Uncompetitive inhibition (which Laidler and Bunting preferred to call anti-competitive inhibition, but this term has not been widely adopted) is a type of enzyme inhibition in which the apparent values of the Michaelis–Menten parameters V {\displaystyle V} and K m {\displaystyle K_{\mathrm {m} }} are decreased in the same proportion. It can be recognized by two observations: first, it cannot be reversed by increasing the substrate concentration a {\displaystyle a} , and second, linear plots show effects on V {\displaystyle V} and K m {\displaystyle K_{\mathrm {m} }} , seen, for example, in the Lineweaver–Burk plot as parallel rather than intersecting lines. It is sometimes explained by supposing that the inhibitor can bind to the enzyme-substrate complex but not to the free enzyme. This type of mechanism is rather rare, and in practice uncompetitive inhibition is mainly encountered as a limiting case of inhibition in two-substrate reactions in which one substrate concentration is varied and the other is held constant at a saturating level.
Mathematical definition
In uncompetitive inhibition at an inhibitor concentration of i {\displaystyle i} the Michaelis–Menten equation takes the following form:
v = V a K m + a ( 1 + i / K i u ) {\displaystyle v={\frac {Va}{K_{\mathrm {m} }+a(1+i/K_{\mathrm {iu} })}}}
in which v {\displaystyle v} is the rate at concentrations a {\displaystyle a} of substrate and i {\displaystyle i} of inhibitor, for limiting rate V {\displaystyle V} , Michaelis constant K m {\displaystyle K_{\mathrm {m} }} and uncompetitive inhibition constant K i u {\displaystyle K_{\mathrm {iu} }} . This has exactly the form of the Michaelis–Menten equation, as may be seen by writing it in terms of apparent kinetic constants:
v = V a p p a K m a p p + a {\displaystyle v={\frac {V^{\mathrm {app} }a}{K_{\mathrm {m} }^{\mathrm {app} }+a}}}
in which V a p p = V 1 + i / K i u and K m a p p = K m 1 + i / K i u {\displaystyle V^{\mathrm {app} }={\frac {V}{1+i/K_{\mathrm {iu} }}}{\text{ and }}K_{\mathrm {m} }^{\mathrm {app} }={\frac {K_{\mathrm {m} }}{1+i/K_{\mathrm {iu} }}}}
V a p p {\displaystyle V^{\mathrm {app} }} and K m a p p {\displaystyle K_{\mathrm {m} }^{\mathrm {app} }} decrease in the same proportions as a result of the inhibition. This is apparent when viewing a Lineweaver-Burk plot of uncompetitive enzyme inhibition: the ratio between V and Km remains the same with or without an inhibitor present. This may be seen in any of the common ways of plotting Michaelis–Menten data, such as the Lineweaver–Burk plot, for which for uncompetitive inhibition produces a line parallel to the original enzyme-substrate plot, but with a higher intercept on the ordinate:
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