6| Enzymes

CHAPTER 6 Enzymes

– Physiological significance of enzymes

– Origin of catalytic power of enzymes

– Chemical mechanisms of catalysis

– Mechanisms of chymotrypsin and lysozyme

– Description of enzyme kinetics and inhibition

topics about enzyme function:

What are enzymes?

• Enzymes are catalysts

• Increase reaction rates without being used up

• Most enzymes are globular proteins

• However, some RNA (ribozymes and ribosomal RNA)

also catalyze reactions

• We will celebrate my inspiration, the Biochemist Louis

Pasteur.

Why do cells evolve biocatalysis over inorganic

catalysts?

• Greater reaction specificity: avoids side products

• Milder reaction conditions: conducive to conditions in cells

• Higher reaction rates: in a biologically useful timeframe

• Capacity for regulation: control of biological pathways

COO

OH

O COO

COO

O COO

NH2

OOC

COO

O

OH

OH

COO

NH2

COO

-

-

-

-

-

-

-

-Chorismate mutase

• Metabolites have many

potential pathways of

decomposition

• Enzymes make the

desired one most

favorable

Enzyme-Substrate Complex

• Enzymes act by binding substrates

– The noncovalent enzyme substrate complex is known as the Michaelis complex

– Description of chemical interactions

– Development of kinetic equations

][

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m

cat

Enzyme-Substrate Complex

• Binding of a substrate to

an enzyme at the active

site. The enzyme

chymotrypsin with bound

substrate (PDB ID 7GCH).

• Some key active-site

amino acid residues

appear as a red splotch on

the enzyme surface.

Enzymatic Catalysis

• Enzymes do not affect equilibrium (ΔG)

• Slow reactions face significant activation barriers (ΔG‡) that must be surmounted during the reaction

• Enzymes increase reaction rates (k) by

decreasing ΔG‡

k kBT

h

expG

RT

Reaction Coordinate Diagram

• Reaction coordinate diagram.

The free energy of the system is

plotted against the progress of the

reaction S P. A diagram of this

kind is a description of the energy

changes during the reaction, and

the horizontal axis (reaction

coordinate) reflects the progressive

chemical changes (e.g., bond

breakage or formation) as S is

converted to P. The activation

energies, ∆G‡, for the S P and

P S reactions are indicated. ∆G ’

° is the overall standard free-

energy change in the direction S

P.

Enzymes Decrease ΔG‡

• Reaction coordinate diagram

comparing enzyme-catalyzed

and uncatalyzed reactions. In

the reaction S P, the ES and

EP intermediates occupy

minima in the energy progress

curve of the enzymecatalyzed

reaction. The terms ∆G‡uncat

and ∆G‡cat correspond to the

activation energy for the

uncatalyzed reaction and the

overall activation energy for the

catalyzed reaction,

respectively. The activation

energy is lower when the

enzyme catalyzes the reaction.

Rate Enhancement by Enzymes

How to Lower G

Enzymes organize reactive groups into close proximity and

proper orientation

• Uncatalyzed bimolecular reactions

two free reactants single restricted transition state

conversion is entropically unfavorable

• Uncatalyzed unimolecular reactions

flexible reactant rigid transition state conversion is

entropically unfavorable for flexible reactants

• Catalyzed reactions

Enzyme uses the binding energy of substrates to organize

the reactants to a fairly rigid ES complex

Entropy cost is paid during binding

Rigid reactant complex transition state conversion is

entropically OK

Support for the Proximity Model

The rate of anhydride formation from esters and carboxylates shows a strong dependence on proximity of two reactive groups.

