Enzymes

CH339K

Transition State

• On the way from reactants to products, the reaction goes through a high-energy intermediate structure

• Amount of energy to reach transition state controls rate

• Picture is from an O-Chem text – sorry - ugggghhhhhhhh

Reaction Pathways Go’ is the difference in Free Energy between reactants and

products Go’determines Keq Rate depends on EA or G‡ how much energy is required to

reach transition state.

What are enzymes?• There are two basic ways to increase the rate of a

reaction– Increase the energy of the reactants (heat it up)– Lower the activation energy (catalysis)

• Enzymes are protein catalysts.• Virtually every biochemical reaction is mediated by

an enzyme.

For the Visual Thinkers: Two Options

Raise the temperature of the reactants

Use a catalyst

Which is:a)Faster?b)Less likely to result in being eaten?

Activation Energy (you knew it would get to math)

• Let’s look at a first-order reaction where substance X is converted to substance Y, going through the transition state X’:

X ⇌ X’ ⇌ Y• The rate can be expressed as a rate constant k times the

concentration of the reactant X:

[1] v = k * [X]

Reaction Coordinate

G

EA

G0

X X' Y

Activation Energy (cont.)But if we think about it, Y is actually produced from the transition state, so the reaction velocity should really be governed by the concentration of transition state:

[2] v = k’ * [X’] Now let’s assume we have a situation where X’ is far more likely to fall back to X than to proceed to form the product Y. Then X’ will essentially be in equilibrium with X, and the equilibrium will be governed by the same thermodynamic rules we have seen before:

[3] X ⇌ X’ (forget Y for a second)

[4]

or[5]

RTE AeX

XKeq /

][

]'[

][]'[ / XeX RTE A

Activation Energy (cont.)

• so combining [2] and [5]

[6]

• Lowering the activation energy from EA1 to EA

2 thus changes the rate by a factor of

[7]

i.e. lowering EA from 20 kJ/mol to 8 kJ/mol increases the rate by over 100x at 37o C!!!

]['* / Xekv RTE A

RT

EE AA

ev

v 21

1

2

Enzymes tend to be really good catalysts

21,000,000-fold rate increase

How do enzymes work?

• Enzymes bind substrates in an active site, where the reaction takes place

• Lock and key vs. induced fit (distortion of both enzyme and substrate plays a role in catalysis)

Active site

• The active site frequently forms a cleft in the molecule

• Substrate binding typically includes van der Waals contacts, H-bonds, and salt links, but can include covalent links.

Mechanisms

• Increase effective concentrations• Orient the substrates• Stabilize the transition state

– The energy of binding can subsidize conformational strain in the substrate

– Acids and bases can participate in catalysis

• Covalent or redox participation by the enzyme

• Use of enzyme cofactors

Acid-base catalysis:Triose Phosphate Isomerase

• Triose phosphate isomerase interconverts the two three-carbon sugars formed by the action of aldolase on fructose-1,6-bisphosphate in the glycolytic pathway

Acid-base catalysis:Triose Phosphate Isomerase

• Glu165 acts as a base, extracting a proton from the substrate

• His95 acts as an acid, donating a proton.

DHAP G3P

Acid-Base + Conformational ChangeLysozyme

• In 1922, Alexander Fleming plated bacterial cultures along with samples of his own snot.

• Bacteria near his nasal mucus dissolved away.

• The active ingredient, lysozyme, cleaves bacterial cell wall polysaccharides.

• There is an extended substrate binding cleft that bonds a stretch of 6 sugars.

• Lysozyme cleaves its substrate between the fourth and fifth residues in a hexasaccharide

Repeating Structure of Cell Wall

Lysozyme cleaves here

Acid-Base + Conformational ChangeLysozyme (from egg white, not snot)

Active Site Cleft

Lysozyme with 3 NAG in the active site

Lysozyme with hexose in the active site

Acid-Base + Conformational ChangeLysozyme

• Glu35 acts as an acid (has abnormally high pKa).• Asp52 stabilizes the charge on the oxycarbonium transition

state.• Binding of 6 sugars subsidizes the torsion of the target sugar

bond into a half-chair conformation.• This mimics the conformation of the intermediate, decreasing

G‡ for reaching the transition state.

