Biochemistry

Chapter 13: Enzymes

Chapter 14: Mechanisms of enzyme action

Chapter 15: Enzyme regulation

Chapter 17: Metabolism- An overview

Chapter 18: Glycolysis

Chapter 19: The tricarboxylic acid cycle

Chapter 20: Electron transport & oxidative phosphorylation

Chapter 22: Gluconeogenesis, glycogen metabolism, and the pentose phosphate pathway

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Chapter 13

Enzymes – Kinetics and Specificity

Biochemistry

by

Reginald Garrett and Charles Grisham

What are enzymes, and what do they do?

Biological Catalysts Increase the velocity of chemical

reactions

What are enzymes, and what do they do?

• Thousands of chemical reactions are proceeding very rapidly at any given instant within all living cells

• Virtually all of these reactions are mediated by enzymes--proteins (and occasionally RNA) specialized to catalyze metabolic reactions

• Most cells quickly oxidize glucose, producing carbon dioxide and water and releasing lots of energy:

C6H12O6 + 6 O2 6 CO2 + 6 H2O + 2870 kJ of energy

• It does not occur under just normal conditions• In living systems, enzymes are used to accelerate and

control the rates of vitally important biochemical reactions

Figure 13.1Reaction profile showing large G‡ for glucose oxidation, free energy change of -2,870 kJ/mol; catalysts lower G‡, thereby accelerating rate.

Enzymes are the agents of metabolic function

• Enzymes form metabolic pathways by which– Nutrient molecules are degraded

– Energy is released and converted into metabolically useful forms

– Precursors are generated and transformed to create the literally thousands of distinctive biomolecules

• Situated at key junctions of metabolic pathways are specialized regulatory enzymes capable of sensing the momentary metabolic needs the cell and adjusting their catalytic rates accordingly

Figure 13.2The breakdown of glucose by glycolysis provides a prime example of a metabolic pathway. Ten enzymes mediate the reactions of glycolysis. Enzyme 4, fructose 1,6, biphosphate aldolase, catalyzes the C-C bond- breaking reaction in this pathway.

13.1 – What Characteristic Features Define Enzymes?

• Enzymes are remarkably versatile biochemical catalyst that have in common three distinctive features:1. Catalytic power2. Specificity3. Regulation

• Enzymes can accelerate reactions as much as 1016 over uncatalyzed rates!

• Urease is a good example:

– Catalyzed rate: 3x104/sec

– Uncatalyzed rate: 3x10 -10/sec

– Ratio is 1x1014 (catalytic power)

Catalytic power

Specificity

• Enzymes selectively recognize proper substances over other molecules

• The substances upon which an enzyme acts are traditionally called substrates

• Enzymes produce products in very high yields - often much greater than 95%

Figure 13.2The breakdown of glucose by glycolysis provides a prime example of a metabolic pathway. Ten enzymes mediate the reactions of glycolysis. Enzyme 4, fructose 1,6, biphosphate aldolase, catalyzes the C-C bond- breaking reaction in this pathway.

Figure 13.3 A 90% yield over 10 steps, for example, in a metabolic pathway, gives an overall yield of 35%. Therefore, yields in biological reactions must be substantially greater; otherwise, unwanted by-products would accumulate to unacceptable levels.

Specificity• The selective qualities of an enzyme are

recognized as its specificity

• Specificity is controlled by structure of enzyme – the unique fit of substrate with enzyme controls the

selectivity for substrate and the product yield

• The specific site on the enzyme where substrate binds and catalysis occurs is called the active site

Regulation • Regulation of an enzyme activity is essential to the

integration and regulation of metabolism• Because most enzymes are proteins, we can

anticipate that the functional attributes of enzymes are due to the remarkable versatility found in protein structure

• Enzyme regulation is achieved in a variety of ways, ranging from controls over the amount of enzyme protein produced by the cell to more rapid, reversible interactions of the enzyme with metabolic inhibitors and activators (chapter 15)

