enzyme kinetics

Enzyme kinetics

Dihydrofolate reductase from E. coli with its two substratesdihydrofolate (right) and NADPH (left), bound in the active site.The protein is shown as a ribbon diagram, with alpha helicesin red, beta sheets in yellow and loops in blue. Generated from7DFR.

Enzyme kinetics is the study of the chemical reactionsthat are catalysed by enzymes. In enzyme kinetics, thereaction rate is measured and the effects of varying theconditions of the reaction are investigated. Studying anenzymes kinetics in this way can reveal the catalyticmechanism of this enzyme, its role in metabolism, howits activity is controlled, and how a drug or an agonistmight inhibit the enzyme.Enzymes are usually protein molecules that manipulateother molecules the enzymes substrates. These targetmolecules bind to an enzymes active site and are trans-formed into products through a series of steps known asthe enzymatic mechanismE + S ES ES*< > EP E +P. These mechanisms can be divided into single-substrate and multiple-substrate mechanisms. Kineticstudies on enzymes that only bind one substrate, such astriosephosphate isomerase, aim to measure the affinity

with which the enzyme binds this substrate and theturnover rate. Some other examples of enzymes are phos-phofructokinase and hexokinase, both of which are im-portant for cellular respiration (glycolysis).When enzymes bind multiple substrates, such asdihydrofolate reductase (shown right), enzyme kineticscan also show the sequence in which these substrates bindand the sequence in which products are released. An ex-ample of enzymes that bind a single substrate and releasemultiple products are proteases, which cleave one pro-tein substrate into two polypeptide products. Others jointwo substrates together, such as DNA polymerase link-ing a nucleotide to DNA. Although these mechanismsare often a complex series of steps, there is typically onerate-determining step that determines the overall kinetics.This rate-determining step may be a chemical reactionor a conformational change of the enzyme or substrates,such as those involved in the release of product(s) fromthe enzyme.Knowledge of the enzymes structure is helpful in in-terpreting kinetic data. For example, the structure cansuggest how substrates and products bind during catal-ysis; what changes occur during the reaction; and eventhe role of particular amino acid residues in the mecha-nism. Some enzymes change shape significantly duringthe mechanism; in such cases, it is helpful to determinethe enzyme structure with and without bound substrateanalogues that do not undergo the enzymatic reaction.Not all biological catalysts are protein enzymes; RNA-based catalysts such as ribozymes and ribosomes are es-sential to many cellular functions, such as RNA splic-ing and translation. The main difference between ri-bozymes and enzymes is that RNA catalysts are com-posed of nucleotides, whereas enzymes are composed ofamino acids. Ribozymes also perform a more limited setof reactions, although their reaction mechanisms and ki-netics can be analysed and classified by the same meth-ods.

1 General principles

The reaction catalysed by an enzyme uses exactly thesame reactants and produces exactly the same productsas the uncatalysed reaction. Like other catalysts, en-zymes do not alter the position of equilibrium betweensubstrates and products.[1] However, unlike uncatalysedchemical reactions, enzyme-catalysed reactions display

1

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2 2 ENZYME ASSAYS

As larger amounts of substrate are added to a reaction, the avail-able enzyme binding sites become filled to the limit of Vmax . Be-yond this limit the enzyme is saturated with substrate and the re-action rate ceases to increase.

saturation kinetics. For a given enzyme concentration andfor relatively low substrate concentrations, the reactionrate increases linearly with substrate concentration; theenzyme molecules are largely free to catalyse the reac-tion, and increasing substrate concentration means an in-creasing rate at which the enzyme and substratemoleculesencounter one another. However, at relatively high sub-strate concentrations, the reaction rate asymptotically ap-proaches the theoretical maximum; the enzyme activesites are almost all occupied and the reaction rate is deter-mined by the intrinsic turnover rate of the enzyme. Thesubstrate concentration midway between these two limit-ing cases is denoted by KM.The two most important kinetic properties of an enzymeare how quickly the enzyme becomes saturated with aparticular substrate, and the maximum rate it can achieve.Knowing these properties suggests what an enzyme mightdo in the cell and can show how the enzyme will respondto changes in these conditions.

2 Enzyme assays

Main article: Enzyme assayEnzyme assays are laboratory procedures that measurethe rate of enzyme reactions. Because enzymes are notconsumed by the reactions they catalyse, enzyme assaysusually follow changes in the concentration of either sub-strates or products to measure the rate of reaction. Thereare many methods of measurement. Spectrophotometricassays observe change in the absorbance of light betweenproducts and reactants; radiometric assays involve theincorporation or release of radioactivity to measure theamount of product made over time. Spectrophotometricassays are most convenient since they allow the rate of thereaction to be measured continuously. Although radio-metric assays require the removal and counting of sam-ples (i.e., they are discontinuous assays) they are usuallyextremely sensitive and can measure very low levels ofenzyme activity.[2] An analogous approach is to use massspectrometry to monitor the incorporation or release of

Initial rate period

Time

Pro

duct

form

ed

Progress curve for an enzyme reaction. The slope in the initialrate period is the initial rate of reaction v. The MichaelisMenten equation describes how this slope varies with the con-centration of substrate.

stable isotopes as substrate is converted into product.The most sensitive enzyme assays use lasers focusedthrough a microscope to observe changes in single en-zyme molecules as they catalyse their reactions. Thesemeasurements either use changes in the fluorescence ofcofactors during an enzymes reaction mechanism, or offluorescent dyes added onto specific sites of the proteinto report movements that occur during catalysis.[3] Thesestudies are providing a new view of the kinetics and dy-namics of single enzymes, as opposed to traditional en-zyme kinetics, which observes the average behaviour ofpopulations of millions of enzyme molecules.[4][5]

An example progress curve for an enzyme assay is shownabove. The enzyme produces product at an initial ratethat is approximately linear for a short period after thestart of the reaction. As the reaction proceeds and sub-strate is consumed, the rate continuously slows (so longas substrate is not still at saturating levels). To measurethe initial (and maximal) rate, enzyme assays are typi-cally carried out while the reaction has progressed only afew percent towards total completion. The length of theinitial rate period depends on the assay conditions andcan range from milliseconds to hours. However, equip-ment for rapidly mixing liquids allows fast kinetic mea-surements on initial rates of less than one second.[6] Thesevery rapid assays are essential for measuring pre-steady-state kinetics, which are discussed below.Most enzyme kinetics studies concentrate on this initial,approximately linear part of enzyme reactions. However,it is also possible to measure the complete reaction curveand fit this data to a non-linear rate equation. This wayof measuring enzyme reactions is called progress-curveanalysis.[7] This approach is useful as an alternative torapid kinetics when the initial rate is too fast to measureaccurately.

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3.1 MichaelisMenten kinetics 3

3 Single-substrate reactions

Enzymes with single-substrate mechanisms includeisomerases such as triosephosphateisomerase orbisphosphoglycerate mutase, intramolecular lyases suchas adenylate cyclase and the hammerhead ribozyme,an RNA lyase.[8] However, some enzymes that onlyhave a single substrate do not fall into this categoryof mechanisms. Catalase is an example of this, as theenzyme reacts with a first molecule of hydrogen peroxidesubstrate, becomes oxidised and is then reduced bya second molecule of substrate. Although a singlesubstrate is involved, the existence of a modified enzymeintermediate means that the mechanism of catalase isactually a pingpong mechanism, a type of mechanismthat is discussed in the Multi-substrate reactions sectionbelow.

3.1 MichaelisMenten kinetics

Main article: MichaelisMenten kineticsAs enzyme-catalysed reactions are saturable, their rate

Km

Vmax

Vmax

0 1000 2000 3000 40000.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Substrate concentration

Rea

ctio

n ra

te

Saturation curve for an enzyme showing the relation between theconcentration of substrate and rate.

E + S ES E + Pk

k k

-1

1 2

Substrate binding Catalytic step

Single-substrate mechanism for an enzyme reaction. k1, k1and k2 are the rate constants for the individual steps.

of catalysis does not show a linear response to increasingsubstrate. If the initial rate of the reaction is measuredover a range of substrate concentrations (denoted as [S]),the reaction rate (v) increases as [S] increases, as shownon the right. However, as [S] gets higher, the enzyme be-comes saturated with substrate and the rate reaches V ,the enzymes maximum rate.

