Enzymes:Basic Concepts

and Kinetics

Enzymes: catalysts of biological systems, speed up selective chemical reactions needed for life.

They have remarkable catalytic power and specificity.

Nature selected some protein molecules to be enzymes.

There are very specific cases when other biomacromolecules can also carrycatalytic functions, like RNA (ribozymes) or antibodies (abzymes).

Catalysis takes place on a distinct part of the protein molecule called the active site.

Enzymes use the full repertoire of intermolecular forces to attract, opti-mally orient and VERY specifically bind “the substrates” (the moleculesought to be converted faster), then in the favored spatial positions thechemical reaction between the two molecules will be highly facilitated.

Catalysis happen because enzymes stabilize the transition state (TS, thehighest energy species in the reaction). Selective stabilization of TS dis-criminates amongst potential reaction pathways.

Acceleration factor can be up to a million or more. Most reactions without the enzyme practically does not occur at all.

carbonic anhydrase1 million CO2/s

An enzyme generally catalyses only one reaction or very similar reactions.

Side reactions resulting in by-products are rare unlike in case of regular chemical reactions.

Substrate specificity, however, may sometimes be kind of “loose” for someenzymes (like Papain – very undiscriminating protease).

Some rather specific enzymes:Trypsin: digestive enzyme, cleaves peptide bond on the –COOH side at Lys or Arg.Thrombin: participates in blood clotting, hydrolyzes Arg-Gly bonds in specific peptide sequences only.

Specificity and such a high precision in molecular action is possible becauseof the intricately accurate design of the 3D structure of the enzyme specializing in that particular reaction and substrate structures. Thisfunction to develop needed millions of years of evolution.

Catalytic action sometimes needs some small extra molecular entities attached covalently or non-covalently to the enzyme (cofactors).

Enzyme w/o its cofactor: apoenzyme, with it: holoenzyme.

Cofactors: 1. metals 2. coenzymes (small organic molecules, often derivedfrom vitamins; the tightly bound coenzymes are the prosthetic groups; loosely bound coenzymes are rather just called cosubstrates)

Some enzymes use the same coenzymes showing similar mechanisms.

Enzymes may also transfer energy from one form to another, e.g. photo-synthesis: light energy to chemical energy or in mitochondria: energy fromfood to an ion gradient then to ATP. Other enzymes then can use the energy of these molecules to convert energy or molecules even further (e.g. myosin converts ATP energy to mechanical energy of contracting muscles, or membrane transport proteins to move molecules/ions across membranes).

Classification of enzymes:

There are common names (trypsin – no info on what it does), but also many Es are named after the substrates and the reactions + the “ase” suffix. E.g. peptide hydrolase – hydrolyzes peptide bonds, ATP synthase – synthesizes ATP.

1964: EC (Enzyme Commission) numbers: a 4 digit number to unambiguously iden-tify enzymes.

Example: nucleoside monophosphate (NMP) kinase (transfers a phosphoryl group – a transferase (group 2)

Since it transfers a phosphoryl group: 2.7

Since the acceptor in the reaction is a phosphate: 2.7.4.

More precisely the acceptor is a nucleoside monophosphate: 2.7.4.4.

What drives (enzymatic) reactions? Which reaction will be spontaneous?

All answers are told by the thermodynamics considerations learned in Physical Chemistry (please consult your previous studies and the Bioener-getics lectures).

Enzymes are “only” catalysts which enhance the rate of formation of thedynamic reaction equilibria and the process gives the catalyst back “unaltered” (enzymes also have a half-life though and then new moleculesof them are generated [expressed]).

TS is a transitory structure that is no longer the substrate but also notyet the product, either. It is the least stable and most-seldom-occupiedspecies along the reaction pathway. It has the highest free energy.

G‡ is (one expression of) the activation energy. Enzymes lower the activa-tion energy facilitating the formation (stabilization) of the transition state.

