Chapter 6
Protein Function: Enzymes
Part 2
Enzymes, Part 2
Learning Goals: To Know
– Chemical mechanisms of catalysis: Chymotrypsin
– Multi-substrate enzyme reaction kinetics
– Reversible enzyme inhibitors and inhibition kinetics
More fun with Practicase
– Regulation of enzyme activity.
Part of Worked Example 6.1
An enzyme, happyase, is discovered to catalyze:
SAD  HAPPY
It is known that the kcat is 600 s-1.
When [Et] = 20 nM, and [SAD] = 40 μM, the reaction velocity
(vo) is 9.6 μM/s. What is the KM?
Solution combines the kcat equation and the MichaelisMenten equation.
kcat = Vmax/ [Et] so: Vmax = kcat [Et]
Substitute into Michaelis-Menten equation for Vmax:
vo = [ Vmax (S)] / [Km + (S)]
vo = [kcat [Et] (S)] / [Km + (S)]
Answer: Km = 10μM
So Far… … … it has just been single substrate:
S + E  ES  E + P
Now lets go to multiple substrates and
multiple products (we will only go as
much as 2 substrates  2 products):
Enz
A + B

C + D
Multiple Substrate Reactions
Lineweaver Burke Plot – Enzymes forming
Ternary Complexes – Ordered or Random
Lineweaver Burke Plot – Enzymes Without
Ternary Complexes
Enzyme Inhibition
Inhibitors are compounds that decrease enzyme’s activity
•Irreversible inhibitors (inactivators) react with the enzyme
• One inhibitor molecule can permanently shut off one enzyme molecule
• They are often powerful toxins but also may be used as drugs
•Reversible inhibitors bind to and can dissociate from the enzyme
• They are often structural analogs of substrates or products
• They are often used as drugs to slow down a specific enzyme
•Reversible inhibitor can bind:
• to the free enzyme and prevent the binding of the substrate
• to the enzyme-substrate complex and prevent the reaction
Reversible Inhibitors - Competitive
Lineweaver Burke - Competitive Inhibition
α = 1 + [I]/Ki
-1/Km
-1/αKm
Reversible Inhibitors - Uncompetitive
Lineweaver Burke: Uncompetitive Inhibition
α’ = 1 + [I]/Ki’
Reversible Inhibitors – Mixed Inhibition
Lineweaver Burke – Mixed Inhibition
α = 1 + [I]/Ki
α’ = 1 + [I]/Ki’
α’/Vmax
- 1/Km
- α’/αKm
Shows Region of Inhibitor Effect
Apparent Vmax or Apparent Km refers to y or x axis intercept only.
The Next Slide is MUCH BETTER
Calculation of Enzyme Constants
Type of Inhibition
X axis intercept
Y axis intercept
None
-1/Km
1/Vmax
Competitive
-1/αKm
1/Vmax
Uncompetitive
- α’/Km
α’/Vmax
Mixed
- α’/αKm
α’/Vmax
EOC Problem 12: Lets figure out what sort of inhibitor
ibuprofen (active ingredient in Advil) is. Ouch!!! or Ahhhh!
And, next there is our friend Practicase and inhibitors.
Inhibition of Practicase
[Studentose],mM vo, uninhibited
vo Inhbitor A vo Inhibitor B vo Inhibitor C
1
12
4.3
5.5
2
20
8
9
8.69
4
29
14
13
13.7
8
35
21
16
19.6
12
40
26
18
22.2
Inhibitor A at 1 mM
Inhibitor B at 3 mM
Inhibitor C at 50 μM
5
L-B plots of Practicase Inhibitiors
We already know KM = 3.33 mM and Vmax= 50
µmoles/mL/s and it is a Competitive Inhibitor
Calculation Inhibitor
A’s Practicase Ki :
The Inhibited curve intersects the X-axis at 0.1 mM, thus
-1/αKM = -0.1 mM
Be sure to calculate
the Ki’s for the other
inhibitor.
Is the inhibitor a
potential drug?
Compare the Ki to
the KM…what does
this tell you?
