Current Biology 23, R972–R979, November 4, 2013 ª2013 Elsevier Ltd All rights reserved http://dx.doi.org/10.1016/j.cub.2013.09.033

of Enzyme Kinetics in Cells

ReviewERK as a Model for Systems Biology

Alan S. Futran,1 A. James Link,1,2 Rony Seger,3

and Stanislav Y. Shvartsman1,2,4,*

A key step towards a chemical picture of enzyme catalysiswas taken in 1913, when Leonor Michaelis and MaudMenten published their studies of sucrose hydrolysis byinvertase. Based on a novel experimental design and amathematical model, their work offered a quantitativeview of biochemical kinetics well before the protein natureof enzymes was established and complexes with sub-strates could be detected. Michaelis–Menten kinetics pro-vides a solid framework for enzyme kinetics in vitro, butwhat about kinetics in cells, where enzymes can be highlyregulated and participate in a multitude of interactions?We discuss this question using the Extracellular SignalRegulatedKinase (ERK), which controls amyriad functionsin cells, as a model of an important enzyme for which wehave crystal structures, quantitative in vitro assays, anda vast list of binding partners. Despite great progress, westill cannot quantitatively predict how the rates of ERK–dependent reactions respond to genetic and pharma-cological perturbations. Achieving this goal, which isimportant from both fundamental and practical stand-points, requires measuring the rates of enzyme reactionsin their native environment and interpreting thesemeasurements using simple but realistic mathematicalmodels — the two elements which served as the corner-stones for Michaelis’ and Menten’s seminal 1913 paper.

IntroductionOne hundred years ago, Leonor Michaelis and MaudMentenpublished their landmark paper on enzyme kinetics, in whichthey studied how a two–ring sugar, sucrose, is hydrolyzed bya yeast–derived enzyme, invertase, so named because hy-drolysis changes optical rotation from positive for sucroseto negative for the mixture of fructose and glucose(Figure 1A) [1–3]. The choice of this chemical reaction canbe traced back to Louis Pasteur, a founding father of micro-biology who made many remarkable discoveries, but wasconvinced that enzyme reactions require the presence ofliving organisms that provide a vital force, irreducible tolaws of physics and chemistry. By 1913, this view had beenlosing ground, largely due to the work of Eduard Buchner,who demonstrated fermentation in the absence of livingcells. This reinforced the view that enzymes can be under-stood using the principles of chemistry, at that time, still anemerging discipline, with Emil Fischer as one of the leadingfigures, famous for his synthesis of natural products,including sugars [4].

Working with synthetic sugars and different types of yeastenzyme preparations, Fischer concluded that enzyme

1Department of Chemical and Biological Engineering, Princeton

University, Princeton, USA. 2Department of Molecular Biology,

Princeton University, Princeton, USA. 3Department of Biological

Regulation, Weizmann Institute of Science, Rehovot, Israel. 4Lewis–

Sigler Institute for Integrative Genomics, Princeton University,

Princeton, USA.

*E-mail: stas@princeton.edu

catalysis requires shape complementarity between enzymesand their substrates and put forward his famous ‘lock–and–key’ model of enzyme action. Michaelis’ and Menten’sapproach to evaluating Fischer’smodel was based on formalchemical kinetics, which is standard today but had been onlya couple of decades old in the beginning of the 20th century.In this approach, one postulates a mechanism and derivesfrom it an algebraic equation for the overall reaction rate asa function of reaction conditions, such as reactant concen-trations. Fitting the derived equation to rates measuredover a range of conditions can be used to assess the validityof the mechanism [5].The first application of kinetic approach to enzymes is

