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NH,lq\-"lVrdomainv a r i a b l ed o m a i no f l i g h t c h a i n( V r )5"rn(A)(B)cooHit with many weak bonds. For this reason, loops often form the ligand-bindingsites in proteins.TheEquilibriumConstantMeasuresBindingStrengthMolecules in the cell encounter each other very frequently because of their continual random thermal movements. Colliding molecules with poorly matchingsurfaces form few noncovalent bonds with one another, and the two moleculesdissociate as rapidly as they come together. At the other extreme, when manynoncovalent bonds form between two colliding molecules, the association canpersist for a very long time (Figure 3-42). Strong interactions occur in cellswhenever a biological function requires that molecules remain associatedfor along time-for example, when a group of RNA and protein molecules cometogether to make a subcellular structure such as a ribosome.We can measure the strength with which any tvvo molecules bind to eachother.
As an example, consider a population of identical antibody molecules thatsuddenly encounters a population of ligands diffusing in the fluid surroundingthem. At frequent intervals, one of the ligand molecules will bump into the binding site of an antibody and form an antibody-ligand complex. The population ofantibody-ligand complexes will therefore increase, but not without limit: overtime, a second process, in which individual complexes break apart because ofthermally induced motion, will become increasingly important. Eventually, anypopulation of antibody molecules and ligands will reach a steady state, or equilibrium, in which the number of binding (association)events per second is precisely equal to the number of "unbinding" (dissociation)events (seeFigure 2-52).From the concentrations of the ligand, antibody, and antibody-ligand complex at equilibrium, we can calculate a convenient measure-the equilibriumconstant (K)-of the strength of binding (Figure 3-43A.).The equilibrium constant for a reaction in which two molecules (A and B) bind to each other to forma complex (AB) has units of liters/mole, and half of the binding sites will beoccupied by ligand when that ligand's concentration (in moles/liter) reaches avalue that is equal to l/K This equilibrium constant is larger the greater thebinding strength, and it is a direct measure of the free-energy differenceFigure3-41 An antibodymolecule,(A)A typicalantibodymoleculeisand hastwo identicalbindingY-shapedsitesfor its antigen,one on eacharm ofthe Y.The protein is composedof fourpolypeptidechains(two identicalheavychainsand two identicaland smallerlightchains)heldtogetherby disulfidebonds.Eachchainis madeup of severaldifferentimmunoglobulindomains,hereshadedeitherb/ueor groy.fheantigen-bindingsiteisformedwherea heavy-chainvariabledomain(VH)and a light-chainvariabledomain(Vr)comeclosetogether.Thesearethe domainsthatdiffermost in their seouenceandstructurein differentantibodies.Eachdomainat the end of the two armsof theantibodymoleculeformsloopsthat bindto the antigen.ln (B)we can seethesefingerlikeloops (red)contributedby theVrdomain.158Chaoter3: Proteinst h e s u r f a c e so f m o l e c u l e sA a n d B ,a n d A a n d C , a r e a p o o r m a t c ha n da r e c a p a b l eo f f o r m i n g o n l y a f e ww e a k b o n d s ;t h e r m a l m o t i o n r a p i d l ybreaksthem aoart((m o l e c u l eA r a n d o m l ye n c o u n t e r so t h e r m o l e c u l e s( 8 , C ,a n d D )(the surfacesof moleculesA and Dmatch well and therefore can formenough weak bonds to withstandt h e r m a lj o l t i n g ;t h e y t h e r e f o r estay bound to each otherbetween the bound and free states (Figure 3-438 and C).
Even a change of a fewnoncovalent bonds can have a striking effect on a binding interaction, as shownby the example in Figure 3-44. (Note that the equilibrium constant, as definedhere is also knor,rmas the association or affinity constant, Ku.)We have used the case of an antibody binding to its ligand to illustrate theeffect of binding strength on the equilibrium state, but the same principlesapply to any molecule and its ligand.
