http powerxeditor.aptaracorp.com ecosal DashBoard Homerothlab.ucdavis.edu/publications/ASMProofs2010.pdffundamental to the whole ﬁeld of bacterial genetics. The experiments also

doi: 10.1128/ecosal.5.6.6

MMoodduullee55..66..66

TThheeOOrriiggiinnooffMMuuttaannttssuunnddeerrSSeelleeccttiioonn::IInntteerraaccttiioonnssooffMMuuttaattiioonn,,GGrroowwtthh,,aannddSSeelleeccttiioonn

DANI.ANDERSSON,1*DIARMAIDHUGHES,2ANDJOHNR.ROTH3

[SECTIONEDITOR:STEVENFINKEL]

Postedxxx2010

DepartmentofMedicalBiochemistryandMicrobiology,UppsalaUniversity,S-75123Uppsala,1andDepartmentofCellandMolecularBiology,

UppsalaUniversity,S-75124Uppsala,2Sweden,andDepartmentofMicrobiology,CBS,UniversityofCalifornia—Davis,Davis,CA956163

*Correspondingauthor.Mailingaddress:DepartmentofMedicalBiochemistryandMicrobiology,UppsalaUniversity,S-75123Uppsala,Sweden.Phone:+460184714175,E-mail:[email protected]

IINNTTRROODDUUCCTTIIOONN

Mutation rates are kept low by multiple mechanisms evolved to protect genetic information and these rates are notregulated in response to the physiological needs of the cell. This broadly held consensus rests on classical bacterialexperiments interpreted as evidence that selective stress does not alter the mutation process (40, 44). This is not to saythat all repair mechanisms are equally active at all times (12, 30). For example, mutation-repair mechanisms withdifferent substrate specificities, such as MMR and VSR, are differentially active under different conditions of bacterialgrowth, although both use the MutL protein (5, 11). The interaction between mutation and selection is complex and hasbeen central to the history of biology. Before publication of Darwin's theory of natural selection, induction of geneticchange by environmental stress was a popular idea (46). Translated into microbiological terms, this idea posited that thestress imposed by growth limitation increases the rate at which new mutations arise (stress-induced mutagenesis).Darwin may have accepted the idea of stress-induced mutation to explain the origin of the variability required fornatural selection (46). However, the lack of experimental evidence on this point contributed to the importance of theclassic work of Luria and Delbrück (44) and of the Lederbergs (40) demonstrating that laboratory selections can detectmutant organisms without causing their formation. These experiments validated the use of positive selection, which isfundamental to the whole field of bacterial genetics. The experiments also provided a way to measure the formation rateof mutations during nonselective growth. Later, these classic experiments were more broadly interpreted as support forthe current consensus that selective stress does not induce mutations in natural populations.

Later,aflawintheevidenceforthebroadinterpretationwaspointedoutbyCairns,Hall,andShapiro(8,21,56).Theclassicexperimentshadusedlethalselectionstodetectmutantswhoseresistancephenotypeappearedonlyseveralgenerationsaftertheformationofthemutation.Thus,theirselectioncouldonlydetectmutantsthatarosewellwithinthepriorperiodofnonselectivegrowth.Anynonmutantcellexposedtoselectionwouldbekilledbeforeanewmutation could arise and acquire a resistance phenotype. The experiments could not have detected mutationsgeneratedinresponsetostressontheselectionplate.Thisreopenedthequestionofstress-inducedmutationinaslightly different form: “Do all mutations arise independently of selection (as did those studied in the classicexperiments) or could some other mutations (missed by the classic experiments) arise in response to growthlimitation?”Thequestionraiseddoubtsregardingthewidelyheldunderpinningsofevolutionarygeneticsandrequiredexperimentalattention.Directevidencethatgrowthlimitationmightincreasemutationratehasbeensoughtinmanymicrobialsystems

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FFIIGG..11 Effectsofselectionandmutationonmutantfrequency.Intheabsenceofselection,newmutantsaccumulatelinearlywithtime.Whenselectionacts,itcausesanexponentialincreaseinthefrequencyofabeneficialmutation.Thus,inanatural

usingnonlethalselections.Inmostcases,theresultswerenegative.However,afewsystemsshowedbehaviorthathasbeeninterpretedassupportfortheideaofstress-inducedmutagenesis,reviewedin(16,19).Inthesesystems,populationsof cells wereheld under conditions that preventedgrowth, but did not kill. Mutants appeared in thepopulationandtheirformationwasattributedtostress-inducedmutagenesis(16,19).Thesesystemsuseaselectionthat looks like a laboratory positive selection and they interpret increases in mutant frequency as evidence forincreasesinmutationrate.Assuch,thesystemsmustadheretotherulesforlaboratoryselectionvalidatedbyLuriaandDelbrückandLederberg.That is, conditionsmustensurethat the increase inmutant frequencyreflectsnewmutationeventsratherthantheexpansionofapreexistingmutantpopulationduringgrowthunderselection.Belowwedescribehowtherelationshipbetweenmutationrateandmutantfrequencycanbeobscuredinnatural

populations. First, we introduce theplayers—growth, selection, and thevastly different formationratesof variousmutant types. Thenweoutline the“SevenPillars”—theessential rules that allowthe fieldof laboratorymicrobialgeneticstoinfermutationratesfrommutantfrequency.Finally,aseriesofexperimentalsystemsaredescribedandcritically analyzed. Each of these systemshas beenused as support for “stress-inducedmutation.” Evidence ispresentedthateachsystemviolatesoneormoreofthe“pillars”andtherebyallowsselectiontoincreasetheobservedphenotypefrequency(withoutmutagenesis).Thisisnottosaythattherearenotconditionsunderwhichmutationrateswillchange(forexample,UVirradiationorgrowthwithanalkylatingagent).Neitherdoweruleoutthat,inprinciple,abiological system with an environmentally regulated mutation rate might exist. However, we will argue that theexperimentalsystemsandphenomenathathavebeenproposedtosupportstress-inducedincreasesinmutagenesisinnongrowingcellscanbetterbeexplainedastheresultofgrowthunderselection.

MMUUTTAATTIIOONNAANNDDSSEELLEECCTTIIOONN

Each mutational event adds a new genetically distinct cell to the population. The phenotypic consequences of mutationsvary from none (most synonymous substitutions) to lethality (loss of an essential function), but many of these mutationsare expected to generate a phenotype that can be detected by selection. One can experimentally measure the frequencyof mutant cells in a culture, but it is more difficult to assess the actual rate at which the responsible mutations arise,especially those with small phenotypic effects. It is especially difficult to measure the formation rate of adaptivemutations in cells growing under selection.

Ifallotherfactorsarekeptconstant,anincreaseinmutationrateshouldcauseanincreaseinthefrequencyofcellswithabnormalphenotypes.Thereversecorrelationismoredifficult—andunderliesthewholefieldofbacterialgenetics.Doesanincreaseinmutationfrequencyindicatemutagenesis?Geneticsofbacteriareliesonselectiontodetectraremutantsinhugepopulations—itusesthefrequencyofdetectedmutationstoinfertherateofmutantformation.Thisprocedureunderliesmeasurementofmutationratebyfluctuationtest,mutagenspecificity,andrecombinationrates.Thereliability of this proceduredependsonsuccessful eliminationof themany factors (especially selection) thatobscuretherelationshipbetweenmutationrateandmutantfrequency.Incontrast,thefieldofpopulationgeneticsdoesnottrytoestablishasimplerelationshipbetweenmutantfrequency

andrate,butdealsprimarilywiththeinterferingfactors.Innaturalpopulations,interferencecausedbyselectionanddriftissogreatthatchangesinphenotypefrequencyarealmostneverattributedtomutagenesis.Thus,thesetwoareasofgeneticsuseselectioninverydifferentways.Inanaturalpopulation,cellsgrowandare

subjecttoselectionbefore,during,andafterformationofanewmutation,whilelaboratoryproceduressharplyseparateselection from growth and mutation. In a natural population, a new mutant is immediately subject to selectiveconditionsthatcanmakeitsgrowthratefasterorslowerthanitsparent.Selectioncanhavehugeconsequencesforphenotype frequency since selection initially causes exponential increases in phenotype frequency over time. Incontrast,theprocessofmutation(intheabsenceofselection)hasalineareffectonmutantfrequencyovertime(seeFig.1).Itshouldbenotedthatwecannevereliminateallselectiveeffectsfromagrowingpopulation,butwecanfindconditionsthatremoveselectionfromparticularmutantphenotypes.


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population,wherebothselectionandmutationoccurtogether,thefrequencyofafavorablemutantismoreheavilyimpactedbyselectionthanbyrecurringmutationalevents.Itisoftendifficulttoappreciatehowpowerfulexponentialincreasescanbe.

FFIIGG..22 Effectsofselectionandmutationonmutantfrequency.Theverticalaxisisalistofallthegenotypespresentwhenapopulationis initiated.Mutationmaychangethenatureofaparticular lineageandtherelativesizeofeachlineagemaychangebecauseofdifferencesintherelativegrowthrate.Lineagesize(logcell number) isdepictedbythethicknessofhorizontal lines—somedwindleandsomeincreaseexponentially. Dashed lines indicate lineagesalteredbymutationbutunaffectedingrowthrate.

Naturalselectioncandetectminusculedifferencesingrowthrateandthuscanactonthemostcommonmutations,whichhavesmalleffectsonphenotype(seebelow).Thus,adaptationcanoccurrapidlyinnaturalpopulationsbecauseselectioncausesexponentialincreasesinfrequentlyoccurringmutationtypes.Incontrast,laboratorygeneticsusesrestrictiveconditionstoensurethatselectiondetectsonlyrarepreexistinglarge-effectmutationsandhasnoeffectontheirfrequency.Prejudicesdevelopedbecauseofexperiencewithrestrictivelaboratoryselectionsmaymakeitdifficulttoappreciatethespeedatwhichgeneticadaptationcanoccuroncetheserestrictionsarelifted.Figure2depictsthesimplebehaviorexpectedofnaturalpopulationsundervariousconditions.Theverticalaxis

representsalistofdifferentcelllineagesinapopulationandthewidthofeachlinerepresentsthelogarithmofthefrequencyofeachlineage.Withneithermutationnorselection,thefrequencyofeachlineageremainsconstantovertime(Fig.2,top).Withmutationbutnotselection,mutationscanalterthegenotypeofanylineagebutthefrequencyofthe(nowaltered)lineagedoesnotchangevis-à-visothersinthepopulation(Fig.2,middle).Byaffectingonelineageafteranother,mutationcausesalinearincreaseinthefrequencyofmutantcells.