Nomenclature• Traditionally, enzymes often were named by adding

the suffix -ase to the name of the substrate upon which they acted: Urease for the urea-hydrolyzing enzyme or phosphatase for enzymes hydrolyzing phosphoryl groups from organic phosphate compounds

• Resemblance to their activity: protease for the proteolytic enzyme

• Trypsin and pepsin• International Union of Biochemistry and Molecular

Biology (IUBMB)http://www.chem.qmw.ac.uk/iubmb/enzyme/

• Enzymes Commission number: EC #.#.#.#

Nomenclature• A series of four number severe to specify a particular

enzyme– First number is class (1-6)– Second number is subclass– Third number is sub-subclass– Fourth number is individual entry

• For example, ATP:D-glucose-6-phosphotransferase (glucokinase) is listed as EC 2.7.1.2.

ATP + D-glucose ADP + D-glucose-6-phosphate– A phosphate group is transferred from ATP to C-6-OH

group of glucose, so the enzyme is a transferase (class 2)– Transferring phosphorus-containing groups is subclass 7– An alcohol group (-OH) as an acceptor is sub-subclass 1– Entry 2

Classification of protein enzymes

1. Oxidoreductases catalyze oxidation-reduction reactions

2. Transferases catalyze transfer of functional groups from one molecule to another

3. Hydrolases catalyze hydrolysis reactions4. Lyases catalyze removal of a group from or addition

of a group to a double bond, or other cleavages involving electron rearrangement

5. Isomerases catalyze intramolecular rearrangement (isomerization reactions)

6. Ligases catalyze reactions in which two molecules are joined (formation of bonds)

Garrett and Grisham, Biochemistry, Third Edition

EC 2.7.1.1 hexokinaseEC 2.7.1.2 glucokinaseEC 2.7.1.3 ketohexokinaseEC 2.7.1.4 fructokinaseEC 2.7.1.5 rhamnulokinaseEC 2.7.1.6 galactokinase...EC 2.7.1.156 adenosylcobinamide kinase

• Many enzymes require non-protein components called cofactors to aid in catalysis1. Coenzymes: many essential vitamins are

constituents of coenzyme

2. Cofactors: metal ions

metalloenzymes

• Holoenzyme: apoenzyme (protien) + prosthetic group

Other Aspects of Enzymes

• Mechanisms - to be covered in Chapter 14

• Regulation - to be covered in Chapter 15

• Coenzymes - to be covered in Chapter 17

13.2 – Can the Rate of an Enzyme-Catalyzed Reaction Be Defined in a

Mathematical Way?• Kinetics is concerned with the rates of chemical

reactions• Enzyme kinetics addresses the biological roles of

enzymatic catalyst and how they accomplish their remarkable feats

• In enzyme kinetics, we seek to determine the maximum reaction velocity that the enzyme can attain and its binding affinities for substrates and inhibitors

• These information can be exploited to control and manipulate the course of metabolic events

Chemical kineticsA P

(A I J P)

• rate or velocity (v)v = d[P] / dt or v = -d[A] / dt

• The mathematical relationship between reaction rate and concentration of reactant(s) is the rate law v = -d[A] / dt = k [A]

• k is the proportional constant or rate constant (the unit of k is sec-1)

Chemical kinetics

v = -d[A] / dt = k [A]

• v is first-order with respect to A The order of this reaction is a first-order

reaction

• molecularity of a reactionThe molecularity of this reaction equal 1

(unimolecular reaction)

Figure 13.4Plot of the course of a first-order reaction. The half-time, t1/2, is the time for one-half of the starting amount of A to disappear.

Chemical kineticsA + B P + Q

• The molecularity of this reaction equal 2 (bimolecular reaction)

• The rate or velocity (v)v = -d[A] / dt = -d[B] / dt = d[P] / dt = d[Q] / dt

• The rate law is v = k [A] [B]

• The order of this reaction is a second-order reaction

• The rate constant k has the unit of M-1 sec-1)

The Transition State• Reaction coordinate: a generalized measure of the

progress of the reaction• Free energy (G)• Standard state free energy (25 , 1 atm, 1 M/each)℃• Transition state

– The transition state represents an intermediate molecular state having a high free energy in the reaction.