Shown here are reactions of an ester with a carboxylate group to form

an anhydride. The R group is the same in each case. (a) For this

bimolecular reaction, the rate constant k is second-order, with units of

M-1s-1. (b) When the two reacting groups are in a single molecule, and

thus have less freedom of motion, the reaction is much faster. For this

unimolecular reaction, k has units of s-1. Dividing the rate constant for

(b) by the rate constant for (a) gives a rate enhancement of about 105

M. (The enhancement has units of molarity because we are comparing

a unimolecular and a bimolecular reaction.) Put another way, if the

reactant in (b) were present at a concentration of 1 M, the reacting

groups would behave as though they were present at a concentration

of 105 M. Note that the reactant in (b) has freedom of rotation about

three bonds (shown with curved arrows), but this still represents a

substantial reduction of entropy over (a). If the bonds that rotate in (b)

are constrained as in (c), the entropy is reduced further and the

reaction exhibits a rate enhancement of 108 M relative to (a).

From previous slide;

How to Lower G

Enzymes bind transition states best

• The idea was proposed by Linus Pauling in 1946 – Enzyme active sites are complimentary to the

transition state of the reaction

– Enzymes bind transition states better than substrates

– Stronger/additional interactions with the transition state as compared to the ground state lower the activation barrier

Illustration of TS Stabilization Idea: Imaginary Stickase

An imaginary enzyme (stickase) designed to catalyze breakage of a

metal stick. (a) Before the stick is broken, it must first be bent (the

transition state). In both stickase examples, magnetic interactions take the

place of weak bonding interactions between enzyme and substrate. (b) A

stickase with a magnet-lined pocket complementary in structure to the stick

(the substrate) stabilizes the substrate. Bending is impeded by the

magnetic attraction between stick and stickase. (c) An enzyme with a

pocket complementary to the reaction transition state helps to destabilize

the stick, contributing to catalysis of the reaction. The binding energy of the

magnetic interactions compensates for the increase in free energy required

to bend the stick. Reaction coordinate diagrams (right) show the energy

consequences of complementarity to substrate versus complementarity to

transition state (EP complexes are omitted). ∆GM, the difference between

the transition-state energies of the uncatalyzed and catalyzed reactions, is

contributed by the magnetic interactions between the stick and stickase.

When the enzyme is complementary to the substrate (b), the ES complex

is more stable and has less free energy in the ground state than substrate

alone. The result is an increase in the activation energy.

Catalytic Mechanisms

– acid-base catalysis: give and take protons

– covalent catalysis: change reaction paths

– metal ion catalysis: use redox cofactors, pKa

shifters

– electrostatic catalysis: preferential interactions with

TS

General Acid-Base Catalysis

• How a catalyst circumvents

unfavorable charge development

during cleavage of an amide. The

hydrolysis of an amide bond, shown

here, is the same reaction as that

catalyzed by chymotrypsin and other

proteases. Charge development is

unfavorable and can be

circumvented by donation of a proton

by H3O+ (specific acid catalysis) or

HA (general acid catalysis), where

HA represents any acid. Similarly,

charge can be neutralized by proton

abstraction by OH– (specific base

catalysis) or B: (general base

catalysis), where B: represents any

base.

Amino Acids in General Acid-Base

Catalysis • Amino acids in general acid-

base catalysis. Many organic

reactions that are used to model

biochemical processes are

promoted by proton donors

(general acids) or proton

acceptors (general bases). The

active sites of some enzymes

contain amino acid functional

groups, such as those shown

here, that can participate in the

catalytic process as proton

donors or proton acceptors.

Covalent Catalysis

• A transient covalent bond between the enzyme and the substrate

• Changes the reaction Pathway

– Uncatalyzed:

– Catalyzed:

• Requires a nucleophile on the enzyme

– Can be a reactive serine, thiolate, amine, or carboxylate

B A B—AOH2

B :X A B X—A :X B—AOH2

Metal Ion Catalysis

• Involves a metal ion bound to the enzyme

• Interacts with substrate to facilitate binding

– Stabilizes negative charges

• Participates in oxidation reactions

Chymotrypsin uses most of

the enzymatic mechanisms

Structure of chymotrypsin. (PDB ID 7GCH) (c) The polypeptide

backbone as a ribbon structure. Disulfide bonds are yellow; the three

chains are colored as in part (a).

