Mary K. Campbell
Shawn O. Farrell
http://academic.cengage.com/chemistry/campbell
Chapter Six
The Behavior of Proteins: Enzymes
Paul D. Adams • University of Arkansas
Enzyme Catalysis
• Enzyme: a _____________________
• with the exception of some __________ that
catalyze their own splicing (Section 10.4), all
enzymes are proteins (???)
• enzymes can increase the rate of a rxn by a
factor of up to 1020 over an uncatalyzed rxn
• some enzymes are so specific that they
catalyze the rsn of only one stereoisomer;
others catalyze a family of similar rxns
• The rate of a reaction depends on its
activation energy, DG°‡
• an enzyme provides an alternative pathway
with a ______________________________
Enzyme Catalysis (Cont’d)
• For a reaction taking place at constant temperature
and pressure, e.g., in the body
A
B
• the change in __________________________ is
DG° = DH° - TDS°
• Difference in energies between initial state
and final state
DG° = RT l n Keq
• The change in free energy is related to the
equilibrium constant, Keq, for the reaction by
Enzyme Catalysis (Cont’d)
• Consider the reaction
H2O2 → H2O + O2
Temperature dependence of catalysis
• Temperature can also
“catalyze reaction”
(increase rate)
• This is dangerous, why?
• Increasing temperature will
lead to _______________
______________________
Enzyme Kinetics
• For the reaction
A + B
P
• The rate of reaction is given by rate equation
D[A]
D[B]
_
Rate = _
=
Dt
Dt
=
D[P]
Dt
Rate = k[A] f[B] g
• Where k is a proportionality constant called the
___________________________________________
• ______________________________: the sum of the
exponents in the rate equation: f+g
Enzyme Kinetics (Cont’d)
• Consider the reaction
A + B
C + D
Whose rate equation is given by the expression
Rate = k[A]1[B]1
• Determined experimentally, not from _______________
• The reaction is said to be first order in A,
first order in B, and second order overall
• Consider this reaction of glycogen with phosphate
Gl ycogenn + HPO42-
Gl ucose-1-phosphate + Glycogen
n-1
1
Rate = k[Glycogen]
[HPO42-]1 = k[Glycogen][HPO42-]
How Enzymes bind to Substrate
• In an enzyme-catalyzed reaction
• ____________________________, S: a reactant
• ______________________: the small portion of the
enzyme surface where the substrate(s) becomes
bound by noncovalent forces, e.g., hydrogen bonding,
electrostatic attractions, van der Waals attractions
E + S
ES
e nz ym e -substrate
com ple x
Binding Models
• Two models have been developed to describe
formation of the_____________________ complex
• __________________ model: substrate binds to that
portion of the enzyme with a complementary shape
• _________________ model: binding of the substrate
induces a change in the conformation of the enzyme
that results in a complementary fit
Two Modes of E-S Complex Formation
Formation of Product
An Example of Enzyme Catalysis
____________________ catalyzes
• The selective hydrolysis of ___________________
where the ________ is contributed by _____ and ____
• It also catalyzes hydrolysis of the ____________ bonds
An Example of Enzyme Catalysis (Cont’d)
Non-Allosteric Enzyme Behavior
Point at which the rate
of reaction does not
change, enzyme is
__________________,
maximum rate of
reaction is reached
ATCase: An Example of Allosteric Behavior
• ____________ shape - characteristic of __________
• Again max velocity reached, but different mechanism
Michaelis-Menten Kinetics
Initial rate of an enzyme-catalyzed rxn vs [S]
Michaelis-Menten Model
• For an enzyme-catalyzed reaction
E + S
k1
k-1
ES
k2
P
• The rates of formation and breakdown of ES are
given by these equations
rate of formation of ES = 1k[E][S]
rate of breakdown of ES = k
-1 [ES] + k2[ES]
• At steady state
k1[E][S] = k-1[ES] + k2[ES]
Michaelis-Menten Model (Cont’d)
• When ______________is reached, the concentration
of free enzyme is the total minus that bound in ES
[E] = [E]T - [ES]
• Substituting for the concentration of free enzyme and
collecting all rate constants in one term gives
([E]T - [ES]) [S]
=
[ES]
k-1 + k2
= KM
k1
• KM is called the ____________________________
