_4P (basal) | 0.03 s−1 | 0.03 s−1 * k4r_basal (k4r_basal = 1) |
| k_5P (basal) | 0.014 s−1 | 0.014 s−1 * k5r_basal (k5r_basal = 1) |
| k_4P (stimulated) | 0.19 s−1 | 0.03 s−1 * k4r_stim (k4r_stim = 6.25) |
| k_5P (stimulated) | 0.042 s−1 | 0.014 s−1 * k5r_stim (k5r_stim = 3) |
| kf_RL | 0.75 µm2*molecules−1*s−1 | Rate constant for phosphorylation of ligand-bound receptor-reaction 1 |
| kr_RLP | 0.0125 s−1 | Rate constant for dephosphorylation of ligand-bound phosphorylated receptor-reaction 1 |
| kf_R (basal) | 0.0001 s−1 | Basal phosphorylation rate constant of receptor-reaction 3 |
| kr_RP (basal) | 2 s−1 | Basal dephosphorylation rate constant of phosphorylated receptor-reaction 3 |
| kf_R (stimulated) | 10 s−1 | Stimulated phosphorylation rate constant of receptor |
| kr_RP (stimulated) | 4 s−1 | Stimulated dephosphorylation rate constant of receptor. We assumed that rate of dephosphorylation of RP doubles after ligand treatment-reaction 3 |
| kf_L2 | 0.09333 µM−1 * s−1 | Binding rate constant of ligand to RP, depending on the dissociation constant (K_L2) and dissociation rate constant (kr_L2) |
| kr_L2 | 5.6 s−1 | Dissociation rate constant of ligand from RP, assuming that it has same dissociation rate constant compared to the native receptor (R) |
| K_L2 | 60 µM | Dissociation constant of ligand bound to RP, which has slightly lower affinity compared with native receptor (R) based on the supplemental data (Fig. S5) |
| kf_RLP | 0.003 s−1 | Rate constant of β-arrestin 2 binding to phosphorylated ligand-bound receptor to make best fitting compared with Figs. 4 F and 8 F. For β-arrestin 1, we used 0.006 s−1-reaction 2 |
| kr_RLPA1 or kr_RLPA2 | 10−6 s−1 | Rate constant of β-arrestin dissociation from phosphorylated ligand-bound receptor. Same for Arrestins 1 and 2-reaction 2 |
The rate constants for the phosphorylation of receptors were chosen to fit experimental data. In our model, we did not consider spatial information, e.g., diffusion of molecules in space. The rate constant for the PI4K (k_4K during stimulation) = fold PIP2 * (k_4K_rest + (stim_4K − k_4K_rest + k_4K_basal) * scale_4K * (1 − exp(−t/tau_on))). Where, tau_on = 1 s, fold PIP2 = 3, scale_4K = 0.75, k_4K_rest = 0.00026 s−1, k_4K_basal = 0.0002353 s−1, and stim_4K = 0.00117 s−1. The rate constant for PIP5K (k_5K during stimulation) = fold PIP2 * (k_5K_rest + (stim_5K − k_5K_rest + k_5K_basal) * scale_5K * (1 − exp(−t/tau_on))), where tau_on = 1 s, fold PIP2 = 3, scale_5K = 1, k_5K_rest = 0.02 s−1, k_5K_basal = 0.0181 s−1, stim_5K = 5.75 * [unspecified contribution (0.5) + β-arrestin–dependent contribution (0.5) * exp(−t/tau_off)], tau_off = 40 * [β-arrestin]4, and β-arrestin = β-arrestin 1 + β-arrestin 2.