Active Site of Chymotrypsin with Substrate • Structure of chymotrypsin. (PDB ID

7GCH) (d) A close-up of the active site

with a substrate (white and yellow)

bound. The hydroxyl of Ser195 attacks

the carbonyl group of the substrate (the

oxygens are red); the developing

negative charge on the oxygen is

stabilized by the oxyanion hole (amide

nitrogens from Ser195 and Gly193, in

blue), as explained in Figure 6–22. The

aromatic amino acid side chain of the

substrate (yellow) sits in the

hydrophobic pocket. The amide nitrogen

of the peptide bond to be cleaved

(protruding toward the viewer and

projecting the path of the rest of the

substrate polypeptide chain) is shown in

white.

Chymotrypsin Mechanism Step 1: Substrate Binding

(step 1) Hydrolytic cleavage of a peptide bond by chymotrypsin.

The reaction has two phases. In the acylation phase (steps 1 to 4),

formation of a covalent acyl-enzyme intermediate is coupled to cleavage

of the peptide bond. In the deacylation phase (steps 5 to 7), deacylation

regenerates the free enzyme; this is essentially the reverse of the

acylation phase, with water mirroring, in reverse, the role of the amine

component of the substrate.

Chymotrypsin Mechanism Step 2: Nucleophilic Attack

Chymotrypsin Mechanism Step 3: Substrate Cleavage

Chymotrypsin Mechanism Step 4: Water Comes In

Chymotrypsin Mechanism Step 5: Water Attacks

Chymotrypsin Mechanism Step 6: Break-off from the Enzyme

Chymotrypsin Mechanism Step 7: Product Dissociates

Peptidoglycan and Lysozyme

• Peptidoglycan is a polysaccharide found in many bacterial cell walls

• Cleavage of the cell wall leads to the lysis of bacteria

• Lysozyme is an antibacterial enzyme

Peptidoglycan and Lysozyme

Hen egg white lysozyme and the

reaction it catalyzes. (b) Reaction

catalyzed by hen egg white lysozyme. A

segment of a peptidoglycan polymer is

shown, with the lysozyme binding sites

A through F shaded. The glycosidic C—

O bond between sugar residues bound

to sites D and E is cleaved, as indicated

by the red arrow. The hydrolytic

reaction is shown in the inset, with the

fate of the oxygen in the H2O traced in

red. Mur2Ac is N-acetylmuramic acid;

GlcNAc, N-acetylglucosamine. RO—

represents a lactyl (lactic acid) group;

—NAc and AcN—, an N-acetyl group

(see key).

X-ray structures of lysozyme with bound substrate analogs show that the C-1 carbon is located between Glu 35 and Asp 52 residues.

General Acid-Base + Covalent Catalysis: Cleavage of Peptidoglycan by Lysozyme

From previous slide; Lysozyme reaction.

• In this reaction, the water introduced into the product

at C-1 of Mur2Ac is in the same configuration as the

original glycosidic bond. The reaction is thus a

molecular substitution with retention of configuration.

(b) A surface rendering of the lysozyme active site

with the covalent enzyme-substrate intermediate

shown as a ball-and-stick structure. Side-chains of

active-site residues are shown as ball-and-stick

structures protruding from ribbons (PDB ID 1H6M).

Cleavage of Peptidoglycan by Lysozyme: Two Successive SN2 Steps Model

• Asp 52 acts as a nucleophile to attack the anomeric carbon in the first SN2 step

• Glu 35 acts as a general acid and protonates the leaving group in the transition state

• Water hydrolyzes the covalent glycosyl-enzyme intermediate

• Glu 35 acts as a general base to deprotonate water in the second SN2 step

Experimental work I

am no longer

allowed to enjoy!

What are enzymes?