Michaelis-Menten Model (Cont’d)
• It is now possible to solve for the concentration
of the enzyme-substrate complex, [ES]
[E]T [S ] - [ES ][S ]
= KM
[ES ]
[E]T [S ] - [ES ][S ]= KM [ES ]
[E]T [S ] = [ES ](KM + [S ])
• Or alternately
[ES]
[E] T [S]
=
KM + [S]
Michaelis-Menten Model (Cont’d)
• In the initial stages, formation of product depends only on the
_______________________________________________
Vinit
= k2 [ES]
k 2[E]T [S]
=
KM + [S]
• If substrate concentration is ________________________ is
_______________________ [ES] = [E]T
Vinit
= Vmax = k2[E]T
• Substituting k2[E]T = Vmax into the top equation gives
Vinit =
Vmax [S]
KM + [S]
Mi chae l is-Mente n
e quation
Michaelis-Menten Model (Cont’d)
When _______________ the equation
reduces to
V=
Vmax [S]
KM + [S]
=
Vmax [S]
[S] + [S]
=
Vmax
2
Linearizing The Michaelis-Menten Equation
• Vmax is difficult to ___________________________________
• The equation for a hyperbola
Vmax [S]
V=
KM + [S]
(an equati on for a hype rbol a)
• Can be transformed into the equation for a ________ by taking
__________________________________
1
V
=
1
V
=
KM + [S ]
Vmax [S ]
=
KM
+
Vmax [S ]
KM
1
+
Vmax [S ]
Vmax
[S]
Vmax [S ]
Lineweaver-Burk Plot
• The _______________________ plot has the form y = mx + b,
and is the formula for a straight line
1
V
KM
=
Vmax
1
•
[S]
+
1
Vmax
y
=
•
+
b
m
x
• a plot of 1/V versus 1/[S] will give a straight line with slope of
_______________ and y intercept of _______________
• known as a __________________________________________
Lineweaver-Burk Plot (Cont’d)
• KM is the ________________________________________
• the greater the value of KM, the ________ tightly S is bound to E
• Vmax is the ___________________________________
Turnover Numbers
• Vmax is related to the ___________________________
of enzyme: also called kcat
V max 

 turnover_ num ber kcat
[ET ] 
Number of moles of substrate that react to form product
_____________________________________________

Enzyme Inhibition
• ____________ inhibitor: a substance that binds to an
enzyme to inhibit it, but can be released
• ____________________________ inhibitor: binds to the
active (catalytic) site and blocks access to it by substrate
• _____________________ inhibitor: binds to a site other
than the active site; inhibits the enzyme by changing its
conformation
• ________________________inhibitor: a substance that
causes inhibition that cannot be reversed
• usually involves formation or breaking of covalent bonds to
or on the enzyme
Competitive Inhibition
• Substrate competes with inhibitor for the active site;
more substrate is required to reach a given reaction
velocity
EI
I
+
E + S
ES
• We can write a dissociation constant, KI for EI
EI
I
+
E
KI =
[E][I]
[EI]
P
Competitive Inhibition
Competitive Inhibition
y =
•
No i nhibi ti on
1 = KM
V
Vmax
m •
1
S
+
x
+
1
Vmax
b
In the pre sence of a compe ti ti ve inhi bitor
1
V
y
KM
=
Vmax
=
1 +
[I]
KI
1
S
+
m
•
x
+
1
Vmax
b
In a Lineweaver-Burk plot of 1/V vs 1/[S], the
__________________ (and the x intercept) changes
but the ______________________ does not change
A Lineweaver-Burke Plot, Competitive Inhibition
Noncompetitive Inhibition (Cont’d)
• Several equilibria are involved
+S
E
-I
ES
E + P
-S
+I
-I
+S
EI
+I
ES I
-S
• The maximum velocity Vmax has the form
V
I
max
=
V max
1 + [I]/K I
Noncompetitive Inhibition (Cont’d)
Lineweaver-Burke Plot, Noncompetitive Inhibition
• Because the inhibitor does not interfere with ______________
to the active site, KM is ______________________
• Increasing substrate concentration ____________________
noncompetitive inhibition
No i nhibi ti on
1 = KM • 1
V
S
Vmax
y =
m •
x
+
1
Vmax
+
b
In the pre se nce of a noncompe titive i nhi bitor
[I]
1
1 = KM 1 + [I] 1
+
1 +
V
S
Vmax
Vmax
KI
KI
y
=
m
•
x+
b
Lineweaver-Burke Plot, Noncompetitive Inhibition
Other Types of Inhibition
• _____________________ - inhibitor can bind to the
ES complex but not to free enzyme; Vmax decreases
and KM decreases.
• __________________ - Similar to noncompetitive,
but binding of I affects binding of S and vice versa.