The first form of the indicator reaction we will consider is the case when k 3 and k 4 are very large (in comparison to k 1 and k 2 ), and the indicator reaction is incredibly fast. What phase space trajectories do in the case of the coupled auxiliary enzyme reaction is chase x * . Given the limits computed in , we expect the phase plane trajectory to "catch" x * very quickly when the indicator reaction is fast. This means that the coordinates given in will serve as a very good approximation to the mass action equations over measurable timescales. In fact, we can simplify the expression even further in the limiting case: if the phase-plane trajectory slides down the c 2 -nullcline at a distance from x * that is negligibly small, then