• Activation energy:– Barriers to chemical reactions occur because a reactant

molecule must pass through a high-energy transition state to form products.

– This free energy barrier is called the activation energy.

Figure 13.5Energy diagram for a chemical reaction (A→P) and the effects of (a) raising the temperature from T1 to T2 or (b) adding a catalyst. Raising the temperature raises the average energy of A molecules, which increases the population of A molecules having energies equal to the activation energy for the reaction, thereby increasing the reaction rate. In contrast, the average free energy of A molecules remains the same in uncatalyzed versus catalyzed reactions (conducted at the same temperature). The effect of the catalyst is to lower the free energy of activation for the reaction.

Decreasing G‡ increase reaction rate

Two general ways may accelerate rates of chemical reactions

1. Raise the temperatureThe reaction rate are doubled by a 10℃

2. Add catalysts• True catalysts participate in the reaction, but are

unchanged by it. Therefore, they can continue to catalyze subsequent reactions.

• Catalysts change the rates of reactions, but do not affect the equilibrium of a reaction.

• Most biological catalysts are proteins called enzymes (E).

• The substance acted on by an enzyme is called a substrate (S).– Enzymes accelerate reactions by lowering the

free energy of activation – Enzymes do this by binding the transition state

of the reaction better than the substrate – The mechanism of enzyme action in Chapter

14

13.3 – What Equations Define the Kinetics of Enzyme-Catalyzed

Reactions?

• The Michaelis-Menten Equation

• The Lineweaver-Burk double-reciprocal plot

• Hanes-Woolf plot

Vmax [S]

Km + [S]v =

Figure 13.6 A plot of v versus [A] for the unimolecular chemical reaction, A→P, yields a straight line having a slope equal to k.

Figure 13.7 Substrate saturation curve for an enzyme-catalyzed reaction. The amount of enzyme is constant, and the velocity of the reaction is determined at various substrate concentrations. The reaction rate, v, as a function of [S] is described by a rectangular hyperbola. At very high [S], v = Vmax. That is, the velocity is limited only by conditions (temperature, pH, ionic strength) and by the amount of enzyme present; v becomes independent of [S]. Such a condition is termed zero-order kinetics. Under zero-order conditions, velocity is directly dependent on [enzyme]. The H2O molecule provides a rough guide to scale. The substrate is bound at the active site of the enzyme.

The Michaelis-Menten Equation• Louis Michaelis and Maud Menten's theory • It assumes the formation of an enzyme-substrate

complex (ES)

E + S ES

• At equilibriumk-1 [ES] = k1 [E] [S]

And

Ks = =

k1

k-1

[E] [S]

[ES]

k-1

k1

The Michaelis-Menten Equation

E + S ES E + P

• The steady-state assumptionES is formed rapidly from E + S as it disappears by dissociation to generate E + S and reaction to form E + P

d[ES] dt• That is; formation of ES = breakdown of ES

k1 [E] [S] = k-1[ES] + k2[ES]

k1

k-1

= 0

k2

Figure 13.8Time course for the consumption of substrate, the formation of product, and the establishment of a steady-state level of the enzyme-substrate [ES] complex for a typical enzyme obeying the Michaelis-Menten, Briggs-Haldane models for enzyme kinetics. The early stage of the time course is shown in greater magnification in the bottom graph.