attributed to Victor Henri, whose dissertation, published in1903, contains the now familiar mechanism in which revers-ible formation of a complex precedes its irreversible decom-position into enzyme and product (Figure 1B) [4,5]. However,analysis of Henri’s data was complicated by product inhibi-tion, which was significant at high substrate conversions inhis experiments. Michaelis and Menten worked at low sub-strate conversions and measured initial rates of reaction,which allowed them to neglect product inhibition and simpli-fied kinetic analysis. Their analysis revealed that the rate ofreaction is accurately described by a simple formula, linearat small substrate concentrations and approaching a con-stant value when substrate concentrations are high(Figure 1C,D) [6]. The fact that one formula fit the data overa wide range of substrate concentrations was clearly consis-tent with Fischer’s idea and Henri’s mechanism. A rigorousproof of this mechanism, based on direct observation ofenzyme–substrate complexes, appeared only decades later,after the protein nature of enzymes was established [7,8].Nevertheless, the clarity of the paper made it an instantclassic and ensured that kinetic approach was rapidlyapplied to other enzymes.The groundbreaking studies on invertase took the first

steps towards establishing a chemical picture of a constitu-tively active enzyme that processes a single substrate. Butthings are much more complex inside cells, where enzymescan be highly regulated and need to work on multiple sub-strates. Our understanding of such systems is still incom-plete, despite great advances in conceptual analysis ofintracellular processes and their experimental analysis.Here, we use the Extracellular Signal–Regulated Kinase1/2(henceforth, ERK) as a model to highlight some of the mostimportant aspects of enzyme kinetics in cells. Some ofthem, such as substrate selectivity, can be addressed bystudies with a small number of purified components. Otherfeatures, such as spatial control of enzyme activity, requirestudies in vivo. The general concepts developed by Michae-lis and Menten still hold, but they must be applied in thecontext of enzyme networks and complex intracellularenvironments.

A Brief History of ERKERK was discovered in studies of protein phosphorylation,in the context of cell stimulation by growth factors, whichact through receptor tyrosine kinases [9,10]. The first pro-tein shown to undergo phosphorylation in response togrowth factors was the ribosomal protein S6. As this pro-tein is phosphorylated on serine residues, it cannot be a

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Figure 1. The Michaelis–Menten model of enzyme kinetics.

(A) Yeast invertase and the hydrolysis of sucrose to glucose (top) andfructose (bottom). Structure of Saccharomyces cerevisiae invertasedrawn from PDB file 4EQV [1]. (B) The model proposed by Michaelisand Menten, wherein an enzyme and a substrate bind reversibly toform a complex, which is converted to a product and the enzyme. (C)The Michaelis–Menten equation and its graphical representation. Plot-ting the initial rate against the substrate concentration enables thedetermination of both Vmax andKm. (D) Lineweaver Burk representationof the Michaelis–Menten equation. Taking the reciprocal of both sidesof the Michaelis–Menten equation yields a linear relationship. Plottingthe reciprocal of the initial rate vs. the reciprocal of substrate concen-tration allows the determination of Km and Vmax from the y and x inter-cept and the slope of the line.

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Figure 2. Patterns of ERK activation in organisms.

(A) ERK activation requires its phosphorylation by MEK. Active ERKcontrols cellular processes by phosphorylating multiple substrates.(B) Active ERK (red) at three different time points in Drosophila em-bryos. Active ERK is first detected at the embryonic poles, where itspecifies the nonsegmented terminal regions of the future larva. Withinthe next 30minutes, ERK is activated in a lateral domain correspondingto the presumptive neurogenic ectoderm. After gastrulation, ERK isactive along the ventral midline and in tracheal pits.

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direct substrate of tyrosine kinases. This led to the identi-fication of the protein Ser/Thr kinases RSK and S6K,which are themselves activated by phosphorylation onserines and threonines. The kinase responsible for thephosphorylation of RSK was discovered by Sturgill andRay [11], and the corresponding gene was subsequentlycloned by Cobb and collaborators [12,13]. Although itwas initially known by several distinct acronyms, the en-zyme’s name settled on the Extracellular Signal–RegulatedKinase (ERK).

