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correspondingto weakbinding.called the turnouer number. The turnover number is often about 1000 substratemolecules processedper second per enzyme molecule, although turnover numbers between 1 and 10,000are known.The other kinetic parameter frequently used to characterizean enzyme is itsK-, the concentration of substrate that allows the reaction to proceed at onehalf its maximum rate (0.5 V-*) (seeFigure 3-45). A low K^value means that theenzyme reaches its maximum catalytic rate at a low concentration of substrateand generally indicates that the enzyme binds to its substrate very tightly,whereas a high K- value corresponds to weak binding.
The methods used tocharacterize enzymes in this way are explained in Panel 3-3 (pp. 162-163).EnzymesSpeedReactionsby SelectivelyStabilizingTransitionStatesEnzymes achieve extremely high rates of chemical reaction-rates that are farhigher than for any synthetic catalysts.There are several reasons for this efficiency. First, the enzyme increases the local concentration of substratemolecules at the catal)'tic site and holds all the appropriate atoms in the correctorientation for the reaction that is to follow.
More importantly, however, some ofthe binding energy contributes directly to the catalysis. Substrate moleculesmust pass through a series of intermediate states of altered geometry and electron distribution before they form the ultimate products of the reaction. The freeenergy required to attain the most unstable transition state is called the actiuation energyfor the reaction, and it is the major determinant of the reaction rate.Enzymes have a much higher affinity for the transition state of the substratethan they have for the stable form.
Becausethis tight binding greatly lowers theenergies of the transition state, the enzyme greatly acceleratesa particular reaction by lowering the activation energy that is required (Figure 3-46).By intentionally producing antibodies that act like enzymes, we candemonstrate that stabilizing a transition state can greatly increase a reactionrate. Consider, for example, the hydrolysis of an amide bond, which is similar tothe peptide bond that joins two adjacent amino acids in a protein. In an aqueous solution, an amide bond hydrolyzes very slowly by the mechanism shownin Figure 3-47A. In the central intermediate, or transition state, the carbonylcarbon is bonded to four atoms arranged at the corners of a tetrahedron.
Bygenerating monoclonal antibodies that bind tightly to a stable analog of thisvery unstable tetrahedral intermediate, one can obtain an antibody that functions like an enzyme (Figure 3-47F_).Becausethis catalytic antibodybinds to andstabilizes the tetrahedral intermediate, it increases the spontaneous rate ofamide-bond hydrolysis more than 10,000-fold.EnzymesCan Use5imultaneousAcid and BaseCatalysisFigure 3-48 compares the spontaneous reaction rates and the correspondingenzyme-catalyzed rates for five enzyrnes. Rate accelerations range from 109to1023.
Clearly, enzymes are much better catalysts than cata\tic antibodies.a c t i v a t i o ne n e r g yfor uncatalyzedreactionIAoqcoEPprogressof reactionacTrvaron energyfor catalyzed reactionFigure3-46 Enzymaticaccelerationofchemicalreactionsby decreasingtheactivation energy.Often both theuncatalyzedreaction(A)and the enzymecatalyzedreaction(B)cango throughseveraltransitionstates.lt isthetransitionstatewith the highestenergy(Srand ESr)that determinestneactivationenergyand limitsthe rateofp = productthe reaction.(S= substrate;of the reaction;ES= enzyme-substratecomplex;EP= enzyme-productcomplex.)PROTEINFUNCTION161( A ) H Y D R O L Y SOI SF A N A M I D EB O N Doo-o'Hl(tetrahedralintermediatewater( B )T R A N S I T I O N - s T AATNEA L O GF O RA M I D EH Y D R O L Y S I So\D'NozFigure3-47 Catalyticantibodies.Theof a transitionstateby anstabilizationantibodycreatesan enzyme.(A)Thereactionpath for the hydrolysisof anamidebond goesthrougha tetrahedraltransitionthe high-energyintermediate,statefor the reaction.(B)The moleculeonthe left wascovalentlylinkedto a proteinand usedasan antigento generateanantibodythat bindstightlyto the regionof the moleculeshown in yellow.Becausethis antibodyalsoboundtightlyto thetransitionstatein (A),it was found tofunctionasan enzymethat efficientlyof the amidethe hydrolysiscatalyzedbond in the moleculeon the riqht.NozoanalogEnz).rynesnot only bind tightly to a transition state, they also contain preciselypositioned atoms that alter the electron distributions in those atoms that participate directly in the making and breaking of covalent bonds.