The Michaelis-Menten Equation k1 [E] [S] = k-1[ES] + k2[ES] = (k-1+ k2) [ES]

[ES] = ( ) [E] [S]

Km =

Km is Michaelis constant

Km [ES] = [E] [S]

k-1+ k2

k1

k-1+ k2

k1

The Michaelis-Menten Equation Km [ES] = [E] [S]

Total enzyme, [ET] = [E] + [ES]

[E] = [ET] – [ES]

Km [ES] = ([ET] – [ES]) [S] = [ET] [S] – [ES] [S]

Km [ES] + [ES] [S] = [ET] [S]

(Km + [S]) [ES] = [ET] [S]

[ES] = Km + [S]

[ET] [S]

The Michaelis-Menten Equation

[ES] =

The rate of product formation is

v = k2 [ES]

v =

Vmax = k2 [ET] v =

Km + [S]

[ET] [S]

Km + [S]

k2 [ET] [S]

Km + [S]

Vmax [S]

Understanding Km

• The Michaelis constant Km measures the substrate concentration at which the reaction rate is Vmax/2.

• Associated with the affinity of enzyme for substrate

• Small Km means tight binding; high Km means weak binding

v =

When v = Vmax / 2

Vmax Vmax [S]

2 Km + [S]

Km + [S] = 2 [S]

[S] = Km

Km + [S]

Vmax [S]

=

Understanding Vmax

The theoretical maximal velocity • Vmax is a constant • Vmax is the theoretical maximal rate of the reaction -

but it is NEVER achieved in reality • To reach Vmax would require that ALL enzyme

molecules are tightly bound with substrate • Vmax is asymptotically approached as substrate is

increased

The dual nature of the Michaelis-Menten equation

Combination of 0-order and 1st-order kinetics

• When S is low ([s] << Km), the equation for rate is 1st order in S

• When S is high ([s] >>Km), the equation for rate is 0-order in S

• The Michaelis-Menten equation describes a rectangular hyperbolic dependence of v on S

• The actual estimation of Vmax and consequently Km is only approximate from each graph

Vmax [S]

Km + [S]v =

When S is low ([s] << Km), Km + [S]=Km

When S is high ([s] >>Km), Km + [S]= [S]

Vmax

Km

v = [S]

Vmax v =

The turnover numberA measure of catalytic activity

• kcat, the turnover number, is the number of substrate molecules converted to product per enzyme molecule per unit of time, when E is saturated with substrate.

• kcat is a measure of its maximal catalytic activity

• If the M-M model fits, k2 = kcat = Vmax/Et

• Values of kcat range from less than 1/sec to many millions per sec (Table 13.4)

The catalytic efficiency

Name for kcat/Km

An estimate of "how perfect" the enzyme is

• kcat/Km is an apparent second-order rate constant

v = (kcat/Km) [E] [S]• kcat/Km provides an index of the catalytic

efficiency of an enzyme • kcat/Km = k1 k2 / (k-1 + k2)

Linear Plots of the Michaelis-Menten Equation

• Lineweaver-Burk plot

• Hanes-Woolf plot

• Smaller and more consistent errors across the plot

• Nonlinear Lineweaver-Burk or Hanes-Woolf plots are a property of regulatory enzymes (allosteric enzymes)

Figure 13.9The Lineweaver-Burk double-reciprocal plot, depicting extrapolations that allow the determination of the x- and y-intercepts and slope.

V =

1 Km + [S]V Vmax [S]

Vmax [S]

Km + [S]

=

Figure 13.10A Hanes-Woolf plot of [S]/v versus [S], another straight-line rearrangement of the Michalelis-Menten equation.

Figure 13.11The pH activity profiles of four different enzymes. Trypsin, an intestinal protease, has slightly alkaline pH optimum, whereas pepsin, a gastric protease, acts in the acidic confines of the stomach and has a pH optimum near 2. Papain, a protease found in papaya, is relatively insensitive to pHs between 4 and 8. Cholinesterase activity is pH sensitive below pH 7 but not between pH 7 and 10. The cholinesterase pH activity profile suggests that an ionizable group with pK' near 6 is essential to its activity. Might it be a histidine residue within the active site?

Enzymatic activity is strongly influenced by pH

Figure 13.12 The effect of temperature on enzyme activity. The relative activity of an enzymatic reaction as a function of temperature. The decrease in the activity above 50°C is due to thermal denaturation.