ERK became the founding member of Mitogen ActivatedProtein Kinases (MAPKs), a class of serine/threonine kinaseswhich control a wide range of processes in adult and devel-oping cells [14]. Enzymatic activity of ERK requires its phos-phorylation on Tyr and Thr within the activation loop of thekinase [15]. The dual–specificity protein kinase responsiblefor this activation was identified [16,17] and cloned [18,19]shortly after the cloning of ERK itself, and was termed MAPKinase/ERK Kinase (MEK). The reverse modification, whichdephosphorylates and deactivates ERK, is accomplished

by phosphatases, which were identified relatively early inERK research [20,21].In the beginning of the 1990s, studies in model genetic

organisms, most notably Drosophila melanogaster, beganto complement experiments in cultured cells and establishedthat ERK plays a key role in embryogenesis [22]. In vivoeffects of ERK were initially studied by observing con-sequences of ERK mutations on morphological structures,such as the faceted Drosophila eye [23]. An antibody thatrecognizes the active, dually phosphorylated form ofthe enzyme (dpERK) (Figure 2) revealed intricate spatiotem-poral patterns of ERK activation in vivo [24,25]. The emer-gence of these patterns and analysis of their effects onprocesses such as gene expression and morphogenesis isa subject of intensive research in different model systems,from gonad development in worms to segmentation invertebrates [26,27].Over time, multiple substrates of ERK have been identified

and their sensitivity to ERK dissected at the molecular level[28–30]. These studies revealed the importance of dockinginteractions, which use distinct parts of the ERK molecule,bringing it together with a wide range of binding partners[31,32]. The first structures of ERK, active or inactive[33,34], and in complexes with some of its regulators andsubstrates appeared over the past two decades, providingimportant insights into the mechanisms of ERK activationand specificity.The first proof of association between deregulated ERK

activation and human disease appeared in 1994 [35]. Subse-quent work established that deregulation can result fromgain of function mutations in the signaling cascade that linksRTKs to ERK. In particular, gain of function mutations in en-zymes that activate ERK were identified in a broad spectrum

F-sites:Elk1 GESQVFQFPPSAP1 PAKLSFQFPSKsr1 HQPSQFNFPNDUS4 TSQFVFSFPVMKP1 STTTVFNFPVAraf RDQEHFSFPAConsensus -----F-FP-D-sites:Elk1 PQKGRKPRD-LELPLScJun NPKILKQSMTLNLADPMKP3 MLRRLQKGN-LPVRALMKP1 IVRRRAKGA-MGLEHIMEK1 MPKKKPTP--IQLNPAMKK2 KSKRKKD---LKLSCMConsensus --++++----ϕϕ-ϕ---

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(A) ERK2 structure with docking domains —DRS domain (left) and FRS domain (right) —and active site (middle) in space filling repre-sentation. Structure drawn from PDB file1ERK [33]. (B) Schematic representation ofERK2 substrate sequence containing a dock-ing site and a (S/T)P phosphorylation site. (C)Alignment of F-site and D-site sequencesfrom multiple ERK2 interacting substratesand regulators. (D) Schematic representationof ERK2 interactions with substrate dockingsite and (S/T)P phosphorylation motif. (E) Ef-fects of mutations on substrate docking siteand phosphorylation site and insights intomolecular mechanisms of ERK2 catalysis. (i)Wild-type substrate and associated Michae-lis–Menten parameters. (ii) Substrate withdocking site mutations and associatedMichaelis–Menten parameters. Mutating thedocking site significantly increases the Km

but has little effect on kcat. (iii) Substrate withphosphorylation motif mutations and associ-ated Michaelis–Menten parameters. Mutatingthe phosphorylation motif significantly de-creases the kcat but has little effect on Km.

