8. The statistical mechanics of DNA · 2017. 5. 1. · B. Role of DNA Gyrase The requirement that the parent DNA unwind at the repli-cation fork (Fig. 30-3) presents a formidable

IntroductorybiophysicsA.Y.2016-17

8.ThestatisticalmechanicsofDNA

EdoardoMilottiDipartimento diFisica,Università diTrieste

EdoardoMilotti- Introductorybiophysics- A.Y.2016-17

DNAisnotastaticstructure,ithasacomplexandvarieddynamics.

Thisdynamicscanonlybedescribedinstatisticalterms.

HereweconsidersomespecificissuesofDNAthermodynamics.

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Replica DNAs

Parent DNA

Replication eye

1174 Chapter 30. DNA Replication, Repair, and Recombination

the presence of replication “eyes” or “bubbles” (Fig. 30-2).These so-called ! structures (after their resemblance to theGreek letter theta) indicate that double-stranded DNA(dsDNA) replicates by the progressive separation of its twoparental strands accompanied by the synthesis of their com-plementary strands to yield two semiconservatively repli-cated duplex daughter strands (Fig. 30-3). DNA replicationinvolving ! structures is known as ! replication.

A branch point in a replication eye at which DNA syn-thesis occurs is called a replication fork. A replication bub-ble may contain one or two replication forks (unidirec-tional or bidirectional replication). Autoradiographicstudies have demonstrated that ! replication is almostalways bidirectional (Fig. 30-4). Moreover, such experi-ments, together with genetic evidence, have establishedthat prokaryotic and bacteriophage DNAs have but onereplication origin (point where DNA synthesis is initiated).

B. Role of DNA Gyrase

The requirement that the parent DNA unwind at the repli-cation fork (Fig. 30-3) presents a formidable topologicalobstacle. For instance, E. coli DNA is replicated at a rate of!1000 nucleotides/s. If its 1300-"m-long chromosomewere linear, it would have to flail around within the con-fines of a 3-"m-long E. coli cell at !100 revolutions/s

Figure 30-1 Action of DNA polymerase. DNA polymerasesassemble incoming deoxynucleoside triphosphates on

Figure 30-2 Autoradiogram and its interpretive drawing of areplicating E. coli chromosome. The bacterium had been grownfor somewhat more than one generation in a medium containing[3H]thymidine, thereby labeling the subsequently synthesizedDNA so that it appears as a line of dark grains in thephotographic emulsion (red lines in the interpretive drawing). Thesize of the replication eye indicates that the circular chromosomeis about one-sixth duplicated in the present round of replication.[Courtesy of John Cairns, Cold Spring Harbor Laboratory,New York.] Figure 30-3 Replication of DNA.

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EdoardoMilotti- Introductorybiophysics- A.Y.2016-17FromR.P.Wagner,“UnderstandingInheritance”,LosAlamosScience,n.20(1992)

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Replica DNAs

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1174 Chapter 30. DNA Replication, Repair, and Recombination

the presence of replication “eyes” or “bubbles” (Fig. 30-2).These so-called ! structures (after their resemblance to theGreek letter theta) indicate that double-stranded DNA(dsDNA) replicates by the progressive separation of its twoparental strands accompanied by the synthesis of their com-plementary strands to yield two semiconservatively repli-cated duplex daughter strands (Fig. 30-3). DNA replicationinvolving ! structures is known as ! replication.

A branch point in a replication eye at which DNA syn-thesis occurs is called a replication fork. A replication bub-ble may contain one or two replication forks (unidirec-tional or bidirectional replication). Autoradiographicstudies have demonstrated that ! replication is almostalways bidirectional (Fig. 30-4). Moreover, such experi-ments, together with genetic evidence, have establishedthat prokaryotic and bacteriophage DNAs have but onereplication origin (point where DNA synthesis is initiated).

B. Role of DNA Gyrase

The requirement that the parent DNA unwind at the repli-cation fork (Fig. 30-3) presents a formidable topologicalobstacle. For instance, E. coli DNA is replicated at a rate of!1000 nucleotides/s. If its 1300-"m-long chromosomewere linear, it would have to flail around within the con-fines of a 3-"m-long E. coli cell at !100 revolutions/s

Figure 30-1 Action of DNA polymerase. DNA polymerasesassemble incoming deoxynucleoside triphosphates on

Figure 30-2 Autoradiogram and its interpretive drawing of areplicating E. coli chromosome. The bacterium had been grownfor somewhat more than one generation in a medium containing[3H]thymidine, thereby labeling the subsequently synthesizedDNA so that it appears as a line of dark grains in thephotographic emulsion (red lines in the interpretive drawing). Thesize of the replication eye indicates that the circular chromosomeis about one-sixth duplicated in the present round of replication.[Courtesy of John Cairns, Cold Spring Harbor Laboratory,New York.] Figure 30-3 Replication of DNA.

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(recall that B-DNA has !10 bp per turn). But since theE. coli chromosome is, in fact, circular, even this could notoccur. Rather, the DNA molecule would accumulate !100supercoils/s (see Section 29-3A for a discussion of super-coiling) until it became too tightly coiled to permit furtherunwinding. Naturally occurring DNA’s negative supercoil-ing promotes DNA unwinding but only to the extent of!5% of its duplex turns (recall that naturally occurringDNAs are typically underwound by one supercoil per !19duplex turns; Section 29-3Bb). In prokaryotes, however,negative supercoils may be introduced into DNA throughthe action of a type IIA topoisomerase (DNA gyrase; Sec-tion 29-3Cd) at the expense of ATP hydrolysis.This processis essential for prokaryotic DNA replication as is demon-strated by the observation that DNA gyrase inhibitors,such as novobiocin, arrest DNA replication except in mu-tants whose DNA gyrase does not bind these antibiotics.

C. Semidiscontinuous Replication

The low-resolution images provided by autoradiogramssuch as Figs. 30-2 and 30-4b suggest that dsDNA’s twoantiparallel strands are simultaneously replicated at an ad-vancing replication fork. Yet, all known DNA polymerasescan only extend DNA strands in the 5¿ S 3¿ direction. How,then, does DNA polymerase copy the parent strand thatextends in the 5¿ S 3¿ direction past the replication fork?This question was answered in 1968 by Reiji Okazakithrough the following experiments. If a growing E. coli cul-ture is pulse-labeled for 30 s with [3H]thymidine, much ofthe radioactive and hence newly synthesized DNA has asedimentation coefficient in alkali of 7S to 11S. These so-called Okazaki fragments evidently consist of only 1000 to2000 nucleotides (nt; 100–200 nt in eukaryotes). If, how-ever, following the 30 s [3H]thymidine pulse, the E. coli aretransferred to an unlabeled medium (a pulse–chase exper-iment), the resulting radioactively labeled DNA sedimentsat a rate that increases with the time that the cells hadgrown in the unlabeled medium. The Okazaki fragmentsmust therefore become covalently incorporated into largerDNA molecules.

Okazaki interpreted his experimental results in terms ofthe semidiscontinuous replication model (Fig. 30-5). Thetwo parent strands are replicated in different ways. Thenewly synthesized DNA strand that extends 5¿ S 3¿ in the di-rection of replication fork movement, the so-called leadingstrand, is essentially continuously synthesized in its 5¿ S 3¿direction as the replication fork advances. The other newlysynthesized strand, the lagging strand, is also synthesized inits 5¿ S 3¿ direction but discontinuously as Okazaki frag-ments.The Okazaki fragments are only covalently joined to-gether sometime after their synthesis in a reaction catalyzedby the enzyme DNA ligase (Section 30-2D).

The semidiscontinuous model of DNA replication iscorroborated by electron micrographs of replicatingDNA showing single-stranded regions on one side of the

Section 30-1. DNA Replication: An Overview 1175

Figure 30-4 Autoradiographic differentiation of unidirectionaland bidirectional ! replication of DNA. (a) An organism isgrown for several generations in a medium that is lightly labeledwith [3H]thymidine so that all of its DNA will be visible in anautoradiogram. A large amount of [3H]thymidine is then addedto the medium for a few seconds before the DNA is isolated(pulse labeling) in order to label only those bases near thereplication fork(s). Unidirectional DNA replication will exhibitonly one heavily labeled branch point (above), whereasbidirectional DNA replication will exhibit two such branchpoints (below). (b) An autoradiogram of E. coli DNA so treated,demonstrating that it is bidirectionally replicated. [Courtesy ofDavid M. Prescott, University of Colorado.]

Unidirectionalreplication

Heavilylabeled DNA

Bidirectionalreplication

Lightlylabeled DNA

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(b)

3′

5′

3′

5′

3′

5′

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Leading strand

Lagging strand (Okazaki fragments)Parental strands

Motion ofreplicationfork

Figure 30-5 Semidiscontinuous DNA replication. In DNAreplication, both daughter strands (leading strand red, laggingstrand blue) are synthesized in their 5¿ S 3¿ directions. Theleading strand is synthesized continuously, whereas the laggingstrand is synthesized discontinuously.

JWCL281_c30_1173-1259.qxd 8/10/10 9:10 PM Page 1175

(recall that B-DNA has !10 bp per turn). But since theE. coli chromosome is, in fact, circular, even this could notoccur. Rather, the DNA molecule would accumulate !100supercoils/s (see Section 29-3A for a discussion of super-coiling) until it became too tightly coiled to permit furtherunwinding. Naturally occurring DNA’s negative supercoil-ing promotes DNA unwinding but only to the extent of!5% of its duplex turns (recall that naturally occurringDNAs are typically underwound by one supercoil per !19duplex turns; Section 29-3Bb). In prokaryotes, however,negative supercoils may be introduced into DNA throughthe action of a type IIA topoisomerase (DNA gyrase; Sec-tion 29-3Cd) at the expense of ATP hydrolysis.This processis essential for prokaryotic DNA replication as is demon-strated by the observation that DNA gyrase inhibitors,such as novobiocin, arrest DNA replication except in mu-tants whose DNA gyrase does not bind these antibiotics.

