Steady State Analysis of Enzyme Kinetics

The discussion above of enzyme reactions treated the formation of the initial ES complex as an isolated equilibrium that is followed by slower chemical steps of catalysis. This rapid equilibrium model was first proposed by Henri (1903) and independently by Michaelis and Menten (1913). However, in most laboratory studies of enzyme reactions the rapid equilibrium model does not hold instead, enzyme 

The term Vmax refers to the maximum velocity obtained at infinite substrate concentration. VW is mathematically equivalent to the product of kC3) and the enzyme concentration  

Subsequently Briggs and Haldane (1925) demonstrated that a similar treatment could be used to describe steady state enzyme velocity as a saturable function of substrate concentration  

Equations (2.10) and (2.12) are identical except for the substitution of the equilibrium dissociation constant Ks in Equation (2.10) by the kinetic constant Ku in Equation (2.12). This substitution is necessary because in the steady state treatment, rapid equilibrium assumptions no longer holds. A detailed description of the meaning of Ku, in terms of specific rate constants can be found in the texts by Copeland (2000) and Fersht (1999) and elsewhere. For our purposes it suffices to say that while Ku is not a true equilibrium constant, it can nevertheless be viewed as a measure of the relative affinity of the ES encounter complex under steady state conditions. Thus in all of the equations presented in this chapter we must substitute Ku for Ks when dealing with steady state measurements of enzyme reactions. 

Like Ks, the kinetic term Ku (which is commonly referred to as the Michaelis constant) has units of molarity. Considering Equation (2.12), if we were to fix the substrate concentration term to be equivalent to KM, the equation would reduce to 

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