Transition State Analogs

Raising Monoclonal Antibodies

Transition State Analogs

• One can create catalytic antibodies by rearing antibodies against transition state analogs

Hydrolysis of Aryl Carbonates using p-nitrophenyl-4- carboxybutanephosphonate as antigen – rate acceleration > 104.Patten, P.A. et al, (1996) Science 271: 1086-1091.

Covalent Participation - Chymotrypsin• Three key catalytic side chains - Far apart in sequence but

adjacent in active site

– Ser195

– His57

– Asp102

Covalent Participation - Chymotrypsin• Chymotrypsin is a serine protease.• Serine, Histidine, and Aspartic Acid form a charge relay system.

Subtilisin• From Bacillus subtilis• Same catalytic mechanism

• Totally different protein; no evolutionary connection.

• Triad: Ser221, His64, Asp32

Inorganic Cofactors

Coenzymes

Example of use of a cofactor• Histidine Decarboxylase

Flavin Adenine Dinucleotide(FAD)

Nicotinamide Adenine Dinucleotide (NAD+)

Nicotinamide Adenine Dinucleotide Phosphate (NADP+)

Redox cofactors

Example of a redox cofactor

N

N

NH

N O

O

H3C

H3C

H

H

H+

N

N

NH

N O

O

H3C

H3C

HO CO2-

H H

O CO2-

H

Glycolate Oxidase Uses Flavin Mononucleotide (FMN)

Glycolic acid(reduced)

Glyoxylic acid(oxidized)

FMN (oxidized) FMN (reduced)

+ H+

STOP HEREENOUGH IS ENOUGH

Enzyme Kinetics

• Let's make a simple model of an enzyme-catalyzed reaction that converts one molecule of substrate (S) to one molecule of product:

• Let's also make a few assumptions:– The reaction has just started, so [P] = 0 and k4 can be

ignored.– [S] >>> [E], so substrate is in no way limiting.– As a result of (2), [S] isn't going to change appreciably

during our observation of the reaction and we can assume [ES] is approximately constant.

Enzyme Kinetics

• We will define [Etotal] as the total concentration of the enzyme.

[Etotal] = [E] + [ES]• We will define v as the reaction velocity for

formation of product

v = k3[ES]

Enzyme Kinetics

• Since [ES] is approximately constant, its rate of formation is equal to its rate of destruction:

k1 [E][S] = (k2 + k3)[ES]

[E][S] = ((k2 + k3)/k1)[ES]

• Let's give a name to the combined constants. Let's call it Km (for the Michaelis constant):

[E][S] = Km[ES]

([Etotal] - [ES])[S] = Km[ES] (since [Etotal] = [E] + [ES])

[Etotal][S] - [ES][S] = Km[ES]

Enzyme Kinetics

[Etotal][S] - [ES][S] = Km[ES]

• Rearranging:Km[ES] + [ ES][S] = [Etotal][S]

[ES] = [Etotal][S] / (Km + [S])

• Remember v = k3[ ES], sov = k3[Etotal][S] / (Km + [S])

• The maximum velocity for the rxn is when every enzyme molecule is part of an ES complex:

Vmax = k3[Etotal]

Enzyme Kinetics

• The maximum velocity for the rxn is when every enzyme molecule is part of an ES complex:

Vmax = k3[Etotal] andv = k3[Etotal][S] / (Km + [S])

• Simplifying the above:v = Vmax[S] / (Km + [S])

– This is the Michaelis - Menten equation, which does a pretty good job of describing the overall kinetics of many enzyme catalyzed reactions.

There’s that blue arrow again!

You’ve seen this before

2

2

mmax

m

max

pOp50

pO )3(

SK

S

V

v )2(

SK

SV v)1(

kcat

• Vmax will change with changing enzyme concentration. It would be nice if we could define a term equivalent to Vmax which was independent of enzyme concentration.

• In addition, there are many enzyme catalyzed reactions that have several intermediate steps in the pathway from reactants to products. For example:

where EI1, EI2, EI3 are complexes between the enzyme and successive intermediates.

