Fig. 3: Optimal properties of the Hinshelwood cycle.

a Schematic representation of the Hinshelwood cycle with two types of species: red species (A or C) and blue species (B or D). b Global flux normalized by its maximum value \({{{{{{{{\mathcal{J}}}}}}}}}^{* }\) as a function of Q/K when a specific species of the cycle is chemostatted. This flux has a zero-derivative maximum (blue triangle) if a blue species is chemostatted or simply reaches its maximal value at Q = 0 (red square) if a red species is chemostatted. c Cloud of points for the exponential of the global affinity \({{{{{{{{\mathcal{A}}}}}}}}}^{* }\), for randomly chosen sets of kinetic rate constants indexed by N. If a blue species is chemostatted, points are lower-bounded by 4 (blue triangles) otherwise, the affinity diverges (red squares). d Global flux normalized by its maximum value \({{{{{{{{\mathcal{J}}}}}}}}}^{* }\) as a function of the degradation rate κ of a specific species. When a blue species is degraded, a zero-derivative maximum exists and is reached at a finite value of κ, while if a red species is degraded, the global flux is monotonously increasing and reaches its maximal value at infinity. Simulation parameters for b and d are k₊₁ = k₊₃ = 1 and k₊₂ = k₊₄ = k₋₁ = k₋₂ = k₋₃ = k₋₄ = 0.1.