13.4 – What Can Be Learned from the Inhibition of Enzyme Activity?

• Enzymes may be inhibited reversibly or irreversibly

1. Reversible inhibitors may bind at the active site (competitive) or at some other site (noncompetitive)

2. Enzymes may also be inhibited in an irreversible manner• Penicillin is an irreversible suicide

inhibitor

Competitive inhibition

km = km (1 + )app

E + S ES E + P+I

EI

k-1

k3

k1 kcat

V = = = kcat [E]t [S]

km (1 + [I]/ KI) + [S]

kcat [E]t [S] Vmax[S]

km + [S] km + [S]app app

[I]

KI

A competitive inhibitor competes with substrate for the binding site. It changes the apparent km.

k-3

KI= k-3 / k3

Figure 13.13Lineweaver-Burk plot of competitive inhibition, showing lines for no I, [I], and 2[I]. Note that when [S] is infinitely large (1/[S] 0), Vmax is the same, whether I is present of not. In the presence of I, the negative

mI

-1-intercept

[I]K 1 +

K

x

Noncompetitive inhibition

E + S ES E + P+ +I I

EI + S EIS

k-1

k3

k1 kcat

k-1

k1

Vmax = Vmax (1 + )app

V= = = {kcat (1 + [I]/ KI)} [E]t [S]

km + [S]

kcat [E]t [S] Vmax [S]

km + [S] km + [S]

app app

[I]

KI

k-3 k-3k3

Figure 13.15Lineweaver-Burk plot of pure noncompetitive inhibition. Note that I does not alter Km but that it decreases Vmax. In the presence of I, the y-intercept is equal to (1/Vmax)(1 + I/KI).

KI = KI’

Figure 13.16Lineweaver-Burk plot of mixed noncompetitive inhibition. Note that both intercepts and the slope change in the presence of I. (a) When KI is less than KI'; (b) when KI is greater than KI'.

KI = KI’

E + S ES E + P + I

EIS

k-1

k1 kcat

k-3k3

Uncompetitive inhibition

Figure 13.17Lineweaver-Burk plot of pure uncompetitive inhibition. Note that I does not alter Km but that it decreases Vmax. In the presence of I, the y-intercept is equal to (1/Vmax)(1 + I/KI).

Irreversible inhibition• Irreversible inhibition occurs when substances

combine covalently with enzymes so as to inactivate them irreversibly.

• Suicide substrates are inhibitory substrate analogs designed, via normal catalytic actions of the enzyme, a very reactive group is generated. This reactive group then forms a covalent bond with a nearby functional group within the active site of the enzyme, thereby causing irreversible inhibition

• Almost all irreversible enzyme inhibitors are toxic substances, either natural or synthetic. Such as penicillin

Figure 13.18Penicillin is an irreversible inhibitor of the enzyme glycoprotein peptidase, which catalyzes an essential step in bacterial cell wall synthesis. Penicillin consists of a thiazolidine ring fused to a -lactam ring to which a variable group R is attached. A reactive peptide bond in the -lactam ring covalently attaches to a serine residue in the active site of the glycopeptide transpeptidase. (The conformation of penicillin around its reactive peptide bond resembles the transition state of the normal glycoprotein peptidase substrate.) The penicilloyl-enzyme complex is catalytically inactive. The bond between the enzyme and penicillin is indefinitely stable; that is, penicillin binding is irreversible.

13.5 - What Is the Kinetic Behavior of Enzymes Catalyzing Bimolecular

Reactions?• Enzymes often use two (or more) substrates

Bisubstrate reactions:

A + B P + Q

1 Reactions may be sequential or single-displacement reactions

E + A + B AEB PEQ E + P + Q– And they can be random or ordered

2 Ping-pong or double-displacement reactions

enzyme

Figure 13.19 Single-displacement bisubstrate mechanism. Double-reciprocal plots of the rates observed with different fixed concentrations of one substrate (B here) are graphed versus a series of concentrations of A. Note that, in these Lineweaver-Burk plots for single-displacement bisubstrate mechanisms, the lines intersect to the left of the 1/v axis.