The MichaelisMenten kinetic model of a single-substrate reaction is shown on the right. There is an ini-tial bimolecular reaction between the enzyme E and sub-strate S to form the enzymesubstrate complex ES butthe rate of enzymatic reaction increase with the increaseof the substrate concentration up to a certain level butthen more increase in substrate concentration does notcause any increase in reaction rate as there no more Eremain available for reacting with S and the rate of reac-tion become dependent on ES and the reaction becomeunimolecular reaction. Although the enzymatic mecha-nism for the unimolecular reaction ES kcatE+P can bequite complex, there is typically one rate-determining en-zymatic step that allows this reaction to be modelled as asingle catalytic step with an apparent unimolecular rateconstant k . If the reaction path proceeds over one orseveral intermediates, k will be a function of several el-ementary rate constants, whereas in the simplest case of asingle elementary reaction (e.g. no intermediates) it willbe identical to the elementary unimolecular rate constantk2. The apparent unimolecular rate constant k is alsocalled turnover number and denotes the maximum num-ber of enzymatic reactions catalysed per second.The MichaelisMenten equation[9] describes how the(initial) reaction rate v0 depends on the position of thesubstrate-binding equilibrium and the rate constant k2.

v0 =Vmax[S]KM+[S] (MichaelisMenten equation)

with the constants

KMdef=

k2 + k1k1

KD

Vmaxdef= kcat[E]tot

This MichaelisMenten equation is the basis for mostsingle-substrate enzyme kinetics. Two crucial assump-tions underlie this equation (apart from the general as-sumption about the mechanism only involving no inter-mediate or product inhibition, and there is no allostericityor cooperativity). The first assumption is the so-calledquasi-steady-state assumption (or pseudo-steady-state hy-pothesis), namely that the concentration of the substrate-bound enzyme (and hence also the unbound enzyme)changes much more slowly than those of the product andsubstrate and thus the change over time of the complexcan be set to zero d[ES]/dt != 0 . The second as-sumption is that the total enzyme concentration does notchange over time, thus [E]tot = [E] + [ES]

!= const . A

complete derivation can be found here.The Michaelis constant KM is experimentally defined asthe concentration at which the rate of the enzyme reactionis half V , which can be verified by substituting [S] =K into the MichaelisMenten equation and can also beseen graphically. If the rate-determining enzymatic step

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4 3 SINGLE-SUBSTRATE REACTIONS

is slow compared to substrate dissociation ( k2 k1), the Michaelis constant KM is roughly the dissociationconstant KD of the ES complex.If [S] is small compared toKM then the term [S]/(KM+[S]) [S]/KM and also very little ES complex isformed, thus [E]0 [E] . Therefore, the rate of productformation is

v0 kcatKM

[E][S] if[S] KM

Thus the product formation rate depends on the enzymeconcentration as well as on the substrate concentration,the equation resembles a bimolecular reaction with a cor-responding pseudo-second order rate constant k2/KM .This constant is a measure of catalytic efficiency. Themost efficient enzymes reach a k2/KM in the range of108 1010 M1 s1. These enzymes are so efficient theyeffectively catalyse a reaction each time they encounter asubstrate molecule and have thus reached an upper theo-retical limit for efficiency (diffusion limit); these enzymeshave often been termed perfect enzymes.[10]

3.2 Direct use of the MichaelisMentenequation for time course kinetic anal-ysis

Further information: Rate equationFurther information: Reaction Progress Kinetic Analysis

The observed velocities predicted by the MichaelisMenten equation can be used to directly model the timecourse disappearance of substrate and the production ofproduct through incorporation of the MichaelisMentenequation into the equation for first order chemical kinet-ics. This can only be achieved however if one recognisesthe problem associated with the use of Eulers numberin the description of first order chemical kinetics. i.e.ek is a split constant that introduces a systematic errorinto calculations and can be rewritten as a single constantwhich represents the remaining substrate after each timeperiod.[11]

[S] = [S]0(1 k)t

[S] = [S]0(1 v/[S]0)t

[S] = [S]0(1 (Vmax[S]0/(KM + [S]0)/[S]0))t

In 1983 Stuart Beal (and also independently SantiagoSchnell and Claudio Mendoza in 1997) derived a closedform solution for the time course kinetics analysis ofthe Michaelis-Menten mechanism.[12][13] The solution,known as the Schnell-Mendoza equation, has the form:

[S]

KM= W [F (t)]

where W[] is the Lambert-W function.[14][15] and whereF(t) is

F (t) =[S]0KM

exp([S]0KM

VmaxKM

t

)This equation is encompassed by the equation below, ob-tained by Berberan-Santos (MATCH Commun. Math.Comput. Chem. 63 (2010) 283), which is also validwhen the initial substrate concentration is close to thatof enzyme,

[S]

KM= W [F (t)] Vmax

kcatKM

W [F (t)]

1 +W [F (t)]

where W[] is again the Lambert-W function.

3.3 Linear plots of the MichaelisMentenequation

See also: LineweaverBurk plot and Eadie-Hofstee dia-gramThe plot of v versus [S] above is not linear; although ini-

LineweaverBurk or double-reciprocal plot of kinetic data,showing the significance of the axis intercepts and gradient.

tially linear at low [S], it bends over to saturate at high[S]. Before the modern era of nonlinear curve-fitting oncomputers, this nonlinearity could make it difficult toestimate KM and V accurately. Therefore, severalresearchers developed linearisations of the MichaelisMenten equation, such as the LineweaverBurk plot, theEadieHofstee diagram and the HanesWoolf plot. Allof these linear representations can be useful for visual-ising data, but none should be used to determine kineticparameters, as computer software is readily available thatallows for more accurate determination by nonlinear re-gression methods.[16]

The LineweaverBurk plot or double reciprocal plot is acommonway of illustrating kinetic data. This is producedby taking the reciprocal of both sides of the MichaelisMenten equation. As shown on the right, this is a lin-ear form of theMichaelisMenten equation and produces

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3.5 MichaelisMenten kinetics with intermediate 5

a straight line with the equation y = mx + c with a y-intercept equivalent to 1/V and an x-intercept of thegraph representing 1/KM.

1

v=

KMVmax[S]

+1

Vmax

Naturally, no experimental values can be taken at negative1/[S]; the lower limiting value 1/[S] = 0 (the y-intercept)corresponds to an infinite substrate concentration, where1/v=1/Vmax as shown at the right; thus, the x-interceptis an extrapolation of the experimental data taken at pos-itive concentrations. More generally, the LineweaverBurk plot skews the importance of measurements takenat low substrate concentrations and, thus, can yield inac-curate estimates of V and KM.[17] A more accuratelinear plotting method is the Eadie-Hofstee plot. In thiscase, v is plotted against v/[S]. In the third common lin-ear representation, the Hanes-Woolf plot, [S]/v is plottedagainst [S]. In general, data normalisation can help dimin-ish the amount of experimental work and can increase thereliability of the output, and is suitable for both graphicaland numerical analysis.[18]

3.4 Practical significance of kinetic con-stants

The study of enzyme kinetics is important for two basicreasons. Firstly, it helps explain how enzymes work, andsecondly, it helps predict how enzymes behave in livingorganisms. The kinetic constants defined above, KM andV , are critical to attempts to understand how enzymeswork together to control metabolism.Making these predictions is not trivial, even for sim-ple systems. For example, oxaloacetate is formedby malate dehydrogenase within the mitochondrion.Oxaloacetate can then be consumed by citrate syn-thase, phosphoenolpyruvate carboxykinase or aspartateaminotransferase, feeding into the citric acid cycle,gluconeogenesis or aspartic acid biosynthesis, respec-tively. Being able to predict how much oxaloacetate goesinto which pathway requires knowledge of the concen-tration of oxaloacetate as well as the concentration andkinetics of each of these enzymes. This aim of predict-ing the behaviour of metabolic pathways reaches its mostcomplex expression in the synthesis of huge amounts ofkinetic and gene expression data into mathematical mod-els of entire organisms. Alternatively, one useful simplifi-cation of themetabolic modelling problem is to ignore theunderlying enzyme kinetics and only rely on informationabout the reaction networks stoichiometry, a techniquecalled flux balance analysis.[19][20]

3.5 MichaelisMenten kinetics with inter-mediate

One could also consider the less simple case

E + Sk1k1

ESk2EI k3E + P

where a complex with the enzyme and an intermedi-ate exists and the intermediate is converted into prod-uct in a second step. In this case we have a very similarequation[21]

v0 = kcat[S][E]0

K M + [S]

but the constants are different

K Mdef=

k3k2 + k3

KM =k3

k2 + k3 k2 + k1

k1

kcatdef=

k3k2k2 + k3

We see that for the limiting case k3 k2 , thus when thelast step from EI to E + P is much faster than the previousstep, we get again the original equation. Mathematicallywe have thenK M KM and kcat k2 .

