Enzyme kinetics

Dihydrofolate reductase from E. coli with itstwo substrates, dihydrofolate (right) andNADPH (left), bound in the active site. Theprotein is shown as a ribbon diagram, withalpha helices in red, beta sheets in yellowand loops in blue. Generated from 7DFR.

Enzyme kinetics is the study of the chemic-al reactions that are catalysed by enzymes,with a focus on their reaction rates. Thestudy of an enzyme’s kinetics reveals thecatalytic mechanism of this enzyme, its rolein metabolism, how its activity is controlled,and how a drug or a poison might inhibit theenzyme.

Enzymes are usually protein moleculesthat manipulate other molecules — the en-zymes’ substrates. These target moleculesbind to an enzyme’s active site and are trans-formed into products through a series ofsteps known as the enzymatic mechanism.These mechanisms can be divided into single-substrate and multiple-substrate mechan-isms. Kinetic studies on enzymes that onlybind one substrate, such as triosephosphateisomerase, aim to measure the affinity with

which the enzyme binds this substrate andthe turnover rate.

When enzymes bind multiple substrates,such as dihydrofolate reductase (shownright), enzyme kinetics can also show the se-quence in which these substrates bind andthe sequence in which products are released.An example of enzymes that bind a singlesubstrate and release multiple products areproteases, which cleave one protein sub-strate into two polypeptide products. Othersjoin two substrates together, such as DNApolymerase linking a nucleotide to DNA. Al-though these mechanisms are often a com-plex series of steps, there is typically onerate-determining step that determines theoverall kinetics. This rate-determining stepmay be a chemical reaction or a conforma-tional change of the enzyme or substrates,such as those involved in the release ofproduct(s) from the enzyme.

Knowledge of the enzyme’s structure ishelpful in interpreting the kinetic data. Forexample, the structure can suggest how sub-strates and products bind during catalysis;what changes occur during the reaction; andeven the role of particular amino acidresidues in the mechanism. Some enzymeschange shape significantly during the mech-anism; in such cases, it is helpful to determ-ine the enzyme structure with and withoutbound substrate analogs that do not undergothe enzymatic reaction.

Not all biological catalysts are protein en-zymes; RNA-based catalysts such as ri-bozymes and ribosomes are essential to manycellular functions, such as RNA splicing andtranslation. The main difference between ri-bozymes and enzymes is that the RNA cata-lysts perform a more limited set of reactions,although their reaction mechanisms and kin-etics can be analysed and classified by thesame methods.

General principlesThe reaction catalysed by an enzyme uses ex-actly the same reactants and produces ex-actly the same products as the uncatalysedreaction. Like other catalysts, enzymes do

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Reaction rates increase as substrate concen-tration increase, but become saturated atvery high concentrations of substrate.

not alter the position of equilibrium betweensubstrates and products.[1] However, unlikeuncatalysed chemical reactions, enzyme-cata-lysed reactions display saturation kinetics.For a given enzyme concentration and for rel-atively low substrate concentrations, the re-action rate increases linearly with substrateconcentration; the enzyme molecules arelargely free to catalyze the reaction, and in-creasing substrate concentration means anincreasing rate at which the enzyme and sub-strate molecules encounter one another.However, at relatively high substrate concen-trations, the reaction rate asymptotically ap-proaches the theoretical maximum; the en-zyme active sites are almost all occupied andthe reaction rate is determined by the intrins-ic turnover rate of the enzyme. The substrateconcentration midway between these twolimiting cases is denoted by KM.

The two most important kinetic propertiesof an enzyme are how quickly the enzyme be-comes saturated with a particular substrate,and the maximum rate it can achieve. Know-ing these properties suggests what an en-zyme might do in the cell and can show howthe enzyme will respond to changes in theseconditions.