Solving for α, α = 3
So, α = 1 + [ I ]/Ki we know the inhibitor in the
experiment was 1 mM
Thus, 3 = 1 + 1mM/Ki
2 = 1mM/Ki
Ki = 0.5 mM
Thus inhibitor A binds the enzyme BETTER
than the substrate!
Practicase Inhbitiors
Calculation of Mixed Inhibitor’s Ki’s
This is Inhibitor 2
This inhibitor has α and α’… to calculate Ki and Ki’
So, FIRST you need to calculate α’ … the best place to
do that is from the y-axis intercept = α’/Vmax
Then to get α, go to the x-axis intercept = α’/αKm
then from each, α and α’ you can determine Ki and Ki’
Remember this one inhibitor binds both to E and ES.
Enzymes and Fashion
“Stonewashed Jeans”
Jeans are washed with
cellulase (an enzyme that
hydrolyzes celluose –
major component in
cotton) at a low
concentration for a short
time…..the effect looks
“stonewashed”.
If they were really
stonewashed how would
they get all the stones
out of the pockets?
Irreversible Inhibition
Mechanism Based
Suicide Inhibitors
Effect of pH on Enzyme Activity
Effect of pH on Chymotrypsin
Chymotrypsin – Our Model Enzyme
Active Site of Chymotrypsin with Substrate
Aromatic Part of
Substrate = Green
Chymotrypsin – Our Model Enzyme
Amide Nitrogens
Stabilize Oxyanion
Reactive Groups in Enzymes are Either:
Chymotrypsin Mechanism
Step 1: Substrate Binding
Chymotrypsin Mechanism
Step 2: Nucleophilic Attack
Chymotrypsin
Mechanism
Step 3: Substrate
Cleavage
Chymotrypsin Mechanism
Step 4: Water Comes In
Chymotrypsin Mechanism
Step 5: Water Attacks
Chymotrypsin Mechanism
Step 6: Break-off from the Enzyme
Chymotrypsin Mechanism
Step 7: Product Dissociates
Drug Company
Recruiting Ad
The importance of structural
protein chemistry !!! And
transition state analogs…
Which bind the active site
exceptionally well.
from C&EN, Aug 13, 2007
Hexokinase Reaction : Induced Fit
What happens when glucose binds 
Induced Fit with Glucose Binding
Daniel Koshland 60’s
Remember in Part 1 of this
Chapter glucose prevented
thermal destruction of
hexokinase…EOC problem 4.
Xylose is One Carbon Shorter than Glucose
Xylose causes Hexokinase to become an
ATPase
When Xylose reacts with Hexokinase – it causes induced
fit and Mg++ ATP binds…
but xylose does not exclude water from the active site
where the 6th carbon would be.
Normally the Induced fit is the active form, and catalyses
the phospho-transfer from ATP to glucose  glucose-6phosphate + ADP, but when xylose is there:
Xylose + H2O + ATP  Xylose + ADP + Pi…. A futile use of
ATP!
Enzyme activity can be regulated
• Regulation can be:
– noncovalent modification
– covalent modification
– and either
• irreversible
• reversible
Noncovalent Modification: Allosteric
Regulators
The kinetics of allosteric regulators differ from
Michaelis-Menten kinetics.
Allosteric Effectors – Bind to Allosteric Site
Feedback Inhibition is the
Classic Form of Allosteric
Inhibition
Allosteric Enzymes Often Have Sigmoid Kinetics
Allosteric Positive and Negative Regulators:
Affecting KM
Allosteric Positive and Negative Regulators:
Affecting the Vmax
Enzyme Regulation by Covalent Modification
Glycogen Synthase Regulation: Both
Allosteric and Covalent
From Ch 15
PP1: Protein
Phosphatase-1
Zymogen Regulation
Things to Know and Do Before Class
1. Know the chymotrypsin reaction and the concept of
how enzymes participate in the reaction.
2. Kinetics of multisubstrate reactions.
3. Types and kinetics of reversible enzyme inhibitors.
And, the importance of Ki.
4. Types enzyme regulation and their Michaelis Menten
kinetics.
5. Be able to do EOC Problems 12, 18, 19.