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of human cancers and developmental abnormalities [36]. Theemerging picture of ERK regulation and function is complex,involving numerous components and layers of regulation[14,37]. Mathematical modeling, which was an integral partof the Michaelis and Menten paper, provides a sensibleway of dealing with this complexity [38–41]. Mathematicalmodels have been used to integrate data from a wide rangeof experimental approaches and predict howERK activity re-sponds to genetic and pharmacological perturbations. All ofthese models use the Michaelis–Menten description ofenzyme kinetics as a building block of more complex net-works. As this description was established based on studieswith isolated components, it is reasonable to askwhether it isappropriate for enzymes in cells. Belowwewill try to addressthis question for ERK, keeping in mind that studies of oneenzyme can have broad implications for biological regulationin general. Indeed, this turned out to be true for invertase.

Quantitative Analysis of ERK–Substrate InteractionsMichaelis and Menten studied an enzyme that is highlyspecific: invertase only acts on sucrose. Such specificityis fairly common for enzymes with small molecule sub-strates that bury themselves in clefts where catalysis oc-curs. Thus, the formation of the enzyme–substratecomplex is closely coupled to catalysis. However, other en-zymes — especially those that act on proteins — behavedifferently and have multiple substrates. ERK is a vividexample of an enzyme with broad specificity and is believedto have over 250 substrates [42–44]. Protein substrates aremodified at specific positions that interact with the activesite. However, the large size of these substrates enables

binding between the substrate andenzyme at positions that are distal tothe site of catalysis. These dockingsite interactions play an importantrole in targeting the activity of en-zymes to their substrates.

While ERK phosphorylation is targeted to specific sites —a serine or a threonine followed by a proline ((S/T)P) — thesesites are quite common, occurring in approximately 80% ofall proteins [45]. Clearly, catalytic site targeting is insufficientto guide ERK to substrates. Instead, specific dockingdomains on ERK and its substrates are used to enhancetargeting. There are two well-characterized docking do-mains on ERK termed the D Recruitment Site (DRS; alsocalled CD domain), which interacts with D site motifs (alsocalled DEJL motifs) on ERK-interacting proteins, and the FRecruitment Site (FRS), which interacts with proteins con-taining an F site (also called FXF motif, DEF motif) [32,46–49] (Figure 3A–C).Docking sites do not only increase the specificity of the

ERK–substrate interaction, they often increase efficiency ofERK-mediated phosphorylation [49]. This may seem coun-terintuitive; tight docking interactions could theoreticallyreduce substrate turnover if ERK substrates are not releasedpromptly after phosphorylation. It appears that many ERK–substrate interactions are destabilized after phosphorylation[50] and others may be sufficiently weak, allowing ERK todissociate from a phosphorylated product after catalysishas occurred.Because the formation of the enzyme–substrate complex

employs interactions distal to the active site, the formationof the complex can be functionally separated from catalysis.This can be clearly seen in theMichaelis–Menten parametersextracted from studies of ERK-dependent phosphorylationin vitro. For example, Ets1, a transcription factor phosphory-lated by ERK, contains both an ERK binding site and a distalphosphorylation site (TP). Phosphorylation of this substrate

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Figure 4. Identification of ERK substrates in C. elegans.

(A) Dissected C. elegans hermaphrodite germ line from wild-type ani-mals oriented from left to right, stained for dpERK (red) and DNA(white). Wild-type germ lines reveal two zones of ERK activation,zone 1 and 2, with brief downregulation of active ERK in the loop re-gion. (B) Schematic representation of ERK substrates identified inC. elegans by searching the genome for ERK docking site motifs andscreening putative substrates in vivo [26].

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was studied by separating and quantifying the role of thebinding site and phosphorylation motif [51]. Interestingly,mutations to each of these sites have a distinct effect onERK-mediated phosphorylation. Mutating the proline in theTP site to different amino acids has a significant effect onthe rate of phosphorylation, kcat, despite the relativelyweak effect these mutations have on equilibrium dissocia-tion constants. On the other hand, mutations in the dockingsite do not have a significant effect on kcat, but lead to muchweaker binding to ERK and thus increase the dissociationconstant and Km (Figure 3D,E).

