Michaelis–Menten kinetics

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 v {displaystyle v} (rate of formation of product, [ P ] {displaystyle } ) to [ S ] {displaystyle } , the concentration of a substrate S. Its formula is given by 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 v {displaystyle v} (rate of formation of product, [ P ] {displaystyle } ) to [ S ] {displaystyle } , the concentration of a substrate S. Its formula is given by This equation is called the Michaelis–Menten equation. Here, V max {displaystyle V_{max }} represents the maximum rate achieved by the system, at saturating substrate concentration. The Michaelis constant K M {displaystyle K_{mathrm {M} }} is the substrate concentration at which the reaction rate is half of V max {displaystyle V_{max }} . Biochemical reactions involving a single substrate are often assumed to follow Michaelis–Menten kinetics, without regard to the model's underlying assumptions. 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 where k f {displaystyle k_{f}} (forward rate), k r {displaystyle k_{r}} (reverse rate), and k c a t {displaystyle k_{mathrm {cat} }} (catalytic rate) 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 [ S ] ≪ K M {displaystyle ll K_{M}} so that v = k c a t [ E ] 0 [ S ] K M . {displaystyle v=k_{mathrm {cat} }_{0}{frac {}{K_{mathrm {M} }}}.} Under these conditions the reaction rate varies linearly with substrate concentration [ S ] {displaystyle {ce {}}} (first-order kinetics). However at higher [ S ] {displaystyle {ce {}}} with [ S ] ≫ K M {displaystyle gg K_{M}} , the reaction becomes independent of [ S ] {displaystyle {ce {}}} (zero-order kinetics) and asymptotically approaches its maximum rate V max = k cat [ E ] 0 {displaystyle V_{max }=k_{{ce {cat}}}_{0}} , where [ E ] 0 {displaystyle {ce {_0}}} is the initial enzyme concentration. This rate is attained when all enzyme is bound to substrate. k c a t {displaystyle k_{mathrm {cat} }} , the turnover number, is the maximum number of substrate molecules converted to product per enzyme molecule per second. Further addition of substrate does not increase the rate which is said to be saturated. The Michaelis constant K M {displaystyle K_{mathrm {M} }} is the [ S ] {displaystyle {ce {}}} at which the reaction rate is at half-maximum, and is an inverse measure of the substrate's affinity for the enzyme—as a small K M {displaystyle K_{mathrm {M} }} indicates high affinity, meaning that the rate will approach V max {displaystyle V_{max }} with lower [ S ] {displaystyle {ce {}}} than those reactions with a larger K M {displaystyle K_{mathrm {M} }} . The constant is not affected by the concentration or purity of an enzyme. The value of K M {displaystyle K_{mathrm {M} }} is dependent on both the enzyme and the substrate, as well as conditions such as temperature and pH The model is used in a variety of biochemical situations other than enzyme-substrate interaction, including antigen-antibody binding, DNA-DNA hybridization, and protein-protein interaction. It can be used to characterise a generic biochemical reaction, in the same way that the Langmuir equation can be used to model generic adsorption of biomolecular species. When an empirical equation of this form is applied to microbial growth, it is sometimes called a Monod equation. Parameter values vary widely between enzymes: