Champion CS DeivanayagamCenter for Biophysical Sciences and EngineeringUniversity of Alabama at BirminghamBirmingham, AL 35294-4400

Enzyme Kinetics

Lectures 1 and 2

August 21st 2009

What are enzymes, and what do they do?What characteristic features define enzymes?Can the rate of an enzyme-catalyzed reaction be defined in a

mathematical way?What equations define the kinetics of enzyme-catalyzed

reactions?What can be learned from the inhibition of enzyme activity?What is the kinetic behavior of enzymes catalyzing bimolecular

reactions?How can enzymes be so specific? Are all enzymes proteins?Is it possible to design an enzyme to catalyze any desired

reaction?

What are you supposed to know from the lecture: (for your exam )1. Definitions of :

A. An Enzyme (catalytic power, specificity and regulation)B. Co-enzyme, co-factors, holoenzyme, apoenzymeC. Active site

2. How do enzymes affect the thermodynamics of a reaction ?

3. Understanding the Michaelis-Menten constants (Km, Vmax)

4. Define turn-over rate

5. Define catalytic efficiency

6. What are single and double displacement reactions ?

7. The lock and key as well as induced fit hypothesis as related to the specificity of enzymes

Virtually All Reactions in Cells Are Mediated by Enzymes

• Enzymes catalyze thermodynamically favorable reactions, causing them to proceed at extraordinarily rapid rates

• Enzymes provide cells with the ability to exert kinetic control over thermodynamic potentiality

• Living systems use enzymes to accelerate and control the rates of vitally important biochemical reactions

• Enzymes are the agents of metabolic function

Reaction profile showing the large free energy of activation for glucose oxidation. Enzymes lower ΔG‡, thereby accelerating rate.

What Characteristic Features Define Enzymes?

• Catalytic power is defined as the ratio of the enzyme-catalyzed rate of a reaction to the uncatalyzed rate

• Specificity is the term used to define the selectivity of enzymes for their substrates

• Regulation of enzyme activity ensures that the rate of metabolic reactions is appropriate to cellular requirements

• Enzyme nomenclature provides a systematic way of naming metabolic reactions• Coenzymes and cofactors are nonprotein components essential to enzyme activity.

The ratio of the Enzyme-catalyzed rate of reaction to the uncatalyzed rate

Enzymes can accelerate reactions as much as 1016 over uncatalyzed rates

Urease is a good example: O ||

H2N –C-NH2 + 2H2O + H+ 2NH4+ + HHCO3

-

Catalyzed rate: 3x104/sec Uncatalyzed rate: 3x10 -10/sec Ratio is 1x1014

Catalytic power

Specificity

• Enzymes selectively recognize proper substrates over other molecules

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

• Specificity is controlled by structure - the unique fit of substrate with enzyme controls the selectivity for substrate and the product yield

Regulation

• Regulation of enzyme activity is essential to the integration and regulation of metabolism.

• Availability of substrates and co-factors determines how fast the reaction goes

• Genetic regulation of enzyme synthesis and decay determines the amount of enzyme present at any moment.

Enzyme Nomenclature Provides a Systematic Way of Naming Metabolic Reactions

• Suffix –ase added to the substrate is the traditional way of naming enzymes

• Examples: Phosphotase, protease.• Outliers: Trypsin, pepsin, catalase

• International commission on Enzymes• Six classes of reactions (Oxidoreductases, Transferases,

Hydrolases, Lyases, Isomerases, Ligases).• Each class has subclasses• Depending on the type of reactions

Coenzymes and Cofactors are Nonprotein components essential to Enzyme Activity

Co-factors: are generally metal ionsCo-Enzymes: Vitamins, NAD, TPP, FAD

Tightly bound co-enzymes are referred to as ‘Prosthetic groups’ of the enzyme, and such a combination is called a ‘Haloenzyme’ and in the absence of the co-enzyme the protein is referred to as ‘Apo-enzyme’

Can the Rate of an Enzyme-Catalyzed Reaction Be Defined in a Mathematical Way?

• Kinetics is the branch of science concerned with the rates of reactions

• Enzyme kinetics seeks to determine the maximum reaction velocity that enzymes can attain and binding affinities for substrates and inhibitors

• Analysis of enzyme rates yields insights into enzyme mechanisms and metabolic pathways

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

Several kinetics terms to understand

• rate or velocity • rate constant • rate law • order of a reaction • molecularity of a reaction

Exploring Enzyme Kinetics

• Consider a reaction of overall stoichiometry as shown:

• The rate is proportional to the concentration of A

[ ] [ ]

[ ] [ ]

A Pd P d Avdt dtAv k Adt

Enzyme Kinetics• The simple elementary reaction of A→P is a first-order reaction• Figure shows the course of a first-order reaction as a function of time

• .

