An Introduction to Enzyme Science - Elsevier...Chapter 1 An Introduction to Enzyme Science Enzymes...

Chapter 1

An Introduction to Enzyme Science

Enzymes are astonishing catalysts – often achieving rateenhancement factors1 of 1,000,000,000,000,000,000!Water, electrolytes, physiologic pH, ambient pressure andtemperature all conspire to suppress chemical reactivity tosuch a great extent that even many metabolites as thermo-dynamically unstable as ATP (DGhydrolysis z �40 kJ/mol)and acetyl-phosphate (DGhydrolysis z �60 kJ/mol) are inertunder normal physiologic conditions. Put simply, metabo-lism would be impossibly slow without enzymes, and Life,as we know it, would be unsustainable.2 As a consequence,enzymes are virtual on/off- switches, with efficientconversion to products in an enzyme’s presence andextremely low or no substrate reactivity in an enzyme’sabsence. At millimolar concentrations of glucose andMgATP2�, for example, substantial phosphorylation ofglucose would require hundreds to thousands of years in theabsence of hexokinase, but only seconds at cellularconcentrations of this phosphoryl transfer enzyme. Withouthexokinase, there would also be no way to assure exclusivephosphorylation at the C-6 hydroxymethyl group. And evenwhen an uncatalyzed reaction (termed the reference

reaction) is reasonably fast – as is the case for the reversiblehydration of carbon dioxide to form bicarbonate anion or forthe spontaneous hydrolysis of many lactones – an enzyme(in this case, carbonic anhydrase) is required to assure thatthe reaction’s pace is compatible with efficient metabolismunder the full range of conditions experienced by thatenzyme. Most enzymes also exhibit rate-saturation kinetics,meaning that velocity ramps linearly when the substrateconcentration is below the Michaelis constant, and reachesmaximal activity when the substrate is present at a con-centration that is 10–20 times the value of the Michaelisconstant. In this respect, an enzyme’s action is more akin toa variable-voltage rheostat than a simple on/off switch.

Biochemists recognize that substrate specificity isanother fundamental biotic strategy for effectively organ-izing biochemical reactions into metabolic pathways. Twoanalogous chemical reactions can take place within thesame (or adjoining) subcellular compartments simplybecause their respective enzymes show substrate or cofactorspecificity directing metabolic intermediates to and throughtheir respective pathways, often without any need for sub-cellular co-localization or enzyme-to-enzyme channeling.Substrate specificity also minimizes formation of unwanted,and potentially harmful, by-products. By controlling therelative concentrations of such enzymes, cells also avoidundesirable kinetic bottlenecks or the undue accumulationof pathway intermediates.3 Experience tells us thatextremely reactive chemical species can also be sequesteredwithin the active sites of those enzymes requiring their

1 Catalytic rate enhancement (symbolized here as 3) equals the unit-less

ratio kcat/kref, where the catalytic rate constant kcat (units ¼ s�1) is the

catalytic frequency (i.e., the number of catalytic cycles per second per

enzyme active site), and kref (units ¼ s�1) is the corresponding

first-order rate constant for the uncatalyzed reaction. The value of 3 will

be a direct measure of catalytic proficiency (i.e., an enzyme’s ability to

enhance substrate reactivity), if and only if the enzymatic and

nonenzymatic reactions operate by the very same chemical mechanism,

in which case the nonenzymatic reaction is called the reference

reaction. Note also that the value of 3 achieved by any given enzyme

need only be sufficient to assure unimpeded metabolism. In the

Principle of Natural Selection, mutation is the underlying search

algorithm for evolution, and any mutation that markedly improves 3

beyond that needed for an organism’s survival should be inherently

unstable and subject to reduction over time.2 The upper limit on the room temperature rate constant for nonenzymatic

water attack on a phosphodiester anion, for example, is about 10�15 s�1,

necessitating 100-million year period for uncatalyzed P–O cleavage

(Schroeder et al., 2006). Depending on reaction conditions, the

corresponding rate constant for hydrolysis of the b�g P–O bond in

MgATP2� is around 10�4 to 10�6 s�1, and given that bimolecular

processes obey the simple rate law v ¼ k[A][B], rates for phosphoryl

group transfer reactions (e.g., MgATP2� þ Acceptor # Phosphoryl �Acceptor þ MgADP) would be suppressed even further at low

micromolar-to-millimolar concentrations of acceptor substrates within

most cells.

3 The term intermediate has several distinctly different meanings in

biochemistry. In the context of the above sentence, intermediate refers

to a chemical substance that is produced by an enzyme reaction within

a metabolic pathway (A / B / C / P / Q / R, where B, C, P,

and Q are metabolic intermediates) and is likewise a substrate in

a subsequent enzyme-catalyzed reaction in that or another pathway. In

the very next sentence, intermediate refers to a enzyme-bound substrate,

enzyme-bound reactive species, or enzyme-bound product formed

during the catalysis (E þ S # ES1 # ES2 # EXz # EP1 # EP2 #E þ P, where ES1, ES2, EXz, EP1, and EP2 are various enzyme-bound

species/intermediates) in a single enzymatic reaction. For reactions

occurring in the absence of a catalyst, chemists routinely use the term

intermediate to describe any reactive species Xi-1, formed during the

course of chemical transformation, whether formed reversibly (i.e.,

Xi-1 # Xi # Xiþ1) or irreversibly (i.e., Xi-1 / Xi / Xiþ1). All such

usages of intermediacy connote metastability and/or a transient nature.

Enzyme Kinetics

Copyright � 2010, by Elsevier Inc. All rights of reproduction in any form reserved. 1

formation, while hindering undesirable side-reactions thatwould otherwise prove to be toxic. So enzyme catalysis isinherently tidy. Enzyme active sites can also harbor metalions that attain unusually reactive oxidation states that rarelyform in aqueous medium and even less often in the absenceof side-reactions. The resilience of living organisms stems inlarge measure from the capacity of enzymes to specifically orselectively bind other ligands (e.g., coenzymes, cofactors,activators, inhibitors, protons and metal ions).

Attesting to the significance of enzyme stereospecificity inthe biotic world is that most metabolites and natural productscontain one or more asymmetric carbon atoms. The stereo-specific action of enzymes is the consequence of the fact thatboth protein and nucleic acid enzymes are polymers ofasymmetric units, making resultant enzymes intrinsicallyasymmetric. It should be obvious that any L-amino acid-containing polypeptide having even a single D-amino acidresidue cannot adopt the same three-dimensional structure asa natural polypeptide. Although some enzymes utilize bothenantiomers of a substrate (e.g., glutamine synthetase isalmost equally active on D-glutamate and L-glutamate),proteins containing exclusively L-amino acids are producedby the ribosome’s peptide-synthesizing machinery. Thisoutcome is the result of the stereospecificity of aminoacyl-tRNA synthases that supply ribosomes with activatedsubunits, the stereochemical requirements of peptidesynthesis, as well as ubiquitinylating enzymes and protea-somes that respectively recognize and hydrolyze wronglyfolded proteins. Cells also produce a range of enzymes, suchas D-amino acid oxidase (Reaction: D-Amino Acid þ O2 þH2O # 2-Oxo Acid þ NH3 þ H2O2), that remove certainenantiomers (in this case, D-amino acids) from cells. In thecase of protein enzymes, certain aspartate residues are alsosusceptible to spontaneous racemization as well as N-to-Oacyl shifts, and cells produce enzymes that recognize andmediate the repair or destruction of proteins containingmonomers having improper stereochemistry.

Additional metabolic pathway stability is afforded bysteady-state fluxes that resist sudden changes in rate orreactant concentrations. The processes lead to the phenom-enon of homeostasis, wherein reactant concentrations appearto be time invariant merely because the processes producingand destroying these reactants are so exquisitely controlled.In some respects, the behavior of the whole of metabolismappears to exceed the sum of behaviors of its individualreactions. Experience has shown that hierarchically complex,large-scale networks often give rise to emergent properties(i.e., properties of a highly integrated metabolic or physio-logic system that are not easily predicted from the analysis ofindividual components). Beyond the coordinated operationand regulation of the many pathways comprising interme-diary metabolism, other emergent properties of livingsystems are evident in the adaptive resilience of signaltransduction, long-range actions affecting chromosomalorganization, as well as cellular morphogenesis and motility.

The creation of organizationally complex neural networks, asfacilitated by the capacity of single neuronal cells to engagein tens of thousands of cell–cell interactions with otherneurons via synapse formation, is also thought to underliewhat we sense as our own consciousness. And at all suchlevels, enzyme catalysis and control are inevitably needed foreffective intracellular and intercellular communication.

As the essential actuators of metabolism, enzymes areoften altered conformationally via biospecific bindinginteractions with substrates and/or regulatory molecules(known as modulators or effectors) to achieve optimalmetabolic control. An additional feature is the capacity ofmulti-subunit enzymes to exhibit cooperativity (i.e.,enhanced or suppressed ligand binding as a consequence ofinter-subunit cross-talk). Because enzyme structure changescan be triggered by changes in the concentrations ofnumerous ligands, enzymes possess an innate capacity tointegrate diverse input signals, thereby generating the mostappropriate changes in catalytic activity. An interaction issaid to be allosteric if binding of a low-molecular weightsubstance results in a metabolically significant conforma-tional change. In most cases, modulating effects are nega-tive (i.e., they result in inhibition), but positive effects (i.e.,those resulting in activation) are also known. Feedbackregulation has proven to be a highly effective strategy forcontrolling the rates of metabolic processes. When presentat sufficient concentration, a downstream pathway inter-mediate or product (known as a feedback inhibitor) altersthe structure of its target enzyme to the extent that theinhibited enzyme exhibits little ot no activity (Scheme 1.1).Target enzymes (shown below in red) are most often posi-tioned at the first committed step within a pathway or ata branch point (or node) connecting two or more pathways.The lead reactions are frequently highly favorable (DG <<0), whereas the intervening reactions are generally revers-ible (DG ¼ 0), or nearly so (DG z 0).

A B C D E

F G

I J

EA

EB EC ED

EE F

EE I

EF EG

EI EJ

H

K

Scheme 1.1

Feedback inhibition (shown in blue) of target enzymestherefore precludes unnecessary accumulation of possiblytoxic metabolic pathway intermediates. By contrast, elevatedmetabolic throughput (or flux) is observed when an enzymeresponds to an allosteric activator. In the latter case, theenzyme achieves no or partial catalytic activity in the absenceof an activator, and biospecific binding of the activator altersthe target enzyme’s conformation in a way that increases itscatalytic efficiency. Although the hallmark of allosteric

2 Enzyme Kinetics

enzymes is cooperativity (i.e., subunit–subunit interactionsaltering the apparent substrate binding affinity), metaboliccontrol is also achieved by the regulated synthesis anddegradation of specific enzymes, by interconversion betweenenzyme activity states via enzyme-catalyzed covalent modi-fication, by effector molecule mediated signal amplification,and in some instances by substrate channeling.

Molecular life scientists have uncovered countlessinstances wherein improper catalysis and/or regulation ofeven a single enzyme reaction can greatly distress a livingorganism. Such mutant enzymes wreak havoc on cellularphysiology. In fact, animal and plant diseases frequentlyarise from point mutations that result in site-specificsubstitution of a single amino acid residue in an enzyme.Elaborate proofreading mechanisms permit replication,transcription, and translation to proceed at rapid rates, whileminimizing error propagation, and a battery of repairenzymes correct DNA damage arising unavoidably fromphotolysis, oxidation, alkylation, hydrolysis, and racemi-zation. The same is true of errors occurring during thesynthesis, splicing, and turnover of RNA transcripts. Ribo-somes must also occasionally commit errors, but with thepossible exception of prion protein formation the impact oflow-level occurrence of ‘‘translational mutations’’ is apt tobe minimal. Other more injurious mistakes made duringreplication and transcription are known to culminate inenzyme over-/under-production, defective regulation,impaired stability, incorrect post-translational modification,improper subcellular targeting and compartmentalization,defective turnover, etc. A notable example is amyotrophiclateral sclerosis or ALS (widely known as Lou Gehrig’sdisease). This devastating neurodegenerative disorder islinked to the impaired action of superoxide dismutase; over-accumulation of superoxide (O2

��) damages neurons, aninjury that is attended by profound pathological sequelae.Another example is the discovery that Pin1-catalyzed cis-trans prolyl residues isomerization can alter the structure ofthe microtubule-associated protein Tau in axons and thatPin1 gene knockouts bring about progressive age dependentneuropathy characterized by motor and behavioral deficits,attended by hyper-phosphorylation of Tau, as well as Taupolymerization into neurodegenerative paired helical fila-ments (Liou et al., 2003). Although more research isrequired to assess the significance of such findings to theonset of Alzheimer’s disease, it is already clear that reducedprolyl cis-trans isomerization activity can profoundlyimpair neuronal function.

Enzyme chemists investigate biological catalysis byassessing the structural and energetic features of theelementary reactions comprising a multi-step enzymemechanism. They seek to understand how activators andinhibitors alter the energetics of catalytic reaction cycles tobring about effective metabolic regulation. The dauntingtask of determining how an enzyme operates is never aneasy matter, and without a systematic approach, one is

forced to glean information haphazardly. A more effectivestrategy starts with a reliable assay of catalytic activity andrequires the experimenter to use this assay in the isolation ofthe enzyme of interest from other contaminants (e.g.,proteins, solutes, etc.) affecting the enzyme’s activity. Inpractice, absolute purity is not required as long as othercontaminating enzymes and proteins are without effect onthe enzyme of interest. It is helpful to apply the principles oforganic chemistry to infer likely chemical transformationsoccurring during catalysis, using literature precedents toguide one’s thoughts about the roles of coenzymes andcofactors and to focus on probable reaction intermediates.Ultimately, however, it is necessary to test whether eachreaction step occurs on a time-scale consistent with its rolein catalysis. This latter pursuit, called enzyme kinetics,combines an interest analyzing temporal aspects of enzymecatalysis with the principles of physical chemistry andquantitative rigor of analytical chemistry.

Some of the stages in the characterization of a completeenzyme mechanism are listed in Fig. 1.1. Because initial-ratekinetics is a relatively straightforward tool for analyzingenzyme catalysis, we may regard such experimentalapproaches as the first stage in the systematic characteriza-tion of an enzyme of interest. Pursuit of subsequent stagesdepends on the objectives of the particular investigation.

This reference explains how enzyme kineticists formulateand test models to: (a) explain the reactivity and energeticsof enzyme processes; (b) gain the most complete description

Stage-1: Initial Rate Kinetics

v versus [substrate(s)] → Km,Vm & VmIKmSubstrate Specificity & Side-Reactions

Product Inhibition → Substrate Binding OrderCompetitive Inhibition → Substrate Binding Order

pH Kinetics → pK’s of Catalytic GroupsSite-Directed Mutagenesis

Stage-2: Chemical Studies

Determination of Reaction StereochemistryDetection of Tightly Bound Coenzymes & Metal Ions

Detection of Covalent IntermediatesIdentification of Active-Site Residues by Affinity Labeling

Stage-3: Isotope Kinetics

Partial Exchange Reaction → Substrate Binding OrderIsotope Exchange at Equilibrium → Substrate Binding Order

Isotope Trapping & Partition Kinetics → “Stickiness”Positional Isotope Exchange → Reaction Intermediates

Kinetic Isotope Effects → Reaction IntermediatesStage-4: Fast Reaction Kinetics

Continuous, Stopped-Flow & Mix/Quench TechniquesTemperature-Jump & Pressure-Jump Techniques

Stage-5: Single-Molecule Reactions

Reaction TrajectoriesMechanochemistry of Force Generation

FIGURE 1.1 Kinetic tools in modern enzyme science. Depicted here

are the typical stages in order of complexity for the characterization of

an enzyme-catalyzed reaction. Within each stage are various experimental

approaches that will be discussed in detail in later chapters. Very few

enzymes have actually been exhaustively investigated at all five stages.

Chapter j 1 An Introduction to Enzyme Science 3

of catalysis; and (c) understand how an enzyme’s regulatoryinteractions affect the catalytic reaction cycle. Ideally, oneshould consider as many reasonable models as possible forthe reaction/process of interest. These rival kinetic modelsshould be as simple as possible: when stripped down to thebare essentials, any failure of a model to account for anexperimentally determined property of the system becomessufficient justification for outright rejection of that model orfor modifying it to account for other by essential properties/interactions. Simplicity, precision, and generativity – theseare the inherent virtues of highly effective models.Simplicity demands that a system’s known properties arerepresented by the least number of components and/orinteractions. Precision requires explicit presentation of allrequired interactions, thus providing an opportunity todistinguish testable model-specific characteristics of rivalmodels. Generativity implies that the model should facili-tate hypothesis-driven experimentation to test newly pre-dicted properties in a recursive manner that stimulates newrounds of experimentation. Put plainly, a model is not worthmuch, unless it fosters the formulation of new hypothesesthat spur additional rounds of experimentation.

Modern molecular life scientists have become, for want ofa more appropriate appellation, ‘‘interaction spectroscopists’’– focusing on the spectrum of interactions of proteins andenzymes with other proteins, nucleic acids, membranes, andlow molecular-weight metabolites, most often in terms oflocation, specificity, affinity, and catalysis. And becauseenzymes are Life’s actuators, it should not be surprisingthat, whenever a significant problem in the molecular lifesciences reaches a sophisticated level of understanding, anenzyme is almost invariably involved. Because all kineticapproaches are fundamentally similar, those gainingmastery over the topics presented in this book can becomeproficient at inventing their own kinetic approaches fortesting their own models. Moreover, because biochemicalprinciples underlie the entirety of the molecular lifesciences, these strategies should also be useful for investi-gators seeking to unravel the time-ordered events of highlycomplex biotic processes in the fields of molecular andcell biology, physiology and neuroscience, as well asmicrobiology and the plant sciences.

Finally, it is worth noting the distinction betweenchemical kinetics and chemical dynamics. Both chemicalkinetics and chemical dynamics allow us to infer propertiesof transition states and how reactants gain access to them,but the approaches are fundamentally different. The formerrefers to the reactivity (i.e., reaction rates) and bond-making/breaking mechanisms of chemical transformations,whereas the latter refers to the atomic and molecularmotions that influence reactivity and stability. Like allchemical processes, both depend on energy differences(e.g., DG� for the overall reaction, DEact for each elemen-tary reaction, D3¼ hDv for each quantized event, Dw¼ FDxfor the incremental work, where F is a bond force constant

or a mechanically generated force, etc.), space (e.g., posi-tionally defined parameters x, y, z in Cartesian coordinatesor r in fields), and time expressed in seconds. In chemicalkinetics, we analyze the dependence of reaction rate on theconcentrations of reactant(s), and although kinetic isotopeeffects depend on the masses of nuclei at or near the reactioncenter, we are mainly concerned with electronic rear-rangements in molecules, as reflected by the nature of thechemical bonds within reactants, intermediates, and prod-ucts. (Reaction rate is defined by the product of a reactionrate constant and its reactant concentration(s), and forstochastic kinetic approaches, probabilities are often used inplace of macroscopic variables.) In chemical dynamics, themain goal is to depict how the potential energy changes asone varies the relative coordinates and momenta of theatomic nuclei involved in the reaction (Polanyi andSchreiber, 1974). The latter most often entails the applica-tion of classical scattering theory relying on classicalcollision theory, with solution of the appropriate equationsfor atomic and molecular motions as reactants proceedalong a trajectory on the potential energy surface. At thesingle molecule level, population-averaged parameters Xgive way to probabilistic expectations <X>, with mostevents inevitably stochastic. (Under highly favorableconditions, one may also pursue quantum mechanicalsolutions by solving the appertaining Schrodinger equa-tion(s) for solutions to the appropriate wave function, butthese approaches are only rarely applicable to enzymeprocesses, and even then are limited to a small number ofatoms.) Experimental chemical dynamics is most oftenpursued in crossed molecular beam experiments, whereeach type of reactant molecules, say A or B, is acceleratedwithin its own beam of molecules to attain a certain energy,and their reaction (A þ B / C) occurs only where thebeams intersect in an otherwise ultrahigh vacuum thatexcludes reactions and interactions with other components.Changes in chemical composition are then analyzed bystate-resolved spectroscopic techniques. Experiments onenzymes, however, must be conducted in solution and cannever be analyzed rigorously in the absence of watermolecules. Therefore, the most popular methods for treatingthe quantum mechanical sub-systems for enzyme-catalyzedreactions have been semi-empirical molecular orbitalmethods. Alternatively, one may use quantum and classicaldynamics to account for electronic and nuclear effects toglimpse the time-dependent motion (trajectory) of atomswithin the enzyme and reactant as the solvated enzyme-bound substrate is transformed into product. Of course,chemistry and physics are convergent disciplines, and ascomputational power expands, enzyme kinetics and enzymedynamics will likewise ultimately converge. Again, ratherthan settling for the population-averaged properties, enzy-matic processes will no longer need to obey simple differ-ential equations, smoothly and deterministically, as definedby classical chemical kinetics, and we will instead be in

4 Enzyme Kinetics

a position to consider the detailed stochastic behavior ofindividual or small ensembles of enzyme molecules.

1.1 CATALYSIS

Only fifty years ago, the most reliable way to estimate thetechnological status of a country was to obtain an accurateestimate of its annual output of sulfuric acid and chlorinegas or the annual gross production tonnage of aluminum orsteel, especially stainless steel. In this post-industrial era,the types and amounts of catalysts produced and/or used areapt to be far more trustworthy indices of economicallyadvanced countries. Surprisingly, ~20–30% of the GrossNational Product of a so-called first world country dependsin one way or another on catalysis – from cracking ofhydrocarbons, to the synthesis of ammonia and countlessorganic molecules, to the formation of high-fructose cornsyrup, and extending to biotechnologies, depending onenzymes for producing and expressing recombinant DNA,as well as in stereoselective drug synthesis. Likewise, by re-oxidizing auto emissions, in-line catalytic converters reducenitrogen oxide pollutants from internal combustion engines.Catalysis is a mainstay of any modern economy, andproducts of catalysis play essential roles in our everydaylife – from the petrochemistry and agrochemistry to medi-cine and nutrition. As endo- and exo-cellulases become themainstay for ethanol production from an ever-wideningrange of cellulosic sources, enzyme catalysis will take oneven greater significance in biofuel production. It is likelythat a country’s GNP will soon be as inextricably linked toits enzyme technology as to its gold supply.

1.1.1 Roots of Catalysis in the EarliestChemical Sciences

Exactly when humans first became aware of catalysis willalways remain a mystery, but its effects were manifestlysignificant to hominids. Through trial-and-error and a keenperception, the ancients discovered a variety of substancesthat accelerate or retard chemical reactions. By nurturing analready glowing ember as a primitive oxidative surfacecatalyst, they learned how to harness combustion. Later, theymastered the use of friction to create their own embers, andigniting new fires at will. Long before its first mention in theIliad, herders had observed that the contents of goat andsheep stomachs curdled milk, thus discovering a key enzy-matic reaction that greatly facilitated cheese production.They likewise learned to dehydrate and stabilize foodstuffsthrough salting and smoking – unwittingly inhibitinghydrolases and deactivating oxidases. The early Egyptianslikewise mastered the fine art of mummification, again byinhibiting digestive and oxidative enzymes. Humans alsofound that strong alkali hastened saponification of tallow, andthe art of soap making was born. Others observed that the

presence of certain metal ions promoted vinegar formation.Archeological evidence for their pervasive use suggests thatearly humans recognized and prized these catalyst-basedtechnologies long before the existence of a written record.

The Russian chemist Gottlieb Kirchhoff in 1812 iscredited as the first to document the enhanced rate of glucoseformation from starch in the presence of various acids. TheEnglish chemist Humphry Davy likewise observed that manygases burned more vigorously in the presence of metallicplatinum, and his Irish namesake Edmund Davy was the firstto discover a spongy form of platinum with remarkable gasabsorptive and catalytic properties. Yet, it was the Swedishchemist Jons Jacob Berzelius, whose studies of diastase,a crude preparation of a-amylase, unified these and otherobservations with the germinal concept that, to hastenproduct formation, a catalyst must first combine with itsreactant(s). In his extraordinary writings, Berzelius combinedthe Greek words kata and lyein to coin the term catalyst asany agent that promotes chemical reactivity by firstcombining with a reactant to weaken its stabilizing bonds. Inthe translation of Jorpes (1966), Berzelius said that the word‘‘catalyst’’ denotes ‘‘substances that are able to awakenaffinities that are asleep at one temperature by their merepresence and not their affinity.’’ The former propertyimplicitly anticipates the catalyst’s ability to lower a reac-tion’s activation energy, with the latter suggesting that theequilibrium poise should be unaffected. While others hadsuggested that catalysts acted at a distance, Berzeliuscorrectly inferred that catalytic action required complexationof catalyst and reactant. Through the examination of thethermal decomposition of HI into H2 and I2, the Frenchchemist Lemoine also suggested that, while the presence ofmetallic platinum accelerated the reaction, the catalyst iswithout effect on the reaction’s final equilibrium position.

Kinetic experiments proved to be indispensable inefforts to define many fundamental chemical principles.Ludwig Wilhemy (1850), for example, used polarimetry toquantify the rate of acid-catalyzed hydrolysis of sucrose4

4 In this reaction, the dextrarotatory reactant sucrose (specific rotation ¼þ66.5�) is converted to an overall levorotary product mixture, owing to

the fact that for D-glucose equals þ52.7� and that for D-fructose equals

�92.4�. The hydrolysis of sucrose therefore yields a net leftward

rotation of �39.7�. Because the state of polarization ‘‘inverts’’ (i.e.,

changes from a (þ) to a (�) rotation), the enzyme catalyzing this

hydrolysis of sucrose into D-glucose and D-fructose was accorded the

name invertase. Prior to the advent of photomultiplier tubes and stable

electronic circuitry, polarimetry offered a simple and reliable

quantitative way of assessing the concentration of optically active

substances as well as those optically inactive compounds that generate

optically active product(s). To assess concentration, chemists of that era

also used split-field optical comparitors, relying on the naked eye to

assess the color intensity of an experimental solution relative to that of

a solution of known concentration. In addition to being less accurate

and far less sensitive than polarimeters, comparitors proved to be far

more susceptible to experimental bias.


to show that the rate of this reaction is linearly dependenton the concentration of sugar. Berthelot (1862) andBerthelot and de Saint-Gilles (1862) reached the sameconclusion from studies on ethyl acetate hydrolysis, andsuch observations led Guldberg and Waage (1867; 1979) topostulate that chemical reactions must be highly dynamic,with reactants and products relentlessly interconvertinginto each other, even at equilibrium. In advancing thisprinciple, widely known as the Law of Mass Action, theysuggested that the rate in each direction of a reversiblereaction depends on reactant concentration (oftenexpressed as the intensive variable molarity) and not theamount of substance (commonly given by the extensivevariable mole).

As discussed at length in Chapter 3, the modernconceptual framework for the discipline known aschemical kinetics was founded late in the nineteenthcentury by the powerfully insightful contributions of theSwedish chemist Svante Arrhenius and the Germanchemist Jacob van’t Hoff, who both became NobelLaureates in chemistry. They and German physicalchemist Wilhelm Ostwald, the Nobelist credited for firstexpressing reaction velocity as a change in reactantconcentration per unit time (i.e., v ¼ �d[Reactant]/dt),established the enduring concept that catalysts promotereactivity without altering the equilibrium position of theoverall chemical reaction. These investigators recognizedthat thermodynamics constrains catalysis: after eachcatalytic round, the catalyst releases its product andtherefore cannot exert any cumulative effect on thereaction’s standard Gibbs free energy change DG�. Thisdiscovery increased the determination of chemists todiscover catalytic substances and even to design artificialcatalysts endowed with special properties. Speed andyield are the essence of catalysis, but the idea that onemay impart reactivity to otherwise unreactive substanceslies at the heart of modern chemical enterprises. Nowhereis this more evident than in the work of Fritz Haber, thenotorious German chemical engineer5 and NobelLaureate. Haber’s research team overcame the virtualinertness of dinitrogen by carrying out some 20,000experiments, utilizing thousands of catalyst preparationsunder a wide range of reaction conditions. They eventu-ally settled on the use of iron filings to catalyze ammoniasynthesis from N2 and H2 at high temperature (600–800K) and extreme pressure (300 atm). High temperaturefacilitated dissociation of highly stable bonds within N2

and H2, and pressure displaced the reaction equilibrium in

favor of ammonia (Reaction: N2 þ 3H2 ¼ 2 NH3). Thatprocess – now bearing Haber’s name – has forever alteredthe human condition by augmenting Nature’s output of‘‘fixed’’ nitrogen by some 20–30%. To improve cropyields, farmers routinely inject synthetic ammoniadirectly into the soil.

In considering the nature of a catalytic cycle, one maytake the case of heterogeneous catalytic decomposition ofthe toxic atmospheric pollutant N2O within the catalyticconverter of a modern automobile. The cycle begins withchemisorption of N2O onto the platinum/palladium cata-lyst, a step that weakens the bonds stabilizing nitric oxide,to the effect that the N–O bond can dissociate. The latterproduces N2, which desorbs from the surface, leavingoxygen radicals on the catalyst. At the catalyst’s operatingtemperature, these radicals diffuse along the metallicsurface until two of them encounter each other andcombine to form O2, the latter then desorbing from thesurface. French Chemist Paul Sabatier (Nobel Laureate in1912) is credited with a principle bearing his name. Statedin its simplest form, the Sabatier Principle asserts that foreffective catalysis, substrates and products must bindsufficiently tightly, so as to promote catalysis, but not tootightly so to prevent catalysis. Sabatier stressed themomentary nature of catalytic intermediates, a point thatunderscores their celerity and the importance of kinetics inanalyzing their nature.

As discussed below, catalytic selectivity/specificityalso allows chemists to control the stereochemicaloutcome of reactions that would be otherwise nonspe-cific. And while organic chemistry of the 1950s relied onjust a few catalysts (mainly Hþ, OH�, Al3þ, Fe3þ, aswell as elemental Pt, Ni, and Pd) that were almostinvariably stereochemically unselective, modern organicchemists have exploited a much wider repertoire ofmetallo-catalysts.