Overall, mutations to both the phosphorylation motif andthe docking site affect the ability of Ets1 and ERK to form acatalytically relevant complex, but in very different ways.The binding site increases the local concentration of the TPmotif near the catalytic site, but has little effect on catalysis.On the other hand, the TP sequence is critical for positioningresidues for the transfer of a phosphoryl group to Ets1, butdoes not have a significant effect on the strength of theERK–Ets1 binding (Figure 3D,E). Thus, studies of enzymecatalysis using modern techniques such as directed muta-genesis and kinase activity and binding assays revealedmechanisms that could never have been imagined in 1913.Yet, we are still able to interpret and model these mecha-nisms using the language of the 1913 paper.

Identification of ERK SubstratesElucidating the parameters that describe ERK activity in atest tube provides valuable information, but it says nothingabout which substrates it is acting on in a cell or an organism.This question goes beyond the scope of studies enabled bythe Michaelis–Menten model, which focuses on one enzymeand one substrate. However, knowing what makes a proteinan ERK substrate—such as sequences of binding andphos-phorylation sites — and the advent of post-genomic tech-niques have enabled us to begin to piece together thepuzzle [26,43,52–58].

The proteomic approach aims to find proteins whose inter-actions with ERK or phosphorylation state change upon ERKactivation. A number of studies have used two-dimensionalgel electrophoresis to separate proteins by mass and iso-electric point in cells with and without initiation of ERK activ-ity. Proteins that have been phosphorylated will shiftpositions on a gel, and characterization by mass spectrom-etry enables the identification of the proteins that displaythis behavior [53,54]. These studies provide lists of ERKpathway targets and can identify its novel physiologicalfunctions. For example, Kosako et al. [43] used this approachto identify a component of the nuclear pore as a new ERKsubstrate and proposed that ERK regulates nucleocytoplas-mic transport. Clearly, intracellular proteins phosphorylatedin response to ERK activation are not necessarily ERK sub-strates. Instead, their phosphorylation may be induced byenzymes controlled by the ERK pathway. A different set oftechniques aims to identify direct binding partners of ERK[52,55–58]. In particular, von Kriegsheim and colleagues[56] assessed the relative amounts of proteins that co-immu-noprecipitate with ERK from cells which had been exposedto ERK activation for different periods of time. This study re-vealed the highly dynamic nature of the ERK interactome andits sensitivity to the level of pathway activation.

Knowledge about the molecular-level mechanisms ofenzyme–substrate interactions and genome sequencingmade it possible to combine bioinformatics with genetics

and biochemistry to identify ERK substrates in vivo. In arecent study of ERK effects in Caenorhabditis elegans germ-line development (Figure 4A), consensus sequences of bind-ing and phosphorylation sites were used to computationallysearch for ERK substrates in the C. elegans genome [26]. Alist of substrate candidates was generated by searching theproteome for ERK docking sites in the vicinity of phosphory-lation motifs. Candidate substrates were then screenedin vivo, using RNAi knockdown to identify which are respon-sible for translating ERK signaling into multiple aspects ofgerm-line development. In this way, a list of 161 candidatespredicted by bioinformatics led to 37 proteins that regulateERK-dependent biological processes in vivo. Finally, in vitrophosphorylation assays confirmed that many of these pro-teins are true ERK substrates (Figure 4B). Thus, in this com-bined bioinformatic, genetic and biochemical approach ERKsubstrateswerenotonly identified, but tied tospecificcellularand developmental processes, such as translational control.These studies reveal that analysis of the biological effects

of ERK activity requires simultaneous consideration of multi-ple substrates. To model the enzymatic activity of ERK incells, even under highly simplified assumptions, we needin vivo concentrations of ERK and its interactors, as well asrates of association, dissociation and catalysis. Currently,we have very little of this information for most ERK

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Figure 5. Substrate competition in the ERKpathway.