C. Semidiscontinuous Replication

The low-resolution images provided by autoradiogramssuch as Figs. 30-2 and 30-4b suggest that dsDNA’s twoantiparallel strands are simultaneously replicated at an ad-vancing replication fork. Yet, all known DNA polymerasescan only extend DNA strands in the 5¿ S 3¿ direction. How,then, does DNA polymerase copy the parent strand thatextends in the 5¿ S 3¿ direction past the replication fork?This question was answered in 1968 by Reiji Okazakithrough the following experiments. If a growing E. coli cul-ture is pulse-labeled for 30 s with [3H]thymidine, much ofthe radioactive and hence newly synthesized DNA has asedimentation coefficient in alkali of 7S to 11S. These so-called Okazaki fragments evidently consist of only 1000 to2000 nucleotides (nt; 100–200 nt in eukaryotes). If, how-ever, following the 30 s [3H]thymidine pulse, the E. coli aretransferred to an unlabeled medium (a pulse–chase exper-iment), the resulting radioactively labeled DNA sedimentsat a rate that increases with the time that the cells hadgrown in the unlabeled medium. The Okazaki fragmentsmust therefore become covalently incorporated into largerDNA molecules.

Okazaki interpreted his experimental results in terms ofthe semidiscontinuous replication model (Fig. 30-5). Thetwo parent strands are replicated in different ways. Thenewly synthesized DNA strand that extends 5¿ S 3¿ in the di-rection of replication fork movement, the so-called leadingstrand, is essentially continuously synthesized in its 5¿ S 3¿direction as the replication fork advances. The other newlysynthesized strand, the lagging strand, is also synthesized inits 5¿ S 3¿ direction but discontinuously as Okazaki frag-ments.The Okazaki fragments are only covalently joined to-gether sometime after their synthesis in a reaction catalyzedby the enzyme DNA ligase (Section 30-2D).

The semidiscontinuous model of DNA replication iscorroborated by electron micrographs of replicatingDNA showing single-stranded regions on one side of the

Section 30-1. DNA Replication: An Overview 1175

Figure 30-4 Autoradiographic differentiation of unidirectionaland bidirectional ! replication of DNA. (a) An organism isgrown for several generations in a medium that is lightly labeledwith [3H]thymidine so that all of its DNA will be visible in anautoradiogram. A large amount of [3H]thymidine is then addedto the medium for a few seconds before the DNA is isolated(pulse labeling) in order to label only those bases near thereplication fork(s). Unidirectional DNA replication will exhibitonly one heavily labeled branch point (above), whereasbidirectional DNA replication will exhibit two such branchpoints (below). (b) An autoradiogram of E. coli DNA so treated,demonstrating that it is bidirectionally replicated. [Courtesy ofDavid M. Prescott, University of Colorado.]

Unidirectionalreplication

Heavilylabeled DNA

Bidirectionalreplication

Lightlylabeled DNA

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(b)

3′

5′

3′

5′

3′

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Motion ofreplicationfork

Figure 30-5 Semidiscontinuous DNA replication. In DNAreplication, both daughter strands (leading strand red, laggingstrand blue) are synthesized in their 5¿ S 3¿ directions. Theleading strand is synthesized continuously, whereas the laggingstrand is synthesized discontinuously.

JWCL281_c30_1173-1259.qxd 8/10/10 9:10 PM Page 1175

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Polymerasechainreaction,ashorthistory(editedversionofhttps://en.wikipedia.org/wiki/History_of_polymerase_chain_reaction)

• OnApril25,1953JamesD.WatsonandFrancisCrickpublished"aradicallydifferentstructure"forDNA,therebyfoundingthefieldofmoleculargenetics.Theirstructuralmodelfeaturedtwostrandsofcomplementarybase-pairedDNA,runninginoppositedirectionsasadoublehelix.Theyconcludedtheirreportsayingthat"Ithasnotescapedournoticethatthespecificpairingwehavepostulatedimmediatelysuggestsapossiblecopyingmechanismforthegeneticmaterial". ForthisinsighttheywereawardedtheNobelPrizein1962.

• Startinginthemid-1950s,ArthurKornbergbegantostudythemechanismofDNAreplication.By1957hehasidentifiedthefirstDNApolymerase.Theenzymewaslimited,creatingDNAinjustonedirectionandrequiringanexistingprimertoinitiatecopyingofthetemplatestrand.Overall,theDNAreplicationprocessissurprisinglycomplex,requiringseparateproteinstoopentheDNAhelix,tokeepitopen,tocreateprimers,tosynthesizenewDNA,toremovetheprimers,andtotiethepiecesalltogether. KornbergwasawardedtheNobelPrizein1959.

• Intheearly1960sH.GobindKhoranamadesignificantadvancesintheelucidationofthegeneticcode.Afterwards,heinitiatedalargeprojecttototallysynthesizeafunctionalhumangene.Toachievethis,KhoranapioneeredmanyofthetechniquesneededtomakeandusesyntheticDNAoligonucleotides.Sequence-specificoligonucleotideswereusedbothasbuildingblocksforthegene,andasprimersandtemplatesforDNApolymerase. In1968KhoranawasawardedtheNobelPrizeforhisworkontheGeneticCode.