Recognizing that all reactions proceed through theformation and turnover of transition-state intermedi-ate(s), one may consider the conversion of reactant Ainto product P in the absence and presence of catalyst C.In the uncatalyzed case, reactant A isomerizes througha succession of intermediates and transiently reaches theactivated complex Xz. As the least stable intermediate,Xz exhibits an equal likelihood of reconverting to thereactant or going onward to product, such that the systemeventually reaches thermodynamic equilibrium. In thecatalyzed reaction, reactant A first combines with cata-lyst C to form the C$A, which then passes througha series of intermediates (e.g., C$X1, C$X2, etc.) to reachC$Xz. As was true for the uncatalyzed process, theintermediate C$Xz can either return to C$A or advance toC$P, with product-release subsequently regenerating thecatalyst. Michael Polanyi, father of Nobel chemistrylaureate John Polanyi, was arguably the first to articulatethe notion that stabilization of the reaction transition-state

5 During World War I, Haber supervised firsthand battlefield tests on the

efficacy of chemical warfare agents that later proved to irreversibly

inhibit the enzyme acetylcholine esterase. Such activities would be

subject to prosecution under the international treaties on war crimes

signed at the close of that war.

6 Enzyme Kinetics

Xz as the complex of catalyst and transition-state C$Xz

should greatly increase the forward and reverse reactionrates. The enhancement factor 3 (equal to vcat/vuncat)therefore applies both to the forward and reverse reac-tions, and a reaction’s equilibrium constant can beexpressed as:

K ¼ 3� vuncatalyzed

3� vreverseuncatalyzed

¼ vuncatalyzed

vreverseuncatalyzed

¼ Keq 1.1

Autocatalysis is a special case of chemical catalysis inwhich the active catalyst is also a product. An example is theformation of pepsin on its storage form pepsinogen in acidicgastric juices:

Initiating Reaction: Pepsinogeninact + H+ →

Pepsinact

Autocatalytic Reaction: Pepsinogeninact + Pepsinact → 2 Pepsinact

Scheme 1.2

where the inactive zymogen Pepsinogeninact is at firstconverted slowly by acid catalysis to the active enzymePepsinact, it then rapidly catalyzes the conversion ofany remaining zymogen to its active form. Note thateach catalytic round during the autocatalytic phasedoubles the amount of active enzyme until the concen-tration of inactive enzyme is depleted (see Section 3.9.4:Autocatalysis).

Finally, the catalyst concentrations approach theconcentrations of substrate(s) or product(s), the equilib-rium position of the reaction, depending on the catalyst’srelative affinity for the reactant(s) and product(s). Thiseffect can manifest itself in some rapid-mixing experi-ments, particularly when reagent concentrations of enzymeare utilized.

1.1.2 Synthetic Catalysts

Chemists have created powerful catalysts that facilitatechemical transformations in chemistry laboratories, oilrefineries, and even automotive exhaust systems. Table 1.1summarizes some of the most widely used catalysts thatcontribute to the trillion dollar petrochemical and agri-chemical industry worldwide. Although metallic platinum,palladium and nickel are constituents in many catalysts, theactive forms consist of small surface imperfections, or stepdefects, and not merely the projected geometry of the metal’sinternal crystal surface. These agents are often calledheterogeneous catalysts, a term that indicates the presence oftwo phases: gaseous or liquid reactants binding and reactingon the surface of a solid catalyst. Catalysts, such as hydroxideions and protons, which remain in the same phase as thereactants, are referred to as homogeneous catalysts.

Synthetic catalysts are often highly stable, allowingthem to operate efficiently even in the face of elevatedtemperatures and pressures, as well as extremes of pH.One unrelenting problem has been to design catalysts thatresist fouling, or quenching, by tight-binding reactionproducts and/or metal ions. Most synthetic catalysts arealso inferior to biological catalysts in at least four otherrespects, as they: (1) are less efficient at physiologictemperature, low pressure, and neutral pH; (2) are rela-tively unselective; (3) rarely display sufficiently highchiral recognition, a property that greatly limits their usein preparing optically active biomolecules; and (4) are notregulated by feedback activators and/or inhibitors.

1.1.2a Catalytic Hydrogenation

The classical case of catalytic hydrogenation (Fig. 1.2) isa two-phase, or heterogeneous, process. The alkene oralkyne is first adsorbed on the surface of the catalystalongside a dihydrogen molecule, whereupon the catalyst

TABLE 1.1 Selected Man-made Catalysts and the Reactions Catalyzed

Catalyst Category Process/Properties

Platinum-containing Chlorinated Alumina Heterogeneous Hydroisomerization (conversion of n-butane intoisobutane)

Platinum, Nickel, Palladium Heterogeneous Hydrogenation of double bondsIron Shavings/Dust Heterogeneous Haber ammonia process (Reaction: 3 H2 þ N2 # 2 NH3)Silica/Alumina Zeolites; NiCoMo tri-metallics Heterogeneous Cracking of petroleum into volatile fuelsVanadium(V) Oxide, Palladium Heterogeneous Oxidation of exhaust from internal combustion enginesAcids/Bases Heterogeneous/

HomogeneousHydrolysis of carboxylic/phosphoric esters and anhydrides

Grubbs and Hoyeyda Ruthenium Catalysts Heterogeneous Metathesis (see text for details)Chiral Catalysts Homogeneous Enantiomeric selectivity/specificityCatalytic Antibodies Homogeneous Over 100 different reaction types


weakens their respective bonds and may even change theposition and/or orientation of these bound species. The twohydrogen atoms then shift from their interactions with themetal surface to the carbon atoms comprising a double ortriple bond, with attendant formation of a more saturatedhydrocarbon. The latter is more weakly adsorbed and soondeparts from the catalyst’s surface. The exact nature andtiming of these events is still incompletely understood.What is clear is that the metal surface acts as a rigid rack onwhich the reactants are stretched to weaken the s-bond ofH–H as well as the p-bond of an alkene (or alkyne), with theeffect that hydrogenation is facilitated. Because H–H andR–C]C–R9 (or R–R9) bond lengths differ by ~0.5 A, eachbond must be polarized to a different degree to reach theoptimal reaction transition-state. (A corollary is that thelikelihood of achieving this alignment in the catalyst’sabsence is extraordinarily low.)

Classical transition metal catalysts, such as platinum,palladium, nickel and rhodium, rely on their intrinsicinter-atomic spacing in their crystalline state or as multi-atom aggregates. That said, some catalysts actually relyon step-dislocations on their roughened surfaces to createthe best sites for catalytic hydrogenation. To achievehigher catalytic rate enhancements, many synthetic cata-lysts are deliberately designed to contain reactive surfacedefects or atomic dislocations. No metal surface is

perfectly flat, and catalysis may be more effective insurface microenvironments. Another useful strategy is todeposit metal atoms onto other solid substrates that cangreatly influence the resulting surface geometry andcoverage.

Given the great cost of metals like platinum, palladiumand even nickel, chemists have attempted to maximizethe active catalytic surface of metal catalysts. In suchcases, platinum and palladium are combined with a char-coal support (also called the substratum or substrate).Raney nickel, for example, is a solid hydrogenationcatalyst composed of fine grains of a nickel-aluminumalloy, and the catalyst known as ‘‘platinum on charcoal’’consists of 5% platinum and 95% charcoal by weight.Gold nanoparticles have also been employed as catalysts.To explain why ordinarily inert gold becomes a powerfulcatalyst, chemists have proposed that: (a) nanometer-sized particles contain many more surface dislocationsthat serve as unusually reactive domains; (b) they aremore or less electron dense than bulk gold; (c) suchparticles contain numerous perimeter sites and/or‘‘sticky’’ paracrystalline surfaces, and/or (d) nanometersized particles have different metallic properties thanthose of bulk gold (Bell, 2003). Other industrial catalystsinclude di- and poly-nuclear metal cluster complexes,such as di-molybdenum and di-tungsten complexes, di-rhodium (II) complexes, as well as multinuclear Rh, Rh-Co, and Ir-Co complexes.

1.1.2b Metathesis

The process known as olefin metathesis refers to positionchanging organochemical catalysis occurring in thepresence of suitable transition metal complexes, includingvarious metal carbenes. These catalysts (particularly theGrubbs Ruthenium Catalyst and Hoveyda RutheniumCatalyst) facilitate bond-breaking and exchange ofsubstituents directly attached to the double bonds of thecoordinated olefins. A metal carbene initiates olefinmetathesis by reacting with an olefin to form a metal-lated-cyclobutane intermediate, which then breaks apartto form a new olefin and a new metal carbene. This highlyversatile chemical process can be used to: (a) swapgroups between two acyclic olefins (a process calledcross-metathesis); (b) close large rings (ring-closingmetathesis); (c) form dienes from cyclic and acyclicolefins (ring-opening metathesis); (d) polymerize cyclicolefins (ring-opening metathesis polymerization); and (e)polymerize acyclic dienes (acyclic diene metathesispolymerization).

The commercial availability of these catalysts hasgreatly promoted the use of metathesis in macrolidesynthesis, where closure of large rings (i.e., those havingten or more atoms within them) is typically a low-yieldreaction. The power of olefin metathesis is that it

H

H

H

H

H

H

CC

FIGURE 1.2 Schematic of catalytic hydrogenation of ethylene on

a nickel, platinum, or palladium surface. In this idealized representa-

tion, the metal surface acts as a rack, on which each of the reactants is

stretched by binding to adjacent metal atoms. This physisorptive process

occurs by interactions of reactant electrons with empty electron-deficient

orbitals of the metal. Catalytic hydrogenation results from the heightened

reactivity among the weakened intramolecular bonds of H–H and

CH2]CH2, depicted above as dashed lines between reactant atoms. In

many metals, step-like dislocations on the crystal surface are the actual

sites of enhanced catalytic action. Except for the fact that heterogeneous

catalysis occurs at the interface of a gas-solid, liquid-solid, or immiscible

liquid-liquid phases, the process of catalytic hydrogenation resembles

a random bisubstrate enzyme-catalyzed reaction (i.e., reactants A and B

add randomly to form an Enz$A$B, followed by conversion to product

complex Enz$C, from which C desorbs from the active site to complete

the catalytic cycle).

8 Enzyme Kinetics

transforms the –C]C– double bond, a functional groupthat is often unreactive toward many reagents. With certaincatalysts, new –C]C– double bonds are formed at or nearroom temperature, even in aqueous media using startingmaterials that bear a variety of functional groups. ChemistsYves Chauvin, Robert Grubbs and Richard Schrock sharedthe 2005 Nobel Prize in chemistry ‘‘for the development ofthe metathesis method in organic synthesis.’’ That theseprocesses are highly relevant to the synthesis of enzymeinhibitors and therapeutic agents is illustrated by the use oftandem ring-closing metathesis to and subsequent hydro-genation to synthesis conformationally restricted cyclicdinucleotides joined with saturated connections betweenthe nucleobase and the phosphate moieties (Borsting andNielsen, 2002). Metathesis also holds great promise forindustrial-scale reactions that are environmentally com-patible (so-called Green Chemistry). One concern, however,is the high cost, currently around $100 per millimol cata-lyst. Another is the use of toxic ruthenium, molybdenum,tantalum, etc. A third concern is the relative inefficiency ofthese catalysts, which typically operate at concentrationsthat are 2�10 mol-% of the reactant concentrations.

1.1.2c Chiral Catalysts

To mimic the remarkable enantiomeric preference exhibi-ted by many enzymes toward their chiral substrates,chemists have struggled to design homogeneous catalyststhat are enantioselective. The trick is to introduce the rightmix of binding energy, functional group chemistry, and oneor more chiral and/or dissymmetric sites (Yoon andJacobsen, 2003).

One such catalyst, known simply as TADDOLateligand, is based on the structure of tartaric acid,6 one of theleast expensive, naturally occurring chiral substances.(Asymmetric carbon atoms are indicated by asterisks.)TADDOL catalyzes aldehyde alkylation, ester acoholysis,and iodo-lactonization. Another Diels-Alder catalyst

Bis(oxazoline) is loosely based on the structure of vitaminB12. Metal ion-containing catalysts, known as Salencomplexes, facilitate epoxidation, epoxide ring-opening,imine cyanation, and conjugate addition reactions. Suchcompounds combine with reactive metal centers to producecatalysts that effectively create asymmetric environmentsthat promote the selective binding and/or enhanced reac-tivity. As pointed out by Yoon and Jacobsen (2003), exactlywhat structural features account for the broad applicability ofsynthetic chiral catalysts remains unclear. They suggest these

H3C

H3C

OHOHO

O ****

C

C H3C

H3C H3C

H3C

CH3

CH3

CH3

CH3

O O

* *N N

C C

TADDOLate bis(Oxazoline)

OO O O O

O

OOOO

Co

Co

OO

* *

* *

H H

HH

t-Bu t-Bu

t-But-Bu

N N

N N

Salen Complex

6Tartrate enjoys the distinction as the substance that Pasteur used to formulate his germinal ideas about stereochemistry as well as the first to have its

absolute stereochemical configuration determined (Bijvoet, Peerdeman, and van Bommel, 1951). By verifying Emil Fischer’s fortuitous assignment

for (þ)-glyceraldehyde (Rosanoff, 1906), there was no need to revise existing chemistry textbooks.

COOH

OHH

COOH

HO H

Fischer Projection

COOH

C

C

COOH

OHH

HHO

OH

CH3

HOOCH

H OH COOH

H OH

COOH

OHH

Cahn-Ingold-Prelog Newman Projection

(R)

(R)

Fischer Projection

Shown above are various equivalent projections depicting the absolute stereochemical configuration of (þ)-tartrate. It is also worth noting that Pasteur

(1858) reported the first stereospecific enzyme-catalyzed reaction, in which yeast fermented dextrarotatory tartaric acid, while leaving levorotatory

tartaric acid completely intact.


catalysts possess rigid structures with multiple oxygen,nitrogen, and phosphorus atoms that allow them to interactstrongly with reactive metal centers. Because these agentshave a two-fold axis of symmetry, the number of possibletransition-state geometries is likely to be more limited.

An inherent limitation in the design of chiral catalysts is thecurrent inability of chemists to reliably predict the type ofreactions that will be facilitated by a particular agent, theextent of its stereoselectivity, or the achievable catalytic rateenhancement. For example, titanium complexes of chiralpeptide-based Schiff’s base (or imine) ligands catalyzecyanation of epoxides, aldehydes, and imines with highenantioselectivity; the corresponding copper complexescatalyze allylic substitution of dialkyl-zinc nucleophiles;whereas analogous zirconium complexes catalyze dialkyl-zinc addition to imines (Josephson et al., 2001). Absenta predictable outcome, one is left with the unenviable task ofsurveying the reaction spectrum of each newly preparedsynthetic catalyst. The advent of High-Throughput Screening(HTS) promises to lessen the load of determining a catalyst’sreactivity profile, but this approach remains to be perfected.

1.1.2d Catalytic Antibodies

Among ‘‘semi-synthetic’’ catalysts listed in Table 1.1 arecatalytic antibodies (also known as abzymes). These bio-engineered proteins can be designed to accelerate specificorganic chemical reactions. Basing his ideas on assertionsabout transition-state stabilization (Haldane, 1930; Pauling,1946; Evans and Polanyi, 1936), Jencks (1969) succinctlyadvanced the following argument for catalytic antibodies:

If complementarity between the active site and the transi-tion state contributes significantly to enzymatic catalysis,it should be possible to synthesize an enzyme by construct-ing such an active site. One way to do this is to prepare anantibody to a haptenic group, which resembles the transi-tion state of a given reaction. The combining sites ofsuch antibodies should be complementary to the transitionstate and should cause an acceleration by forcing boundsubstrates to resemble the transition state.

Because transition states are intrinsically unstable,catalytic antibodies are selected by using chemically stabletransition-state analogues used as immunogens. Forexample, antibodies generated against a bent porphyrin ringwere found to catalyze the metallation of heme groups,presumably by straining the planar substrate toward a benttransition-state conformation.

In the classical ‘‘Bait-and-Switch’’ approach, one designsa hapten (i.e., an immunogenic molecule that serves as the‘‘bait’’) that structurally resembles a likely transition-statespecies (Pollack, Jacobs and Schultz, 1986; Tramontano,Janda and Lerner, 1986). In selecting the best haptens, onefocuses on key features of the transition-state intermediate,such as the arrangement of its atoms and/or its electrostatic

charge. For example, were one interested in producing anantibody with the activity of a glycosidase, one might chosea modified sugar that resembles the oxa-carbenium ionintermediate with a half-chair conformation at or near theglycosyl carbon atom (see nucleoside hydrolase mechanismin Section 8.12.4; or lysozyme mechanism in Section 9.8.5c).The desired outcome is that the chosen hapten elicits anti-bodies that, when switched to bind on substrates, have thecapacity to facilitate the desired reaction. The candidatehapten is then coupled to a protein carrier, typically keyholelimpet hemocyanin (KLH), and the resulting conjugate isused to immunize mice to produce one or more monoclonalantibodies. Catalytic antibodies are then identified on thebasis of their ability to catalyze the reaction of interest whenexposed to the desired substrate instead of the hapten (i.e., is‘‘switched’’). Because catalytic antibodies may not attain thesame stereospecificity as natural enzymes, and becausecatalytic antibodies may catalyze side-reactions, the exper-imenter is well advised to characterize the products withrespect to structure and enantiomeric purity.

In the case of ester hydrolysis, a phosphonate isa reasonably good isostere of the enzyme’s tetrahedraloxyanion transition state, with specificity determined in partby the side chains R and R9.

C R

OH O

O P

R

O O

O

R' R'

Transition-State

Structure

Transition-State

Analogue

One then raises monoclonal antibodies against the phos-phonate-modified keyhole limpet hemocyanin (KLH). Alter-natively, one may select bacteria that express catalytic Fab’s(i.e., antigen-binding fragments of antibodies) that are gener-ated by recombinant DNA methodology. Each antibody is thenisolated and then evaluated for its ability to catalyze thehydrolysis reaction of interest. Observed rate enhancementsshould correlate with an antibody’s affinity for transition-stateanalogue (TSA) versus reactant (R) (i.e., KTSA/KR, where KTSA

¼ [Ab$TSA]/[Ab][TSA] and KR ¼ [Ab$R]/[Ab][R]). Experi-mental results, however, often fail to satisfy the simplisticassumption that the more closely an analogue resemblesa reaction transition state, the more effective is the antibody asa catalyst.

One inherent limitation in the use of transition-stateanalogues to generate catalytically proficient antibodies is thatmany interesting enzyme reactions are inevitably multi-stepreactions, each with its own transition states. Therefore, nosingle analogue is likely to be an adequate template for eachtransition state. A second factor limiting the catalytic effi-ciency of catalytic antibodies is the relative inflexibility ofmost antibodies. While most enzymes are highly flexible and

10 Enzyme Kinetics

contain few internal disulfide bonds, the opposite is true ofantibodies. A third limitation is that there is no easy way toincrease the rate of product release in the design of catalyticantibodies. For most enzyme-catalyzed reactions, chemicalinterconversion of enzyme-bound substrate and enzyme-bound product is fast, and product release is frequently therate-limiting step. The observed rate enhancements forenzyme-catalyzed reactions therefore most often measure therates of product release. So increasing the rate of chemicalinterconversion of an antibody-bound substrate and antibody-bound product may not do much to improve the observed rateenhancements for antibody-catalyzed reactions.

Reactive immunization is a new procedure for generatingcatalytic antibodies that tackles this problem by employing anantigen that is so highly reactive that a chemical reaction occursin the antibody-combining site during immunization (Wirschinget al., 1995). In the initial application of this approach, anorganophosphorus diester hapten was used as a ‘‘reactiveimmunogen.’’ A large number of the resulting antibodies cata-lyzed the formation and cleavage of phosphorylated intermedi-ates and subsequent ester hydrolysis. Wagner, Lerner and Barbas(1995) applied the reactive immunization technique to generateantibodies that catalyze the aldol reaction. The mechanism forantibody catalysis of this reaction mimics that used by naturalClass-I aldolase enzymes. Immunization with a reactivecompound covalently trapped a Lys residue in the binding pocketof the antibody by formation of a stable vinylogous amide. Thereaction mechanism for the formation of the covalent antibody-hapten complex was recruited to catalyze the aldol reaction. Theantibodies use the epsilon-amino group of Lys to form anenamine with ketone substrates and use this enamine as a nascentcarbon nucleophile to attack the second substrate, an aldehyde, toform a new carbon–carbon bond. Barbas et al. (1997) laterdesigned additional antibody catalysts for aldol condensationreaction, based on the intermediates shown in Scheme 1.3.

The observed rate enhancement 3 of 4,000,000 for thiscatalytic antibody far exceeds the 103 to 105 values forothers (Barbas et al., 1997), but falls short of aldolase(Reaction: Fructose-1,6 Bisphosphate # Glyceraldehyde-3-Pþ Dihydroxyacetone-P) by 8 to 10 orders of magnitude.

A fortuitous case of an engineered antibody catalyzinga multi-stage transesterification reaction was reported byWirsching et al. (1995). This antibody behaved as a Ping Pongenzyme (Catalytic Reactions: Eþ S1 # E$S1; E$S1 # Fþ P1;F þ S2 # F$S2; F$S2 # E þ P2, where E and F are the freeenzyme and the acyl-enzyme, respectively). Evidence for multi-stage catalysis was adduced by the parallel-line patterns observedin a plot of 1/v versus [Ester] at several constant levels of the acyl-acceptor alcohol (AAA) and in a plot of 1/v versus [AAA] atseveral constant levels of the ester. The resulting steady statekinetic parameters were 3 and 7.3 mM, respectively, for the esterand alcohol, and kcat was 21 min�1 (the latter obviously muchslower that natural enzyme counterparts). The authors found that,when a structurally related p-nitrophenyl ester was added tovarying concentrations of the antibody with rapid mixing, equi-molar amounts of p-nitrophenol formed quickly, followed bya slower, steady-state release phase. The amplitude of the burst-phase was proportional to the catalyst concentration.

Other semi-synthetic enzymes have been prepared bymodifying binding proteins and enzymes. For example, Zemal(1987) observed catalysis of p-nitrophenylester hydrolysis(enhancement factor 3¼ 1900) by heme-depleted myoglobin,a property that can be explained by the apolar binding pocketwith its two imidazoles that normally interacts with the heme.Likewise, upon attachment of a flavin cofactor to Cys-25within papain’s active site, the resulting synthetic enzyme (orsynzyme) was found to catalyze oxidation of dihy-dronicotinamide to nicotinamide with concomitant reductionof the flavin (Kaiser and Lawrence, 1984; Slama et al., 1984).

What becomes clear from model studies is that enzymes domuch more than stabilize reaction transition states: they bind,orient, desolvate, and destabilize substrates; they push/pullprotons to/from substrates, intermediates and products; theypromote nucleophilic reactivity; and they exploit metal ions astemplates, as Lewis acids, and as highly reactive redox speciesthat are otherwise inaccessible in aqueous medium. Enzymesalso exhibit a remarkable capacity to manage enthalpy andentropy changes throughout the catalytic reaction cycle,culminating in the release of reaction products. Although themost up-to-date approach uses a transition-state analogue togenerate the initial specificity, followed by site-directedmutagenesis to provide essential catalytic groups, obtainingcatalytic antibodies is still hit-or-miss.

Underscoring the limited rate enhancements achieved withcatalytic antibodies is the discovery that a so-called off-the-shelfprotein (bovine serum albumin) exhibits rate enhancements thatrival tailor-made catalytic antibodies. Noting that Thorn et al.(1995) described an antibody catalyzing the eliminative ring-opening of benzisoxazole, Hollfelder, Kirby and Tawfik (2001)tested whether the lysine side-chainamines mightalsoparticipate

O

CH3

O

CH3

O

CH3

O

O

Substrate

Product

HO R3

N EnzH

R1

R2

Intermediates

R1

O HR3

HN Enz

R2

Scheme 1.3


in this general base-catalyzed reaction. With human albumin,they obtained a kcat of 28.8 � 9.7 min�1, albeit with a promptonset of product inhibition after only around 10 catalytic cycles.They also found that the rate enhancements reported for catalyticantibodies depended on the somewhat arbitrary choice of solventconditions applied to the reference reaction. Until chemists canincrease the flexibility of catalytic antibodies, the ability to‘‘teach’’synthetic catalysts and antibodies to mimic enzymes willremain an insuperable task.

1.1.2e Synthetic Enzymes

Enzyme chemists have labored assiduously to fashion novelcatalysts from structural proteins or to transform biospecificligand binding sites into active sites. Although the develop-ment of crown ethers by Nobelist Donald Cram is oftenerroneously credited as an early breakthrough in the synthesisof artificial enzymes, U.S. chemists Myron Bender and RonaldBreslow pioneered these efforts. Bender and Breslow usedsynthetic organic chemistry to introduce catalytically activesubstituents (e.g., chiefly carboxyl and imidazole groups) onthe rim of cavity containing cyclodextrins (see Section 7.11 fora discussion of cyclodextrin inclusion complexes). Before hisearly demise, the American chemist E. Thomas Kaiser hadattempted to refashion the active sites of various heme proteinsand a few enzymes to create synthetic enzymes with novelcatalytic properties. His creative efforts were met with modestprogress toward the goal of fashioning new biocatalysts. Themonograph Artificial Enzymes edited by Breslow (2005)presents a series of cogent reviews on artificial enzymes,including biomimetic chemistry, vitamin B6-based enzymemodels, synthetic polymers with enzymatic activity, catalyticantibodies, protein-based artificial enzymes, artificial metal-loenzymes, as well as artificial restriction enzymes. To date,these efforts have met with uninspiring success, often for thesame reasons already noted above for catalytic antibodies.

1.2 BIOLOGICAL CATALYSIS

That the rates of enzyme-catalyzed reactions7 were studiedlong before corresponding organic chemical reactions

shouldn’t be surprising. While Fritz Wohler had succeededin synthesizing urea in 1826, the field of physical organicchemistry, which deals with the underlying kinetics andmechanisms of organochemical reactions, developed rela-tively slowly until the late nineteenth century. What mostlimited the progress in chemical kinetics of organic andinorganic reactions was the lack of reliable methods forquantifying changes in the concentration of reactants orproducts. Spectrophotometers were nonexistent, becausethe then primitive electronic circuitry and low voltagesavailable from batteries precluded the fabrication of pho-tomultiplier tubes. The need for a conveniently observableproperty led to early studies on the action of a crudepreparation of emulsin on the hydrolysis of emulsifiedamygdalin, a sparingly soluble ester isolated from apricotpits. Emulsin later proved to be an enzyme that readilyconverts the visibly milky white, aqueous suspension ofamygdalin into transparent (water-soluble) products. Withthat simple assay, the concept of catalysis could bedemonstrated. It was, however, the advent of the polar-imeter that made possible the quantitative investigation ofhow reaction rate depends on changes in the concentrationof optically active reactants or products. Even so, organicchemists lacked the means to synthesize chiral compounds,the latter being the sole province of physiologic chemistry(biochemistry). Because the degree of rotation of plane-polarized light was a linear function of the molarconcentration of an optically active substance, this tech-nique provided the opportunity to demonstrate unambigu-ously that the acid-catalyzed hydrolysis of sucrose broughtabout stereochemical inversion (i.e., a change in thedirection of rotation of plane polarized light. Likewise, thecorresponding action of the enzyme invertase (Reaction:Sucrose þ H2O # D-Fructose þ D-Glucose) could bemonitored reliably. The availability of polarimetry asa simple, highly sensitive, and reproducible quantitativetechnique essentially established chemical kinetics asa rigorous physical science.

1.2.1 Roots of Enzyme Science

The origins of enzymology as a scientific discipline can betraced to Spallanzani who, in 1783, demonstrated thatgastric juices liquefied meat, and to Gay-Lussac who, in1810, reported that yeast growing anaerobically couldferment sugars into ethanol and CO2. Enzymes were firstdiscovered in 1833 when Anselme Payen and Jean Persozfound that an alcohol precipitate of malt extract containedthe thermolabile substance diastase, which converted starchinto sugar. Justus von Liebig proposed that fermentation anddigestive processes were inherently the result of chemicalaction. In 1835, the German physiologist Theodor Schwanndiscovered that, in a manner similar to that of acid (asdiscovered decades earlier by American physiologist JohnYoung), gastric juice also contained its own digestive

7 It is helpful to understand some basic terminology used by enzymologists.

A simple enzyme is a biological catalyst made wholly of protein, although

more than one polypeptide chain may be part of the active enzyme. A

complex enzyme is composed of one or more polypeptide chains plus

a low-molecular-weight organic molecule or metal ion at its active site.

The term holoenzyme refers to the entire complex enzyme, whereas the

term apoenzyme refers only to the protein component. If the non-protein

component binds non-covalently to the apoenzyme, it is called

a coenzyme. (Many coenzymes contain structural elements of vitamins.) A

metal ion that binds directly to the protein is called a metal ion cofactor.

A prosthetic group is a relatively small organic molecule that is usually

extremely tightly, or even covalently, bound. Some prosthetic groups also

contain a metal ion (e.g., heme is protoporphyrin IX plus Fe(II) or Fe(III)

ion) held in place by coordinate covalent bonds.

12 Enzyme Kinetics

substance that became known as pepsin (from the Greekpepsis for digestion). Work many years later established thatpepsin is an enzyme.

Given his remarkable chemical intuition and role asa reductionist, it is remarkable that the great Frenchchemist Louis Pasteur steadfastly adhered to the view thatfermentation was uniquely the province of living yeastcells. His view supported the vitalists, who asserted thatlife is the manifestation of a vital force (or, e lan vital), thelife-creating principle immanent in all living organisms.The opposing mechanistic view that living systems wouldinevitably be shown to obey the laws of chemistry andphysics was held by the German physiologist WilliamKuhne, who in 1878 coined the phrase enzyme (from theGreek en and zyme, standing for ‘‘in’’ and ‘‘yeast’’) forthe fermentative substance in yeast. In 1893, the Latvianscientist Wilhelm Ostwald formally classified enzymes ascatalysts, even though their chemical nature was stillwidely debated (Ostwald, 1894). To explain the specificaction of glycolyzing (i.e., sugar-cleaving) enzymes, EmilFischer (1894) proposed his Lock-and-Key Hypothesisasserting that enzymes are rigid templates, into whichsubstrates must insert with the same high precision asa key fitting into its corresponding lock. However, it wasanother German chemist Eduard Buchner, who in 1897proved that metabolism can take place outside intactliving cells. He innovated the procedure of grinding yeastin abrasive sand, followed by passage through a paperfilter to obtain a cell-free extract. Noting the release ofCO2 bubbles after adding the resulting extract to a sucrosesolution, Buchner correctly inferred that the extract itselfacted as a catalyst, even in the absence of intact cells andtherefore any possibility of a vital force. The clean-cutresult earned Buchner the Nobel Prize in Chemistry, andthe simplicity of his protocol ushered in the modern era ofsystematic biochemical research. In 1898, Duclaux sug-gested that the suffix ‘‘-ase’’ be used in biochemicalnomenclature to distinguish enzymes from biologicalsubstances devoid of catalytic activity.

