enzymes kinetics & regulation

8/9/2019 Enzymes Kinetics & Regulation

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Enzymes: Kinetics,Specificity, and

Regulation

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Outline

Enzymes Catalytic Power, Specificity,and Regulation

Introduction to Enzyme Kinetics

Kinetics of Enzyme-Catalyzed ReactionsEnzyme Inhibition

Kinetics of Enzyme-Catalyzed ReactionsInvolving >1 Substrates

RNA and Antibody Molecules AsEnzymes: Ribozymes & Abzymes


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Outline contd

Specificity Is the Result of MolecularRecognition

Controls over Enzymatic Activity

The Allosteric Regulation of EnzymeActivity

A Model for the Allosteric Behavior of

Proteins

A Paradigm of Enzyme Regulation:Glycogen Phosphorylase

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Enzymes

Enzymes endow cells with the remarkable

capacity to exert kinetic control over

thermodynamic potentiality

Enzymes are the agents of metabolic

function


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Enzymes

Biological catalysts

that function in dilute, aqueous solutions undermild cellular conditions (e.g., pH andtemperature) to increase reaction rate

Catalytic power

Ratio of catalyzed rate to uncatalyzed rate

Specificity

Regulation of catalysis

Enzyme levels and types regulated genetically

Inhibitors and activators modify enzyme activity

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Types of Enzymes

Simple enzymes

Composed solely of protein, single or multiple

subunits

Complex enzymesProtein plus small organic molecule(s) or metal

Entire complex called holoenzyme

Protein part called apoenzyme

Non-protein part called coenzyme orprosthetic group


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Non-protein Components

Cofactors

Inorganic molecules

Coenzymes

Organic moleculesOften vitamins

Prosthetic group

Firmly bound coenzymeHoloenzyme

Apoenzyme plus prosthetic group

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Catalytic Power

Enzymes can accelerate reactions as muchas 1016 over uncatalyzed rates!

Urease is a good example:

Catalyzed rate: 3x104

/secUncatalyzed rate: 3x10 -10/sec

Ratio is 1x1014 !


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Specificity

Enzymes selectively recognize propersubstrates over other molecules

Enzymes produce products in very highyields - often much greater than 95%

Specificity is controlled by structure - theunique fit of substrate with enzyme

controls the selectivity for substrate andthe product yield

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Other Aspects of Enzymes

Regulation - to be covered in Chapter 14

Mechanisms - to be covered in Chapter 11

Coenzymes - to be covered in Chapter 22


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Enzyme Kinetics

Several terms to know!

rate or velocity

rate constant

rate law

order of a reaction

molecularity of a reaction

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Kinetics

Kinetics is the study of the rate ofchange of reactants to products

Velocity refers to the change in conc. Of

substrate or product per unit timeRate refers to the change in total quantity

per unit time

Initial velocity is the change in reactantor product conc. during the linear phase ofa reaction


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Chemical Kinetics

Rate lawPA

k

nAk

dt

dAv ][

k = rate constant

n = order of reactionMolecularity

Number of molecules that must simultaneously react

Unimolecular

n = 1 k = first order rate constantBimolecular

k second order rate constant

n = 2, or

v = k[A][B]

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Reaction rates

Limited by activation barrierFree energy needed to reach transition state

Arrhenius equation

Reaction rate is influenced by

RT

Gtr

Aek

Temperature

Catalysts

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Chemical Reactions and Rates

For reaction:AB the rate can beexpressed as either the decrease in conc.of A or the increase in conc. of B

-[A] =k

[B] (neg. sign indicates decrease) [B] = k[A]

The k is the rate constant which isrelated to the equilibrium constant, Keq

Keq refers to the state where the forwardand reverse reactions are equal


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Chemical Reactions and Rates2

The rate constant for the forward reactionis defined as k+1 and that of the reversereaction as k-1

Rate is defined as velocity (v) thus atequilibrium vforward = vreverse

Where vforward = k+1[A] and visa versa

Therefore, Keq = [B]/[A]

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Enzyme kinetics

P1

21EESSE

MentenMichealis

k

kk

1

21kkk

Km

2

][

maxVv

when

SKm

][][maxSK

m

SVv

Saturation: Zero-order kinetics at high [S]