• In1969ThomasD.BrockreportedtheisolationofanewspeciesofbacteriumfromahotspringinYellowstoneNationalPark.Thermusaquaticus (Taq),becameastandardsourceofenzymesabletowithstandhighertemperaturesthanthosefromE.Coli.

• In1970KlenowreportedamodifiedversionofDNAPolymeraseIfromE.coli.TheoverallactivityoftheresultingKlenowfragmentisbiasedtowardsthesynthesisofDNA,ratherthanitsdegradation.

• By1971researchersinKhorana'sproject,concernedovertheiryieldsofDNA,beganlookingat"repairsynthesis"– anartificialsystemofprimersandtemplatesthatallowsDNApolymerasetocopysegmentsofthegenetheyaresynthesizing.

• Circa1971KjellKleppe,aresearcherinKhorana'slab,envisionedaprocessverysimilartoPCR.Attheendofapaperontheearliertechnique,hedescribedhowatwo-primersystemmightleadtoreplicationofaspecificsegmentofDNA.

• Alsoin1971,CetusCorporationwasfoundedinBerkeley,CaliforniabyRonaldCape,PeterFarley,andDonaldGlaser.Initiallythecompanyscreenedformicroorganismscapableofproducingcomponentsusedinthemanufactureoffood,chemicals,vaccines,orpharmaceuticals.AftermovingtonearbyEmeryville,theybeganprojectsinvolvingthenewbiotechnologyindustry,primarilythecloningandexpressionofhumangenes,butalsothedevelopmentofdiagnostictestsforgeneticmutations.


• In1976aDNApolymerase[12]wasisolatedfromT.aquaticus.Itwasfoundtoretainitsactivityattemperaturesabove75°C.

• In1977FrederickSangerreportedamethodfordeterminingthesequenceofDNA.Thetechniqueemployedanoligonucleotideprimer,DNApolymerase,andmodifiednucleotideprecursorsthatblockfurtherextensionoftheprimerinsequence-dependentmanner. ForthisinnovationhewasawardedtheNobelPrizein1980.

• By1980allofthecomponentsneededtoperformPCRamplificationwereknowntothescientificcommunity.

• In1979CetusCorporationhiredKaryMullistosynthesizeoligonucleotidesforvariousresearchanddevelopmentprojectsthroughoutthecompany.Theseoligoswereusedasprobesforscreeningclonedgenes,asprimersforDNAsequencingandcDNAsynthesis,andasbuildingblocksforgeneconstruction.Originallysynthesizingtheseoligosbyhand,Mullislaterevaluatedearlyprototypesforautomatedsynthesizers.

• ByMay1983MullissynthesizedoligonucleotideprobesforaprojectatCetustoanalyzeasicklecellanemiamutation.Hearingofproblemswiththeirwork,MullisproposedanalternativetechniquebasedonSanger'sDNAsequencingmethod.RealizingthedifficultyinmakingtheSangermethodspecifictoasinglelocationinthegenome,Mullisthenmodifiedtheideatoaddasecondprimerontheoppositestrand.Repeatedapplicationsofpolymerasecouldleadtoachainreactionofreplicationforaspecificsegmentofthegenome– PCR.

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strand adjacent to the site where the primer binds.

W hat r did not realize at the time was that there were many good reasons why

my sequencing idea could not work. The problem was that oligonudeo-tides sometimes hybridize with DNA sequences other than those intend-ed; these unavoidable pairings would have made my results ambiguous. Even in the hands of those skilled in the art of careful hybridization, it was impossible to bind oligonucleotides to whole human DNA with sufficient specificity to get ,anything even ap-proaching a meaningful result.

It was because of this limitation that researchers had resorted to more dif-ficult procedures for looking at hu-man DNA. For instance, restriction en-zymes could be employed to cleave the DNA sample into various frag-ments that could be separated from each other by electrophoresis; in this way, the sample could be "purified," to some extent; of all DNA except the target fragment before the hybridiza-tion of oligonucleotide probes. This approach reduced erroneous hybridi-zations sufficiently to provide mean-ingful data, but just barely. Moreover, this procedure was lengthy and would not work on degraded or denatured samples of DNA.

Another technique that was much too lengthy for routine DNA analysis involved cloning. A human DNA se-quence of interest could be cloned, or copied, into a small ring of DNA called a plasmid. Copies of this plasmid and the targeted sequence could then be produced in bacteria, and sequence information could be obtained by oli-gonucleotide hybridization and dide-oxy sequencing. In the early 1980's dideoxy sequencing of cloned DNA was the method by which most human DNA sequence information had been obtained.

In proposing my simple-minded ex-periment, I was implicitly assuming that no such cloning or other step would be necessary to detect specif-ic human DNA sequences by a single oligonucleotide hybridization. In to-ken defense of my misguided putter-ing, I can point out that a group down the hall led by Henry A. Erlich, one of Cetus's senior scientists, was trying another method based on the hybridi-zation of a single oligonucleotide to a human DNA target. No one laughed out loud at Henry, and we were all being paid regularly. In fact, we were being paid enough to lead some of us to assume, perhaps brashly, that we

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DNA POLYMERASE, an enzyme, can lengthen a s hort strand of DNA, called an oli-gonucleotide primer, if the strand is bound to a longer "template" strand of DNA. The polymerase does this by adding the appropriate complementary nucleotide to the three-prime end of the bound primer. If a dideoxynucleotide triphosphate (ddNTP) s uch as dideoxyadenine (ddA) is added, however, no further extension is possible, because the three-prime end of the ddA will not link to other nucleotides.

were somewhere near the cu tting edge of DNA technology.

