FEBS Letters 587 (2013) 2767–2771

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Review

Michaelis and Menten and the long road to the discovery ofcooperativity

0014-5793/$36.00 � 2013 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.febslet.2013.07.014

E-mail address: cardenas@imm.cnrs.fr

María Luz CárdenasUnité de Bioénergétique et Ingénierie des Protéines, Institut de Microbiologie de la Méditerranée, CNRS-Aix-Marseille Université, 31 chemin Joseph-Aiguier,13402 Marseille Cedex 20, France

a r t i c l e i n f o

Article history:Received 16 June 2013Revised 3 July 2013Accepted 4 July 2013Available online 13 July 2013

Edited by Christian P. Whitman

Keywords:Michaelis–MentenCooperativityFeedbackAllostery

a b s t r a c t

This article sketches the road from the establishment of the principles of enzyme kinetics, at thebeginning of the 20th century, to the discovery of regulatory mechanisms and the models to explainthem, from the middle of the century onwards. A long gap in time separates the two periods, inwhich technological advances were made that allowed the discovery of feedback inhibition andcooperativity. In particular, these discoveries and the theory needed to explain them could not havebeen made without knowledge of the major metabolic pathways and the enzymes and metabolitesinvolved in them.� 2013 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.

1. Introduction

This year marks not only the centenary of the Michaelis–Men-ten equation, published in Biochemische Zeitschrift [1], but alsothe half-centenary of the allosteric concept proposed by Monod,Changeux and Jacob in the Journal of Molecular Biology [2] thatopened the way for understanding cooperativity and feedbackinhibition. As we will see (Fig. 1), a long road separates the twoevents, as the first reports of feedback effects did not appear untilseveral decades after Michaelis and Menten.

Leonor Michaelis’s contribution to enzyme kinetics is enor-mous, in particular his work with Maud Menten [1], and their arti-cle can be considered an inflection point in the curve of thedevelopment of the field. In the 19th century researchers had stud-ied chemical reactions that in general proceeded in a single step, sothat following the course of reaction presented no great problem.However, when the study of enzyme reactions started, althoughthe idea of the formation of an enzyme–substrate complex alreadyexisted [3,4], people continued trying to analyse the kinetics interms of the progress curve of the reaction, until Michaelis andMenten drew attention to a better strategy. They not only used cor-rect algebra for analysing their data, but also emphasized twoimportant points, the advantages of working in conditions of initialvelocity and the necessity of controlling the pH (the pH scale

having been introduced a little earlier [5]). If these conditions weresatisfied the curve of velocity in function of the concentration ofsubstrate needed to be a hyperbola, defined by two parameters,what we now call the Michaelis constant, Km, and the maximalvelocity V (or, more appropriately, the limiting velocity) [6]. Thereanalysis of Michaelis and Menten’s results in terms of thesteady-state interpretation [7] did not alter the fundamentalcorrectness of their approach.

This realization and the establishment of a correct experimentalprotocol were crucial, because they meant that any deviation fromhyperbolic behaviour needed an explanation. The possibility ofrecognizing deviations allowed enzyme cooperativity to be discov-ered, and models were developed to explain it. These deviationsfrom hyperbolic behaviour were initially received with surpriseand worry, as it was not easy to show that they were not artefacts.Umbarger [8], for example, referred to ‘peculiar kinetic behavior’and Gerhart and Pardee, although several years later, still talkedabout ‘complex kinetics’ [9]. By that time, of course, the coopera-tive binding of oxygen to haemoglobin was well known [10,11]and was a source of inspiration for the development of models thatcould explain the peculiar kinetic behaviour. It may appear surpris-ing, however, that it took so long, more than 40 years from the timeof Michaelis and Menten, to recognize the first cases of deviationfrom hyperbolic kinetics; in fact it is not so surprising, as discussedbelow, because to detect a deviation an adequate range ofsubstrate concentrations must be studied and the velocity pre-

Fig. 1. Chronology of the main steps from establishing the principal kinetic characteristics of enzyme-catalyzed reactions (1902–1925) to the discovery and analysis ofregulatory mechanisms (from 1956). The long gap between Michaelis and Menten (1913) on the one hand and Umbarger (1956) and Yates and Pardee (1956) on the othercorresponds to the period in which the major metabolic pathways were elucidated, and the metabolites and enzymes involved in them characterized.