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Whenmutationandselectionoccurtogether,somelineagesacquiredeleteriousmutationsandareremovedfromthepopulationbyselection(linebecomesvanishinglythin).Lineagesthatacquirebeneficialmutationsarefavoredbyselectionandexpandexponentially,increasingthesizeofthelineageandtherebythefrequencyofmutanttypesinthepopulation(Fig.2,bottom).

TThheeMMoossttFFrreeqquueennttMMuuttaattiioonnssHHaavveetthheeSSmmaalllleessttPPhheennoottyyppiiccEEffffeecctt

There is a wide distribution in the magnitude of mutant phenotypes and a wide variation in the rate of forming differentmutation types. The mutation types arising at the highest rates are ones with the smallest phenotypic effect. Forexample, one might consider changes in some enzyme activity and the fraction of the parent activity added or lost by amutation—mutations that cause small changes are more common. This may in part be a consequence of how selectionhas shaped the genetic code (17) and the several systems that prevent mutations and repair DNA damage. Mutations thatmost often escape quality-control systems appear to be those with the smallest phenotypic consequences. Naturalselection can detect vanishingly small differences in growth rate and can therefore act on a larger number of mutations.In contrast, experimental genetics focuses on large-effect mutations that are relatively rare (conventional pointmutations). The experience of a laboratory geneticist may often generate an intuitive feel for the speed of genetic


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FFIIGG..33 Rateofformationofdifferenttypesofmutationsandtheirphenotypiceffects.

adaptation that is at odds with the situation in natural populations. A very high rate of genetic adaptation is possiblewhen natural selection acts on common variants and causes exponential increases in mutant frequency. We suggest thatthese considerations may underlie some of the problems inherent in interpreting experiments on mutation underselection.

ThebasicideaisoutlinedinFig.11(seebelow),whichclassifies100spontaneousmutationsthatmightaffectasingle gene. This table attempts to convey the nature of genetic variability at the moment it arises and beforefrequencyhasbeenacteduponbyselection.Thedatapresentedsummarizeresultsofavarietyofstudiesandmustremainacrudeestimatesinceeveryexperimentalsituationusedtogeneratesuchdatausesadifferentsequenceanddetectsadifferentspectrumofmutanttypes.Thesefrequencyestimatesarederivedfrommanysourcesplusourownexperience in characterization of spontaneous mutations (18, 41, 42, 45, 47, 48, 51). In most of these studies,frequencieswereestimatedforcellsgrowingineitherrichmediumorminimalmediumwithglucose.Itcanbeseenthat,amongbasesubstitutions,transitions(A/T←→G/C)aremorecommonthantransversions(all

othersubstitutiontypes).Thisseemsreasonablesincetransitionsinvolveafailuretodiscriminatebetweentwopurines(ortwopyrimidines),whiletransversionsexchangeapurineforapyrimidine.Becauseofthestructureofthecode,transitionsarepronetocausesynonymouscodonchangeswithnoeffectontheencodedproteinsandconservativesubstitutionsofstructurallyrelatedaminoacids(17).Transversionsarelesscommonthantransitions,butmorepronetoalterproteinstructure.Ifoneconsidersloss-of-

function mutations, transitions are likely (30%) to be synonymous and therefore silent. Relatively few basesubstitutions(3/64)resultinthecreationofnonsensecodonswithanessentiallynullphenotype.Frameshiftmutations(likenonsense)arelikelytocauselargeloss-of-functionphenotypesbutarerarerthanbasesubstitutions.Forgain-of-functionmutations,thesamegradientofeffectsareexpected—large-effectmutationsarerare.Missensemutationsthatimproveanexistingfunctionorcreateanovelfunctionarerestrictedtoparticularchangesatasmallnumberofsites.Smallimprovementsarelikelytobemorecommonthanthosewithalargepositiveeffect.Thegeneraltendencyisforcommonmutationstocausesmallphenotypicchanges—whetherlossesorgainsinfunction.Thesametrendisseenformutationsthatcausechangesincopynumber—deletionsthateliminateageneare

ratherrare,butduplicationsareamongthemostcommonofmutations.Perhapsthemostcommonmutationsarecopynumber changes in genomes with two or more copies of a region. These events contribute to amplification ordeamplificationbyunequalrecombinationbetweenidenticalcopiesinsisterchromosomes.Figure3diagramstheserelationships.Note,inparticular,thatduplications(causingatwofoldincreaseingene

dosage)ariseatavastlyhigherratethanthelarge-effectmutationsincommonuseinthelaboratory.Evenmorefrequentarechangesingenecopynumber,whichcanaddorremovecopies.Thiscopynumberchangesalmostalwaysinvolverepeatslocatedadjacenttoeachotherinthesameorientation(intandem),butsomecopynumbervariantshaveinverse-orderrepeats(KugelbergandJ.R.Roth,unpublisheddata). [[CCEE--QQ11::AAUU]] PPlleeaasseessuuppppllyyiinniittiiaallssffoorrKKuuggeellbbeerrgg.. Becausecommonsmall-effectmutationsarise(andrecur)frequentlytheyarepresentathighestfrequencyinapopulationbeforeselection.Naturalselectioncandetectthesesmall-effectmutationsmakingthemmajorplayersingeneticadaptation.Commonsmall-effectmutationsarenotoftendetectedinexperimentalgeneticsandthereforetendtobeignoredinthinkingabouttheprocessofadaptation.(Asseenbelow,laboratorygeneticsdeliberatelyavoidsthesemutations.)Yetduringgrowthunderselectionthesemutationscaninitiatehugephenotypicchangesthatoccurbya cascadeof successive small improvements, whose frequencies increaseexponentially duringgrowthunderselection(seebelow).


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FFIIGG.. 44 Adaptive evolution proceeds by pathways of sequential frequent, small-effect mutations. During growth under

Theresponseofselectiontocopynumbervariantsisparticularlyrapidbecausethefrequencyofthesemutantscomesrapidlytoaveryhighsteady-statefrequencyevenbeforeselectionisimposed.Typicallociareduplicatedinabout 1cell in a1,000of anunselectedculture. Thissteadystate is reachedbecause formationratesarehigh(10−5/cellperdivision)andlossratesareevenhigher(10−2).Inaddition,duplicationscanhaveverysignificantfitnesscosts,whichcontributetotherapidapproachoffrequencytoasteadystate.Whileduplicationsarecommonbeforeselection,highercopynumbervariantsareexpectedtoalsoreachsteady-statefrequenciesatasomewhatlowerlevel(ReamsandJ.R.Roth,unpublisheddata). [[CCEE--QQ22::AAUU]] PPlleeaasseessuuppppllyyiinniittiiaallssffoorrRReeaammss..

WWhheennSSeelleeccttiioonnAAccttssoonnCCoommmmoonnMMuuttaattiioonnss,,IImmpprroovveemmeennttFFoolllloowwssPPaatthhwwaayyssooffGGeenneettiiccAAddaappttaattiioonn

It is suggested above that the nature of the mutation process and the structure of the code dictate that genetic adaptationis likely to occur by series of minor improvements. This seems likely because (i) the most frequent spontaneousmutations are those of small phenotypic effect, (ii) natural selection can detect these small differences, and (iii) causetheir frequency in the population to rise exponentially.

Seriesofimprovementsarelikelybecauseincreasesinthefrequencyofonemutationcanproduceasubpopulationlargeenoughforasecondcommonsmall-effectmutationtoariseandprovideanadditionalimprovement.Themostcommonsecondarymutations(liketheinitial improvement)arelikelytoprovidesmall fitnessimprovements.Eachimprovementallowsexpansionofasubpopulationinwhichthenexteventcanoccur.Asthefrequencyofimprovedcellsrises,theprobabilityofsubsequentimprovementalsorises,simplybecausetherearemorecellsinwhichtheycanoccur.Theseselectivepathwaysallowapopulationtorespondquickly.ThiscascadingprocessisdiagrammedinFig.4.Itwillbearguedbelowthatsuchsequencesofeventsunderliemanyphenomenathathavebeeninterpretedasevidenceforstress-inducedmutation.


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FFIIGG..55 Thelaboratoryprocedurethatallowsmutantfrequencytoindicatemutationrate.Selectioniscleanlyandcompletelyseparatedfromgrowthandmutation.Mutationsareallowedtoaccumulate(linearly)duringtheinitialnonselectivepregrowthperiod.Precautionseliminatetheeffectoffluctuationorstochasticdistributionoftimesatwhichmutationsarise.Samplesofnonselectivegrowthcultureareplatedunderstrongselectiveconditionsthatblockallgrowthoftheparenttypeandallofthecommonsmall-effectmutations.Onlyrarelarge-effectmutationsareallowedtogrowunderselection.Thesemutationsareassumedtobefullyfitandrequirenoadaptivechangetobedetectedontheselectionplate.

Apoint tonote inFig.4 isthatseveralmultisteppathwaysof improvementmayoperate inparallel andsomegenotypesmayarisebymultipleroutes.However,whenapopulationadaptsinthisway,thefinalproductmaybeveryhardtoanalyzegeneticallysincemanymutationshavecontributedtothefinalphenotype.Inothercases,earlysmall-effectmutationsmayallowapopulationlargeenoughforalaterlarge-effectmutationtoarise.Insomecasesthefinalphenotypemaynolongerrequiretheearlyeventsthatallowedittoarise.Thedifficultyofreconstructingthesepathwaysisonethatunderliestheproblemofunderstandingtheoriginsof

cancer.

UUSSEESSOOFFSSEELLEECCTTIIOONNIINNLLAABBOORRAATTOORRYYGGEENNEETTIICCSS

Bacterial genetics relies on positive selection to detect rare mutants in astronomically large populations (>109 cells).The frequency of detected mutants is used to estimate the rates at which the mutants formed. This procedure is centralto assessment of mutation rates, recombination rates, and mutagen activity. To achieve these ends, selection is used in aspecial way that detects mutants without contributing to their frequency. This essentially is defect of natural selectionand is difficult to achieve because growth under selection is such a potent force for changing mutant frequency (asoutlined above). However, this defect of natural selection is essential to the practice of experimental bacterial genetics.

Todefeatnatural selection, laboratorygeneticsseparatesselection fromgrowthandmutation. Mutationsariseduringaninitialperiodofnonselectivegrowth.Thisisfollowedbyasharplyseparatedperiodofverystrongselectiononsolidmediuminwhichparentcellscannotgrowandnonewmutationscanarise(Fig.5).Theselectionismadesostrongthatitpreventsgrowthofcommonsmall-effectmutantsthatmightgrowslowlyontheplateandproduceavisible colony during growth under selection. When selection is too weak some of these common small-effectmutations growunder selection and improve sufficiently under selection to produce a visible colony. When thishappens,theprocessofdetectingpreexistingmutantsgoesawryandthenumberofmutantsisinflatedbycommonsmall-effectmutationswhoseprobabilityofbeingdetectedisenhancedbygrowthunderselection.Useofverystrongselectionpreventsthedetectionprocessfromgettingembeddedintheprocessofrapidadaptationbyaseriesofcommon,small-effectmutationsasdiagrammedinFig.4.Thetwo-stageprocess(Fig.5)allowsmutantfrequenciestoreflectonlymutationrate(priortoselection)andpreventsselectionfrominfluencingmutantfrequency(asitdoesinnaturalpopulations).


