lecture 15 - university of michigan
TRANSCRIPT
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Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of
chemical reactions and the design of the reactors in which they take place.
Lecture 15
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Today’s lecture Enzymes
Michealis-Menten Kinetics Lineweaver-Burk Plot Enzyme Inhibition Competitive Uncompetitive
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Last lecture
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Last lecture
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Enzymes Michaelis-Menten Kinetics. Enzymes are protein like substances with catalytic properties.
Enzyme unease. [From Biochemistry, 3/E by Stryer, copywrited 1988 by Lubert Stryer. Used with permission of W.H. Freeman and Company.]
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Enzymes It provides a pathway for the substrate to proceed at a faster rate. The substrate, S, reacts to form a product P.
A given enzyme can only catalyze only one reaction. Example, Urea is decomposed by the enzyme urease.
Slow S P
Fast
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A given enzyme can only catalyze only one reaction. Urea is decomposed by the enzyme urease, as shown below.
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The corresponding mechanism is:
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Michaelis-Menten Kinetics
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Michaelis-Menten Kinetics
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Vmax=kcat* Et
Turnover Number: kcat Number of substrate molecules (moles) converted to product in a given time (s) on a single enzyme molecule
(molecules/molecule/time) For the reaction
40,000,000 molecules of H2O2 converted to product per second on a single enzyme molecule.
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H2O2 + E →H2O + O + E kcat
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Summary
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(Michaelis-Menten plot) Vmax
-rs
S1/2
Solving:
KM=S1/2
therefore KM is the concentration at which the rate is half the maximum rate
CS
Michaelis-Menten Equation
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Inverting yields
Lineweaver-Burk Plot
slope = KM/Vmax
1/Vmax
1/S
1/-rS
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Types of Enzyme Inhibition
Competitive
Uncompetitive
Non-competitive
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Competitive Inhibition
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1) Mechanisms:
Competitive Inhibition
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2) Rates:
Competitive Inhibition
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Competitive Inhibition
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From before (no competition):
Intercept does not change, slope increases as inhibitor concentration increases
Competitive Inhibition
No Inhibition
Competitive Increasing CI
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Competitive
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Uncompetitive Inhibition Inhibition only has affinity for enzyme-substrate complex
Developing the rate law
(1)
(2) 24
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Adding (1) and (2)
From (2)
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Total enzyme
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Slope remains the same but intercept changes as inhibitor concentration is increased
Lineweaver-Burk Plot for uncompetitive inhibition 27
€
1−rS
=1
Vmax S( )KM + S( ) 1+
I( )KI
⎛
⎝ ⎜
⎞
⎠ ⎟
⎛
⎝ ⎜
⎞
⎠ ⎟
1−rS
=KM
Vmax1S( )
⎛
⎝ ⎜
⎞
⎠ ⎟ +
1Vmax
1+I( )KI
⎛
⎝ ⎜
⎞
⎠ ⎟
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Both slope and intercept changes
Increasing I
No Inhibition
E + S E·S P + E
(inactive)I.E + S I.E.S (inactive) +I +I -I -I
Noncompetitive Inhibition (Mixed)
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End of Lecture 15
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