Thermodynamics of biochemical reactions xxAlberty生物化学生物技术教案 1

Thermodynamics of biochemical reactions xx Alberty生物化学生物技术教案 1 Thermodynamics of Biochemical ReactionsRobert A.Alberty MassachusettsInstitute ofTechnology Cambridge,MA WILEY-INTERSCI ENCEA John Wiley and Sons PublicationCopyright cxxby John Wiley&Sons,Inc.All rightsreserved.Published byJohn Wiley&Sons,Inc.,Hoboken,New Jersey.Published simultaneouslyin Canada.No partof thispublication may be reproduced,stored in a retrievalsystem,or transmittedin anyform orby anymeans,electronic,mechanical,photocopying,recording,scanning,or otherwise,except aspermitted underSection107or108of the1976United StatesCopyright Act,without eitherthe prior written permissionof the Publisher,or authorizationthrough paymentof theappropriate per-copy feeto theCopyright ClearanceCenter,Inc.,222Rosewzood Drive,Danvers,MA01923,978-750-8400,fax978-750-4470,or on the webat .copyright.Requests to thePublisherfor permissionshuld beaddressed to the PermissionsDepartment,John Wiley&Sons,Inc.,111River Street,Hoboken,NJ07030, (201)748-6011,fax (201)748-6008,e-mail:permreqfuwiley.Limit ofLiability/Disclaimer ofWarranty:While thepublisher and author haveused theirbest effortsin preparingthis book,they makeno representationsor warrantieswith respectto theauracy orpleteness of the contentsof this book andspecifically disclaimany impliedwarranties ofmerchantability orfitness for a particularpurpose.No warrantymaybecreated orextended bysales representativesorwrittensales materials.The adviceand stratgiescontained hereinmay notbe suitablefor yoursituation Youshould consultwith aprofessional where appropriate.Neither thepublisher norauthor shallbe liablefor anyloss ofprofit orany othermercial damages.including butnot limitedto special,incidental.consequential,or otherdamages.For generalinformation onour otherproducts andservices pleasecontact ourCustomer CareDepartment within the U.S.at877-762-2974,outside theLJ.S.at317-572-3993or fax317-572-4002.Wiley alsopublishes itsbooks ina varietyof electronicformats.Some conttthat appearsin print,however,may notbe available in electronicformat.Library ofCongress Cataloin-in-Publtion Data:Alberty,Robert A.Thermodynamics of biochemical reactions/Robert A.Alberty.p.em.Includes bibliographicalreferences andindex.ISBN0-471-22851-6(cloth:acid-free paper)1.Thermodynamics.2.Physical biochemistry.3.Bioenergetics.I.Title.QP517.T48A42xx547.2-d21xx155481Printed in the UnitedStates ofAmerica10987654321Contents Prefacevii Chapter1Introduction toApparent Equilibrium Constants Chapter2Structure ofThermodynamics Chapter3Chemical Equilibriumin AqueousSolutions Chapter4Thermodynamics of Biochemical Reactionsat SpecifiedpH Chapter5Matrices inChemical andBiochemical ThermodynamicsChapter6Systems ofBiochemical ReactionsChapter7Thermodynamics ofBinding of the Ligandsby ProteinsChapter8Phase Equilibriumin AqueousSystems Chapter9Oxidation-Reduction ReactionsChapter10Calorimetry ofBiochemical ReactionsChapter11Use ofSemigrand PartitionFunctions GlossaryReferences PartTwo:Mathematica Solutionsto ProblemsBasicBiochemData2.nb Solutionsto Problems119355789105121141153171179186190Index ofMathematica ProgramsIndex389Preface This book is about the thermodynamics of enzyme-catalyzed reactions that makeup themetabolism ofliving organisms.It is not anintroductory text,but thefundamental principlesof thermodynamicsare reviewed.The readerdoes needsome backgroundin thermodynamics,such asthat providedby afirst coursein physicalchemistry.The bookuses ageneralized approachto thermodynamicsthat makesit possible to calculatethe effectsof changingpH,free concenrations of metal ions that are boundby reactants,and steady-state concentrations of coenzymes.This approachcan beextended toother typesof workthat maybe involved ina living organism.The conceptsinvolved in this approachare simple,but the equations beerather plicated.Biochemical reactions are written in terms of reactantslike ATPthat aremade up of sums of species,and theyare referred to asbiochemical reactionsto differentiatethem fromthe underlyingchemical reactions that arewritten in terms of species.The thermodynamics of biochemical reactions is independent of the propertiesof theenzymes thatcatalyze them.However,the fact that enzymesmay couplereactions thatmight otherwiseour separatelyincreases thenumber ofconstraints that have to be consideredin ther-modynamics.Biochemical thermodynamicsis plicatedfor severalreasons: (1)Bio-chemical