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Acaveatshouldbenoted.Whenevercellsgrow,andmutationscanoccur,naturalselectionisexpectedtoact(e.g.,anydeleteriousmutationisdisfavored).Forthepurposesofthisdiscussion,theassumptionismadethatonecaneliminatetheeffectsofselectionontheparticularphenotypebeingstudied.Forexample,richmediumisassumedtoeliminateselectiononauxotrophicmutants.During the nonselective pregrowth period (Fig. 5, left), mutants with some particular selectable phenotype

accumulate linearly inthepopulation; their frequencyisdictatedbymutationrateandbythetimingofmutationaleventsandthetargetsizeformutationswiththatparticularphenotype(comparewithFig.2,middle).Theimposedstrongselection(Fig.5,right)preventsgrowthofparentcellsandsmall-effectmutants,butallowslarge-effectmutantcellstogrowandformvisiblecolonies.Inthisway,selectiondetectsmutationsthataroseduringpriornonselectivepregrowth,butdoesnotcontributetothefrequencyofdetectablemutants.Thenextsection("SevenPillarsofLaboratorySelection")describestheaboveconsiderationsasasetofrulesthat

support thewholeedificeof bacterial genetics. Theserulesareseldomstated, but theyare theunderpinningofbacterialgeneticsbecauseonlywiththeserulescanoneselectivelydetectmutantsinaculturewithoutinfluencingtheanswer.Therulesmakeitpossibletoanalyzegeneticeventsinhugebacterialpopulations.Theyallowphenotypefrequency to be a reliable indicator of mutation rate. Extensive routine use of this procedure may have led totrivializationoftheunderlyingrules,therebyleadingtomisinterpretationofsomeexperimentalresults.Therulesarenotlegalobligations.Theyneedtobeobeyedonlyifyouneedtoreliablyandaccuratelymeasuremutantfrequencyandrates.

SSEEVVEENNPPIILLLLAARRSSOOFFLLAABBOORRAATTOORRYYSSEELLEECCTTIIOONN

AAssssuummppttiioonnssTThhaattUUnnddeerrlliieetthheeUUsseeooffPPhheennoottyyppeeFFrreeqquueennccyyTTooEEssttiimmaatteeMMuuttaattiioonnRRaattee

The following seven assumptions underlie the use of phenotype frequency to estimate mutation rate:

NNoopprreeeexxiissttiinnggmmuuttaannttssInoculatethepreselectionculturewithapopulationtoosmalltoincludeanyofthe

mutanttypesofinterest.Thiseliminatesfoundereffectsandassuresthatallofthemutantsthataredetected

laterbyselectionwereformedduringthepreviousnonselectivegrowthperiod

1.


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NNoo ggrroowwtthh ddeeffeecctt oorr aaddvvaannttaaggee dduurriinngg ggrroowwtthh bbeeffoorree sseelleeccttiioonnAssure that mutant types to be

selectedgrowat the samerate as the parent cells during the preselection period—their frequency in that

populationisdictatedonlybymutation.

2.

NNoollaaggiinneexxpprreessssiioonnAssumethatthemutantphenotypeappearsimmediatelywhenthemutationforms(no

phenotypiclag).Adelayinphenotypeappearanceallowslate-arisingmutationstoescapedetection.Halfofthe

mutationeventsthatoccurinthepregrowthcultureareexpectedtooccurinthefinalgenerationofthepregrowth

culture. Acorollaryassumption is that mutant cells arisingduringpregrowthcan(whenplatedonselective

medium)formavisiblecolonywith100%efficiency.Thus,thephenotypefrequencyintheunselectedpopulation

istheratioofobservedcoloniesonselectionmediumtotheviablecellsplacedunderselection.

3.

TThheerreeiiss nnoossttoocchhaassttiicc fflluuccttuuaattiioonniinn mmuuttaattiioonneevveennttssAssume that the mutant frequencyperfectly

reflectsthemutationrate.Thisruleisdifficultytoobey,butcanbeapproximated.Althougheachmutationarises

withthesameprobability,theexactmomentofitsformationissubjectstochasticvariation.Mutantsthathappen

toariseearlyinthehistoryoftheculturewillcontributemoreheavilytothefinalmutantfrequency.Asoutlined

below,theLuria-Delbrücktheorypredictsthatidenticalcultureswillaccumulatedifferentnumbersofmutants

simplybecauseofvariationinthetimingofmutations.Onecancorrectforthisinavarietyofways(52).Arough,

short-handcorrectionistosimplyuseofthemedianphenotypefrequencyofmultipleculturesandtherebyavoid

themajor “jackpots” or “low-pots” cultures in whichmutation timinghascausedanabnormally highor low

phenotypefrequency.

4.

EEaacchh mmuuttaanntt ggeenneerraatteess oonnee ccoolloonnyyPerformselection on solid medium. By immobilizing cells of the

pregrowthculture,itisassuredthateachmutantcellinthatpopulationformsonedistinctcountablecolony.

5.

NNoo ppaarreennttaall ggrroowwtthhUse selection conditions that completely prevent growth of parent strain and any

preexistingsmall-effectmutants.Thisprohibitsnewmutationsfromarisingduringtheperiodofselectionand

preventsgrowthunderselectionfromenhancingthenumberofdetectedmutants.Whilethispillarsupportsthe

wholehistoryofbacterialgenetics,itisastickingpointforseveralsystemsusedasevidenceforstress-induced

mutagenesis.Thesesystemsassumethat(contrarytothisrule)nongrowingcellsaresubjecttomutagenesis.

Thequestionofwhetherornotmutationsoccurinnongrowingcellswillbediscussedbelow.

6.

NNoohheetteerrooggeenneeiittyyiinnmmuuttaannttccoolloonniieessEachmutantcolonyisassumedtobeahomogeneouspopulationof

cellswiththesamegenotypeasthecellthatinitiatedit.Noneofthecountedcolonieshasbeeninitiatedbya

commonsmall-effectmutantwhoseabilitytoformavisiblecolonydependsonacquisitionofadditionalmutations

duringgrowthunderselection.

7.

HHoowwGGrroowwtthhCCoommpplliiccaatteessDDeetteerrmmiinnaattiioonnooffMMuuttaattiioonnRRaatteeffrroommMMuuttaannttFFrreeqquueennccyy((EEvveennwwiitthhoouuttSSeelleeccttiioonn))

Mutation rates are generally expressed as mutation/cell/division since it is usually assumed that most mutations arise aserrors in chromosome replication. Therefore when a laboratory selection is used to estimate mutation rate, it is essentialto know how many generations (acts of DNA replication) occurred at which a mutation might have occurred. Forexample, a mutant would be defined as common if it arise during 100 acts of replication, but as rare if it arose only oncein 109 acts of division. This calculation is rather easy if one knows the inoculum size and the size of the final populationin which mutants are detected. To fairly estimate a mutation rate one must know how many divisions occurred.


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FFIIGG..66 Growthwithoutapparentpopulationsizeincrease.Thepopulationdiagrammedherereachesaplateau(108/ml)whensomeresourceisexhausted.Amutantformedduringthepriorgrowthcontinuestodivide(inthisexampleforanadditional27generations,resultinginadoublingofthetotalpopulation).

Estimatingthenumberofdivisionsthatserveasthebasisfortheestimatedmutationratecanbedifficultespeciallyinapopulationwhosenetsize isnot increasing.Several suchsystemsareusedasevidenceforstress inducedmutagenesis.Mutationsaresaidtoariseinatime-dependentmannerwithnoactsofcelldivision.Ifthisisaprominentphenomenon, many conclusions of bacterial genetics are called into question. If this is not often true, then theevidenceforstress-induced(stationaryphase)mutagenesisiscalledintoquestion.

CCeellllggrroowwtthhaannddtthheeooccccuurrrreenncceeooffmmuuttaattiioonnss..

DNA replication provides an opportunity for mutation, and mutation rates are generally expressed per cell/pergeneration. Thus if a population is heterogeneous and includes a subset with a faster growth rate, that subpopulation isexpected to acquire a disproportionate number of new mutations over a given time span simply because it undergoesmore acts of replication and includes an increasing proportion of the parent population. This is expected even if all cellshave the same probability of error per act of replication. Thus interpreting increases in mutant frequency (assuming noselection) depends on knowing how many acts of replication actually occurred to provide the cells with the assayedmutant phenotype.

GGrroowwtthhccaanneevveennbbeeaapprroobblleemmiinnppooppuullaattiioonnsssshhoowwiinngglliittttlleenneettggrroowwtthh..

In several of the experimental systems discussed below, growth of the parent population is blocked (as is true in astandard laboratory selection). However, in some cases these populations are incubated for extended periods of timebefore the number of mutant colonies is counted. Interpretation of these experiments has assumed that all coloniesappearing are due to large-effect mutations that either (i) arose during pregrowth of the culture, or (ii) were induced innongrowing cells by a novel (stress-induced) mechanism after plating of the culture. That is, some mutations areassumed to arise in a nongrowing population and to accumulate in a time-dependent manner, without any scheduledDNA replication. Whenever a mutation is attributed to nongrowing cells in this manner, the problem of growth becomesprofound. It is difficult to eliminate the possibility that a subpopulation is growing and giving rise to the observedmutants. Establishment of the idea of “stationary-phase” mutagenesis requires elimination of the possibility of crypticgrowth. The difficulty of detecting a growing subpopulation is illustrated in Fig. 6.


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FFIIGG..77 Abacterialpopulationofconstantsizeinwhichcellsaredyingandbeingreplacedbyslowgrowthofthepopulationatlarge.

Supposethatselectionlimitsgrowthofapopulationat108cells,andaresistantmutantarisesduringthegrowthofthatpopulation.Thenewmutantcangrowexponentiallywhiletheparentcellsshownogrowth.Whenthemutantsubpopulationreaches108cells,thetotalpopulationwillhavedoubledwhichmaybedifficulttodetectexperimentally.Thus an apparently resting population shows a substantial increase in mutation frequency. It appears that anongrowingpopulationwasmutagenizedbysomenovel(growth-independent,stress-induced)mechanism.Onceoneisawareoftheexistenceofagrowingsubpopulation,nomutagenesisisrequiredtoexplainthefrequencyincrease,whichisdueentirelytonaturalselection.ItshouldbenoticedthatattheendoftheexperimentinFig.6,halfofthepopulationwillhavegonethrough27extragenerationsofgrowthandhavea27-foldhigherprobabilityofacquiringanymutation.Anotherpotentialproblemisthatofapopulationofconstantsizeinwhichcellsaredyingandbeingreplacedby

slowgrowthofthepopulationatlarge.ThisisdiagrammedinFig.7.Hereaconstantpopulationmaybereplicatingcontinuously(withdifferentsubpopulationspossiblyreproducingatdifferentrates)andaccumulatingmutationsthatappeartoforminastationary-phasepopulation.