4 Multi-substrate reactions

Multi-substrate reactions follow complex rate equationsthat describe how the substrates bind and in what se-quence. The analysis of these reactions is much simplerif the concentration of substrate A is kept constant andsubstrate B varied. Under these conditions, the enzymebehaves just like a single-substrate enzyme and a plot ofv by [S] gives apparent KM and V constants for sub-strate B. If a set of these measurements is performed atdifferent fixed concentrations of A, these data can be usedto work out what the mechanism of the reaction is. Foran enzyme that takes two substrates A and B and turnsthem into two products P and Q, there are two types ofmechanism: ternary complex and pingpong.

4.1 Ternary-complex mechanisms

In these enzymes, both substrates bind to the enzymeat the same time to produce an EAB ternary complex.The order of binding can either be random (in a randommechanism) or substrates have to bind in a particular se-quence (in an ordered mechanism). When a set of v by[S] curves (fixed A, varying B) from an enzyme with aternary-complexmechanism are plotted in a LineweaverBurk plot, the set of lines produced will intersect.

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6 5 NON-MICHAELISMENTEN KINETICS

A B

E

B A

EA

EB

EQ

EP

P Q

Q P

EEAB EPQ

Random-order ternary-complex mechanism for an enzyme reac-tion. The reaction path is shown as a line and enzyme interme-diates containing substrates A and B or products P and Q arewritten below the line.

Enzymes with ternary-complex mechanisms includeglutathione S-transferase,[22] dihydrofolate reductase[23]and DNA polymerase.[24] The following links showshort animations of the ternary-complex mechanismsof the enzymes dihydrofolate reductase[] and DNApolymerase[].

4.2 Pingpong mechanisms

E EEA

BA P Q

E*P E* E*B EQ

Pingpong mechanism for an enzyme reaction. Intermediatescontain substrates A and B or products P and Q.

As shown on the right, enzymes with a ping-pong mech-anism can exist in two states, E and a chemically mod-ified form of the enzyme E*; this modified enzyme isknown as an intermediate. In such mechanisms, substrateA binds, changes the enzyme to E* by, for example, trans-ferring a chemical group to the active site, and is then re-leased. Only after the first substrate is released can sub-strate B bind and react with the modified enzyme, regen-erating the unmodified E form. When a set of v by [S]curves (fixed A, varying B) from an enzyme with a pingpong mechanism are plotted in a LineweaverBurk plot,a set of parallel lines will be produced. This is called asecondary plot.Enzymes with pingpong mechanisms includesome oxidoreductases such as thioredoxin per-oxidase,[25] transferases such as acylneuraminatecytidylyltransferase[26] and serine proteases such astrypsin and chymotrypsin.[27] Serine proteases are avery common and diverse family of enzymes, includingdigestive enzymes (trypsin, chymotrypsin, and elastase),several enzymes of the blood clotting cascade and manyothers. In these serine proteases, the E* intermediateis an acyl-enzyme species formed by the attack of anactive site serine residue on a peptide bond in a proteinsubstrate. A short animation showing the mechanism ofchymotrypsin is linked here.[]

5 Non-MichaelisMenten kinetics

Main article: Allosteric regulationSome enzymes produce a sigmoid v by [S] plot, which of-

25

20

15

10

5

00 50 100 150 200

Concentration of substrate

Rat

e of

reac

tion

Saturation curve for an enzyme reaction showing sigmoid kinet-ics.

ten indicates cooperative binding of substrate to the ac-tive site. This means that the binding of one substratemolecule affects the binding of subsequent substratemolecules. This behavior is most common in multimericenzymes with several interacting active sites.[28] Here,the mechanism of cooperation is similar to that ofhemoglobin, with binding of substrate to one active sitealtering the affinity of the other active sites for substratemolecules. Positive cooperativity occurs when bindingof the first substrate molecule increases the affinity of theother active sites for substrate. Negative cooperativityoccurs when binding of the first substrate decreases theaffinity of the enzyme for other substrate molecules.Allosteric enzymes include mammalian tyrosyl tRNA-synthetase, which shows negative cooperativity,[29]and bacterial aspartate transcarbamoylase[30] andphosphofructokinase,[31] which show positive coopera-tivity.Cooperativity is surprisingly common and can help regu-late the responses of enzymes to changes in the concen-trations of their substrates. Positive cooperativity makesenzymes much more sensitive to [S] and their activitiescan show large changes over a narrow range of substrateconcentration. Conversely, negative cooperativity makesenzymes insensitive to small changes in [S].The Hill equation (biochemistry)[32] is often used to de-scribe the degree of cooperativity quantitatively in non-MichaelisMenten kinetics. The derived Hill coefficientn measures how much the binding of substrate to oneactive site affects the binding of substrate to the otheractive sites. A Hill coefficient of 1 indicates positivecooperativity.

https://en.wikipedia.org/wiki/Glutathione_S-transferasehttps://en.wikipedia.org/wiki/Dihydrofolate_reductasehttps://en.wikipedia.org/wiki/DNA_polymerasehttps://en.wikipedia.org/wiki/Enzyme%2520kinetics#endnote_Bnonehttps://en.wikipedia.org/wiki/Enzyme%2520kinetics#endnote_Cnonehttps://en.wikipedia.org/wiki/Reactive_intermediatehttps://en.wikipedia.org/wiki/Secondary_plot_(kinetics)https://en.wikipedia.org/wiki/Oxidoreductaseshttps://en.wikipedia.org/wiki/Peroxidasehttps://en.wikipedia.org/wiki/Peroxidasehttps://en.wikipedia.org/wiki/Transferaseshttps://en.wikipedia.org/wiki/Serine_proteasehttps://en.wikipedia.org/wiki/Trypsinhttps://en.wikipedia.org/wiki/Chymotrypsinhttps://en.wikipedia.org/wiki/Digestionhttps://en.wikipedia.org/wiki/Coagulationhttps://en.wikipedia.org/wiki/Serinehttps://en.wikipedia.org/wiki/Peptide_bondhttps://en.wikipedia.org/wiki/Enzyme%2520kinetics#endnote_Dnonehttps://en.wikipedia.org/wiki/Allosteric_regulationhttps://en.wikipedia.org/wiki/Sigmoid_functionhttps://en.wikipedia.org/wiki/Cooperative_bindinghttps://en.wikipedia.org/wiki/Protein_structurehttps://en.wikipedia.org/wiki/Hemoglobinhttps://en.wikipedia.org/wiki/Aspartate_transcarbamoylasehttps://en.wikipedia.org/wiki/Phosphofructokinasehttps://en.wikipedia.org/wiki/Hill_equation_(biochemistry)https://en.wikipedia.org/wiki/Cooperativity

7

6 Pre-steady-state kinetics

Amount of enzyme

Amou

nt o

f pro

duct

Time (seconds)

Burst phase

Pre-steady state progress curve, showing the burst phase of anenzyme reaction.

In the first moment after an enzyme is mixed with sub-strate, no product has been formed and no intermediatesexist. The study of the next few milliseconds of thereaction is called Pre-steady-state kinetics also referredto as Burst kinetics. Pre-steady-state kinetics is there-fore concerned with the formation and consumption ofenzymesubstrate intermediates (such as ES or E*) untiltheir steady-state concentrations are reached.This approach was first applied to the hydrolysis reactioncatalysed by chymotrypsin.[33] Often, the detection of anintermediate is a vital piece of evidence in investigationsof what mechanism an enzyme follows. For example, inthe pingpong mechanisms that are shown above, rapidkinetic measurements can follow the release of productP and measure the formation of the modified enzyme in-termediate E*.[34] In the case of chymotrypsin, this in-termediate is formed by an attack on the substrate by thenucleophilic serine in the active site and the formation ofthe acyl-enzyme intermediate.In the figure to the right, the enzyme produces E* rapidlyin the first few seconds of the reaction. The rate thenslows as steady state is reached. This rapid burst phaseof the reaction measures a single turnover of the en-zyme. Consequently, the amount of product released inthis burst, shown as the intercept on the y-axis of thegraph, also gives the amount of functional enzyme whichis present in the assay.[35]

7 Chemical mechanism

An important goal of measuring enzyme kinetics is todetermine the chemical mechanism of an enzyme reac-tion, i.e., the sequence of chemical steps that transformsubstrate into product. The kinetic approaches discussedabove will show at what rates intermediates are formedand inter-converted, but they cannot identify exactly whatthese intermediates are.