reactantsconsist of sums of species whenevera reactanthas a pK withinabout twounits of the pHof interestor bindsmetal ionsreversibly. (2)Species of a biochemicalreactant are often ions,and theactivity coefficientsof ionsare functions of ionic strength. (3)Enzyme catalysismay introduceconstraints in biochemical reactions in addition to balancesof atomsof elements. (4)Metab-olism issufficiently plicatedthat it is importantto findways to obtain amore globalview. (5)In biochemistryother kindsof work,such aselectric work,elongation work,and surfacework maybe involved.It isremarkable that the samebasic reactionsare foundin allliving systems.The mostimportant thingabout these reactions is that theyprovide themeans tocarry outthe oxidation of organicmatter ina sequenceof stepsthat storeenergy that is neededfor thesynthesis oforganic molecules,mechanical work,and otherfunctions requiredfor life.The themeof thisbook isthat Legendre transforms makethe application of thermodynamicsmore convenientfor theusers.The logicused hereis acontinu-ationof the processdescribed byGibbs thatintroduced theenthalpy H,.VU PrefaceHelmholtz energyA,and the Gibbs energy G by use of Legendre transformsof theinternal energyU.In Chapter4a Legendre transform is used tointroduce pH and pMgas independent intensive variables.In Chapter6the steady-state concentrationsof variouscoenzymes are introduced as independentintensive variables indiscussing systemsofenzyme-catalyzed reactions.In Chapter8a Legendretransform isused tointroduce theelectric potentialof aphase as an independentintensivevariable.These usesof Legendretransforms illustratethe mentby Callen (1985)thatThe choiceof variables in terms of whicha givenproblem isformulated,while aseemingly innocuousstep,is oftenthe mostcrucial stepin thesolution.Choices ofdependent andindependent variablesare notunique,and sochoices can be madeto suitthe convenienceof theexperimenter.Gibbs hasprovided a mathematical structurefor thermodynamicsthat isexpand-ableinmany directions and isrich ininterrelationships betweenmeasurable propertiesbecause thermodynamic properties obeyall therules ofcalculus.Thisbookon thermodynamicsdiffers fromothers inits emphasis on thefundamental equationsof thermodynamicsand theapplicationof these equationsto systemsof biochemical reactions.The emphasison fundamentalequations leadsto newthermodynamic potentialsthat providecriteria for spontaneous change and equilibriumunder the conditions inalivingcell.The equilibriumposition of a reactionsystem involvingone ormore enzyme-catalyzed reactionsusually depends on the pH,and sothe Gibbs energy Gdoes notprovide the criterion for spontaneous change and equilibrium.It is necessary to use a Legendretransform to define a transformed Gibbs energyGthat providesthe criterion forspontaneous changeand equilibrium at the specified pH.This processbrings ina transformed entropy Sand a transformed enthalpy H,but thisnew worldof thermodynamicsis similarto thefamiliar worldof G,S,and H,in spiteof thefactthat there aresignificant differences.Since coenzymes,and perhapsother reactants,are insteady statesin livingcells,it isof interestto useaLegendretransformtodefine a further transformedGibbsenergyGthat providesthecriterionforspontaneouschangeandequilib-rium at a specifiedpHandspecified concentrationsof coenzymes.This processbrings inafurther transformedentropy Sand afurthertransformed enthalpyH,but therelations between these propertieshave thefamiliar form.Quantitative calculationson systemsof biochemical reactionsaresufficiently plicatedthat it isnecessary tousea personalputer with amathematicalapplication.Mathematica(Wolfram Research,Inc.100World TradeCenter,Champaign,IL,61820-7237)is wellsuited for these purposesand isused in thisbookto makecalculations,construct tablesand figures,and solveproblems.The lastthird of the bookprovides aputer-readable database,programs,and worked-out solutionsto puterproblems.The databaseBasicBiochemData2is availableon theWeb at:,/.mathsource./cgi-bin/msitem?O211-662.Systems of biochemical reactions can berepresented bystoichiometric num-ber matricesand conservationmatrices,which contain the sameinformation and can beinterconverted by use oflinear algebra.Both are needed.The advantageof writingputer programsin terms of matricesisthatthey canthen be used withlarger systemswithout change.This fieldowes atremendous debtto theexperimentalists whohave measured apparent equilibrium constants andheats ofenzyme-catalyzed reactions