Km Vmax Kcat

Km is [S] at 1/2 VmaxIt is a constant for a given enzyme at a particular temp and pressureKm is unique to each Enzyme and Substrate. It describes properties of enzyme-substrate interactions. Dependent on temp, pH etc. Independent of enzyme conc.

It is an ESTIMATE of equilibrium constant for substrate binding to enzyme

Small Km= tight binding, large Km=weak bindingIt is a measure of substrate concentration required for effective catalysis

Vmax is THEORETICAL MAXIMAL VELOCITYVmax is constant for a given enzyme. It is directly dependent on enzyme conc. It is attained when all of the enzyme binds the substrate. (Since these are equilibrium reactions enzymes tend towards Vmax at high substrate conc but Vmax is never achieved. So it is difficult to measure)

To reach Vmax, ALL enzyme molecules have to be bound by substrate

Kcat is a measure of catalytic activity- direct measure of production of product under saturating conditions.

Kcat is turnover number- number of substrate molecules converted to product per enzyme molecule per unit time

Catalytic efficiency = kcat/kmAllows comparison of effectiveness of an enzyme for different substrates

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Enzyme Km examples

Hexokinase prefers glucose as a substrate over ATP

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Km values of enzymes range from 10-1M to 10-7M for their substrates. It also varies depending on substrate, pH, temp, ionic strength etc.

Kcat

Catalase is very efficient-it generates 40 million molecules of product per second.Fumarase is not efficient-it generates only 800 molecules/per second

kkcatcat = V = Vmaxmax / [E] / [E]TT

Turnover numberTurnover numberNumber of reaction processes each active site catalyzes per unit timeNumber of reaction processes each active site catalyzes per unit time

Measure of how quickly an enzyme can catalyze a specific reactionMeasure of how quickly an enzyme can catalyze a specific reactionFor M-M systems kFor M-M systems kcatcat = k = k22

Kcat is turnover number for the enzymenumber of substrate molecules converted into product per unit time by that enzyme3

Kcat/Km

Rate constant of rxn E + S Rate constant of rxn E + S --->---> E + P E + PSpecificity constantSpecificity constantGauge of catalytic efficiencyGauge of catalytic efficiencyCatalytic perfection ~ 10Catalytic perfection ~ 1088 --10109 9 MM-1 -1 ss-1 -1 (close to diffusion)(close to diffusion)

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The catalytic constant, kcat iskcat = Vmax/[ET]for simple reactions, kcat = k2

When [S] << Km, very little ES is formed, such that [E] is almost equal to [ET].

In this case, vo = k2[ET][S]/Km + [S]

becomes = (k2/Km)[ET][S] = (kcat/Km)[ET][S]

Kcat/Km

Rate constant of rxn E + S Rate constant of rxn E + S --->---> E + P E + PSpecificity constantSpecificity constantGauge of catalytic efficiencyGauge of catalytic efficiencyCatalytic perfection ~ 10Catalytic perfection ~ 1088 --10109 9 MM-1 -1 ss-1 -1 (close to diffusion)(close to diffusion)

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Enzyme cofactors 7

Coenzymes

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How do ENZYMES carry out catalysis?

•Entorpy reduction- holds substrates in proper positionBringing two reactants in close proximity (reduce entropy & increase effective reactant concentrat)

•Substrate is desatbilized when bound to enzyme favoring reaction-(change of solvent, charge-charge interactions strain on chemical bonds).

•Desolvation of substrate- H bonds with water are replaced by H bonds with active site

Enzymes form a covalent bond with substrate which stabilizes ES complex (Transition state is stabilized)Enzyme also interacts non-covalently via MANY weak interactions

Bond formation also provides selectivity and specificity (H bonds- substrates that lack appropriate groups cannot form H bonds and will be poor substrates) (Multiple weak interactions between enzyme and substrate)

Free energy released by forming bonds is used to activate substrate (decrease energy barrier/lower activation energy of reaction)

Induced fit-binding contributes to conformation change in enzyme

Whats the Bill?5.7 kJ/mol is needed to achieve a 10x increase in rate of a reactionTypical weak interactions are 4-30 kJ/molTypical binding event yields 60-100 kJ/molMORE THAN ENOUGH ENERGY!!!