Kinetic measurements taken under various solution con-ditions or on slightly modified enzymes or substrates of-ten shed light on this chemical mechanism, as they re-veal the rate-determining step or intermediates in the re-action. For example, the breaking of a covalent bondto a hydrogen atom is a common rate-determining step.Which of the possible hydrogen transfers is rate deter-mining can be shown by measuring the kinetic effectsof substituting each hydrogen by deuterium, its stableisotope. The rate will change when the critical hydro-gen is replaced, due to a primary kinetic isotope effect,which occurs because bonds to deuterium are harder tobreak than bonds to hydrogen.[36] It is also possible tomeasure similar effects with other isotope substitutions,such as 13C/12C and 18O/16O, but these effects are moresubtle.[37]

Isotopes can also be used to reveal the fate of various partsof the substrate molecules in the final products. For ex-ample, it is sometimes difficult to discern the origin of anoxygen atom in the final product; since it may have comefrom water or from part of the substrate. This may bedetermined by systematically substituting oxygens sta-ble isotope 18O into the various molecules that partici-pate in the reaction and checking for the isotope in theproduct.[38] The chemical mechanism can also be eluci-dated by examining the kinetics and isotope effects un-der different pH conditions,[39] by altering the metal ionsor other bound cofactors,[40] by site-directed mutagene-sis of conserved amino acid residues, or by studying thebehaviour of the enzyme in the presence of analogues ofthe substrate(s).[41]

8 Enzyme inhibition and activation

Main article: Enzyme inhibitorEnzyme inhibitors are molecules that reduce or abolish

E + S+I

Ki

EI

+I

K'i

ESI

ES E + P

Kinetic scheme for reversible enzyme inhibitors.

enzyme activity, while enzyme activators are moleculesthat increase the catalytic rate of enzymes. These inter-actions can be either reversible (i.e., removal of the in-hibitor restores enzyme activity) or irreversible (i.e., theinhibitor permanently inactivates the enzyme).

https://en.wikipedia.org/wiki/Reactive_intermediatehttps://en.wikipedia.org/wiki/Burst_kineticshttps://en.wikipedia.org/wiki/Steady_state_(chemistry)https://en.wikipedia.org/wiki/Chymotrypsinhttps://en.wikipedia.org/wiki/Nucleophilehttps://en.wikipedia.org/wiki/Reactive_intermediatehttps://en.wikipedia.org/wiki/Covalent_bondhttps://en.wikipedia.org/wiki/Hydrogenhttps://en.wikipedia.org/wiki/Atomhttps://en.wikipedia.org/wiki/Deuteriumhttps://en.wikipedia.org/wiki/Isotopehttps://en.wikipedia.org/wiki/Kinetic_isotope_effecthttps://en.wikipedia.org/wiki/Oxygenhttps://en.wikipedia.org/wiki/Cofactor_(biochemistry)https://en.wikipedia.org/wiki/Site-directed_mutagenesishttps://en.wikipedia.org/wiki/Site-directed_mutagenesishttps://en.wikipedia.org/wiki/Enzyme_inhibitor

8 8 ENZYME INHIBITION AND ACTIVATION

8.1 Reversible inhibitors

Traditionally reversible enzyme inhibitors have been clas-sified as competitive, uncompetitive, or non-competitive,according to their effects on K and V . These dif-ferent effects result from the inhibitor binding to the en-zyme E, to the enzymesubstrate complex ES, or to both,respectively. The division of these classes arises froma problem in their derivation and results in the need touse two different binding constants for one binding event.The binding of an inhibitor and its effect on the enzy-matic activity are two distinctly different things, anotherproblem the traditional equations fail to acknowledge. Innoncompetitive inhibition the binding of the inhibitor re-sults in 100% inhibition of the enzyme only, and failsto consider the possibility of anything in between.[42]The common form of the inhibitory term also obscuresthe relationship between the inhibitor binding to the en-zyme and its relationship to any other binding term beit the MichaelisMenten equation or a dose responsecurve associated with ligand receptor binding. To demon-strate the relationship the following rearrangement can bemade:

Vmax

1 +[I]

Ki

Vmax

[I] +Ki

KiAdding zero to the bottom ([I]-[I])

Vmax

[I] +Ki

[I] +Ki [I]

Dividing by [I]+K

Vmax

1

1[I]

[I] +Ki

Vmax Vmax[I]

[I] +Ki

This notation demonstrates that similar to the MichaelisMenten equation, where the rate of reaction depends onthe percent of the enzyme population interacting withsubstratefraction of the enzyme population bound by substrate

[S]

[S] +Km

fraction of the enzyme population bound by inhibitor

[I]

[I] +Ki

the effect of the inhibitor is a result of the percent of theenzyme population interacting with inhibitor. The onlyproblem with this equation in its present form is that itassumes absolute inhibition of the enzyme with inhibitorbinding, when in fact there can be a wide range of effectsanywhere from 100% inhibition of substrate turn over tojust >0%. To account for this the equation can be easilymodified to allow for different degrees of inhibition byincluding a delta V term.

Vmax Vmax[I]

[I] +Ki

or

Vmax1 (Vmax1 Vmax2)[I]

[I] +Ki

This term can then define the residual enzymatic activitypresent when the inhibitor is interacting with individualenzymes in the population. However the inclusion of thisterm has the added value of allowing for the possibilityof activation if the secondary V term turns out to behigher than the initial term. To account for the possiblyof activation as well the notation can then be rewrittenreplacing the inhibitor I with a modifier term denotedhere as X.

Vmax1 (Vmax1 Vmax2)[X]

[X] +Kx

While this terminology results in a simplified way of deal-ing with kinetic effects relating to the maximum velocityof the MichaelisMenten equation, it highlights potentialproblems with the term used to describe effects relatingto the K . The K relating to the affinity of the enzymefor the substrate should in most cases relate to potentialchanges in the binding site of the enzyme which would di-rectly result from enzyme inhibitor interactions. As sucha term similar to the one proposed above to modulateV should be appropriate in most situations:[43][44]

Km1 (Km1Km2)[X]

[X] +Kx

8.2 Irreversible inhibitors

Enzyme inhibitors can also irreversibly inactivate en-zymes, usually by covalently modifying active site

9

residues. These reactions, which may be called suicidesubstrates, follow exponential decay functions and areusually saturable. Below saturation, they follow first orderkinetics with respect to inhibitor.

9 Mechanisms of catalysis

Main article: Enzyme catalysisThe favoured model for the enzymesubstrate interac-

without enzyme

with enzyme activationenergy withenzyme

activationenergy withoutenzyme

overall energyreleased duringreaction

reactantse.g. C H O O6 12 6 2+

productsO2+HCO2

Ene

rgy

Reaction coordinate

The energy variation as a function of reaction coordinate showsthe stabilisation of the transition state by an enzyme.

tion is the induced fit model.[45] This model proposesthat the initial interaction between enzyme and sub-strate is relatively weak, but that these weak interactionsrapidly induce conformational changes in the enzyme thatstrengthen binding. These conformational changes alsobring catalytic residues in the active site close to thechemical bonds in the substrate that will be altered in thereaction.[46] Conformational changes can bemeasured us-ing circular dichroism or dual polarisation interferome-try. After binding takes place, one or more mechanismsof catalysis lower the energy of the reactions transitionstate by providing an alternative chemical pathway forthe reaction. Mechanisms of catalysis include catalysis bybond strain; by proximity and orientation; by active-siteproton donors or acceptors; covalent catalysis and quan-tum tunnelling.[34][47]

Enzyme kinetics cannot prove which modes of catalysisare used by an enzyme. However, some kinetic data cansuggest possibilities to be examined by other techniques.For example, a pingpong mechanism with burst-phasepre-steady-state kinetics would suggest covalent catalysismight be important in this enzymes mechanism. Alter-natively, the observation of a strong pH effect on V but not K might indicate that a residue in the active siteneeds to be in a particular ionisation state for catalysis tooccur.

