Figure 1.
The Cubic Ternary Complex Model and the Cubic Ternary Complex Activation Model
The cTCM (black) is a thermodynamically complete equilibrium representation of ligand (L), receptor (R), and G protein (G) interactions [11]. Association and dissociation of L and R is represented here from top to bottom, R and G interactions from front to back, and the interconversion of inactive and active R states from left to right of the cube. Based on the cTCM, the cTCAM (black and red) incorporates the dynamics of activation and recycling of G protein (dashed lines) into a kinetic model of LRG interactions [22]. A brief summary of model parameters is found in Table 1. Description of model parameters, assumptions, and equations are given in Text S1.
Table 1.
The 16 Independent Parameters of the cTCAM
Figure 2.
Time Course of Representative Model Outputs
Parameter values are sampled using LHS, and the differential equations describing the cTCAM are solved according to the equations in Text S1. G protein activation as quantified by GαGTP is tracked over time (see Equation S.27 in Text S1).
(A) Values of GαGTP (number/cell) for eight parameter sets from LHS sampling of the ranges in Table 1 are plotted over the course of the simulation.
(B) Percent change in the value of GαGTP relative to basal values (%OverBasal) was calculated and tracked over time according to Equation 1. [L] = 0.1 μM.
Table 2.
Parameters Significantly Correlated with G Protein Activation
Figure 3.
Example of the Time Course of PRCC Values
Time course of PRCC values for LR association rate constant (k3) and LR equilibrium association constant (Ka) correlated to %OverBasal (as given by Equation 1) when [L] = 1 nM.
Figure 4.
The Effect of Changing Receptor and G Protein Expression on the Activation of G Protein
Dose response curves measuring the percent accumulation of GαGTP (%Accum) were calculated according to Equation 2 as described in Methods.
(A) Total G protein (Gtotal) is varied from 1,000,000/cell to 3,000 per cell, and Rtotal = 5,000/cell.
(B) Total receptor (Rtotal) is varied from 30,000 to 1,000 per cell, and Gtotal = 10,000/cell. Parameter values: k1 = 1 s−1, k3 = 1 × 107 M−1s−1, k11 =1 × 10−4 (number/cell)−1s−1, kGact = 5 s−1, kGTP = 1 s−1, kG = 1 × 10−4 (number/cell)−1s−1, Ka = 1 × 10−8 M−1, Kg = 1 × 10−4 (number/cell)−1, Kact = 0.01, α = 5, β = 5, δ = 0.5, γ = 0.1, η = 0.1.
Figure 5.
The Effect of the Ratio of Receptor to G Protein on G Protein Activation
Rtotal was set at 5,000/cell and Gtotal varied (dashed line). As G protein expression increases, the response changes from negative to positive agonism. Gtotal was set at 100,000 per cell and Rtotal varied (solid line). As receptor expression increases, the response changes from negative to positive agonism.
Figure 6.
Protean Agonism in the α2A-Adrenergic System
(A) Effect of levomed on cAMP production. Note that the y-axis in this plot is inverted from the usual to show positive agonists to have a positive slope and inverse agonists to have a negative slope. Levomed acts as an inverse agonist in HEL 92.1.7 cells (•, with curve fit). Data taken from Jansson et al. (1998), Figure 4. Levomed acts as a positive agonist in PC12 cells (line only). Data reconstructed from EC50 and max percent inhibition reported in Jansson et al. (1994), Table 1.
(B–D) Simulations of protean agonism of levomed at the α2A-adrenergic receptor. Small changes in parameter values can cause the response to switch from positive to negative.
(B) 3.3-Fold variation in G protein expression, β = 10.
(C) A 4-fold variation in the G protein activation rate constant kGact, Gtotal = 100,000.
(D) The equilibrium ratio of active to inactive receptors is varied 5-fold, Gtotal = 10,000, kGact = 5 s−1. Parameter values are equal to those listed in Figure 5 except when otherwise noted. Rtotal = 3,500 number/cell. Simulated dose response curves (B–D) measuring the percent accumulation of GαGTP (%Accum) were calculated according to Equation 2 as described in Methods.
Figure 7.
Protean Agonism in the β2-Adrenergic Receptor System
(A) Dichloroisoproterenol (DCI) effect on adenylyl cyclase activity in Sf9 cells. DCI was found to be both a partial agonist (•) and an inverse agonist (○) in this study. Data replotted from Chidiac et al. (1996).
(B) Simulations of DCI activation of GαGTP. Protean agonism properties of DCI caused by 5-fold difference in G protein concentration.
(C) After desensitizing treatment with isopreterenol, DCI was found to inhibit adenylyl cyclase activity in membranes where previously positive agonism was seen (•). This treatment further decreased activity of adenylyl cyclase in membranes where inverse agonism was observed (○). Data replotted from Chidiac et al. (1996).
(D) Desensitization treatment by isopreterenol is simulated by decreasing G protein (Gtotal) by 50%. Parameter values are equal to those listed in Figure 4 except when otherwise noted. Rtotal = 4,000/cell, α = 0.5, δ = 5. Simulated dose response curves (B,D) measuring the percent accumulation of GαGTP (%Accum) were calculated according to Equation 2 as described in Methods.