Many proteins are enzymes, which, as wenow discuss, first bind to their ligands and then catalyze the breakage or formation of covalent bonds in these molecules.Figure3-42 How noncovalentbondsmediate interactionsbetweenmacromolecules,EnzymesAre Powerfuland HighlySpecificCatalystsMany proteins can perform their function simply by binding to anothermolecule. An actin molecule, for example, need only associatewith other actin1dissociationAB-A+BThe relationshipbetweenfree-energydifferencesandequilibriumconstants(37"C)d i s s o c i a t i o.n" 1 " = d i s s o c i a t i o n x c o n c e n t r a t i o nrate constantof ABequilibriumconstantd i s s o c i a t i orna t e = k o r [ A B ]A+lassociationrate =ABassoclatlonrate constantof AB minus o f A B m i n u sfree enerqv f r e e e n e r g ytAllBlofA+B-OTA+ts(liters/mole) (kcal/mole)(kJ/mole)lABlassociationc o n c e n t r a t i o n concentrationofAofB1101021031041os10610710810e10101olla s s o c i a t i o nr a t e = k o n [ A ] [ B lAT EQUILIBRIUM:a s s o c i a t i orna t e = d i s s o c i a t i o rna t ekon[A] [B](A)=fre*energydifferencek"r [AB](B)A l t h o u g hj o u l e sa n dk i l o j o u l e s( 1 0 0 0j o u l e s )a r estandard units of energy,c e l l b i o l o g i s t su s u a l l yr e f e rt o f r e e e n e r g yv a l u e si nt e r m so f c a l o r i e sa n dkilocalories.K0-'t 4-2.8-4.3-5.7- 7.
1-8.5-9.9- 11 3-12.80-5.9-11.9-17.8-23.7-29.7-35.5-41.547.4-53 4- 1 56-55.3-J9.4O n e k i l o c a l o r i e( k c a l )i se q u a lt o 4 . 1 8 4k i l o j o u l e s(kJ).T h e r e l a t i o n s h i pb e t w e e nthe f ree-energychange,A G ,a n d t h e e q u i l i b r i u mconstant isAG = -0.00458 r log KwhereAGis in kilocaloriesa n d f i st h e a b s o l u t et e m p e r a t u r ei n K e l v i n s( 3 1 0K = 3 7 " C )(c)Figure3-43 Relatingbinding energiesto the equilibriumconstantfor an associationreaction.(A)TheequilibriumbetweenmoleculesA and B and the complexAB is maintainedby a balancebetweenthe two opposingreactionsshowninpanels1 and 2.
MoleculesA and B mustcollideif they areto react,and the associationrateis thereforeproportionalto theproductof their individualconcentrationsAs shownin panel3, the ratio[A]x [B].(Squarebracketsindicateconcentration.)of the rateconstantsfor the associationand the dissociationreactionsis equalto the equilibriumconstant(K)for thereaction.(B)Theequilibriumconstantin panel3 is that for the reactionA + B + AB,and the largeritsvalue,the strongerthe bindingbetweenA and B.Notethat for everyl.41 kcal/mole(5.91kJlmole)decreasein freeenergythe equilibriumconstantincreasesby a factor of 10 at 37'C.Theequilibriumconstantherehasunitsof liters/mole:for simplebindinginteractionsit is alsocalledthe affinityconstantot associationconstant,denoted Ku.The reciprocalof Kuis calledthe dissociationconstant,K6(in units of moles/liter).159P R O T E IFNU N C T I O Nmolecules to form a filament.
There are other proteins, however, for which ligand binding is only a necessaryfirst step in their function. This is the casefor thelarge and very important class of proteins called enzyrnes. As described inChapter 2, enzymes are remarkable molecules that determine all the chemicaltransformations that make and break covalent bonds in cells. They bind to oneor more ligands, called substrates, and convert them into one or more chemically modified products, doing this over and over again with amazing rapidity.Enzymes speed up reactions, often by a factor of a million or more, withoutthemselves being changed-that is, they act as catalysts that permit cells tomake or break covalent bonds in a controlled way.
lt is the catalysisof organizedsets of chemical reactions by enzymes that createsand maintains the cell, making life possible.We can group enzymes into functional classesthat perform similar chemicalreactions (Table 3-1). Each type of enzyme within such a classis highly specific,catalyzing onll, a single type of reaction.
Thus, hexokinase adds a phosphategroup to o-glucose but ignores its optical isomer t-glucose; the blood-clottingenzyme thrombin cuts one tlpe of blood protein between a particular arginineand its adjacent glycine and nowhere else, and so on. As discussed in detail inChapter 2, enzymes work in teams, with the product of one enzvme becomingthe substrate for the next. The result is an elaborate network of metabolic pathways that provides the cell with energy and generatesthe many large and smallmoleculesthat the cell needs (seeFigure2-35).SubstrateBindingls the FirstStepin EnzymeCatalysisC o n s i d e r1 0 0 0m o l e c u l e so f A a n d1 0 0 0m o l e c u l e so f B i n a e u c a r y o t i cc e l l T h e c o n c e n t r a t i o no f b o t h w i l lb e a b o u t 1 0 - eMl f t h e e q u i l i b r i u m .
