Signal Processing in the TGF-β Superfamily Ligand-Receptor Network
Figure 5
Typical Time Courses of the Number of Active Receptor Complexes upon Addition of TGF-β
The typical response to sustained changes in TGF-β concentration shows partial adaptation after reaching a maximum of activity. Different values of the parameters of the model lead to this characteristic behavior. In all panels, the TGF-β concentration is increased at time 0 to saturating values and kept constant afterward, as in inset in (A).
(A) Behavior of the model for typical trafficking rates: internalization, ki = (3 min)−1; recycling, kr = (30 min)−1; constitutive degradation, kcd = (36 min)−1; ligand-induced degradation klid = (4 min)−1; efficiency of recycling of active receptors, α = 1. Note that the trafficking rate constants are given as the inverse of the corresponding characteristic times. The production of receptors is chosen to be pRI = 8 min−1 and pRII = 4 min−1, which leads to ~103 receptors per cell under stationary conditions in the absence of ligand. The units of ligand concentration are chosen so that the association rate constant is the unit, ka = 1. For these units, EC50 ≈ 2 × 10−4. At time 0, the ligand concentration changes from 3×10−5 to 0.01. The signal peaks at ~60 min.
(B) Comparison of the model time course (upper lane) with an experimental time course of nuclear phosphorylated Smad2 (P-Smad) as reported by Inman et al. (bottom lane) [16]. The model results from (A) are shown at the experimental time points and color-coded to ease comparison.
(C) Behavior of the model with the same parameter values as in (A), with the exception of the rate constants for internalization and recycling that have been decreased to ki = (10 min)−1 and kr = (100 min)−1. The signal peaks at ~180 min.
(D) Behavior of the model with the same parameter values as in (A), with the exception of the rate constants for internalization and recycling that have been increased to ki = (1 min)−1 and kr = (10 min)−1. The signal peaks at ~20 min.
(E) Behavior of the model with the same parameter values as in (A), with the exception of the rate constant for ligand-induced degradation that has been decreased to klid = 0 and the efficiency of recycling of active receptors that has been decreased to α = 0.5. This implies that ligand-receptor complexes are not degraded via the caveolae pathway. In contrast, 50% of the active ligand-receptors that come back to the plasma membrane after they have signaled are degraded.
(F) Behavior of the model with the same parameter values as in (A), with the exception of the efficiency of recycling of active receptors that has been decreased to α = 0.5. These parameters account for both types (caveola-dependent and recycling-dependent) of ligand-induced degradation.