0 ne Friday evening late in the spring I was driving to Men-docino County with a chemist

friend. She was asleep. U.S. 101 was undemanding. I liked night driving; every weekend r went north to my cabin and sat still for three hours in the car, my hands occupied, my mind

free. On that particular night I was thinking about my proposed DNA-se-quencing experiment.

My plans were straightforward. First I would separate a DNA target into single strands by heating it. Then I would hybridize an oligonucleotide to a complementary sequence on one of the s trands. I would place portions of this DNA mixture into four different tubes. Each tube would contain all

SCIENTIFIC AMERICAN April 1990 59

DNAPOLYMERASE,anenzyme,canlengthenashortstrandofDNA,calledanoli-gonucleotideprimer,ifthestrandisboundtoalonger"template"strandofDNA.Thepolymerasedoesthisbyaddingtheappropriatecomplementarynucleotidetothethree-primeendoftheboundprimer.Ifadideoxynucleotidetriphosphate(ddNTP)suchasdideoxyadenine(ddA)isadded,however,nofurtherextensionispossible,becausethethree-primeendoftheddAwillnotlinktoothernucleotides.

(fromMullis,“TheUnusualOriginsofthePolymeraseChainReaction”ScientificAmerican,vol.262,pp.56–65(April1990))


• Laterin1983Mullisbegantotesthisidea.Mullisconsideredtheseexperimentsasuccess,butcouldnotconvinceotherresearchers.

• InJune1984CetushelditsannualmeetinginMonterey,California.Itsscientistsandconsultantspresentedtheirresults,andconsideredfutureprojects.Mullispresentedaposterontheproductionofoligonucleotidesbyhislaboratory,andpresentedsomeoftheresultsfromhisexperimentswithPCR.OnlyJoshuaLederberg,aCetusconsultant,showedanyinterest.Lateratthemeeting,MulliswasinvolvedinaphysicalaltercationwithanotherCetusresearcheroveradisputeunrelatedtoPCR.Theotherscientistleftthecompany,andMulliswasremovedasheadoftheoligosynthesislab.

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• InSeptember1984TomWhite,VPofResearchatCetus(andaclosefriend),pressuredMullistotakehisideatothegroupdevelopingthegeneticmutationassay.Together,theyspentthefollowingmonthsdesigningexperimentsthatcouldconvincinglyshowthatPCRisworkingongenomicDNA.Unfortunately,theexpectedamplificationproductwasnotvisible,leadingtoconfusionastowhetherthereactionhadanyspecificitytothetargetedregion.

• InNovember1984theamplificationproductswereanalyzedwithamoresensitivemethod,whichclearlydemonstratingincreasingamountoftheexpected110bpDNAproduct.Havingthefirstvisiblesignal,theresearchersbeganoptimizingtheprocess.Later,theamplifiedproductswereclonedandsequenced,showingthatonlyasmallfractionoftheamplifiedDNAisthedesiredtarget,andthattheKlenowfragmentthenbeingusedonlyrarelyincorporatesincorrectnucleotidesduringreplication.


• Aspernormalindustrialpractice,theresultswerefirstusedtoapplyforpatents.MullisappliedforapatentcoveringthebasicideaofPCRandmanypotentialapplications,andwasaskedbythePTOtoincludemoreresults.OnMarch28,1985theentiredevelopmentgroupfiledanapplicationthatismorefocused.Aftermodification,bothpatentswereapprovedonJuly28,1987.

• Inthespringof1985thedevelopmentgroupbegantoapplythePCRtechniquetoothertargets.PrimersandprobesweredesignedforavariablesegmentoftheHumanleukocyteantigenDQαgene.Theamplificationproductsfromvarioussourceswerealsoclonedandsequenced,thefirstdeterminationofnewallelesbyPCR.

• Alsoearlyin1985,thegroupbeganusingathermostableDNApolymerase(theenzymeusedintheoriginalreactionisdestroyedateachheatingstep).ThatsummerMullisattemptedtoisolatetheenzyme,andagroupoutsideofCetuswascontractedtomakeit,allwithoutsuccess.IntheFallof1985SusanneStoffelandDavidGelfandatCetussucceedinmakingthepolymerase,anditwasimmediatelyfoundbyRandySaikitosupportthePCRprocess.

• Withpatentssubmitted,workproceededtoreportPCRtothegeneralscientificcommunity.AnabstractwassubmittedinApril1985,andthefirstannouncementofPCRwasmadetherebySaikiinOctober.Twopublicationswereplanned– an'idea'paperfromMullis,andan'application'paperfromtheentiredevelopmentgroup.MullissubmittedhismanuscripttothejournalNature,whichrejecteditfornotincludingresults.Theotherpaper,mainlydescribingtheORanalysisassay,wassubmittedtoScienceonSeptember20,1985andwasacceptedinNovember.AftertherejectionofMullis'reportinDecember,detailsonthePCRprocesswerehastilyaddedtothesecondpaper,whichappearsonDecember20,1985.


