The Michaelis-Menton Equation has a very similar form to the Hill Equation but the key difference is that it deals with enzyme rates not ligand/receptor or drug/target interactions per se. Basically, it describes how fast an enzyme (E) makes its product (P) as a function of the total concentration of substrate ([S]t). This rate of production formation (d[P]/dt) is proportional to the kcat and the amount of complex ([ES]) which is exact what the Michaelis-Menton equation models. The Michaelis-constant (Km = (koff+kcat) / kon) describes how tightly the substrate binds the enzyme and the kcat is a rate-constant that describes how quickly the enzyme can make the product. Here,brackets denote concentrations and a t subscript indicates “total concentrations.”
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