10 History

In 1902 Victor Henri proposed a quantitative theory ofenzyme kinetics,[48] but at the time the experimentalsignificance of the hydrogen ion concentration was notyet recognized. After Peter Lauritz Srensen had de-fined the logarithmic pH-scale and introduced the con-cept of buffering in 1909[49] the German chemist LeonorMichaelis and his Canadian postdoc Maud LeonoraMenten repeated Henris experiments and confirmed hisequation, which is now generally referred to as Michaelis-Menten kinetics (sometimes alsoHenri-Michaelis-Mentenkinetics).[50] Their work was further developed by G. E.Briggs and J. B. S. Haldane, who derived kinetic equa-tions that are still widely considered today a starting pointin modeling enzymatic activity.[51]

The major contribution of the Henri-Michaelis-Mentenapproach was to think of enzyme reactions in two stages.In the first, the substrate binds reversibly to the enzyme,forming the enzyme-substrate complex. This is some-times called the Michaelis complex. The enzyme thencatalyzes the chemical step in the reaction and releasesthe product. The kinetics of many enzymes is adequatelydescribed by the simple Michaelis-Menten model, but allenzymes have internal motions that are not accountedfor in the model and can have significant contributionsto the overall reaction kinetics. This can be modeledby introducing several Michaelis-Menten pathways thatare connected with fluctuating rates,[52][53][54] which is amathematical extension of the basic Michaelis Mentenmechanism.[55]

11 Software

11.1 ENZO

ENZO (Enzyme Kinetics) is a graphical interface toolfor building kinetic models of enzyme catalyzed reac-tions. ENZO automatically generates the correspondingdifferential equations from a stipulated enzyme reactionscheme. These differential equations are processed bya numerical solver and a regression algorithm which fitsthe coefficients of differential equations to experimen-tally observed time course curves. ENZO allows rapidevaluation of rival reaction schemes and can be used forroutine tests in enzyme kinetics.[56]

12 See also

Protein dynamics

Diffusion limited enzyme

https://en.wikipedia.org/wiki/Exponential_decayhttps://en.wikipedia.org/wiki/Reaction_ratehttps://en.wikipedia.org/wiki/Enzyme_catalysishttps://en.wikipedia.org/wiki/Reaction_coordinatehttps://en.wikipedia.org/wiki/Conformational_changehttps://en.wikipedia.org/wiki/Tertiary_structurehttps://en.wikipedia.org/wiki/Circular_dichroismhttps://en.wikipedia.org/wiki/Dual_polarisation_interferometryhttps://en.wikipedia.org/wiki/Dual_polarisation_interferometryhttps://en.wikipedia.org/wiki/Transition_statehttps://en.wikipedia.org/wiki/Transition_statehttps://en.wikipedia.org/wiki/Ionizationhttps://en.wikipedia.org/wiki/Victor_Henrihttps://en.wikipedia.org/wiki/PHhttps://en.wikipedia.org/wiki/S._P._L._S%C3%B8rensenhttps://en.wikipedia.org/wiki/Buffer_solutionhttps://en.wikipedia.org/wiki/Leonor_Michaelishttps://en.wikipedia.org/wiki/Leonor_Michaelishttps://en.wikipedia.org/wiki/Maud_Leonora_Mentenhttps://en.wikipedia.org/wiki/Maud_Leonora_Mentenhttps://en.wikipedia.org/wiki/Michaelis-Menten_kineticshttps://en.wikipedia.org/wiki/Michaelis-Menten_kineticshttps://en.wikipedia.org/wiki/George_Edward_Briggshttps://en.wikipedia.org/wiki/George_Edward_Briggshttps://en.wikipedia.org/wiki/J._B._S._Haldanehttps://en.wikipedia.org/wiki/Protein_dynamicshttps://en.wikipedia.org/wiki/Protein_dynamicshttps://en.wikipedia.org/wiki/Diffusion_limited_enzyme

10 14 REFERENCES

13 Footnotes

. ^ Link: InteractiveMichaelisMenten kinetics tutorial(Java required). ^ Link: dihydrofolate reductase mechanism (Gif). ^ Link: DNA polymerase mechanism (Gif). ^ Link: Chymotrypsin mechanism (Flash required)

14 References

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[2] Danson, Michael; Eisenthal, Robert (2002). Enzyme as-says: a practical approach. Oxford [Oxfordshire]: OxfordUniversity Press. ISBN 0-19-963820-9.

[3] Xie XS, Lu HP (June 1999). Single-molecule en-zymology. J. Biol. Chem. 274 (23): 1596770.doi:10.1074/jbc.274.23.15967. PMID 10347141.

[4] Lu H (2004). Single-molecule spectroscopy studiesof conformational change dynamics in enzymatic reac-tions. Current pharmaceutical biotechnology 5 (3): 2619. doi:10.2174/1389201043376887. PMID 15180547.

[5] Schnell J, Dyson H, Wright P (2004). Struc-ture, dynamics, and catalytic function of di-hydrofolate reductase. Annual review of bio-physics and biomolecular structure 33: 11940.doi:10.1146/annurev.biophys.33.110502.133613. PMID15139807.

[6] Gibson QH (1969). Rapid mixing: Stopped flow. Meth-ods Enzymol. Methods in Enzymology 16: 187228.doi:10.1016/S0076-6879(69)16009-7. ISBN 978-0-12-181873-9.

[7] Duggleby RG (1995). Analysis of enzyme progresscurves by non-linear regression. Methods Enzymol.Methods in Enzymology 249: 6190. doi:10.1016/0076-6879(95)49031-0. ISBN 978-0-12-182150-0. PMID7791628.

[8] Murray JB, Dunham CM, Scott WG (January 2002).A pH-dependent conformational change, rather than thechemical step, appears to be rate-limiting in the ham-merhead ribozyme cleavage reaction. J. Mol. Biol.315 (2): 12130. doi:10.1006/jmbi.2001.5145. PMID11779233.

[9] Michaelis L. and Menten M.L. Kinetik der Invertin-wirkung Biochem. Z. 1913; 49:333369 English trans-lation Accessed 6 April 2007

[10] Stroppolo ME, Falconi M, Caccuri AM, Desideri A(2001). Superefficient enzymes. Cell. Mol. Life Sci.58 (10): 145160. doi:10.1007/PL00000788. PMID11693526.

[11] Walsh R, Martin E, Darvesh S. A method to describeenzyme-catalyzed reactions by combining steady state andtime course enzyme kinetic parameters. Biochim BiophysActa. 2010 Jan;1800:15

[12] Beal, S. L. (1983). Computation of the explicit so-lution to the Michaelis-Menten equation. Journal ofPharmacokinetics and Biopharmaceutics 11 (6): 641657.doi:10.1007/BF01059062. PMID 6689584.

[13] Schnell, S.; Mendoza, C. (1997). Closed FormSolution for Time-dependent Enzyme Kinetics.Journal of Theoretical Biology 187 (2): 207212.doi:10.1006/jtbi.1997.0425.

[14] Goudar, CT; Sonnad, JR; Duggleby, RG (1999).Parameter estimation using a direct solution of the in-tegrated Michaelis-Menten equation. Biochimica et bio-physica acta 1429 (2): 37783. doi:10.1016/s0167-4838(98)00247-7. PMID 9989222.

[15] Goudar, C. T.; Harris, S. K.; McInerney, M. J.; Su-flita, J. M. (2004). Progress curve analysis for en-zyme and microbial kinetic reactions using explicit so-lutions based on the Lambert W function. Jour-nal of Microbiological Methods 59 (3): 317326.doi:10.1016/j.mimet.2004.06.013. PMID 15488275.

[16] Jones ME (1992). Analysis of algebraic weighted least-squares estimators for enzyme parameters. Biochem. J.288 (Pt 2): 5338. PMC 1132043. PMID 1463456.

[17] Tseng SJ, Hsu JP (August 1990). A comparison ofthe parameter estimating procedures for the Michaelis-Menten model. J. Theor. Biol. 145 (4): 45764.doi:10.1016/S0022-5193(05)80481-3. PMID 2246896.

[18] Bravo IG, Busto F, De Arriaga D et al. (September 2001).A normalized plot as a novel and time-saving tool in com-plex enzyme kinetic analysis. Biochem. J. 358 (Pt 3):57383. PMC 1222113. PMID 11577687.

[19] Almaas E, Kovcs B, Vicsek T, Oltvai ZN, BarabsiAL (February 2004). Global organization of metabolicfluxes in the bacterium Escherichia coli. Nature 427(6977): 83943. doi:10.1038/nature02289. PMID14985762.

