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Paul D. Adams • University of Arkansas
Mary K. CampbellShawn O. Farrellhttp://academic.cengage.com/chemistry/campbell
Chapter SixThe Behavior of Proteins: Enzymes
Enzyme Catalysis
• Enzyme: a biological catalyst• with the exception of some RNAs that
catalyze their own splicing (Section 10.4), all enzymes are proteins
• enzymes can increase the rate of a reaction by a factor of up to 1020 over an uncatalyzed reaction
• some enzymes are so specific that they catalyze the reaction of only one stereoisomer; others catalyze a family of similar reactions
• The rate of a reaction depends on its activation energy, G°‡
• an enzyme provides an alternative pathway with a lower activation energy
Enzyme Catalysis (Cont’d)
• For a reaction taking place at constant temperature and pressure, e.g., in the body
• the change in free energy is
• Difference in energies between initial state and final state
• The change in free energy is related to the equilibrium constant, Keq, for the reaction by
A B
G° = H° - TS°
G° = RT ln Keq
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 eventually lead to protein denaturation
Enzyme Kinetics
• For the reaction
• The rate of reaction is given by rate equation
• Where k is a proportionality constant called the specific rate constantspecific rate constant
• Order of reactionOrder of reaction: the sum of the exponents in the : the sum of the exponents in the rate equationrate equation
A + B P
Rate = [A]t
[B]t
[P]t
_ _= =
Rate = k[A]f[B]g
Enzyme Kinetics (Cont’d)
• Consider the reaction
Whose rate equation is given by the expression
• Determined experimentally, not always from balanced
equations • 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
A + B C + D
Rate = k[A]1[B]1
Glycogenn + HPO42- Glucose-1-phosphate + Glycogenn-1
Rate = k[Glycogen]1[HPO42-]1 = k[Glycogen][HPO4
2-]
How Enzymes bind to Substrate
• In an enzyme-catalyzed reaction• SubstrateSubstrate, S:, S: a reactant• Active siteActive site:: 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 ESenzyme-substrate
complex
Binding Models
• Two models have been developed to describe formation of the enzyme-substrate complex
• Lock-and-key modelLock-and-key model:: substrate binds to that portion of the enzyme with a complementary shape
• Induced fit model:Induced fit model: binding of the substrate induces a change in the conformation of the enzyme that results in a complementary fit
2 Modes of E-S Complex Formation
Formation of Product
An Example of Enzyme Catalysis
• Chymotrypsin catalyzes • The selective hydrolysis of peptide bonds where the
carboxyl is contributed by Phe and Tyr
• It also catalyzes hydrolysis of the ester bonds
An Example of Enzyme Catalysis (Cont’d)
Non-Allosteric Enzyme Behavior
• Point at which the rate of reaction does not change, enzyme is saturated, maximum rate of reaction is reached
ATCase: An Example of Allosteric Behavior
• Sigmoidal shape- characteristic of allosterism
• Again Max. velocity reached, but different mechanism
Michaelis-Menten Kinetics
• Initial rate of an enzyme-catalyzed reaction versus substrate concentration
Michaelis-Menten Model
• For an enzyme-catalyzed reaction
• The rates of formation and breakdown of ES are given by these equations
• At the steady state
rate of formation of ES = k1[E][S]
rate of breakdown of ES = k-1[ES] + k2[ES]
k1[E][S] = k-1[ES] + k2[ES]
E + S ES Pk1
k-1
k2
Michaelis-Menten Model (Cont’d)
• When the steady state is reached, the concentration of free enzyme is the total less that bound in ES
• Substituting for the concentration of free enzyme and collecting all rate constants in one term gives
• Where KM is called the Michaelis constant
[E] = [E]T - [ES]
([E]T - [ES]) [S]
[ES] k-1 + k2
k1
= = KM
