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

€

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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