[20] Reed JL, Vo TD, Schilling CH, Palsson BO (2003). Anexpanded genome-scale model of Escherichia coli K-12 (iJR904 GSM/GPR)". Genome Biol. 4 (9): R54.doi:10.1186/gb-2003-4-9-r54. PMC 193654. PMID12952533.

[21] for a complete derivation, see here

[22] Dirr H, Reinemer P, Huber R (1994). X-ray crystalstructures of cytosolic glutathione S-transferases. Impli-cations for protein architecture, substrate recognition andcatalytic function. Eur. J. Biochem. 220 (3): 64561. doi:10.1111/j.1432-1033.1994.tb18666.x. PMID8143720.

[23] Stone SR, Morrison JF (July 1988). Dihydrofolate re-ductase from Escherichia coli: the kinetic mechanismwith NADPH and reduced acetylpyridine adenine dinu-cleotide phosphate as substrates. Biochemistry 27 (15):54939. doi:10.1021/bi00415a016. PMID 3052577.

https://en.wikipedia.org/wiki/Enzyme%2520kinetics#ref_Anonehttp://cti.itc.virginia.edu/~cmg/Demo/scriptFrame.htmlhttp://cti.itc.virginia.edu/~cmg/Demo/scriptFrame.htmlhttps://en.wikipedia.org/wiki/Enzyme%2520kinetics#ref_Bnonehttp://chem-faculty.ucsd.edu/kraut/dhfr.htmlhttps://en.wikipedia.org/wiki/Enzyme%2520kinetics#ref_Cnonehttp://chem-faculty.ucsd.edu/kraut/dNTP.htmlhttps://en.wikipedia.org/wiki/Enzyme%2520kinetics#ref_Dnonehttp://web.archive.org/web/20070319235224/http://courses.cm.utexas.edu/jrobertus/ch339k/overheads-2/06_21_chymotrypsin.htmlhttps://en.wikipedia.org/wiki/International_Standard_Book_Numberhttps://en.wikipedia.org/wiki/Special:BookSources/0-395-63696-5https://en.wikipedia.org/wiki/Special:BookSources/0-395-63696-5https://en.wikipedia.org/wiki/International_Standard_Book_Numberhttps://en.wikipedia.org/wiki/Special:BookSources/0-19-963820-9https://en.wikipedia.org/wiki/Digital_object_identifierhttps://dx.doi.org/10.1074%252Fjbc.274.23.15967https://en.wikipedia.org/wiki/PubMed_Identifierhttps://www.ncbi.nlm.nih.gov/pubmed/10347141https://en.wikipedia.org/wiki/Digital_object_identifierhttps://dx.doi.org/10.2174%252F1389201043376887https://en.wikipedia.org/wiki/PubMed_Identifierhttps://www.ncbi.nlm.nih.gov/pubmed/15180547https://en.wikipedia.org/wiki/Digital_object_identifierhttps://dx.doi.org/10.1146%252Fannurev.biophys.33.110502.133613https://en.wikipedia.org/wiki/PubMed_Identifierhttps://www.ncbi.nlm.nih.gov/pubmed/15139807https://en.wikipedia.org/wiki/Digital_object_identifierhttps://dx.doi.org/10.1016%252FS0076-6879%252869%252916009-7https://en.wikipedia.org/wiki/International_Standard_Book_Numberhttps://en.wikipedia.org/wiki/Special:BookSources/978-0-12-181873-9https://en.wikipedia.org/wiki/Special:BookSources/978-0-12-181873-9https://en.wikipedia.org/wiki/Digital_object_identifierhttps://dx.doi.org/10.1016%252F0076-6879%252895%252949031-0https://dx.doi.org/10.1016%252F0076-6879%252895%252949031-0https://en.wikipedia.org/wiki/International_Standard_Book_Numberhttps://en.wikipedia.org/wiki/Special:BookSources/978-0-12-182150-0https://en.wikipedia.org/wiki/PubMed_Identifierhttps://www.ncbi.nlm.nih.gov/pubmed/7791628https://en.wikipedia.org/wiki/Digital_object_identifierhttps://dx.doi.org/10.1006%252Fjmbi.2001.5145https://en.wikipedia.org/wiki/PubMed_Identifierhttps://www.ncbi.nlm.nih.gov/pubmed/11779233http://web.lemoyne.edu/~giunta/menten.htmlhttp://web.lemoyne.edu/~giunta/menten.htmlhttps://en.wikipedia.org/wiki/Digital_object_identifierhttps://dx.doi.org/10.1007%252FPL00000788https://en.wikipedia.org/wiki/PubMed_Identifierhttps://www.ncbi.nlm.nih.gov/pubmed/11693526https://en.wikipedia.org/wiki/Digital_object_identifierhttps://dx.doi.org/10.1007%252FBF01059062https://en.wikipedia.org/wiki/PubMed_Identifierhttps://www.ncbi.nlm.nih.gov/pubmed/6689584https://en.wikipedia.org/wiki/Digital_object_identifierhttps://dx.doi.org/10.1006%252Fjtbi.1997.0425http://rdbiotech.drivehq.com/Biblio/Pubs/Pub103.pdfhttp://rdbiotech.drivehq.com/Biblio/Pubs/Pub103.pdfhttps://en.wikipedia.org/wiki/Digital_object_identifierhttps://dx.doi.org/10.1016%252Fs0167-4838%252898%252900247-7https://dx.doi.org/10.1016%252Fs0167-4838%252898%252900247-7https://en.wikipedia.org/wiki/PubMed_Identifierhttps://www.ncbi.nlm.nih.gov/pubmed/9989222https://en.wikipedia.org/wiki/Digital_object_identifierhttps://dx.doi.org/10.1016%252Fj.mimet.2004.06.013https://en.wikipedia.org/wiki/PubMed_Identifierhttps://www.ncbi.nlm.nih.gov/pubmed/15488275https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1132043https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1132043https://en.wikipedia.org/wiki/PubMed_Centralhttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC1132043https://en.wikipedia.org/wiki/PubMed_Identifierhttps://www.ncbi.nlm.nih.gov/pubmed/1463456https://en.wikipedia.org/wiki/Digital_object_identifierhttps://dx.doi.org/10.1016%252FS0022-5193%252805%252980481-3https://en.wikipedia.org/wiki/PubMed_Identifierhttps://www.ncbi.nlm.nih.gov/pubmed/2246896http://www.biochemj.org/bj/358/0573/bj3580573.htmhttp://www.biochemj.org/bj/358/0573/bj3580573.htmhttps://en.wikipedia.org/wiki/PubMed_Centralhttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC1222113https://en.wikipedia.org/wiki/PubMed_Identifierhttps://www.ncbi.nlm.nih.gov/pubmed/11577687https://en.wikipedia.org/wiki/Digital_object_identifierhttps://dx.doi.org/10.1038%252Fnature02289https://en.wikipedia.org/wiki/PubMed_Identifierhttps://www.ncbi.nlm.nih.gov/pubmed/14985762https://www.ncbi.nlm.nih.gov/pmc/articles/PMC193654https://www.ncbi.nlm.nih.gov/pmc/articles/PMC193654https://www.ncbi.nlm.nih.gov/pmc/articles/PMC193654https://en.wikipedia.org/wiki/Digital_object_identifierhttps://dx.doi.org/10.1186%252Fgb-2003-4-9-r54https://en.wikipedia.org/wiki/PubMed_Centralhttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC193654https://en.wikipedia.org/wiki/PubMed_Identifierhttps://www.ncbi.nlm.nih.gov/pubmed/12952533https://commons.wikimedia.org/wiki/File:Enzyme%2520Kinetics.pdfhttps://en.wikipedia.org/wiki/Digital_object_identifierhttps://dx.doi.org/10.1111%252Fj.1432-1033.1994.tb18666.xhttps://en.wikipedia.org/wiki/PubMed_Identifierhttps://www.ncbi.nlm.nih.gov/pubmed/8143720https://en.wikipedia.org/wiki/Digital_object_identifierhttps://dx.doi.org/10.1021%252Fbi00415a016https://en.wikipedia.org/wiki/PubMed_Identifierhttps://www.ncbi.nlm.nih.gov/pubmed/3052577

11

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[43] Walsh, R.; Martin, E.; Darvesh, S. (2007). A ver-satile equation to describe reversible enzyme inhibi-tion and activation kinetics: Modeling -galactosidaseand butyrylcholinesterase. Biochimica et BiophysicaActa (BBA) - General Subjects 1770 (5): 733746.doi:10.1016/j.bbagen.2007.01.001. PMID 17307293.