Michaelis-Menten Model (Cont’d)
• It is now possible to solve for the concentration of the enzyme-substrate complex, [ES]
• Or alternatively [ES] =[E]T [S]KM + [S]
[E]T [S] - [ES][S]
[ES]= KM
= KM[ES]
[E]T [S] = [ES](KM + [S])
[E]T [S] - [ES][S]
Michaelis-Menten Model (Cont’d)
• In the initial stages, formation of product depends only on the rate of breakdown of ES
• If substrate concentration is so large that the enzyme is saturated with substrate [ES] = [E]T
• Substituting k2[E]T = Vmax into the top equation gives
Vinit = k2[ES] = k2[E]T [S]KM + [S]
Vinit = Vmax = k2[E]T
Vmax [S]Vinit = KM + [S]
Michaelis-Mentenequation
Michaelis-Menten Model (Cont’d)
• When [S]= KM, the equation reduces to
Vmax [S]V =
KM + [S]=
Vmax [S]
[S] + [S]=
Vmax
2
Linearizing The Michaelis-Menten Equation
• It is difficult to determine Vmax experimentally
• The equation for a hyperbola
• Can be transformed into the equation for a straight line by taking the reciprocal of each side
V1 =
KM + [S]
Vmax [S]=
KM [S]Vmax [S] Vmax [S]
+
V1 =
KM
Vmax [S] Vmax
+ 1
Vmax [S]V =
KM + [S](an equation for a hyperbola)
Lineweaver-Burk Plot
• The Lineweaver-Burke plot has the form y = mx + b, and is the formula for a straight line
• a plot of 1/V versus 1/[S] will give a straight line with slope of KM/Vmax and y intercept of 1/Vmax
• such a plot is known as a Lineweaver-Burk double reciprocal Lineweaver-Burk double reciprocal plotplot
V1 =
Vmax
+ 1Vmax [S]
1
y m x + b
V1 =
KM •
= •
Lineweaver-Burk Plot (Cont’d)
• KM is the dissociation constant for ES; the greater the value of KM, the less tightly S is bound to E
• Vmax is the turnover number
Turnover Numbers
• Vmax is related to the turnover number of enzyme:also called kcat
• Number of moles of substrate that react to form product per mole of enzyme per unit of time
V max
[ET ]
turnover _ number kcat
Enzyme Inhibition
• Reversible inhibitorReversible inhibitor:: a substance that binds to an enzyme to inhibit it, but can be released
• competitive inhibitor:competitive inhibitor: binds to the active (catalytic) site and blocks access to it by substrate
• noncompetitive inhibitor:noncompetitive inhibitor: binds to a site other than the active site; inhibits the enzyme by changing its conformation
• Irreversible inhibitorIrreversible 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 must compete with inhibitor for the active site; more substrate is required to reach a given reaction velocity
• We can write a dissociation constant, KI for EI
E+IEI KI =[E][I][EI]
E + S ES P+IEI
Competitive Inhibition
Competitive Inhibition
• In a Lineweaver-Burk double reciprocal plot of 1/V versus 1/[S], the slope (and the x intercept) changes but the y intercept does not change
V1 =
KM
Vmax Vmax
+ 1
No inhibition
S1•
y = m• b+x
y =
In the presence of a competitive inhibitor
V1 =
KM
Vmax Vmax+ 11 +[I]
KI S1
+ bm x•
A Lineweaver-Burke Plot for Competitive Inhibition
Noncompetitive Inhibition (Cont’d)
• Several equilibria are involved
• The maximum velocity Vmax has the form
E ES E + P+S
-I
EI+S
-I+I +I
-S
ESI-S
VImax =
Vmax
1 + [I]/KI
Noncompetitive Inhibition (Cont’d)
A Lineweaver-Burke Plot for Noncompetitive Inhibition
• Because the inhibitor does not interfere with binding of substrate to the active site, KM is unchanged
• Increasing substrate concentration cannot overcome noncompetitive inhibition
y = m x
In the presence of a noncompetitive inhibitor
V1 =
KM
Vmax Vmax+ 11 +[I]
KI S1
+ b
1 +[I]
KI
•
V1 =
KM
Vmax Vmax
+ 1
No inhibition
S1
y = m• b+x
•
A Lineweaver-Burke Plot for Noncompetitive Inhibition (Cont’d)
Other Types of Inhibition
• Uncompetitive- inhibitor can bind to the ES complex but not to free E. Vmax decreases and KM decreases.
• Mixed- Similar to noncompetitively, but binding of I affects binding of S and vice versa.