Theory Manual Version 3.4
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Subsection 5.13.2: Mass Action Reversible Up Section 5.13: Chemical Reaction Production Rate Section 5.14: Specific Reaction Rate

### 5.13.3 Michaelis-Menten

Michaelis-Menten is a model for enzyme kinetics as represented by the reactions where is the enzyme, is the substrate, is the enzyme-substrate complex, and is the product. The molar mass supply producing is related to the concentration of the substrate via where is the maximum rate achieved by the system, at maximum (saturating) substrate concentrations. is the substrate concentration at which the reaction rate is half of .
This relation may be derived by applying the law of mass action to the two reactions in (5.13.3-1). under the simplifying assumption that the reversible reaction between the enzyme and substrate reaches steady state much faster than the subsequent forward reaction forming the product. If the first and second reactions are denoted by subscripts 1 and 2, respectively, the law of mass action for the first (reversible) and second (forwar) reaction produces The total enzyme concentration remains constant at , so that. Assuming that the first reaction equilibrates much faster than the second is equivalent to letting , in which case where . Then, where represents the maximum value of , when . In practice, choosing can produce the desired effect.
Subsection 5.13.2: Mass Action Reversible Up Section 5.13: Chemical Reaction Production Rate Section 5.14: Specific Reaction Rate