Conditions applicable[S] initial > [Enzyme]pH, temperature, ionicstrength,[enzyme] constant

Initial rate measured[S] essentially equal to [So][P] essentially zero


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Enzymes as Catalysts

Enzymes increase the rate of reactionswithout themselves being altered in theprocess of substrate conversion to product

This defines a catalyst

Enzymes increase reaction rates by loweringthe energy input needed to form a complex ofreactant competent to form product

This occurs via the formation of a complexbetween enzyme and substrate (ES)


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Michaelis Michaelis-Menten Menten

Kinetics

Developed the rate equation used by allbiochemists

Three basic assumptions

ES complex is in a steady state, i.e. remainsconstant during the initial phase of a reaction

when enzyme is saturating all is in ES

complexif all enzyme in ES then rate of product

formation is maximal

i.e. Vmax = k2[ES]

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Michaelis Michaelis-Menten MentenKinetics

The Michaelis-Menten equation is aquantitative description of the relationshipbetween the rate of an enzyme catalyzedreaction (v1), substrate concentration [S], the

M-M rate constant (Km) and maximal velocity(Vmax)


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Michaelis Michaelis-Menten Menten

Kinetics

Utilizing the M-M equation it can be shownthat the Km is equal to the concentration ofsubstrate required to attain half maximalvelocity for any given reaction

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The Transition State

Understand the difference between G and

G

The overall free energy change for areaction is related to the equilibriumconstant

The free energy of activation for a reactionis related to the rate constant

It is extremely important to appreciatethis distinction!


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G= G S - GS

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What Enzymes Do....

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

Much more of this in Chapter 11 next

lecture!


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The Michaelis-MentenEquation

You should be able to derive this!

Louis Michaelis and Maude Menten's theory

It assumes the formation of an enzyme-substrate complex

It assumes that the ES complex is in rapidequilibrium with free enzyme

Breakdown of ES to form products is assumedto be slower than:

formation of ES and

breakdown of ES to re-form E and S


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Understanding Km

The "kinetic activator constant"

Km is a constant

Km is a constant derived from rateconstants

Km is, under true Michaelis-Mentenconditions, an estimate of thedissociation constant of E from S

Small Km means tight binding highaffinity; high Km means weak binding low affinity


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Understanding Vmax

The theoretical maximal velocity

Vmax is a constant

Vmax is the theoretical maximal rate ofthe reaction - but it is NEVER achieved inreality

To reach Vmax would require that ALLenzyme molecules are tightly bound withsubstrate

Vmax is asymptotically approached assubstrate is increased

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The dual nature of the Michaelis-Menten equation

Combination of 0-order and1st-order kinetics

When S is low, theequation for rate is 1storder in S

When S is high, theequation for rate is 0-order in S

The Michaelis-Mentenequation describes arectangularhyperbolicdependence of v on S!


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The Turnover Mumber

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

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The catalytic efficiency

Name for kcat/KmAn estimate of "how perfect" the enzyme

is

kcat/Km is an apparent second-order rateconstant

It measures how the enzyme performs

when S is lowThe upper limit for kcat/Km is the diffusion

limit - the rate at which E and S diffusetogether

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Enzyme parameters

k1 sets upper limit on catalytic efficiency

Reaction can go no faster than rate at which E and S

form ES

International unit

Amount to catalyze formation of one

micromole of product in one minute

Turnover number

kcat = k2 = Vmax/[ET]

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Linear Plots of the Michaelis-Menten Equation

Be able to derive these equations!

Lineweaver-Burk

Hanes-Woolf

Hanes-Woolf is best - why?

