In biochemistry, Michaelis–Menten kinetics, named after Leonor Michaelis and Maud Menten, is the simplest case of enzyme kinetics, applied to enzyme-catalysed reactions involving the transformation of one substrate into one product. In 1913, Michaelis and Menten expanded on Victor Henri's fundamental equation of enzyme kinetics, which was established in 1902. It takes the form of a differential equation describing the reaction rate v {\displaystyle v} (rate of formation of product P, with concentration p {\displaystyle p} ) as a function of a {\displaystyle a} , the concentration of the substrate A (using the symbols recommended by the IUBMB). The formula below is given by the Michaelis–Menten equation:
v = d p d t = V a K m + a {\displaystyle v={\frac {\mathrm {d} p}{\mathrm {d} t}}={\frac {Va}{K_{\mathrm {m} }+a}}} .
V {\displaystyle V} , which is often written as V max {\displaystyle V_{\max }} , represents the limiting rate approached by the system at saturating substrate concentration for a given enzyme concentration. The Michaelis constant K m {\displaystyle K_{\mathrm {m} }} has units of concentration, and for a given reaction is equal to the concentration of substrate at which the reaction rate is half of V {\displaystyle V} . Biochemical reactions involving a single substrate are often assumed to follow Michaelis–Menten kinetics, without regard to the model's underlying assumptions. Only a small proportion of enzyme-catalysed reactions have just one substrate, but the equation still often applies if only one substrate concentration is varied.
Michaelis–Menten plot
The plot of v {\displaystyle v} against a {\displaystyle a} has often been called a "Michaelis–Menten plot", even recently, but this terminology is historically misleading, as Michaelis and Menten did not use such a plot. Instead, they plotted v {\displaystyle v} against log a {\displaystyle \log a} , which has some advantages over the usual ways of plotting Michaelis–Menten data. If v {\displaystyle v} is the dependent variable, then it does not distort any experimental errors in v {\displaystyle v} . Michaelis and Menten did not attempt to estimate V {\displaystyle V} directly from the limit approached at high log a {\displaystyle \log a} , something difficult to do accurately with data obtained with modern techniques, and almost impossible with their data. Instead they took advantage of the fact that the curve is almost straight in the middle range and has a maximum slope of 0.576 V {\displaystyle 0.576V} i.e. 0.25 ln 10 ⋅ V {\displaystyle 0.25\ln 10\cdot V} . With an accurate value of V {\displaystyle V} it was easy to determine log K m {\displaystyle \log K_{\mathrm {m} }} from the point on the curve corresponding to 0.5 V {\displaystyle 0.5V} . This plot is virtually never used today for estimating V {\displaystyle V} and K m {\displaystyle K_{\mathrm {m} }} , but it remains valuable to compare the properties of several enzymes across a broad range of substrate concentrations - such as isoenzymes. For example, the four mammalian isoenzymes of hexokinase are half-saturated by glucose at concentrations ranging from about 0.02 mM for hexokinase A (brain hexokinase) to about 50 mM for hexokinase D ("glucokinase", liver hexokinase), spanning a 2500-fold range. A conventional (linear) plot would compromise on readability for the high-affinity isoenzyme graphs, but a semi-logarithmic plot allows to read off the kinetic parameters for all isoenzymes.
Model A decade before Michaelis and Menten, Victor Henri found that enzyme reactions could be explained by assuming a binding interaction between the enzyme and the substrate. His work was taken up by Michaelis and Menten, who investigated the kinetics of invertase, an enzyme that catalyzes the hydrolysis of sucrose into glucose and fructose. In 1913, they proposed a mathematical model of the reaction. It involves an enzyme E binding to a substrate A to form a complex EA that releases a product P regenerating the original form of the enzyme. This may be represented schematically as
E
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