Enzyme assaysEnzyme assays are laboratory proceduresthat measure the rate of enzyme reactions.Because enzymes are not consumed by thereactions they catalyse, enzyme assays usu-ally follow changes in the concentration ofeither substrates or products to measure therate of reaction. There are many methods ofmeasurement. Spectrophotometric assays ob-serve change in the absorbance of lightbetween products and reactants; radiometric

Progress curve for an enzyme reaction. Theslope in the initial rate period is the initialrate of reaction v. The Michaelis-Mentenequation describes how this slope varies withthe concentration of substrate.

assays involve the incorporation or release ofradioactivity to measure the amount ofproduct made over time. Spectrophotometricassays are most convenient since they allowthe rate of the reaction to be measured con-tinuously. Although radiometric assays re-quire the removal and counting of samples(i.e., they are discontinuous assays) they areusually extremely sensitive and can measurevery low levels of enzyme activity.[2] An ana-logous approach is to use mass spectrometryto monitor the incorporation or release ofstable isotopes as substrate is converted intoproduct.

The most sensitive enzyme assays uselasers focused through a microscope to ob-serve changes in single enzyme molecules asthey catalyse their reactions. These measure-ments either use changes in the fluorescenceof cofactors during an enzyme’s reactionmechanism, or of fluorescent dyes addedonto specific sites of the protein to reportmovements that occur during catalysis.[3]These studies are providing a new view of thekinetics and dynamics of single enzymes, asopposed to traditional enzyme kinetics, whichobserves the average behaviour of popula-tions of millions of enzyme molecules.[4][5]

A typical progress curve for an enzyme as-say is shown above. The enzyme producesproduct at a linear initial rate at the start ofthe reaction. Later in this progress curve, therate slows down as substrate is used up orproducts accumulate. The length of the initialrate period depends on the assay conditions

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and can range from milliseconds to hours.Enzyme assays are usually set up to producean initial rate lasting over a minute, to makemeasurements easier. However, equipmentfor rapidly mixing liquids allows fast kineticmeasurements on initial rates of less thanone second.[6] These very rapid assays areessential for measuring pre-steady-state kin-etics, which are discussed below.

Most enzyme kinetics studies concentrateon this initial, linear part of enzyme reac-tions. However, it is also possible to measurethe complete reaction curve and fit this datato a non-linear rate equation. This way ofmeasuring enzyme reactions is calledprogress-curve analysis.[7] This approach isuseful as an alternative to rapid kineticswhen the initial rate is too fast to measureaccurately.

Single-substratereactionsEnzymes with single-substrate mechanismsinclude isomerases such as triosephos-phateisomerase or bisphosphoglyceratemutase, intramolecular lyases such as ad-enylate cyclase and the hammerhead ri-bozyme, a RNA lyase.[8] However, some en-zymes that only have a single substrate donot fall into this category of mechanisms.Catalase is an example of this, as the enzymereacts with a first molecule of hydrogen per-oxide substrate, becomes oxidised and isthen reduced by a second molecule of sub-strate. Although a single substrate is in-volved, the existence of a modified enzymeintermediate means that the mechanism ofcatalase is actually a ping–pong mechanism,a type of mechanism that is discussed in theMulti-substrate reactions section below.

Michaelis–Menten kinetics

Single-substrate mechanism for an enzymereaction. k1, k-1 and k2 are the rate constantsfor the individual steps.

As enzyme-catalysed reactions are saturable,their rate of catalysis does not show a linear

Saturation curve for an enzyme showing therelation between the concentration of sub-strate and rate.

response to increasing substrate. If the initialrate of the reaction is measured over a rangeof substrate concentrations (denoted as [S]),the reaction rate (v) increases as [S] in-creases, as shown on the right. However, as[S] gets higher, the enzyme becomes satur-ated with substrate and the rate reachesVmax, the enzyme’s maximum rate.