• InMay1986MullispresentedPCRattheColdSpringHarborSymposium,andpublishedamodifiedversionofhisoriginal'idea'manuscriptmuchlater.Thefirstnon-CetusreportusingPCRwassubmittedonSeptember5,1986,indicatinghowquicklyotherlaboratoriesbeganimplementingthetechnique.

• TheuseofTaqpolymeraseinPCRwasannouncedbyHenryErlichatameetinginBerlinonSeptember20,1986,submittedforpublicationinOctober1987,andwaspublishedearlythenextyear'.ThepatentforPCRwithTaqpolymerasewasfiledonJune17,1987,andisissuedonOctober23,1990.

• In1986EdwardBlake,aforensicsscientistworkingintheCetusbuilding,collaboratedwithHenryErlicharesearcheratCetus,toapplyPCRtotheanalysisofcriminalevidence.ApanelofDNAsamplesfromoldcaseswascollectedandcoded,andwasanalyzedblindbySaikiusingtheHLADQαassay.Whenthecodewasbroken,alloftheevidenceandperpetratorsmatched.BlakeandErlich'sgroupusedthetechniquealmostimmediatelyin"Pennsylvaniav.Pestinikas",thefirstuseofPCRinacriminalcase.

• ThisDQαtestisdevelopedbyCetusasoneoftheir"Ampli-Type"kits,andbecamepartofearlyprotocolsforthetestingofforensicevidence,suchasintheO.J.Simpsonmurdercase.

• By1989AlecJeffreys,whohadearlierdevelopedandappliedthefirstDNAFingerprintingtests,usedPCRtoincreasetheirsensitivity.Withfurthermodification,theamplificationofhighlypolymorphicVNTRlocibecamethestandardprotocolforNationalDNADatabasessuchasCODIS.


• In1987RussHiguchisucceededinamplifyingDNAfromahumanhair.ThisworkexpandedtodevelopmethodsfortheamplificationofDNAfromhighlydegradedsamples,suchasfromAncientDNAandinforensicevidence.

• OnDecember22,1989thejournalScienceawardedTaqPolymerase(andPCR)itsfirst"MoleculeoftheYear".The'TaqPCR'paperbecameforseveralyearsthemostcitedpublicationinbiology.

• AfterthepublicationofthefirstPCRpaper,theUnitedStatesGovernmentsentasternlettertoRandySaiki,admonishinghimforpublishingareporton"chainreactions"withouttherequiredpriorreviewandapprovalbytheU.S.DepartmentofEnergy.Cetusresponded,explainingthedifferencesbetweenPCRandtheatomicbomb.

• OnJuly23,1991CetusannouncedthatitssaletotheneighboringbiotechnologycompanyChiron.Aspartofthesale,rightstothePCRpatentsweresoldforUSD$300milliontoHoffman-LaRoche(whoin1989hadboughtlimitedrightstoPCR).ManyoftheCetusPCRresearchersmovedtotheRochesubsidiary,RocheMolecularSystems.

• OnOctober13,1993KaryMullis,whohadleftCetusin1986,wasawardedtheNobelPrizeinChemistry.Onthemorningofhisacceptancespeech,hewasnearlyarrestedbySwedishauthoritiesforthe"inappropriateuseofalaserpointer".


TheforcesthatkeeptheDNAtogether

• covalentbondsalongthesugar-phosphatebackbone

• hydrogenbondsbetweencomplementarybases

• stackinginteractionsbetweenadjacentbasepairs(mostlyVanderWaalsinteractions,about0.5kcal/mole,approximately10timesweakerthanhydrogenbondsinwater)


Ingeneral,thestrengthofthehydrogenbonds(about5kcal/mole)isintermediatebetweenVanderWaalsinteractions(about0.3kcal/mole),andcovalentchemicalbonds(about100kcal/mole).

Notethat

5kcal/mole≈0.2eV/molecule

Thismustbecomparedwiththethermalenergyatroomtemperature

3/2kT ≈0.04eV/molecule

ThereforethermalagitationcandestroythehydrogenbondsthatpairbasesintheDNAmolecule.


FromM.Peyrard,“NonlineardynamicsandstatisticalphysicsofDNA”,Nonlinearity17(2004)R1

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M#*$*(#/$)&".L%..1&#H&H%.."#-&#H&+I>&<$1.13&H%#-&=**,JKKb_"/$?#%LK$%*(2).1K1..(/L8(18:/".%1*$/"(/L8$18G.))8$18<.)(.5(/L


FromC.R.Calladine,H.R.Drew,B.F.Luisi,andA.A.Travers,“UnderstandingDNA:TheMolecule&HowItWorks”,3rd ed.(Elsevier,2004).