• What we can normally measure is not the set of individual reaction rates but rather an overall 'k3apparent' or kcat.• kcat is enzyme-adjusted measured Vmax; that is,

kcat = Vmax/[Etotal] (units of sec-1)

Km

• Km is th Substrate concentration at which the reaction is occurring at one-half its maximal rate. It is thus a measure of how much substrate is required for reasonable enzyme activity. Km is often looked on as a dissociation constant for the Enzyme -Substrate complex. Since

Km = (k2 + k3)/k1,

• this will only be true when k3 << k2! This is frequently the case, but not necessarily!

kcat/Km

• At low substrate concentrations, the Michaelis-menten equation reduces to

v = (kcat/Km)*[Etotal][S]

• i.e. at low [S], [E] ~ [Etotal] and Km + [S] ~ Km.

• kcat/Km is thus a rate constant and as such is a measure of catalytic efficiency.

• Theoretical maximum for the reaction rate is in the range of 108 - 109 M-1sec-1.

• Many enzymes approach this limit and are thus said to have

achieved catalytic perfection.

Sample Kinetic Parameters for Enzymes

Measuring Km and Vmax (if you only have a pencil and a ruler)

• Lineweaver-Burke

• Eadie-Hofstee

maxmax

1

][

11

vSv

Km

v

max][v

S

vKmv

Rearrange Michaelis-Menten Equation:

Lineweaver-Burke

Eadie-Hofstee

Control by Inhibition

• Inhibitors alter enzyme activity (Km and kcat)• Often used to control enzyme activity• Often used as toxins• Two basic flavors

– Irreversible

– Reversible

• Which are pretty much like they sound

Irreversible Inhibition at the NM Junction

Nerve Gases

Sarin

Soman

Tabun

VX

Symptoms: Contraction of pupils, profuse salivation, convulsions, involuntary urination and defecation and eventual death by asphyxiation as control is lost over respiratory muscles.

Nerve Gases - Properties

Toxicity of Nerve Agents

Agent LD50 LCt50

Tabun (GA) 1000 mg 400 mg/min-m3

Sarin (GB) 1700 mg 100 mg/min-m3

Soman (GD) 50 mg 70 mg/min-m3

VX 10 mg 50 mg/min-m3

Action of Nerve Agents

Nerve Gas Antidotes

Atropine sulfate from Atropa belladonna (left) competes with acetylcholine for the receptor binding site

Blocks ACH and offsets the effects of the nerve agent

How do I take atropine?

Instructions for use is outlined in STP21-1-SMCT, Soldier’s Manual of Common Tasks- Skill Level 1. You may self-administer the injection as follows:• Hold the injector in your hand forming a fist around the injector without covering or holding the needle end. • Place the end of the injector against your outer (lateral) thigh muscle anywhere from about a hand’s width above the knee to a hand’s width below the hip joint. Very thin soldiers should give the injection in the upper outer part of the buttocks. • Push the injector into the muscle with firm, even pressure until it functions. • Hold the injector in place for 10 seconds to allow the 2-PAM CL to be administered. • After you have given yourself the first set of injections, you most likely will not need an additional antidote if you can walk and know who and where you are. If needed, the second and third sets of injections will most likely be given by a buddy or by medical personnel.

From Atropine Nerve Agent Autoinjector – What You Need to Know, U.S. Army Center for Health Promotion and Preventive Medicine (USACHPPM)

Pralidoxime Hydrochloride

Usually given along with atropine

Reversibly binds to the enzyme acetylcholinesterase, competing with organophosphate binding.

Doesn’t inhibit acetylcholinesterase – reactivator.

2-PAM Action

Reversible Inhibition

CompetitiveInhibition

• Inhibitor binds to active site• Competes with normal substrate• Effect of inhibitor can be

overcome by increasing [S]• In presence of inhibitor:

– Vmax unchanged

– Km increases

Im

appm K

IKK

][1

Competitive Lineweaver-Burke

Competitive - Example• Ethylene Glycol (Antifreeze) is a poison.• It is converted into Oxalic Acid.• Oxalic acid binds calcium and forms crystals in the kidney and brain• The old treatment for antifreeze poisoning was legal drunkenness.

Ethanol acts as a competitive inhibitor for ethylene glycol on alcohol dehydrogenase.

Substrate* Km

Ethylene Glycol 30 mM

Methanol 7 mM

Ethanol 0.45 mM

* Data from Goldfrank, L.R. et al, Goldfrank’s Toxologic Emergencies, 1998, New York

Diagnosis (in critters)

• Presence of calcium oxalate crystals in the urine.

