Michaelis steady-state concept

The Michaelis-Menten equation, especially if derived with the steady-state concept as above, is a rigorous rate law which not only fits almost all one-substrate enzyme kinetics, except in the case of inhibition (see Section 5.3), but also allows identification of the kinetic constants with the elementary steps in Eq. (5.1). 

While we are still self-constrained to limit our treatment to what we believe is essential to physical chemistry, we have added further examples to the Chapter 7 treatment of reaction kinetics, which include some aspects of multistep mechanisms and introduced the steady-state approximation. The steady-state concept was then extended to the Eyring transition-state concept and used again for the critical step in the Michaelis-Menten treatment of enzyme kinetics. This has been a fast tour of some complicated algebra but in our experience students who learn the derivations have a deeper appreciation for the concepts. Casual interviews of students from past classes have revealed that the Michaehs-Menten derivations have been the most useful aspect of this chapter. 

Fig. 6.2 Illustration of the steady-state concept in enzymatic catalysis. (From http //chemwiki.ucdavis. edu/ api/deki/files/54230/512px-Michaelis Menten S P E ES.svg.png revision—l).

Steady-state approximation is based on the concept that the formation of [ES] complex by binding of substrate to free enzyme and breakdown of [ES] to form product plus free enzyme occur at equal rates. A graphical representation of the relative concentrations of free enzyme, substrate, enzyme-substrate complex, and product is shown in figure 7.8 in the text. Derivation of the Michaelis-Menten expression is based on the steady-state assumption. Steady-state approximation may be assumed until the substrate concentration is depleted, with a concomitant decrease in the concentration of [ES]. 

There is almost no biochemical reaction in a cell that is not catalyzed by an enzyme. (An enzyme is a specialized protein that increases the flux of a biochemical reaction by facilitating a mechanism [or mechanisms] for the reaction to proceed more rapidly than it would without the enzyme.) While the concept of an enzyme-mediated kinetic mechanism for a biochemical reaction was introduced in the previous chapter, this chapter explores the action of enzymes in greater detail than we have seen so far. Specifically, catalytic cycles associated with enzyme mechanisms are examined non-equilibrium steady state and transient kinetics of enzyme-mediated reactions are studied an asymptotic analysis of the fast and slow timescales of the Michaelis-Menten mechanism is presented and the concepts of cooperativity and hysteresis in enzyme kinetics are introduced. 

As the above example shows, catalysis implies consecutive reactions. One of the historically most useful ideas in the treatment of such processes has been the steady state assumption—i.e., that the intermediates in such a reaction sequence might rapidly reach a given stationary concentration, which then, in the steady state, remains invariant. This concept was first used by Bodenstein and by Michaelis and Menten, and was generalized by Christiansen and Kramers " to reactions involving possible chain mechanisms in the gas phase. It is of some importance, since it illustrates early concepts in the collision theory of reactions. 

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