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GGrroowwtthh((aannddrreepplliiccaattiioonn))ccoonnttrriibbuutteessttootthheeaappppeeaarraanncceeoofftthheepphheennoottyyppee..

After a DNA sequence change, some time may be required before the mutant phenotype appears (phenotypic lag).Escherichia coli cells growing under different growth conditions can have from 1 to 8 chromosomes per cell (1). Thistime lag may allow a recessive new mutant allele to segregate from parental copies present in a sister chromosome orsecond bacterial nucleoid. It may allow new mutant enzymes to dilute out preexisting parental protein. If appearance ofthe mutant phenotype requires two cell divisions, then the phenotype frequency assessed at any moment will fail todetect mutations that arose within the final two generations. If the population is growing exponentially, more that 75%of the mutational events will have arisen during that period and will escape detection. (Half of the acts of chromosomereplication occur at the final cell division and another quarter at the previous cell division.) This phenomenon isparticularly relevant in the context of the debate on “stress-induced mutation” because the classic experimentsdemonstrating that mutations arise before selection all used phenotypes with a very long lag (streptomycin resistanceand phage resistance). In both situations, the selected phenotype appears several generations after the mutation arises.Any new mutation arising under selective conditions, would be immediately counterselected and could never getthrough the lag period and attain a resistant phenotype. Thus phenotypic lag biased these experiments in favor ofmutations that arose several generations prior to exposure to selection. Any growth under selection was prevented bythe lethal selection—any new mutant that had not escaped lag (or arose after plating) was killed by the selectionconditions.

GGrroowwtthhaalllloowwssmmuuttaattiioonnssttooaarriisseeaattvvaarriiaabblleettiimmeessiinntthheehhiissttoorryyoofftthheeppooppuullaattiioonn..

The work of Luria and Delbrück clarified the kinetics of phenotype accumulation in unselected populations bydemonstrating how the stochastic distribution of mutation occurrence times contributes to the frequency of mutantphenotypes (44). The rate at which any mutation arises is essentially a probability statement, expressing the number ofmutations expected to form per act of cell division. In practice, any particular population growing from a small numberof nonmutant cells will realize its first mutation at a range of times, distributed around that predicted by the mutationrate. The phenotype frequencies in a series of such cultures can vary widely (fluctuate) based on the time of firstmutation. The expected statistical distribution was described by Luria and Delbrück. The result of this fluctuation is thatindependent cultures with the same mutation rate are expected to contain widely different phenotype frequencies. Thereare a variety of ways to compensate for this problem experimentally (52) and thereby to determine the actual mutationrate.

HHoowwCCaannOOnneeBBeeSSuurreetthhaatttthheePPiillllaarrssooffWWiissddoommHHaavveeBBeeeennSSuucccceessssffuullllyyFFoolllloowweedd??

The classical test to ensure that a selection is detecting preexisting mutations is through a Luria-Delbrück fluctuationtest. In doing this test, series of independent cultures are all initiated using a small innoculum. Each culture is


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independently plated on selective medium. If colonies appearing on the selective plate reflect colonies present in theplated population, then you expect to see statistical fluctuation from one culture to the next. The way to perform this testand treat the data has been described in detail (52).

Ifoneseesfluctuation,thequestioniswhetherallmutantcolonieswereinitiatedbypreexistentcellsoronlysomefraction(enoughtocausetheobservedfluctuation).Awaytotesttheobservedfluctuationhasbeendescribed(52).Theyplotonthexaxisthelogofthenumberofmutants/tube(N)versusthelogoftheprobabilityofatubecontainingNormoremutants.Ifthisplotgivesastraightlineofslope=2,thenthedistributionofmutants/tubeinyourseriesoftubereflectsaLuria-Delbrückdistributionandallobservedcolonieswereinitiatedbymutantsthataroseduringthepregrowthculture.Ifsomemutantsariseontheplatethisplotshowsaplateaufollowedbyasharpdrop.Thereisadifficultyhereinthecaseofcopynumbervariants.TheabovetestwasperformedfortheCairnsselection

andnofluctuationwasnoted.Theconclusionwasmadethatallmutantsaroseontheplate(providingsupportfortheidea of stress-induced mutation). However, in the case of duplications, fluctuation is not expected because thefrequencyofduplicationsapproachesasteady-statefrequencybeforeselection.Thatis,anydifferencesinthetimeofappearanceofthefirstduplicationarereducedbecausefrequenciesallapproachthesamesteady-statevalue.Thispreventedthefluctuationtestfromdemonstratingthattherevertantsappearing(over6daysofselection)areactuallyinitiatedbymutantcells(withalacamplification)thatarosebeforeselection.AtesthasrecentlybeendevisedwhichshowsthatthenumberofrevertantsintheCairnssystemisinfactdeterminedbythenumberofcellsinthepregrowthculturethathavealacamplificationbeforeselection [[CCEE--QQ33::AAUU]] PPlleeaasseepprroovviiddeeiinniittiiaallssffoorrSSaannoo.. (SanoandJ.R.Roth,unpublisheddata).

CCoonnttrriibbuuttiioonnooffGGeenneettiiccDDrriiffttaannddFFoouunnddeerrEEffffeeccttssttooDDiiffffeerreenncceessiinnPPhheennoottyyppeeFFrreeqquueennccyy

If a population is initiated by an inoculum that already contains mutant cells, these founders can result in a higherphenotype frequency than one might expect to see if all mutations arise only during the history of the population. Thiscan complicate interpretation of phenotype frequencies and is systematically avoided by one of the rules of laboratoryselections described.

Foundereffectsaresimilartoconsequencesofgeneticdrift.Insmallpopulations,thefrequencyofmutanttypescanvaryfromgenerationtogeneration,simplybyrandomsuccessinreproductionorstochastickillingthatisnotinfluencedbygeneticdifferences.Driftwillbeignoredherebecauselargemicrobialpopulationsreduceitsimportance.

TTHHRREEEEKKEEYYSSYYSSTTEEMMSSUUSSEEDDTTOOSSTTUUDDYYTTHHEEEEFFFFEECCTTSSOOFFSSEELLEECCTTIIOONNOONNMMUUTTAATTIIOONN

Our understanding of the origins of mutations has been strongly influenced by a few key experiments. Luria andDelbrück's experiment, and the Lederbergs' follow-up experiments, showed that mutants could preexist selection in abacterial culture. This was critically important in establishing bacteria as a valid genetic system for analysis of mutationrates. The Cairns-Foster experiments raised serious questions about the general validity of conclusions based onLuria and Delbrück's experiment. Cairns-Foster raised the issue of whether under nonlethal selection bacteria werecapable of "directing mutations" or of selectively increasing mutation rates in response to environmental pressure. Thequestion of whether bacteria could respond to stress by increasing mutation rates was taken further by Radman,Taddei, and Matic when they showed that bacteria apparently increased mutation rates in response to nutrient limitationand aging. Below we examine each of these critical experimental systems to explore their strengths, limitations, andpossible weaknesses.

11..TThheeLLuurriiaa--DDeellbbrrüücckkaannddLLeeddeerrbbeerrggEExxppeerriimmeennttss——tthheeCCllaassssiiccEEvviiddeenncceetthhaatt((SSoommee))MMuuttaattiioonnssAArreeNNoottIInndduucceeddbbyySSttrreessss

In some sense, the Luria-Delbrück experiment established the “seven pillars” of laboratory selection (44). Theexperiment was designed to demonstrate that laboratory selections detect preexisting mutants and do not contribute tothe creation of mutants. This experiment validates the use of selection as a means of detecting mutants and is thereforefundamental to bacterial genetics. If exposure to selection actually caused mutations, the whole field of bacterialgenetics would be called into question.


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FFIIGG..88 ThebasicformoftheCairnsexperiment.AsintheLuria-Delbrückexperiment,parentcellsareplatedonselectivemediummutant(revertant)coloniesappearwithtime.Thesecolonieshavebeenattributedtomutationsinducedbystressinthenongrowingparentpopulation.ThemainfeaturesoftheCairns-Fosterexperimentaredescribedinthetextandthendiscussedintermsofmodelsofferedtoexplainthem.

ThebasicobservationintheLuria-Delbrückexperimentwasthatthenumberofdetectedmutantsinaseriesofindependentpreselectionculturesvariesinamannerthatcanbepredictedmathematically,ifoneassumesthatthevariabilityreflectsastochasticdistribution in thetimingof mutational eventsduringnonselectivepregrowthof theplated cultures. This variability demonstrates that the mutations arose before exposure to selection. The sameconclusionwasreachedbytheLederbergs'usingamoregraphic,nonmathematicalmethodinvolvingreplicaprintingamastercelllawntomultipleplatesofselectivemediumandseeingthesamepatternofresistantclonesoneachreplica(40).

UUsseeoofflleetthhaallsseelleeccttiioonnssttooddeetteeccttmmuuttaannttsswwiitthhpphheennoottyyppiiccllaagg..Both Luria-Delbrück and Lederberg used lethal selections (phage resistance and streptomycin resistance,

respectively)inwhichthedetectedmutantphenotypeappearsonlyseveralgenerationsfollowingoccurrenceoftheDNAsequencechange.Theselectionconditionsmadetheresultsparticularlyclearbecausetheyenforcedabroadseparationofselectionfromgrowthandmutation.(Theyfollowthe"sevenpillars"totheletterofthelaw.)Nogrowthwasallowedunderselection(conditionswere lethal). Large-effect mutationsaredetected.Mutationshadtoariseseveral generations before plating and thus were certain to arise within the nonselective growth period. MutantfrequencywillbesubjecttothefluctuationsinfrequencyanalyzedbyLuriaandDelbrück.Thelongphenotypiclagalsoensuresthat,intheLederbergexperiment,cellsresistanttostreptomycinarelikelytobepresentassizablecloneswithin the lawnsofunselectedcells thatwerereplicaprinted.Phenotypic lagmade it extremelyunlikely thatanymutations arise following plating on the lethal selection plates—cells would have to escape killing for severalgenerationsifanewresistantmutantweretobedetected.

