enzyme_kinetics_inhib

Enzyme_kinetics_inhi - Enzyme Kinetics In 1913 Michaelis and Menten published the idea that enzymes and substrates formed reasonably stable

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Enzyme Kinetics In 1913, Michaelis and Menten published the idea that enzymes and substrates formed reasonably stable complexes with their substrates that then subsequently undergo reaction. This is represented by the following reaction scheme that is in every biochemistry textbook. E + S E . S E + P K M k cat This mechanism states that enzyme and substrate are at true equilibrium with the E . S complex, and that the E . S complex undergoes reaction to E and P. How do we get from this mechanism to the Michaelis-Menten equation, shown below? Michaelis-Menten Equation: d[P] dt = v i = k cat . [E] tot . [S] K M + [S] = V max . [S] K M + [S] (1) First, we can simply write down by inspection a differential rate equation for the appearance of products: d[P] dt = [ES] k cat ( 2 ) In and of itself, this equation does not do us a lot of good because we can not experimentally measure [E . S]. What can we measure? We can easily measure [E] tot by one of several means for measuring protein concentration and [S], but not [E] or [E . S]. Thus, we have to get the equation in terms of [E] tot and [S]. The following derivation is the simplest possible for the Michaelis-Menten mechanism and does not involve the application of the steady state assumption.
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2 We take note of two relationships: K M = [E][S] [E . S] and [E] = [E] tot - [E . S] Stick the second into the first and you get: K M = ([ E] tot [E . S])[S] [E . S] Rearranging this to solve for [E . S]: K M [E . S] = ([E] tot -[E . S]) [S] = [E] tot [S] - [E . S] [S] then K M [E . S] + [E . S] [S] = [E] tot [S] Factoring out [E . S], [E . S] (K M + [S]) = [E] tot [S] Dividing both sides by (K M + [S]) we get [E . S] = [E] tot [S] K M + [S] We've got [E . S] in terms of measurables. Now stick this expression for [E . S] into (2) and what do you get? d[P] dt = v i = k cat . [E] tot . [S] K M + [S] You have now derived the Michaelis-Menten equation. What are the assumptions of this mechanism and the derivation? The main one is that E and S are at equilibrium with E . S. The second one is that the catalytic step is irreversible. The latter
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3 is pretty good if there is no product present, since product coming off the enzyme will be approximately infinitely diluted. The first is not always so good, and we examine this below (Briggs-Haldane mechanism). (The unmentioned assumption is, again, that [S] free = [S] tot ). The Michaelis-Menten equation has the form of a rectangular hyperbola. It has a saturation term, [S]/(K M + [S]), that gives the fraction of the total enzyme in the reactive ES form. This is multiplied by [E] tot to give [ES], which is then multiplied by k cat , the rate constant for the reaction of the ES complex. The [S]/(K
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This note was uploaded on 05/04/2008 for the course BIS 102 taught by Professor Hilt during the Fall '08 term at UC Davis.

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Enzyme_kinetics_inhi - Enzyme Kinetics In 1913 Michaelis and Menten published the idea that enzymes and substrates formed reasonably stable

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