Peptide bonds,for example, can be hydrolyzed in the absence of an enzyme by exposing apolypeptide to either a strong acid or a strong base, as illustrated in Figure 3-49.Enzymes are unique, however, in being able to use acid and base catalysissimultaneously, since the rigid framework of the protein binds the acidic and basicresidues and prevents them from combining with each other (as they would doin solution) (Figure 3-49D).The fit between an enzyme and its substrate needs to be precise. A smallchange introduced by genetic engineering in the active site of an enzyme canhave a profound effect. Replacing a glutamic acid with an aspartic acid in oneenz)ryne,for example, shifts the position of the catalytic carborylate ion by onlyI A (about the radius of a hydrogen atom); yet this is enough to decreasetheactivity of the enzyme a thousandfold.LysozymelllustratesHow an EnzymeWorks<AGCA>To demonstrate how enzymes catalyze chemical reactions, we examine anenzlrrne that acts as a natural antibiotic in egg white, saliva, tears, and othersecretions.Lysozyme catalyzesthe cutting of polysaccharide chains in the cellwalls of bacteria.
Because the bacterial cell is under pressure from osmoticforces,cutting even a small number of polysaccharide chains causesthe cell wallto rupture and the cell to burst. Lysozl'rneis a relatively small and stable proteinh a l f - t i m ef o r r e a c t i o n1 0 6y e a r s1yearUNCATALYZED1 seccnrnLvzeoFigure3-48 The rate accelerationscausedby five different enzymes,(Adaptedfrom A, Radzickaand1995.R.Wolfenden,Science267'.90-93,from AAAS.)With permissionWHY ANALYZETHE KINETICSOF ENZYMES?Enzymesare the most selectiveand powerful catalystsknown.An understandingof their detailedmechanismsprovidesacriticaltool for the discoveryof new drugs,for the large-scaleindustrialsynthesisof usefulchemicals,and for appreciatingthe chemistryof cellsand organisms.A detailedstudyof theratesof the chemicalreactionsthat are catalyzedby a purifiedenzyme-more specificallyhow theserateschangewithchangesin conditionssuchasthe concentrationsof substrates,products,inhibitors,and regulatory Iigands-allowsbiochemiststo figure out exactlyhow eachenzymeworks.For example,this is the way that the ATP-producingreactionsof glycolysis,shown previouslyin Figure2-72, weredeciphered-allowing us to appreciatethe rationalefor thiscriticalenzymaticpathway.In this Panel,we introducethe important field of enzymekinetics,which hasbeen indispensablefor derivingmuch ofthe detailedknowledgethat we now haveabout cellchemistry.STEADY-sTATEENZYME KINETICSMany enzymeshaveonly one substrate,which they bind andthen processto produceproductsaccordingto the schemeoutlined in Figure3-504.
In this case,the reactionis written askrE.S*.rate of ESbreakdownk-l [E5]+ kcat[Es]Kr:tEs -;At this steadystate,[ES]is nearlyconstant,so thatrate of ESformationkr tEltslE+pK_lHerewe haveassumedthat the reversereaction.in which E + Precombineto form EPand then ES,occursso rarelythat we canignore it.
In this case,EPneed not be represented,ano we canexpressthe rate of the reaction- known as its velocity,V, asor, sincethe concentrationof the free enzyme,[E],is equalto [Eo]- [E5],r,,r= (;|;)-,,,,),,,r,r'r = (-jr-_; (,,",V= k'"t [ES]where IES]is the concentrationof the enzyme-substratecomplex, Rearranging,and defining the constantKmasand k.". is the turnover number,a rate constantthat hasa valuek-1 + k.",equal to the number of substratemoleculesprocessedperenzymemoleculeeachsecond.k1But how doesthe value of IES]relateto the concentrationsthatwe know directly,which are the total concentrationof thewe getenzyme,IEo],and the concentrationof the substrate,[S]?Whenenzymeand substrateare first mixed,the concentrationIES]willlE,lIs]tEsl =riserapidlyfrom zero to a so-calledsteady-statelever,asK. + [5]illustratedbelow.or, rememberingthat V = kr"t [E5],we obtain the famousMichaelis-MentenequationIck."t IEo][S]gK.
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