In his 1894 paper, Fischer asserted that among theagents that serve the living cell, the proteins are the mostimportant, but the mounting evidence that enzymes wereproteins was stubbornly resisted by Richard Willstatter.Having earned the Nobel Prize for working out thestructures of chlorophyll and heme, Willstatter held thatlow-molecular-weight substances associated with proteinswere the true catalytic entities. His view persisted until theAmerican scientist James B. Sumner (1926) crystallizedurease, demonstrating that its catalytic power rested in theprotein itself. Subsequent work by John H. Northropdemonstrated that proteases could likewise be crystallizedand that the protein was the sole component responsiblefor catalysis. The weight of their combined findingspersuasively overwhelmed all doubters, and so doingearned them the Nobel Prize.

1.2.2 Enzyme Technology

In many respects the forerunner of modern biotechnology,the field of enzyme technology was born in Copenhagen in1874 with the establishment of the Christian Hansen’sLaboratory. Although mainly focusing on the production ofwax as a coating for cheeses, Hansen’s Laboratory becamethe first company to market a standardized preparation ofthe enzyme rennet for use in cheese-making (Tauber, 1943).By controlling the rate and extent of milk curdling,Hansen’s efforts greatly increased the quantity, quality, andshelf life of European cheeses. While living in the UnitedStates in the early 1890s, the Japanese scientist JokichiTakamine developed a water–alcohol extraction method toisolate the powerful starch digesting enzyme Takadiastase.The latter was the trade name derived by combining ‘‘Taka’’from his name with ‘‘diastase,’’ the latter by then an alreadywell-known amylase preparation from the fungusAspergillus oryzae. His patent, granted as No. 525,823 bythe U.S. Patent Office on September 11, 1894, was the firstto teach proprietary aspects of enzyme technology.

Takamine’s efforts inspired what is now a century-oldJapanese tradition of using enzymes and highly controlledfermentation to improve production of sugars, cheese,beer, vinegar, bread, fermented soy products, etc., toproduce fine chemicals like monosodium glutamate, ino-sinic acid, and vitamins, and to isolate new drugs and anti-metabolites.

It is important to recognize that fermentation science andenzymology have profoundly altered the course of history.A notable example is acetone-butanol fermentation. Pasteurwas the first to identify butyric acid as a fermentationmetabolite, and acetone formation was later demonstratedby Schardinger (1905). In 1911, Fernbach and Weizmannfirst reported on bacteria that produced amyl alcohol,ethanol, and acetone as stable metabolic end-products ofpotato starch fermentation. A year later, Weizmann isolatedan organism that fermented all known starches andproduced acetone in much higher yield. Those weredesperate times, and sensing the significance of hisdiscovery in low-residue lacquers to waterproof cloth-sidedairplanes as well as for explosives, the ardent ManchesterZionist wrangled a promise (now known as the BalfourDeclaration) that England would support his life-long goalof returning Jews to Palestine. British reluctance to fulfillthat promise led to the post World War II struggle thatultimately established Israel, with Weizmann elected its firstpresident. Ironically, the Axis Powers relied on the immenseintellect of none other than Emil Fischer to manage theGerman chemical industry during World War I. Failure ofthe Axis, loss of his two sons in that great war, andadvancing cancer overwhelmed Fischer, who committedsuicide in 1919.

Today, beyond the use of enzymes in biomedicine,enzyme technology (Tables 1.2 and 1.3) has expanded to


TABLE 1.2 Some Commercial Applications of Enzyme Technologya

Product Enzyme application

Animal Feed Phytases hydrolyze abundant phytate (myo-inosital hexaphosphate) stores in plants used asanimal feed, thereby increasing the nutritional value of the feed by releasing phosphate andbound metals from the phytate.

Cheese-making Rennet cleaves k-casein between Phe-105 and Met-106, thereby destroying the latter’sability to stabilize milk as a colloidal suspension, resulting in its calcium ion-inducedcoagulation into curd and liquid whey. (Treatment of soft cheeses with hen egg whitelysozyme destroys Listeria monocytogenes, an infectious bacterial pathogen in those withcompromised cell-mediated immunity.)

Baking Industry Combined action of glucose oxidase and catalase removes glucose from egg whites prior todrying into dried egg white. Glucoamylase releases b-D-glucose from 1,4-a-, 1,6-a- and 1,3-a-linked glucans to yield high-glucose syrup. b-Amylases liberate maltose from barley starchin the production of high-maltose syrup. Invertase action on sucrose yields glucose andfructose, providing a sweeter syrup that is less apt to granulate than pure sucrose syrups.

High-fructose Corn Syrup (HFCS) In this three-step process, Bacillus species a-amylase acts on cornstarch to produce shorter-chain polysaccharides, Aspergillus glucoamylase yields glucose, and glucoisomerase actionincreases fructose content to ~42%. Because HFCS is substantially sweeter than glucose orsucrose, less is required as a sweetener primarily in baked goods, candy, and soft drinks.

Ethanol Production Fermgen� protease is a proprietary fungal enzyme (pH optimum ¼ 3.0–4.5) that promiseshigher rates and yields of ethanol from fermentation for corn-, milo-, or wheat-basedsubstrates by: (a) increasing availability of essential yeast nutrients in the form of amino acids,peptides and free amino nitrogen; and (b) hydrolyzing protein matrices within kernels,thereby facilitating use of otherwise hydrolysis-recalcitrant starches.

Meat Tenderizing Papaya juice (rich in papain), pineapple juice (rich in bromelin), and orange juice (rich inficin) are all highly effective tenderizers. (Processed papaya latex extract is sold under thebrand name Accent�.)

Fruit Juices, Wine, and Beer Combined action of Aspergillus pectinase and Monilia diastastase greatly reducescloudiness, especially important for sparkling wines. In the absence of colloidal pectin,improved filtration/pressing also increases volume by 15–20%.

Textiles Laccases (polyphenol oxidases) are used in the textile industry for dye bleaching in theproduction of ‘‘stone-washed’’ denim. Cellulases are sold to the textile industry for cottonsoftening and denim finishing. Alkaline pectinase, poly(vinyl alcohol)-degrading enzyme,cutinase and catalase are also used for cotton preparation. Pectinase and hemicellulases areused to soak and loosen bast (long and strong central) fibers for high-quality fabrics. Proteasesremove contaminating proteins from silk fibers without effect on fibroin. Transglutaminase isused to introduce cross-links into wool, thereby strenthening fibroin strands. Amylasesremove insoluble starchs and sizing from silk and cotton to improve quality of dyeing andprinting processes.

Tobacco Catalase reduces nicotine content. Glucosidases form the desired brown pigment byhydrolysis of quercitin-rhamnoglucoside (rutin). Amylases and invertases increase glucoseand fructose content for improved taste.

Leather Proteases (pepsin and trypsin as well as extracts of Aspergillus oryzae cultivated on rice,elastin, and keratin) remove flesh, blood and hair from fresh hides without affecting leather’scollagen network. Lipases remove oils that retard tanning and dyeing.

Paper Production b-Xylanases are used in the treatment of paper pulp to reduce the use of chlorine forbleaching.

Detergents Proteases (mainly subtilysin) remove proteins from food, skin, and saliva that accumulate onclothing. Haloperoxidases are now employed to generate ‘‘color safe’’ bleaches. Theseenzymes are often stabilized by intramolecular –S–S– linkages. More than half of alldetergents now contain enzymes as a proprietary constituent.

Sewage Treatment Lipases release enzymes from microbes to greatly accelerate the degradation of rawsewerage.

Reducing Spread of Prion Diseases Residing deep within the fissures in the surfaces of stainless steel surgical devices, prionscausing variant Creuzfeldt-Jakob Disease (vCJD) can resist standard sterilization procedures.Prionzyme� (a proprietary enzyme), the Bacillus-derived MSK103 protease, as well asa combination of proteinase K and pronase (the latter in the presence of SDS) can hydrolyzevCJD prions. These enzymes may therefore facilitate the sterilization of neurological anddental surgery instruments.

aThe interested reader should consult Tauber (1943) for detailed early accounts of the commercial utility of enzymes. Chaplin and Bucke (1990) present

lucid descriptions of these and other more contemporary applications of enzymes in commerce.

14 Enzyme Kinetics

include the use of enzymes in the production of foodstuffs,including hydrolysis of starch, production of glucose- andmaltose-rich syrups as well as high fructose corn starch,derivation of glucose from cellulose, use of lactases in thedairy industry, extended applications of enzymes in thepreparation and storage of fruit juices, and improvement ofwines, beers and distilled spirits and (Chaplin and Bucke,1990). Enzyme technology has likewise improved produc-tion of detergents, color-safe bleach, leather and wool.

Modern biotechnology grew out of genetic engineeringin the early 1970s by the discovery of restriction enzymesby Daniel Nathans, Hamilton Smith and Werner Arber andthe advent of recombinant DNA techniques, pioneeredlargely by Paul Berg, Herbert Boyer, and Stanley Cohen.Nothing written here can adequately encapsulate themomentous growth of biomedicine arising from recombi-nant DNA. In vitro protein synthesis promises to revolu-tionize the production of pyrogen-free proteins, enzymes,and antibodies for use in highly specific and low-toxicitytherapies.

For many years, enzymes found limited application inthe organic chemistry laboratory. The notable exception wasthe use of pig kidney acylase for the resolution of secondaryalcohols via stereoselective ester synthesis, followed bychromatography to separate the product.

H3C H3C CN

OH

CN

OAc Esterase

Enzyme-mediated enantiomeric enrichment is discussedin greater detail in Section 5.10. The widespread utility ofenzymes in organic and pharmaceutical chemistry has now

burgeoned over the years. Those interested in such appli-cations should consult Biocatalysts and Enzyme Technology(Buchholz, Kasche and Bornscheuer, 2005). Another valu-able resource is Enzyme Catalysis in Organic Synthesis: AComprehensive Handbook (Drauz and Waldmann, 2002),which provides tried and true methods for using enzymes inorganic synthesis, a exhaustive table of all the commerciallyavailable enzymes, as well as comprehensive registers fortargeted searching according to enzyme, compound, orreaction type.

1.3 DEVELOPMENT OF ENZYME KINETICS

The idea that an enzyme first combines with its substratewas suggested by Wurtz (1880), who found that papainappeared to form an insoluble compound with fibrin prior tohydrolysis of the latter. O’Sullivan and Tompson (1890)reached a similar conclusion, based on their observation thatinvertase is protected by its substrate sucrose againstthermal denaturation. The theoretical basis of enzymekinetics was consolidated through the work of AdrianBrown (1892, 1902) and Victor Henri (1903), whose workon enzyme-substrate complex formation foreshadowed(‘‘adumbrated’’, as J. B. S. Haldane (1930) put it) themonumental paper by Leonor Michaelis and Maude Menten(1913). Their famous relationship (Eqn. 1.2) explains thekinetic behavior of literally thousands of enzyme-catalyzedreactions.

v ¼ Vm

1þ K

½S�

1.2

The Michaelis-Menten treatment is based on the rapid-equilibrium assumption that the concentrations of free

TABLE 1.3 Several Commercially Important Enzymesa

Type Enzymes

Carbohydrases a-Amylases; Alkaline a-Amylase; b-Amylase; Cellulase; Cyclodextrin glycosyl tranferase; Dextranase;a-Galactosidase; Glucoamylase; a-Glucosidase; Hemicellulase; Invertase; Lactase; Lysozyme; Naringanase;Pectinase; Pentosanase; Pullulanase; and Xylanase.

Proteases Acid protease (Pepsin); Alkaline protease; Bromelain; Chymosin; Ficin; Neutral proteases (Trypsin, Chymotrypsin);Papain; Peptidases; Rennet; Rennin; Subtilisin; and Thermolysin.

Lipases Triglyceridases and Phospholipases.Other hydrolases Amidases; Aminoacylase; Apyrase; Chlorophyllase; DNA restriction endonucleases (300þ enzymes); Feruloyl

esterases; Glutaminase; Penicillin acylase; Phytase; Phosphatases; Pregastric esterases; and Ribonucleases.Oxidoreductases Amino acid oxidase; Catalase; Chloroperoxidase; Glucose oxidase; Glutathione peroxidase; Hydroxysteroid

dehydrogenase; Laccase; Lactate dehydrogenase; Lipoxygenase; Lysyl hydroxylase; Lysyl oxidase; Peroxidase;Polyphenol oxidase; Sorbitol oxidase; Sulfhydryl Oxidase; and Xanthine oxidase.

Decarboxylases Acetolactate decarboxylase; Aspartic b-decarboxylase.Polymerases RNA-dependent DNA polymerase (reverse transcriptase); Taq DNA polymerase; Vent DNA polymerase.Lyases Fumarase; Histidase.Isomerases Glucose isomerase; Xylose (Glucose) isomerase.

aThe interested reader should consult Tauber (1943) for detailed accounts of the commercial utility of enzymes. Chaplin and Bucke (1990) present lucid

descriptions of these and other more contemporary applications of enzymes in commerce.


enzyme EF, free substrate SF, and enzyme-bound substrateE$X are defined thermodynamically: Kd ¼ [EF][SF]/[E$X].John B. S. Haldane later introduced the concept of a steady-state flux (e.g., d[E$X]/dt z 0) to enzyme kinetics andmetabolism (Briggs and Haldane, 1925; Haldane, 1930).Both approaches sample rate behavior over the course ofmany catalytic reaction cycles.8 Haldane’s use of thesteady-state approximation pre-dated the development ofnon-equilibrium thermodynamic theory that now helps us tocomprehend the robust stability of steady states.

By the mid-nineteenth century, chemists MichaelFaraday and Antoine Lavoisier showed that all redoxreactions (Overall Reaction: Aox þ Bred # Aredþ Box) canbe treated as the sum of two half-reactions (Reduction Half-Reaction: Aoxþ e # Ared; and Oxidation Half-Reaction: Bred

# Boxþ e, where e represents an electron). This concept ledto the idea that other chemical processes may likewise bedissected kinetically into component (or elementary)reactions.

In 1910, the German electrochemist and Nobel LaureateWalther Nernst extended Maxwell’s theory of gases bysuggesting that fast elementary steps in solution-phasereactions might be gainfully explored by chemical relaxa-tion techniques. However, instrumentation of suitablestability and sufficient sensitivity was unavailable at thattime. Recognizing a need to probe the kinetics of hemo-globin oxygenation in much greater detail, Hamilton Har-tridge and Francis Roughton (1923, 1926) introduced therapid-mixing technique, known as continuous-flow, thatnecessitated the use of 0.1–0.5 liter volumes of reactants.Britton Chance (1943) perfected their designs through hisingenious design of a low-volume, stopped-flow rapid-mixing device that used a spectrophotometer to detect andanalyze intermediates formed transiently by horse radish

peroxidase (Reaction: Leuko-malachite Green (colorless)þH2O2 # Malachite Green (lmax ¼ 612 nm) þ 2 H2O).Chance also introduced the use of analogue (and later pio-neered digital) computers for modeling the kinetic behaviorof individual enzymes as well as those forming a metabolicpathway. Exactly how the Nobel Institute has failed torecognize Chance’s enormous contributions to modernchemistry is an enigma.

After the discovery of the phenomenon of nuclearmagnetic resonance in 1946 by Bloch and Purcell, biolog-ical NMR spectroscopy was ushered in by Mildred Cohnand others over the ensuing decades. Likewise, surginginterest in sonar and shock-wave technology during WorldWar II, coupled with the theory of pressure-inducedchemical relaxation (Einstein, 1920) provided the impetusfor the investigation of individual steps (elementary reac-tions) within multi-step kinetic mechanisms. Fast reactionmethods, especially those pioneered by Nobel LaureatesManfred Eigen (temperature-jump technique), RonaldG. W. Norrish (shock-tube and pressure-jump techniques)and George Porter (flash photolysis), completely revolu-tionized experimental chemical kinetics.

Although somewhat beyond the current discussion, onecannot minimize the impact of developments in physicalorganic chemistry on the emergence of enzyme science. TheBritish chemist Keith Ingold introduced the terms electro-phile for an electron-seeking functional group, nucleophilefor nucleus-seeking functional group, tautomerism for keto-enol isomeric rearrangements, and inductive effect toaccount for electronic effects of nearby entities on func-tional group reactivity. A fundamental advance was hisconceptualization of the respective dissociative and asso-ciative features of SN1 and SN2 nucleophilic substitutionmechanisms at saturated carbon bonds. (Later work dis-closed that corresponding SN1 and SN2 mechanisms are alsoat play in phosphotransfer reactions.) Another Briton,Ronald Bell, connected the acid base theory of his mentorBrønsted to the origins of hydrogen isotope effects andcorrectly predicted that the kinetic isotope effect should bemaximal when the proton is half-transferred in the reac-tion’s transition state. Perhaps the most influential of Bell’scontributions was his development and understanding ofquantum mechanical tunneling, or as he called it the tunnelcorrection for isotope effects involving proton (and hydride)transfer processes. With their later keen interest in under-standing biological proton transfer, Bell’s disciples JohnAlbery and Jeremy Knowles found warm acceptance oftheir novel ideas on enzyme catalysis.

Over the past half-century, enzyme kinetics has maturedinto a highly sophisticated and innovative discipline.Although the current state of any field is the sum of contri-butions of countless investigators, the following scientistsmade advances so notable that they personify the field:Robert Abeles – Mechanism-based inhibitor design;Cobalamin-dependent reactions; Robert Alberty – pH

8 Initial-rate enzyme experiments analyze multiple-turnover processes

averaged over numerous catalytic turnovers. Multiple-turnover kinetic

phenomena are usually examined at low concentrations of enzyme, and

the accumulation or depletion of an enzyme-bound reactant species

during the steady-state phase is assumed to be time invariant (i.e.,

D[EX]/dt z 0). The number of turnovers occurring during an initial-rate

measurement equals D[P]/[EX] ¼ D[P]/{[P]t¼t � [P]t¼0}, where [P] is

the concentration of product formed, and [EX] is the concentration of

enzyme-bound reactant over the period of measurement. The term

single-turnover process refers to events occurring over one turnover or

cycle of catalysis. As discussed in Chapter 10, single-turnover properties

are usually measured at high concentrations of enzyme using rapid

reaction techniques, such that the accumulation or depletion of an

enzyme-bound reactant species, say EX, may be detected and quantified.

Because the observed rate is a population average for many molecules

undergoing a single-turnover, the rate constants obtained are likewise

average values. The term single-molecule kinetic process refers to events

occurring at the level of individual enzyme molecules undergoing one or

more catalytic reaction cycles, observed by a suitable high-sensitivity

microscopical technique. As discussed in Chapter 12, one can also study

reactions at the single-molecule by measuring local accumulation of

product molecules generated by spatially isolated enzyme molecules.

16 Enzyme Kinetics

TABLE 1.4 Nobel Prizes Awarded for Research in Enzyme Sciencea

Year Laureate Award Cited achievement

2009 Venkatraman Ramakrishnan Chemistry Ribosome structure and mechanism2009 Thomas A. Steitz Chemistry Ribosome structure and mechanism2009 Ada E. Yonath Chemistry Ribosome structure and mechanism2006 Roger Kornberg Chemistry Mechanism of transcription (RNA polymerase)2004 Aaron Ciechanover Chemistry Mechanism of enzymatic ubiquitination2004 Avram Hershko Chemistry Mechanism of enzymatic ubiquitination2004 Irwin Rose Chemistry Mechanism of enzymatic ubiquitination2000 Paul Greengard Med/Phys Signal transduction and brain protein kinases1997 Paul Boyer Chemistry ATP synthase rotary catalysis mechanism1997 John Walker Chemistry ATP synthase structure1997 Jens Skou Chemistry Discovery of sodium, potassium ATPase1994 Alfred Gilman Med/Phys Signal-transducing GTP-regulatory enzymes1994 Martin Rodbell Med/Phys Signal-transducing GTP-regulatory enzymes1993 Kary Mullis Chemistry Polymerase chain reaction1992 Edmond Fischer Med/Phys Protein kinases1992 Edwin Krebs Med/Phys Protein kinases1989 Sidney Altman Chemistry Catalytic RNA1988 Thomas Cech Chemistry Catalytic RNA1988 Johann Deisenhofer Chemistry Structure of a photosynthetic reaction center1988 Robert Huber Chemistry Structure of a photosynthetic reaction center1988 Hartmut Michel Chemistry Structure of a photosynthetic reaction center1982 Sune Bergstrom Med/Phys Prostaglandin biosynthesis1982 Bengt Samuelsson Med/Phys Prostaglandin biosynthesis1978 Peter Mitchell Chemistry Chemiosmotic principle1978 Werner Arber Med/Phys Discovery of restriction enzymes1978 Daniel Nathans Med/Phys Discovery of restriction enzymes1978 Hamilton Smith Med/Phys Discovery of restriction enzymes1975 John Cornforth Med/Phys Stereochemistry of enzyme-catalyzed reaction1972 Christian Anfinsen Chemistry RNase folding1972 Stanford Moore Chemistry RNase sequence and active-site chemistry1972 William Stein Chemistry RNase sequence and active-site chemistry1971 Earl Sutherland Med/Phys Discovery of 39,5-cyclic-AMP1970 Louis Leloir Chemistry Structure and biosynthesis of sugar nucleotides1970 Julius Axelrod Med/Phys Enzymatic synthesis of epinephrine1964 Konrad Bloch Med/Phys Cholesterol metabolism1964 Feodor Lynen Med/Phys Fatty acid metabolism1961 Melvin Calvin Chemistry Photosynthesis1959 Arthur Kornberg Med/Phys Enzymatic synthesis of DNA1959 Severo Ochoa Med/Phys Enzymatic synthesis of RNA1955 Hugo Theorell Med/Phys Mechanisms of redox enzymes1953 Hans Krebs Med/Phys Citric acid pathway1953 Fritz Lipmann Med/Phys Coenzyme A and fatty acid enzymology1947 Carl Cori Med/Phys Enzymatic synthesis of glycogen1947 Gerty Cori Med/Phys Enzymatic synthesis of glycogen1947 George Wald Med/Phys Retinal cis-trans isomerization in visual processes1946 James Sumner Chemistry Urease crystallization1946 John Northrop Chemistry Protease crystallization1937 Albert Szent-Gyorgyi Med/Phys Vitamin C and catalysis of fumaric acid1931 Otto Warburg Med/Phys Mode of action of respiratory enzymes1929 Arthur Harden Chemistry Sugar fermentation pathway1929 Hans von Euler-Chelpin Chemistry Fermentative enzymes1922 Otto Meyerhof Med/Phys O2 and lactic acid metabolism1907 Eduard Buchner Chemistry Cell-free enzyme-catalyzed reactions

aAlthough receptor-mediated endocytosis and prions have little to do with enzymes, their respective discoverers, Michael Brown (Nobel Laureate in

Medicine and Physiology, 1987) and Stanley Prusiner (Nobel Laureate in Medicine and Physiology, 1997), both received their post-doctoral research training

in enzymology under the late Earl R. Stadtman.


kinetics; Bisubstrate enzyme kinetics; Thermodynamics ofATP hydrolysis of biochemical reactions; Application ofLegendre transforms in biochemical thermodynamics;Christian Anfinsen, Stanford Moore and William Stein –Ribonuclease structure and folding, identification of cata-lytic residues; John Albery and Jeremy Knowles – Novelisotopic approaches for defining the energetics of the triose-phosphate isomerase and proline racemase reactions;Enzyme evolution, Catalytic efficiency, and Catalyticperfection; Max Bergmann and Joseph Fruton – Poly-sitebinding theory of enzyme specificity; Introduction ofsynthetic N-carbobenzoxy-peptides as alternative substratesfor proteases and peptidases; Paul Boyer – Multi-substrateenzyme kinetics; Definition of kinetic reaction mechanismsthrough the novel application of isotope exchangemeasurements at thermodynamic equilibrium; Oxygen-18tracer methods in carboxyl- and phosphoryl-group transferreactions; ‘‘Binding-Change Mechanism’’ for rotary catal-ysis of ATP synthase (see Table 1.4: Nobel Laureates);Britton Chance – Invention of the stopped-flow technique;First spectral detection of enzyme reaction intermediates;First application of computers to simulate enzyme reactionkinetics; Development of the Theorell-Chance bisubstratekinetic mechanism; W. Wallace Cleland – Systematicenzyme nomenclature of multi-substrate enzyme kinetics;Steady-state treatment of isotope exchange kinetics;Development of exchange-inert metal-nucleotide com-plexes; Development of equilibrium perturbation techniqueto evaluate kinetic isotope effects for detecting rate-limitingchemical steps; Mildred Cohn and Albert Mildvan –Oxygen-18 probes of P–O and C–O bond cleavage inphosphotransfer reactions; Development of NMR-baseddistance measurements using proton relaxation in para-magnetic environments; NMR approaches for definingenzyme exchange kinetics; Keith Dalziel – Development ofthe F-parameter method for discriminating the order ofsubstrate binding by bisubstrate enzymes; Edward Dennis,Pierre Desnuelle, Michael Gelb, Mahendra Jain and RobertVerger – Use of nonionic detergents and Langmuir troughsto investigate interfacial catalysis by lipases and phospho-lipases; Lipase processivity; Zacharias Dische – Discoveryof allosteric feedback inhibition; Pierre Douzou andAnthony Fink – Development of ultra-low temperature(cryoenzymology) techniques to investigate enzyme kineticproperties; Manfred Eigen – Chemical relaxation process;Temperature-jump technique; Prion protein polymerization(see Table 1.4: Nobel Laureates); Fritz Eckstein, JeremyKnowles, David Usher and Martin Webb – Stereochemicalprobes of phosphomonoester- and phosphodiester-utilizingreactions; Alan Fersht – Site-directed mutagenesis asmechanistic probes; Mechanisms for kinetic proofreadingby aminoacyl-tRNA synthetases; Novel approaches fordefining protein folding mechanisms; Carl Frieden – pHkinetics of fumarase reaction; Three-substrate enzymekinetics; Kinetic aspects of enzyme cooperativity and

hysteresis; Development of KINSIM and FITSIM softwarefor simulating enzyme rate processes; Herbert Fromm – Useof reversible inhibitors (including product inhibitors,alternative substrate inhibitors, as well as competitiveinhibitors) to distinguish multi-substrate kinetic mechanisms;Implications of abortive complex formation in enzymekinetics; Definition of kinetic reaction mechanisms (withBoyer) through isotope exchange measurements at thermo-dynamic equilibrium; Constant-ratio approaches foranalyzing three-substrate enzyme kinetics; Fallacy of ade-nylate energy charge hypothesis for ATP-utilizing/regener-ating enzymes; Quentin Gibson – Development of stopped-flow rapid mixing instrumentation; Heme-protein kinetics;Herbert Gutfreund – Fast reaction kinetics of enzymereactions; Kinetic criteria (with P. Boon Chock) for evalu-ating substrate channeling; Gordon Hammes – Temperature-jump reaction techniques to enzyme systems; Fast reactionkinetics of complex multi-enzyme processes; BrianHartley – Chymotrypsin catalysis; Enzyme burst method fordetecting enzyme-bound, covalent reaction intermediates;Charles Huang – Multisubstrate enzyme kinetics; Modelsfor calcium ion complexation in calmodulin mediated acti-vation of target enzymes; Kinetic analysis of allostericenzymes; William Jencks – Catalytic strategies in chemistryand enzymology; Conceptual basis for catalytic antibodies,Energetics and mechanism of calcium ion pump; KasparKirschner – Fast reaction kinetics of allosteric enzymes;Daniel Koshland – Induced-fit hypothesis; Sequential modelfor cooperativity of allosteric enzymes; Role of orbitalalignment (Orbital Steering) in enzyme catalysis; KeithLaidler – Application of absolute rate theory to enzymesystems; Temperature and immobilization effects onenzyme kinetics; Richard Lerner and Peter Schultz –Development of catalytic antibodies, based on a predictionby W. P. Jencks; Vincent Massey – pH Kinetics of fumarase;Kinetic and mechanistic approaches in flavoenzyme catal-ysis; Peter Mitchell – Chemiosmotic principle of trans-membrane gradients (see Table 1.4: Nobel Laureates);Jacques Monod, Pierre Changeaux and Jeffries Wyman –Concerted transition model for allosteric interactions andcooperativity; Dexter Northrop – Two-site ping-pongkinetics; Exploiting the Swain-Schaad relationship to isolateand evaluate intrinsic kinetic isotope effects; Dieter Palm,Bryce Plapp and Judith Klinman – Kinetic isotope effects inenzyme-catalyzed hydride transfer; Role of quantummechanical tunneling in hydride transfer; Arthur Pardee andEdwin Umbarger – Kinetics and feedback inhibition ofallosteric enzymes; Ephraim Racker – First demonstrationthat covalent enzyme-substrate compounds are formedduring enzyme catalysis; Michael Raftery – Early applica-tion of secondary kinetic isotope effects to detect the oxa-carbenium ion intermediate formed in lysozyme catalysis;Irwin Rose – Isotopic probes of enol intermediates inisomerases; Isotope trapping methods; Dynamic stereo-chemical probes (or positional isotope exchange);

18 Enzyme Kinetics

Elucidation of the ubiquitin ligase mechanism (seeTable 1.4: Nobel Laureates); Vern Schramm – Application ofmultiple kinetic isotope effect data to the rationale design oftransition-state analogues for uses as specific, high-affinityenzyme-targeted drugs; Earl Stadtman – Kinetic and regu-latory behavior of signal transduction cascades via posttranslational modification, as demonstrated in his pioneeringstudies of enzyme-catalyzed adenylylation/deadenylylationof Escherichia coli glutamine synthetase; Edwin Taylor,David Trentham, Clive Bagshaw and Martin Webb –Mechanoenzyme kinetics of actomyosin, as probed by fastreaction kinetics, ‘‘photo-caged’’ ATP, and continuousassay with fluorescent phosphate-binding protein; HugoTheorell – Bisubstrate reaction kinetics of redox enzymes(see Table 1.4: Nobel Laureates); Frank Westheimer –Stereochemistry NADH hydride transfer; Stereochemistryof phosphoryl transfer, including pseudorotation; Kineticisotope effects; Photoaffinity labeling of enzyme activesites; Bioinorganic reaction mechanisms; Richard Wolf-enden – Development of a rational basis for analyzingtransition-state inhibitor potency; Catalytic proficiency; andJeffrey Wong – Theoretical treatment of steady-state enzymekinetics; Alternative substrate kinetics.