The conversion of AEB to PEQ is the rate-limiting step in random, single-displacement reactions

Figure 13.20Random, single-displacement bisubstrate mechanisms where A does not affect B binding, and vice versa. Note that the lines intersect at the 1/[A] axis. (If [B] were varied in an experiment with several fixed concentrations of A, the lines would intersect at the 1/[B] axis in a 1/v versus 1/[B] plot.)

Figure 13.21The structures of creatine and creatine phosphate, guanidinium compounds that are important in muscle energy metabolism.

In an ordered, single-displacement reaction

Similar to 1st-order reaction

double-displacement (ping-pong) reactions

Figure 13.22Double-displacement (ping-pong) bisubstrate mechanisms are characterized by Lineweaver-Burk plots of parallel lines when double-reciprocal plots of the rates observed with different fixed concentrations of the second substrate, B, are graphed versus a series of concentrations of A.

Figure 13.23Glutamate:aspartate aminotransferase, an enzyme conforming to a double-displacement bisubstrate mechanism. Glutamate:aspartate aminotransferase is a pyridoxal phosphate-dependent enzyme. The pyridoxal serves as the -NH2 acceptor from glutamate to form pyridoxamine. Pyridoxamine is then the amino donor to oxaloacetate to form asparate and regenerate the pyridoxal coenzyme form. (The pyridoxamine: enzyme is the E' form.) 

Glutamate:aspartate aminotransferase

13.6 – How Can Enzymes Be So Specific?

• “Lock and key” was the first explanation for specificity

• “Induced fit” provides a more accurate description

• Induced fit favors formation of the transition-state intermediate

Figure 13.24 A drawing, roughly to scale, of H2O, glycerol, glucose, and an idealized hexokinase molecule. Note the tow domains of structure in hexokinase (a), between which the active site is located. Binding of glucose induces a conformational change in hexokinase. The two domains close together, creating the catalytic site (b). The shaded area in (b) represents solvent inaccessible surface area in the active site cleft that results when the enzyme binds substrate.

13.7 – Are All Enzymes Proteins?

• Ribozymes– Segments of RNA that display enzyme activity in

the absence of protein

– Examples: RNase P and peptidyl transferase

• Abzymes– Antibodies raised to bind the transition state of a

reaction of interest

Figure 13.25RNA splicing in Tetrahymena rRNA maturation: (a) the guanosine-mediated reaction involved in the autocatalytic excision of the Tetrahymena rRNA intron, and (b) the overall splicing process. The cyclized intron is formed via nucleophilic attack of the 3'-OH on the phosphodiester bond that is 15 nucleotides from the 5'-GA end of the spliced-out intron. Cyclization frees a linear 15-mer with a 5'-GA end.

Figure 13.26 (a) The 50S subunit from H. marismortui. (b) The aminoacyl-tRNA (yellow) and the peptidyl-tRNA (orange) in the peptidyl transferase active site.

The Ribosome is a ribozymes

Figure 13.27 The peptidyl transferase reaction.

•Antigen: Transition state•1000X

Antibody molecules can have catalytic activity - Abzymes

13.8 Is It Possible to Design An Enzyme to Catalyze Any Desired Reaction?

• A known enzyme can be “engineered” by in vitro mutagenesis, replacing active site residues with new ones that might catalyze a desired reaction

• Another approach attempts to design a totally new protein with the desired structure and activity– This latter approach often begins with studies “in

silico” – i.e., computer modeling– Protein folding and stability issues make this approach

more difficult– And the cellular environment may provide

complications not apparent in the computer modeling

Figure 13.29 cis-1,2-Dichloroethylene (DCE) is an industrial solvent that poses hazards to human health.

Site-directed mutations (F108L, I129L, and C248I) have enabled the conversion of a bacterial epoxide hydrolase to catalyze the chlorinated epoxide hydrolase reaction.

(limited reaction)