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A Hypothetical reaction

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Breaking a stick

Imagine you have to break a stick. You hold the two ends of the stick together and apply force. The stick bends and finally breaks.You are the catalyst. The force you are applying helps overcome the barrier.

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A stickase with a pocket complementary in structure to the stick (the substrate) stabilizes the substrate. Bending is impeded by the attraction between stick and stickase.

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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 interactions between stickase and stick compensates for the energy required to bend the stick.

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Role of binding energy in catalysis. The system must acquire energy equivalent to the amount by which G‡ is lowered. Much of this energy comes from binding energy (GB) contributed by formation of weak noncovalent interactions between substrate and enzyme in the transition state.

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Lock/Key or Induced Fit

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Lock/Key- Complementary shape

The enzyme dihydrofolate reductase with its substrate NADP+

NADP+ binds to a pocket that is complementary to it in shape and ionic properties, an illustration of "lock and key" hypothesis of enzyme action. In reality, the complementarity between protein and ligand (in this case substrate) is rarely perfect,

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Induced Fit

Hexokinase has a U-shaped structure (PDB ID 2YHX). The ends pinch toward each other in a conformational change induced by binding of D-glucose (red).

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Substrate specificity

The specific attachment of a prochiral center (C) to an enzyme binding site permits enzyme to differentiate between prochiral grps

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Enzyme-substrate

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•

• •

•

•

Catalysis

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•Acid-Base Catalysis- donate or accept protons/electrons from and to substrate•Covalent Catalysis-transient covalent link between substrate and enzyme side chain•Metal-Ion Catalysis-Metal in active site donate or accept protons with substrate

•Proximity & Orientation Effects (reduction in entropy-two mol brought together and oriented in specific manner)•Transition State Preferential Binding

Catalysis

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R GroupsThe active sites of enzymes contain amino acid R groups.Active site is lined with hydrophobic residues

Polar amino acid residues in active site are ionizable and participate in the reaction. Anion/cation of some amino acids are involved in catalysis

Lysozyme: Cleaves glycosidic bonds in carbohydrates

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Covalent Catalysis

All or part of a substrate is transiently covalently bound to the enzyme to form a reactive intermediate

Group X can be transferred from A-X to B in two steps via the covalent ES complex -EX

A-X+ E <-----> X-E + A

X-E + B <-----> B-X+ E

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Two mechanisms for acid catalysisSpecific acid catalysis:- A proton is transferred to the substrate in a rapid preequilibrium; Subsequently, the protonated substrate reacts further to form the productSpecific acid–base catalysis means specifically, –OH or H+ accelerate the reaction. The reaction rate is dependent on pH only.

The rate is only dependent on the pH, not on [HA]

General acid catalysis:- Proton transfer occurs in a slow, rate determining step; Subsequently, the protonated substrate rapidly reacts to give the product.

the reaction rate is dependent on all acids/bases present, dependent on the buffer concentration, at constant pH.

General acid/base catalysis by enzymesEnzymes often use general acid or base catalysis:

• They work at neutral pH, so low [H+] and [OH-]

• High localized concentration of general acid/base

• Correct orientation of the acidic/basic group around the substrate

• Optimum catalysis at pH around pKa

General acid-base catalysis involves a molecule besides water that acts as a proton donor or acceptor during the enzymatic reaction. It facilitates a reaction by stabilizing charges in the transition state through the use of an acid or base, which donates protons or accepts them, respectively.

Nucleophilic and electrophilic groups are activated as a result of the proton addition or removal and causes the reaction to proceed.

Side chains of various amino acids act as general acids or general basis

Amino acid residues such as His often have a pKa that is close to neutral pH and are therefore able to act as a general acid or base catalysts

X H

:B

:X- HB+

B + H A B H A B H A + AHB(1) (2) (3)

Without a catalyst the intermediate converts back to the reactants and does not proceed forward (high barrier).Donation of a proton by water or an acid helps the process move forward.

The active sites of enzymes contain amino acid R groups, that participate in the catalytic process as proton donors or proton acceptors.