Finally, those familiar with enzyme kinetics know thatthe complexity of certain enzymes generated suchcompelling interest that some enzyme chemists madecareer-long commitments to the study of a single enzyme orpathway. So strong was their attachment to their favoriteenzyme that the late Ephraim Racker once told the authorthat he was convinced that the perceived importance of anenzyme was often a manifestation of the interestingpersonalities investigating that enzyme. He was particularlyfond of the humanistic saying that ‘‘Interesting people makefor interesting enzymes.’’ In this respect, the above list isadmittedly incomplete and fails to acknowledge theimmense contributions of so many other creative andinteresting scientists.

1.4 THE CONCEPT OF A REACTIONMECHANISM

The chief ambition of enzyme chemists is to obtain the mostcomplete description possible of an enzyme-catalyzedreaction. An enzyme’s overall catalytic mechanism may besubdivided into four parts:

1. Chemical Mechanism – A reaction scheme showing allbond-breaking/-making steps, rearrangements, transi-tion state(s), as well as the stereochemistry of partialand overall reactions.

2. Kinetic Mechanism – A scheme accounting for thetime-dependent accumulation and breakdown of eachenzyme-bound species, including the energetics of anyrate-determining step(s).

3. Structural Mechanism – An atomic-level modelshowing the structural basis for catalytic facilitation ofthe chemistry of substrate-to-product interconversionas well as the physics of substrate adsorption andproduct release.

4. Regulatory Mechanism – A scheme offering a detailedunderstanding of activator and inhibitor effects that area direct consequence of binding cooperativity, allostericinteractions with activators and/or inhibitors, post-trans-lational modification, etc.

Undertaking such investigations begins with elucidation ofa chemical reaction mechanism explaining all of the bond-breaking and bond-making steps needed to transformsubstrate(s) into product(s), as well as all detectableelementary reactions comprising the kinetic scheme ofenzyme interactions with substrates, intermediates, andproducts. Although many studies are initiated with theconvenient use of unnatural substrates that are chromo-genic or fluorogenic (i.e., the products of these weaklyabsorbing or fluorescing substrates have quantifiableabsorbance or fluorescence spectra), these studies shouldideally be carried out with the natural substrates to fullyunderstand the biological role of the enzyme under inves-tigation. (In fact, altered reactivity of alternative substratesmust always be anticipated.) The chemical and kineticmechanisms must be consistent with the reaction’s overallstoichiometry, its stereochemistry, its kinetic and thermo-dynamic properties, the location and energetics of ratedetermining step(s), the structures of detected intermedi-ates as well as any inferred transition state(s), as well aseffects of temperature, pH, ionic strength, and solvent. Thestructural mechanism begins with high-resolution struc-tures of the free enzyme as well as it complexes withreaction substrate(s) and product(s), as well as any acti-vators or inhibitors of interest. But a structural interpreta-tion is incomplete unless it unifies the chemical, kinetic,and regulatory mechanisms. The regulatory mechanismshould explain how an effector molecule lowers (activa-tion) or raises (inhibition) the activation energy of one ormore steps in the catalytic reaction cycle. Likewise, theeffect of any post-translational modifications should bereconciled with changes in the catalytic reactionmechanism.

The optimal approach for integrating such informationis to construct rival hypotheses that make testablepredictions connecting structure, energetics, and kinetics.Ideally, these rival explanations will result in kineticallydistinguishable properties. Enzyme chemists makestrenuous demands on structural and chemical informa-tion, and kinetic data often offer additional constraints fordeciding on the most likely of rival reaction mechanisms.Modern enzymology has benefited enormously from theatomic-level molecular structures, as provided by X-raycrystallography and high-resolution, multidimensional


NMR spectroscopy. Even so, while structural biologistshave glimpsed various stages of catalysis, there is no suchthing as a tell-all ‘‘motion picture’’ of even the simplestcatalytic process. These days, there are those enzymechemists who won’t believe anything without first seeingit, while others don’t see anything without first believingit. While we would desire to view catalysis froma vantage point of quantum mechanics, the chief obstacleto applying quantum mechanical approaches is thatenzymes are complex structures, frequently possessing10,000–15,000 atoms, the positions of which are rarelyknown with adequate accuracy. Enzyme structures arealso strongly influenced by seemingly countless non-covalent bonding interactions, and each non-covalentinteraction contributes a relatively small increment to theconformational energy associated with an enzyme’scatalytically active conformation. Dealing with so manyweak interactions remains a daunting challenge forcomputer software developed to treat far simpler mole-cules. Even when quantum mechanical calculations arelimited to a small segment or region within an enzyme(say the active site region), quantum mechanical andmolecular mechanical models can quickly becomeunwieldy. Even so, one can safely predict that, withadvances in computer-based calculations, quantummechanics may eventually prevail, as it promises to offerthe ultimate picture of catalysis.

An enzyme mechanism must provide much more thanjust the changes in covalent structure. A mechanism mustalso explain the enzyme’s actions during catalysis – allsubstrate binding interactions, all stereochemical trans-formations, all pathways for product release, solvationchanges in active site, etc. The same also goes for changesin coenzymes, cofactors and metal centers. Enzyme kinet-icists also seek to understand those structural, dynamic, andcatalytic changes that are the basis of an enzyme’s regula-tory behavior. Allosteric activators and inhibitors ofenzymes have the effect of respectively lowering and raisingreaction barrier(s), as do the activating and inhibitory effectsof post-translational covalent modifications of enzymes.Allosteric transitions often involve a manifold of proteinconformational states, the complexity of which imposessuch kinetic ambiguity that one cannot reach penetratingconclusions about how an allosteric modifier alterscatalysis.

1.4.1 Chymotrypsin: The PrototypicalBiological Catalyst

Chymotrypsin was among the earliest crystallizedenzymes, and its purity and abundance stimulated greatinterest in this amidohydrolase. The probable catalyticmechanism for chymotrypsin has been worked out duringthe past half-century of intensive investigation. This

enzyme cleaves peptide bonds within peptides andproteins, acting preferentially at sites where the carboxyl-donating amino acid residue has a hydrophobic side-chain.The reaction is facilitated by push–pull proton transferinvolving specific imidazole, carboxyl, and hydroxylgroups that are common to hundreds of other mechanisti-cally related enzymes in the ‘‘serine’’-protease super-family. An acyl-serine intermediate permits one product(designated by the R-group in Fig. 1.3) to dissociate, suchthat water can replace the departing amino group ina manner that leads to hydrolysis of the peptidyl acyl-enzyme and subsequent release of the second peptidefragment (designated by I9). Enzyme chemists arereasonably confident of the general outline of the stepsillustrated in Fig. 1.3, especially in the light of the wealthof structural, chemical, and kinetic information gleanedfrom persistent and systematic investigation.

Figure 1.4 illustrates the following key points aboutserine-protease (and serine esterase) catalysis: (a) thesubstrate and enzyme are structurally complementary withrespect to each other, with specificity determined by thenature of charged residues deep within the active site;(b) the mechanism exploits general base catalysis (seeSection 7.3.9: Brønsted Theory of Acid and Base Catal-ysis) by imidazole to activate the hydroxyl group of theactive-site serine residue; (c) the latter exhibits nucleo-philic catalysis, as evidenced by the formation of a tetra-hedral adduct; (d) the enzyme stabilizes the tetrahedraltransition state (and the transient covalent intermediate)through hydrogen bonding between enzyme and interme-diates, particularly within the oxy-anion hole and by theelectrostatic environment, provided in part by Asp-102;(e) the reaction proceeds onward by means of general acidcatalysis that facilitates the departure of the leaving groupto form the acyl-enzyme (covalent) intermediate anddeparture of the amine (or alcohol) leaving group; and (f)the remaining steps in the catalytic cycle are formally thereverse of the above steps, resulting in hydrolysis of theacyl-enzyme, which commences with the imidazole groupactivating water by general base catalysis, so as to facil-itate nucleophilic attack by water at the carbonyl carbonatom. A major limitation relates to an almost exclusivereliance on synthetic chromogenic substrates (i.e., thosegenerating a change in the substrate’s or product’s UV/visible spectrum upon peptide bond cleavage). Virtuallynothing is known about the details (e.g., steady-state andfast kinetics, reaction cycle energetics, hydrogen bondingof the water substrate, conformational dynamics, as wellas the formation and turnover of key intermediates)describing chymotrypsin catalysis when proteins serve assubstrates. In this respect, the mechanism shown inFig. 1.4 is still somewhat incomplete.

It is also worth emphasizing that despite the many stepsin the catalytic reaction cycle, chymotrypsin is a powerfulcatalyst, as evidenced by the infinitesimally low

20 Enzyme Kinetics

uncatalyzed rate (k ¼ ~10�13 s�1 at pH 7 at 298 K) ofpeptide bond hydrolysis compared to the correspondingreaction carried out in the presence of chymotrypsin (kcat ¼~10 s�1). The catalytic rate enhancement for chymotrypsinis thus an astonishing 100,000,000,000,000! As discussedthroughout this textbook, the occurrence of covalent reac-tion intermediates during catalysis in no way impedes an

enzyme. Enzyme chemists also learned for certain thatenzymes exploit a myriad of intermediates to achieve suchhigh catalytic rate enhancements.

Finally, chymotrypsin is first biosynthesized as theinactive storage form chymotrypsinogen. The latter is anexample of a zymogen – an inactive enzyme precursor, fromwhich an active enzyme can be generated enzyme-catalyzed

FIGURE 1.3 Likely mechanism for chymotrypsin catalysis. Form-1 is the substrate-free enzyme, with its catalytic triad consisting of the

solvent-inaccessible, side-chain carboxyl group of Aspartate-102, the side-chain imidazole group of Histidine-57, and the side-chain hydroxyl group

of Serine-195. The location of these functional groups within the active-site cleft is depicted in the accompanying chymotrypsin structure (inset on

upper right), based on the X-ray crystallographic work of David Blow. After substrate binding to an initial, reversible enzyme-substrate Michaelis

complex, the catalytic triad in Form-2 facilitates nucleophilic attack by activating the otherwise poorly reactive serine hydroxyl group. A key point

is that partial bond formation, and the resulting hydroxyl group polarization is sufficient to accelerate catalysis; formal ionization of the serine

hydroxyl group is unlikely, because the alkoxide (pK near 15) is a far stronger base than the imidazole (pK¼6). Upon nucleophilic attack, the

carbonyl group is converted to the tetrahedral ‘‘oxy-anion’’ intermediate (Form-3), a transition-state that is stabilized by two hydrogen bonds (dashed

lines) supplied by two backbone peptide N–H groups from Glycine-193 and Serine-195. The oxy-anion spontaneously rearranges to form the covalent,

acylated enzyme (Form-4). After the amine-containing product departs, the reaction cycle then proceeds with its second phase, commencing with the

entry of water molecule into the active site (Form-5). Nucleophilic attack by this water molecule results in the second tetrahedral intermediate (Form-6),

again stabilized by the hydrogen bond network. This second oxy-anion species spontaneously rearranges to form the reversible Michaelis complex

(Form-7), with the active site occupied by the carboxyl group-containing product. The same double-displacement, or Ping Pong, pathway is likely to

apply to hundreds of other members of the ‘‘serine’’ protease superfamily, including trypsin, elastin, and thrombin. Specificity is achieved by inter-

actions with other substrate-recognition residues not indicated here.


proteolysis. While still elongating from the ribosome, thenascent polypeptide chain is directed to and translocated intothe lumen of secretory granules, where it is oxidativelyprocessed to introduce essential –S–S– bonds. Uponhormone-stimulated release into the small intestine,chymotrypsinogen is then cleaved between residues 15 and16 by trypsin to yield two polypeptide chains that remainlinked by means of a single disulfide bond. This peptidecleavage process (Reaction: Chymotrypsinogen þ H2O #p-Chymotrypsin) generates an intermediate species, knownas p-chymotrypsin, which has an imperfectly formed activesite and is hence a feeble catalyst. p-Chymotrypsin thenundergoes autocatalysis (see Section 3.8.4), with peptidebond cleavage (Reaction: p-Chymotrypsin þ H2O #Chymotrypsin þ Peptides) achieved through the action ofchymotrypsin and itself forms a second fully active chymo-trypsin molecule. The latter consists of three disulfide-linkedpolypeptides: Chain-A, the N-terminal region ending atresidues 1 to 14; Chain-B, the longest chain comprisingresidues 16 to 146; and Chain-C, comprising the C-terminalregion, beginning at residue 149. Note that two shortpeptides, consisting of residues 14–15 and 147–148, have nocatalytic role and are released to form the active enzyme.Fully active chymotrypsin possesses an ‘‘oxy-anion hole’’that accommodates the negatively charged tetrahedralintermediates already described in Fig. 1.3, thereby affordingyet another way to promote catalysis by stabilizing anobligatory reaction intermediate.

1.4.2 Ribozymes

From the earliest times, enzymes were always associatedwith proteins, and the inspired work of Nobel LaureateJohn B. Sumner on the crystallization of jack bean urease

placed such ideas on a firm footing. Even so, NobelLaureates Thomas Cech and Sidney Altman demonstratedthat certain RNA molecules are highly efficient catalystsfor RNA self-splicing, phosphotransfer, and evenpeptide bond formation (Altman, 1993; Cech, 1993). Thesecatalytic RNA molecules, also known as ribozymes,often achieve rate enhancements approaching 1011. Thehammerhead-shaped ribozyme (Fig. 1.5) was the first RNAmotif observed to catalyze sequence-specific self-cleavageby a magnesium ion-dependent transesterification. Con-taining only around 30 nucleotides in their catalytic cores,these ribozymes are the smallest of the catalytic RNAmolecules. These enzymes display Michaelis-Mentenkinetics in their action on substrates (see Section 5.6:Ribozyme Kinetics), with Michaelis constants (Km) valuesranging from 20 to 200 nM and turnover numbers (i.e.,kcat) in the range of 0.03 s�1. Product release is generallyfast, suggesting that the rate-determining step is phospho-diester bond-scission.

Ribozyme-mediated phosphoryl transfer appears toinvolve destabilization of the substrate’s ground-state(see also Section 1.5.4: ‘‘Reacting Group Approxima-tion, Orientation and Orbital Steering’’ under Section1.5: Explaining the Efficiency of Enzyme Catalysis).Magnesium ion complexation and hydrogen bondingstabilize the negative charge that develops on theleaving group during entry of the nucleophile. Thistransesterification reaction is mechanistically analogousto that used in the mRNA spliceosome as well as inother DNA topoisomerase and transposition reactions.The true catalytic nature of the ribozyme was demon-strated by the discovery that the RNA component ofRNase P catalytically processed tRNA precursors(Altman, 1993).

N

NH 2

O

N O

O O

O P O

HO

O

P

O O O

2+ (O H 2 ) 4

5'-End

5'

Me

Group-Leaving

Scheme 1.4

Scheme 1.4 illustrates the likely catalytic path for self-splicing reaction of group-II introns, which requires theproper folding of intronic RNA into its enzymatically

Catalytic

RNALoop-3

Loop-2Loop-1

Stem-3

Stem-2Stem-1

N N

N N N

N

N

N N N N

N,

U,

N, N, N, N,N, 5, 3,

N, N,

N,N,

N, N,

Cleavage Site

CU

AA

AA

A

G

G

X

FIGURE 1.4 Generalized base-pair structure of hammerhead ribo-

zymes. Shown are consensus nucleotide residues (marked G, C, A, U)

within the central ring consisting of 17 nucleotides (aqua) as well as vari-

able nucleotides (N). This secondary structure is stabilized by three runs of

hydrogen-bonded nucleotide pairs forming the same type of ‘‘stem-and-

loop’’ structural elements that are frequently observed in folded, single-

stranded messenger RNA and ribosomal RNA. The central ring and the

variable-length loops (indicated by dashed lines) facilitate folding into

a compact, sphere-shaped tertiary structure. Self-cleavage site is indicated

in red.

22 Enzyme Kinetics

active form. The reaction mechanism probablycommences with metal ion-assisted loss of a proton ribose29-OH, allowing the incipient 29-alkoxide to attack thephosphodiester. Upon forming a pentavalent oxy-phosphorane intermediate (with opposing nucleophile andexiphile), the rate-limiting step is likely to involve P–Obond scission. The active-site metal ion both facilitatesintronic RNA folding as well as stabilizes the transitionstate. With the notable exception that pancreatic Ribo-nuclease A employs imidazole group in place of a metalion to polarize the 29-OH, the catalytic reaction cycles ofRNase and self-splicing reaction of group-II introns areremarkably similar.

The discovery of catalytic RNA reminds us that oneshould not dismiss the possibility that other biologicalsubstances (e.g., polysaccharides, complex lipids, etc.) mayprove to be biological catalysts. The phenomenon ofmicellar catalysis, for example, is already firmly rooted inmodern organic chemistry. In fact, some micellar catalystseven exhibit chiral recognition (i.e., the capacity to combinewith and transform substrate molecules in a stereoselectivemanner). The likely role of biomembranes in catalysisremains to be determined.

1.4.3 Mechanoenzymes

Over the past century, biochemists have discoveredliterally thousands of different enzyme catalyzed reac-tions. A compilation by Purich and Allison (2002) putsthe number at nearly 7,000 unique catalytic activities, butdata from various genome projects suggest there arelikely to be another three to five thousand more enzymeswhose reactions remain to be defined. A large numberappear to be protein kinases, receptor-linked GTP-regu-latory proteins, and chromatin remodeling enzymes, aswell as enzymes mediating micro-nutrient metabolism.Based on the ways that enzymes break, rearrange, andform covalent bonds, and guided largely by organicchemical principles that distinguish reaction types, theEnzyme Commission defined the following classificationscheme.

Class-1: Oxidoreductases – catalyze oxidation/reductionreactions.

Class-2: Transferases – catalyze group-transfer reactions.

Class-3: Hydrolases – catalyze hydrolytic cleavage ofcovalent bonds.

Class-4: Lyases – catalyze addition and elimination of func-tional groups to unsaturated and saturated carbon atoms.

Class-5: Isomerases – catalyze rearrangement of atoms orgroups of atoms.

Class-6: Ligases – catalyze joining of molecules or func-tional groups.

Enzyme science has traditionally focused on the organicchemistry of biochemical reactions, particularly the changesin covalent bonding as substrate is transformed into product.This rewarding enterprise helped to establish the role ofcountless covalent and ionic intermediates as well as therole of coenzymes and other cofactors. It’s a historic fact,however, that Boyer’s discovery of the ATP synthasemechanism was delayed by the failure of researchers torealize that the driving force for ATP synthesis was nota high-energy covalent intermediate, as ironically he hadhimself originally proposed (Boyer, 2002). Peter Mitchell’schemiosmotic principle ultimately illuminated the need torationalize how Gibbs free energy, stored in the form ofa transmembrane proton gradient, can drive ATP synthesisfrom ADP, Pi, and Hþ, and vice versa.

Contemporary biochemistry has demonstrated time andtime again that many reactions have: (a) substrate-like orproduct-like protein conformational states differing only intheir non-covalent bonding interactions: or (b) substrate-like or product-like state corresponding to transmembranesolute gradients. Various ATP- and GTP-dependent molec-ular motors, for example, rely on the free energy of ATPhydrolysis to drive protein conformational changes, whichin turn drive processes like muscle contraction, organelletrafficking, and cell crawling. Structural metabolismrepresents the ceaseless building-up and tearing-down of thecell’s macromolecular and supramolecular structurethrough the ATP- and GTP-dependent affinity-modulatedinteractions of chaperonins and proteasomes, molecularmotors, pumps, latches, and switches. Other reactions, suchas the facilitated exchange of tightly bound protein–ligandcomplexes or membrane carriers, strictly involve changes innon-covalent bonding and proceed without the breaking/making of even a single covalent bond. In short, mecha-noenzyme catalysis involves non-covalent substrate-likeand product-like states, and the failure to include these indescribing mechanoenzyme reaction has led to confusion inenzyme nomenclature and classification.

To provide a rational framework for the systematicclassification of enzymes, including mechanoenzymes,Purich (2001) offered a new definition for an enzyme:

‘‘An enzyme is a biological catalyst for making and/orbreaking chemical bonds.’’

While appearing to be no more encompassing thanexisting definitions of enzyme catalysis, the crucialdifference lies in the use of chemical in place of covalentto describe the bonding changes. This definitionacknowledges those enzymes catalyzing the interconver-sion of non-covalent substrate- and product-like states orconditions:

Interaction State-1 + ATP + H20 Interaction State-2 + ADP+ Pi

Scheme 1.5


Biological catalysis of this type is observed in instanceswhere the substrate is a protein with a very slowly disso-ciating ligand. An example is the adenine nucleotideexchange reaction of the cytoskeletal protein actin.Hydrolysis of actin-bound ATP during cell motility leads tothe formation of tightly bound Actin$ADP. Spontaneousexchange of solution-phase ATP with Actin$ADP toregenerate Actin$ATP is too slow to sustain the high fila-ment assembly rates (400–500 monomer/filament/sec)needed to sustain cell motility. To overcome this kineticobstacle, motile cells have high concentrations of profilin,a 15-kDa regulatory protein that catalyzes the followingprotein–ligand exchange reaction:

Profilin + Actin·ADP Profilin·Actin·ADP

Profilin·Actin·ADP [Profilin·Actin·__ ]‡ + ADP

[Profilin·Actin·__ ]‡ + ATP Profilin·Actin·ATP

Profilin·Actin·ATP Profilin + Actin·ATP

Scheme 1.6

Red- and blue-colored nucleotides are used in Scheme1.6 to indicate that the reaction is one of physical exchange,as opposed to the transfer of a phosphoryl group fromunbound ATP to form actin-bound ATP. Profilin acceleratesthis reaction by a factor of 150, and profilin’s action iswithout effect on the exchange reaction equilibrium. Asshown in Fig. 1.5, profilin binds preferentially to nucleotide-free actin, approximately 12-times more tightly than toactin$ATP, and 72-times more tightly than to actin$ATP(Selden et al., 1999). Profilin’s preferential interaction withnucleotide-free actin explains its ability to promote

nucleotide exchange, and this property is indistinguishablefrom the cardinal feature of all catalysts, namely transition-state stabilization. Such considerations demonstrate unam-biguously that biological catalysis can take place withoutthe breaking and making of covalent bonds.

In his timeless book The Nature of the Chemical Bond,Linus Pauling (1945) offered the following definition thathas guided my thinking about enzyme catalysis:

‘‘We shall say that there is a chemical bond between twoatoms or groups of atoms in case the forces acting betweenthem are such as to lead to the formation of an aggregatewith sufficient stability to make it convenient for the chemistto consider it as an independent molecular species.’’

Significantly, Pauling made no mention of covalent bonds,stressing instead the unifying nature of chemical bonds.That many protein conformational states and numerousprotein–ligand complexes have been shown to be suffi-ciently long-lived to exhibit chemically definable propertiessuggests that transformations in these non-covalent inter-actions ought to be treated as chemical reactions. And withmodest tinkering, Pauling’s definition of a chemical bondcan be extended to include the persistent, definable positionof a solute relative to the inner and outer faces ofa membrane. Solutein and Soluteout therefore representsubstrate-like and product-like states in reactions catalyzedby passive transporters (e.g., Solutein # Soluteout) andactive transporters (e.g., Solutein þ ATP # Soluteout þADP þ Pi; or, Solutein þ Gradient-State1 # Soluteout þGradient-State2). The now classical work by Americanbiochemist Ronald Kaback demonstrated how lactosepermease couples lactose transport to a transmembraneproton gradient.

Another example of non-covalent catalysis is the Naþ-glucose symport system, which mechanochemically linksthe energy stored in a transmembrane sodium gradient todrive glucose uptake. This transporter operates by the samerandom substrate addition mechanism as that observed withenzymes like hexokinase and creative kinase.

Na+

Na+

Na+

Na+

Glc Glc

Glc Glc

Tin

Tout Na+

Tout

Tout GlcTout Glc Na+ Tin Glc Na+

Tin Na+

Tin Glc

Scheme 1.7

In Scheme 1.7, the isomerization of the central pathwayrepresents the conversion of the transporting enzyme fromits outside conformation Tout to its inside conformation Tin.Only when the sodium ion and glucose sites are occupied

Uncatalyzed

Catalyzed

Reaction Progress

Complex2 Complex1

PE+ AD+T PE+AT+ D

G

PE▪X++

X++

FIGURE 1.5 Profilin catalysis of exchange of solution-phase ATP

with actin-bound ADP to form solution-phase ADP with actin-bound

ATP. Symbols used are: A, Actin, AD, Actin$ADP ¼ Substrate; AT,

Actin-ATP ¼ Product, PE, Profilin acting as an Enzyme; Complex1 ¼ProfilinE$Actin$ADP ¼ Enzyme$Substrate Complex; Complex2 ¼ProfilinE$Actin$ATP ¼ Enzyme$Product Complex. Note: Profilin

catalyzes physical exchange of the entire nucleotide molecule, and not

phosphoryl transfer.

24 Enzyme Kinetics

does the symporter operate. Note again that no covalentbond-making/-breaking steps are involved. Binding ofsodium ion actually increases the affinity of enzyme forglucose to such an extent that greatly favors the upper path(Crane and Dorando, 1980).

Foldases are mechanoenzymes that catalyze rate-limiting steps along the folding pathway of a protein,including the cis-trans isomerization of peptidyl-prolylbonds as well as the formation/isomerization of disulfidebonds. Molecular chaperones (sometimes regarded to bea specialized class of foldases) are highly conservedconformation-isomerizing enzymes found in all livingsystems. They facilitate folding by interacting with mis-folded polypeptide chains, but they do NOT become part ofthe final structure or alter the equilibrium poise of theProteinunfolded # Proteinfolded equilibrium. Among the best-characterized molecular chaperones are GroEL-GroES andDnaK-DnaJ-GrpE systems that are found in the cytoplasmof Escherichia coli. Other molecular chaperones includeClp ATPases, HtpG and IbpA-IbpB.

As will be discussed in Chapter 12, non-covalentsubstrate-like and product-like states are of paramountimportance in the action of mechanochemical enzymes (orsimply mechanoenzymes). These highly specializedenzymes use chemical bond energy to perform work (i.e.,generate a force F over a distance Dx). Chemical-to-mechanical energy transduction is accomplished by meansof an affinity-modulated binding interaction, generallyusing the Gibbs free energy of ATP (or GTP) hydrolysis tocontrol the strength of their binding to their metabolic target(e.g., other enzymes, proteins, transported substances,cytoskeletal and membrane components, as well as nucleicacids). Although each mechanoenzyme has its distinctivemechanistic features, the general scheme can be depicted asfollows:

where the braces are used to indicate complexes, and theasterisk indicates a conformationally energized species.Note also the various states where the mechanical work canbe accomplished. The field of cell biology can be largelyregarded as structural metabolism, where the supramolecular

components are formed, remodeled, and degraded enzy-matically. Endocytosis and organelle traffic, cell crawling,signal transduction, and mitosis/meiosis are processes thatare taking on the appearance of the pathways of intermediarymetabolism. Even long-term potentiation, a neuronalprocess lying at the root of our memory and consciousness, isnow known to depend on actin polymerization motors tomaintain and/or remodel dendritic spines into synapses.

Because these energy-driven, affinity-modulated mechano-enzymes must be distinguished from energy-dissipatinghydrolases (e.g., ‘‘ATPases’’ and ‘‘GTPases’’), Purich(2001) indicated the need for an additional enzyme class:

Proposed New Class: Energases – catalyze the transduc-tion of chemical-bond energy into noncovalent interactionsthat generate force and do work.

While instituting a new class represents a challengingtask – one involving upwards of 1,000 enzymatic activities,those resisting such change ignore the obvious: enzymenames and classes should account for the entire chemicalreaction – and not just the covalent chemical bonds.

Finally, although many of the enzymes described hereare relatively feeble catalysts (e.g., profilin’s rate enhance-ment e is only ~140–150), especially compared to otherenhancement factors of 1015, the phenomenon of catalysishas nothing to do with the magnitude of rate enhancements.If the uncatalyzed reaction (or reference reaction) is alreadyfairly rapid, the catalytic rate enhancement need not be greatfor the catalyzed rate to proceed on a physiologicallymeaningful time-scale. Natural selection provides a ration-ale for the attainment and maintenance of evolutionaryadvantages. Mutations making an enzyme more efficientthan necessary (i.e., ‘‘over-perfection’’) offer the cell nodurable advantage, and may even prove to be deleterious(e.g., by allowing undesirable accumulation of pathwayintermediates). Simply put, an enzyme need only be as gooda catalyst as Nature demands in the context of the overallbiochemical process.

1.5 EXPLAINING THE EFFICIENCYOF ENZYME CATALYSIS

Biochemists and chemists alike have struggled to explainwhy enzyme catalysis is so extraordinarily fast. As stated byWarshel et al. (2006), ‘‘the real puzzle is why the enzymereaction with the specific chemical groups (e.g., acids andbases) is so much faster than the reaction with the samegroups in solution.’’