AAvvooiiddiinnggtthheeccaavveeaattiinnhheerreennttiinntthheeccllaassssiicceexxppeerriimmeennttss..Whileuseofalethalselectionandmutationswithphenotypiclagallowedonetoseparatemutationfromselection,it

reducedthepoweroftheexperimentstodemonstratethatallmutationsariseindependentofstress.Thedesignoftheclassicexperimentsensuredthatonlypreexistingmutationscouldbedetected.Thiscaveatwaspointedoutbyseveralinvestigators(8,22,56).Toavoidtheshortfall of theclassicexperimentsonemustsomehowmeasuremutationrates ingrowth-limited

(stressed)cells.Thiscanbedoneifonelimitsgrowthinonewayandfollowsaccumulationofmutationsthatareneutralunderthoseconditions.Suchexperimentshavenotdemonstratedageneralincreaseinmutationsratesduringgrowthlimitation(33).Itismuchmoredifficulttolimitgrowthandmeasuretherateofformationofadaptivemutationsthatarepositivelyselectedassoonas theyarise. (Inprinciple, thiscouldbedoneby fluctuationtestsusingthe“zero-tube”method,butthegrowthandimprovementofsmall-effectmutationsmakesthistechnicallydifficult.)TheCairns-Fosterexperimentwasdevisedtofillthegapsintheclassicexperiments.

22..TThheeCCaaiirrnnss--FFoosstteerrEExxppeerriimmeenntt——aannAAtttteemmppttTTooAAsssseessssMMuuttaattiioonnRRaatteessuunnddeerrSSeelleeccttiioonn

The possibility that some fraction of mutations are stress induced has been most aggressively addressed using a systemdesigned by Cairns and coworkers (8) and modified by Cairns and Foster (7). In this experiment the conditions used byLuria and Delbruck were varied in hopes of detecting mutations induced by stress. The selection is nonlethal, and themutations scored show no phenotypic lag. Parent tester cells are mutants unable to use lactose. These cells are plated onselective medium (lactose), which prevents their growth but does not kill. Over 5 to 6 days, revertant (Lac+) coloniesappear above a lawn of nongrowing parent cells (Fig. 8).


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IntheCairnsexperiment,asintheLuria-Delbrückexperiment,parentcellsareplatedonselectivemediummutant(revertant) coloniesappearwith time.Thesecolonieshavebeenattributed tomutations inducedbystress in thenongrowingparent population. Themain featuresof theCairns-Foster experiment aredescribedbelowand thendiscussedintermsofmodelsofferedtoexplainthem.

TheplatedLac−testercells(108)carryarevertable+1frameshiftmutation.1.

The tester's lac allele providesabout 2%of theβ-galactosidase level found in Lac+ revertant strains. This

residualfunctionallowscolonyformationonstandardlactosemedium.

2.

Growthofthetesterstrainispreventedbyscavengercellshavingalacdeletion.A10-foldexcessofscavenger

cellsisplatedwithtestersandrestrictsgrowthofthetestercells,probablybyconsumingexcretedmetabolites.

3.

Thetestersarepoised(bythetitratedexcessofscavengercells)onthebrinkofgrowth,suchthatanytiny

increaseinβ-galactosidasecanallowthemtogrow.

4.

During6daysonselectivemedium(withscavengers),thelawnoftestercellsgrowsverylittle.5.

Within1to2daysunderselection,afewcoloniesappearwhichareattributedtomutantcellsthataroseduring

thegrowthbeforeselection(asinastandardlaboratoryselection).Basedonsuchcolonies,theunselected

reversionratetoLac+is10−8/cell/division.

6.

Overthefollowing4days,about100additionalcoloniesaccumulateabovethecelllawn.Insomeexperiments,

theaccumulationislinearwithtime—inothersitshowssomeupwardinflection.

7.


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Thecoloniesarisingafter4days,requiremutationaleventsoccurringafterexposuretoselectivemedium.(When

independent cultures are tested, the revertant frequencydoesnot show the fluctuation predictedby Luria-

Delbrück.)

8.

Thestressedparentpopulation in the lawn isnotmutagenizedduringtheperiodof revertantaccumulation.

Samples taken fromthe lawn(betweenLac+ revertant colonies) showno increase in genome-widemutant

frequency.

9.

ThedescribedaccumulationofLac+revertantsaboveanongrowinglawnhasbeeninterpretedasevidencethatstress induces a mechanism for genome-wide mutagenesis. This mechanism chooses a randomsubset (about1/1,000)ofthepopulationandmutagenizesitheavilyandnonspecifically.Theproposedmechanismisthoughttohaveevolvedunderselectionbecausethemutationsitprovideshelpcellsadapttostressfulconditions.Supportfortheseconclusionshavebeenreviewedrecentlyalthoughitshouldbenotedthattherearedifferentversionsofthemodel(16,19).Mostofthisevidenceassumesthevalidityofthebasicexperimentalobservations—thatmutationsareinfactinducedbystress.Mechanismstoexplainthismutagenesishavebeenproposedandtested,butthebasicassumption—stress-inducedmutation—hasnotbeenquestioned.Canthebasicresultsbeexplainedbyselectionratherthanmutagenesis?Toevaluatethisquestion,weconsiderthebasicexperimentinthelightofthegeneralconsiderationsoutlinedaboveandthenexplorealternativeexplanations.

CCoommppaarriinnggtthheeCCaaiirrnn--FFoosstteerreexxppeerriimmeennttttooaassttaannddaarrddllaabboorraattoorryysseelleeccttiioonn..TheCairns-Foster experiment resemblesastandard laboratoryselection in that (i) parent cells areplatedon

selectivemediumand(ii)thenumberofcoloniesarisingunderselectionisusedtoestimateamutationrate.Inferringmutationratefrommutantfrequencydemandsthattherules(PillarsofLaboratorySelection)beobeyed.Onemustpreventselectionfrominfluencingthenumberofdetectedmutants.TheCairns-Fosterexperimentdiffersradicallyfromastandardlaboratoryselectioninthat(i)mutationsariseunder

selectiveconditions,(ii)mutationsariseinnongrowingcells,and(iii)mutationratesareexpressedperunittimenotpernumberofcelldivisions.Thesefeaturescreateseriousproblemscomparingmutationratesunderselectionwiththosemeasuredduringunrestrictedgrowth.Theonlybarriertoselectiveenrichmentofmutantfrequencyisthatthetesterpopulationappearsunabletogrow.Thisleavesopenthepossibilitythatsomesubpopulationgrowsandcontributestomutantyield

TThheeCCaaiirrnnss--FFoosstteerreexxppeerriimmeennttvviioollaatteesstthheerruulleessooffllaabboorraattoorryysseelleeccttiioonn..

This experiment deviates from the rules for selection in that the selective conditions are not strong enough to assure thatonly large-effect mutations (compensating frameshifts) are detected (rules 6 and 7). Selection is weak because theparent tester cells have 2% of the revertant level of β-galactosidase before being exposed to selection. They are poisedon the brink of growth by added the scavenger cells. Any small-effect mutant with a slight increase in β-galactosidaseactivity can upset this poise and initiate a slow-growing colony. Small-effect mutations are especially common sinceduplications and amplifications can serve to initiate a cascade of selectable events (see below). Small-effect mutationscan contribute to the number of counted visible revertant clones if they can improve and form a visible colony. This isfacilitated because cells with residual β-galactosidase are held under selection for a very long time period (6 days).These extra colonies can inflate the revertant frequency on which the mutation rate estimation is based.

Selection(withoutmutagenesis)canenhancetheyieldofmutantsinthisexperimentbecauseitcontributestotheimprovementofplatedcommonsmall-effectmutants.Duringnonselectivegrowth,thesesmall-effectmutationswouldescapedetection.Thefrequencyofthecoloniesappearingunderselectionmaybedictatedbythefrequencyofthesesmall-effectmutantsandtheprobabilitythattheycanimprovesoastoformacolonywithin6days—averylongselectionperiod.Iftheexperimentcouldensurethateverycolonyisinitiatedbyasingle,rare(lac→lac+)frameshiftmutationformedontheplate,thensomeinducedmutagenesiswouldappeartobeneeded.However, if commonsmall-effectmutantscaninitiateclones,thengrowthunderselectioncanexplaintheenhancedrevertantyield.As longascoloniescan improvebycommonsmall-effect mutationsoccurringat standardmutationrates, the


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FFIIGG..99 ExplainingtheCairnssystemwithgrowthunderselection(nomutagenesis).

phenomenologycanbeexplainedbystandardgeneticeventsexpectedinnaturalpopulations—rapidmultistepgeneticadaptationduringgrowthunderselection.Ifthisistrue,theunusualsetofassumptionsneededtoexplainthissystemintermsof"stress-induced"mutagenesisarenolongerneeded.

Noneedtoproposemutagenesisofnongrowingcells.1.

Noneedtoproposemutagenesisofasubsetofthepopulation.2.

Noneedtoproposeanevolvedmechanismtocontravenetheelaboratemechanismsalreadyknowntominimize

mutationrates.

3.

AAmmooddeellttooeexxppllaaiinntthheeCCaaiirrnnss--FFoosstteerrrreessuullttssbbyysseelleeccttiioonn((wwiitthhoouuttiinndduucceeddmmuuttaaggeenneessiiss))..ThebasicobservationsdiagrammedinFig.8canbeexplainedwithoutrecoursetostress-inducedincreaseinthe

standardmutationrates.Duplicationsandfurther increasesincopynumberaremutationsthatoccuratveryhighfrequenciesunderallgrowthconditions(seeFig.3).Morethan0.1%ofcellsinanunselectedpopulationtypicallycarryaduplicationofanyspecifiedpointinthechromosome(3).Thishighduplicationfrequencyisasteadystateachievedbecauseofthehighformationrate,higherlossrate,andfitnesscostofduplications(describedabove).Unselectedpopulationalsocarryhighercopynumbervariantsatlowersteady-statefrequencies(51).ThelacoperonusedintheCairnsexperimentisduplicatedinapproximately0.5%oftheplatedcells.Suchmutationsdoublethesmallamountofβ-galactosidaseproducedbytheleakymutantlacallelesuch.Thus,105to106ofthe108platedcellshavetwoormorelaccopies.Furtherchangesincopynumber(increasesordecreases)occuratarateofabout0.1/cell/divisionbyunequalrecombinationbetweenduplicatedcopiesinsisterstrands.Thus,extremelycommoncopynumberincreasesmay serve as small-effect mutations allowing frequent colony initiation under selective conditions. TheseconsiderationsunderlieamodelwhosebasicfeaturesareoutlinedbelowanddiagrammedinFig.9.

Aduplicationofthemutantlacoperoniscarriedbyabout1in200ofthe108platedtestercells.Thislacalleleis1.


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leaky,producingabout2%oftheenzymeactivefoundinalac±revertant.Thus106cellshaveatleasttwolac

copies,somemayhavemore.MostoftheseduplicationsformedbetweenthecopiesofIS3thatflankthelac

region.The lacduplicationsarelarge(120kbinsize)andhaveasignificantfitnesscost(ReamsandRoth,

unpublisheddata).

