The Behavior of Proteins: Enzymes

Chapter 02 : Enzyme kinetics2.0 Factors affecting rate of reaction

2.1 Michelis-Menten & Lineweaver-Burke

2.2 Enzyme inhibition & regulation

Recall…• Activation energy?

- the energy that used to initiate the reaction, where this energy is needed to break the chemical bonding so that the reaction can occur.

- this energy is low with the usage of enzyme; do not influence the product (P), path of reaction and final concentration of molecules.

• Catalysis?

- speed up the reaction; the catalysts that serve this function called enzymes.

proteins

specific

Fig. 6-1a, p.132

Fig. 6-1b, p.132

Table 6-1, p.133

p.133

Enzyme characteristics

ProteinCatalystsSpecific reactionReacts at optimal pH and temperatureRegulate/control the metabolism processesNeed in a low amountReversible reactionReaction may be inhibited by inhibitor

Factors affecting rate of reaction

i. Enzyme concentration [E] – with a constant [S], the rate of reaction increased with the increasing [E]

ii. Substrate concentration [S] – the rate of reaction increased until the amount of S = E

iii. pH – depends on functional group (R); -COOH or -NH2

iv. Effect of temperature – increment of temperature will increase the rate of reaction

v. Effect of inhibitor – chemical substance that binds on the active site/other site on the enzyme (allosteric site) → competitive and non-competitive inhibition

Fig. 6-2, p.134

• The Lock-and-key model: high degree of similarity between the shape of substrate and the geometry of the binding site on the enzyme.

• The substrate binds to a site whose shape compliments to its own.

• eg. Like a key in lock or the correct piece in jigsaw puzzle.

• Weakness?

• The induced-fit model: the binding of the substrate induces the conformational change in the enzyme.

• The binding site has a different 3-D shape before the substrate is bound.

• The shape of the active site becomes complementary to the shape of the substrate only after the substrate binds to the enzyme.

• Mimics the transition state.

Michaelis-Menten model

• Devised in 1913 by Leonor Michelis and Maud Menten.

• Basic model for nonallosteric enzyme.• The main feature of this model for enzymatic

reaction is the formation of an E-S complex.• The [E-S] is low but remains unchanged to any

appreciable extent over the course of the reaction.• The S → P; released from the E.• The E is regenerated at the end of the reaction.

E + S ↔ ES → E + P

k1

k-1

k2

• The rate (velocity) of an enzymatic reaction depends on the [S].

• Fig. 6-8 shows the rate and the observed kinetics of an enzymatic reaction.

• In lower region of the curve (at low level of S) – V0 depends on S.

• In upper portion of the curve (at higher levels of S), the reaction is zero.

• At infinite [S], the reaction would proceed at its max velocity (Vmax)

• The [S] at which the reaction proceeds at one-half its Vmax has a special significance.

• It’s given the symbol KM (Michaelis constant) which considered an inverse measure of the affinity of the E for the S.

• The lower the KM, the higher the affinity.

• The Vmax for the E can be estimated from the graph. Thus, the value of KM also can be estimated from the graph. Fig. 6-9, p.142

SK

SVV

M max

• When experimental conditions are adjusted so that [S] = KM,

and

Note : Michaelis-Menten model is the simplest enzyme equation, where it’s considered the reaction of one single S to a single P.

: the term KM only appropriate for E that exhibit a hyperbolic curve of V vs [S].

SK

SVV

M max

SS

SVV

max

2maxV

V

Linearizing the

Michaelis-Menten

Equation• The curve that describe

the rate of nonallosteric enzymatic reaction is hyperbolic.

• It is considerably easier to work with straight line than a curve.

• The equation for a hyperbola transformed into an equation for a straight line by taking the reciprocal of both sides: Lineweaver-Burk double reciprocal plot

Fig. 6-10, p.143

maxmax

maxmax

max

111

1

1

VSV

K

V

SV

S

SV

K

V

SV

SK

V

M

M

M

Significance of KM and Vmax

• When V = Vmax / 2, then KM = [S] → interpret that KM is equals the concentration of S at which 50% of the enzyme’s active sites are occupied by S.

• Another interpretation of KM relies on the assumptions of the original Michaelis-Menten model of enzyme kinetics.

• The KM is a measure of how tightly the S is bound to the E. KM >>, the less tightly the S bound to the E.

• Vmax is related to the turnover number of an E, a quantity equal to the catalytic constant,k2. ( Vmax / [ET]) = turnover number = kcat or kp

- no. of moles of S that react to form P/mole E/unit time.

Illustrate the efficiency of enzymatic catalysis

How Do Enzymatics Reactions Respond to

Inhibitors?

Fig. 6-11, p.146

Inhibitor – a substance that interferes with the action of an enzyme and slows the rate of a reaction.

2 ways in which inhibitors can affect an enzymatic reaction:i.A reversible inhibitorii.An irreversible inhibitor

There 2 major classes of reversible inhibitors which can be distinguished on the basis of the sites on the E to which they bind:i.Competitive inhibitionii.Noncompetitive inhibition

Fig. 6-11b, p.146

Fig. 6-11c, p.146

Fig. 6-12, p.148

Kinetics of competitive inhibitionIn the presence of competitive inhibitor, the equation for an enzymatic reaction becomes

EI ↔ E ↔ ES → E + P

The dissociation constant for the E-I complex can be written:EI E + I KI = [E] [I] / [EI]

+ I +S

↔

Important: substrate or inhibitor can bind the enzyme, not both. Because both are vying for the same location, sufficiently high substrate will “outcompete” the inhibitor. This is why the Vmax does not change.

bxmy

VSK

I

V

K

V I

M

maxmax

1

][

1)][

1(1

Fig. 6-13, p.149

Kinetics of noncompetitive inhibitionIn the presence of noncompetitive inhibitor, the reaction pathway has become more complicated

E ↔ ES → E + P↕ ↕EI ↔ ESI

•The value of Vmax decreases, but KM remains the same; the inhibitor doesn’t interfere with the binding of S to the active site.

+I+S

+I

+S

bxmy

K

I

VSK

I

V

K

V II

M

)][

1(1

][

1)][

1(1

maxmax

Kinetics of uncompetitive inhibition

•The inhibitor can bind to the ES complex but not to free E.

•The Vmax decreases and KM decreases as well.

•Once the uncompetitive inhibitor biond to the complex, it will remain there. The enzymes loss their biology function → reaction STOP.

•e.g. drugs, heavy metal (Boron), iodoacetic acid

• Practice session

Sucrose is hydrolyzed to glucose and fructose. The reaction is catalyzed by the enzyme invertase. Using the following data, by the Lineweaver-Burk method, whether the inhibition of this reaction by 2 M is competitive or noncompetitive.

p.151a

[Sucrose] (mol L-1)

V, no inhibitor V, Inhibitor present

0.0292 0.182 0.083

0.0584 0.265 0.119

0.0876 0.311 0.154

0.117 0.330 0.167

0.175 0.372 0.192

Enzyme inhibition in the treatment of AIDS – important target is HIV protease that essential to the production of new virus particles in infected cells.Treatment is most effective when combination of drug therapies is used and HIV protease inhibitors play an important role.