The Michaelis-Menten kinetic model of asingle-substrate reaction is shown on theright. There is an initial bimolecular reactionbetween the enzyme E and substrate S toform the enzyme–substrate complex ES. Al-though the enzymatic mechanism for the un-

imolecular reaction reac-tion can be quite complex, there is typicallyone rate-determining enzymatic step that al-lows this reaction to be modelled as a singlecatalytic step with an apparent unimolecularrate constant kcat. If the reaction path pro-ceeds over one or several intermediates, kcatwill be a function of several elementary rateconstants, whereas in the simplest case of ansingle elementary reaction reaction (e.g. nointermediates) it will be identical to the ele-mentary unimolecular rate constant k2. Theapparent unimolecular rate constant kcat isalso called turnover number and denotes themaximum number of enzymatic reactionscatalyzed per second.

The Michaelis–Menten equation[9] de-scribes how the (initial) reaction rate v0 de-pends on the position of the substrate-bind-ing equilibrium and the rate constant k2.

(Michaelis-Mentenequation)

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with the constants

This Michaelis-Menten equation is the basisfor most single-substrate enzyme kinetics.Two crucial assumptions underlie this equa-tion (apart from the general assumptionabout the mechanism only involving no inter-mediate or product inhibition, and there is noallostericity or cooperativity). The first as-sumption is the so called quasi-steady-stateassumption (or pseudo-steady-state hypothes-is), namely that the concentration of thesubstrate-bound enzyme (and hence also theunbound enzyme) changes much more slowlythan those of the product and substrate andthus the change over time of the complex can

be set to zero . The secondassumption is that the total enzyme concen-tration does not change over time, thus

. A com-plete derivation can be found here.

The Michaelis constant KM is experiment-ally defined as the concentration at which therate of the enzyme reaction is half Vmax,which can be verified by substituting [S] =Km into the Michaelis-Menten equation andcan be seen graphically too. If the rate-de-termining enzymatic step is slow comparedto substrate dissociation ( ), theMichaelis constant KM is roughly the dissoci-ation constant KD of the ES complex.

If [S] is small compared to KM then theterm andalso very little ES complex is formed, thus

. Therefore, the rate of productformation is

Thus the product formation rate depends onthe enzyme concentration as well as on thesubstrate concentration, the equation re-sembles a bimolecular reaction with acorresponding pseudo-second order rate con-stant k2 / KM. This constant is a measure ofcatalytic efficiency. The most efficient en-zymes reach a k2 / KM in the range of 108 -1010 M−1 s−1. These enzymes are so efficient

they effectively catalyze a reaction each timethey encounter a substrate molecule andhave thus reached an upper theoretical limitfor efficiency (diffusion limit); these enzymeshave often been termed perfect enzymes.[10]

Linear plots of the Michaelis-Menten equationSee also: Lineweaver–Burk plot and Eadie-Hofstee diagram

Lineweaver–Burk or double-reciprocal plot ofkinetic data, showing the significance of theaxis intercepts and gradient.

Using an interactive Michaelis–Menten kinet-ics tutorial at the University of Virginia,[α]the effects on the behaviour of an enzyme ofvarying kinetic constants can be explored.

The plot of v versus [S] above is not linear;although initially linear at low [S], it bendsover to saturate at high [S]. Before the mod-ern era of nonlinear curve-fitting on com-puters, this nonlinearity could make it diffi-cult to estimate Km and Vmax accurately.Therefore, several researchers developed lin-earizations of the Michaelis-Menten equa-tion, such as the Lineweaver–Burk plot, theEadie-Hofstee diagram and the Hanes-Woolfplot. All of these linear representations canbe useful for visualizing data, but noneshould be used to determine kinetic paramet-ers, as computer software is readily availablethat allows for more accurate determinationby nonlinear regression methods.[11]

The Lineweaver–Burk plot or double recip-rocal plot is a common way of illustrating kin-etic data. This is produced by taking the re-ciprocal of both sides of the Michaelis–Men-ten equation. As shown on the right, this is alinear form of the Michaelis–Menten equation

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and produces a straight line with the equa-tion y = mx + c with a y-intercept equivalentto 1/Vmax and an x-intercept of the graph rep-resenting -1/Km.