S X‡ PK

‡ v

V α [X‡]

G‡ α 1/[X‡]

V (overall rate of reaction) ~ G‡

I think that enzymes are molecules that arecomplementary in structure to the activatedcomplexes of the reactions that they cata-lyze, that is, to the molecular configurationthat is intermediate between the reacting substances and the products of reaction forthese catalyzed processes. The attractionof the enzyme molecule for the activated complex would thus lead to a decrease in itsenergy and hence to a decrease in the ener-gy of activation of the reaction and to an increase in the rate of reaction.

Linus Pauling, Nature 161 (1948): 707

Remark: I think Stryer: Biochemistry, 6th ed. p.212, last eq. is not correct.

An enzyme-substrate complex (ES) forms to facilitate the stabilization ofthe TS of the reaction.

first verification:

Uncatalyzed reactions do not saturate.

all catalytic sites are occupied.

X-ray showed substrates and analogs bound to active sites.

Time-resolved crystallography uses a light-sensitive substrate analog. Photons are shed on resulting substrate and then ES complex that is captured in a fraction of a secondby polychromatic synchrotron radiation X-ray beams.

cyt P450 – camphor complex

Also spectroscopic characteristics of enzymes and/or substrates some-times change upon the formation of the ES complex. It is particularly obvious if there is a colored prosthetic group bound to an enzyme.

Trp synthetase uses a pyridoxal phosphate (PLP)prosthetic group to make L-Trp from Ser and indole. Addition of Ser changes drastically the fluorescence of PLP. Addition of the 2nd substrate, indole, decreases fluorescence to lower than the free enzyme. This proves the existence of the E-Ser and the E-Ser-indole complexes. NMR and ESR can also prove ES complex formations.

Active site (AS): -binds substrates-binds cofactors-contains the residues that brakeand make bonds (catalytic groups)-a 3D cleft or crevice formed from amino acids (aa) that might be far in primary sequence -H2O is excluded unless a substrate-non-polar microenvironments with often polar (“active”) residues in special positions

Lysozyme

Why to have a big protein for those few “active” amino acids?

The “extra” aa are making the scaffold that position the “active” aa intothe exact 3D configuration required for action.

But why does not a protein use neighboring aa to form the AS?

Those aa are often sterically constrained from adopting the necessary configuration.

The “extra” amino acids often constitute regulatory sites, sites of inter-action with other proteins or ligands, or channels to bring the substratesto the AS. Not to mention enzymes with multiple (but sometimes also coupled) enzymatic functions.

Substrates are bound to enzymes by multiple weak interactions asdiscussed earlier. The directional character of H-bonding among specificsites on E and S makes the interaction often very specific.

The close contacts that hold the ES together assume a matching shape ofS to E. Ribonuclease

Emil Fischer (1890): “lock and key” analogy (seems now an oversight).

Daniel E. Koshland, Jr. (1958): E is flexible and dynamic and the shape ofthe AS can considerably change upon substrate binding. The AS of most Egets complementary in shape to S only after S is bound (induced fit).

Very current and still unsolved question: Does protein dynamics have anything to do with the catalytic action? So far we believe the answer is (suprisingly) NO!! /Protein Society Meeting, Stockholm, 2011/

Binding energy (BE) is released upon S binding to E. Only the correct subs-trate can participate in the maximal number of possible interactions bet-ween E and S, thus release the highest BE. But all possible interactionscan only be formed in the TS!! The release of BE can be thought of as lowering the activation energy (see Linus Pauling earlier).

Paradox:Paradox: the highest BE is released (the most stable interaction is) in theTS where the least stable reaction intermediate exists.

The TS is too unstable to exist for long, it will collapse to either substrateor product. Which accumulates in excess over time is decided by the G ofthe reaction.

The Michaelis-Menten (M-M) kinetics (true for mostenzymes)

E + S ES E + Pk1

k-1

k2

k-2

E + S ES E + Pk1

k-1

k2

If t ~ 0, k-2[P][E] ~ 0, so

Vo should be measured early in time before P accumulates!

