Figure 1: Phase–plane illustration of the Sisyphus manifold for the reaction mechanism (1)–(2).

The numerical solution of the mass action equations (6) (thick black curve that is barely visible) moves up, then down, the c₂-nullcline (dashed red curve) in the phase-plane for the coupled auxiliary enzyme reaction mechanism. Movement is illustrated dynamically in Movie 1 available in the Supplementary Material. The dimensionless units used in the numerical integration of 6) are: $s_1^0=1000,e_1^0=1,e_2^0=1$, k₁ = 1, k₂ = 10, k_-1 = 1, k₃ = 1, k₄ = 10, k_-3 = 1. The concentrations of substrate and complex have been scaled by their numerically-obtained maximum values.