Naturally, no experimental values can betaken at negative 1/[S]; the lower limitingvalue 1/[S] = 0 (the y-intercept) correspondsto an infinite substrate concentration, where1/v=1/Vmax as shown at the right; thus, the x-intercept is an extrapolation of the experi-mental data taken at positive concentrations.More generally, the Lineweaver–Burk plotskews the importance of measurementstaken at low substrate concentrations and,thus, can yield inaccurate estimates of Vmaxand Km.[12] A more accurate linear plottingmethod is the Eadie-Hofstee plot. In thiscase, v is plotted against v/[S]. In the thirdcommon linear representation, the Hanes-Woolf plot, [S]/v is plotted against [S]. In gen-eral, data normalisation can help diminishthe amount of experimental work and can in-crease the reliability of the output, and issuitable for both graphical and numericalanalysis.[13]

Practical significance of kineticconstantsThe study of enzyme kinetics is important fortwo basic reasons. Firstly, it helps explainhow enzymes work, and secondly, it helpspredict how enzymes behave in living organ-isms. The kinetic constants defined above,Km and Vmax, are critical to attempts to un-derstand how enzymes work together to con-trol metabolism.

Making these predictions is not trivial,even for simple systems. For example, oxalo-acetate is formed by malate dehydrogenasewithin the mitochondrion. Oxaloacetate canthen be consumed by citrate synthase, phos-phoenolpyruvate carboxykinase or aspartateaminotransferase, feeding into the citric acidcycle, gluconeogenesis or aspartic acid bio-synthesis, respectively. Being able to predicthow much oxaloacetate goes into which path-way requires knowledge of the concentrationof oxaloacetate as well as the concentrationand kinetics of each of these enzymes. Thisaim of predicting the behaviour of metabolicpathways reaches its most complex

expression in the synthesis of huge amountsof kinetic and gene expression data intomathematical models of entire organisms. Al-though this goal is far in the future for anyeukaryote, attempts are now being made toachieve this in bacteria, with models ofEscherichia coli metabolism now being pro-duced and tested.[14][15]

Michaelis Menten kinetics withintermediateOne could also consider the less simple case

where an complex with the enzyme and an in-termediate exists and the intermediate isconverted into product in a second step. Inthis case we have a very similar equation[16]

but the constants are different

We see that for the limiting case ,thus when the last step from EI to E + P ismuch faster than the previous step, we getagain the original equation. Mathematicallywe have then and .

Multi-substrate reactionsMulti-substrate reactions follow complex rateequations that describe how the substratesbind and in what sequence. The analysis ofthese reactions is much simpler if the con-centration of substrate A is kept constant andsubstrate B varied. Under these conditions,the enzyme behaves just like a single-sub-strate enzyme and a plot of v by [S] gives ap-parent Km and Vmax constants for substrateB. If a set of these measurements is per-formed at different fixed concentrations of A,these data can be used to work out what themechanism of the reaction is. For an enzymethat takes two substrates A and B and turnsthem into two products P and Q, there are

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two types of mechanism: ternary complexand ping–pong.

Ternary-complex mechanisms

Random-order ternary-complex mechanismfor an enzyme reaction. The reaction path isshown as a line and enzyme intermediatescontaining substrates A and B or products Pand Q are written below the line.

In these enzymes, both substrates bind to theenzyme at the same time to produce an EABternary complex. The order of binding caneither be random (in a random mechanism)or substrates have to bind in a particular se-quence (in an ordered mechanism). When aset of v by [S] curves (fixed A, varying B)from an enzyme with a ternary-complexmechanism are plotted in a Lineweaver–Burkplot, the set of lines produced will intersect.

Enzymes with ternary-complex mechan-isms include glutathione S-transferase,[17] di-hydrofolate reductase[18] and DNA poly-merase.[19] The following links show shortanimations of the ternary-complex mechan-isms of the enzymes dihydrofolate re-ductase[β] and DNA polymerase[γ].