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cisely determined. Furthermore, in general only enzymes showingfeedback inhibition show cooperativity, so the number of possibleexamples was not large.

2. Practical problems for obtaining adequate saturation curves

The necessity of working in conditions of initial velocity [1] notonly showed how to do kinetic experiments well, but it also im-posed a very significant constraint on kinetic studies, because itimplied a capacity to detect small amounts of product with suffi-cient accuracy, or small decreases in substrate concentration, andat that time this was not easy. In practice it required analyticalmethods sensitive enough to cope with this restriction. Further-more, as the initial velocity is a measure of the tangent to the pro-gress curve at time zero, which requires a curve with a sufficientnumber of points, the ideal situation is to use an analytical methodwhose results could be registered continuously, such as a spectro-photometric test. Nowadays, this is no problem, as any laboratoryhas such equipment, but that was not the case at the time ofMichaelis, nor for a considerable time afterwards. Furthermore,even when people started to have spectrophotometers, many reac-tions could not be followed directly, as they produced no observa-ble spectrophotometric change. The realization that coupled assayscould be used [12–14], where, for example, the oxidation ofNAD(P)H or the reduction of NAD(P) could be followed, was animportant step in the right direction. Much later, the developmentof the theory of coupled assays [15–17] allowed a reliable protocolto be established, and this provided a powerful tool for studyingenzyme kinetics and contributed strongly to the field.

A deviation from hyperbolic behaviour does not necessarilymean, however, the existence of cooperativity. Enzymes are oftenunstable, and they can become inactivated in the assay conditions,and as substrates usually act as stabilizing factors, an increase insubstrate concentration may produce increases in product forma-tion, above what the Michaelis–Menten equation would predict.In such a case the curve of rate as a function of substrate concen-tration may appear sigmoidal instead of hyperbolic. The problemof enzyme instability is serious, and it was especially so duringthe first half of the 20th century when there was not enoughknowledge about how to stabilize enzymes. It is not surprising

then, that many of the studies were done with enzymes chosenfor their stability, such as extracellular enzymes, usually studiedwith artificial substrates. As a matter of fact, both Henri [4] andMichaelis and Menten [1] made their pioneering kinetic studieswith invertase, an extracellular enzyme secreted by yeast.(Although invertase is little studied in modern biochemistry, it iswidely used in the confectionary industry for production of choco-lates with liquid centres.)

Extracellular enzymes have also the advantage that they havefewer ‘contaminants’ than intracellular ones and tend to be easierto purify. Obtaining pure enzymes and even partially purified oneswas a difficult task, and progress required knowledge of how tostabilize enzymes, and the development of purification techniquesand of such appropriate materials as ion-exchange resins and fil-tration gels. Affinity chromatography, which contributed greatlyto the field, only developed in the 1970s.

Something crucial to bear in mind is that at the time of Michae-lis and Menten, and for several decades afterwards, metabolicpathways and intermediates had not been well established, andthe corresponding enzymes were also not well known: for exam-ple, the Krebs cycle was not proposed until 1937 [18], and re-mained controversial for a considerable time afterwards, withsome of the enzymes, such as isocitrate dehydrogenase [19] stillneeding to be characterized. Many studies were done using crudetissue extracts. Only when knowledge of protein chemistry had ad-vanced sufficiently could the study of intracellular enzymes beaccomplished with the use of natural substrates, which were inmany cases metabolites, and the phenomena of cooperativity andallostery could be revealed.