(A) Substrate competition and its effects onenzyme kinetics. When multiple substratescompete for the activity of a single enzyme,the rate of conversion of a single substratedecreases as the concentration of competingsubstrates increases. (B) ERK substratecompetition in the Drosophila embryo. Threesubstrates — Bicoid (Bcd), Capicua (Cic)and Hunchback (Hb) — compete for ERKactivity. (C) ERK-mediated downregulation ofCic. At the embryonic poles, where ERK isactive, Cic is exported out of the nucleusinto the cytoplasm, where it is degraded. (D)Distribution of ERK and its substrates in theDrosophila embryo in the presence andabsence of substrate competition. ERK isdoubly phosphorylated and activated at thepoles of the embryo. Two substrates — Bcdand Hb — are present only at the anteriorpole of the embryo. In wild-type embryos,Cic is downregulated at the poles unevenly,with a higher concentration at the anteriorpole. However, when the anteriorly locatedERK substrates Bcd and Hb are removed,Cic is downregulated more evenly, indicatingthat ERK’s ability to phosphorylate and down-regulate Cic is inhibited by the presence ofthese other ERK substrates at the anteriorpole.

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substrates. Furthermore, the identification of multiple sub-strates and processes regulated by ERK raises a numberof questions that did not apply to the single substrate systemstudied by Michaelis and Menten. One of these questions isrelated to ERK substrate competition.

ERK Substrate CompetitionHow does ERKmultiplex between itsmultiple substrates at agiven time point (Figure 5A,B)?One can imagine two differentscenarios: in the first scenario, active ERK is present inexcess of its substrates. In this case, the enzyme is mostlyfree, and its substrates can be viewed as independent sen-sors of ERK activity which do not affect each other. Geneticremoval or overexpression of any given substrate will notaffect the extent towhich ERKmodifies other substrates pre-sent in the cell. In this regime, the enzyme can be readily re-cruited to modify new substrates. In a second scenario,active ERK is saturated by substrates. What happens whenthe expression levels of different substrates are perturbedin this regime? A simplemathematicalmodel, where differentsubstrates of ERK act as competitive inhibitors of eachother, shows that the effect depends on substrate con-centrations and their relative affinities for the enzyme(Figure 5A,B). When ERK deals with a large number of sub-strates, each of which amounts to a small fraction of its inter-action partners, substrates are independent of each other,just as in the case when ERK is present in excess. On theother hand, when a substrate constitutes a significant frac-tion of ERK interaction partners, its knockdown or over-expression can strongly influence the effects of ERK onother substrates.

Which of the two scenarios reflects the situation in cells?At this point, as we are only beginning to identify ERK sub-strates in different cell types and have no reliable estimatesof their concentrations and relative affinities for ERK, theanswer to this question is still unknown. Some insights can

be provided by studies in model organisms, such asDrosophila, where multiple ERK substrates have been iden-tified and several methods exist for perturbing their expres-sion in vivo. A recent study of ERK signaling in the earlyDrosophila embryo suggests that competition betweenERK substrates is appreciable in magnitude and functionallysignificant [59]. In the early embryo, ERK is activated in alocalized pattern, with pronounced peaks at the anteriorand posterior poles (Figure 2B). One of the ERK substratesin this system is a transcriptional repressor Capicua (Cic),which is excluded from nuclei and degraded in the cyto-plasm in response to phosphorylation by ERK (Figure 5C)[60]. The spatial pattern of Cic downregulation is highlyasymmetric: Cic is downregulated much more strongly atthe posterior pole. Genetic experiments established thatthis asymmetry reflects ERK substrate competition. Specif-ically, at least two ERK substrates, the transcription factorsBicoid and Hunchback, are localized to the anterior polewhere they act as competitive inhibitors of ERK-dependentdownregulation of Cic. Accordingly, genetic removal of thesesubstrates from the embryo increases the level of Cic down-regulation at the anterior pole and makes the pattern of Cicdownregulation symmetric (Figure 5D) [59].These observations are consistent with a simple Mass Ac-

tionmodel, where ERK substrates inhibit each other compet-itively (Figure 5A,B). These competitive interactions canspread through a larger network that controls gene regula-tion in the embryo and subdivides it into different tissuetypes [61]. Thus, at least in this particular system, it appearsthat competition between ERK substrates is appreciable andplays a role in determining the biological effects of ERK acti-vation. These observations motivate multiple lines of inquiry:first, it remains to be determined whether the observedcompetition between ERK substrates implies that they usethe same docking site; second, it is important to determinewhether substrate competition is appreciable in other

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Figure 6. Regulation of ERK activity.