The efficiency of biological catalysis is in fact so greatthat the best way to assess the efficiency is to compare thefree energies of activation DGact, which are by definitionproportional to ln(k). When comparing catalyzed anduncatalyzed processes, it is also essential to compare theactivation energies for and enzyme-catalyzed reaction and

StateS + Enz·ATP StateS·Enz-ATP

StateS·Enz·ATP + H20 StateS*·Enz·ADP·Pi·H+

StateS*·Enz·ADP·Pi·H+ StateP·Enz·ADP + Pi + H+

StateP·Enz·ADP + ATP StateP + Enz·ATP + ADP

StateS + ATP + H20 StateP + ADP + Pi + H+

Scheme 1.8


the corresponding reaction (i.e., the reference reaction) thatoperate by the very same mechanism, rather than just thesame chemical reaction as it occurs in water. Figure 1.6presents such a graph from Warshel et al. (2006) comparingeighteen different reactions in terms of DGcat, the activationenergy for the enzymatic reactions, DGp,w, the activationenergy for the corresponding reference reactions operatingby the very same mechanism in water, as well as DGw,w, theactivation energy for the actual mechanism in water.

Among the explanations for such phenomenal efficiencyare: the use of binding energy to stabilize reaction transitionstates, the catalysis-promoting role of electrostatics instabilizing transition states, the role of reactant approxi-mation and orientation (including orbital steering) inguiding substrate interactions with catalytic groups, the roleof low-barrier hydrogen bonds in stabilizing reaction tran-sition states, the coordination of acidic and basic groups in‘‘pushing’’ or ‘‘pulling’’ protons to and from reactants, therole of the enzyme in destabilizing substrate ground states,the formation of covalent intermediates in preserving grouptransfer potential, the roles of metal ions as templates,Lewis acids, and special redox states, as well as the catalyticrole of enzyme conformational dynamics, includinginherent force-sensing, force-managing and force-gener-ating mechanisms.

While enzymes simply must decrease the activationenergy for the reactions they catalyze, determining exactlyhow this is accomplished has stubbornly resisted quantita-tive explanations. Part of the answer is that enzymes aremost often catalytically processive, meaning that, beyond

some point in their respective catalytic cycles, they remaintenaciously associated with their reaction intermediatesuntil catalysis is accomplished. Their active sites are alsohighly flexible, facilely adapting to meet the needs for rapidacid-base and/or electron transfer reactions. Whencombined with their substrate, these active sites serve asideal ‘‘solvents’’ – at times aqueous protic solvents, and atother times nonaqueous protic solvents, while alwaysstabilizing the succession of enzyme-bound intermediatescomprising a catalytic cycle.

As we shall see throughout this book, virtually all classesof organic reactions observed in the chemical laboratoryhave one or more enzyme counterparts. Much as the mostsuccessful chemists, who exploit the laboratory to improvethe rates and yields of these reactions, enzymes haveexploited evolution to become highly effective catalysts. Atthis point, they have developed highly effective mechanismsthat doubtlessly take fullest advantage of catalytic strategiesas described in Sections 1.5.1 through 1.5.11, but optimizedfrom start to finish for extreme efficiency. The late British-American chemist Jeremy Knowles adopted the title‘‘Enzyme Catalysis: Not Different, Just Better’’ for hiscogent discussions of catalytic rate enhancement (Knowles,1991). His view was that enzymes operate by highly per-fected catalytic mechanisms that, with the exception of theirspeed and specificity, resemble those explored for decadesby physical organic chemists. That said, the development ofa precise quantitative model for enzymatic rate enhance-ment, even for a single enzyme, remains an elusive goal.While various explanations discussed below are based onprinciples from physical organic chemistry, nearly all focuson the stability of enzyme transition states and/or thedynamic flexibility of enzymes.

1.5.1 Stabilization of Reaction TransitionStates

Without specifying how, J. B. S. Haldane (1930) offeredthe idea that enzymes lower the activation energy forcatalysis. Linus Pauling (1946; 1947) took the matterfurther by attributing enhanced catalysis to an enzyme’sability to interact with and stabilize the reaction transitionstate (a proposal now known as Transition-StateStabilization).

EX++

EX

++

Stabilize EX++

ES ES

E+S E+S

The idea was that each enzyme becomes structurallycomplementary to the transition state, such that the

1 2 3 4 6 7 8 9 10 11 12 13 14 15 16 17 185Reaction System

50

40

30

20

10

0

G (kcal/m

ol)

ΔG++cat

ΔG++w,w

ΔG++p,w

FIGURE 1.6 Activation free energies for representative enzymatic

reactions (DGcat), reference reactions operating by the same mecha-

nism (DGp,w), as well as the actual mechanism in water (DGw,w). The

reactions are those catalyzed by: 1, ketosteroid isomerase; 2, aldose reduc-

tase; 3, carbonic anhydrase; 4, chorismate mutase; 5, trypsin; 6, haloalkane

delahogenase; 7, alkaline phosphatase; 8, Ras GTPase complexed to its

activating protein GAP; 9, triose phosphate isomerase; 10, acetylcholine

esterase; 11, lysozyme; 12, RNase (mono-ionic intermediate); 13, RNase

(di-ionic intermediate); 14, ATPase; 15, bacteriophage T7 DNA poly-

merase; 16, orotidine 59-monophosphate decarboxylase; 17, exonuclease

activity of DNA polymerase I (Klenow fragment); and 18, staphylococcal

nuclease. Figure and legend reproduced from Warshel et al. (2006) with

permission of the authors and publisher.

26 Enzyme Kinetics

geometry, polarity, and electrostatic charge of the enzymeand the transition-state configuration of the substrate aremutually stabilizing. Pauling (1947) wrote:

From the standpoint of molecular structure and thequantum mechanical theory of chemical reaction, theonly reasonable picture of catalytic activity of enzymesis that which involves an active form of the surface ofthe enzyme which is precisely complementary in structurenot to the substrate molecule itself, but rather to thesubstrate molecule in a strained configuration correspond-ing to the ‘activated complex’ for the reaction catalyzed bythe enzyme: the substrate molecule is bound to enzyme,and caused by forces of attraction to assume the strainedstate which favors the chemical reaction – that is, the acti-vation energy of the reaction is decreased by the enzyme toan extent as to cause the reaction to proceed at an appre-ciably greater rate than it would in the absence of theenzyme.

The key point is that the enzyme need not initially becomplementary to the transition state configuration. Anactive site that accommodates a reaction transition statewould also tend to stabilize those forms of the substrate thatmost closely resemble the transition state both geometri-cally and/or electronically. Transition-state stabilizationthus makes it easier for the substrate to reach and surmountthe transition-state, and the net effect should be greatlyenhanced chemical reactivity.

Note that little advantage would be gained if an enzymewere to stabilize both the E$S and E$Xz equally, because theactivation energy would remain the same as that occurringin the absence of the enzyme.

EX++ EX

++

EX++ EX

++

Stabilize

ES Only

Stabilize

EX

++Only Stabilize

ES & EX

++

ES

ES

ES

ES

E+S E+S E+S E+S

As we shall see in Section 8.6, these ideas are alsoconsistent with the action of both naturally occurring andsynthetic enzyme inhibitors that are structurally analogousto the reactant’s transition-state. By mimicking the transi-tion state, these analogues can bind to an enzyme withextraordinary affinity, simply because the enzyme need notdivert a great deal of its binding energy to rearrange theanalogue into a configuration resembling the reactant in itstransition state (Schramm, 2003; Wolfenden, 1969).

1.5.2 Electrostatic Stabilizationof Transition States

As the name implies, electrostatic catalysis is the conse-quence of the strong local Coulombic interactions that

stabilize ionic and polarized transitions states. The presenceof such charged groups actually makes the active site’s localenvironment significantly more polar than water (Warsheland Florian, 1998), allowing ionic transition states to bestabilized by nearby fixed dipoles. The nucleophilic andelectrophilic properties of functional groups on the catalystand reactant are also increased by dehydration of the cata-lytic center. In addition, electrostatic attraction and chargeneutralization tend to release water from enzyme activesites, thereby exerting a powerful activating effect onnucleophilic reactions.

Note that stabilization of the very same transition state inbulk water would require a substantial thermodynamicpenalty, referred to as a reorganization energy, for watermolecules to be arranged in a manner that stabilizes ionictransition states. In enzymes, the ionic groups are pre-organized by protein folding, such that the resulting facili-tated catalysis is attended by a very small reorganizationenergy. Folding of the enzyme creates a constellation ofpositively and negatively charged functional groups that areappropriately positioned for optimal catalysis. This conceptmay be extended to include catalysis-promoting changes inelectrostatic interactions as reactants proceed through thereaction cycle, including effects of conformational changesand hence enzyme dynamics on electrostatic interactionsand vice versa.

Coulombic interactions mainly occur among acid andbase groups in the enzyme (as well as ionizable groupswith its substrate). Metal ions also play important roles inelectrostatic catalysis. In some cases, other permanentlycharged side-chain groups (e.g., the guanidinium of argi-nine and the quaternary ammonium group of 3-methyl-histidine) may contribute to electrostatic stabilization oftransition states. Another advantage of electrostatic effectsis that they are ‘‘tunable,’’ meaning that the local envi-ronment can alter the pKa values of acidic and basicgroups. For example, when placed into a hydrophobicenvironment, acids tend to exhibit higher pKa values (i.e.,formation of the carboxylate anion –COO� is disfavored),whereas bases tend to have lower pKa values (i.e.,formation of cationic –NH3

þ groups is disfavored). Whenin the vicinity of a residue of like charge, acids likewisetend to exhibit higher pKa values, whereas bases tend tohave lower pKa values. When in the vicinity of a residue ofopposite charge, acids likewise tend to exhibit lower pKa

values, whereas bases tend to have higher pKa values.Finally, a-helices also have associated dipole momentsthat can also exert electrostatic effects on active-sitefunctional groups (Hol, 1985). Knowles (1991) discussedhow one particularly well-aimed helix in triose phosphateisomerase is trained on His-95, lowering the pKa value ofthe latter from an unperturbed value of 6 to below 4.5.

Charge neutralization can also exert a strong desolvatingeffect within active sites. Prior to neutralization, eachactive-site cation and anion binds several water molecules,


such that [Cation$(H2O)k]xþ þ [Cation$(H2O)l]

y� ¼[Salt$(H2O)(kþl)�m] þ mH2O.

Warshel et al. (2006) presented persuasive argumentsthat the catalytic power of enzymes may well be almostentirely the consequence of electrostatic stabilization ofthe transition state. Among the many examples, twoclassical cases are the lysozyme reaction, for which theoxacarbenium ion is stabilized by nearby carboxylgroups, and the chymotrypsin reaction, in which thetetrahedral oxy-anion intermediate is stabilized by theintrinsically electrostatic phenomenon of hydrogenbonding.

O

OHO

HOOH

OHO

O

O

O

The lysozyme mechanism was first analyzed computa-tionally by Warshel and Levitt (1976), who were among theearliest proponents of computer-based molecular modelingto assess the origin of enzyme rate enhancements. Ideally,one desires a quantum mechanical (QM) model defining allthe atoms in the reactant and catalyst. An inherent limitationon QM calculations, however, is that the required compu-tational time rises very steeply with increasing numbers ofatoms and electrons in the molecule(s) of interest, makingstudies of entire enzyme-reactant interactions totallyunworkable. To maneuver around this limitation, Warsheland Levitt (1976) pioneered a combined QM and molecularmechanical (MM) approach, restricting the quantumchemical description to the reaction center, while relying ona computationally efficient classical treatment for theremainder of the molecule. Based on their QM/MM resultswith lysozyme, Warshel and Levitt (1976) suggested thatthe positive charge developing on the C-1 carbon of theglucopyranosyl residue would be stabilized by the adjacent,electron-rich ring oxygen and the charge-neutralizingeffects of nearby glutamate and aspartate. Importantly, Sun,Liao and Remington (1989) used classical electrodynamicsto find that C–O bond breakage and the consequent chargeseparation is promoted by a large electrostatic field acrosslysozyme’s active-site cleft, created in part by a veryasymmetric distribution of charged residues on the enzymesurface. That other lysozymes of unrelated primarysequence have similarly distributed charged residues andelectric fields suggests the generality of electrostatic stabi-lization (~9 kcal/mol) as the basis for catalytic rateenhancement in lysozyme.

Because the hydrogen bond is primarily an acid-baseneutralization, electrostatic catalysis also explains the role

of hydrogen bonding in fostering catalysis. Two hydrogenbonds stabilizing the oxyanionic tetrahedral intermediate inchymotrypsin catalysis can contribute 7–8 kcal/mol oftransition-state stabilization, resulting in considerablecatalytic rate enhancement.

1.5.3. Intrinsic Binding Energy

Binding energy effects arise from the sum total of favorablenon-covalent interactions between an enzyme and itssubstrate(s), including a substantial contribution from vander Waals interactions associated with structural comple-mentarity of the enzyme and its substrate as well as desol-vation. The favorable enthalpy of substrate binding isthought to overcome the unfavorable entropy associatedwith bringing two (or more) molecules together. Onceformed, the E$S complex allows the catalysis to be effec-tively an intramolecular process.

Jencks (1975) suggested that enzymes gain greatadvantage over ordinary catalysts by managing the energyof binding interactions to orient substrates relative to eachother and with respect to catalytic groups within the activesite. Page and Jencks (1971) showed that the loss inentropy in going from a bimolecular to a unimolecularreaction (i.e., E þ S # E$S) results in the loss of trans-lational, rotational and vibrational degrees of freedom, thusaccounting for around 108 of the rate enhancementobserved in enzyme-catalyzed reactions. Based on resultsof their computer modeling of subtilisin interactions withmodel substrates, Villa et al. (2000) reached a completelydifferent conclusion – namely that the contribution of DSz

to DGz is much smaller than previously thought. Theysuggest that this is true because: (a) many of the motionsthat are free in the reactant state of the reference reactionare also free at the transition state; (b) the binding to theenzyme does not completely freeze the motion of thereacting fragments, so that DSz in the enzyme is not zero;and (c) the binding entropy is not necessarily equal toDSzwater.

1.5.4 Reacting Group Approximation,Orientation and Orbital Steering

Substrate binding to the active site promotes catalysis:(a) by converting multi-substrate reactions from bimolec-ular rate processes to what essentially becomes a uni-molecular rate process; (b) by increasing the effective localconcentration of reactants with respect to each other; and (c)by arranging and orienting reactant functional groups withrespect to each other. In most instances, intramolecularreactions occur at much faster rates than correspondingbimolecular reactions, and both proximity and orientationcan increase the effective local concentrations of reactants.As discussed in Chapter 3, this behavior is related in part tothe brief lifetime of collision and encounter complexes,

28 Enzyme Kinetics

leaving fleetingly short times for productive chemicalreactions to occur. Proper placement and orientation ofreactive groups is also recognized to play a major role incatalytic rate enhancement through stereo-electronic assis-tance, wherein reactants are arranged for maximal reac-tivity. Of course, orientation comes at a price (i.e., oftenmanifested by a decrease in entropy) which must be offsetby some other favorable catalyst–substrate binding inter-actions in regions that are immediately adjacent to the bondsthat are broken and/or made during catalysis.

Inspired by the then obvious success of the conservation-of-orbital-symmetry rules (Woodward and Hoffmann,1970) in explaining reactivity, Storm and Koshland (1970)proposed and Dafforn and Koshland (1971; 1973) suggestedthat enzymes may promote catalysis by precisely aligning(steering) the molecular orbitals of their substrates. In theearliest versions of Orbital Steering, enzyme-enforcedconstraints on molecular orbital alignment were viewed asso restrictive as to be physically unrealistic, and theproposal was roundly dismissed on the basis of the antici-pated high thermodynamic penalty for extremely preciseorbital alignment and the weak dependence of forceconstants on slight changes in bond angle (Bruice, 1972;Jencks and Page, 1974).

Noting that the contribution of orbital steering tocatalytic rate enhancement cannot be quantified in theabsence of an accurate means for correlating structuralinteractions and catalytic enhancement, Scott (2001)argued that orbital steering may explain aspects of RNAcatalysis. For ribozymes, orbital steering appears to befortuitously uncoupled from conformational, distance andorientation effects. During hammerhead ribozyme catal-ysis, two conformational changes appear to align theorbitals of reacting atoms, and Scott (2001) suggested thateach of these two conformational changes is likely toprovide rate enhancement 3 of ~1,000. With an overallrate enhancement of 106 that is solely attributable toorbital steering, Scott (2001) suggested that orbital steer-ing is a significant factor in the catalysis of ribozymes andprotein enzymes.

For additional comments on orbital steering and itsimplications, the interested readers should consult valuablereviews by Hackney (1990) and Mesecar, Stoddard andKoshland (1997).

1.5.5 Reactant State Destabilization

In this case, the enzyme strains or distorts the substratewhile still in its ground-state, making the reactant(s) lessstable and thereby lowering the energy difference (indicatedby red arrows) between strained reactant(s) and transitionstate. (Note: The terms ground-state destabilization (GSD)and reactant-state destabilization (RSD) are interchange-able.) Some form of reactant distortion, bond strain, bond

polarization, E$S conformational change, and/or electro-static effect would presumably be required.

EX

EX++

EX

++Only

Form Unstable

ES Complex

Stabilize

ES ES

E+S E+S

Perhaps the best-known version of ground-state destabi-lization is the Circe Effect. Jencks (1969) suggested thathighly favorable substrate binding interactions in a substrate’snonreactive region may facilitate catalysis by forcing thesubstrate’s reaction center into a destabilizing environment.The Circe Effect is viewed as using substrate binding energyto help reacting groups to approach the transition state. Thename of this effect derives from the mythic Greek enchantressCirce whose sweet songs beguiled passersby to her island,where they were then transformed through the action of hervarious spells and potions.

Bruice (2002) suggested that an enzyme positions itssubstrate(s) in a conformation, such that thermal fluctua-tions allow that conformation to easily surmount the barrierto reaction. The basic idea is that for covalent bondformation, reacting atoms of substrate and enzyme mustfirst come together within a suitable reaction distance (say3–4 A) and approach angle (say 5–10�), such that suitablyrearranged and highly reactive ground-states, termed Near-Attack-Conformers (NACs), would thereby acceleratecatalysis. In this explanation, the enzyme might bindstrongly to a transition-state structure, but this bindingenergy is not thought to be released specifically to speedthe reaction (Luo and Bruice, 2004; Torres, Schiott andBruice, 1999). Except for the speculative role of anti-correlated motions of proximal residues in destabilizing thesubstrate (Luo and Bruice, 2004), the notion of NACsmerely restates the obvious, in that reactant-state destabi-lization is merely an alternative description of transition-state stabilization. Warshel et al. (2006) noted that, if boththe reactant state (RS) and transition state (TS) for anenzyme-catalyzed reaction were to have similar chargedistributions, the same preorganization effects are apt tostabilize the RS and TS, leading to an apparent NAC effectby making the RS structure closer to that of the TS. Theythus argue that the so-called NAC effect is an expectedresult of the TS stabilization rather than the underlyingcause of catalysis.

In a sense, if Near-Attack-Conformers are viewed asenzyme-stabilized ‘‘pre-transition-state’’ structures facingonly a modest barrier to reaction, they might just as well bethought of as part of an ensemble of enzyme-stabilizedtransition states. Indeed, the smaller the barrier to reaction,the more like a stabilized transition state would be an NAC.


1.5.6 Acid/Base Catalysis

As discussed in Chapter 2, formation of formal cationic oranionic species, each respectively possessing fully devel-oped electronic charges on the electron deficient or electron-rich atom, is a highly improbable event that necessarilyresults in a high DEact for reaction. Acids and bases oftenimprove reactivity, and transfer of a proton (to the reactant byan active-site acid and from the reactant by an active-sitebase) has the effect of lowering the energy of the transitionstate, thereby reducing the activation energy DEact. An evengreater enhancement is attained by the coordinated action ofan acid and base, as in the case of an active-site base attackinga carbonyl, with attendant protonation by an active-site acid.

R S

O

R

A

H

B:

Scheme 1.9

The virtually simultaneous action of nucleophilic attackand protonation (Scheme 1.9) requires additional structuralorganization within the active site, requiring appropriateorientation of enzyme functional groups. If the energypenalty for pre-organization is ‘‘paid’’ upon folding of thenascent protein, much as suggested for electrostatic catal-ysis, then acid/base catalysis requires no additional energypenalty for functional group orientation.

Numerous observations confirm that complete protontransfer need not occur. In fact, significant advantagesaccrue when a Brønsted acid partially donates a proton to(or when a Brønsted base partially abstracts a proton from)a reaction center (see Section 7.3.9: Brønsted TheoryExplains Important Aspects of Acid/Base Catalysis).

Finally, because the equilibrium between the active-sitebase and its conjugate acid (or the active-site acid and itsconjugate base) is coupled to the catalytic cycle, enzymeactivity frequently displays a pH-dependence. Althoughsteady-state kinetics is effective in discerning the pHdependencies for Km, Vm, or Vm/Km, the pH-dependence ofelementary reactions rates is far more revealing. This is truebecause steady-state parameters like Km, Vm, or Vm/Km arecomplex collections of elementary reaction rate constants,whereas fast kinetic studies directly establish the pHdependence of individual elementary rate constants.

1.5.7 Covalent Catalysis

Covalent catalysis refers to any catalytic rate enhancementgained from transient formation of covalent reaction inter-mediates. That thousands of enzymes form covalent

intermediates confirms that significant advantages must begained from their formation. Enzymes organize covalentintermediate formation and turnover into discrete stages:first, there is a nucleophilic stage, in which a catalyticfunctional group attacks the substrate to form a covalentbond; second, electrons are withdrawn by the now electro-philic catalyst; and third, rupture of the covalent bondpermits further reaction and regenerates the enzyme-basednucleophile. The latter is typically the functional group ofa lysine, histidine, cysteine, aspartate, glutamate, and serineresidue within an enzyme’s active site. Many coenzymes(e.g., pyridoxal 5-phosphate, biotin, lipoamide, thiamindiphosphate, tetrahydrobiopterin, and even NADþ and FAD)also play essential roles in forming covalent intermediates.

As discussed by Jencks (1963; 1969), formation of a covalentintermediate per se is insufficient for highly effective covalentcatalysis: beyond reacting rapidly, the active-site nucleophilemust yield a product that is itself highly reactive. He alsoasserted that the chief advantage of enzymatic covalent catalysisis that reaction mechanism can be organized in a manner thatmanages entropy changes (Jencks, 1975) while maintaining thegroup transfer potential of substrate-derived moieties (e.g.,phosphoryl groups, amino groups, nucleotidyl groups, etc.).

That covalent catalysis requires a highly reactive active-site nucleophile is well illustrated by the following tworeactions. In the case of bacterial acetoacetate decarboxylase(Reaction: Acetoacetate # Acetone þ CO2), the groupheaded by Frank Westheimer at Harvard Universitydemonstrated that the enzyme exploits its surprisingly acidice-amino group (pKa z 6.5), which is displaced by some fourpH units from that of a typical lysine side-chain amino group.

H2N NH

NH N

N H

NH2

H3C CH2C

O

CO

OH3C C

H2C C

O

O

EnzEnz

Enz

Enz

Enz

H3C CH2C C

O

OH3C C C H2

Enz

CO2

H

H

H3C C CH3

H3C C C H3

O

OH

Scheme 1.10

Shown in Scheme 1.10 is the likely mechanism showinghow the formation of imine and eneamine intermediates

30 Enzyme Kinetics

organizes stepwise decarboxylation (see Section 7.3.4 fora detailed discussion of this enzyme mechanism). Likewise,the research group headed by Daniel Santi at UC SanFrancisco demonstrated that thymidylate synthase (Reac-tion: dUMP þ Methylenetetrahydrofolate (CH2–H4Folate)# dTMP þ Dihydrofolate (H2Folate)) exploits covalentcatalysis to activate dUMP for subsequent substitution(Carreras and Santi, 1995). After forming a reversibleternary complex with its substrates, this synthase directs thenucleophilic attack of its active-site thiol on C-6 of dUMP,converting C-5 into a nucleophilic enol(ate) intermediate.Subsequent covalent bond formation ensues between thatsite and the one-carbon unit (at C-11) of CH2–H4Folate,itself having been activated by formation of an N-5 iminiumion. Proton abstraction from the second key intermediateand b-elimination of H4Folate yields the exocyclicmethylene intermediate. Hydride transfer from non-covalently bound H4Folate to the exocyclic methyleneintermediate is followed by b-elimination of the enzyme,producing dTMP and H2Folate as well as regenerating theoriginal active enzyme.

An added benefit of covalent catalysis is that reactiveintermediates can be shuttled from one active site to anotherin multi-enzyme complexes. One example is trans-carboxylase (Reaction: Methylmalonyl-CoAþ Pyruvate #Propionyl-CoA þ Oxaloacetate), which catalyzes a multi-site Ping Pong mechanism (Northrop, 1969).

H N

ENZYMEO

S

N

NH O

O2C

The transferred carboxyl group (shown in red) is carriedfrom one active site (First Half-Reaction: Enz þ Methyl-malonyl-CoA # Propionyl-CoAþ Enz–CO2

�) to a secondactive site (Second Half-Reaction: Enz–CO2

� þ Pyruvate# Oxaloacetate þ Enz) by means of a long arm consistingof a biotin cofactor (blue) covalently tethered to an3-amino group of transcarboxylase lysine residue (black).Another example is pyruvate dehydrogenase (PDH),a multi-enzyme system that uses five cofactors: NADþ,coenzyme A, thiamin diphosphate (TDP), lipoamide, andFAD. PDH catalyzes the overall reaction of pyruvate withNADþ and coenzyme A to produce acetyl-CoA, NADH,and CO2. PDH first catalyzes the TDP-dependent reactionof pyruvate with lipoamide to form S-acetyl-dihy-drolipoamide and CO2. Dihydrolipoamide S-acetyl-transferase next catalyzes the reaction of S-acetyl-dihydrolipoamide with coenzyme A to produce dihy-drolipoamide and acetyl-CoA. Then the FAD-dependentdihydrolipoamide dehydrogenase uses its active site tocatalyze the reaction of dihydrolipoamide with NADþ toproduce lipoamide and NADH. Without the intervening

synthesis of covalent intermediates, pyruvate dehydroge-nase catalysis would presumably require additional steps aswell as the release of reactive intermediates.

Finally, in some enzyme-catalyzed reactions, forma-tion of covalent intermediates also affords the opportu-nity to control overall reaction stereochemistry. Two SN2reactions are needed to form and transfer a reactivecovalent intermediate, a scheme that results in overallretention of configuration. With direct in-line transfer,however, only one SN2 reaction is needed, resulting inoverall inversion. Interestingly, for SN1 mechanisms, thestereochemical outcome depends on how the carbeniumion intermediate is intercepted. Because subsequentenzyme-catalyzed reactions within a metabolic pathwayare often stereospecific, the stereochemical course ofa preceding enzyme must be maintained, and a mecha-nism requiring covalent catalysis successfully fulfills thisrequirement.

1.5.8 Transition-State Stabilizationby Low-Barrier Hydrogen Bonds

A special type of transition-state stabilization, first sug-gested by Schowen (1988) and promoted by Cleland andKreevoy (1994), concerns the possibility that the protectedinterior of certain active sites may favor formation of stronghydrogen bonds, known as low-barrier hydrogen bonds(LBHBs). Unlike most other hydrogen bonds, which have2.9–3.3 A distance between electronegative atoms, thebond-length of low-barrier H-bonds is less than 2.5 A.Neutron diffraction experiments on crystalline compoundscontaining LBHBs indicate that the shared proton isdiffusely distributed around the bond’s midpoint, a findingsuggesting that LBHBs exhibit covalent nature (see alsoSection 2.2.3).

Cleland, Frey and Gerlt (1998) suggested that low-barrier hydrogen bonds may contribute upwards of fiveorders of magnitude in rate acceleration in any enzymaticreaction involving proton transfer from a general acid or toa base. Their argument goes as follows: LBHBs form whenthe atoms sharing the proton have identical pKa values; soany equalization of their pKa values should enhance H-bondoverlap, thus stabilizing the transition state and promotingcatalysis. Cleland and Kreevoy (1994) suggested thatLBHBs may provide up to 10–20 kcal/mol of transition-state stabilization; however, model studies on LBHBs putthe value at 4–5 kcal/mol in dimethyl sulfoxide and 3–6kcal/mol in tetrahydrofuran (Shan, Loh and Herschlag,1996). Usher et al. (1994) estimated the value to be nearer to2 kcal/mol, a value that comports with mutagenesis data(Fersht, 1987). Shurki et al. (2002) also questioned whetherLBHBs can account for catalytic rate enhancementsobserved with protein enzymes. Paradoxically, Warshelet al. (2006) argue that, when consistently defined,


low-barrier hydrogen bonds are more apt to exert an anti-catalytic effect.

1.5.9 Catalytic Facilitation by Metal Ions

Although enzyme- and substrate-bound metal ions exertpowerful electrostatic stabilization of transition states,metal ions are known to facilitate catalysis in many otherways. By taking advantage of the well-defined geometricarrangement of their inner-coordination spheres, transitionmetal ions often serve as templates that hold and orientreactive molecules during one or more phases of the cata-lytic reaction cycle. Metal ions are also highly versatileLewis acids (i.e., electron-pair acceptors) that can alter thereactivity of acidic and basic functional groups. Metal ionsalter the pKas of bound substrates as well as bound water,thereby improving their tendency to react. Metal ions alsotransiently switch oxidation states during catalysis, and insome cases, they achieve unusually reactive higher oxida-tion states. Ca2þ and Mg2þ also bind to ATP4� to formCaATP2� and MgATP2�, thereby activating the lattertoward nucleophilic agents (see Section 2.5: Metal Ions inEnzyme Active Sites).

1.5.10 Promotion of Catalysis via EnzymeConformational Flexibility

In seeking to summarize the mounting evidence for a role ofprotein dynamics in enzyme catalysis, Hammes (2002)offered the following comments:

When a substrate binds to an enzyme, it becomes an inte-gral part of the macromolecule. The subsequent dynamicsof the macromolecular conformational changes are thenthe catalytic process itself. This view of catalysis meansthat the making and breaking of non-covalent bonds withinthe structure are part of the catalytic process, and that theseevents can occur close to and far from the active site. Theadvantage of having hundreds of intramolecular interac-tions dynamically involved in catalysis is that the ener-getics of the reaction can be easily manipulated toproduce catalysis, and extremely fine-tuning is providedby hundreds of intramolecular interactions. This mecha-nism could be viewed as a ‘gear shift’ mechanism: theconformational transitions are analogous to shifting gears,and the interactions between the enzyme and substratecorrespond to the gear coupling mechanism. Asking what‘drives’ the reaction is not terribly meaningful, as theessence of cooperative processes is that many events areoccurring essentially simultaneously.