Catalysts

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Proton donor/acceptor (Nucleophile/electrophile)

Asp and Glu are negatively charged at pH7.0 and their side chains are acidic.These side chains ACCEPT protons which neutralize the charge.

Lys, Arg, His are positively charged at pH 7.0 and their side chains are basic.These side chains DONATE protons to neutralize their charge.

Asp/Glu COO- + H+ <-----------> COOH Lys/Arg NH3+ <----------> NH2 + H+

NucleophilesR-OH <---> R-O: + H+ (hydroxyl)R-SH <---> R-S: + H+ (sulphydryl)R-NH3 <---> R-NH2: + H+ (amino)

ElectrophilesH+ ProtonM+ Metal ion

+C O

R

R’

Carbonyl

Nucleophiles-groups rich in and capable of donating electron (attracted to nucleus)Electrophile- group deficient in electron (attracted to electron)Reactions are promoted by proton donors (general acids) or proton acceptors (general bases). The active sites of some enzymes contain side groups, that can participate in the catalytic process as proton donors or proton acceptors.

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Acid base catalysis

RNaseA cleavage of RNA

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Roles of metals in catalysis:• As “super acid”: comparable to H+ but stronger

• As template: metal ions are able to coordinate to more than 2 ligands and can thereby bring molecules together

• As redox catalyst: many metal ions can accept or donate electrons by changing their redox state

Metal Ion catalysis

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Enzyme Inhibition

SS

EE

ES

PP

EE

EP

PP

EE

E + P

EE

SS

E + S

EE

What happens if a reactant does not leave the active site?

–Enzyme is blocked (inhibited) from further interactions

–Why inhibit?

To control [S] or [P]

–Increase [S] unreacted

–Decrease [P] formed33

Enzyme Inhibition

Many molecules inhibit enzymes

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Enzyme Inhibition

Many molecules inhibit enzymesReversible

Competes with substrateDoes not compete with substrate

Irreversible (covalently bound to enzyme)

ReversibleReversibleCompetitiveCompetitiveUncompetitiveUncompetitiveMixedMixedNoncompetitiveNoncompetitive

IrreversibleIrreversibleSuicide inactivatorsSuicide inactivators

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To figure out what kind of inhibitor we have,conduct two sets of rate experiments:

([E] constant in each case)

• [S] constant, test effect of increasing [I] on Vo• [I] constant, vary [S]

• Plot the results as 1/Vo vs. 1/[S]

Competitive Inhibitor

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Most commonMost common

Inhibitor competes with natural substrate for binding to active siteInhibitor competes with natural substrate for binding to active site

Inhibitor similar in structure to natural substrate and binds active site of enzyme Inhibitor similar in structure to natural substrate and binds active site of enzyme (reducing effective enzyme conc)(reducing effective enzyme conc)

Binds more stronglyBinds more stronglyMay or may not reactMay or may not reactIf reacts, does so very slowlyIf reacts, does so very slowlyGives info about active site through comparison of structuresGives info about active site through comparison of structures

Competitive Inhibitor

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Drug targets

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Gleevec

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Gleevec: How it works

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HIV protease structure

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Protease Inhibitors

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Protease + Inhibitor

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I and S compete for EI and S compete for EIncreasing [I]Increasing [I]

Increases [EI]Increases [EI]Reduces [E] available for substrate bindingReduces [E] available for substrate binding

Need to keep [I] high to ensure inhibitionNeed to keep [I] high to ensure inhibitionDosageDosage

S overcome inhibitor effects; saturateS overcome inhibitor effects; saturate

As [I] increases, KAs [I] increases, KMM increases increasesMore S required to reach ½ VMore S required to reach ½ Vmaxmax

Rate does not increase rapidly with [S] due to inhibition but the rate reaches Rate does not increase rapidly with [S] due to inhibition but the rate reaches the same maximal rate, just at a higher substrate concthe same maximal rate, just at a higher substrate conc

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Reversible Inhibition (competitive)

[Substrate]

vo

Vmax

-Inh+inh

1/2 Vmax

Km Km(app)

+Inh

-Inh

-1/Km -1/Km (app)

1/Vmax

1/v

1/[S]