• Enzymes are catalysts

• Increase reaction rates without being used up

• Most enzymes are globular proteins

• However, some RNA (ribozymes and ribosomal RNA)

also catalyze reactions

• We will celebrate my inspiration, the Biochemist Louis

Pasteur.

Why biocatalysis over inorganic catalysts?

• Greater reaction specificity: avoids side products

• Milder reaction conditions: conducive to conditions in cells

• Higher reaction rates: in a biologically useful timeframe

• Capacity for regulation: control of biological pathways

COO

OH

O COO

COO

O COO

NH2

OOC

COO

O

OH

OH

COO

NH2

COO

-

-

-

-

-

-

-

-Chorismate mutase

• Metabolites have many

potential pathways of

decomposition

• Enzymes make the

desired one most

favorable

What is enzyme kinetics?

• Kinetics is the study of the rate at which compounds react

• Rate of enzymatic reaction is affected by:

– enzyme

– substrate

– effectors

– temperature

Why study enzyme kinetics?

• Quantitative description of biocatalysis

• Determine the order of binding of substrates

• Elucidate acid-base catalysis

• Understand catalytic mechanism

• Find effective inhibitors

• Understand regulation of activity

How to Do Kinetic Measurements Experiment:

1)Mix enzyme + substrate

2)Record rate of substrate disappearance/product formation as a

function of time (the velocity of reaction)

3)Plot initial velocity versus substrate concentration.

4)Change substrate concentration and repeat

A theoretical enzyme catalyzes the reaction S ↔ P, and is

present at a concentration sufficient to catalyze the

reaction at a maximum velocity, Vmax, of 1 μM/min. The

Michaelis constant, Km (explained in the text), is 0.5 μM.

Progress curves are shown for substrate concentrations

below, at, and above the Km. The rate of an enzyme-

catalyzed reaction declines as substrate is converted to

product. A tangent to each curve taken at time = 0 defines

the initial velocity, V0, of each reaction.

From previous slide; Initial velocities of enzyme- catalyzed reactions

Effect of Substrate Concentration

• Ideal rate: • Deviations due to:

– limitation of measurements – substrate inhibition – substrate prep contains inhibitors – enzyme prep contains inhibitors

SK

SVv

m

][max

Effect of Substrate Concentration • Effect of substrate concentration on the

initial velocity of an enzyme-catalyzed

reaction. The maximum velocity, Vmax, is

extrapolated from the plot because V0

approaches but never quite reaches Vmax.

The substrate concentration at which V0 is

half maximal is Km, the Michaelis constant.

The concentration of enzyme in an

experiment such as this is generally so low

that [S] >> [E] even when [S] is described

as low or relatively low. The units shown

are typical for enzyme-catalyzed reactions

and are given only to help illustrate the

meaning of V0 and [S]. (Note that the

curve describes part of a rectangular

hyperbola, with one asymptote at Vmax. If

the curve were continued below [S] = 0, it

would approach a vertical asymptote at [S]

= –Km.)

Saturation Kinetics:

At high [S] velocity does not depend on [S]

• Dependence of initial velocity on

substrate concentration. This graph shows

the kinetic parameters that define the limits

of the curve at high and low [S]. At low [S],

Km >> [S] and the [S] term in the

denominator of the Michaelis-Menten

equation (Eqn 6-9) becomes insignificant.

The equation simplifies to V0 = Vmax[S]/Km

and V0 exhibits a linear dependence on [S],

as observed here. At high [S], where [S] >>

Km, the Km term in the denominator of the

Michaelis-Menten equation becomes

insignificant and the equation simplifies to V0

= Vmax; this is consistent with the plateau

observed at high [S]. The Michaelis-Menten

equation is therefore consistent with the

observed dependence of V0 on [S], and the

shape of the curve is defined by the terms

Vmax/Km at low [S] and Vmax at high [S].

Determination of Kinetic Parameters

Nonlinear Michaelis-Menten plot should be used to calculate parameters Km and Vmax.

Linearized double-reciprocal plot is good for analysis of two-substrate data or inhibition.

