A. Proportion of ligand-receptor tetrameric complexes at equimolar receptor at physiological conditions. The heterodimer-heterotetramer is only the fourth most abundant tetrameric complex. B. Proportion of ligand-receptor tetrameric complexes in a simulation with no homodimer ligand. Heterodimer-heterotetramer production is still not kinetically favored. C. Visualization of the prevalence of heterodimer-heterotetramer compared to other ligand-receptor tetramers in 3,375 points of a 84,375 point screen. The red region represents parameter space in which the heterodimer-heterotetramer is the most prevalent species (3.84% of this sample. D. The portion of the parameter space in which each ligand-receptor tetrameric complex is the most abundant. E. The portion of the parameter space in which the heterodimer-heterotetramer is the most abundant ligand-receptor tetrameric complex (5.66%) and the predominant tetrameric complex (0.0%).

A. Shows the distributions of the complexes as a function of ligand concentration in a system with excess Acvr1. The level of BmpR1 receptor complexes exceeds the level of Bmp2/7-Acvr1-BmpR1-(Type II)₂ except for a narrow band from ~.4nM to 1 nM. B. The weakest possible Acvr1 –Bmp2/7 binding affinity in which Bmp2/7-Acvr1-BmpR1-(Type II)2 is the most prevalent receptor tetramer at a ligand concentration of 0.1 nM. Recall that higher K_D (nM) indicates weaker binding affinity. C-D. Same as A and B with higher amounts of Type II receptor in the model. E. In the Bmp2/7-only system with 10nM type II receptor, 9-fold excess Acvr1 leads to greater heterodimer-heterotetramer complex formation over a wide range of ligand concentration.

A-D. Bmp2 = Bmp7 = Bmp2/7 = 0.3 nM; (A-C) Type II = 10 nM; (D) Acvr1 = 10 nM. (A) Bmp2/7-heteromeric receptor complex formation (y-axis) exhibits low sensitivity to Acvr1 levels (x-axis), but B. high sensitivity to increasing BmpR1 levels (x-axis). C-D. Levels of BMP2/7-BmpR1-BmpR1 signaling complexes (y-axis) versus increasing levels of BmpR1 for different levels of Acvr1 C. or Type II D. receptors. E-F. Dynamic range, i.e. ligand concentrations needed to produce a single (red point) ligand-receptor complex and maximal ligand receptor complex (black point) for each of the nine plausible tetrameric ligand-receptor oligomers. Oligomers represented by a single point are unable to produce a single tetrameric ligand receptor complex at these ligand and receptor concentrations. The red point signifies, for each tetramer, the higher of a single molecule of ligand, or G. Shows a 343 point parameter screen measuring dynamic range under different receptor concentrations. The heterodimer-heterotetramer has the largest dynamic range in 63.56% of the tested conditions.

A. Cartoon depiction of ‘overhead view’ of BMP ligand-dimer receptor-tetramer complexes. BMP signaling occurs through an oligomeric signaling complex which necessarily consists of a ligand dimer (red/gold plus) bound to a receptor tetramer. The receptor tetramer requires two Type II receptors (green square) and two Type I receptors (BmpR1 in purple and/or Acvr1 in cyan). The heterodimer-heterotetramer is underlined in red. B. Network of BMP ligand-receptor interactions. Oligomeric signaling complexes are formed through reversible reactions (double-sided arrows). Tetrameric complexes are underlined in the figure above. The heterodimer-heterotetramer, Bmp2/7-Acvr1-BmpR1-(Type II)₂ is double underlined.