[44] Walsh, Ryan (2012). Ch. 17. Alternative Perspectives ofEnzyme Kinetic Modeling. In Ekinci, Deniz. MedicinalChemistry and Drug Design. InTech. pp. 357371. ISBN978-953-51-0513-8.

[45] Koshland DE (February 1958). Application of aTheory of Enzyme Specificity to Protein Synthesis.Proc. Natl. Acad. Sci. U.S.A. 44 (2): 98104. doi:10.1073/pnas.44.2.98. PMC 335371. PMID16590179.

[46] Hammes G (2002). Multiple conformational changesin enzyme catalysis. Biochemistry 41 (26): 82218.doi:10.1021/bi0260839. PMID 12081470.

[47] Sutcliffe M, Scrutton N (2002). A new conceptualframework for enzyme catalysis. Hydrogen tunnellingcoupled to enzyme dynamics in flavoprotein and quino-protein enzymes. Eur. J. Biochem. 269 (13): 3096102. doi:10.1046/j.1432-1033.2002.03020.x. PMID12084049.

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12 16 EXTERNAL LINKS

[48] Henri V (1902). Theorie generale de l'action de quelquesdiastases. Compt. Rend. Hebd. Acad. Sci. Paris 135:9169.

[49] Srensen PL (1909). Enzymstudien {II}. ber die Mes-sung und Bedeutung der Wasserstoffionenkonzentrationbei enzymatischen Prozessen [Enzyme studies III: Aboutthe measurement and significance of the hydrogen ionconcentration in enzymatic processes]. Biochem. Z. (inGerman) 21: 131304. Vancouver style error (help)

[50] Michaelis L, Menten M (1913). Die Kinetik derInvertinwirkung [The Kinetics of Invertase Action].Biochem. Z. (in German) 49: 333369.; Michaelis L,Menten ML, Johnson KA, Goody RS (2011). Theoriginal Michaelis constant: translation of the 1913Michaelis-Menten paper. Biochemistry 50 (39): 82649. doi:10.1021/bi201284u. PMC 3381512. PMID21888353.

[51] Briggs GE, Haldane JB (1925). A Note on the Kinet-ics of Enzyme Action. The Biochemical Journal 19 (2):339339. PMC 1259181. PMID 16743508.

[52] Flomenbom O, Velonia K, Loos D, Masuo S, Cotlet M,Engelborghs Y et al. (Feb 2005). Stretched exponentialdecay and correlations in the catalytic activity of fluctuat-ing single lipase molecules. Proceedings of the NationalAcademy of Sciences of the United States of America 102(7): 23682372. doi:10.1073/pnas.0409039102. PMC548972. PMID 15695587.

[53] English BP, Min W, van Oijen AM, Lee KT, LuoG, Sun H et al. (Feb 2006). Ever-fluctuating sin-gle enzyme molecules: Michaelis-Menten equation re-visited. Nature Chemical Biology 2 (2): 8794.doi:10.1038/nchembio759. PMID 16415859.

[54] Lu HP, Xun L, Xie XS (Dec 1998). Single-molecule en-zymatic dynamics. Science (New York, N.Y.) 282 (5395):18771882. doi:10.1126/science.282.5395.1877. PMID9836635.

[55] Xue X, Liu F, Ou-Yang ZC (Sep 2006). Singlemolecule Michaelis-Menten equation beyond quasistaticdisorder. Physical Review. E, Statistical, Nonlin-ear, and Soft Matter Physics 74 (3 Pt 1): 030902.doi:10.1103/PhysRevE.74.030902. PMID 17025584.

[56] Bevc S., Konc J., Stojan J., Hodoek M., Penca M.,Matej Praprotnik M., Janei D. (2011). ENZO: AWeb Tool for Derivation and Evaluation of Kinetic Mod-els of Enzyme Catalyzed Reactions. PLoS ONE 6(7): e22265. doi:10.1371/journal.pone.0022265. PMC3139599. PMID 21818304. ENZO server

15 Further reading

Introductory

Cornish-Bowden, Athel (2004). Fundamentals ofenzyme kinetics (3rd ed.). London: Portland Press.ISBN 1-85578-158-1.

Stevens, Lewis; Price, Nicholas C. (1999). Funda-mentals of enzymology: the cell and molecular biol-ogy of catalytic proteins. Oxford [Oxfordshire]: Ox-ford University Press. ISBN 0-19-850229-X.

Bugg, Tim (2004). Introduction to Enzyme andCoenzyme Chemistry. Cambridge, MA: BlackwellPublishers. ISBN 1-4051-1452-5.

Advanced

Segel, Irwin H. (1993). Enzyme kinetics: behaviorand analysis of rapid equilibrium and steady stateenzyme systems (New ed.). NewYork: Wiley. ISBN0-471-30309-7.

Fersht, Alan (1999). Structure and mechanism inprotein science: a guide to enzyme catalysis and pro-tein folding. San Francisco: W.H. Freeman. ISBN0-7167-3268-8.

Santiago Schnell, Philip K. Maini (2004). A cen-tury of enzyme kinetics: Reliability of the KM andv estimates. Comments on Theoretical Biology 8(23): 16987. doi:10.1080/08948550302453.

Walsh, Christopher (1979). Enzymatic reactionmechanisms. San Francisco: W. H. Freeman. ISBN0-7167-0070-0.

Cleland, William Wallace; Cook, Paul (2007). En-zyme kinetics and mechanism. New York: GarlandScience. ISBN 0-8153-4140-7.

16 External links

Animation of an enzyme assay Shows effects ofmanipulating assay conditions

MACiE A database of enzyme reaction mecha-nisms

ENZYME Expasy enzyme nomenclaturedatabase

ENZOWeb application for easy construction andquick testing of kinetic models of enzyme catalyzedreactions.

ExCatDB A database of enzyme catalytic mech-anisms

BRENDA Comprehensive enzyme database,giving substrates, inhibitors and reaction diagrams

SABIO-RK A database of reaction kinetics

Joseph Krauts Research Group, University of Cali-fornia San Diego Animations of several enzymereaction mechanisms