Lineweaver-Burk Plot: Linearized, Double-Reciprocal

Derivation of Enzyme Kinetics Equations

• Start with a model mechanism

• Identify constraints and assumptions

• Carry out algebra ...

– ... or graph theory for complex reactions

• Simplest Model Mechanism: E + S ES E + P

– One reactant, one product, no inhibitors

Identify Constraints and Assumptions

• Total enzyme concentration is constant – Mass balance equation for enzyme: ETot = [E] + [ES]

– It is also implicitly assumed that: STot = [S] + [ES] ≈ [S]

• Steady state assumption

• What is the observed rate? – Rate of product formation

vnet dP

dt k[ES]

0ESofbreakdownofrateESofformationofrate][

dt

ESd

Carry out the algebra

• The final form in case of a single substrate is

• kcat (turnover number): how many substrate molecules

can one enzyme molecule convert per second

• Km (Michaelis constant): an approximate measure of

substrate’s affinity for enzyme

• Microscopic meaning of Km and kcat depends on the details

of the mechanism

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SK

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m

totcat

Enzyme efficiency is limited by diffusion: kcat/KM

• Can gain efficiency by having high velocity or affinity for substrate

– Catalase vs. acetylcholinesterase

Two-Substrate Reactions

• Kinetic mechanism: the order of binding of substrates and release of products

• When two or more reactants are involved, enzyme kinetics allows to distinguish between different kinetic mechanisms

– Sequential mechanism – Ping-Pong mechanism

• Common mechanisms for enzyme-

catalyzed bisubstrate reactions. (a) The enzyme and both substrates come together to form a ternary complex. In ordered binding, substrate 1 must bind before substrate 2 can bind productively. In random binding, the substrates can

bind in either order. (b) An enzyme-substrate complex forms, a product leaves the complex, the altered enzyme forms a second complex with another substrate molecule, and the second product leaves, regenerating the enzyme. Substrate 1 may transfer a functional group to the enzyme (to form the covalently modified E’), which is subsequently transferred to substrate 2. This is called a Ping-Pong or double-displacement mechanism.

Sequential Kinetic Mechanism

• We cannot easily distinguish random from ordered • Random mechanisms in equilibrium will give

intersection point at y-axis • Lineweaver-Burk: lines intersect

• Steady-state kinetic analysis

of bisubstrate reactions. In

these double-reciprocal plots

(see Box 6-1), the concentration

of substrate 1 is varied while the

concentration of substrate 2 is

held constant. This is repeated

for several values of [S2],

generating several separate

lines. (a) Intersecting lines

indicate that a ternary complex is

formed in the reaction.

Ping-Pong Kinetic Mechanism

Lineweaver-Burk: lines are parallel • Steady-state kinetic

analysis of bisubstrate

reactions. In these double-

reciprocal plots (see Box 6-

1), the concentration of

substrate 1 is varied while

the concentration of

substrate 2 is held constant.

This is repeated for several

values of [S2], generating

several separate lines. (b)

parallel lines indicate a

Ping-Pong (double-

displacement) pathway.

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

• Competes with substrate for binding – Binds active site – Does not affect catalysis

• No change in Vmax; apparent increase in KM

• Lineweaver-Burk: lines intersect at the y-axis

Competitive Inhibition

Competitive Inhibition

Competitive Inhibition

Uncompetitive Inhibition

• Only binds to ES complex • Does not affect substrate binding • Inhibits catalytic function

• Decrease in Vmax; apparent decrease in KM

• No change in KM/Vmax • Lineweaver-Burk: lines are parallel

Uncompetitive Inhibition

Uncompetitive Inhibition

Mixed Inhibition

• Binds enzyme with or without substrate ― Binds to regulatory site ― Inhibits both substrate binding and catalysis

• Decrease in Vmax; apparent change in KM • Lineweaver-Burk: lines intersect left from the y-axis • Noncompetitive inhibitors are mixed inhibitors such

that there is no change in KM

Mixed Inhibition

Mixed Inhibition

Enzyme activity can be regulated

• Regulation can be: – noncovalent modification

– covalent modification

– irreversible

– reversible

Noncovalent Modification: Allosteric Regulators

The kinetics of allosteric regulators differ from Michaelis-Menten kinetics.