Cellswithasufficientnumberoflaccopiesinitiatecolonies.Growthofcellswithinthesecoloniescanleadtoa

visiblecolonyifonelacallelerevertsorattainsasufficientlyhighcopynumberbyamplificationunderselection.

2.

Theduplicationandamplificationeventsarefrequenteventswithwithoutselection. [[CCEE--QQ44::AAUU]] IInniitteemm33,,wwhhiicchhiiss

ccoorrrreecctt,,wwiitthhoorrwwiitthhoouutt??

3.

Theprobabilityofareversion(frameshift)eventtolac+isafunctionofthenumberoflacallelesontheselection

plate.Theallelenumberincreaseswithinanydevelopingcolonybecauseof increasesinthenumberof lac

allelespercellandthenumberofcellsinthecolony.Forexample,if105duplication-bearingcellsinitiateclones

thatgrowtoreach1,000cellswith10laccopies,atotalof108actsofcelldivisionoccurand109replicationsof

thelacallele.Thisissufficienttogenerate10reversioneventsonaplatewithnoincreaseinmutationrate.(The

standardlacreversionrateis10−8/cell/division.)

4.

Whenareversioneventoccurs,onefullyfunctionallac+alleleisgeneratedwithinanarrayoftandemmutantlac

copies.Selectionfavorscellsthatretainthelac+alleleandlosetheremainingmutantcopies.Theextracopies

imposeasignificantfitnesscostandincreasethelikelihoodoflosingthelac+allele.Ultimatelyacellarisesthat

ishaploidforalac+allele,isfullyLac+inphenotype,suffersnolossduetosegregationornofitnesscost.These

haploidrevertanttypesovergrowtheoriginalcolony.ThestepslistedabovearedescribedontheleftsideofFig.

9.

5.

Coloniescanformwithoutreversioniftheysufficientlyamplifythemutantlacallele.Thiscanoccuronlyifa

deletionmutationreducesthesizeandthefitnesscostofthelacamplification.AdeletionoftheIS3duplication

joinpointelementplaceslacwithinasmallerrepeatedunitwithalowerfitnesscost(Fig.9,middle).Suchcost

reductionallowshigherlacamplificationandfastergrowthonlactose.

6.

Deletioneventsarecommonsinceeachendpoint can lie anywhere in a50-kbregionof onecopyof the

duplicated region. Any higher amplification of the large IS3-duplication provides additional pairs of copies

betweenwhichaneffectivedeletioncanoccur.Thenumberofpairedcopiesthatmightformisexpectedto

increaseasafunctionofcopynumber(n)bythefunctionD=n(n-1)/2.

7.

Clonesgrowingbyvirtueofamplificationaloneachievesufficientlaccopynumberthatsomerevertantallelesare

expectedtoariseineveryclone.If aclonereaches108 cellsbyhaving100copiesofthe lac region,each

populationdoublingisexpectedtoadd100lac+cellstothecolony.Cellswithsuchrevertantallelesarelikelyto

growfasterthancellswithahighlyamplifiedmutantlacallele.

8.

Twotypesofrevertantcoloniesarisebytheeventsabove.ColoniesrichinstableLac+cellsformwhenreversion

occursearlyinoneofthemanysmallcloneswithlarge,low-copyamplification.Insuchcolonies,lac+haploid

9.


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cells areable to formandovergrowtoproduceacolonydominatedby lac+ haploidcells. Coloniesrich in

unstableLac+cellsarisewhendeletionmutationsallowhighamplification.Theseclonesarerichinunstable

Lac+cellsthatgrewbyvirtueofamplificationalone.Thesebifurcatingpathwaysaredescribedattheleftsideof

Fig.9andcorrespondtothepathwaysofadaptationdiagrammedinFig.4.

Athirdpathwayalsoappearstocontributetoreversion.Theeventsinthispathwayarenotyetfullyelucidated,

butamodelisdescribedattherightsideofFig.9.Itisduplicationfrequentlyariseasasymmetricaltandem

inversionduplication(sTID),withextendedpalindromesateachoftwojunctions.Theseduplicationsarelikelyto

beunstableanddeleterious,buttheyprovidemultiplelaccopiesandaresubjecttoamplificationbyexchanges

betweenflankingdirectrepeats.Whilebeingmaintainedbyselectionforincreasesinlaccopynumber,these

rearrangements canacquire deletions that render the junctions asymmetric and reduce the fitness costof

amplification.Amplificationsofthistypeareestimatedtounderlieabout30%oftheunstable-richLac+revertant

colonies.Thejunctionsofasymmetricderivatives(aTID)havebeenidentifiedandsequenced(37).

10.

SSuummmmaarryyoofftthheeaammpplliiffiiccaattiioonnmmooddeell..

ThismodelsuggeststhattheCairns-Fosterexperimentallowsselectiontoaffectthenumberofdetectedmutants,becausethebasicrulesoflaboratoryselectionhavebeenskirted.Inparticular,selectionistooweaktopreventgrowthofextremelycommonsmall-effectmutantswithmultiplecopiesoflac.Thesecellsinitiatecoloniesthatsometimessucceedingeneratingavisiblecolony.Mostoftheobservedcoloniesareinitiatedbycommonsmall-effectduplicationmutations.Therareframeshiftmutations,whichareassumedtounderliethesecolonies,arenotrequiredforcolonyinitiation,buttheymayariseandevenpredominateinthefinalcolonybecauseofselectivegrowth.Thefrequencyofobservablecoloniesisdictatedbycommoneventsthatinitiatetheclonethatbecomesvisibleinthecourseof6daysonselectivemedium.Asexpectedforanaturalpopulation,geneticadaptationoccursbyapathwayofsuccessivecommonevents,each

providingaminorgrowthimprovement.Herethesuccessionofeventsthatimprovegrowthis(i)duplicationofthemutant lac allele, (ii) stepwise further lac amplification, (iii) reversion of one copy to lac+, (iv) stepwise loss ofnonrevertantlacalleles,and(v)appearanceofahaploidcellwitharevertantlac+allele.Aspredictedforclonesthatimproveinthisway,eachcolonyisamixtureofcelltypes,somewithanamplificationofthelacregion,andsomethathaverevertedtolac+andsegregatedtohaploid.Very slight changes in experimental conditionsof theCairns-Foster experiment can reestablish the laboratory

selectionconditions(theSevenPillars)andallowdetectionofonlyrare,large-effectframeshiftrevertantsarisingduringthenonselectivepregrowthperiod.Forexample,iftheparentframeshiftmutationisrenderednonleakybyaribosomalmutationthatreduceserrorfrequencyorbyadditionofacompetitiveinhibitorofβ-galactosidase(4),thenthetestercells are no longer leaky. This makes selection strong enough to prevent growth of the common small-effectduplications.Undertheseconditions,theCairnsexperimentshowshighlyreducedaccumulationofrevertantswithtime,anddetectsprimarilythepreexisting,large-effectrevertants.

TThheeSSeelleeccttiioonnMMooddeelleexxppllaaiinnssrreessuullttsscciitteeddaassssuuppppoorrttooff""ssttrreessss--iinndduucceedd""mmuuttaaggeenneessiiss..

The results most frequently cited in support of the several models for stress-induced mutations (16, 19, 31) areconsistent with growth under selection associated with lac amplification. Below we discuss and evaluate the evidenceprovided in support of stress-induced mutagenesis:

The stress-induced mutagenesis is attributed to the error-prone DinB bypass polymerase. The sequence

changesthatgeneratealac+alleleunderselectionincludeahighproportionof+1frameshiftmutationsinbase

runs;thisischaracteristicofmutationscausedbyDinB(36).RevertantsarisingunderselectionintheCairns

systemaremorelikelytocarryassociated,unselectedmutations(inothergenes)thanrevertantsarisingduring

1.


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nonselectivegrowth.

IntheSelectionModeltheseresultsreflectthefactthatthedinBgenehappenstobelocatedclosetolaconthe

F′plasmidandisincludedinallofthelargeIS-dependent lacduplicationsandinabout30%ofthesmaller

high-copy lac amplifications. This interpretation is supported by the observation that associated mutations

require that dinB is locatedclose to lac. dinBalleles far from lacdonot contribute torevertant yieldor to

associatedmutations.WhiletheeffectofamplifyingdinBcontributesaboutfourfoldtotheyieldofrevertants

under selection, selection still enhances reversion to lac+ in strains devoid of dinB and that residual

enhancement depends on recombination. The observed mutagenesis is in essence an artifact due to the

proximityofdinBtothelacalleleunderselection.

Stress-inducedmutagenesisisattributedtoerror-pronerecombinationalreplication.

This conclusion is used to explain the fact that mutations arise in the apparent absence of chromosome

replicationandthattheyieldofmutantsunderselectionrequiresrecombinationproficiency.IntheSelection

Modelrecombinationisresponsibleforduplication,amplification,andsegregationeventsthatallowsmall-effect

mutationstoimprovegrowthunderselection.

2.

SomerevertantcoloniesincludecellswhoseLac+phenotypeisunstable.Thesecellsincludeamplificationsof

thelacoperon.Amplificationsareattributedtoaseparatestress-inducedeventthatisindependentofframeshift

mutation. In the Selection model, the amplification cells are precursors to reversion that allowgrowth and

enhancetheprobabilityofareversionevenbyprovidingmoretargetsequences.

3.

Short-junctionamplificationsandasymmetricTIDmutationsarecommonamongunstableLac+revertantsinthe

Cairnssystem,butarerareinunselectedpopulations.TheStress-inducedMutationModelsuggeststhatthese

eventsoccuronlywhenstressinducesanovelmechanismthatdoesnotoperateinunstressedcultures.The

Selection Model proposes that these mutations form by a series of genetic events that seldom goes to

completion without selection, because short-lived and deleterious intermediates are usually lost from the

population. Under long-term selection for increases in lac copy number, these precursors are held under

selectionlongenoughtoacquirethedeletioneventsneededtocompletetheprocess.

4.

TheaccumulationofmutantsunderselectionintheCairnssystemrequiresthatthelacmutationbeleaky.The

Stress-InducedMutagenesismodelproposesthatthisresidualfunctionprovidesenergythatisneededtopermit

acostlymechanismtocreatemutationsinnongrowingcells.TheSelectionModelproposesthatthisbasallevel

allowscopynumbervariantstoincreaselacenzymesandinitiateclonesunderselection.

5.

33..TThheeRRaaddmmaann--TTaaddddeeii--MMaattiiccSSyysstteemm,,aaNNoonnlleetthhaallSSeelleeccttiioonnSShhoowwiinnggtthheeAAccccuummuullaattiioonnooffRRiiffRRMMuuttaannttssiinn""AAggiinngg""CCoolloonniieess..