and tothose whohave madeprevious thermodynamic tables thatcontain informationneeded in biochemical thermodynamics.Although Ihave beeninvolved with the thermodynamics of biochemical reactions since1950,I didnot understand the usefulnessof Legendretransforms until1had spentthe decadeof the1980s workingon the thermodynamics ofpetroleum processing.During thisperiod Ilearned fromIrwin Oppenheim(MIT)and FredKrambeck(Mobil Researchand Development)about Legendretrans-forms,calculations usingmatrices,and semigrandpartition functions.In the1990s1returned tobiochemical thermodynamicsand profitedfrom manyhelpful Prefaceix discussionswith RobertN.Goldberg(NIST).The new nomenclature that isusedhere wasremended by an IUPAC-IUBMB reportby Alberty,Cornish-Bowden,Gibson,Goldberg,Hammes,Jencks,Tipton,and Veechin1994.The use ofLegendretransforms inchemical thermodynamicsis thesubject of an IUPACTechnical Reportby Alberty,Barthel,Cohen,Ewing,Goldberg,and Wilhelm (xx).I amindebted toNIH for award5-R01-GM48458for supportof myresearch onbiochemical thermodynamics.My AssociateManaging Editor,Kristin CookeFasano ofJohnWileyandSons,was veryhelpful.Robert A.Alberty Cambridge,Massachusetts1.6Brief HistoryoftheThermodynamics ofBiochemical ReactionsAcid Dissociation Constants andDissociation Constants of ComplexIons Binding of Hydrogen Ions and Magnesium Ions by Adenosine Triphosphate Apparent Equilibrium ConstantsofBiochemical Reactions Productionof Hydrogen Ions and Magnesium Ionsin theHydrolysis ofAdenosine TriphosphatepKs ofWeak AcidsTwo typesof equilibrium constant expressionsareneededin biochemistry.The thermodynamics of biochemical reactionscan be discussed in terms of specieslike ATP4-,HATP3-,and MgATP2-or in termsof reactants(sums of species)like ATP.The use of speciescorresponds withwriting chemical reactions thatbalance atomsof elementsand electriharges;the correspondingequilibrium constantsare representedby K.This approachis requiredwhen chemicaldetails arebeing discussed,asinconsidering themechanism ofenzymatic catalysis.But discussion in termsof metabolismmust involve,in greatdeal detail,acid dissociation constants and dissociation constants of plexeswith metal ions.Therefore metabolismis discussedby writingbiochemical reactions in termsofreactants-that is,sumsof species,like ATP-ata specifiedpHand perhapsspecified concentrationsof freemetal ions that are bound reversiblyby reactants.Bio-chemical reactionsdo notbalance hydrogen ions because the pH is held constant,and theydo notbalance metal ions forwhich free concentrations are held constant.When the pH isheldconstant,there is the implicationthat acidor alkaliwill beadded tothe systemto hold thepHconstant ifthe reactionproduces orconsumes hydrogen ions.In actualpractice abuffer isused toholdthepH nearlyconstant,and thepHismeasured at equilibrium.The correspondingequilibrium constantsare representedby K,which arereferred to as apparent equilibrium constantsbecause theyare functionsof pHand perhapsthe freeconcentrations1Thernwdyanamics ofBiochemicalReactions.Robert A.Alberty Copyright0xxJohnWiley&Sons,Inc.ISBN0-471-22851-62Introduction toApparent EquilibriumConstantsofone ormore freemetal ions.Biochemical thermodynamicsis more plicated thanthe chemicalthermodynamics of reactions in aqueous solutionsbecause there are moreindependent variablesthathaveto bespecified.This introductorychapter is primarily concerned withthe hydrolysis of ATP at specified7;P,pH,pMg,and ionic strength.The thermodynamics ofthehydrolysis of ATP andclosely relatedreactions havereceived a good deal of attentionbecause ofthe importanceof thesereactions in energy metabolism.1.1BRIEF HISTORYOF THETHERMODYNAMICS OFBIOCHEMICAL REACTIONSThe firstmajor publicationon thethermodynamicsof biochemical reactions was byBurton inKrebs and Kornberg,Energy Transformationsin LivingMatter,1957.Before thattime,apparent equilibrium constants had been measuredfor anumber ofenzyme-catalyzed reactions,but Burtonrecognized thatthese apparentequi-librium constantstogether withstandard Gibbs energies offormation A,Go of species determined by chemicalmethods canyield Af Go for biochemical speciesto makea tablethat can beusedto calculateequilibrium constants ofbiochemicalreactionsthathave notbeen studied(Burton andKrebs,1953).In retrospectit iseasy tosee thatin1953to1957there weresome problemsthat wereapparently notclearly recognizedor solved.Since Burtonwas thefirst,it isworth sayinga littlemore abouthis1957thermodynamic tables.The