V0=k2[ES]

Rate of formation of ES: k1[E][S]Rate of breakdown of ES: (k-1 + k2)[ES]

According to the steady-state (Bodenstein`s) principle the concentrations of the reaction intermediates under particular conditions do not change as a function oftime and remain approximately constant (d[ES]/dt ~ 0)

in steady state these are equal

[E][S]/[ES]=(k-1 + k2)/k1=KM (Michaelis constant)

KM has a unit of concentration and it is independent of [S] or [E]

[ES]=[E][S]/KM

[E]=[E]T-[ES] [ES]=([E]T-[ES])[S]/KM

[ES]=([E]T[S]/KM)/(1+[S]/KM)

[ES]=[E]T[S]/([S]+KM)

V0=k2[ES]

V0=k2[E]T[S]/([S]+KM)

Vmax is reached when [ES]=[E]T (all catalytic sites are occupied by substrate)

Vmax=k2[E]T

V0=Vmax [S]/([S]+KM)

M-M equation

When [S] << KM

V0=Vmax [S]/([S]+KM)

V0=(Vmax/KM)[S] (1st order; linear with [S])

When [S] >> KMV0=Vmax (zero order, independent of [S])

KM and Vmax is determined from kinetic experiments by curve-fitting analyses in computers. Before computers it was easier to linearize theequation (error prone, it weighs data points differently at low and high [S]).

1/V0=(KM/Vmax)(1/[S]) + 1/Vmax

double-reciprocal or Lineweaver-Burk plot

KM depends on: substrate, ionic strength, pH, temperature

Significance/meaning of KM:

- KM is the substrate concentration when half of the AS are occupied (sig-nificant catalysis takes place)

- A good approximation of the substrate concentration present in vivo

- ONLY when k-1 >> k2 (this is though very rarely the case for most enzymes) KM approximates the Kd of ES (high KM then means weak bindingand vica versa) – frequent misinterpretation of KM (as Kd) even in today’sscientific literature

Vmax reveals the turnover number (TN) of an enzyme. TN is the # of Sconverted to P by a single E in unit time when E is fully saturated with S.

TN = k2 = kcat = Vmax/[E]T

e.g. a 10-6 M carbonic anhydrase solution catalyzes the formation of 0.6 MH2CO3 in each second as long as the enzyme is fully saturated with CO2.

1.7 s/reaction

Fraction of active sites filled fES = V0/Vmax = [S]/([S] + KM)

In a “normal” situation an enzyme is not always fully saturated with subst-rates in vivo; rather the [S]/KM ~ 0.01 – 1.0 typically.

V0=k2[ES] [ES]=[E][S]/KM

V0=(kcat/KM)[E][S]

When [S] << KM [E] ~ [E]T

V0=(kcat/KM)[E]T[S]

rate constant for the interaction of S and E

determines the substratepreference of an enzyme

Is there any physical limit for kcat/KM?

kcat/KM=(kcatk1)/(k-1 + kcat)=(kcat/(k-1 + kcat))k1 < k1

If kcat >> k-1, then kcat/KM ~ k1, so the ultimate limit on kcat/KM is k1

(the rate of formation for the ES). But this rate cannot be faster thanthe diffusion-controlled encounter of an enyzme and its substrate!!

Diffusion controls k1, so k1 as well as kcat/KM cannot realistically be higherthan ~108-109 s-1M-1.

These enzymes attained “kinetic perfection”. Their catalytic velocities practically are restricted only by how fast they can get to the substrate.

How can every encounter between E and S be productive, for the “kinetically perfect enzymes”, when S can only effectively bind to the AS (which is a small part/portion of E)? They suspect there are attractive electrostatic forces originated from E which lure substrates to the AS. This is called the Circe effect.

Diffusion in solution can also be partly overcome by confining S and P in thelimited volume of a multienzyme complex.

If an enzyme is well characterized and known (and also in clinical practice) then they use the so-called “activity” of the enzyme, as a unit of effect-iveness. This actually means reaction velocity, under precisely known andcontrolled conditions. It tells us how much S can be converted (or P be generated) by the actual amount of E present in solution, (generally) at the saturating concentration of S in unit time.