Ping–pong mechanisms

Ping–pong mechanism for an enzyme reac-tion. Enzyme intermediates contain sub-strates A and B or products P and Q.

As shown on the right, enzymes with a ping-pong mechanism can exist in two states, Eand a chemically modified form of the en-zyme E*; this modified enzyme is known asan intermediate. In such mechanisms, sub-strate A binds, changes the enzyme to E* by,for example, transferring a chemical group tothe active site, and is then released. Onlyafter the first substrate is released can sub-strate B bind and react with the modified en-zyme, regenerating the unmodified E form.

When a set of v by [S] curves (fixed A, vary-ing B) from an enzyme with a ping–pongmechanism are plotted in a Lineweaver–Burkplot, a set of parallel lines will be produced.

Enzymes with ping–pong mechanisms in-clude some oxidoreductases such asthioredoxin peroxidase,[20] transferases suchas acylneuraminate cytydilyltransferase[21]and serine proteases such as trypsin andchymotrypsin.[22] Serine proteases are a verycommon and diverse family of enzymes, in-cluding digestive enzymes (trypsin,chymotrypsin, and elastase), several enzymesof the blood clotting cascade and many oth-ers. In these serine proteases, the E* inter-mediate is an acyl-enzyme species formed bythe attack of an active site serine residue ona peptide bond in a protein substrate. A shortanimation showing the mechanism ofchymotrypsin is linked here.[δ]

Non-Michaelis–Mentenkinetics

Saturation curve for an enzyme reactionshowing sigmoid kinetics.

Some enzymes produce a sigmoid v by [S]plot, which often indicates cooperative bind-ing of substrate to the active site. This meansthat the binding of one substrate molecule af-fects the binding of subsequent substrate mo-lecules. This behavior is most common inmultimeric enzymes with several interactingactive sites.[23] Here, the mechanism of co-operation is similar to that of haemoglobin,with binding of substrate to one active site al-tering the affinity of the other active sites forsubstrate molecules. Positive cooperativityoccurs when binding of the first substratemolecule increases the affinity of the other

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active sites for substrate. Negative cooper-ativity occurs when binding of the first sub-strate decreases the affinity of the enzymefor other substrate molecules.

Allosteric enzymes include mammaliantyrosyl tRNA-synthetase, which shows negat-ive cooperativity,[24] and bacterial aspartatetranscarbamoylase[25] and phosphofructok-inase[26], which show positive cooperativity.

Cooperativity is surprisingly common andcan help regulate the responses of enzymesto changes in the concentrations of their sub-strates. Positive cooperativity makes en-zymes much more sensitive to [S] and theiractivities can show large changes over a nar-row range of substrate concentration. Con-versely, negative cooperativity makes en-zymes insensitive to small changes in [S].

The Hill equation[27] is often used to de-scribe the degree of cooperativity quantitat-ively in non-Michaelis–Menten kinetics. Thederived Hill coefficient n measures how muchthe binding of substrate to one active site af-fects the binding of substrate to the otheractive sites. A Hill coefficient of <1 indicatesnegative cooperativity and a coefficient of >1indicates positive cooperativity.

Pre-steady-state kinetics

Pre-steady state progress curve, showing theburst phase of an enzyme reaction.

In the first moment after an enzyme is mixedwith substrate, no product has been formedand no intermediates exist. The study of thenext few milliseconds of the reaction is calledpre-steady-state kinetics. Pre-steady-statekinetics is therefore concerned with theformation and consumption of enzyme–sub-strate intermediates (such as ES or E*) untiltheir steady-state concentrations arereached.

