Velocity Equations for Rapid Equilibrium Systems

Velocity equations can be obtained easily, even for seemingly complex systems, if rapid equilibrium conditions prevail. No derivation is really necessary. In fact, the velocity equation for any rapid equilibrium system can be written directly from an inspection of the equilibria between enzyme species (Briggs Haldane, 1925 Fromm, 1975 Wong, 1975 Fromm, 1979). 

Let us illustrate this statement with the following example, a rapid equilibrium bireactant system  

Now all we need to do is express the concentration of each species in terms of [E]. If we substitute fccat[Eo] wift Vmax. we shall obtain 

After substituting the concentrations of various forms of enzyme with kinetic constants, we obtain 

after rearranging, we obtain a usual velocity equation for the Rapid Equilibrium Random bisubstrate mechanism  

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The velocity equation for rapid equilibrium system was easily derived by inversing the numerator and denominator of (5.9.4.10) ... 

All velocity equations for rapid equilibrium systems can be derived in the above manner. The numerator of the right-hand side of the final equation will contain terms corresponding to the complexes that yield product. The denominator will contain a term for each enzyme species present. The term... 

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