play roles in various other parts of the body as well. It is part of the mechanism by which NMDA (N-methyl-D-aspartate) glutamate receptors are inhibited in the brain, for example. Specifically, this type of inhibition impacts the granule cells that make up a layer of the cerebellum. These cells have the aforementioned NMDA receptors, and the activity of said receptors typically increases as ethanol is consumed. This often leads to withdrawal symptoms if said ethanol is removed. Various uncompetitive blockers act as antagonists at the receptors and modify the process, with one example being an inhibitor called memantine. In fact, in similar cases (involving over-expression of NMDA, though not necessarily via ethanol), it has been shown that uncompetitive inhibition helps in nullifying the over-expression due to its particular properties. Since uncompetitive inhibitors block high concentrations of substrates very efficiently, their traits alongside the innate characteristics of the receptors themselves lead to very effective blocking of NMDA channels when they are excessively open due to massive amounts of NMDA agonists. Derivation of Uncompetitive Michaelis–Menten Equation Uncompetitive inhibition can be described using the following set of reaction equations: The reaction rate of the first rule defined above where [E] and [S] bind to form the complex [ES] and [ES] can separate to reform the products can be written as: is a second order rate constant representing the rate in which [E] and [S] bind to form the [ES] complex under mass action kinetics is a first order rate constant representing the rate of [ES] unbinding to reform [E] and [S] The second reaction rate describing the rate of [ES] complex creating the product from substrate [S] and regenerating a free enzyme [E] can be described with the following mass action rate: Where: is a first order reaction rate of the [ES] complex forming the product [P] and free enzyme [E] With uncompetitive inhibition, the enzyme substrate complex can be tied up into an enzyme-substrate-inhibitor complex under the following rate: Where: is a second order rate constant representing the rate in which [ES] and [I] bind to form the [ESI] complex under mass action kinetics is a first order rate constant representing the rate of [ESI] unbinding to reform [ES] and [I] Putting the above information into a set of ordinary differential equations yields: In order to derive the modified Michaelis-Menten equation, the following assumptions have to be made: The substrate is not