https://en.wikipedia.org/wiki/Help:CS1_errors#vancouverhttp://pubs.acs.org/doi/suppl/10.1021/bi201284u/suppl_file/bi201284u_si_001.pdfhttp://pubs.acs.org/doi/suppl/10.1021/bi201284u/suppl_file/bi201284u_si_001.pdfhttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC3381512https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3381512https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3381512https://en.wikipedia.org/wiki/Digital_object_identifierhttps://dx.doi.org/10.1021%252Fbi201284uhttps://en.wikipedia.org/wiki/PubMed_Centralhttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC3381512https://en.wikipedia.org/wiki/PubMed_Identifierhttps://www.ncbi.nlm.nih.gov/pubmed/21888353https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1259181https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1259181https://en.wikipedia.org/wiki/PubMed_Centralhttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC1259181https://en.wikipedia.org/wiki/PubMed_Identifierhttps://www.ncbi.nlm.nih.gov/pubmed/16743508https://www.ncbi.nlm.nih.gov/pmc/articles/PMC548972https://www.ncbi.nlm.nih.gov/pmc/articles/PMC548972https://www.ncbi.nlm.nih.gov/pmc/articles/PMC548972https://en.wikipedia.org/wiki/Digital_object_identifierhttps://dx.doi.org/10.1073%252Fpnas.0409039102https://en.wikipedia.org/wiki/PubMed_Centralhttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC548972https://en.wikipedia.org/wiki/PubMed_Identifierhttps://www.ncbi.nlm.nih.gov/pubmed/15695587https://en.wikipedia.org/wiki/Digital_object_identifierhttps://dx.doi.org/10.1038%252Fnchembio759https://en.wikipedia.org/wiki/PubMed_Identifierhttps://www.ncbi.nlm.nih.gov/pubmed/16415859https://en.wikipedia.org/wiki/Digital_object_identifierhttps://dx.doi.org/10.1126%252Fscience.282.5395.1877https://en.wikipedia.org/wiki/PubMed_Identifierhttps://www.ncbi.nlm.nih.gov/pubmed/9836635https://en.wikipedia.org/wiki/Digital_object_identifierhttps://dx.doi.org/10.1103%252FPhysRevE.74.030902https://en.wikipedia.org/wiki/PubMed_Identifierhttps://www.ncbi.nlm.nih.gov/pubmed/17025584https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3139599https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3139599https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3139599https://en.wikipedia.org/wiki/Digital_object_identifierhttps://dx.doi.org/10.1371%252Fjournal.pone.0022265https://en.wikipedia.org/wiki/PubMed_Centralhttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC3139599https://en.wikipedia.org/wiki/PubMed_Identifierhttps://www.ncbi.nlm.nih.gov/pubmed/21818304http://enzo.cmm.ki.si/https://en.wikipedia.org/wiki/International_Standard_Book_Numberhttps://en.wikipedia.org/wiki/Special:BookSources/1-85578-158-1https://en.wikipedia.org/wiki/International_Standard_Book_Numberhttps://en.wikipedia.org/wiki/Special:BookSources/0-19-850229-Xhttps://en.wikipedia.org/wiki/International_Standard_Book_Numberhttps://en.wikipedia.org/wiki/Special:BookSources/1-4051-1452-5https://en.wikipedia.org/wiki/International_Standard_Book_Numberhttps://en.wikipedia.org/wiki/Special:BookSources/0-471-30309-7https://en.wikipedia.org/wiki/International_Standard_Book_Numberhttps://en.wikipedia.org/wiki/Special:BookSources/0-7167-3268-8http://web.archive.org/web/20060221045110/http://www.informatics.indiana.edu/schnell/papers/ctb8_169.pdfhttp://web.archive.org/web/20060221045110/http://www.informatics.indiana.edu/schnell/papers/ctb8_169.pdfhttp://web.archive.org/web/20060221045110/http://www.informatics.indiana.edu/schnell/papers/ctb8_169.pdfhttps://en.wikipedia.org/wiki/Digital_object_identifierhttps://dx.doi.org/10.1080%252F08948550302453https://en.wikipedia.org/wiki/International_Standard_Book_Numberhttps://en.wikipedia.org/wiki/Special:BookSources/0-7167-0070-0https://en.wikipedia.org/wiki/International_Standard_Book_Numberhttps://en.wikipedia.org/wiki/Special:BookSources/0-8153-4140-7http://www.kscience.co.uk/animations/model.swfhttp://www.ebi.ac.uk/thornton-srv/databases/MACiE/http://us.expasy.org/enzyme/http://enzo.cmm.ki.si/http://mbs.cbrc.jp/EzCatDB/http://www.brenda-enzymes.info/http://sabio.h-its.org/http://chem-faculty.ucsd.edu/kraut/dhfr.htmlhttp://chem-faculty.ucsd.edu/kraut/dhfr.html

13

Symbolism and Terminology in Enzyme KineticsA comprehensive explanation of concepts and ter-minology in enzyme kinetics

An introduction to enzyme kineticsAn accessibleset of on-line tutorials on enzyme kinetics

Enzyme kinetics animated tutorial An animatedtutorial with audio

http://www.chem.qmul.ac.uk/iubmb/kinetics/http://web.archive.org/web/20040612065857/http://orion1.paisley.ac.uk/kinetics/contents.htmlhttp://www.wiley.com/college/pratt/0471393878/student/animations/enzyme_kinetics/index.html

14 17 TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES

17 Text and image sources, contributors, and licenses

17.1 Text Enzyme kinetics Source: http://en.wikipedia.org/wiki/Enzyme%20kinetics?oldid=647674344 Contributors: Graft, Michael Hardy, Shya-

mal, SebastianHelm, Samsara, Raul654, Diberri, Alan Liefting, Giftlite, Adenosine, Sonjaaa, Ukexpat, Clemwang, Qef, Poccil, Rich Farm-brough, Cacycle, ESkog, Bobo192, R. S. Shaw, Brim, Arcadian, Storm Rider, Alansohn, SnowFire, Stillnotelf, ClockworkSoul, Suruena,Cmprince, Gene Nygaard, Kmg90, Dmol, Bbatsell, Karam.Anthony.K, V8rik, Kane5187, Rjwilmsi, Koavf, Rschen7754, Brighterorange,RobertG, Sodin, OpenToppedBus, YurikBot, Hede2000, Chaser, Rsrikanth05, Kimchi.sg, Wknight94, Mastercampbell, AndrewWTaylor,Itub, KnightRider, SmackBot, Espresso Addict, Saravask, Slashme, Kjaergaard, TheTweaker, Yaser al-Nabriss, Chris the speller, RDBrown,Moonsword, Flyguy649, Xcomradex, Richard001, Mion, Vina-iwbot, Scientizzle, Mgiganteus1, Knights who say ni, Kyoko, SandyGe-orgia, Domitori, Outriggr, Pro bug catcher, Dr Zak, WillowW, Carstensen, Kozuch, Thijs!bot, Opabinia regalis, Java13690, BokicaK,Luna Santin, TimVickers, Gkhan, Igodard, DRHagen, WolfmanSF, Jeff Dahl, Shauun, Economo, Adrian J. Hunter, MartinBot, R'n'B,Leyo, RockMFR, Spidrak, Nigholith, Chymo72, JoNo67, BanjoCam, Xiahou, VolkovBot, Alexandria, Hannes Rst, CarinaT, Jacoban-drew2012, Wabaman44, Sxenko, Britzingen, SieBot, The Parsnip!, Oda Mari, Lightmouse, BecR, A2a2a2, Forluvoft, ClueBot, Snigbrook,The Thing That Should Not Be, Spoladore, Blanchardb, Tom Doniphon, ToNToNi, Joshwa-hayswa, Davo22, Fourthhour, Xijkix, Das-dasdase, Manysplintered, Legalvoice123, Rasikraj, I need a game, Ruute, NuclearWarfare, Muro Bot, Dana boomer, Wnt, Addbot, DOIbot, Laurinavicius, MrOllie, Download, CountryBot, Luckas-bot, Yobot, AnomieBOT, Materialscientist, Citation bot, Angmar09, Xqbot,08cflin, Rhodydog, Some standardized rigour, FrescoBot, Citation bot 1, Evenap, Stefano Garibaldi, Mauegd, Tbhotch, Onel5969, Eskeptic,RjwilmsiBot, Todd40324, Oliverlyc, Tommy2010, Tolly4bolly, ClueBot NG, Michael A. Wilkins, Savantas83, TheoThompson, HelpfulPixie Bot, Leonxlin, Anylai, NotWith, C.Rose.Kennedy.2, Dlituiev, Joannatrykowska, ChrisGualtieri, Dexbot, DionT71, 069952497a,Evolution and evolvability, Monkbot, Chaan19881, Pratyay Seth, Finagle29, Simon kinyanjui and Anonymous: 133

17.2 Images File:Activation2_updated.svg Source: http://upload.wikimedia.org/wikipedia/commons/e/e3/Activation2_updated.svg License: CC-

BY-SA-3.0 Contributors: en:Image:Activation2.png Original artist: Originally uploaded by Jerry Crimson Mann, vectorized by Tutmosis,corrected by Fvasconcellos

File:Allosteric_v_by_S_curve.svg Source: http://upload.wikimedia.org/wikipedia/commons/4/44/Allosteric_v_by_S_curve.svgLicense:Copyrighted free use Contributors: from en.wiki [1] Original artist: by TimVickers.

File:Burst_phase.svg Source: http://upload.wikimedia.org/wikipedia/commons/a/ab/Burst_phase.svg License: Public domain Contrib-utors: Vectorised SVG version of http://en.wikipedia.org/wiki/Image:Burst_phase.png Original artist: Original bitmap version byTimVickers, SVG version traced over it in Inkscape by Qef.

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General principlesEnzyme assaysSingle-substrate reactionsMichaelisMenten kineticsDirect use of the MichaelisMenten equation for time course kinetic analysisLinear plots of the MichaelisMenten equationPractical significance of kinetic constantsMichaelisMenten kinetics with intermediate

Multi-substrate reactionsTernary-complex mechanismsPingpong mechanisms

Non-MichaelisMenten kineticsPre-steady-state kineticsChemical mechanismEnzyme inhibition and activationReversible inhibitorsIrreversible inhibitors

Mechanisms of catalysisHistorySoftwareENZO

See alsoFootnotesReferencesFurther readingExternal linksText and image sources, contributors, and licensesTextImagesContent license

enzyme kinetics

Documents

enzymes substrates

enzymes structure

examples of enzymes

enzyme kineticscan

enzymes active site

determinethe enzyme

example of enzymes

reaction mechanisms