An artefactual deviation from hyperbolic behaviour could alsobe attributed to problems of controlling the concentration of thereal substrate. This could happen if, for example, the real substratewas a complex with a metal ion, and the variation of substrate con-centration had failed to take this into account. A good example isATP, for the real substrate is nearly always MgATP.

Furthermore, in order to clearly detect a deviation from the ex-pected hyperbolic behaviour it is necessary to make measurementsat several substrate concentrations, both above and below half-sat-uration. At the lower concentrations the problems of enzyme insta-bility just mentioned and of lacking an adequate detecting method

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can arise, and quite often, experimental studies are done with toofew observations at these low concentrations.

For all these reasons it is not surprising that several decadespassed after the pioneering work of Michaelis and Menten beforethe first cases of deviation from the expected behaviour were re-ported [8,9]. Probably such deviations had been observed before,but experimenters lacked the confidence to report them, and re-garded them as artefacts.

3. Feedback inhibition and cooperativity: two faces of the samecoin

Among the first enzyme reactions known not to follow the clas-sical hyperbolic behaviour were threonine deaminase [8] andaspartate transcarbamoylase [9], and such enzymes also showedfeedback inhibition. In other words cooperativity and feedbackinhibition were discovered at the same time.

During the 1950s there was great interest in cybernetics, thestudy of control systems originated by Wiener [20] and still withsome influence today [21]. There were indications that feedbackcontrol could exist in living organisms: for example, in Escherichiacoli the presence of isoleucine in the culture medium preventedthreonine from being metabolized to isoleucine [22]. In 1956Umbarger shed light on this phenomenon in a classic paper of asingle page in Science [8]. He studied the effect of isoleucine ondeamination of threonine, the first step in the conversion of threo-nine to isoleucine, and found that isoleucine was a very stronginhibitor, 100 times stronger than leucine. Surprisingly, in spiteof the structural difference with the substrate, the inhibition wascompetitive. Furthermore, the kinetic results were ‘peculiar’, be-cause to obtain a straight line in the double-reciprocal plot heneeded to use the square of the substrate concentration. So, to-gether with finding the existence of deviations from the expectedhyperbolic behaviour he found evidence of a negative feedback.

Umbarger’s observation on threonine deaminase was veryimportant, as it is one of the first cases of deviation from the ex-pected hyperbolic kinetic behaviour to be reported. However, asthis could have been an artefact, for the reasons mentioned earlier,he added: ‘Further experiments are in progress in an effort to de-cide whether this peculiar kinetic behavior is apparent or real.’These results were confirmed later [23], but they continued to beworried. In relation to their Fig. 5 the authors said: ‘It is to be notedthat the abscissa is 1/S2 rather than the usual 1/S since this reactionappears to be bimolecular with respect to both substrate andinhibitor. Attempts to alter the conditions of assaying enzymeactivity so as to obtain the usual monomolecular kinetic behaviorhave been unsuccessful.’ [23].

Umbarger’s observations [8,23] were later confirmed by Jean-Pierre Changeux during his thesis work [24] using a derepressedmutant which produced more than ten times more enzyme thanthe wild type. Like Umbarger, he found that the kinetics of L-thre-onine deamination, both in the absence and presence of L-isoleu-cine, were ‘somewhat complex’ and ‘does not follow simpleMichaelis–Menten kinetics’. Furthermore, he found that the inhib-itory effect of isoleucine was competitive with respect to threo-nine, even with purified enzyme (Umbarger’s experiments weredone with crude extracts). The complexity of the kinetics inducedhim to postulate that distinct binding groups would exist on thesurface of the enzyme, and that consequently it would be possibleto desensitize the enzyme, that is to have a threonine deaminasestill active but insensitive to isoleucine. p-Chloromercuribenzoateproved to be very effective for achieving this, indicating that par-tially different groups are involved in the binding of threonineand isoleucine in spite of the competitive character of the inhibi-tion. So here are the roots that would lead to the concept of theallosteric site [2]. Another concept that also emerges from the work

of Changeux and his observation of the deviation of Michaelis–Menten kinetics is the idea of a threshold, very important in meta-bolic regulation. Thus he said ‘it is worth noting that as a result ofthe ‘‘bimolecular’’ kinetics of inhibition the effect of metabolitebecomes significant above a threshold value. In other words, theintracellular metabolic pool should become effective in the feedbacksystem only when the concentration rises above a critical level’.