Inhibitor competes with substrates for binding to active siteInhibitor is similar in structure to substrate

binds more stronglyreacts more slowly

Increasing [I] increases [EI] and reduces [E] that is available for substrate bindingNeed to constantly keep [I] high for effective inhibition (cannot be metabolized away in body)

Slope is largerSlope is larger

Intercept does not change (VIntercept does not change (Vmaxmax is the same) is the same)

KKMM is larger is larger

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Uncompetitive Inhibitor

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Uncompetitive Inhibitor

Binds only to ES complex but not free enzyme Binds at location other than active site

Does not look like substrate. Binding of inhibitor distorts active site thus preventing substrate binding and catalysis

Cannot be competed away by increasing conc of substrate (Vmax is affected by [I])

Increasing [I] lowers Vmax and lowers Km.

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Increasing [I]Increasing [I]Lowers VLowers Vmaxmax (y-intercept (y-intercept

increases)increases)Lowers KLowers KMM (x-intercept (x-intercept

decreases)decreases)Ratio of KRatio of KMM/V/Vmaxmax is the same is the same

(slope)(slope)

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Mixed

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Mixed

Inhibitor binds E or ESBinds site distinct from active siteIncreasing [I]Increasing [I]

Lowers VLowers Vmaxmax (y-intercept (y-intercept

increases)increases)Raises KRaises KMM (x-intercept (x-intercept

increases)increases)Ratio of KRatio of KMM/V/Vmaxmax is not the same is not the same

(slope changes)(slope changes)

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Non-competitive inhibition

Inhibitor binds ES or EIt is a special case of mixed inhibition where Vmax is lowered when [I] increases but Km does not change

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Reversible Inhibition (non-competitive)

[Substrate]

vo

Vmax-Inh

+inh

1/2 Vmax

Km Km(app)

1/2 Vmax(app)

Vmax(app)_

+Inh

-Inh

-1/Km

1/Vmax

1/v

1/[S]

1/Vmax(app)

Vmax is decreased proportional to inhibitor conc 53

Reversible Inhibition (non-competitive)

A inhibitor binds the enzyme but not in its active site. It affects the Kcat because substrate can still bind the active site.Rate of catalysis is affected

[Substrate]

vo

Vmax-Inh

+inh

1/2 Vmax

Km Km(app)

1/2 Vmax(app)

Vmax(app)_

+Inh

-Inh

-1/Km

1/Vmax

1/v

1/[S]

1/Vmax(app)

Vmax is decreased proportional to inhibitor conc 54

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Uncompetitive and mixed inhibition only seen for enzymes with two or more substrates

Example

When a slice of apple is cut, it turns brown- enzyme o-diphenol oxidase oxidizes phenols in the appleLets determine max rate at which enzyme functions (Vmax), and Km1 When it acts alone (we will use catechol as substrate). Enz converts this to o-quinone which is

dark and can be measured via absorbance at 540 nm 2 when it acts in presence of competitive inhibitor para hydroxy benzoic acid which bind active site

but is not acted upon3 when it acts in the presence of a non-competitive inhibitor- phenylthiourea which binds copper in

the enzyme which is necessary for enzyme activity

Make a supernatant of the apple-enzyme. Measure color produced (product)Set up 4 tubes with different conc of cathecol and a fixed amount of enzyme (apple pulp).Measure change in absorbance at 1 min intervals for several minutes and record average change in

absorbance. Absorbance is directly proportional to product, we can measure rate of reaction (velocity)

TubeA TubeB TubeC TubeD

[S] mM mM mM mM

1/[S]

Vi (OD)

1/Vi

1/Vmax=10Vmax=0.1-1/Km=-0.8Km=1.25mM

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Example

When a slice of apple is cut, it turns brown- enzyme o-diphenol oxidase oxidizes phenols in the appleLets determine max rate at which enzyme functions (Vmax), and Km1 When it acts alone (we will use catechol as substrate. Enz converts this to o-quinone which is dark

and can be measured via absorbance at 540 nm 2 when it acts in presence of competitive inhibitor para hydroxy benzoic acid which bind active site

but is not acted upon3 when it acts in the presence of a non-competitive inhibitor- phenylthiourea which binds copper in

the enzyme which is necessary for enzyme activity

Make a supernatant of the apple-enzyme. Measure color produced (product)Set up 4 tubes with different conc of cathecol and a fixed amount of enzyme (apple pulp).Measure change in absorbance at 1 min intervals for several minutes and record average change in

absorbance. Absorbance is directly proportional to product, we can measure rate of reaction (velocity)