Hammes’ cogent comments are tantamount to sayingthat an enzyme creates a dynamic catalytic environment,one that promotes the trajectory of substrate to product byway of one or more reaction intermediates. Much as well-rehearsed actors cue each other, a succession of structuralcues, each created as the enzyme and reactant proceed

step-by-step through the catalytic cycle. As indicated inFig. 1.4, the same catalytic histidine residue acts as a: (a)general base by accepting the proton from the catalyticserine, thereby activating the latter’s nucleophilicity; (b)general acid by donating a proton to the nitrogen on theleaving group; and (c) general base that deprotonates andactivates the ‘‘hydrolytic’’ water.

In the context of Hammes’ comments, it seems clear thatconformational changes in chymotrypsin trigger changes incatalytic group reactivity and vice versa. Radisky et al.(2006), for example, found that atomic-resolution structuresof acyl-trypsin and enzyme-bound tetrahedral intermediateanalogue, along with earlier structures for the Michaeliscomplex, provide evidence of subtle active-site adjustmentsfavoring the forward progress of the acylation reaction. Itshould be emphasized that the energetics at each reactionstage can be finely tuned to facilitate catalysis withoutviolating the constraint that an enzyme cannot alter theoverall reaction’s equilibrium poise.

Mutual cuing between catalyst and reactant also fits withaction–reaction principles of classical mechanics. There-fore, although E$Xz is almost universally employed torepresent an enzyme-bound transition state, (E$X)z isperhaps a more appropriate indicator that both the catalystand substrate are mutually altered as they proceed througheach catalytic cycle. This effect represents an example ofthermodynamic reciprocity (i.e., a catalyst cannot affect thereactant without the reactant affecting the catalyst). Use ofE$Xz leaves a mistaken impression that only the substratereaches the activated complex or transition-state configu-ration. If this were the case, the intimacy of motions withinan enzyme-substrate would be ignored. Writing the overalltransition state as (E$X)z implies that enzyme and substratejointly achieve transition-state intermediacy, a processrequiring simultaneous motions in reactant and enzyme.

Another way of explaining the comparatively large sizeof enzymes is that catalysis is a complex, multi-step processrequiring an active-site environment that optimally stabi-lizes multiple transition states, each associated with its ownstep. Conformational flexibility is apt to be a hallmark ofeffective multistage reaction catalysis and even suggestswhy protein enzymes are apt to be more highly perfectedthan nucleic acid enzymes. Benkovic, Hammes andHammes-Schiffer (2008) suggested that:

Enzyme mechanisms should be viewed as catalyticnetworks with multiple conformations that occur seriallyand in parallel in the mechanism. These coupled ensemblesof conformations require a multi-dimensional standardfree-energy surface that is very rugged, containing multipleminima and transition states.

These features are shown in Fig. 1.7. As considered inSection 12.3, this concept was anticipated in the derivation ofa single-molecule Michaelis-Menten equation by Kou et al.(2005) who present a virtually identical view of an enzyme

32 Enzyme Kinetics

operating by a catalytic network with multiple conformations(see also Section 3.8: Transition State Theory).

Finally, although some nucleic acids serve as biologicalcatalysts, they are feeble in comparison to protein enzymes(Purich, 2005). One may therefore speculate that the fargreater conformational flexibility of proteins and theirconsequentially higher catalytic efficiency may have beenmajor driving forces in the early evolution away fromnucleic acid-based catalysts in favor of the far more versa-tile protein-based catalysts. Organisms managing to cata-lyze a reaction much faster than a rival should have enjoyeda substantial advantage. Retention of some roles for cata-lytic RNA also suggests that rate enhancement may not beas important for the catalysis of certain reactions.

1.5.11 Promotion of Catalysis via Force-Sensing and Force-Gated Mechanisms

As scientists, we should keep an open mind as to thepossibility that we have been trapped into thinking thatenzyme chemistry must operate by mechanisms thatresemble those for gas-phase and solution-phase organo-chemical reactions. The chemistry within enzyme activesites may eventually prove to be fundamentally different.All the enzymes that are known to catalyze some 10,000to 20,000 different reactions in living organismsconstitute an infinitesimally small subset of 20500 possiblepolypeptides of molecular masses of 50 kDa or less. Whatmay distinguish these 10,000 to 20,000 enzymes as therarest of the rare among those 20500 polypeptides is thateach has its respective reaction trajectory already pro-grammed into its conformationally compliant structure. Ifthis unique catalytic choreography avoids the nonproductivemolecular configurations inevitably made in gas-phase andsolution-phase reactions, an enzyme may not requirea significant energy input to populate productive configu-rations. For example, the observation that heating gas-phaseand solution-phase reactants increases molecular agitationand generally enhances reactivity is thought to be theconsequence of populating high-lying transition-stateconfigurations needed to convert a reactant into its product.Even so, heating of reactants also produces countlessnonproductive configurations, thereby greatly limiting thefraction of molecules that are appropriately oriented. Thus,while we now think in terms of reaction coordinatediagrams resembling those for solution-phase models,enzymes may accelerate reactions in ways that are beyondour reckoning, simply because we may be incorrectlyperpetuating the notion that enzyme mechanisms are ‘‘notdifferent, just better.’’ In carrying out covalent bond trans-formations, most enzymes may be acting in a manner that isfunctionally complementary to the action of mecha-noenzymes, meaning that they are programmed to makedirected motions via precise noncovalent bond rearrange-ments of the active site, and perhaps even the entire protein,so as to convert the covalent bonds of the substrate into thecovalent bonds of the product. Simply put, althoughenzymes undergo the same types of reactions and alsolikewise form many of the same types of intermediates asthose observed in cognate gas-phase and solution-phaseorganochemical, enzymes may not be confined by the rulesof physical organic chemistry, at least those rules gleanedfrom studies of corresponding gas-phase and solution-phasereactions.

There is reasonably general recognition that no singleproperty of an enzyme likely to underlie the origin of enzymerate enhancements and that each enzyme may exploitmore than one in the course of its catalysis. What becomesevident is that many of the above ideas converge, if oneconceives of all enzymes – not just mechanoenzymes – as

G°

Ensem

ble

Conform

atio

ns

Reaction Coordinate

E+S

E+P

FIGURE 1.7 Schematic representation of the standard free-energy

landscape for a catalytic network of an enzyme reaction. The catalytic

process is viewed as proceeding through a network consisting of a multi-

tude of conformations and numerous catalytic reaction cycles, each written

horizontally as a reaction path (e.g., E1 # A1 # B1 # �� # P1 # E1;

E2 # A2 # B2 # ��# P2 # E2; and E3 # A3 # B3 # ��# P3 #E3, etc.), where each species is connected vertically to its corresponding

conformer (e.g., E1 # E2 # E3 # �� # En–1 # En). The result is

a network similar to that shown in Scheme 12.5 describing the results of

single-molecular enzyme kinetic data. For simplicity, only one substrate

S and one product P are shown. Note that enzyme conformational changes

actually occur along both axes: (a) those changes along the reaction coordi-

nate axis correspond to the environmental reorganization facilitating chem-

ical reaction; and (b) those changes occurring along the ‘‘ensemble

conformations’’-axis represent the ensembles of configurations existing at

all stages along the reaction coordinate. Therefore, a plane parallel to the

axis labeled ensemble conformations bisects this catalytic ‘‘mountain

range’’ along the red mountaintop, with reactants E þ S are on one side

of the plane and the products Eþ P on the other. This free energy landscape

thus illustrates the multiple populations of conformations, intermediates,

and transition states. Strong coupling can occur between the reaction coor-

dinates and the conformation ensembles (i.e., the reaction paths can slide

along and between both coordinates). For real enzymes, the number of

maxima and minima along the coordinates is expected to be greater than

shown. The dominant catalytic pathways will be altered by external condi-

tions and protein mutations. Figure (originally created by S. J. Edwards)

and legend adapted from Benkovic, Hammes and Hammes Schiffer

(2008) with permission of the authors and the publisher.


force-generating and force-sensing molecular machines thatare exquisitely well designed to: (a) recognize and bindspecific substrates; (b) avoid unduly tight binding inter-actions with the substrate as well as catalytic cycle inter-mediates and reaction products; (c) bring aboutconformational changes that continually re-position active-site groups as the catalytic cycle proceeds; and (d) promoteenzyme evolution and perfection by adjusting the energeticlandscape to create alternative mechanochemical pathwaysfor catalysis. In this way, some steps within a catalyticreaction cycle may be viewed as force-gated conformationalchanges that constantly readjust catalytic determinantswithin the active-site to optimize the local push-pull forcebalance between the enzyme and various forms of boundreactant. All reaction coordinate diagrams plot DG (orchange in potential energy DU) on the ordinate versus‘‘Reaction Progress’’ (often indicated as some inter-atomicdistance, say d, representing a bond making or bond-breaking event) on the abscissa. The slope DG/Dd (or DU/Dd) corresponds to a pushing or pulling force F that ismutually experienced by enzyme and its bound reactant(s) asthey jointly approach and surmount the transition state.

Such ideas also fit with the universal occurrence ofdomains and motifs that are connected by hinges and joints,where forces can be localized and/or managed (Williams,1993). In this respect, an enzyme’s mechanochemicalproperties appear to be a natural complement to its bond-breaking/making properties, as illustrated by the capacity ofATP synthase to use ATP hydrolysis to drive the confor-mational changes that energize transmembrane protongradients or that use the latter to drive ATP synthesis(Purich, 2001).

1.6 PROSPECTS FOR ENZYME SCIENCE

Predicting the likely direction that a scientific field willtake is an inherently hazardous enterprise, mainly becausefield-changing intellectual realization occurs in bursts andoften exploits completely unanticipated opportunities. Aseemingly insignificant advance in one scientific disciplinemay also trigger a breakthrough in another field. What isself-evident is that enzymes have been bestowed witha special status in the chemical sciences, and for nearlytwo centuries, the chemical, biochemical, and physiologicactions of enzymes have continually piqued the intellec-tual curiosity of highly creative individuals. By enrichingour understanding of enzymes and the physiologicbehavior, many enzymologists have even earned NobelPrizes (Table 1.4).

One may therefore assert that enzyme science willsurely enjoy a brilliant future, and it’s safe to assume thatthis intellectually stimulating, and yet immensely prac-tical, enterprise will doubtlessly prosper from the dev-elopment of new kinetic approaches. The following

sections describe areas where sustained inquiry is apt toreap great rewards.

1.6.1 We Need Better Methods for AnalyzingEnzyme Dynamics to Understand theDetailed Mutual Changes in Both Substrateand Enzyme During Catalysis

As noted earlier in this chapter, the distinction betweenchemical kinetics and chemical dynamics is that the formerfocuses on the measurement of reactivity (i.e., reactionrates) with an emphasis on bond-making/breaking mecha-nisms of chemical transformations, whereas the latter refersto the atomic and molecular motions that influence reac-tivity and stability. While chemical intuition guides thenotion that internal enzyme flexibility is essential foractivity, the nature of catalytic motions is poorly under-stood. A longstanding question about biological catalysisconcerns the functional coupling of reactant motions to theenzyme’s local conformational dynamics in various Enzy-me$Substrate, Enzyme$Intermediate, and Enzyme$Productcomplexes. The great speed of catalysis has been a majorobstacle for ‘‘on-the-fly’’ analysis of conformationaldynamics. Because the time-scale of each catalytic reactioncycle sets the longest lifetime of any intermediate, anenzymic reaction proceeding at a rate of 5,000 cycles/s hasa 0.2 millisec catalytic cycle-time, one that is too short formost techniques that can detect individual residue side-chain motions.

There is in fact mounting evidence that protein dynamicsmay play a central role in enzymatic catalysis, well beyondthe standard models of loop motions that help to holdsubstrate(s) within a desolvated active site (Hentzler-Wild-man and Kern, 2007). Directed motions of the enzyme perse may be coupled to the catalytic mechanism, especially inthose cases where hydrogen tunneling seems to be operating(Basran, Sutcliff and Scrutton, 1999). The basic idea is thatrate-promoting vibrations are intrinsic motions of theprotein catalyst that form a dynamic matrix surroundingthe substrate, and that these vibrational modes can alter thegeometry of the bonding barrier(s) to chemical reaction.When viewed from this perspective, the defining nature ofa promoting vibration is to be found in the nature of thecoupling of that protein matrix motion to the reactioncoordinate (Caratzoulas, Mincer and Schwartz, 2002).Antoniou et al. (2002) described how a catalysis-promotingvibration within the enzyme may be coupled to a vibrationalmode of a reactant proceeding along the reaction coordi-nate. Their view is that evolution created a protein structurethat moves in such a way that lowers and narrows the barrierto reaction. This lowering of the barrier is not merelya statistical lowering of a potential of mean force throughthe release of binding energy; rather, the enzyme is believedto use highly directed energy in the form of a vibration

34 Enzyme Kinetics

acting in a specific direction. It is believed that rate-promoting vibrations within protein catalysts have150-cm�1 frequencies, corresponding to vibrations on thesub-picosecond time-scale. Because enzyme catalysisoccurs with frequencies of 104–107 s�1, there is an unex-plained disparity in vibrational and catalytic time-scales.Many hundreds of thousands of these rate promotingvibrations occur over the time needed for a single catalyticround. Because vibrational energy obeys the Boltzmanndistribution (see Section 3.6: Thermal Energy: The Boltz-mann Distribution Law), it’s possible that a rare (and hencesubstantially more energetic) vibration may be needed totrigger catalysis. Finally, Caserta and Cervigni (1974)offered a more rudimentary suggestion that nonethelesspostulated electron induced, selective amplification of low-frequency vibrational waves in the enzyme, such that thesevibrations are coupled to a susceptible region of thesubstrate, with consequential lowering of the activationenergy.

Although hydrogen-deuterium and disulfide-trappingtechniques can clearly detect 15-A protein motions onthe millisecond time-scale (Careaga and Falke, 1992;Englander and Kallenbach, 1983; Falke and Koshland,1987; Huyghues-Despointes et al., 2001), these methodsare uninformative about faster processes. For example, thehydrogen deuterium exchange technique, which quantifiesthe time-course for the release of protons bound up ina-helix and b-sheet structures, is incapable of providingsuch information on a sub-millisecond time-scale. Ofparticular interest is whether picosecond and nanosecondtime-scale structural fluctuations are coupled to thestructural changes associated with the catalytic rate-limiting step, the latter typically occurring on the micro-second-to-millisecond time-scale (Daniel et al., 1999). Animportant question is whether the fast motions need to beanharmonic, such that picosecond-to-nanosecond motionsin the protein may be needed to permit slower micro-second millisecond dynamics across the highest-energyreaction barrier.

The first parallel comparison of the activity anddynamics of glutamate dehydrogenase (GDH), as probedpicosecond time-scale motions, showed no deviation fromArrhenius behavior through the dynamical transition(Daniel et al., 1998). The experiments were performed ina 70% vol/vol methanol/water cryosolvent in which theenzyme is active and stable. For the thermophilic microbialGDH operating near 350 K, the turnover number of theenzyme is ~1500 s�1 at ~350 K, and in fully deuteratedcryosolvent at 220 K, the turnover number is ~0.01 s�1.Their results indicated that over the 190–220 K temperaturerange, the enzyme’s rate-limiting step(s) is(are) unaffectedby picosecond protein motions. To extend the time-scaleproblem, Daniel et al. (1999) used advanced neutron scat-tering spectrometers to compare the temperature depen-dence of GDH activity and dynamics. The IN6 spectrometer

probed motions on time-scales shorter than ~100 ps, and theIN16 spectrometer extended the time-scale to ~5 ns. Theirresults demonstrated a marked dependence on the time-scale of the temperature profile of the mean squaredisplacement. Several dynamical transitions were observedin the slower dynamics. Comparison with the temperatureprofile of the activity of the enzyme in the same solventreveals dynamical transitions having no effect on GDHfunction. Representing the first assessment of the globaldynamics of an active enzyme measured under similarconditions over a range of time-scales, these studies suggestthat anharmonic, picosecond motions are not required at alltemperatures for the enzyme rate-limiting step. The authorssuggest that anharmonic fast motions are not necessarilycoupled to the much slower motions describing transitionsalong the enzyme reaction coordinate. They caution,however, that the neutron technique reveals averagedynamics, and it is conceivable that functionally importantfast motions may occur locally in the protein at the activesite, but below noise levels.

Eisenmesser et al. (2002) used magnetic resonancespectroscopy to analyze conformational exchange in thereaction catalyzed by prolyl-peptidyl isomerase (Reaction:cis-X–Pro Isomer # trans-X–Pro Isomer), also known ascyclophyllin A:

N H C N

O

H O

H

N O

H R 1

C H

O

N H

peptidyl-trans-proline peptidyl-trans-proline

R 1

R 2 R 2

The simplest catalytic cycle consistent with knowncatalytic properties is shown in Scheme 1.11, with threemicroscopic reaction steps:

E

E-Prolinetrans

E-Prolinecis

kcis,onk

trans,on

ktrans,off kcis,off

kc-to-t,cat

kt-to-c,cat

Scheme 1.11

where Ktrans,D ¼ ktrans,off/ktrans,on and Kcis,D ¼ kcis,off/kcis,on.Eisenmesser et al. (2002) conducted 15N spin relaxation

experiments in the absence and presence of the substrateN-Succinyl-L-Ala-L-Phe-L-Pro-4-NA. Chemical-shift mappingwith 15N yields a single resonance (or a single peak in a two-dimensional NMR spectrum) for each amide bond. Bychanging the relaxation delay time, they determined thetransverse relaxation rate constant R2, which obeys therelation: R2 ¼ R20 þ Rex. The latter represents the exchange


contribution to R2 and provides information about therelevant motions that occur on the microsecond-to-milli-second time-scale. To separate the effects of binding fromcis-trans isomerization, the authors characterized substrateconcentration-dependent changes in R2. The relativecontributions to R2 from exchange due to binding and cis-trans isomerization exhibited different dependencies onsubstrate concentration. For most residues, Rex z pApBdv2/kex where pA and pB are the fractional populations of freeenzyme and the bound states, dv is the chemical shiftdifference between E and SE$Si, and kex is the exchangerate. As substrate concentration is increased, Rex thereforerises and then falls; maximal chemical exchange occurs atintermediate substrate concentrations, where Efree z(E$Scis þ E$Strans). The observed rate behavior fits with thepresence of significant concentrations of the three proteinforms (i.e., E, E$Scis, and E$Strans). When plotted as the 15NR2 relaxation rate constant versus residue number (Fig. 1.8),it became clear that certain regions in the enzyme exhibitedchanges in R2 due to steady-state catalytic turnover. Bynonlinear regression analysis of the exchange contributionto R2 for those residues sensing substrate binding andcatalysis, the authors obtained Km values ranging from 0.95to 1.2 mM, and koff values of 10,700 to 14,800 s�1.

Based on other quantitative estimates of the rateconstants for the protein’s structural dynamics, theauthors reached the important conclusion that areasaround residues 55, 82, 101–103, and 109 play a role insubstrate binding at or near the diffusion limit. After thesubstrate is bound, the enzyme catalyzes a 180�-rotationof the prolyl peptide bond, and the substrate tail on theC-terminal side with respect to the prolyl residue isviewed as swinging around to make contact with theenzyme near residues 98 and 99. Meanwhile, the sub-strate’s N-terminal tail stays fixed, allowing the E$Scomplex to remain intact, despite substantial rearrange-ments during the cis-trans isomerization at a rate of9,000 s�1. Most notably, motions of the substrate and theenzyme coincide, and the catalytic Arg-55 also moveswith the same rate constant.

The beauty of this investigation on cyclophyllin Acatalysis is that Eisenmesser et al. (2002) succeeded inidentifying those regions of the enzyme whose dynamicsmatch the essential enzyme kinetics of catalysis. They alsomapped the microsecond time-scale dynamics to specificregions of the cis-trans isomerase. Despite the fact thatadditional analysis is needed to define the motions duringthe actual catalytic event, their systematic approach defineddynamic ‘‘hot spots’’ during catalysis and revealed that thetime-scales for protein dynamics coincide with those forsubstrate turnover. Finally, Bosco, Eisenmesser and Kern(2002) also described CypA’s catalytic action on Pro-90 inthe HIV capsid protein. Their work is the first documentedcase of catalyzed cis-trans isomerization on a prolyl residuewithin a natively folded protein substrate.

Earlier two-dimensional heteronuclear (1H–15N) nuclearmagnetic relaxation studies suggested that the dihydrofolatereductase$dihydrofolate complex exhibits a diverse range ofbackbone fluctuations on the psec-to-nsec time-scale(Epstein, Benkovic and Wright, 1995). To assess whetherthese dynamical features influence Michaelis complexformation, Miller and Benkovic (1998) used mutagenesisand kinetic measurements to assess the role of the strictlyconserved residue Gly-121, which displays large-amplitudebackbone motions on the nanosecond time-scale. Deletionof Gly-121 dramatically reduces the hydride transfer rate by550 times; there is also a 20-times decrease in NADPHcofactor binding affinity and a 7-fold decrease for NADPþ

relative to wild type. Insertion mutations significantlydecreased both substrate and cofactor binding. Their resultssuggest that distant residues, such as Gly-121 in DHFR,

FIGURE 1.8 Residues in cyclophyllin A exhibiting microsecond time-

scale dynamics during catalysis. Structures of the enzyme-bound cis and

trans conformations of the substrate N-Succinyl-Ala-Phe-Pro-4-NA

(green) bound to the enzyme (including expanded views shown at right),

based on the X-ray structure of CypA complexed to the cis form of

N-Succinyl-Ala-Phe-Pro-4-NA (1RMH) (Zhau and Ke, 1996). CypA resi-

dues with chemical exchange in both the presence and absence of substrate

are color-coded in blue (namely Phe-67, Gln-71, Gly-74, Ser-77, and Ser-

100). Residues in red exhibit chemical exchange only during turnover

(Arg-55, Lys-82, Leu-98, Ser-99, Ala-101, Gln-102, Ala-103, and Gly-

109). Residues shown in magenta (Thr-68 and Gly-72) exhibit chemical

exchange in the absence of the substrate but increase in its presence.

CypA catalyzes prolyl isomerization by rotating the C-terminal part of

the prolyl peptide bond by 180� to produce the trans conformation of

the substrate. In this model, the observed exchange dynamics of residues

in strand-5 of the enzyme can be explained. Reproduced from Eisenmesser

et al. (2002) with the permission of the authors and the American Associ-

ation for the Advancement of Science.

36 Enzyme Kinetics

may influence the formation of liganded complexes as wellas the proper orientation of substrate and cofactor during thecatalytic cycle.

Finally, it is also worthwhile to ponder a related question:Why are enzymes so large? Aside from the structuralcomplexity of allosteric enzymes, the most common answeris that most enzymes are made up of domains and motifs,the binding properties of which have been honed throughNatural Selection. In numerous lectures on chemical andenzyme catalysis, the late Daniel Koshland was fond ofcomparing a hydroxide ion to a hand-drill and an enzyme toa milling machine. His point was that enzyme catalysisalmost certainly requires highly precise interactions of anenzyme with its substrate(s). In the context of transition-state stabilization, it is reasonable to anticipate that a strongand exact fit of enzyme and substrate within the (E$X)z

transition-state complex is critically important. Similarly,binding energy is an essential ingredient for ground-statedestabilization. From the perspective of enzymes as force-actuated catalytic devices, however, the oil-like propertiesof the hydrophobic cores of globular enzymes may absorb,redirect, and align forces imparted by thermal energy withrespect to the trajectory of E$S along the reaction coordi-nate. In this respect, domains may also focus these forces atcritical stages within the catalytic cycle, much like latticedislocations are thought to facilitate heterogeneous catalysison metal surfaces. While the breaking of discrete chemicalbonds occurs on the picosecond time-scale, proteinconformation changes occur on the same nanosecond-to-microsecond time-scale, as is observed for enzyme catal-ysis. Any force F exerted over a distance Dx along thereaction coordinate should have the effect of reducing thezero-force DEact,0 value to the effective activation energyDEact,effective, such that DEact,effective ¼ DEact,0 – FDx. Alarge protein may even have the effect of increasing themagnitude of Dx, thereby further reducing the effectiveactivation energy.

1.6.2 We Need New Approaches forDetermining the Channels Allowing EnergyFlow During Enzyme Catalysis

A related outstanding problem in enzyme science concernsthe if’s, where’s, when’s, and how’s of energy flow withinenzyme molecules during catalysis. For nearly a century, themain approach of enzyme chemists has been the determi-nation of the enzyme-catalyzed transformations of substratesto intermediates and thence to products, without dueconsideration of how enzymes might manipulate the flow ofenergy to achieve their enormous catalytic rate enhance-ments. The origin of that energy and its detailed path(s)within an enzyme molecule could, in principle, explain whyNature relies on such a small number of proteins for catal-ysis. Current estimates put the number of different enzymes

at around 20,000 to 30,000 for all species, not counting manybillions of largely inconsequential, but naturally occurringamino acid substitutions; however great the number of suchnaturally occurring enzymes, the combinatorial variability ofpolypeptides, with say 400 residues, would be an astonish-ingly great (~20400). Present day ideas about critical enzymeresidues and the focused flow of energy within proteins arebest characterized for redox proteins like the cytochromes,rhodopsin, green fluorescent protein, as well as photosyn-thetic reaction centers. Even then, the actual energy-flowpathways are at best sketchy.

As reviewed by Leitner (2008), energy flow withina protein may be treated as a percolation process involvinga network of sites, some resulting in fast transport whendistant points are directly connected by energy-flow chan-nels, with others exhibiting slow transport along numerouspathways that most often reach dead ends. This connectioncan be made more precise by comparing statistically energyflow in proteins with flow related to the nature and densityof a protein’s vibrational states. Energy transfer can occur asmolecular vibrations or by dipole–dipole interactions inphotoexcited states. The former, which is limited by thespeed of sound and is most frequently carried by the rela-tively low-frequency modes of a protein, occurs on the orderof 10 A/psec�1. With a mean free path on the order of 1 A,the shortest time over which diffusion can be observed isaround 0.1 picoseconds. For proteins consisting of 100residues, energy diffuses from the interior to the surface ina few picoseconds, so vibrational energy flow in proteinsexhibits anomalous subdiffusion, with times of approxi-mately 0.1 picoseconds. Although the nature of fluorescenceresonance energy transfer (FRET) will be described inSection 4.5.6, it is sufficient here to say that the efficiency ofFRET depends on the relative orientation of the donor andacceptor moieties as well as the distance between them,with the latter imposing an inverse sixth power dependenceon that distance. When the acceptor is photo-emissive,a photon will be emitted after a red-shift (i.e., the donor willabsorb shorter wavelength light than that emitted by theacceptor), and the timescale will depend mainly on thefluorescence lifetime of the acceptor. When the acceptor isa quencher, one must entertain the possibility that theresulting thermal energy of the excited-state acceptor mayconceivably be channeled into discrete vibrational modesand/or conformational changes.

Little solid information exists concerning the internaltransmission of energy within enzymes, and even less isknown for enzymes during catalysis. The extreme celerityof enzymic catalysis imposes both technical limitations onthe detection and quantification of transient changes inenzyme structure as well as substantial uncertaintiesregarding the positions, motions, and momenta of criticalcatalytic residues. Even a fraction of an Angstrom in theposition of a catalytic functional group could easily spell thedifference between a poor and highly efficient catalyst.


1.6.3 We Need Additional Probesof Enzyme Catalysis

To define the mechanisms of energase-type mechano-chemical reactions, one must learn how the DGhydrolysis (orDGelectron-transport) drives protein transitions between non-covalent substrate- and product-like interaction states.Although modern protein science seeks to understand howconformational energy is generated, stored, and managed,there are as yet no rules for predicting likely reactionintermediates and transition states in energase catalysis.From this perspective, the task of elucidating energasemechanisms represents a monumental challenge for enzy-mologists and structural biologists alike. Although fluores-cence and Forster resonance energy transfer are powerfultools for detecting and quantifying noncovalent interactionsand conformational transitions, Angstrom-scale resolutionis needed to unambiguously define structural alterations thatattend enzyme catalysis. Enzyme science will thereforebenefit enormously by the development of additionalspectroscopic and crystallographic tools capable ofdiscerning the small structural changes occurring in theenzyme during catalysis. When coupled with appropriatecomputer-based modeling of enzyme interactions withsubstrates and inhibitors, a fuller picture of catalysis shouldemerge.

The promise of time-resolved X-ray crystallographymust not be underestimated. Of particular note is the Lauediffraction method, which uses polychromatic X-rays(typically l < 2.0 A) to collect sufficient structural data tocompute a series of images on a short time-scale (Moffat,2001). Although Laue diffraction and computationalmolecular dynamics (MD) were developed as independentways to visualize and assess transient structural states,their combined use may allow mutual refinement ofcomputational MD simulations of Michaelis complexesand difference Fourier electron density maps obtained inLaue experiments. Because a realistic molecular dynamicsstudy of a 50-kDa protein requires one to determine thepositions of ~10,000 atoms, every 10�15 seconds, large-scale MD simulations necessarily create huge data sets.The technique known as Principal Component Analysis isa mathematical tool for detecting correlations in large datasets. By expressing a molecular dynamics trajectory asa linear combination of principal components, the back-ground atomic fluctuations (i.e., thermal noise) are elimi-nated, affording a better view of the protein’s collectivemotions (Balsera et al., 1996; Hayward, Kitaom and Go,1994; Mongan, 2004). When combined with appropriatephysical models for protein motion, PCA can help one todetect genuine conformational changes. For example,mutual use of MD and crystallographic refinement allowedStoddard, Dean and Bash (1996) to assign a number ofadditional contacts and features for hydride transfer byisocitrate dehydrogenase. They reported that unrestrained

independent MD simulations provide a very useful cross-validation method for highly mobile regions that exhibitpoorly defined experimental density. Likewise, informa-tion from Laue difference maps provides informationabout substrate conformation and interactions that greatlyfacilitate MD simulations.