• This is a unimolecular reaction• For a bimolecular reaction, the rate law is:• v = k[A][B]• Kinetics cannot prove a reaction mechanism• Kinetics can only rule out various alternative hypotheses because they don’t fit

the data

The half-time, t1/2 is the time for one-half of the starting amount of A to disappear

Catalysts Lower the Free Energy of Activation for a Reaction

• A typical enzyme-catalyzed reaction must pass through a transition state• The transition state sits at the apex of the energy profile in the energy diagram• The reaction rate is proportional to the concentration of reactant molecules with the

transition-state energy• This energy barrier is known as the free energy of activation• Decreasing ΔG‡ increases the reaction rate• The activation energy is related to the rate constant by: /G RTk Ae

Understand the difference between G and G‡

• The overall free energy change for a reaction is related to the equilibrium constant • The free energy of activation for a reaction is related to the rate constant • It is extremely important to appreciate this distinction

What Equations Define the Kinetics of Enzyme-Catalyzed Reactions?• Simple first-order reactions display a plot of the reaction rate as a function of

reactant concentration that is a straight line

• Enzyme-catalyzed reactions are more complicated• At low concentrations of the enzyme substrate, the rate is proportional to S, as in

a first-order reaction• At higher concentrations of substrate, the enzyme reaction approaches zero-

order kinetics• This behavior is a saturation effect

[ES] Remains Constant Through Much of the Enzyme Reaction Time Course in Michaelis-Menten Kinetics

Time course for a typical enzyme-catalyzed reaction obeying the Michaelis-Menten, Briggs-Haldane models for enzyme kinetics. The early state of the time course is shown in greater magnification in the bottom graph.

d[ES]/dt = 0 defines a steady state

The Michaelis-Menten Equation is the Fundamental Equation of Enzyme Kinetics• Louis Michaelis and Maud Menten's theory

• The second step defines the formation of the product P

Km = (k-1 + k2)/k1

Km is the Michaelis constant

E + S ESk1

k-1

k-1[ES] = k1 [E][S]Ks= k-1/ k1 = [E][S]/[ES]

Ks – enzyme:substrate dissociation constant

E + S ES E + Pk1

k-1

k2

ET = E + ES

ET = E + ES or alternatively E = ET -ES

At steady state d[ES]/dt = 0 then, Vf = Vd then

vf = k1 ([ET] – [ES]) [S)Rate of formation

vd = (k-1 + k2)[ES]Rate of disappearance

k1 ([ET] – [ES]) [S] / [ES] = (k-1 + k2)/k1 = Km or alternatively [ES] = [ET] [S]/ Km + [S]

E + S ES E + Pk1

k-1

k2

Assume that the ES complex is in rapid equilibrium with free enzyme

Product formation: v = d[P]/dt = k2 [ES]

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

v= k2 [ET] [S] / Km + [S]

At saturation [ES] complex is equal to the total enzyme concentration ET , then[S] >> [ET] (and Km), [ET] = [ES] and therefore

v = Vmax = k2 [ET] = Vmax [S] / Km + [S] -Michealis-Menton Equation

When [S] = Km, then V = Vmax / 2

Understanding Km

The "kinetic activator constant"

• Km is a constant

• Km is a constant derived from rate constants

• Km is, under true Michaelis-Menten conditions, an estimate of the dissociation constant of E from S

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

The Km values for some enzymes and their substrates

Understanding VmaxThe 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, the equation for rate is 1st order in S

• When S is high, the equation for rate is 0-order in S

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

The Turnover Number Defines the Activity of One Enzyme Molecule

A 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.

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

• Values of kcat range from less than 1/sec to many millions per sec

The Ratio kcat/Km Defines the Catalytic Efficiency of an EnzymeThe catalytic efficiency: kcat/Km

An estimate of "how perfect" the enzyme is • kcat/Km is an apparent second-order rate constant • It measures how the enzyme performs when S is low • The upper limit for kcat/Km is the diffusion limit - the rate at which E and S diffuse

together

Linear Plots Can Be Derived from the Michaelis-Menten Equationderive these equations • Lineweaver-Burk:• Begin with v = Vmax[S]/(Km + [S]) and take the reciprocal of both sides

• Rearrange to obtain the Lineweaver-Burk equation:

• A plot of 1/v versus 1/[S] should yield a straight line

max max

1 1 1[ ]

mKv V S V

• Hanes-Woolf:• Begin with Lineweaver-Burk and divide both sides by [S] to obtain:

• Hanes-Woolf is best - why? • Because Hanes-Woolf has smaller and more consistent errors across the plot

max max

[ ] 1 [ ] mKS Sv V V

Enzymatic Activity is Strongly Influenced by pH• Enzyme-substrate recognition and catalysis are greatly dependent on pH• Enzymes have a variety of ionizable side chains that determine its secondary and

tertiary structure and also affect events in the active site• Substrate may also have ionizable groups• Enzymes are usually active only over a limited range of pH• The effects of pH may be due to effects on Km or Vmax or both

The Response of Enzymatic Activity to Temperature is Complex• Rates of enzyme-catalyzed reactions generally increase with increasing

temperature• However, at temperatures above 50° to 60° C, enzymes typically show a decline

in activity• Two effects here:

– Enzyme rate typically doubles in rate for ever 10°C as long as the enzyme is stable and active

– At higher temperatures, the protein becomes unstable and denaturation occurs

What Can Be Learned from the Inhibition of Enzyme Activity?• Enzymes may be inhibited reversibly or irreversibly• Reversible inhibitors may bind at the active site or at some other site• Enzymes may also be inhibited in an irreversible manner• Penicillin is an irreversible suicide inhibitor

Competitive Inhibitors Compete With Substrate for the Same Site on the Enzyme

Lineweaver-Burk plot of competitive inhibition, showing lines for no I, [I], and 2[I].

The Vmax is unaffected, but the Km’s are affected by the inhibitor.

Pure Noncompetitive Inhibition – where S and I bind to different sites on the enzyme

Lineweaver-Burk plot of pure noncompetitive inhibition. Note that I does not alter Km but that it decreases Vmax.

Mixed Noncompetitive Inhibition: binding of I by E influences binding of S by E

Lineweaver-Burk plot of mixed noncompetitive inhibition. Note that both intercepts and the slope change in the presence of I.

Uncompetitive Inhibition, where I combines only with E, but not with ES

Lineweaver-Burk plot of uncompetitive inhibition. Note that both intercepts change but the slope (Km/Vmax) remains constant in the presence of I.

What Is the Kinetic Behavior of Enzymes Catalyzing Bimolecular Reactions?

• Enzymes often catalyze reactions involving two (or more) substrates• Reactions may be sequential or single-displacement reactions• These can be of two distinct classes:• Random, where either substrate may bind first, followed by the other

substrate• Ordered, where a leading substrate binds first, followed by the other substrate

Kinetic Behavior of Enzymes Catalyzing Bimolecular Reactions?

Single-deplacement bisubstrate mechanism.

E + A + B AEB PEQ E + P + Q

Conversion of AEB to PEQ is the Rate-Limiting Step in Random, Single-Displacement Reactions

In this type of sequential reaction, all possible binary enzyme-substrate and enzyme-product complexes are formed rapidly and reversibly when enzyme is added to a reaction mixture containing A, B, P, and Q.

Creatine Kinase Acts by a Random, Single-Displacement Mechanism

The overall direction of the reaction will be determined by the relative concentrations of ATP, ADP, Cr, and CrP and the equilibrium constant for the reaction.

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

In an Ordered, Single-Displacement Reaction, the Leading Substrate Must Bind First

The leading substrate (A) binds first, followed by B. Reaction between A and B occurs in the ternary complex and is usually followed by an ordered release of the products, P and Q.

The Double Displacement (Ping-Pong) Reaction

Double-Displacement (Ping-Pong) reactions proceed via formation of a covalently modified enzyme intermediate. Reactions conforming to this kinetic pattern are characterized by the fact that the product of the enzyme’s reaction with A (called P in the above scheme) is released prior to reaction of the enzyme with the second substrate, B.

The Double Displacement (Ping-Pong) Reaction

Double-displacement (ping-pong) bisubstrate mechanisms are characterized by parallel lines.

Glutamate:aspartate Aminotransferase

An enzyme conforming to a double-displacement bisubstrate mechanism.

How Can Enzymes Be So Specific?

• The “Lock and key” hypothesis was the first explanation for specificity• The “Induced fit” hypothesis provides a more accurate description of specificity• Induced fit favors formation of the transition-state• Specificity and reactivity are often linked. In the hexokinase reaction, binding of

glucose in the active site induces a conformational change in the enzyme that causes the two domains of hexokinase to close around the substrate, creating the catalytic site

A drawing, roughly to scale, of H2O, glycerol, glucose, and an idealized hexokinase molecule. Binding of glucose in the active site induces a conformational change in the enzyme that causes the two domains of hexokinase to close around the substrate, creating the catalytic site.

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

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