Download - Lecture 15 - University of Michigan
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
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
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
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
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
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
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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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