“Molecularzipper”modelofDNA(Kittel,1969)

N links

lastlinkstaysfixed

ThereareN states,characterizedbyp =0,...,p =N-1openlinks


Energytoopenonelink:

Energytoopenp links:

Degeneracy(rotational):

Degeneracyofp openlinks:

Partitionfunction

ε

pε

g

gp

Z = gp exp −pε( )kBT

⎛⎝⎜

⎞⎠⎟p=0

N−1

∑


Z = gp exp − pεkBT

⎛⎝⎜

⎞⎠⎟p=0

N−1

∑ = x pp=0

N−1

∑ = 1− xN

1− x

x = gexp − εkBT

⎛⎝⎜

⎞⎠⎟

...itiseasytofindaclosedexpressionforthepartitionfunction


then,themeannumberofopenlinksis

hsi = 1

Z

N�1X

p=0

pg

pexp

✓� p"

kBT

◆=

1

Z

N�1X

p=0

px

p

=

1

Z

N�1X

p=1

px

p=

1

Z

x

d

dx

N�1X

p=0

x

p= x

d lnZ

dx

= x

d

dx

⇥ln(1� x

N)� ln(1� x)

⇤=

Nx

N

x

N � 1

+

x

1� x

=

Ng

Ne

�N"/kBT

g

Ne

�N"/kBT � 1

+

ge

�"/kBT

1� ge

�"/kBT

(where x = ge

�"/kBT)


0.96 0.98 1.00 1.02 1.040

200

400

600

800

1000

s

x


Thefirst-orderTaylorexpansionaboutx=1is

(proveit!),anditshowsthat

andthetransitionatx =1becomesinfinitelysharpasNgrowsindefinitely

s = NxN

xN −1+ x1− x

≈ 12N −1( ) + 1

12N 2 −1( ) x −1( )

sN

= 12N

N −1( ) + 112N

N 2 −1( ) x −1( )

N1⎯ →⎯⎯ 12+ N12

x −1( )


Thetransitionpointcorrespondsto

i.e.,therecanbeatransitionfromtheboundtotheopenstateatfinitetemperature onlyifthedegeneracyg isgreaterthan1,i.e.,ifeachlinkhasatruerotationalfreedom.

x = gexp − εkBT

⎛⎝⎜

⎞⎠⎟= 1 ⇒ g = exp ε

kBT⎛⎝⎜

⎞⎠⎟>1


Noticealsothatforagiveng,thetransitiontemperatureisdeterminedby

x = gexp − εkBT

⎛⎝⎜

⎞⎠⎟= 1

⇒ lng = εkBT

⇒ T = εkB lng


Theprobabilitythatalllinksareopen(except,obviously,thelast,fixedone)is

andatthetransitionpoint(Dx =0)theprobabilityP =1/NisverysmallwhenN >>1.

P = 1ZgN−1 exp −

N −1( )εkBT

⎛⎝⎜

⎞⎠⎟= xN−1

Z

= xN−1 1− x1− xN

≈ 1N1− N −1

2Δx⎛

⎝⎜⎞⎠⎟ ≈

1N

− Δx2

closetothethetransition N>>1


Knowledgeofthepartitionfunctionenablesustocarryoutallsortsofthermodynamiccalculations.Forinstance,themeanenergyis

andthereforethecorrespondingheatcapacityis

U = NZ

pεgp exp − pεkBT

⎛⎝⎜

⎞⎠⎟p=0

N−1

∑ = NεZ

px pp=0

N−1

∑ = Nε s

= Nε NxN

xN −1+ x1− x

⎛⎝⎜

⎞⎠⎟= Nε NgNe−Nε kBT

gNe−Nε kBT −1+ ge−ε kBT

1− ge−ε kBT

⎛⎝⎜

⎞⎠⎟

C = dUdT

= dxdT

dUdx

= − kBxε lng

ln x( )2 Nε ddx

NxN

xN −1+ x1− x

⎛⎝⎜

⎞⎠⎟


Thehelix-to-coiltransitionWhenDNAisheated,hydrogenbondsbreak,andDNA“melts”,(thermalDNAdenaturation)turningthelinearchainsintotangles(coils).

Thisisdifferentfromtheunzippingdescribedearlier.

T


Opticalmeasurementscanbeusedtodetectthe“meltingtransition”

G.L.B

aker&M

.E.A

lden

,“OpticalRotationandtheDN

AHe

lix-To-Co

ilTransition”,J.C

hem.Edu

c.51(1974)591


• TheAandBformsofDNAareright-handed.

• TheZformisleft-handed.

• Thehandednessisdetectedwithopticalrotationmeasurements.

• TheZformmaybebiologicallyimportantduringDNAtranscription.


Theopticalmeasurementscanbetranslatedintoafractionofintactbonds

G.L.B

aker,“DN

Ahe

lix-to

-coiltransition

:Asimplified

mod

el”,Am

.J.Phys.44

(1976)599


WecookupamodelstartingfromthefractionofintactDNAbasepairs

where isaspin-likevariable,suchthat

andwhereJ istheinteractionstrengthbetweentheintactandthebrokenlinks(energychangeinunitsofkB T).

f = 121+σ i( ) = 1

21+ σ i( )

σ i

σ i =+1 pair intact−1 pair broken

⎧⎨⎪

⎩⎪


Thepartitionfunctionforasinglebasepairis

whilethepartitionfunctionforthewholesystemis(neglectingcorrelations)