This approach was first applied to the hy-drolysis reaction catalysed by chymotryp-sin.[28] Often, the detection of an intermedi-ate is a vital piece of evidence in investiga-tions of what mechanism an enzyme follows.For example, in the ping–pong mechanismsthat are shown above, rapid kinetic measure-ments can follow the release of product P andmeasure the formation of the modified en-zyme intermediate E*.[29] In the case ofchymotrypsin, this intermediate is formed bythe attack of the substrate by the nucleophil-ic serine in the active site and the formationof the acyl-enzyme intermediate.

In the figure to the right, the enzyme pro-duces E* rapidly in the first few seconds ofthe reaction. The rate then slows as steadystate is reached. This rapid burst phase ofthe reaction measures a single turnover ofthe enzyme. Consequently, the amount ofproduct released in this burst, shown as theintercept on the y-axis of the graph, alsogives the amount of functional enzyme whichis present in the assay.[30]

Chemical mechanismAn important goal of measuring enzyme kin-etics is to determine the chemical mechanismof an enzyme reaction, i.e., the sequence ofchemical steps that transform substrate intoproduct. The kinetic approaches discussedabove will show at what rates intermediatesare formed and inter-converted, but they can-not identify exactly what these intermediatesare.

Kinetic measurements taken under vari-ous solution conditions or on slightly modi-fied enzymes or substrates often shed lighton this chemical mechanism, as they revealthe rate-determining step or intermediates inthe reaction. For example, the breaking of acovalent bond to a hydrogen atom is acommon rate-determining step. Which of thepossible hydrogen transfers is rate determin-ing can be shown by measuring the kineticeffects of substituting each hydrogen by deu-terium, its stable isotope. The rate willchange when the critical hydrogen is re-placed, due to a primary kinetic isotope ef-fect, which occurs because bonds to deuteri-um are harder to break then bonds to hydro-gen.[31] It is also possible to measure similareffects with other isotope substitutions, suchas 13C/12C and 18O/16O, but these effects aremore subtle.[32]

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Isotopes can also be used to reveal thefate of various parts of the substrate mo-lecules in the final products. For example, itis sometimes difficult to discern the origin ofan oxygen atom in the final product; since itmay have come from water or from part ofthe substrate. This may be determined bysystematically substituting oxygen’s stableisotope 18O into the various molecules thatparticipate in the reaction and checking forthe isotope in the product.[33] The chemicalmechanism can also be elucidated by examin-ing the kinetics and isotope effects under dif-ferent pH conditions,[34] by altering the met-al ions or other bound cofactors,[35] by site-directed mutagenesis of conserved aminoacid residues, or by studying the behaviour ofthe enzyme in the presence of analogues ofthe substrate(s).[36]

Enzyme inhibition

Kinetic scheme for reversible enzymeinhibitors.

Enzyme inhibitors are molecules that reduceor abolish enzyme activity. These are eitherreversible (i.e., removal of the inhibitor re-stores enzyme activity) or irreversible (i.e.,the inhibitor permanently inactivates theenzyme).

Reversible inhibitorsReversible enzyme inhibitors can be classi-fied as competitive, uncompetitive, non-com-petitive or mixed, according to their effectson Km and Vmax. These different effects res-ult from the inhibitor binding to the enzymeE, to the enzyme–substrate complex ES, or toboth, as shown in the figure to the right andthe table below. The particular type of an in-hibitor can be discerned by studying the en-zyme kinetics as a function of the inhibitorconcentration. The four types of inhibitionproduce Lineweaver–Burke andEadie–Hofstee plots[12] that vary in

distinctive ways with inhibitor concentration.For brevity, two symbols are used:

and

where Ki and K’i are the dissociation con-stants for binding to the enzyme and to theenzyme–substrate complex, respectively. Inthe presence of the reversible inhibitor, theenzyme’s apparent Km and Vmax become (α/α’)Km and (1/α’)Vmax, respectively, as shownbelow for common cases.

