Monotonicity of interleukin-1 receptor-ligand binding with respect to antagonist in the presence of decoy receptor

We consider the interaction between interleukin-1 IL-1, its receptor IL-1RI, the receptor antagonist IL-1Ra and a decoy receptor (or trap) that binds both with the ligand and the antagonist. We study how the interaction between IL-1Ra and the decoy receptor influences the effect of either reagent on reducing the equilibrium concentration of the receptor-ligand complex. We obtain that, given a certain relationship among the equilibrium constants and the total concentrations of solutes, IL-1Ra can reverse the effect of the decoy receptor of decreasing the equilibrium concentration of the receptor-ligand complex. This finding derives from a mathematical result applicable to any reversible chemical reaction system comprising four species arranged in a square such that each species binds its two immediate neighbors. The result gives the monotonicity of the equilibrium concentrations of the complex species as functions of the total concentrations of the simple species.