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.