SI unit is: catal (mol/s)

In practice we rather use mol/min (or Unit (U))

Especially during protein (enzyme) purification it is a good practice to measure the specific activity of the enzyme, which means enzyme activityper unit mass of protein (e.g. mol/min/mg). If the specific activity is raised along purification then the protein preparation gets more pure.

We have to consider that there are optimal conditions for E activity (pH, I, T, cofactor) and comparison is only valid if all values have been measured under the same experimental conditions.

Most (bio)chemical reactions include two or more compounds. For enzymes this means multiple (and not only one!) substrates.

A + B P + Q

Many such reactions transfer a functional group, a phosphoryl or an aminogroup from one substrate to another. It is also possible that an electron ortwo are transferred in oxido-reduction reactions.

There are two typical forms of multiple substrate reactions:

sequential or double-displacement reactions

Sequential reactions: all substrates get bound before any product is released. Consequently, a ternary complex must be formed during catalysis(E-S1-S2). There is an ordered (binding of Ss are in a defined seq.) and arandom sequential mechanism.

Good examples for ordered sequential mechanism are reactions that use NAD+ or NADH as substrates, e.g. lactate dehydrogenase

Notation by W. Wallace Cleland

Example for random sequential mechanism:

PC is an important energy source in muscle

(PC)

Double-displacement (ping-pong) mechanisms

One or more products are released before all substrates are bound. There is a substituted E-intermediate where E is temporarily modified.

Typical reactions are the transaminations, e.g.:

S1 S2P1 P2

substrates bounce on&off E: ping-pong analogy

Allosteric enzymes may not always obey M-M kinetics; they might havemultiple subunits, multiple AS, sigmoidal V0 – [S] plots, regulatory ligand (reversible) binding sites

Binding of one S to the 1st AS can alter the properties of the other ASs, generally enhancing the binding probability of the 2nd S, in the same E molecule (cooperativity, see Hb/Mb; positive homotropic effect).

Due to the versatile sorts of possibilities for regulation, allosteric enzymescan satisfy the immediate needs of the cell, thus they are the key regula-tors of metabolic pathways (generally by the action of a heterotropic allos-teric activator or inhibitor ligand on the same polypeptide chain, see later).

cooperativity

Inhibition

It is a major control mechanism in biological systems, where allosteric regulation (inhibition) is a major player through binding small molecules (metabolites) into allosteric sites. Also many drugs and toxic agents actas inhibitors (inhibitor=I from now on).

Knowing the inhibitory mechanism tells us much about the mechanism ofaction of an enzyme and vica versa.

TS analogs are especially potent Is.

There is reversible and irreversible inhibition.

Irreversible inhibition: I dissociates very slowly from E, bound strongly covalently or non-covalently (Kd is small; several drugs are like this, e.g. penicillin covalently modifies transpeptidase preventing bacterial cell wallsynthesis or aspirin covalently modifies cyclooxygenase blocking the synt-hesis of signal molecules involved in inflammation).

Reversible inhibition: more transient binding of I to E. Three types exist.

ES complexEI complex

ESI complex does not exist,S and I aremutually exclu-sive.

S and I oftenresemble oneanother.

I binds onlyto ES.

A competitive I reduces the proportion of E that binds S. Competitive inhibition can be relieved by increasing [S].

Examples:

- methotrexate is a potent competitive inhibitor (structural analog)of dihydrofolate reductase (dTMP synthesis blocker, anticancer drug, binds 1000x better than S to E)

- Ibuprofen competitively inhibits enzymes in signaling of inflammation.

- Statins lower cholesterol by competitively inhibit a key enzyme in cholesterol biosynthesis (HMG-CoA reductase).

Uncompetitive inhibitory site is created only after forming the ES complex.It cannot be overcome by increasing [S].