Newer Treatment (for all you medical types)

Fomepizole• Specifically indicated for use in

ethylene glycol and methanol poisoning

• Also a competitive inhibitor of alcohol dehydrogenase

Competitive - Another Example

• The ricin substrate is an adenosine residue in the large ribosomal RNA

Another example (cont.)

• Pteroic Acid acts as a (not terribly good) competitive inhibitor of ricin, binding to the same residues as adenosine

Pteroic Acid

Pteroic Acid InhibitionSubstrate Km

Intact Eukaryotic Ribosome 2.6 M

28S rRNA 5.8 M

23S (E. coli) rRNA 3.3 M

Pteroic Acid 600 M

NoncompetitiveInhibition

• Inhibitor binds at separate location from active site

• Inhibited ES complex does not proceed to products

• Effect of inhibitor cannot be overcome by increasing [S]

• In presence of inhibitor:– Vmax decreases

– Km unchanged

• Not many purely noncompetitive inhibitors

IKI

app VV

][max

max 1

Noncompetitive Lineweaver-Burk

Noncompetitive - Example• Browning of fruit is caused by a reaction between catechols and

oxygen, catalyzed by catechol oxidase, resulting in benzoquinone.

• Catechol oxidase requires Cu+2 as a cofactor. • Phenylthiourea binds to Cu and is a noncompetitive inhibitor of the enzyme

Uncompetitive Inhibition• Inhibitor binds only to ES complex• Inhibited ES complex does not proceed

to products• Effect of inhibitor potentiated by

increasing [S]• In presence of inhibitor:

– Vmax decreases

– Km decreases

• Uncompetitive inhibitors are relatively rare, typically toxic

I

mappm

KI

KK

][1

I

app

KI

VV

][1

maxmax

Uncompetitive - Example• The enzyme 5-enolpyruvylshikimate-3-phosphate synthase

(EPSPS) catalyzes the reaction of shikimate-3-phosphate (S3P) and phosphoenolpyruvate to form 5-enolpyruvyl-shikimate-3-phosphate (ESP).

• ESP is an essential precursor in plants for the aromatic amino acids.• Glyphosate binds to the EPSPS • S3P complex and inhibits enzyme

activity.• As [S3P] increases, more of the complex is formed and the effect of the

inhibitor increases.

Glyphosate

Glyphosate =

In addition to glyphosate usage, the sale of glyphosate-resistant crop plants has also gone through the roof. $$$$$$$$$!!!

Allostery

allostery• A phenomenon whereby the conformation of

an enzyme or other protein is altered by combination, at a site other than the substrate-binding site, with a small molecule, referred to as an effector, which results in either increased or decreased activity by the enzyme.

• E.g. 2,3-bisphosphoglycerate is an allosteric inhibitor of hemoglobin

Aspartate Transcarbamoylase

• Important enzyme in the biosynthesis of pyrimidine nucleotides (i.e. need it to make DNA)

• Catalyzes addition of carbamoyl phosphate to aspartate to make N-carbamoyl aspartate

Uracil, a Pyrimidine( )

ATCase - Structure

• 12 subunits totalling ~300 kDal• two catalytic components each made up of three

identical subunits (34 kDal each)• three regulatory components each comprising two

subunits (17 kDal each)

ATCase

• Active sites are at the intersections of C subunits

• Allosteric sites are on R subunits

• Latter bind UTP/CTP (inhibitor) and ATP (activator}

• T to R transition opens molecule, making active sites accessible

• ATP binds / stabilizes R• CTP/UTP bind / stabilize T

ATCase – Binding Sites

ATCase – Activation and Inhibition

ATCase – An Interesting Inhibitor

PALA – Another view

PALA Activation/Inhibition

The effect of PALA on the activity ofP. aeruginosa ATCase. The ATCase was assayed using 5 mm carbamoyl phosphate and either 8 (●) or 12 mm (○) aspartate and a variable concentration of the bisubstrate inhibitor, PALA, in the presence of 2 μm ATP.

Vickery, J.F., Herve, G., and Evans, D. R. (2002) J. Biol. Chem. 277: 24490-24498.