Lecture 24. Thursday, November 30. Michaelis-Menten Kinetics

Lecture 24. - Restricted For students enrolled in Chem130/MCB100A UC Berkeley Fall 2006 ONLY Lecture 24 John Kuriyan University of California

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Restricted: For students enrolled in Chem130/MCB100A, UC Berkeley, Fall 2006 ONLY Lecture 24 1 John Kuriyan: University of California, Berkeley Chem C130/MCB 100A, Fall 2006, Lecture 24 Michaelis-Menten Kinetics When we study an enzyme reaction we monitor the increase of product, or the decrease of substrate. For an enzyme catalyzed reaction, the rate of the reaction is determined by the concentration of the enzyme-substrate complex, [E]. If we add more substrate, keeping the enzyme concentration constant, then the rate of the reaction will increase until the enzyme is saturated. At that point the maximum rate, v max , is obtained.
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Restricted: For students enrolled in Chem130/MCB100A, UC Berkeley, Fall 2006 ONLY Lecture 24 2 As we increase the concentration of substrate, the product concentration varies with time as follows:
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Restricted: For students enrolled in Chem130/MCB100A, UC Berkeley, Fall 2006 ONLY Lecture 24 3 We plot these data by showing the rate, v, of the reaction at fixed enzyme concentration as follows: If we do such an experiment, there are two experimentally determined parameters that are obtained readily. The first is v max , the maximum rate. The second is K M (Michaelis constant), which is the substrate concentration at which the rate is half maximal. What we will now do is to relate v max and K M to properties of the enzyme.
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Restricted: For students enrolled in Chem130/MCB100A, UC Berkeley, Fall 2006 ONLY Lecture 24 4 v max , the maximum velocity, is obtained when the enzyme is fully saturated with substrate. The rate is proportional to the value of [ES], the concentration of the enzyme-substrate complex, and when the enzyme is fully saturated, [ES] is given by [E] tot , the total concentration of enzyme. v max is related to [E] tot by the following equation: v max = k cat [E] tot, where k cat is known as the catalytic constant of the enzyme. If we assume that the substrate and the enzyme are in equilibrium, then ν = ν max x f where f is the fractional saturation of the enzyme. Using the expression for fractional saturation from binding thermodynamics: v = max ) ] [ ] [ ( S K S D + (1) where v is the velocity (rate) of the reaction. This is called the Michaelis-Menten equation. Note that this equation is derived by assuming that the enzyme and substrate are in equilibrium. In general, the equilibrium condition does not hold, but a similar looking equation can be derived for “steady-state” conditions:
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Restricted: For students enrolled in Chem130/MCB100A, UC Berkeley, Fall 2006 ONLY Lecture 24 5 Under steady state conditions, the concentrations of the enzyme-substrate complex is constant. When [ES] is constant, d [ ES ] dt = 0 (2) From the general equation for the reaction: E + S k 1 k 1 ES k 2 P (3) d [ ES ] dt = k 1 [ E ][ S ] k 2 [ ES ] k 1 [ ES ] = 0 (4) [ES] and [E] are not directly observable in experiments, so need to eliminate them.
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This note was uploaded on 01/12/2010 for the course MCB 100A taught by Professor Kuryian during the Fall '09 term at University of California, Berkeley.

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Lecture 24. - Restricted For students enrolled in Chem130/MCB100A UC Berkeley Fall 2006 ONLY Lecture 24 John Kuriyan University of California

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