Michaelis-Menten equation using the rapid-equilibrium assumption

Appendix 5.3. Derivation of the Michaelis-Menten Equation using the Rapid Equilibrium Assumption 

The fundamental equation in enzyme kinetics is the Michaelis-Menten equation. These workers worked on the hypothesis that the reaction proceeds through an enzyme-substrate complex (ES) that forms rapidly from the free enzyme (E) and the substrate (S) and may be described by an equilibrium (or Michaelis) constant AT/. Upon reaction, the ES complex then decomposes and is converted to product by a rate-determining step with a rate constant Acat. The scheme is shown below  

The rate of reaction 9t0 depends upon the catalytic rate constant and upon the enzyme-substrate concentration. 

All reactions are to some degree reversible, and many enzyme-catalysed reactions can function in either direction inside a cell. It is therefore interesting to compare the forward and back reactions, especially when the reaction runs to equilibrium as in an enzyme reactor. 

This reaction proceeds via the formation of a single intermediate complex. In the forward reaction it would be regarded as an ES complex while in the back reaction it would be regarded as an EP complex  

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