Type ofinhibition

Kmapparent

Vmaxapparent

Kionly

(

)

competitive

Ki’only

()

uncompetitive

Ki=Ki’

(

)

non-competitive

Ki≠Ki’

(

)

mixed

Non-linear regression fits of the enzyme kin-etics data to the rate equations above[37] canyield accurate estimates of the dissociationconstants Ki and K’i.

Irreversible inhibitorsEnzyme inhibitors can also irreversibly inac-tivate enzymes, usually by covalently modify-ing active site residues. These reactions,which may be called suicide substrates, fol-low exponential decay functions and are usu-ally saturable. Below saturation, they followfirst order kinetics with respect to inhibitor.

Mechanisms of catalysisThe favoured model for the enzyme–substrateinteraction is the induced fit model.[38] Thismodel proposes that the initial interactionbetween enzyme and substrate is relativelyweak, but that these weak interactions rap-idly induce conformational changes in the en-zyme that strengthen binding. These con-formational changes also bring catalyticresidues in the active site close to the chem-ical bonds in the substrate that will be

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The energy variation as a function of reactioncoordinate shows the stabilisation of thetransition state by an enzyme.

altered in the reaction.[39] After bindingtakes place, one or more mechanisms of cata-lysis lower the energy of the reaction’s trans-ition state by providing an alternative chem-ical pathway for the reaction. Mechanisms ofcatalysis include catalysis by bond strain; byproximity and orientation; by active-site pro-ton donors or acceptors; covalent catalysisand quantum tunnelling.[29][40]

Enzyme kinetics cannot prove whichmodes of catalysis are used by an enzyme.However, some kinetic data can suggest pos-sibilities to be examined by other techniques.For example, a ping–pong mechanism withburst-phase pre-steady-state kinetics wouldsuggest covalent catalysis might be import-ant in this enzyme’s mechanism. Alternat-ively, the observation of a strong pH effect onVmax but not Km might indicate that a residuein the active site needs to be in a particularionisation state for catalysis to occur.

Footnotesα. ^ Link: Interactive Michaelis–Menten kin-etics tutorial (Java required)

β. ^ Link: dihydrofolate reductase mech-anism (Gif)

γ. ^ Link: DNA polymerase mechanism(Gif)

δ. ^ Link: Chymotrypsin mechanism(Flash required)

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[28]Hartley B.S. and Kilby B.A. The reactionof p-nitrophenyl esters withchymotrypsin and insulin. Biochem J.1954 Feb;56(2):288-97. PMID 13140189

[29]^ Alan Fersht, Structure and Mechanismin Protein Science : A Guide to EnzymeCatalysis and Protein Folding. W. H.Freeman, 1998. ISBN 0-7167-3268-8

[30]Bender ML, Begue-Canton ML, BlakeleyRL, Brubacher LJ, Feder J, Gunter CR,Kezdy FJ, Killheffer JV Jr, Marshall TH,Miller CG, Roeske RW, Stoops JK. TheDetermination of the Concentration ofHydrolytic Enzyme Solutions : a-Chymotrypsin, Trypsin, Papain, Elastase,Subtilisin, and Acetylcholinesterase. JAm Chem Soc. 1966 Dec20;88(24):5890-913. PMID 5980876

[31]Cleland WW. The use of isotope effectsto determine enzyme mechanisms. ArchBiochem Biophys. 2005 Jan1;433(1):2–12. PMID 15581561

[32]Northrop D (1981). "The expression ofisotope effects on enzyme-catalyzedreactions". Annu. Rev. Biochem. 50:103–31. doi:10.1146/annurev.bi.50.070181.000535. PMID7023356.

[33]Baillie T, Rettenmeier A (1986). "Drugbiotransformation: mechanistic studieswith stable isotopes". Journal of clinicalpharmacology 26 (6): 448–51. PMID3734135.

