In biochemistry, Michaelis–Menten kinetics is one of the best-known models of enzyme kinetics. It is named after German biochemist Leonor Michaelis and Canadian physician Maud Menten. The model takes the form of an equation describing the rate of enzymatic reactions, by relating reaction rate (rate of formation of product, ) to , the concentration of a substrate S. Its formula is given by This equation is called the Michaelis–Menten equation. Here, represents the maximum rate achieved by the system, happening at saturating substrate concentration for a given enzyme concentration. When the value of the Michaelis constant is numerically equal to the substrate concentration, then the reaction rate is half of . Biochemical reactions involving a single substrate are often assumed to follow Michaelis–Menten kinetics, without regard to the model's underlying assumptions. Model In 1901, French physical chemist Victor Henri found that enzyme reactions were initiated by a bond (more generally, a binding interaction) between the enzyme and the substrate. His work was taken up by German biochemist Leonor Michaelis and Canadian physician Maud Menten, who investigated the kinetics of an enzymatic reaction mechanism, invertase, 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, S, to form a complex, ES, which in turn releases a product, P, regenerating the original enzyme. This may be represented schematically as E{} + S <=>[\mathit{k_f}][\mathit{k_r}] ES ->[k_\ce{cat}] E{} + P where (forward rate constant), (reverse rate constant), and (catalytic rate constant) denote the rate constants, the double arrows between S (substrate) and ES (enzyme-substrate complex) represent the fact that enzyme-substrate binding is a reversible process, and the single forward arrow represents the formation of P (product). Under certain assumptions – such as the enzyme concentration being much less than the substrate concentration – the rate of product formation is given by The reaction order depends on the relative size of the two terms in the denominator. At low substrate concentration , so that the reaction rate varies linearly with substrate concentration [S] (first-order kinetics). However at higher [S] with , the reaction becomes independent of [S] (zero-order kinetics) and asymptotically approaches its maximum rate , where [E]_0 is the initial enzyme concentration. This rate is attained when all enzyme is bound to substrate. , the turnover number, is the maximum number of substrate molecules converted