firsttable givesAf Govalues forabout100species inbiochemicalreactions.A largenumber ofthese valueswere takenfrom chemicalthermodynamictablesavailable in the1950s,but anumber werenew valuescalculated frommeasuredapparentequilibriumcon-stants forenzyme-catalyzed reactions.AfGovalues ofspecies can be readilycalculated when the reactantsin theenzyme-catalyzed reactionare allsingle speciesand AfGovalues areknown forall ofthe reactantsexcept one.It isnoteworthy thatBurton omittedthe species of orthophosphatefrom histable andthat hewas notable toinclude species of ATP,ADP,NAD,and NAD,.His secondtable givesstandard Gibbsenergy changesat pH7for oxidation-reduction reactionsthat werecalculated usingthe conventionthatH=1mol L-at pH7;the symbolACwas usedfor thisquantity.This tablealso gives the correspondingstandard cellpotentials for thesereactions.The thirdtable givesAGvalues atpH7foranumber ofreactions inglycolysis andalcoholic fermentation.The fourthtable ison thecitric acidcycle,and thefifth tableisonGibbs energies of hydrolysis.When abiochemicalreactionis studiedata pH wherethere isa predominantchemicalreaction,it is possibletodiscuss ther-modynamics intermsofspecies.But whensome reactantsare representedby anequilibrium distributionof severalspecies withdifferent numbers of hydrogen atoms,this approachisnotsatisfactory.The quantitativetreatment ofreactions involvingreactants with pKs in the neighborhoodof pH7was notpossible untilacid dissociation constants ofthese reactantshadbeendetermined.Some measurementsof acid dissociation constants of ATPand relatedsubstances(Alberty,Smith,and Bock,1951)anddissociation constantsof ionic plexesofthesesubstances withdivalent cations(Smith andAlberty,1956)were madein thisperiod.In the1960s therewas agood dealof interestin thethermodynamicsofthehydrolysisof ATPand ofother organicphosphates(Alberty,1968,1969;Phillips,George,and Rutman,1969),but standard Gibbs energiesofspecieswere notcalculated.The measurementof apparentequilibrium constants forbiochemicalreactionswasextended in the1970s(Guynn andVeech,1973;Veech etal.,1979)and1980s(Tewari and Goldberg,1988).In1969Wilhoit pickedup whereBurton hadleft offand piledthe standardthermodynamic propertiesA,Go andA,Ho ofspecies involved inbiochemicalreactions.He recognizedthe problemsinvolved inincluding species1.2Acid DissociationConstants andDissociationConstantsof ComplexIons3of ATP in sucha tableand madea suggestionas to how tohandle it.In1977Thauer,Jungermann,and Deckerpublished atable ofstandardGibbsenergiesofformation ofmany speciesofbiochemicalinterest,and showedhow toadjust standardGibbsenergiesofreactionto pH7by addingmAfGo(H+),where mis the numberof protonsin thereaction.During the1960sand1970s,newnomenclaturefor treatingthether-modynamicsofbiochemicalreactionswas developed,including theuseofKfor the apparentequilibrium constant writtenintermsofsumsofspecies,but omittingH.These changesled tothe publicationof Remendations,for Measurementand PresentationofBiochemicalEquilibrium Databyan IUPAC-IUB Committee(Wadso,Gutfreund,Privalov,Edsall,Jencks,Armstrong,and Biltonen,1976).Goldberg andTewari publishedan evaluationof thermodynamicand trans-port propertiesof carbohydratesand theirmonophosphates in1989and ofthe ATPseries in1991.Miller andSmith-Magowan publishedon thether-modynamicsofthe Krebscycle andrelated poundsin1990.Alberty(1992a,b)pointed outthat whenthepHorthefreeconcentration ofa metalionis specified,theGibbsenergy Cdoes notprovide thecriterionforspontaneouschangeandequilibrium.When intensivevariablesinadditiontothe temperatureand pressureareheldconstant,it isnecessarytodefineatransformedGibbsenergyGby useofaLegendretransform,as discussedin Chapters2and4.This leadstoaplete setof transformedthermodynamic propertiesatspecifiedpH,thatis,atransformedentropyS,transformedenthalpyH,andatransformed heatcapacity atconstant pressureCim.These changesled tothe publicationof Remendationsfor Nonienclatureand Tablesin BiochemicalThermodynamics byanIUPAC-IUBMB Committee(Alberty,Cornish-Bowden,Gibson,Goldberg,Hammes,Jencks,Tipton,Veech,Westerhoff,and Webb,1994).This introductorychapter describesthethermodynamicsofbiochemicalreactionsintermsofequilibrium constants and apparentequilibrium constants and avoidsreferences toother thermodynamic properties,which areintroduced later.W1.2ACID DISSOCIATION CONSTANTS ANDDISSOCIATIONCONSTANTSOF PLEXIONS Strictly speaking,equilibriumconstant expressions forchemicalreactionsinvolv-ing ionsinaqueous solutions