Two rules of enzyme kinetics for reversible Michaelis-Menten mechanisms

In a Michaelis-Menten type reversible enzyme reaction (one substrate, one product) the rapid equilibrium kinetics in one direction excludes rapid equilibrium in the reverse direction. If rapid equilibrium functions in any direction, in the reverse reaction van Slyke type 'kinetic constant' appears in the rate equation independently of whether steady state is reached in finite time or the final equilibrium is attained at t = infinity. If the reaction proceeds in one direction with rapid equilibrium and in the reverse direction with steady-state kinetics, the thermodynamic equilibrium of the reaction determines that a higher equilibrium concentration of product (or substrate) can be reached only with steady-state kinetics.