Another early case of feedback inhibition was the control ofpyrimidine biosynthesis in E. coli by cytosine derivatives: these in-hibit formation in vivo of the pyrimidine intermediate ureidosuc-cinic acid [25], now known as carbamoylaspartate. Experimentsin vitro with crude extracts showed that cytidine, and especiallycytidine-5-phosphate, acted as competitive inhibitors with respectto aspartate for the formation of ureidosuccinic acid, the first reac-tion unique to pyrimidine biosynthesis [25]. Thus a nucleotide endproduct was able to compete with a structurally very different sub-strate, an aminoacid. As these experiments, like Umbarger’s, weredone in crude extracts one could argue that the inhibition by cyto-sine derivatives could be indirect: for example, these derivativescould have been transformed in the extract to the real inhibitor.Afterwards aspartate transcarbamoylase, the enzyme responsiblefor forming carbamoylaspartate, was purified and the experimentsrepeated with a highly purified enzyme [9]. Gerhart and Pardeeconfirmed that CTP inhibits competitively with respect to aspartate[9]. Furthermore, CTP appeared to bind to a second site differentfrom the active site, which they called the feedback site, as the en-zyme could be desensitized without losing catalytic activity [9].This led them to postulate that ‘the bound end product perhapsinhibits by deforming the enzyme so that the latter has a low affin-ity for the substrate’. This beautiful classic paper, which had greatinfluence on my own research (see below), gives a very good illus-tration of what Monod, Changeux and Jacob would call an allostericsite [2]; it also describes an activator, ATP. However, somethingthat I find very puzzling is that although the deviation from hyper-bolic behaviour leaps out at the modern reader’s eye, with signifi-cant and very noticeable cooperativity with respect to aspartate inFigs. 2, 3 and 5 of that paper, they downplayed this observation: inrelation to their Fig. 2 they only said ‘Despite the complex kinet-ics. . .’, adding in a footnote that ‘Further kinetic studies and possi-ble explanations for their anomalous appearance may be found inthe thesis of J. C. Gerhart, University of California, 1962’. In relationto the desensitized enzyme (their Fig. 3) they just said that ‘thedependence of velocity on aspartate concentration followed acurve unlike the unusual sigmoidal dependence of the native en-zyme’. This lack of emphasis on the cooperativity may perhapsbe because they did not have any explanation for it, whereas theydid have a plausible mechanism for explaining the feedback inhibi-tion. As late as 1962, therefore, the observation of sigmoidaldependence was seen with some suspicion, as it went against theideas established in the article of Michaelis and Menten, despitethe fact that the cooperativity of oxygen binding to haemoglobinhad been known since 1910 [10,11]. It is a great pity that theydid not pay more attention to the sigmoidicity because their articlealso illustrates very clearly the idea that effectors modify the de-gree of cooperativity with respect to the substrate, inhibitors byincreasing it and activators by decreasing it: CTP (inhibitor) in-creased cooperativity with respect to aspartate (their Fig. 2)whereas ATP (activator) decreased it (their Fig. 5).

Once the first cases of deviation from the hyperbolic behaviourwere confirmed (sigmoidal dependence of velocity as a function ofsubstrate concentration), others were reported, and the 1960s and1970s produced several examples. Enzyme cooperativity was thusdiscovered simultaneously with feedback inhibition, and the driv-ing force was the desire to understand feedback mechanisms,which appeared to have a clear physiological importance. It wastherefore not by chance that both properties were discovered at

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the same time, as they are two faces of the same coin, and both requiredmolecular explanations. It is quite probable that what evolution se-lected was feedback inhibition of enzymes involved in pathways con-trolled by demand, with substrate cooperativity being a side effect, assuggested by Hofmeyr and Cornish-Bowden [26]. In fact, substrate sig-moidicity is often small, but it is increased and can even be induced byan allosteric inhibitor [27], whereas feedback inhibition (i.e. allostericinhibition) does tend to be cooperative, probably to allow thepossibility of a threshold in the response to demand.