Thentheaveragevalueforthepseudo-spinvariableis

Zi = exp − 12σ i J

⎛⎝⎜

⎞⎠⎟

σ i=−1

+ exp − 12σ i J

⎛⎝⎜

⎞⎠⎟

σ i=+1

= 2cosh 12J⎛

⎝⎜⎞⎠⎟

Z = Zii∏

σ i = 1Zi

σ i exp − 12σ i J

⎛⎝⎜

⎞⎠⎟

σ i=−1

+σ i exp − 12σ i J

⎛⎝⎜

⎞⎠⎟

σ i=+1

⎡

⎣⎢⎢

⎤

⎦⎥⎥= − tahn 1

2J⎛

⎝⎜⎞⎠⎟


andthenthefractionofintactDNAbasepairsis

Westilldonothaveatemperaturedependence,butherewenotethat

J = J T( ); f TC( ) = 12

⇒ J TC( ) = 0

J T( ) = ′a T −TC( ) + ′b T −TC( )2 +…

criticaltemperature(bydefinition)

expansionaboutthecriticaltemperature

f =

1

2

(1 + h�ii) =1

2

✓1� tanh

J

2

◆=

1

2

exp

✓�J

2

◆sech

✓J

2

◆


Then,keepingonlythefirstorderterms

Veryclosetothetransitionwecanalsowrite

Gibbsfreeenergy

J T( ) ≈ ΔGRT

= ΔH −TΔSRT

J TC( ) = 0

ΔH ≈ TCΔS

f =

1

2

exp [�a(T � TC)] sech [a(T � TC)]

J(T ) ⇡ �H

RTC� T�H

RT 2C

= � �H

RT 2C

(T � TC); a = � �H

2RT 2C


T = 364 K

a ⇡ 0.08 K�1

�H ⇡ 51

kcal

mole

Thisisactuallyanoverestimate:recentcalculationsofH-bondstrengthinDNAyieldvalues

fortheGCbondand

fortheATbond

�H ⇡ 27

kcal

mole

�H ⇡ 13

kcal

mole


HelicasedynamicsandDNAunzipping

dnidt

= − α + β( )ni +αni−1 + βni+1

ni =numberofsystemswithi intactbonds


Equilibriumsolution(attemperatureT)

dnidt

= − α + β( )ni +αni−1 + βni+1 = 0

− α + β( ) +α ni−1ni

+ β ni+1ni

= 0


Sinceatequilibrium(seethepreviousdiscussion)

nl ∝ gN−l exp −N − l( )εkBT

⎡

⎣⎢

⎤

⎦⎥

nl−1nl

=gN−l+1 exp − N − l +1( )ε

kBT⎡

⎣⎢

⎤

⎦⎥

gN−l exp − N − l( )εkBT

⎡

⎣⎢

⎤

⎦⎥

= gexp − εkBT

⎡

⎣⎢

⎤

⎦⎥ = exp − ε − kBT lng

kBT⎡

⎣⎢

⎤

⎦⎥


ε − kBT lng = ε −TΔS = ΔG

nl−1nl

= exp − ΔGkBT

⎡

⎣⎢

⎤

⎦⎥

− α + β( ) +α ni−1ni

+ β ni+1ni

= 0 − α + β( ) +αe− ΔGkBT + βe

ΔGkBT = 0


Therefore

− α + β( ) +αe− ΔGkBT + βe

ΔGkBT = 0

α e− ΔGkBT −1

⎛

⎝⎜⎞

⎠⎟= β 1− e

ΔGkBT

⎛

⎝⎜⎞

⎠⎟= βe

ΔGkBT e

− ΔGkBT −1

⎛

⎝⎜⎞

⎠⎟

αβ= e

ΔGkBT


meansthatunzippingisfasterthanzippingif

i.e.,onlyif

αβ= e

ΔGkBT

β =αe− ΔGkBT >α

ΔG < 0 ⇒ ε − kBT lng < 0 ⇒ T > TM = εkB lng

meltingtemperature,inagreementwiththepreviousanalysisbasedonstatisticalmechanics

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!"#$%"#&'()#**(&8 9/*%#":2*#%;&<(#,=;1(21&8 >?@?&ABCD8CE

=**,JKKGGG?==-(?#%LK<(#(/*.%$2*(5.K,#);-.%$1.82=$(/8%.$2*(#/8,2%


References

• C.R.Calladine,H.R.Drew,B.F.Luisi,andA.A.Travers,“UnderstandingDNA:TheMolecule&HowItWorks”,3rd ed.(Elsevier,2004).

• M.Peyrard,“NonlineardynamicsandstatisticalphysicsofDNA”,Nonlinearity17(2004)R1

• C.Kittel,“PhaseTransitionofaMolecularZipper”,Am.J.Phys.37 (1969)917

• G.L.Baker,“DNAhelix-to-coiltransition:Asimplifiedmodel”,Am.J.Phys.44(1976)599

• S.G.J.Mochrie,“TheBoltzmannfactor,DNAmelting,andBrownianratchets:Topicsinanintroductoryphysicssequenceforbiologyandpremedicalstudents”,Am.J.Phys.79 (2011)1121

• R.P.Wagner,“UnderstandingInheritance”,LosAlamosScience,n.20(1992)

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