Smaller and more consistent errors across

the plot


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Lineweaver Lineweaver-Burk Analysis

In practice determination of Km fromcurvilinear plots is not accurate

Lineweaver and Burk manipulated the MMequation by taking its reciprocal valuesgenerating a double reciprocal plot

Leads to a linear graph of the reciprocalsof velocity and substrate concentration

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Plots Direct plot

v versus [S]

v = (Vmax [S])/(Km+[S])

Rectangular hyperbola

Asymptotically approaches Vmax when[S] high

Km = [S] when v = Vmax/2

Lineweaver-Burk

(double-reciprocal) - Linear

1/v versus 1/[S]

1/v = (Km/Vmax)(1/[S])+1/Vm

Slope = Km/Vmax

y-intercept =1/Vmax

x-intercept = -1/Km


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Temperature dependence ofenzyme-catalyzed reactions

Below 50C

Q10: Ratio of activities at

two temperatures 10apart: For typical enzymeQ10=2

Above 50C

Typically enzymedenatures


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pH dependence of enzyme-catalyzedreactions

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Enzyme Inhibitors

Reversible versus Irreversible

Reversible inhibitors interact with an

enzyme via noncovalent associations

Irreversible inhibitors interact with an

enzyme via covalent associations


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Classes of Inhibition

Two real, one hypothetical

Competitive inhibition

Noncompetitive inhibition

Uncompetitive inhibition

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Competitive inhibition

Inhibitor binds at substrate site of E

inhibitor (I) binds only to E, not to ES as highersubstrate competes for inhibitor,

Vmax unchanged, Km increased

inhibition is reversible


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Noncompetitive inhibition

Inhibitor binds at site other than substrate,

inhibitor (I) binds either to E and/or to ES ESI cannot form product, increased substrate does not

compete,

Km unchanged, Vmax decreased

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Uncompetitive inhibition

Inhibitor only binds to ES complexdue to binding site becoming availableonly when substrate is bound,

inhibitor (I) binds only to ES, not toE. This is a hypothetical case thathas never been documented for areal enzyme, but which makes auseful contrast to competitiveinhibition

Km and Vmax decreased


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Bisubstrate reactions:E + S1 + S2 S1ES2 P1EP2 E + P1 + P2 Sequential or single displacement

Random: Either substrate binds to enzyme, either productis released

Ordered: Leading substrate binds first followed by secondsubstrate


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Ping-Pong or double-displacement: Leading substrate binds, Enzyme modified, Product released Second substrate binds: Enzyme unmodified: Second product

released

Bisubstrate reactions:

E + S1 + S2

S1ES2

P1EP2

E + P1 + P2

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Ribozymes and Abzymes

Relatively new discoveries

Ribozymes - segments of RNA that display

enzyme activity in the absence of protein

Examples: RNase P and peptidyl transferase

Abzymes - antibodies raised to bind thetransition state of a reaction of interest

For a great recent review, see Science, Vol.269, pages 1835-1842 (1995)

We'll say more about transition states in Ch 11


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Regulation of Enzyme Activity

Control the expression of genes and get more orless enzyme

Enzyme exists in inactive form (zymogen) thatmust be modified, primarily by cleavage

Covalent modification to increase or decreaseactivity, most common is phosphorylation

Sequestration

Allosteric regulation, both positive and negative

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Enzyme regulation

Approach to equilibrium

Km of enzymes in the range of in vivo substrateconcentrations

Genetic controls

Covalent modification

Allosteric regulation

Zymogens: Proenzymes or zymogens: Activated byproteolysis Proinsulin: Insulin

Chymotrypsinogen: Chymotrypsin

Blood clotting factors: Serine protease cascade leading tofibrinogen to fibrin

Isozymes: Lactate dehydrogenase: A4, A3B1, A2B2, A1B3,B4

Modular proteins: cAMP-dependent protein kinase: R2C2


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General properties of regulatory

proteins

Kinetic properties

Do not follow simple Michaelis-Menten kinetics

Activity sigmoidal: Higher order dependence on

substrate concentration

Cooperativity

Allosteric inhibition

Often regulated by activation

Oligomeric organization

Effectors alter distribution of conformational isomers

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Cooperativity models

Monod, Wyman, Changeux (1965): Symmetry model

Two conformations: T (tense or taut) and R(relaxed)

R state high affinity, T state lower affinity

Positive homotropic effectors

Substrate binding shifts equilibrium to R

Heterotropic effectors

Positive effector: Binds to R state and shifts equilibriumtoward R

Negative effector: Binds to T state and shifts equilibriumtoward T

Koshland, Nemethy, Filmer (1966) Sequential model:

Induced fit: S-binding induces conformational change


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enzymes kinetics & regulation

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