Chapter 6

Protein Function: Enzymes

Part 2

Enzymes, Part 2

– Chemical mechanisms of catalysis: Chymotrypsin– Multi-substrate enzyme reaction kinetics– Reversible enzyme inhibitors and inhibition kinetics

More fun with Practicase– Regulation of enzyme activity.

Learning Goals: To Know

Part of Worked Example 6.1An 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 Michaelis-Menten 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

- α’/αKm- 1/Km

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 axisintercept 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 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

L-B plots of Practicase Inhibitiors

Calculation Inhibitor A’s Practicase Ki :

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?

We already know KM = 3.33 mM and Vmax= 50 µmoles/mL/s and it is a Competitive Inhibitor

The Inhibited curve intersects the X-axis at -0.1 mM, thus

-1/αKM = -0.1 mM

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’sThis 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 MechanismStep 2: Nucleophilic Attack

Chymotrypsin Mechanism

Step 3: Substrate Cleavage

Chymotrypsin MechanismStep 4: Water Comes In

Chymotrypsin MechanismStep 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-6-phosphate + 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.