In a truly formidable undertaking, Schmidt et al.(2003) successfully determined the number of authenticlate-stage photo-cycle intermediates of PYP, the 14-kDaphotoactive yellow protein from the purple eubacteriumEctothiorhodospira halophila. PYP possesses a 4-hydroxycinnamic acid chromophore linked as a thiolesterto Cys-69. Its 446-nm lmax matches the action spectrumfor negative phototaxis, suggesting that PYP is theprimary cytoplasmic blue-light photoreceptor for thisprocess. Schmidt et al. (2003) used laser light absorptionto trigger the series of room temperature chemical reac-tions in PYP crystals, and they then employed the Lauediffraction technique (see 10.6.1: Flash Photolysis) todetermine atomic structures of PYP after a laser-to-X-rayinterval of 5 ms, 9 ms, 20 ms, 51 ms, 125 ms, 250 ms, 500ms, 850 ms, 1 ms, 2 ms, 7 ms, 15 ms, 30 ms, or 100 ms.They applied singular value decomposition (SVD) to theseries of experimental, time-dependent difference maps.This approach allowed them to evaluate rival chemicalkinetic mechanisms and to arrive at a self-consistentmechanism through their analysis of a set of time-dependent difference electron density maps spanning thetime range from 5 ms to 100 ms. Successful fit ofexponentials to right singular vectors derived froma singular value decomposition of the difference mapsdemonstrates that a chemical kinetic mechanism holds,and that structurally distinct intermediates exist.

Schmidt et al. (2003) identified two time-independentdifference maps, from which they refined the structures ofthe corresponding intermediates, thereby demonstratinghow structures associated with intermediate states can beextracted from the experimental, time-dependent crystallo-graphic data. Stoichiometric and structural constraintsallowed them to exclude one kinetic mechanism proposedfor the photocycle but retain other plausible candidatekinetic mechanisms. Thus, despite the fact that some mightjustifiably quarrel with this author’s views as to whethera 446-nm photon is truly a substrate or whether the PYPphotocycle is catalytic, the approach taken by Schmidt et al.(2003) represents a bench-mark in pioneering efforts toanalyze the time-evolution of an enzyme’s structure duringcatalysis.

1.6.4 We Need to Learn How Proteins Foldand How to Manipulate Protein Stability

Determining how proteins fold is also an enterprise ofcentral significance to enzymology, both with respect tohow unfolded polypeptide chains self-organize to form

38 Enzyme Kinetics

active catalysts and how molecular chaperonins facilitatesuch processes. The challenge is to conceive of and executeexperiments that reveal the time-evolution of evanescentshort-, medium- and long-range structures adopted bya protein during its folding and to develop adequate theoriesand simulation algorithms that capture essential features ofthe folding process. Given the fact that folding can now beviewed as the consequence of a massive, parallel ‘‘diffu-sional’’ search of n-dimensional conformational space, theidea that discrete intermediates accumulate would implythat there are kinetically significant bottlenecks in thefolding process. In their remarkable paper, Laurents andBaldwin (1998) discuss how the image of the transition statehas changed from a unique species (with a strainedconfiguration and a correspondingly high free energy) toa more ordinary folding intermediate reflecting a balancebetween limited conformational entropy and stabilizingcontact places. As they explain, evidence for a broad tran-sition barrier comes from studies showing that mutationscan change the position of the barrier. Controversy remainsas to whether populated folding intermediates (i.e., those atdetectable concentrations) are productive ‘‘on-pathway’’intermediates or ‘‘dead-end’’ traps. Another confoundingissue concerns the generalizability of folding rules discov-ered to govern a particular protein. While these topics liewell beyond the scope of this monograph, readers shouldconsult Dobson and Fersht (1995), Fersht (1998), andRichards et al. (2000).

1.6.5 We Need to Develop a DeeperUnderstanding of Substrate Specificity

Understanding enzyme specificity remains an enormousunfulfilled challenge for structural biologists and enzymechemists alike. Learning the rules governing substratespecificity is essential in efforts to craft new metabolicpathways – a task of ever-greater significance in the designof microorganisms tailored to produce new plastics,renewable fuels, and novel therapeutics. Enzymes of 50-kDa molecular mass have a molecular volume of ~100 nm3,and their active sites are located in ~1-nm3 clefts andcrevices. In a sense, the complex, self-adaptive chemicalprocess that we call Life is only possible because each ofthese 1-nm3 clefts and crevices exhibits a limited repertoireof bio-specific interactions. Most active sites bind substratesand/or coenzyme with a combined molecular weight of800–1,200 Daltons. The challenge of understanding enzymespecificity not only speaks to the need for high-resolutionenzyme structures but also for kinetic data indicating howsubtle changes in enzyme structure determine interactionswith substrates and inhibitors. If generalizable rules forenzyme specificity can be discovered, it should be possibleto rebuild and/or remodel active sites to accommodate newsubstances as substrates.

Directed evolution of novel,9 catalytically proficientenzymes is quickly emerging as a powerful new theme inenzyme science. Biochemists are seeking to modifysubstrate recognition, to eliminate side-reactions, to formspecific products, and to increase catalytic turnover rates.Such efforts have traditionally been limited by the selection(or screening) method. In vivo selections are usuallyrestricted to identifying properties affecting the viability ofthe organism, and full exploitation of these approaches isoften compromised by the complex nature of a living cell’sintracellular environment and the need to transform thatcell’s gene-library. Typically, 103–105 clone libraries arescreened in a plate assay using a fluorogenic or chromo-genic substrate to identify a few colonies of interest. To alterenzyme enantiomeric specificity for eventual use in asym-metric organic synthesis, Reetz et al. (1997) proposeda general approach that does not require any knowledge ofthe structure or the mechanism of the enzyme, namely invitro evolution using a combination of random gene muta-genesis by error-prone PCR (Leung, Chen and Goeddel,1989) and subsequent expression and high-throughputscreening. To achieve error-prone Polymerase ChainReaction (or epPCR), the reaction conditions are variedempirically to reduce Taq polymerase fidelity during DNAamplification, thereby causing base substitutions resultingin one, two, three, or even more amino acid substitutions inthe encoded protein. Reetz (2004) discussed the scope andlimitations of directed mutagenesis approaches, includingthe prospect of obtaining stereoselective hybrid catalystscomposed of robust protein hosts in which transition metalcenters have been implanted. Some efforts have focused onusing in vitro compartmentalization (IVC), an ingeniousapproach wherein a reaction assay solution can be

9 When biochemists most often use the word ‘‘novel’’ to describe

a substance, reaction, enzyme, etc., they are indicating that, to the

best of their knowledge, no such biochemical substance or reaction

has been previously reported. From a biological perspective, such

substances, reactions, enzymes, etc., are not new inasmuch as they

have presumably been essential components for a long time. Given

the introduction of manmade chemical substances into the

environment for nearly two centuries, however, there is an increased

likelihood for inadvertent evolution to give rise to a truly novel

enzymatic activity. A case in point is bacterial phosphotriesterase,

a microbial enzyme that catalyzes the hydrolysis of a broad range of

phosphotriester substrates, including the neurotoxic cholinesterase

inhibitors paraoxon (diethyl p-nitrophenyl-phosphate) and parathion

(diethyl p-nitrophenyl-thiophosphate). As discussed by Shim, Hong

and Rauschel (1998), the rarity of naturally occurring phosphotriester

substrates suggests that phosphotriesterase catalysis may be truly

novel and that no such activity occurred prior to the introduction of

these agents into the environment. Biochemists are also interested in

directed enzyme evolution as a way to create new metabolic

pathways or to improve chemical syntheses. Efforts to modify the

chemical and/or kinetic properties of enzymes or to make catalysts

from previously non-catalytic proteins and nucleic acids also raise the

likelihood for observing truly novel enzymatic activities.


partitioned into microscopic compartments, each of only ~5fL, by forming water-in-oil emulsions. In this way, a 50-mLreaction volume can be dispersed into 1010 physically iso-lated, aqueous compartments, allowing for the selection ofmany genes and making the system highly sensitive andeconomical. Tawfik and Griffiths (1998) and Lee, Tawfikand Griffiths (2002) demonstrated the feasibility of usingIVC to select DNA methyltransferases. Likewise, Levy,Griswold and Ellington (2005) used a compartmentalized invitro selection method to directly select for ligase ribozymesthat are capable of acting on and turning over separableoligonucleotide substrates. Starting from a degenerate pool,they selected a trans-acting variant of the Bartel class Iligase that statistically was likely to be the only activevariant in the starting pool, and isolation of this sequencefrom the population suggests that this selection method isextremely robust at selecting optimal ribozymes.

As a concrete example of a directed evolution experiment,consider the work of Griffiths and Tawflik (2003) on theselection of a high-kcat phosphotriesterase with turnover rates>105 s�1, some 63� higher the wild-type enzyme. Mutantenzymes were selected from a library of 3.4 � 107 mutatedphosphotriesterase genes using the ingenious strategy oflinking genotype and phenotype by means of in vitrocompartmentalization (IVC) in water-in-oil emulsions. First,microbeads, each displaying a single gene and multiple copiesof the encoded protein, were formed by compartmentalized invitro translation. To select for catalytic properties, themicrobeads were re-emulsified in a reaction buffer containinga soluble substrate, and the product and any unreactedsubstrate were coupled to the beads when the reaction rateassay was complete. Product-coated beads, displaying activeenzymes and the genes that encode them, were detected withanti-product antibodies and selected using flow cytometry.With this completely in vitro approach, Griffiths and Tawflik(2003) were able to select for substrate recognition, productformation, rate acceleration and turnover.

Kim et al. (2001) simultaneously incorporated andadjusted functional elements within an existing enzyme byinserting, deleting, and substituting several active-site loops,followed by fine-tuning of catalytic properties by means ofsite-directed point mutation. They successfully introducedb-lactamase activity into the ab/ba-metallohydrolase scaf-fold of glyoxalase II, and the re-engineered enzyme lost itsoriginal activity and gained the ability to catalyze thehydrolysis of cefotaxime with a (kcat/Km)app value of 1.8 �102 M�1 s�1. While this specificity constant value is ratherlow, Escherichia coli containing the redesigned enzymeexhibited 100� greater resistance to cefotaxime. Thepotential for extending these efforts by combining site-directed-mutagenesis and chemical modification to improvethe specificity of enzymes, especially those used by syntheticorganic chemists, should not be underestimated (Jones andDesantis, 1998) (see also Section 2.3: Active SiteDiversification).

An intriguing case of substrate specificity is theD-ribulose-1,5-bisphosphate carboxylase/oxygenase, theCO2-fixing enzyme that exhibits relatively slow catalysisattributed to the need to discriminate between its substratesCO2 and O2. Tcherkez, Farquhar and Andrews (2006)argued that these characteristics arise from difficulty inspecific binding of the structurally featureless CO2 mole-cule, forcing substrate specificity for CO2 versus O2 to bedetermined later (i.e., in the transition state). They suggestthat natural selection for greater CO2/O2 discrimination, inresponse to reducing atmospheric [CO2]/[O2] concentrationratios, resulted in a transition state for CO2 addition thatresembles a carboxylate group. This adaptation maximizesstructural differences between transition states forcarboxylation and oxygenation. However, the resultingincreased similarity between the structure of the carboxyl-ation transition state and its carboxyketone productexposes the carboxyketone to the strong binding needed tostabilize the transition state, causing the carboxyketone tobind so tightly that its cleavage to products is slowed.Tcherkez, Farquhar and Andrews (2006) suggested thatsuch apparent compromises in catalytic efficiency for thesake of specificity represent a new type of evolutionarilyperfected enzyme.

Substrate specificity also reinforces the idea thatenzymes are ideally suited for the synthesis and/or derivi-tization of drugs. Consider, for example, the studies ofKhmelnitsky et al. (1997) focusing on the synthesis ofwater-soluble forms of paclitaxel (taxol), the potent anti-cancer drug that binds selectively to assembled micro-tubules. Scheme 1.12 shows that in the absence of anyselective functional group protection, these investigatorsidentified a two-step enzymatic process for selective acyl-ation and deacylation.

There are two potentially reactive hydroxyl groups(marked in red), but thermolysin selectively transfers theadipoyl moiety to only one, thereby preventing loss ofbiological activity by modification of the taxane ring.Likewise, only one of the two ester-linkages (marked inblue) is cleaved by the fungal lipase. Notice that bothreactions occur in polar organic solvents.

There is also good reason to believe that biochemistshave not as yet identified all of the physiologicallysignificant ligands – even for those enzymes alreadythought to be well characterized. The search for enzymeregulatory molecules is often hit-or-miss, as evidenced bythe serendipitous discovery of the pivotally importantallosteric effector Fructose-2, 6-P2 as well as the recentunanticipated development of synthetic glucokinase acti-vators. In fact, we have no way to reckon just how manycentral pathway activators and inhibitors remain to bediscovered. Moreover, although most enzymes are firstdiscovered and isolated through the use of a well-definedactivity assay, one can never be absolutely certain thata particular substrate is the physiologic substrate or that

40 Enzyme Kinetics

other substrates are also metabolized. Many enzymes areselective in their action toward substrates and are onlyrarely exhibit absolute specificity. Nowhere is this state-ment truer than in the identification of the primary phos-phoryl-acceptor substrate for the numerous signal-transducing protein kinases. An added issue is thephenomenon of ‘‘catalytic promiscuity’’ (see Section2.3.2), wherein a single enzyme operates by more than onecatalytic mechanism, giving rise to multiple enzymaticactivities. Catalytic promiscuity increases the likelihoodthat we have unknowingly failed to identify many physi-ologically important reactions.

Such concerns point the need for a far more comprehensiveX-ray and NMR investigation of many, many more enzymes

to define the structures of their active sites and regulatory sitesat atomic resolution. Consider the fact that the Protein DataBank (PDB) presently lists some 56,000 structures, withnearly one-fourth of human origin. Some 49,000 structureswere established by X-ray techniques, with 7,000 determinedby NMR and fewer than 200 by EM. Also listed in the PDBare ~2,100 nucleic acid structures, with ~1,200 from X-rayanalysis, ~900 from NMR, and<20 from EM. For the nearly2,500 structures for protein-nucleic acid complexes, ~2,300were determined by X-ray, ~150 by NMR, and <65 by EM.While the tally of 56,000 documents the impressive pace ofacquiring protein structures over the past half century, it givesa somewhat distorted view of how much we already know,simply because the ligand-free and -bound structures andmutant forms of certain proteins have been so intensivelyinvestigated that these proteins are disproportionately repre-sented in the PDB. Various hemoglobins, for example,account for ~1.6% of all PDB structures. Among the inten-sively studied enzymes are: lysozyme (2%), angiotensi-nogen-converting enzyme (~1.5%), RNase (~1.4%), theribosome (~1.4%), trypsin (1.3%), chymotrypsin (~1%),actin (1%), carbonic anhydrase (0.6%), adenylate kinase(~0.5%), and myosin (~0.4%). Collectively, the proteins lis-ted above represent one-eighth of all curated structures in thePDB! To fathom the degree to which the overall tally grosslyunder-represents the proteome, one need only consider thathuman and mouse genomes each contain >20,000 protein-encoding genes, with Drosophila at ~13,000, C. elegans at~17,000, Arabidopsis at ~28,000, rice at ~38,000, S. cer-evisiae at ~6,000, and E. coli at ~5,000. In all, more than500,000 proteins would be needed to represent the proteomesof the 100 most frequently studied organisms and viruses.Even after allowing for the 10–15% that are fibrous and/orintrinsically disordered, upwards of 3–5 million differentprotein structures would be required to fully represent theligand-free and -bound states for the remaining globularproteins. An effort exclusively directed toward defining thestructures of all human proteins would itself swell the currentPDB holdings by a factor of 5–10. Obviously, such a massiveundertaking is presently infeasible and would require devel-opment of high-throughput robotic methods for efficientlyexpressing, purifying, crystallizing, and then structurallyanalyzing such a vast array of protein structures.

To reveal telltale structural features underlying molec-ular recognition and substrate specificity, one need notpossess an atomic-level structure for all enzymes withina proteome. One may only need the structures of as few asfive to ten thousand more enzymes with numerous repre-sentatives from each reaction types found in the EnzymeCommission’s classification. Moreover, wider applicationof molecular docking with a suitably robust referencelibrary consisting of all known low-molecular-weightmetabolites would develop criteria for reliably predictingthe most substrate specificity as well as the probable cata-lytic mechanism for those enzymes whose activities have

Ph

NH

Ph

O O

OH

H3C

OH3C

O

CH3

CH3

HO

OH

O

O

CH3

Ph

O

Ph

NH

Ph

O O

OH

H3C

OH3C

O

CH3

CH3

O

OH

O

O

CH3

Ph

O

Divinyl Adipate

in

tert-Amyl Alcohol

Thermolysin

(Salt-Activated)

C

CH2=CH—O-C(=O)—(CH

2)3—CH

2

O

Ph

NH

Ph

O O

OH

H3C

OH3C

O

CH3

CH3

O

OH

O

O

CH3

Ph

O

Acetonitrile

(solvent)

Lipase

Candida antarctica

C

HOOC—(CH2)3—CH

2

O

Scheme 1.12


yet to be established experimentally. Computationalapproaches are also required to provide a means for effi-ciently re-surveying enzyme surfaces, again at atomicresolution, to find previously undiscovered crevices thatserve as activator and inhibitor sites. Such work may alsohelp us to understand how so many different proteinsmanage to co-exist within crowded compartments withengaging in nonspecific aggregation.

Although highly automated robotic acquisition ofenzyme structures may provide us with a catalogue of high-resolution structural data, the value of such a treasure troveof structural data would be underwhelming in the absence ofcommensurate advances in high-throughput biochemicalcharacterization. What ultimately drives discovery scienceis the sense of intrigue and opportunity that researchersexperience when they ponder the properties and complexityof an unsolved scientific problem. Without commensurategrowth in hypothesis-based, experimental enzymology, wewould soon find, as put so well by Tennyson, that‘‘knowledge comes, but wisdom lingers.’’ Structural andfunctional characterization of the entire human proteomewould allow us to comprehend the full spectrum of ligandbinding interactions underlying enzyme catalysis andcontrol as well as to manage disease-causing enzymemutations through the design of new drugs and/or thera-peutic interventions.

To date, most molecular structure analyses stem from aninterest in a particular enzyme or its intriguing biochemicalproperties; even so, there is good reason to believe that wehave not succeeded in identifying likely physiologicallysignificant alternative substrates or all of the allostericactivators and inhibitors. There is thus an emergingrecognition of the need for a more comprehensive investi-gation of numerous active-site structures at atomic resolu-tion by X-ray and neutron crystallography. Sucha coordinated effort, which would focus on perhaps as fewas several thousand more enzymes representing everyEnzyme Commission reaction type, is likely to revealtelltale structural features that underlie substrate specificity.Moreover, wider application of molecular docking witha suitably robust reference library consisting of all knownlow-molecular-weight metabolites (i.e., MW < 1–3 kDa)would develop criteria for reliably predicting the mostsubstrate specificity as well as the probable catalyticmechanism for those enzymes whose activities have yet tobe established experimentally. Efforts to perfect high-throughput computational approaches are also required toprovide a means for re-surveying all enzyme surfaces, againat atomic resolution, thereby fostering the development ofnew ways to predict previously undiscovered activator andinhibitor sites. Such efforts would fulfill a longstandingneed to comprehend the fuller spectrum of ligand bindinginteractions responsible for cell, tissue, organ, and inter-organ regulatory mechanisms. These same approaches canbe extended to the systematic investigation of naturally

occurring, disease-causing enzyme mutations, perhaps evenfacilitating the design of custom-tailored therapeuticinterventions.

Finally, by redesigning enzyme active sites to accom-modate novel substrates, we face the welcome prospect thattherapeutic enzymes may soon be re-fashioned in waysallowing them to modify and/or detoxify natural andmanmade toxins. Given the many millions of syntheticorganic chemicals that have been prepared for commercialand research purposes, the ability to re-jigger enzyme activesites to catalyze novel reactions would increase the reme-dial potential during failures in chemical containment,especially if existing highly abundant enzymes can bealtered for such purposes. We may likewise anticipate theuse of these synthetic enzymes in the conversion of pro-drugs (see Section 8.12.5) into their therapeutically activeforms.

1.6.6 We Need to Develop the Ability toDesign Entirely New Biological Catalysts

Given the trend toward minimizing the environmentalimpact of chemical industries, greater emphasis must beplaced on designing enzymes with new catalytic function.Learning precisely how substrates approach and dockwithin enzyme active sites should permit us to remodelactive sites to create new catalysts.

Shown in Fig. 1.9 is the enlightening and efficient multi-step strategy developed by Jiang et al. (2008) for the rationaldesign of new enzymes, with their study focusing on thecatalysis of retro-aldol reaction (Scheme 1.13).

In the first step of their computational enzyme designeffort, Jiang et al. (2008) defined potential catalytic mech-anisms for a retro-aldol-type reaction. Recall that thisreaction proceeds in distinct stages (Scheme 1.14), eachinvolving acid/base catalysis by either amino acid sidechains or water molecules (see also Fig. 2.27 describingaldolase catalysis).

O

CH3CH

H3C

CH2

C

O

H3C

O

CH3HC

O

CH3

C

O

H3C

Enzyme

Scheme 1.13

42 Enzyme Kinetics

Nucleophilic attack of an enzyme lysine on the sub-strate’s ketone group forms a carbinolamine intermediate,which upon eliminating water forms the imine/iminiumspecies. Carbon–carbon bond cleavage is then triggered bythe deprotonation of the b-alcohol, with the iminiumintermediate acting as an electron sink. Finally, the enaminetautomerizes to an imine, which is then hydrolyzed torelease the covalently bound product and free the enzymefor another round of catalysis. Each elementary reaction insuch a multi-stage mechanism has its own transition state,which must be stabilized by the enzyme.

In the second step of the design process, Jiang et al.(2008) identified known protein scaffolds that mightaccommodate the designed TS ensemble described above.To account for the multi-step reaction pathway, theydesigned a composite structure of acid/base groups that issimultaneously compatible with multiple transition statesand anticipated reaction intermediates. In this effort, theygenerated design models using the four catalytic motifsshown schematically in Fig. 1.10, which employ differentconstellations of catalytic residues to facilitate carbinol-amine formation and water elimination, carbon–carbonbond cleavage, and release of bound product. The authorsemphasize that it is essential to consider a very large set ofactive-site possibilities, simply because the probability ofaccurately reconstructing a given three-dimensional activesite in an input protein scaffold is extremely small. Theygenerated such a set by simultaneously varying: (i) theinternal degrees of freedom of the composite TS; (ii) theorientation of the catalytic side chains with respect tothe composite TS, within ranges that are consistent withcatalysis; and (iii) the conformations of the catalytic sidechains. This combinatorial matching resulted in a total of181,555 distinct solutions for the placement of thecomposite TS and the surrounding catalytic residues.The Rosetta Match algorithm rapidly eliminated mostactive-site possibilities in a given scaffold that are likely

to have unfavorable catalytic geometry or to give rise tosignificant steric clashes.

After optimization of the composite TS rigid bodyorientation and the identities and conformations of thesurrounding residues, a total of 72 designs with 8–20amino acid identity changes in 10 different scaffolds wereselected for experimental characterization based on thepredicted TS binding energy, the extent of satisfaction ofthe catalytic geometry, the packing around the activelysine, and the consistency of side-chain conformationafter side-chain repacking in the presence and absence ofthe TS model. cDNA’s encoding each design were con-structed and the proteins were expressed and purified fromEscherichia coli, yielding soluble purified protein for 70of 72 designs.

Retro-aldolase activity was monitored via a fluores-cence-based assay of product formation for each of thedesigns. Their initial 12 designs used Motif I (Fig. 1.11B),which involves a charged side-chain (Lys-Asp-Lys)-medi-ated proton transfer scheme resembling that for D-2-deoxyribose-5-phosphate aldolase. Of these designs, twoshowed slow enaminone formation with 2,4-pentandione(17), which is indicative of a nucleophilic lysine, but nonedisplayed retro-aldolase activity. Ten designs were madebased on Motif II, which is much simpler and involvesa single imine-forming lysine in a hydrophobic pocket,similar to aldolase catalytic antibodies. Of these designs,one formed the enaminone, but none were catalyticallyactive. The third active site (Motif III) incorporates a His-Asp dyad as a general base to abstract a proton from theb-alcohol; of the fourteen designs tested, ten exhibitedstable enaminone formation, and eight had detectable retro-aldolase activity. In Motif IV, Jiang et al. (2008) experi-mented with the explicit modeling of a water molecule,positioned via side-chain hydrogen bonding groups, whichshuttles between stabilizing the carbinolamine andabstracting the proton from the hydroxyl. Of the thirty-six

O

O OH

H-bond:B

O

OH

H-bond:B

OH

HN

LYS O

NH OH:BLYS

H2O

O

O:B

HN

LYS

H2O

HN

LYS

:BHOH

H-bond

H2N

LYS

:B

OH

H-bondO

NH2LYS

NH2LYS ++

Scheme 1.14


designs tested, twenty formed the enaminone and twenty-three (with eleven distinct positions for the catalytic lysine)had significant retro-aldolase activity, with rate enhance-ments up to four orders of magnitude over the uncatalyzedreaction.

To evaluate the accuracy of the design models, Jianget al. (2008) solved the structures of two of the designs byX-ray crystallography (Fig. 1.11). The 2.2-A resolutionstructure (Panel D) showed that the designed catalyticresidues Lys159, His233, and Asp53 superimpose well onthe original design model, and the remainder of the activesite is nearly identical to the design. The 1.9 A resolutionstructure of the M48K variant of RA61 likewise reveals anactive site very close to that of the design model, with onlyHis46 and Trp178 in alternative rotamer conformations,perhaps resulting from the absence of substrate in the crystalstructure (Panel E).

What is so appealing about the work of Jiang et al. (2008)is that each proposed catalytic mechanism is treated as anexperimentally testable hypothesis through multiple inde-pendent design experiments. A candidate scaffold with itspendant catalytic groups can first be tested in silico bycomputer modeling protocols, then in vitro by kineticmeasurements, and finally in the crystal state by X-raydiffraction. The authors speculate that their computationallydesigned enzymes resemble primordial enzymes more thanhighly refined modern-day enzymes. In any case, Jiang et al.(2008) convincingly demonstrated that novel enzymeactivities can be designed from scratch through the use oftheir systematic approach.

1.6.7 We Need to Define the Efficient Routesfor Obtaining High Potency EnzymeInhibitors as Drugs and Pesticides

Enzyme inhibitors are by far the most effective drugs,because an inhibitor’s effect on metabolism is magnified bythe target enzyme’s catalytic efficiency. It’s also the casethat an enzyme’s specificity for its substrate(s) is oftenmanifested in its interactions with inhibitors.

Hopkins and Groom (2002) concluded that only about3,000 of the 30,000 genes in the human genome can beclassified as ‘‘disease-modifying genes.’’ The ever-expand-ing enterprise of developing the next cadre of billion-dollardrugs depends heavily on the discovery of new enzymes andinhibitors that may serve as drug targets and as lead mole-cules that guide drug design. Most drug discovery effortsbegin with the recognition that a compound shows promiseas an inhibitor of an enzyme of pharmacologic interest. Suchmolecules, called lead compounds (or simply leads), mustrun the gauntlet of criteria for evaluating the promise ofa new drug. Capitalizing on mode-of-action information,pharmacologists and medicinal chemists are perfectingstrategies for developing novel drugs (Copeland, 2005).Combinatorial libraries of organic compounds are alsoemployed to identify leads based on the ability of randomlyshaped molecules to fill cavities within an enzyme’s activesite. Genomics and proteomics are likewise being exploredas new avenues for identifying lead molecules.

Compute TS for each stepwith optimally placed

protein functional groups

Select library ofscaffold proteins

Combine to generatecomposite active site Identify pockets

Identify scaffold positions allowing construction of active site

Optimize composite TS and catalytic side-chain conformations

Design neighboring positions for high affinity TS binding

Optimize entire active site

Rank based on binding energy and catalytic geometry

Experimentally characterize top ranking designs

FIGURE 1.9 Computational design protocol for a multi-step enzyme-

catalyzed reaction. Step-1: Generate ensembles of models of each of the

key intermediates and transition states (TS) in the reaction pathway in the

context of a specific catalytic motif composed of protein functional groups.

Step-2: Superimpose these models, based on the protein functional group

positions, to create an initial composite active-site description. Step-3:

Generate large ensembles of distinct 3D realization of these composite

active sites by simultaneously varying the degrees of freedom of the

composite TS, the orientation of the catalytic side chains relative to the

composite TS, and the internal conformation of the catalytic side chains.

For each composite active site description, candidate catalytic sites are

generated in an input scaffold set by Rosetta Match software (Zanghellini

et al., 2006). Briefly, each rotamer of each catalytic side-chain is placed at

each position within each scaffold, and the ensuing position of the composite

TS is recorded in the hash. After filling out the hash table, which is linear in

the numbers of scaffold positions and catalytic rotamers, the table is

searched for TS positions (termed ‘‘matches’’) that are compatible with all

catalytic constraints; such positions are termed ‘‘matches.’’ Step-4: Opti-

mize the rigid body orientation of the composite TS and the internal coordi-

nates of the catalytic side chains for each match, reducing steric clashes

while maintaining the catalytic geometry within specified tolerances. The

remaining positions (not included in the minimal catalytic site description)

surrounding the docked composite TS model are redesigned to optimize TS

binding affinity by means of the standard Rosetta design methodology (Dan-

tas et al., 2003; Meiler and Baker, 2006). The rigid body orientation of the

composite TS, the side chain torsion angles, and (in some cases) the back-

bone torsion angles in the active site are refined via quasi-Newton optimiza-

tion. Step-5: Rank the resulting designs, based on the total binding energy to

the composite TS and the satisfaction of the specified catalytic geometry.

Step-6: Experimentally characterize the top-ranked designs. Figure and

legend reproduced with minor modification from Jiang et al. (2008) with

permission of the authors and the publisher.

44 Enzyme Kinetics

The most reliable tools, by far, are the mechanisticinsights obtained through kinetic analysis of enzyme action,and such efforts will doubtlessly require advances inenzyme science as well as structural biology, molecularmechanics, and physical biochemistry. A particularlyfruitful approach is to infer the most likely transition-stategeometry through the determination of kinetic isotopeeffects. These concepts and experimental strategies aredescribed in Chapters 8 and 9.