c o n s t a( Kn )tf o r A + B . - A B i s 1 0' ' , t h e n o n e c a nc a l c u l a t et h a t a t e q u i l i b r i u mt h e r ewill be270270730ABABmolecules molecules moleculesl f t h e e q u i l i b r i u mc o n s t a n ti s a l i t t l ew e a k e ra t 1 0 ' , w h i c h r e p r e s e n t sa l o s so f 2 8 k c a l / m o l eo f b i n d i n ge n e r g yf r o m t h e e x a m p l ea b o v e ,o r 2 - 3 f e w e r h y d r o g e nb o n d s ,t h e n t h e r e w i l l b e91591585ABABmolecules molecules moleculesFigure3-44 Smallchangesin thenumberof weak bondscan havedrasticeffectson a binding interaction.Thisthe dramaticeffectofexamoleillustratesor absenceof a few weakthe presencenoncovalentbondsin a bioloqicalconIexI.For a protein that catalyzesa chemical reaction (an enzyme), the binding of eachsubstratemolecule to the protein is an essentialprelude.In the simplest case,ifwe denote the enzyme by E, the substrate by S, and the product by Il the basicreaction path is E + S -+ ES -+ EP -+ E + P From this reaction path, we see thatthere is a limit to the amount of substrate that a single enzyme molecule canprocess in a given time.
An increase in the concentration of substrate alsoincreasesthe rate at which product is formed, up to a maximum value (Figure3-45). At that point the enzyme molecule is saturated with substrate, and therate of reaction ( V-oJ depends only on how rapidly the enzyme can processthesubstrate molecule. This maximum rate divided by the enzvme concentration isTable3-1 SomeCommonTypesof EnzymesENZYMEREACTIONCATALYZEDHydrolasesandproteosesgeneraltermfor enzymesthat catalyzea hydrolyticcleavagereaction;nucleasesaremorespecificnamesfor subclassesof theseenzymes.breakdownnucleicacidsby hydrolyzingbondsbetweennucleotides.breakdownproteinsby hydrolyzingbondsbetweenaminoacids.together.two smallermoleculessynthesizemoleculesby condensingin anabolicreactionscatalyzethe rearrangementof bondswithina singlemolecule.polymerizationof DNAand RNA.catalyzereactionssuchasthe synthesisarean importantgroupgroupsto molecules.Proteinkinasescatalyzethe additionof phosphategroupsto proteins.of kinasesthat attachphosphategroupfroma molecule.catalyzeremovalof a phosphatethe hydrolyticwhilethegeneralnamefor enzymesreactionsin whichonemoleculeisoxidizedthat catalyzenamedeitheroxidases,otheris reduced.Enzymesof this type areoften morespecificallyreductases,or dehydrogeno ses.ATPasehydrolyzeATP.Manyproteinswith a wide rangeof roleshavean energy-harnessingactivityaspart of theirfunction,for example,motor proteinssuchasmyosinandmembranepump.transportproteinssuchas thesodium-potassiumNucleasesProteasesSynthaseslsomerasesPolymerasesKinasesPhosphatasesOxido-ReductasesATPasesthat weredlscoveredthrombinand lysozymeEnzymenamestyp ca ly end in " ase,"with the exc-apttrypsin,suchaspepsln,on of some-onzymes,centuryThecommonnameof an enzymeusuallyand namedb-.forethe conventionbecamegeneraly acceptedat the end of the nineteenthof citrateby a reactioncatayzesthe synthestsndjcatesthe substratecitratesynthaseandthe natureof the reactiorcatayzed Forexample,betweenacetvCoAandoxaloacetate160Chapter3: ProteinsICoE6oo 0 5v.",o6K-s u b s t r a t ec o n c e n t r a t i o n+Figure3-45 Enzymekinetics,The rate ofan enzymereaction(V)increasesasthesubstrateconcentrationincreasesuntilamaximumvalue(Vr"r) is reached.At thispoint all substrate-bindingsiteson theenzymemoleculesarefullyoccupied,and the rateof reactionis limitedby therateof the catalyticprocesson theenzymesurface.Formostenzymes,theconcentrationof substrate(Kr) at whichthe reactionrate is half-maximal(blackdot)is a measureof how tightlythesubstrateis bound,with a largevalueofK.
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