4. Models to explain cooperativity and allostery

Models were then derived to explain the observed sigmoidicityand the effects of inhibitors that were structurally unlike the sub-strates, i.e. allostery. As new ideas do not come out of the blue, butarise in a definite context, it is not surprising that the first modelswere based on binding: that is, the cooperative binding of sub-strates, inhibitors or activators. The importance of haemoglobinin the development of these ideas is great: not for nothing is itcalled an ‘honorary enzyme’. At the time when models were devel-oped little was known about the quaternary structure of enzymeswith cooperativity. One of the few X-ray structures available wasthat of haemoglobin [28]. Structures of allosteric enzymes suchas aspartate carbamoyltransferase came much later [29].

Two principal models appeared in the mid-1960s to explaincooperativity and allostery: the allosteric model, also called thesymmetry model or the concerted model, proposed by Monod et al.[30], and the sequential model proposed by Koshland, Némethyand Filmer a year later [31]. Both attach a functional importanceto multiple conformations, an idea that originated with Koshland’sinduced fit hypothesis [32].

A central feature of the allosteric model is conformational reg-ulation. Thus, an equilibrium exists between two conformationalstates, usually known as the R (‘relaxed’) and T (‘tense’) states, inthe absence of any ligand. Different ligands bind preferentially toone of the two states, and thus perturb the equilibrium betweenthem. Furthermore, all of the subunits in an oligomeric proteinchange between the R and T states in a concerted manner, so sym-metry is maintained.

In contrast, the sequential model did not require conforma-tional symmetry, as the conformational change of each subunit oc-curs only when ligand is bound. Thus in this case it is the ligandthat induces the conformational change. In the absence of ligandthere is a different conformation.

As both models explained the observed kinetic cooperativity onthe basis of cooperativity of substrate binding, this implied that theenzyme should be oligomeric, or there must be more than one ac-tive site per enzyme molecule. However, as there is usually onlyone active site per monomer, with rare exceptions such as verte-brate hexokinase B or II [33,34], this meant that monomeric en-zymes should not be cooperative: they could show allostery, butnot cooperativity.

This limitation encouraged some people in the 1960s, such as Ra-bin [35], to seek models that could explain kinetic cooperativitywithout needing cooperative binding: this could be based, for exam-ple, on enzyme isomerization during the course of the reaction [35].This was initially a sort of intellectual challenge as no monomericenzymes showing deviations from hyperbolic behaviour had beendescribed experimentally, at least, none with natural substrates.

5. Glucokinase: a monomeric enzyme with cooperativity, but nofeedback inhibition

In 1975 this view changed after Hermann Niemeyer and col-leagues in Chile described sigmoidal kinetics for ‘glucokinase’ (i.e.hexokinase D or hexokinase IV) [36], the enzyme responsible for

glucose phosphorylation in hepatocytes, whose activity level inliver depends on diet and hormonal regulation [37]. This glucoseuptake is an essential physiological process, crucial for glucosehomeostasis. It has acquired greatly increased interest and impor-tance with the rise in recent decades of diabetes type 2 as a majorproblem of human health [38,39] (the name ‘glucokinase’ is almostuniversal in the literature, so I shall use it here, but it gives amisleading impression of the specificity [37,40]).