The formation of mutants resistant to the antibiotic rifampicin (RifR) is widely used for measuring mutation rates ingrowing bacteria. The attractions of the method are the following: (i) it can applied to a variety of bacteria with no needto construct special tester strains; (ii) it measures base substitutions (missense mutations) at a variety of sites within anessential gene (rpoB, RNA polymerase β-subunit); (iii) since all RifR mutations affect a single gene, they can be easilycharacterized by DNA sequencing; (iv) at least 69 different base substitution mutations, distributed among 24 codingpositions, result in a RifR phenotype (20); (v) Rif resistance arises at a rate that is easy to measure (~10−8/cell/generation


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in E. coli and Salmonella).

UnselectedmutationratestoRifRaremeasuredbyastandardlaboratoryselection(Fig.2).Cellsaregrowninrichmedium(lackingrifampicin),whereitispresumedthatresistantandsensitivemutationsgrowequallywell.Mutantsformintheseculturesandaredetectedbyplatedonselectivemediumcontainingrifampicin.UnliketheLuria-Delbrückexperiment,thisselectionisnotlethal,butitdoesreliablydetectlarge-effectRifRwithoutinfluencingtheirfrequency.Enumerationofthesecolonieswithallowanceforfrequencyfluctuationallowsonetoestimatetherateofmutationformationduringunselectedgrowth.Radman,Tadei,andMaticmodifiedthissystemtostudytheeffectsofgrowthlimitationonmutationrates(62,61).

ColonieswereallowedtoreachaterminalsizeonrichmediumandthefrequencyofRifRcellswasassayedovertimeasthecellsinthecolony“aged”withoutgrowth.IncreasesinthefrequencyofRifRcellsasafunctionoftimewereattributedtoastress-inducedincreaseinmutationrateexperiencedbyanongrowingpopulation.Colonieswereinitiatedbyspotting100to1,000cellsonnitrocellulosefiltersplacedonrichmedium.Thesmall

startingpopulationensuredthatnoRifRmutantswerepresentatthebeginningofcolonygrowth(nofoundereffects).Bacteriainanycolonycouldbeeasilyretrievedforanalysis.Inthefirstday,viablecells(=colonyformingunits,CFU)increasedto~109. Bythesecondday,cell numberpercolony increasedfurtherto~1010. Nofurther increaseordecreaseincolonypopulationwasseenoverthefollowing5daysofincubation.Manyartificialcolonieswereinitiatedinparallelsothatcellnumberandmutantfrequencycouldbetestedatvarioustimesoveraperiodofaboutaweek.

ItissurprisingthatthefrequencyofRifRcellsincreasedduringtheagingperiod.Laboratorystrainsshowincreasesupto100-foldfromday1today7whilethetotalCFUremainedunchanged(61,62).Asetof787naturalisolatesofE.coli fromdiverse ecological niches (6) showedvariable responseswith a median7-fold increase in RifR mutantfrequencybetweendays1and7—aperiodinwhichthemedianCFUincreasedonly1.2-fold(6).Theseresultswereinterpretedasevidenceof“stress-inducedmutagenesis.”Itwasassumedthatstressedcells

increasedtheirgeneralmutationrate(6,61,62).ThephenomenonwasreferredtoasROSE(restingorganismsinastructuredenvironment)andMAC(mutagenesisinagingcolonies).AsintheCairnssystem,thereisnogrowthtoserveasthebasisforcomparingmutationratesinstressedandunstressedcells.Thatis,thereisnowaytoinflictthestressof“aging”ongrowingcellsandthereisnowaytopreventgrowthwithoutinflictingstress.AsintheCairnssystem,thestress-inducedmutationisbasedonalaboratoryselectionthatusesanincreaseinmutantfrequency(over7daysofaging)toinferanincreaseinmutationrate(inanongrowingpopulation).Thephenomenonwasassumedtoreflectmutagenesisandexperimentsfocusedonhowthismutagenesiswascausedandregulated.Testsexaminedaseriesofmutantstrains,eachlackingsomecandidatefunction,todeterminewhichaffected

accumulationofRifRmutantsduringaging.AccumulationdependedontheabilitytoinducetheSOSsystemforDNArepair and on possession of an active RpoS protein—a stationary-phase sigma factor known to contribute toexpressionofavarietyofgenesingrowth-limitedcells.OneparticularnaturalisolateofE.coli,C4750wastestedforthepredictedgenome-widemutagenesisthatthemodelpredicts(6).Thisisolateshoweda77-foldincreaseinRifR

cellsbetweendays1and7,butshowednoincreaseinthefrequencyofmutantsresistanttostreptomycinornalidixicacid.Thefrequencyofmutantsresistantto5-fluorouracil,mecillinam,orfosfomycin,increasedonly3.4-,1.9-,and4.8-fold,respectively.Whiletheseresultswereinterpretedassupportforgeneralmutagenesis,theyseemtosuggestthatanothermodelisneeded.Thissystemviolatestherulesof laboratoryselectionwhichareessential herebecausean increase inmutant

frequencyisusedtoinferanincreaseinmutationrate.Theconcludedmutagenesisrequiresknowingthatthemutantfrequencyincreaserestsonformationofnewmutationovertimeandnotonfastergrowthofpreexistingmutants.Theonlyevidenceforthisisthatthepopulationasawholeshowednosignificantgrowthbetweentheinitialgrowthperiod(days0–2)andday7.Thesemeasurementscouldnotdetectmutationsarisinginagrowingsubpopulation.Moreimportantly,thetestsdidnotexcludegrowthofaRifRsubpopulationinthevastlylargerpopulationofnongrowingRifS

parentalcells.

Recently,Wrandeetal.(63)readdressedthequestionofhowRifRmutantsaccumulateinagingcolonies.ThebasicphenomenonwasreproducedinbothE.coliandSalmonellaenterica,includingclinicalandnaturalisolates.Asbefore,accumulationof RifR mutants dependedonanactive rpoS gene. However, several strikingandsignificant clues


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FFIIGG..1100 ThedistributionofRifRcells in"aged"coloniesisnonrandom.MostRifRmutantsarefoundtobelocalizedasjackpotsinoneorafewsectorsofthecolony,andwithineachofthesejackpotsthemutantscarrythesamesequence

alteration,consistentwithselectivegrowthofaRifRmutantduringtheperiodof"aging."Adaptedfromreference64withpermission.

concerningthebasisofthisphenomenonemergedfromnewexperiments.

AccumulationofRifRmutantcellscontinuedforuptoonemonthreachingafrequencyof>10−4.1.

Thefrequencyincreasedexponentially(asexpectedforgrowthunderselection)ratherthanlinearly(aspredicted

formutagenesisofanongrowingpopulation).

2.

TheRifRmutantcellswerelocalizedinjustoneorafewsmallsectorsofanagedcolony,asexpectediftheyare

clonalsubpopulationsgrowingfromindividualprecursorcells(Fig.10).Mutagenesisofnongrowingcellspredicts

anormalspatialdistributionofnewmutants.

3.

All RifR cells in an individual sector carried the same rpoB sequencealteration, demonstrating their clonal

relatedness. Incontrast, mutant cells fromdifferent sectorswithin thesamecolonyusually carrieddifferent

sequencealterations.

4.

IncolonieswithmanyRifRmutantcells,themajorityofthemutantswerefoundinasmallernumberoflocalized

subclones, consistent with variation in mutant frequency reflecting differences in clone growth, rather than

differencesinthenumberofclones.

5.

The RifR mutants showedno significant increase in the number of secondary mutations (the frequency of

auxotrophswastested),suggestingthattheyhadnotexperiencedgeneralmutagenesis.

6.

Most of the isolated RifR mutants showed a growth advantage over parent cells in colony reconstruction

experiments.Thisgrowthadvantageexplainswhycellsaccumulateascoloniesage.

7.


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Thus,theaccumulationofRifRmutantinagingcoloniesisreal,butitisexplainedbyselection,notmutagenesis.ApparentlyRifRmutantsgrowbetterin"aging"coloniesthanparentcellsevenwhennorifampicinispresent.ThedetectedRifRmutantsariseduringearlystagesintheexperimentandincreaseinfrequencybygrowingfasterthanthepopulationatlarge(63).MutationsappeartoariseinnongrowingpopulationsbecausethetotaladdedRifRcellsaretoo few to be detected in the total population. This gives the impression that new mutations accumulate in anongrowingpopulationwhen,infact,growthisresponsiblefortheobservedincrease.AdditionalexperimentswillberequiredtoexplainexactlywhyRifRmutantsgrowinagingcolonies.ItseemslikelythatsomemutantformsofRNApolymerasemayallowexpressionofgenesthatpromotegrowthunderagingconditions.ManyRifR mutationsareknowntoaffecttranscriptionelongationortermination(14,34,35,38,54,57,66)includingtwooftherpoBmutationsshowntoenhancegrowthinagingcolonies.OriginallyRpoSwasalsosuggestedtoregulatetheproposedmechanismof"stress-induced"mutagenesis(61)andhasalsobeensuggestedtocontrolmutagenesisintheCairnssystem(19).ItseemsmorelikelythatRpoSsigmafactorandmutantRNApolymerasescanacttogethertofacilitategrowthwithinstressedcolonies.

SSIIXXOOTTHHEERRSSYYSSTTEEMMSSCCIITTEEDDAASSSSHHOOWWIINNGGSSTTRREESSSS--IINNDDUUCCEEDDMMUUTTAAGGEENNEESSIISS

TThheeHHaallllSSyysstteemm——RRaappiiddEEvvoolluuttiioonnooffaaNNeewwββ--GGaallaaccttoossiiddaassee((EEBBGG))

In this extensively studied system, an E. coli lac deletion mutant acquires the ability to utilize lactulose (a lactoseanalogue) as a carbon and energy source (21, 24,25,26, 28). This ability requires two mutations that modify a crypticoperon (ebg, for evolved β-galactosidase), whose normal function is unknown, but does not include use of lactulose.One mutation inactivates the EbgR repressor, thereby allowing constitutive operon expression, and the second mutationalters the EbgAC enzyme, increasing its ability to hydrolyze lactulose. Each mutation alone allows very slow growth onlactulose (generation times >3 days), but when both mutations are present, cells grow rapidly (tgen = 20 min). The

ebgR-inactivating mutation is expected to be common (10−6/cell/generation) and the ebgAC point mutation rare(10−9/cell/generation). Based on these rates, cells with both mutations are expected to arise at a rate of 10−15/cell/generation and (as expected) are not detected in unselected cultures.