(A) Superimposition of inactive (black and red) and active (grey andcyan) ERK2 highlighting the activation loop and phosphorylated resi-dues. Structures of inactive and active ERK2 drawn from PDB files1ERK and 2ERK, respectively [33,34]. [B] Schematic representationof structural changes upon ERK activation and the effects on ATP/sub-strate binding and orientation. Upon activation, the amino-terminal andcarboxy-terminal lobes of ERK rotate toward one another and residuesin the active site are repositioned, allowing proper binding and orienta-tion of substrates for catalysis. (C) A classical single enzyme/substratenetwork, exemplified by the system used by Michaelis and Menten(invertase-mediated hydrolysis of sucrose). (D) A simplified ERK net-work involving multiple individual enzyme–substrate interactions —ERK activation by MEK, ERK inactivation by a phosphatase, andERK–mediated phosphorylation of one substrate.

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biological contexts. If this turns out to be the case, we mightneed to rethink the interpretation of experiments based ongenetic perturbations of individual substrates.

Enzyme Regulation and Enzyme NetworksIn cells, ERK cycles between a catalytically active and inac-tive state. How can an enzyme’s activity be turned on andoff? The answer to this question can be explained by study-ing the three-dimensional enzyme structure in atomic detail,a line of inquiry that could not have been imagined in 1913.ERK is a substrate of activating and deactivating enzymes.The mechanism of this regulation is the addition of aphosphoryl group by MEK to two positions on the ERKactivation loop, which causes a conformational rearrange-ment [34,62,63]. The phosphorylation lip moves consider-ably and the two lobes of the protein rotate closer to oneanother. This forms a pocket allowing the proper bindingand orientation of substrate residues such that ERK cantransfer a phosphoryl group from ATP to the target residue.This conformational change is reversed when ERK is de-phosphorylated by one of a number of phosphatases(Figure 6A,B) [64]. Note that the protein–protein interactionsresponsible for ERK regulation share similarities with thoseinvolved in ERK-mediated catalysis. MEK and phosphatasesoften use the same docking sites to modify ERK’s activitythat ERK uses to phosphorylate its substrates [49]. Thus,docking domains can be thought of as nodes for the multiplereactions that ERK is involved in.

In order to predict the enzymatic activity of ERK in cells, wemust consider its phosphorylation and activation by MEK,ERK-mediated phosphorylation of its many substrates anddeactivation by regulatory phosphatases (Figure 6C,D).Each of these individual interactions can be modeled bythe Michaelis–Menten mechanism, but to fully capture thebehavior of ERK, these modules must be coupled in a modelthat describes a complex network. Molecular level perturba-tions can ripple through such networks and lead to systemslevel responses that could not be predicted by looking at in-dividual reactions [65,66].

One example of the surprising effects of network-levelinteractions arose from the search for mutants of ERKwith increased activity. The sevenmaker gain of functionmutant of ERK was discovered in a genetic screen per-formed in Drosophila [67,68]. The mutation was found tolie in one of the ERK docking domains, the DRS. However,the identification of the location of this mutation raised asmany questions as it answered. The DRS interacts with Dsites on MEK, substrates and deactivators alike, so whywould a mutation in the DRS necessarily lead to increasedERK activity?