The first kinetic studies on glucokinase did not report this sig-moidal behaviour because of the difficulties referred to above: pre-vious studies from various groups had too few observations, and soalthough the possibility of deviations from hyperbolic behaviourwas in the air, it was far from being clear [41,42]. When I joinedNiemeyer’s group and started to work with this enzyme, my night-mare was that the apparent positive cooperativity that I wasobserving could be an artefact, especially because the degree ofcooperativity was rather small, with a Hill coefficient of about1.5, and the enzyme rather unstable. So the paper of 1975 [36] de-scribed several experiments that were intended to convince our-selves that the apparent cooperativity was real, as the enzymeappeared to be a monomer (the form of enzyme with a highermolecular mass mentioned in that paper may have been a complexof glucokinase with the regulatory protein, discovered severalyears afterwards [43]). The fact that the liver glucokinase obtainedfrom different mammalian species, and also from reptiles andamphibians, had a similar degree of cooperativity, despite signifi-cant variations in the half-saturation values, tended to supportthe idea that the cooperativity was not an artefact, and could havea physiological value. It was a relief, therefore, that a year later agroup in England described a similar degree of cooperativity [44],this time with the pure enzyme, and showed that it was a mono-mer [45]. Of course, the crucial question from the point of viewof a plausible cooperative mechanism was the quaternary struc-ture in the assay conditions: it also proved to be monomeric [46].

Glucokinase was thus the first monomeric enzyme with sigmoi-dal kinetics. Influenced by the work of Gerhart and Pardee [9] Itried to ‘desensitize’ it, thinking that it could have an allosteric sitecapable of binding glucose. All the efforts were in vain, as there isno such site: as long as the enzyme retained activity it continued toshow sigmoidicity. In the absence of interacting sites positivecooperativity requires a kinetic mechanism in which binding ofsubstrates is not at equilibrium in the steady state; it can only bea kinetic property that cannot occur at thermodynamic equilib-rium. Two models were postulated at the time for explaining thecooperativity: the mnemonical model [47,48] and the slow-transi-tion model [49,50], as we have reviewed [51]. Briefly, in both mod-els the enzyme exists in two distinct forms, E and E’ that areinterconverted relatively slowly, with the more stable form E’ pre-dominating in the absence of glucose. In the mnemonical modelthe less stable form E is the one released at the end of the catalyticcycle. The slow-transition model is somewhat more complicated,as both conformations can accomplish a catalytic cycle, but withdifferent kinetic parameters. In both models, as glucose binds intwo different steps, the full rate equation contains terms in thesquared concentration of glucose, thereby allowing deviationsfrom Michaelis–Menten kinetics.

Besides being monomeric and showing cooperativity, glucoki-nase is unusual in that it does not show feedback inhibition. As itis an enzyme controlled by supply [52,53] and not by demand, evo-lution appears not to have selected a feedback mechanism, whosefunction in demand-driven pathways is to displace the controlfrom the first enzyme to the demand for the end-product [54],and is crucial for maintaining homeostasis of intermediates. Thislack of feedback appears to have dramatic consequences for humanhealth, because drugs that activate it, which were seen as potentialmedicines for diabetes, as they are effective for decreasing

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glycaemia, at least temporarily, produce undesirable effects in thelong term [55], probably because there is no feedback that controlsthe system.

6. Forty years in the wilderness

The large gap in time visible in Fig. 1 is at first sight surpris-ing: why did it take so long for regulatory mechanisms to bediscovered? This gap, however, corresponds to the period inwhich metabolic pathways were being elucidated, intermediatesbeing identified, methods for purifying and stabilizing proteinsbeing developed, as well as methods for following the progresscurves of the reactions with high sensitivity. This period of about40 years after Michaelis and Menten — 40 years in the wilderness— illustrates very well that progress in science has two require-ments, not only a guiding vision, but also an adequate technology.As Woese [56] commented in relation to the biology of the 21stcentury, but it applies equally well to the early development ofenzymology in the 20th, ‘without an adequate technologicaladvance the pathway of progress is blocked, and without anadequate guiding vision there is no pathway, there is no wayahead’.

Acknowledgements

This work was supported by the Centre National de la Recher-che Scientifique (UMR 7281). I thank Athel Cornish-Bowden forvery helpful discussion.

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