In noncompetitive inhibition S and I can bind simultaneously to E but to different sites. It cannot be overcome by increasing [S]. Here the kcat decreases.

There is a so-called mixed inhibition: substrate binding is hindered and kcat is reduced by I in the same time.

Kinetic pictures of reversible inhibitory mechanisms differ:

We need to measure the reaction rates at different S and I concentrations.

1. Competitive inhibition:

apparent KM increasesVmax does not change

KMapp=KM(1 + [I]/Ki)

1/Vmax

m=KM/Vmax

2. Uncompetitive inhibition:

Vmax and KMapp

decrease

Example: glycophosphate (herbicide; Roundup) is an uncompetitive inhibitorof an enzyme for aromatic amino acidsynthesis.

-1/KM

1/Vmax

3. Noncompetitive inhibition:

Vmax is decreased (Vmaxapp)

KM does not change

Vmaxapp=Vmax/(1 + [I]/Ki)

The inhibitor simply lowers theconcentration of functional E.

Examples: - deoxycycline (antibiotic)noncompetitively inhibits collage-nase (a protease). Used in the treatment of periodontal disease.

- Lead (Pb) poisoning is due to that Pb behaves as noncompetitiveinhibitor to lots of enzymes (Pb can react with –SHs).

-1/KM

To determine the mechanism of action of an enzyme first we need to know which residues (what functional groups) take part in the catalysis from E.

X-ray structure of the ES or an EI (esp. a covalently bound irreversible I)can map the AS. Three types of irreversible Is there are: group-specific reagents (1), reactive substrate analogs (affinity labels, 2) and suicide inhi-bitors (3).

Group-specific reagents:

diisopropylphosphofluoridate (DIPF, nerve gas): reacts only with highly reactive Ser (e.g. ones in chymotrypsin’s and acetylcholinesterase’s ASs)

Iodoacetamide:

Reactive substrate analogs:

Structurally similar to the S and can covalently bind to AS residues.

substrate analog reacting irreversibly with AS His

Suicide (mechanism-based) inhibitors: most specific way to modify the AS. These are generally some versions of modified substrates which initially getconverted by the normal mechanism by E, but then are trapped in a specificstep during the mechanism in forms of intermediates which cannot furtherbe processed by E (due to a specific covalent modification of E, generally). The covalently modified group on E is essential for catalysis.

Example: monoamine oxidase (MAO) inhibitors: N,N-dimethylpropargylamine and Deprenyl. MAO deaminates neurotransmitters serotonin, dopamine lowering their brain levels). Low level of dopamine is implicated in Parkinson‘sDisease, while low serotonin level in depression.

Deprenyl

Transition-state analogs are potent inhibitors

First proposed by Linus Pauling (1948).

Example: Pro-racemase, in TS the tetrahedral -C becomes trigonal.

Reprotonation can go towards either direction.

binds 160x tighter to E than Pro

An analog holding – charge on -C would beeven more potent.

trigonal

Highly potent and specific Is can be designed ifI resembles the TS rather than S itself.

Antibodies (Ab) that recognise TS have catalytic activities.

Example: An Ab can catalyze the insertion of a metal ion into a porphyrin.

Ferrochelatase, last enzyme in heme synthesis, puts Fe2+ into protoporphy-rin IX. During catalysis the planar ring must be bent for Fe2+ to enter. A hard-to-find TS analog turned out to be methylmesoporphyrin (see below).

They used this compound as antigen to produce a catalytic Ab (abzyme) thatalso catalyzes the insertion Fe2+. The Ab was only 10x less potent than theenzyme. In general, an abzyme can be generated by a TS analog. They gene-rated abzymes for many more reactions already. These experiments provethat conformation of the AS is indeed complementary to the TS.

The idea came from the finding that N-Me-proto-porphyrin is a potent inhibitor of ferrochelatase (N-alkylation forces the ring to bend). N-alkylated porphyrins also chelate metals 10,000x better because bending exposes the lone pairs of electrons of pyrrole Ns that binds Fe2+.