From Wikipedia, the free encyclopedia Enzyme kinetics

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[34]Cleland WW. Use of isotope effects toelucidate enzyme mechanisms. CRC CritRev Biochem. 1982;13(4):385–428. PMID6759038

[35]Christianson DW, Cox JD. Catalysis bymetal-activated hydroxide in zinc andmanganese metalloenzymes. Annu RevBiochem. 1999;68:33–57. PMID10872443

[36]Kraut D, Carroll K, Herschlag D (2003)."Challenges in enzyme mechanism andenergetics". Annu. Rev. Biochem. 72:517–71. doi:10.1146/annurev.biochem.72.121801.161617.PMID 12704087.

[37]Leatherbarrow RJ. Using linear and non-linear regression to fit biochemical data.Trends Biochem Sci. 1990Dec;15(12):455–8. PMID 2077683

[38]Koshland DE, Application of a Theory ofEnzyme Specificity to Protein Synthesis.Proc. Natl. Acad. Sci. U.S.A. 1958Feb;44(2):98–104. PMID 16590179

[39]Hammes G (2002). "Multipleconformational changes in enzymecatalysis". Biochemistry 41 (26): 8221–8.doi:10.1021/bi0260839. PMID12081470.

[40]Sutcliffe M, Scrutton N (2002). "A newconceptual framework for enzymecatalysis. Hydrogen tunnelling coupledto enzyme dynamics in flavoprotein andquinoprotein enzymes". Eur. J. Biochem.269 (13): 3096–102. doi:10.1046/j.1432-1033.2002.03020.x. PMID12084049. http://content.febsjournal.org/cgi/content/full/269/13/3096.

Further readingIntroductory• Athel Cornish-Bowden, Fundamentals of

Enzyme Kinetics. (3rd edition), PortlandPress 2004, ISBN 1-85578-158-1.

• Nicholas Price, Lewis Stevens,Fundamentals of Enzymology, OxfordUniversity Press, 1999. ISBN0-19-850229-X

• Tim Bugg, An Introduction to Enzyme andCoenzyme Chemistry BlackwellPublishing, 2004 ISBN 1-4051-1452-5

Advanced

• Irwin H. Segel, Enzyme Kinetics :Behavior and Analysis of RapidEquilibrium and Steady-State EnzymeSystems. Wiley-Interscience; New Ededition 1993, ISBN 0-471-30309-7.

• Alan Fersht, Structure and Mechanism inProtein Science : A Guide to EnzymeCatalysis and Protein Folding. W. H.Freeman, 1998. ISBN 0-7167-3268-8

• Santiago Schnell, Philip K. Maini, Acentury of enzyme kinetics: Reliability ofthe KM and vmax estimates, Comments onTheoretical Biology 8, 169–187, 2004 DOI:10.1080/08948550390206768

• Chris Walsh, Enzymatic ReactionMechanisms. W. H. Freeman andCompany. 1979. ISBN 0-7167-0070-0

• Paul F. Cook and W.W. Cleland Enzymekinetics and mechanism Garland Science,2007 ISBN 0-8153-4140-7

External links• Animation of an enzyme assay — Shows

effects of manipulating assay conditions• MACiE — A database of enzyme reaction

mechanisms• ENZYME — Expasy enzyme nomenclature

database• ExCatDB — A database of enzyme

catalytic mechanisms• BRENDA — Comprehensive enzyme

database, giving substrates, inhibitors andreaction diagrams

• SABIO-RK — A database of reactionkinetics

• Joseph Kraut’s Research Group, Universityof California San Diego — Animations ofseveral enzyme reaction mechanisms

• Symbolism and Terminology in EnzymeKinetics — A comprehensive explanationof concepts and terminology in enzymekinetics

• An introduction to enzyme kinetics — Anaccessible set of on-line tutorials onenzyme kinetics

• Enzyme kinetics animated tutorial — Ananimated tutorial with audio

Retrieved from "http://en.wikipedia.org/wiki/Enzyme_kinetics"

Categories: Enzymes, Catalysis

From Wikipedia, the free encyclopedia Enzyme kinetics

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From Wikipedia, the free encyclopedia Enzyme kinetics

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