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.”
There are two parts to the Michaelis-Menton Equation. First, the maximum velocity term ([V]max) which is equal to kcat[E]t. This term represents the maximum rate at which the enzyme can produce product (basically when the enzyme is saturated with substrate). Second, we have a fractional term which describes the shape of the dose-velocity curve in response to increasing concentrations of substrate. If you data is normalized to 100% then this fractional term is usually sufficient to describe your data.
On limitation of the Michaelis-Menton is that is only works when the receptor concentration is much lower than the Michaelis-constant (i.e. [R]t << Km). While this is often true experimentally (when very low concentrations of enzymes are ultilized), it is typically not true in vivo and a more general, quadratic-equation must be used as is described in a previous post: Understanding Ligand-Receptor Dose-Response Curves.
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