Figure 1: The RSA ensures the validity of the sQSSA: Fast/slow dynamics occur when ε_SS ≪ 1 for the MM reaction mechanism (1).

This figure is an illustration of the phase-plane dynamics when ε_SS ≪ 1 and the sQSSA is valid; it serves to convey conceptual aspects of the phase-plane when the RSA is valid. The red dashed curve is the c-nullcline. The black curve the lies just above the c-nullcline is the invariant slow manifold. The thin lines with double arrows are illustrative of typical phase-plane trajectories when ε_SS ≪ 1: trajectories starting on the s-axis approach the c-nullcline almost vertically. Once the trajectory reaches the c-nullcline it closely follows ${\mathcal{M}}^{\epsilon }$ during the QSS phase of the reaction. Double arrows indicate fast dynamics, and single arrows represent slow dynamics. The reader should bear in mind that, slightly contrary to what is illustrated, the tangent vector to the trajectory is perfectly horizontal when it intercepts the c-nullcline, since its vertical velocity component vanishes at the point of interception.