1.6.8 We Need to Learn More AboutIn Singulo Enzyme Catalysis

Direct visualization of catalytic reaction cycles of an indi-vidual enzyme molecule (hence the term in singulo) is atlong last feasible. Enzyme kinetic experiments have tradi-tionally been carried out with large numbers of enzymemolecules, and even 1-nL volume of 1 nM enzyme containsnearly a million molecules. Advances in protein science,optics, fluorescence and solid-state electronics, however,make possible the direct observations of single enzymemolecules.

The ergodic hypothesis asserts that the time-averageof a physical quantity along a time trajectory of anindividual member within a homogeneous ensemble isequivalent to the ensemble-averaged value of that

quantity at a given time (Gillespie, 1992; Norris, 1997;van Kampen, 1992). A powerful justification for con-ducting single-molecule observations is the need to testwhether individual members are indeed representative ofthe overall population of molecules (Xie and Trautman,1998). Reaction trajectories can now be reliably deter-mined for individual enzyme molecules that are physi-cally isolated from each other by attachment to solidsurfaces or supramolecular structures, during confinementwithin a gel or polymer matrix, or as they operate cata-lytically and move freely within an extremely smallvolume element. As will become clear later in thisreference book, other breakthroughs in materials scienceand chemical physics have also spurred the developmentof single-molecule kinetics.

Enzyme chemists and statistical physicists are similarlyintrigued by the stochastics of enzyme catalysis and coop-erativity (e.g., activity fluctuations, pausing, waiting-timedistributions, static disorder, fluctuating reactant concen-trations, etc.). Such information affords the opportunity tocompare individual and ensemble-averaged propertiesunambiguously, thereby bridging the microscopic andmacroscopic worlds of chemistry.

These concepts and the ever-expanding armamentariumof experimental tools for testing them are explored morefully in Chapter 12.

FIGURE 1.10 Candidate motifs for

catalysis of retro-aldol reaction

mechanisms. Shown are active-site motifs

with quantum mechanically optimized

structures. Motif I, possessing two lysines

positioned nearby each other to lower the

pKa of the nucleophilic lysine, and a Lys-

Asp dyad acting as the base to deprotonate

the hydroxyl group. Motif II, with catalytic

lysine buried in a hydrophobic environment

to lower its pKa, thereby increasing its

nucleophilic character, and a tyrosine that

can function as a general acid or base. HB,

hydrogen bond. (Top right) Motif III,

wherein the catalytic lysine (analogous to

Motif II) is in a hydrophobic pocket to

lower its pKa, and a His-Asp dyad serves as

a general base similar to the catalytic unit

commonly observed in the serine proteases.

Motif IV, with the catalytic lysine is again

positioned in a hydrophobic environment.

Additionally, an explicitly modeled bound

water molecule is placed, such that it forms

a hydrogen bond with the carbinolamine

hydroxyl during its formation, aids in the

water elimination step, and deprotonates the

b-alcohol at the C–C bond-breaking step. A hydrogen-bond donor/acceptor, such as Ser, Thr, or Tyr, is placed to position the water molecule in

a tetrahedral geometry with the b-alcohol and the carbinolamine hydroxyl. The proton abstracting ability of the water molecule is enhanced by a second

hydrogen bond with a base residue. We incorporated, where possible, additional hydrogen-bonding interactions to stabilize the carbinolamine hydroxyl

group and an aromatic side chain to optimally pack along the planar aromatic moiety of the substrate. Figure and legend adapted from Jiang et al.

(2008) are reproduced here with permission of the authors and the publisher.


1.6.9 We Need to Develop ComprehensiveCatalogs of Enzyme Mechanisms and to UseSuch Information in Fashioning NewMetabolic Pathways

A promising development that should foster rationalcomparison of enzyme reaction mechanisms and perhapseven the design of new metabolic pathways is theMACiE database (Holliday et al., 2005, 2006). Thisinternet-accessible bioinformatics database standing forMechanism, Annotation and Classification in Enzymes

(go to: http://www.ebi.ac.uk/thornton-srv/databases/MACiE/glossary.html) categorizes the reaction mechanisms ofwell-characterized enzymes in the Protein DataBase(PDB). MACiE is a collaborative project between JohnMitchell’s Group at the Unilever Center for MolecularInformation at Cambridge University and Janet Thorn-ton’s research group at the European BioinformaticsInstitute, located south of Cambridge. All curatedmechanisms are taken from the primary literature bya suitably trained chemist and biochemist. Each enzymeis assigned an identifying number based on the Enzyme

FIGURE 1.11 Structures of computationally designed enzymes. A–C: Examples of design models for active site designs highlighting groups

important for catalysis. The nucleophilic imine-forming lysine is in orange, the transition-state model is in yellow, the hydrogen-bonding groups

are in light green, and the catalytic water is shown explicitly. The designed hydrophobic binding site for the aromatic portion of the TS model

is indicated by the gray mesh. A: RA60 (catalytic motif IV, jelly-roll scaffold), wherein a designed hydrophobic pocket encloses the aromatic

portion of the substrate and packs the aliphatic portion of the imine-forming Lys48. A designed hydrogen-bonding network positions the bridging

water molecule and the composite TS. B: RA46 (catalytic motif IV, TIM-barrel scaffold), wherein Tyr-83 and Ser-210 position the bridging water

molecule, thereby potentially facilitating required proton shuffling in active site IV. C: RA45 (catalytic motif IV, TIM-barrel scaffold). The bridging

water is hydrogen-bonded by Ser-211 and Glu-233; replacing the Glu-233 with Thr decreases catalytic activity by a factor of three. D and E: Over-

lay of design model (purple) on X-ray crystal structure (green). Designed amino acid side-chains are shown in stick representation, and the TS

model in the design is shown in gray. D: The 2.2 A crystal structure of the Ser-210-Ala variant of RA22 (catalytic motif III, TIM-barrel scaffold).

The root mean square deviation (RMSD) for Ca atoms for the design model and its crystal structure is 0.62 A, and the heavy-atom RMSD in the

active-site is 1.10 A. E: 1.8 A crystal structure of Met-48-Lys variant of RA61 (catalytic motif IV, jelly-roll scaffold). Design-crystal structure Ca-

atom RMSD is 0.46 A, and heavy-atom RMSD is 0.8 A. The small differences in the high-resolution details of packing around the active site are

believed to arise from slight movements in some of the loops above the binding pocket and two rotamer changes in RA61 that may reflect the

absence of a bound TS analogue in the crystal structure. Figure and legend adapted from Jaing et al. (2008) are reproduced here with permission

of the authors and the publisher.

46 Enzyme Kinetics

Commission system (go to: http://www.chem.qmul.ac.uk/iubmb/enzyme/). The MACiE database specifies: (a) reac-tion identifier; (b) overall reaction type; (c) atoms involved;(d) bonds involved; (e) bonds broken; (f) bonds made; (g)substrates, cofactors products, along with suitable KeggLigand Database identifiers (go to: http://www.genome.jp/ligand/); (h) groups transferred; (i) groups eliminated;(j) species reduced; and (k) species oxidized.

While admittedly more daunting, reaction stages areannotated with respect to: (i) involved substrate, cofactorand/or product; (ii) reaction centers; (iii) rate-determiningstep? (iv) reversible step? (v) stage reaction type; (vi)group(s) transferred; (vii) involved nucleophile; (viii) typeof tautomerization; (ix) reaction type; (x) reaction attri-butes; (xi) bond cleaved; (xii) bond formed; (xiii) bond-order change; and (xiv) involved residues, whethera nucleophile, charge stabilizer, spectator, etc. As describedby Holliday et al. (2005; 2006), the process of annotatingthe data contained within MACiE involves advancedmethods to minimize erroneous data entry. Whereverpossible, issues of semantics are resolved by reference to theIUPAC Gold Book (go to: http://goldbook.iupac.org/) aswell as the MACiE dictionary (go to: http://www.mitchell.ch.cam.ac.uk/macie/glossary.html). An added advantageof MACiE is that it should become feasible to identifyknown enzymes as best-case candidates for the generationof novel catalysts via site-directed mutagenesis. Becausethe overall reaction is treated as the composite of mecha-nistic steps, MACiE should eventually resolve short-comings in the EC nomenclature of energase-class enzymes(Purich, 2001).

As noted earlier, fully one-fifth of the gross nationalproduct of an industrialized country depends on catalysis.Unfortunately, most synthetic catalysts exploit specialproperties of aluminum, chromium, manganese, nickel,platinum, palladium, ruthenium, etc., of which most areinherently toxic as elemental metals or simple metaloxides. Techniques that increase their effective surfacearea, such as atomic deposition on carbon or zeolites,also increase their hydrolysis and undesired entry intothe biosphere. Given the significance of catalysis in oureveryday lives, it may be reasonably expected thatnatural or ‘‘remanufactured’’ enzymes will play a majorrole in efforts to develop a ‘‘Green Chemistry’’ that isboth efficient and ecologically sound. Because thecardinal features of enzymes are specificity and highturnover, and because enzymes are completely biocom-patible, enzyme science has much to offer in the devel-opment of catalysts affording high yields and lowtoxicity. For example, enzyme-catalyzed biofuel cellsmay soon offer an alternative to transition metal catalystsfor power generation. They could, in principle, facilitateoxidize alcohols at relatively low over-potential withoutthe production of detrimental carbon monoxide, and arecapable of operation at lower temperatures. Palmore

et al. (1998) described a methanol/O2 biofuel cell thatuses an NADþ-dependent dehydrogenase as catalysts andexploits an electro-enzymatic method to regenerateNADH at modest over-potentials. We may also surmisethat effective photo-electro-enzymatic methods willlikewise harness solar energy to create electrode over-potentials.

Pointing to the overwhelming impact of human activityon Earth’s biosphere, futurists tell us that thermal pollu-tion is unavoidable. Some suggest that the effects ofglobal warming have been grossly underestimated, simplybecause higher temperatures are suppressed by the buff-ering effects of deep ocean currents; once these heat sinksare loaded, unchecked ‘‘temperature creep’’ may mani-festly become what may be regarded as human-generatedheat. The only apparent counter-measure is inventiveconservation, where new efficiencies must be realizedthrough improved machine designs and/or where chemistsdevise better ways to transduce solar energy into chemi-cally stored energy. If chlorophyll is the answer,10 thenone or more enzymes will likewise play a part. If calcium-mediated depletion of CO2 is the answer, then the enzy-mology of biomineralization will enjoy mounting interest.And if bacterial fermentation is the answer, new pathwayswith enhanced enzymatic activities can be developed. U.S.Patent Number 5,000,000, for example, describes a genet-ically engineered Escherichia coli that was transformedwith alcohol dehydrogenase and pyruvate decarboxylasegenes from Zymomonas mobilis (Ingram, Conway andAlterthum, 1991). These genes are expressed at sufficientlevels to confer upon the resulting Escherichia colitransformant an ability to produce ethanol fermentativelyat 80–90% efficiency. This patent shows that bacterialenzymology is already playing a role in converting silage,corn syrup, and even biodegradable landfill refuse intobiofuels.

Another fertile approach, pursued by Synthetic Geno-mics, Inc., is the design of entirely novel metabolic path-ways using microorganisms that possess synthetic, orstripped-down, genomes that are optimized to allow forsingle-purpose production of valuable substances, biofuels,etc. The goal is to modify the operating system of a cell todirect the synthesis of metabolic products with commercialvalue and improve those cellular properties essential forlarge-scale commercial bioprocesses.

10 The following simple calculation indicates that an artificial system with

an efficiency comparable to photosynthesis would be a considerable source

of renewable energy. In the U.S., ~2500 hours per year of sunlight reach

an intensity of ~800 watts per square meter, meaning that one hectare

(104 m2) receives ~2 � 1010 watt-hours of energy. If 50% of this solar

energy could be harvested as H2, the energy output would be ~1010

watt-hours of energy.


1.6.10 We Need to Understand How toAnalyze the Kinetic Behavior of DiscreteEnzyme-Catalyzed Reactions as Well asMetabolic Pathways in their Environment

Our knowledge about how individual enzymes actuallyoperate within cells is surprisingly meager. Systematicinvestigation of the intracellular kinetics of enzymespromises to enrich our understanding of discrete enzymaticprocesses as well as the flow of metabolic information thatis encoded in the ligand binding kinetics and enzymicprocesses associated with signal transduction cascades.Enhanced understanding intracellular enzyme kineticspromises to improve the ways in which drugs are designedand used, including efforts to minimize harmful side-effects.

While we might anticipate that the availability of high-resolution microscopes and high-sensitivity color cameraswould facilitate studies of enzymatic kinetics within livingcells, little progress has been made on measuring enzymekinetics in situ. A major challenge is that spectral signalsfrom substrates and products for an individual enzymereactions are most often obliterated by spectral signals fromthe many chromophores and fluorophores of numerousother metabolites. Consider, for example, the conversion ofNADþ, which itself is virtually transparent at 340 nm, toNADH, which strongly absorbs 340-nm light. The problemis that NADþ and NADH are involved in so many oxido-reductase reactions that cannot be uniquely associate anabsorbance change with a particular enzyme-catalyzedreaction. The only exception is the use of synthetic chro-mogenic and fluorogenic alternative substrates in place oftheir natural counterparts. Another challenge is that theconcentration of a particular enzyme may vary withindifferent subcellular regions. Living cells are also of irreg-ular thickness, making it impossible to apply Beer’s Law(i.e., Abs ¼ 3cl). Likewise, fluorescence measurements areconfounded by light scattering, quenching, as well as inner-filter effects.

Stable and radioactive isotopic tracers (see Chapters 4, 9,and 11) are most often the best ways to analyze metabolicflux, Ji, which is the net reaction rate (units¼ DMolarity/Dt),through the ith step in a pathway. Except for the rare instanceswhere a gaseous metabolite (e.g., CO2, CO, H2, CH4, NO, orN2) is assimilated or released, isotopic assays are rarelycontinuous, and substrate consumption or product formationmust be determined by mass spectrometry or liquid scintil-lation counting after a sample of cells is fixed, extracted, andseparated. In a few cases, NMR can be used if the labeledspecies is present in sufficient quantities. The specialized fieldknown as Metabolic Control Analysis focuses on themeasurement of metabolic fluxes to learn how integratedmetabolic networks operate within its cellular context. InMCA, the researcher seeks to understand large-scale

dynamics of metabolic and physiological systems throughmodeling and simulation that is cast in terms of the sensitivityor responsiveness of metabolic flux to input signals. Meta-bolic Control Analysis is introduced in Section 11.13.

Whether such efforts successfully reproduce an enzy-me’s intracellular interactions is largely a matter forconjecture. Recognizing that the intracellular milieu mayalter the kinetic behavior of enzymes, some investigatorshave conducted in vitro kinetics using suspensions of per-meabilized cells to eliminate barriers to intracellular actionof an enzyme on substrate(s) supplied externally. The basicapproach is to disrupt the peripheral membrane by multiplefreeze-thaw cycles or by treatment with agents like digonin,filipin, Triton X-100, or Lubrol WX. The goal is to allowfree access of low-molecular-weight substrates and meta-bolic effectors to enzymes within treated cells without dis-lodging the enzyme of interest from its normal site andcertainly without loss of proteins from the permeabilizedcells. A good system is the yeast Saccharomyces cerevisiae,the cell wall of which, even after peripheral membranepermeabilization, acts as a semipermeable barrier thatretains intracellular proteins while permitting small mole-cules to enter or leave (Chow and Palecek, 2004; Serrano,Ganceda and Ganceda, 1973).

Students of muscle contraction long ago recognized thepower of cell permeabilization in managing the kinetics of theactomyosin (AM) mechanochemical cycle and in investi-gating the action of myosin light chain kinase in the contractileprocess. Both processes are ATP-dependent, and radioactiveATP and/or photo-caged ATP (see Section 10.6.1) can besupplied exogenously to suitably permeabilized muscle fibers.He et al. (1997), for example, measured the rate of inorganicphosphate (Pi) release, and hence overall ‘‘ATPase’’ activity ofrabbit psoas muscle in single, permeabilized muscle fibers thatwere in rigor prior to laser flash photolysis of caged ATP in thepresence and absence of Ca2þ. The rate of Pi release fromAM$ADP$Pi complex was likewise monitored, based on therise in the fluorescence signal of the Pi-sensitive probe formedby covalent labeling of bacterial phosphate-binding proteinwith the reporter group MDCC (see Section 4.5). Use of thepermeabilized muscle fiber approach also affords the oppor-tunity to pre-load myosin’s active sites with the non-hydrolyzable analogues p(NH)ppA and p(CH2)ppA in order tostudy hydrolysis-sensitive steps in the AM reaction cycle.

Because most of our knowledge of regulatory moleculeinteractions is the result of painstaking in vitro reconsti-tution experiments using fractionated cell components,Mura and Stadtman (1981) opted to use permeabilizedbacterial cells to re-investigate the bicyclic proteinnucleotidylation cascade that was first discovered inStadtman’s laboratory (see Section 11.11). This prototyp-ical system for enzyme-catalyzed reversible covalentinterconversion regulates the interconversion of dodeca-meric glutamine synthetase between its adenylylated

48 Enzyme Kinetics

(catalytically active) and unadenylylated (catalyticallyinactive) forms (Adler, Purich and Stadtman, 1975;Stadtman and Ginsburg, 1974). At high concentration,ammonia suffices for glutamine in numerous amido-syn-thase reactions leading to such nitrogenous metabolites ashistidine, N-acetyl glucosamine, and CTP. Earlier studieswith isolated protein and enzyme components indicatedthat the state of glutamine synthetase adenylylationdepended on indicators of ammonia availability: a-keto-glutarate was found to be a signal for low ammoniaavailability, whereas glutamine was an indicator thatammonia was plentiful. Mura and Stadtman (1981) foundthat permeabilization of Escherichia coli cells resulted incomplete retention of all protein components, presumablythe result of the bacterium’s Gram negative peptidogycancell wall. They found that the state of glutamine synthe-tase within permeabilized cells increased to a high state ofadenylylation in the presence of ATP and glutamine, with~11 of the synthetase’s 12 subunits containing an O-tyrosyl-AMP moiety. However, in the presence of a keto-glutarate, Pi, and ATP, the average number of O-tyrosyl-AMP residues decreased to ~2. Time-dependent changesin the state of adenylylation that occur during incubationsof permeabilized cells in buffers containing these effectorscan be arrested either by sonication in the cold or by theaddition of cetyl-trimethyl-ammonium bromide (to inac-tivate adenylyltransferase). Mura and Stadtman (1981)thus established that Lubrol-permeabilized cells area reliable way to investigate the regulation of glutaminesynthetase adenylylation in situ.

Given the need for additional approaches for investi-gating intracellular enzyme kinetics, it should be possibleto first permeabilize tightly adhered cells and then use anover-layer of mineral oil to physically isolate each cell fromthe others. A chromogenic or fluorogenic substrate couldthen be micro-injected into the small volume of buffersurrounding a cell of interest, and the progress of the reac-tion could then be sensed by absorption or fluorescencespectroscopy.

1.6.11 We Need to Develop Techniquesthat Will Facilitate Investigation ofChromosomal Remodeling, Epigenetics,and the Genetic Basis of Disease and CellSurvival

Few fields within the broad scope of the molecular lifesciences are developing as rapidly as the fields of chro-mosomal remodeling and epigenetics. Recent thrusts inmolecular genetics, for example, led to the discovery ofmany novel chromatin-associated enzymes, including:numerous DNA methylases, which are responsible forepigenetic marking; NAD+-dependent histone deacetylase,

which requires the unprecedented stoichiometric cleavageof the redox coenzyme to facilitate amide hydrolysis;telomerases, which add stabilizing DNA repeats (e.g.,TTAGGG in vertebrates) to chromosome ends; NAD+-dependent poly-ADPR polymerases (or PARPs), whichlikewise modify chromosome stability; as well as a batteryof scores to hundreds of ATP hydrolysis-dependent,chromatin-remodeling mechanoenzymes. Although geno-mics provides an upper bound on the likely number ofunique enzymes, there is no reliable metric for quantifyingthe complexity of interactions among these catalysts andtheir many protein, nucleic acid, and low-molecular-weight metabolic effectors. In epigenetics, for example,we are only beginning to glimpse how individual tissueschange during development, aging, and senescence tomodify the set-points for energy metabolism or howepigenetic marks are maintained within an organism orhow these epigenetic marks undergo multi-generationaltransmission from parent to child, and to succeedinggenerations. And when long-range gene regulation isconsidered (e.g., the multiple gene-coordinating action ofthe locus control region (LCR) for stage-specific expres-sion of hemoglobin genes within conceptus, fetus,neonate, and adult), the likely pivotal importance of ATP-dependent mechanoenzymes in prying open appropriatehighly compacted chromatin regions for active transcrip-tion, while simultaneously limiting RNA polymeraseaccess to those genes that must remain quiescent, cannotbe overstated.

We may likewise anticipate that a strong collaborationamong enzyme kineticists and molecular geneticists willalso quicken the pace of discovery of novel chromosomeregulation at this dawning hour. Learning how and whenvarious chromatin-remodeling mechanoenzymes find andinteract with specific locations within the nucleus alsopromises to provide the opportunity to alter cell functionand/or proliferation. Indeed, timely development of novelkinetic assays allowing one to probe the in situ action ofgene-regulating enzymes is of paramount importance. Soalso will be the rationale design of novel inhibitors thatare based on systematic investigation of the kinetic andcatalytic mechanisms of these enzymes. For example,systematic kinetic isotope effect studies on the NADþ-dependent histone deacetylases and telomerases shouldprovide valuable clues about the transition-state structureand its acid/base properties. As described in Sections8.6.1, 8.12.4, and 9.6, such information is essential forthe design of high-affinity transition-state inhibitors.Ultimately, collaborations among enzyme kineticists andmolecular geneticists will also enlarge the tally of newdruggable target enzymes, thereby expanding theopportunity to develop a wider spectrum of drugs andtherapeutic regimens that should improve the health,performance, and sustained vitality of plants andanimals.


1.6.12 We Need to Develop EffectiveEnzyme Preparations for Use in DirectEnzyme Therapy

The speed and specificity of enzyme catalysis commendsdirect enzyme therapy (i.e., the use of small quantities ofcertain enzymes as drugs to treat patients by modifyingmetabolism and/or ridding cells of disease-producingmetabolites or toxins). This strategy includes and goesbeyond enzyme replacement therapy, wherein a deficient,inactive, or absent enzyme is replaced by gene therapy and,less often, by infusion. The potential of direct enzymetherapy was first entertained over 50 years ago by LinusPauling, who was the first to trace a molecular basis ofa disease (sickle cell anemia) to a likely amino acidsubstitution (later shown to be the Glu-to-Val mutationposition-6 within the b-hemoglobin chain). For Pauling, theobjectives for direct enzyme therapy were deceptivelysimple – identify a disease-causing enzyme defect or defi-ciency and replace that enzyme with one having full cata-lytic and/or regulatory capacity.

Table 1.5 presents those cases in which direct enzymetherapy has been achieved or is nearing realization. Despitemany determined efforts, the successes are still far too few,inviting the question: What limits the use of enzymes as

direct therapeutic agents? To address this issue, we mayfirst categorize therapeutic enzymes as those autologousenzymes – those that are already normally produced byhealthy subjects within a given species versus heterologousenzymes – those that originate in a different species. Thesecategories may be further subdivided on the basis ofwhether an enzyme normally operates within or outsidethe confines of a cell. Autologous extracellular enzymereplacement offers greatest promise, because these enzymesshould exhibit limited immunogenicity, low toxicity, andshould already be well adapted to the inherently oxidizingenvironment outside cells. For those enzymes destined foruse in intracellular therapy, the researcher must overcomethe additional obstacle of delivering the enzyme to thecorrect intracellular compartment as well as in a physio-logically controlled concentration range. The use of foreignenzymes increases the likelihood that the host cells willexhibit apoptotic instability and that the enzyme mayundergo rapid turnover. By far, the greatest obstacles for theclinical efficacy of intracellular enzyme therapy will bespecific or selective delivery of the enzyme to the propercell/tissue target(s) and in the proper dosage. Except inrare circumstances, expression vectors like adenovirus,adeno-associated virus, and lentivirus are rarely deliveredwith adequate specificity, and surface expression of viral

TABLE 1.5 Selected Examples of Direct Enzyme Therapy

Adenosine deaminase Corrects adenosine deaminase-linked severe combined immune deficiency (ADA-SCID), bypreventing accumulation of toxic metabolites that impair cellular and humoral immunity.

Asparaginase and glutaminase Reduces the viability of asparagine- and glutamine-requiring tumor cells by hydrolyzingasparagine and glutamine.

Collagenases Debrides skin lesions, including scar tissue, ulceration, burns, and infected blisters.Dermal RNases Inhibits RNase-sensitive organisms, when applied in conjunction with membrane-lyzing

detergents. (Importantly, dermal RNase activity is not blocked by 5’-capping of mRNA.)DNase Treats chronic bronchitis by reducing bronchial mucous viscosity (a) by hydrolyzing DNA

and (b) by forming high-affinity complex with actin monomers, thereby greatly reducinglevel of filamentous actin.

a-Galactosidase A Treats a variety of clinical manifestations of Fabry’s disorder by reducingglobotriaosylceramide that accumulates in different cell types.

Glucocerebrosidase Treats Gaucher’s disease, which is by far the most common lysosomal storage disease.a-Glucosidase Ameliorates late-onset Type 2 Glycogen Storage (or Pompe) Disease, a progressive multi-

system disease evoked by a deficiency of lysosomal acid a-glucosidase.Lactase Relieves gastrointestinal distress, flatulance, as well as skin lesions in 75% of all adults

worldwide who metabolize lactose poorly.Lecithinized superoxide dismutase Ameliorates severe hypovolemia caused by increased blood vessel permeability following

burns by using its lecithin group to bind securely to dermal membranes, thereby allowingdestruction of surface superoxide.

Lysozyme Prevents microbial overgrowth by lyzing cell walls of various human pathogens.Onconase (RNase) Treats cancer A by triggering apoptosis as a consequence of messenger RNA and micro RNA

degradation.Oxalate decarboxylase Reduces renal calcium oxalate monohydrate stone formation by decomposing dietary

oxalate.Phenylalanine ammonia lyase Treats phenylketonuria by reducing serum levels of phenylalanine, which is converted to

toxic phenylpyruvate.Proteases Treats bacterial infection by hydrolyzing pathogen cell walls and microbial biofilms. Some

preparations also reduce HIV infection.

50 Enzyme Kinetics

antigens raises the specter of cellular immunity andapoptosis. A highly efficient means for incorporatingenzymes and other proteins into cells is afforded by add-ing the membrane-penetrating (or penetratin) sequencesRQIKIWFQNRRMKWKK and RRRQRRKKR, foundrespectively within Drosophila antennapedia and HIV-TATproteins, to the primary sequence of potential therapeuticenzymes. These sequences allow rapid and direct incorpo-ration of proteins into the cytoplasm of all cells tested todate. Even so, delivery to the proper cell target remainsproblematical. Whether delivered by means of viral vectorsor as penetratin-containing fusion enzyme, the elusive goalof maintaining enzyme dosage within a narrow wellcontrolled range represents the Holy Grail for direct enzymetherapy.

As potential therapeutic enzymes are identified anddeveloped, we can be reasonably certain that site-directedmutagenesis and chemical modification (e.g., conjugation topolyethylene glycol for reduced immunogenicity or tolecithin or by recombinant methods to introduce CAAX-type acylation sequences for enhanced membrane docking)will be essential tools for adapting these enzymes for clin-ical use. As will be discussed in Section 7.15.4, every site-directed enzyme mutant must also be treated as though it isan entirely new enzyme, each potentially with its uniquephysical and chemical properties. The same may be said forchemical modified enzymes. Such statements point to theneed for substantial kinetic characterization of thesemodified enzymes to verify their likely effectiveness. Alsorequired are appropriate kinetic tests of the efficiency ofenzyme dissolution and dispersion when formulatedenzymes are introduced into blood or model cell types aswell as kinetic measurements of enzyme turnover.

FURTHER READING

Abeles, R. H., Frey, P. A., & Jencks, W. P. (1992). Biochemistry. Boston:

Jones and Bartlett. pp. 838.

Altman, S. (1989). Ribonuclease P: an Enzyme with a Catalytic RNA

Subunit. Adv. Enzymol., 62, 1.

Cech, T. R. (Ed.). (1993). The RNA World. Cold Spring Harbor, New York:

Cold Spring Harbor Press. pp. 239.

Copeland, R. A. (2005). Evaluation of Enzyme Inhibitors in Drug

Discovery: A Guide for Medicinal Chemists and Pharmacologists.

Hoboken: Wiley-Interscience. pp. 271.

Frey, P. A., & Hegeman, A. D. (2006). Enzymatic Reaction Mechanisms.

New York: Oxford University Press. pp. 768.

Guerrier-Takada, C., Gardiner, K., Maresh, T., Pace, N., & Altman, S.

(1983). The RNA Moiety of Ribonuclease P is the Catalytic Subunit

of the Enzyme. Cell, 35, 849.

Hammes, G. G. (2002). Multiple Conformational Changes in Enzyme

Catalysis. Biochemistry, 41, 8221.

Haldane, J. B. S. (1930). Enzymes. London: Longmans-Green.

Jencks, W. P. (1969). Catalysis in Chemistry and Enzymology. San Fran-

cisco: McGraw-Hill.

Metzler, D. E. (2004). Biochemistry: The Chemical Reactions of Biolog-

ical Systems. New York: Academic Press.

Purich, D. L. (2001). Enzyme Catalysis: A New Definition Accounting for

Non-covalent Substrate- and Product-like States,. Trends in Biochem.

Sci., 26, 417.

Purich, D. L., & Allison, R. D. (2002). The Enzyme Reference. New York:

Academic Press.

Russell, C. A. (2004). Advances in Organic Chemistry Over the Last 100

Years. Annu. Rep. Prog. Chem., Sect. B., 100, 3.

Sinnott, M. (Ed.). (1998). Comprehensive Biological Catalysis: A Mech-

anistic Reference, vols I–IV. San Diego: Academic Press.

Voet, D., & Voet, J. G. (2003). Biochemistry (3rd ed.). New York: J. Wiley.

Zaug, A. J., & Cech, T. R. (1986). The Intervening Sequence RNA of

Tetrahymena is an Enzyme. Science, 231, 470.


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