Aspartate transcarbamylase;

From previous slide

• Substrate-activity curves for representative allosteric enzymes.

Three examples of complex responses of allosteric enzymes to their

modulators. (a) The sigmoid curve of a homotropic enzyme, in which

the substrate also serves as a positive (stimulatory) modulator, or

activator. Note the resemblance to the oxygen-saturation curve of

hemoglobin. The sigmoidal curve is a hybrid curve in which the

enzyme is present primarily in the relatively inactive T state at low

substrate concentration, and primarily in the more active R state at

high substrate concentration. The curves for the pure T and R states

are plotted separately in color. ATCase exhibits a kinetic pattern

similar to this. (b) The effects of several different concentrations of a

positive modulator (+) or a negative modulator (-) on an allosteric

enzyme in which K0.5 is altered without a change in Vmax. The central

curve shows the substrate-activity relationship without a modulator.

For ATCase, CTP is a negative modulator and ATP is a positive

modulator.

Some Reversible Covalent Modifications

Zymogens are activated by irreversible covalent modification

From previous slide; Activation of zymogens by proteolytic cleavage.

• Shown here is the formation of chymotrypsin and trypsin from their zymogens, chymotrypsinogen and trypsinogen. The bars represent the amino acid sequences of the polypeptide chains, with numbers indicating the positions of the residues (the amino-terminal residue is number 1). Residues at the termini of the polypeptide fragments generated by cleavage are indicated below the bars. Note that in the final active forms, some numbered residues are missing. Recall that the three polypeptide chains (A, B, and C) of chymotrypsin are linked by disulfide bonds (see Fig. 6–19).

The blood coagulation cascade uses irreversible

covalent modification

• The coagulation cascades.

The interlinked intrinsic and

extrinsic pathways leading to

the cleavage of fibrinogen to

form active fibrin are shown.

Active serine proteases in

the pathways are shown in

blue. Green arrows denote

activating steps, and red

arrows indicate inhibitory

processes.

Some enzymes use

multiple types of regulation

• Regulation of muscle glycogen phosphorylase activity by

phosphorylation. The activity of glycogen phosphorylase in muscle is

subjected to a multilevel system of regulation involving much more than the

covalent modification (phosphorylation) shown in Figure 6–36. Allosteric

regulation, and a regulatory cascade sensitive to hormonal status that acts on

the enzymes involved in phosphorylation and dephosphorylation, also play

important roles. The activity of both forms of the enzyme is allosterically

regulated by an activator (AMP) and by inhibitors (glucose 6-phosphate and

ATP) that bind to separate sites on the enzyme. The activities of phosphorylase

kinase and phosphorylase phosphatase 1 (PP1) are also regulated by covalent

modification, via a short pathway that responds to the hormones glucagon and

epinephrine. One path leads to the phosphorylation of phosphorylase kinase

and phosphoprotein phosphatase inhibitor 1 (PPI-1). The phosphorylated

phosphorylase kinase is activated and in turn phosphorylates and activates

glycogen phosphorylase. At the same time, the phosphorylated PPI-1 interacts

with and inhibits PP1. PPI-1 also keeps itself active (phosphorylated) by

inhibiting phosphoprotein phosphatase 2B (PP2B), the enzyme that

dephosphorylates (inactivates) it. In this way, the equilibrium between the a and

b forms of glycogen phosphorylase is shifted decisively toward the more active

glycogen phosphorylase a. Note that the two forms of phosphorylase kinase are

both activated to a degree by Ca2+ ion (not shown). This pathway is discussed

in more detail in Chapters 14, 15, and 23.