TubeA TubeB TubeC TubeD

[S] 4.8 mM

1.2mM

0.6mM

0.3mM

1/[S] 0.21 0.83 1.67 3.33

Vi (OD) 0.081 0.048 0.035 0.02

1/Vi 12.3 20.8 31.7 50.0

1/Vmax=10Vmax=0.1-1/Km=-0.8Km=1.25mM

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Example

TubeA TubeB TubeC TubeD

[S] mM mM mM mM

1/[S]

Vi (OD)

1/Vi

Each tube also has a fixed amount of PHBA (competitive inhibitor)

1/Vmax=10Vmax=0.1-1/Km=-0.4Km=2.5 mM

TubeA TubeB TubeC TubeD

[S] mM mM mM mM

1/[S]

Vi (OD)

1/Vi

Each tube has a fixed amount of phenylthiourea (non competitive inhibitor)

1/Vmax=20Vmax=0.05-1/Km=-0.8Km=1.25 mM

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Example

TubeA TubeB TubeC TubeD

[S] 4.8 mM

1.2mM

0.6mM

0.3mM

1/[S] 0.21 0.83 1.67 3.33

Vi (OD) 0.060 0.032 0.019 0.011

1/Vi 16.7 31.3 52.6 90.9

Each tube also has a fixed amount of PHBA (competitive inhibitor)

1/Vmax=10Vmax=0.1-1/Km=-0.4Km=2.5 mM

TubeA TubeB TubeC TubeD

[S] 4.8 mM

1.2mM

0.6mM

0.3mM

1/[S] 0.21 0.83 1.67 3.33

Vi (OD) 0.040 0.024 0.016 0.01

1/Vi 25 41 62 102

Each tube has a fixed amount of phenylthiourea (non competitive inhibitor)

1/Vmax=20Vmax=0.05-1/Km=-0.8Km=1.25 mM

Irreversible

Inhibitor Inhibitor Binds covalently, orBinds covalently, orDestroys functional Destroys functional group necessary for group necessary for enzymatic activity, orenzymatic activity, orVery stable Very stable noncovalent bindingnoncovalent binding

Suicide InactivatorsSuicide InactivatorsStarts steps of Starts steps of chemical reactionchemical reactionDoes not make Does not make productproductCombines irreversibly Combines irreversibly with enzymewith enzyme

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Regulation of enzymes

Catalytic activity is increased or decreased by

1) Enzyme synthesis or degradation2) Covalent modification3) Non-covalent binding and conformational change (allosteric)

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Usually located early in multi-enzyme reaction pathwayUsually located early in multi-enzyme reaction pathwayKinetics differ for allosteric enzymes- sigmoidal curve and K1/2 instead of Km Usually large; multiple subunitsUsually large; multiple subunits

Comparable to HbComparable to Hb Site for allosteric modulator (Site for allosteric modulator (R = regulatoryR = regulatory) generally different from active ) generally different from active

site (site (C = catalyticC = catalytic)) Can be positive or negativeCan be positive or negative

Allosteric regulation

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Aspartate transcarbamoylase (nucleotide synthesis)

Regulatory subunit

Catalytic subunit

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Feed back Inhibition

End product inhibition

Sigmoidal kinetic curves -Positive Homotropic enzyme

Heterotropic modulator

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Covalent regulation

Modifying groups are attached to an enzyme • by a covalent bond…

Glycogen phosphorylase

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Special Regulation by Degradation

Digestive enzymes: Trypsinogen and Chymotrypsinogen

Hormonal regulation: Insulin is synthesized as pro-insulin

Fibrous proteins: Collagen is synthesized as pro-collagen

Blood clotting: Fibrinogen and pro-thrombin

Known as Zymogens (for proteases) or Proproteins