It is thought that the sevenmaker mutation has a detri-mental effect on ERK activation, deactivation, and catalysisindividually. However, increased activity may arise from animbalance of this effect on different ERK-interacting pro-teins. It is possible that deactivation of ERKby phosphatasesis more sensitive to disruption of the DRS than activation bykinases or catalysis by ERK [68,69]. Thus, even if all bindinginteractions involving the DRS are negatively impacted bythe sevenmaker mutation, if the disruption is more pro-nounced in ERK phosphatases relative to ERK’s other bind-ing partners, the ratio of active to inactive ERK increases.Thus, in vivo effects of the sevenmaker mutation cannot bereduced to binary interactions and must be consideredonly in the context of a network.

Mathematical Models for Enzyme Kinetics in CellsAnalysis of enzyme kinetics in cells, especially for highlyregulated enzymes with multiple substrates, requires anal-ysis of enzyme networks. And just as Michaelis and Mentenbased their work on measurements of reaction rates andmathematical models of reaction progress, we need mathe-matical models and experimental tools appropriate for net-works. Are we there yet?Most of the existing models of cell biochemistry assume

that enzymes, substrates, and complexes are perfectlymixed. This might be true in vitro, but not in cells, where re-action medium is highly crowded with macromolecules.Recent work on ERK activation by MEK reveals that crowd-ing has a strong effect on reaction kinetics [70]. When thelevel of mixing is high, MEK phosphorylates ERK followinga distributive mechanism, whereby ERK is phosphorylatedon two different sites, in two distinct enzyme–substrate en-counters, which can involve two different MEK molecules.But when diffusion is slowed down by crowding, the mole-cule that phosphorylated ERK for the first time binds to it

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with high probability before mixing with other molecules inthe medium and carries out the second phosphorylation. Inthis regime, a distributive mechanism appears as proces-sive, whereby sequential modifications of the substraterequire just a single enzyme–substrate encounter.

This change in the apparent kinetics leads to a qualitativechange in the dynamics of the enzymatic cycle that controlsERK phosphorylation. When ERK phosphorylation follows adistributive mechanism, the cycle can have multiple steadystates [71], whereas the cycle in which ERK phosphorylationis processive is always monostable [72]. This effect can bereadily captured by computational models that describe en-sembles of individual enzymes and substrates, but not byconventional chemical kinetics. Thus, some aspects ofenzyme kinetics in cells need models that differ from thoseused by Michaelis and Menten.

A typical model of ERK dynamics provides informationabout biochemical modification and subcellular locations ofmultiple species. While only a small fraction of these speciescan be measured by current experimental techniques, newtools of cellular biochemistry, including quantitative prote-omics, promise to expand the list of species and reactionsthat canbemonitored in the samesample [58,73,74]. Further-more, most of the current models of enzyme kinetics in cellshave been formulated based on data that neglect spatialorganization of cellular processes. However, rapid develop-ment of live imaging techniques can provide data aboutspatial distribution of network components and reactionrates [75]. In parallel, advances in understanding the mecha-nisms by which ERK interacts with substrates have led to thedevelopmentof live reportersof its enzymaticactivity [76–78].

ConclusionsOverall, when it comes to enzyme kinetics in cells, we are stillfar from the experimental and conceptual standards estab-lished by the 1913 paper. Given the complexity of theseprocesses and the fact that some of the key molecularplayers have been discovered only recently, this should notcome as a surprise. At the same time, progress of experi-mental techniques for monitoring different aspects ofenzyme kinetics in cells and our increasing ability to perturbenzyme networks will inevitably lead to more advancedphysicochemical models [79]. Armed with these models,we will be better equipped to predict how these networksrespond to genetic, environmental and pharmacologicalperturbations.

Acknowledgements

This work was supported by R01GM086537 from the National Institute

of General Medical Sciences.We thank Swathi Arur, Kevin Dalby, Ze’ev

Paroush, Alexey Veraksa and Benny Shilo for helpful discussions and

Bomyi Lim and Henry Mattingly for assistance with figure preparation.

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