Incontrasttothisexpectation,thesedoublemutantsarisecontinuouslyoveraperiodofseveralweeksafter108

parentcellsareplatedonselectivemediumcontaininglactulose.Theselectionplatesalsocontainasmallamountofglycerol(0.01%)thatallowssomegrowthandthelactulose-utilizingdoublemutantsaredetectedaspapillaeappearingaboveasparsebacteriallawn.Thelawnpopulation(evenafterperhapsa10-foldincreaseattheexpenseofglycerol)isstill6to7ordersofmagnitudetoosmalltoensurecoincidentoccurrenceofthetworequiredmutations.Theresulthasbeeninterpretedasevidencethatstressinducesmutations.Sincetherecoveredlactulose-usingcellsshownoincreaseinthefrequencyofothermutations,itisconcludedthatthestress-inducedmutagenesissomehowdirectsmutationstositesthatimprovegrowth.AswastruefortheCairnssystem,thisexperimentresemblesastandardlaboratoryselectionalteredsoasto

estimatethenumberofmutationsoccurringinanongrowingpopulation.Thissystemusesthefrequencyofmutants(actuallydoublemutants)todrawaconclusionregardingmutationrate.Asdescribedabove,thisprocedurerequiresthattheselectionconditionsadheretotherulesofselectionandpreventallgrowthunderselection.Itseemslikelythatselectioninthissystemisnotstrongenoughtopreventgrowthofsmall-effectmutations,whichcaninitiateclonesandimprove their growth ability during growth under selection. If this is true, the systemviolates the rules and theconclusionsregardingmutationratesareunfounded.Belowisoneofmanypossiblescenariosbywhichselectionmightexplainthebehaviorofthissystemwithoutrecoursetochangesintherateorsitespecificityofmutation.

Sincethefrequencyofrepressormutantsishigh(10−6),itispredictedthatabout100nullrepressormutantsareincludedintheoriginalpopulation.Manymorecellsmightcarrymoremodestrepressordefects.Duringgrowthonglycerol,eachofthesecellscouldproducealargepopulationinwhichaduplicationoftheebgoperonarises.Thiswouldgivemultiplecopiesofahighlyexpressedoperon.Cellsgrowingwithanebgamplificationcouldproducemanycells,eachwithmultiplecopiesoftheebgACgenes.Thisincreaseintargetgenenumber(morecellsandmoreebgACgenespercell)couldallowararesecondmutationtoarisewithoutanychangeintherateorspecificityofthemutationprocess.


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Inthisexperiment,notestswereperformedtotestforthesequentialappearanceofthetwomutationswithinthepapillae.Onemightexpectsomecellswithintheseclonestoshowunstableamplifications(asseenintheCairnssystem).Thus,thesystemdoesnoteliminategrowthofsequentialsubpopulationsand/orgeneamplification.Whilethescenarioaboveisspeculative,itsuggeststhatthebehaviorofthissystemmaybeexplainedbysomeformofthepathwaysof genetic adaptationused to explain theCairnssystem.This explanationmayalsoexplain the trpABrevertantsdescribedbelow.

GGrroowwtthhaannddSSeelleeccttiioonnEExxppllaaiinnssaannAAppppaarreennttCCaasseeooffSSttrreessss--IInndduucceeddMMuuttaaggeenneessiiss——RReevveerrssiioonnooffTTwwooSSeeppaarraatteeMMuuttaattiioonnss((ttrrppAAaannddttrrppBB))iinnEEsscchheerriicchhiiaaccoollii

In this system, missense mutations in the trpA and trpB genes of E. coli appeared to revert to Trp+ more frequentlywhen starved for tryptophan than when tryptophan was present (23, 29). In a double mutant carrying both of thesemutations, reversion to Trp+ was expected to be astronomically rare (3.3 × 10−19) based on the measured reversion rateof the individual mutations tested singly. The observed Trp+ reversion rate of the double mutant during tryptophanstarvation was 4.5 × 10−11 per cell per day. Thus, the trpA and trpB missense mutations reverted to Trp+ about 108-foldmore frequently than would be expected if the two mutations occurred independently of each other. The genome-widemutation rate (as measured by valine resistance and lac reversion) did not increase during Trp starvation and there wasno effect on Trp reversion when cells were starved for another amino acid, cysteine. Thus it appeared that stress wasinducing mutagenesis and directing mutations preferentially to sites that improve growth.

Hallobservedearlyonthatthestress-inducedhypermutablestatemodel(whichheproposed)wasinconsistentwiththebehaviorofthetrpmutations,becausethemagnitudeofthegenome-widemutagenesisrequiredtoaccountforthereversionwouldcertainlybelethalforanycell.Eachbasewouldhaveaprobabilityofaround0.04ofmutatingduringtheselectionperiodandavastnumberoflethalmutationswouldbeexpected(astheyareexpectedintheCairnssystem).Hallthereforeexaminedthepossibilitythatthetwomutationsoccursequentiallywithinterveninggrowth.ThisanalysiswasbasedonthesuggestionthatthetrpA,trpBdoublemutantisexpectedtoaccumulatetheintermediateindole-glycerol-P(duetothetrpAmutation).Thiscompoundbreaksdownspontaneouslytoindole,whichtheTrpBenzymecanconverttotryptophan.Thus,ifthetrpBmutationrevertedfirst,theresultingtrpA,trpB+cellcouldusethespontaneouslygeneratedindoleandformagrowingcloneinwhichthesecondmutation(totrpA+)couldoccur.Hallmeasured the growth rates of single-mutant cells within double-mutant colonies concluded that the most likelyexplanationoftheenhancedreversionofthedoublemutantwasasequenceoftwosteps,eachgivingprogressivelyimprovedgrowth.Thatis,trpA,trpB→indolaccumulation→,trpAtrpB+→growthonindole→trpA+,trpB+(27).Thisillustrates one of the myriad pathways by which selective conditions that incompletely limit growth can give theappearanceofstress-inducedmutagenesis.Italsomakesclearthepointthatconsiderabledetectiveworkmayberequiredtoseehowthedevioushandofselectioncanupseteventhemostcarefulattemptstofoilit.

SSttrreessss--IInndduucceeddAAccccuummuullaattiioonnooffDDeelleetteerriioouussMMuuttaattiioonnssiinnSSttaattiioonnaarryy--PPhhaasseeCCuullttuurreessooffEE..ccoollii

This system suggests that stressed cells in a nongrowing liquid culture show a stress-induced increase in the formationrate of deleterious mutations (43). Replicate bacterial cultures are grown to full density in liquid medium and thenfurther incubated for up to 100 days with very little additional population increase. Samples were removed from theresting cell suspension at various times and used to inoculate new cultures in fresh medium. These secondary cultureswere used to estimate fitness (growth rate). The median decrease in fitness and the increase in variance among thesample lineages were used to infer mutation rates in the resting cell suspension. The genomic mutation rate inferred forcells in prolonged stationary phase was about 0.03/genome/day, about 10-fold higher than values extrapolated fromexponential cultures.

While this experiment is not astandard laboratoryselection(not doneonsolid medium), it doessharemanyfeatureswithsystemsusedasevidenceforstress-inducedmutation.Thatis,apopulationisheldunderconditionsthatallownonetgrowthandincreasesinmutantfrequency(assessedindirectly)areusedtoinferincreasesinmutationrateinthenongrowingpopulation.Tofairlyinterprettheseresultsrequiresknowingtheamountofgrowththatmightbeoccurringwithintheresting

population and whether selection for growth or survival in the resting period could affect mutant frequency. As


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describedinFigure6andFigure7above,largeculturesthatshownonetchangeinpopulationsizemaysupportsubstantialgrowthofsubpopulationsinwhichmutationscanarise.Thegrowthmaybepopulationstosmalltodetectorbalancegrowthanddeathsuchthatnonetchangeinviablecellsoccurs.Onepotentialexplanationforthisresultthatdoesnotinvolvestarvation-inducedmutagenesisisundetectedgrowth.Criticsofthisexperimenthavesuggestedthatitinvolvesunappreciatedgrowthwherespecificsubpopulationsgrow

extensively(10)withoutanychange in thepopulationasawhole—theGASPphenomenon(13,67). Thiscrypticgrowthprovidesaddedopportunitiesforrandommutationstoformatnormalratesleadingtofitnessdecreasesthatarenotsurprisinginviewofthelargefractionoftotalmutationsexpectedtobedeleterious.Amoreextremepossibilityisthatmutationsarepositivelyselectedduringstationary-phaseincubation.Thesemutationsmayenhancesurvivalinstationaryphasebutbedeleteriousunderthegrowthconditionsusedinthefitnesstests.As inseveral othersystemsthat involvenongrowingpopulations, mutationratescannotbecomparedwithan

unstressedcontrol populationother than theonegrowingwithout restriction. Theauthors express their apparentmutationratesbasedonaclock-likeviewofmutation(mutations/day), whereastheir stress-freecontrol ratesarebasedonmutations/cell/generation.Itisnotobviousifandhowclock-likeandgeneration-dependentmutationratescanbedirectlycompared.

EExxppeerriimmeennttssCCllaaiimmiinnggtthhaattTTrraannssccrriippttiioonnDDiirreeccttssMMuuttaattiioonnssttooSSppeecciiffiiccGGeenneessiinnNNoonnggrroowwiinnggCCeellllss

Yasbin and colleagues made Cairns-type experiments asking whether stress-induced mutagenesis also occurs in Bacillussubtilis, a gram-positive species. They measured the accumulation of late-appearing prototrophs from three differentauxotrophic mutants (his-nonsense, met-nonsense, and leu-missense) and over 10 days observed increases of ~20-foldfor His+, <5-fold for Met+, and 2-fold for Leu+ (50, 59, 60). As in most experiments of this genre the authors made theassumption that the increase in the frequency of prototrophs with time could be interpreted as due to an increase in therate of mutation in nongrowing cells. No direct tests for increased mutagenesis (for example, by testing for an increasein the frequency of unselected mutations at other locations) were made. Instead, attention was focused on identifying amechanism to explain the presumed increase in stationary-phase mutation rate. They were intrigued when they foundthat the accumulation of late-appearing (as well as growth-associated) prototrophs was partly dependent on the gene mfd(53). On this basis they proposed that the late accumulation of prototrophs was associated with transcription of themutant genes. The idea that transcription might "direct" mutations to a particular target, like lac, was proposed shortlyafter publication of the original Cairns experiment (9). The relevance of mfd for this class of model is that it codes forTCRF (transcription-coupled repair factor) (55). When RNA polymerase gets stalled in the process of transcription bybulky DNA lesions, the stalled RNAP can be dislodged by TCRF protein which then recruits Uvr(A)BC to the lesionsite, thus promoting nucleotide excision repair. TCRF activity reduces the rate of mutation on the transcribed strand ofDNA relative to that on the nontranscribed strand (55). The observation by Yasbin and colleagues that the absence ofthe TCRF gene decreases the frequency of prototrophs is not readily explained by the known activities of TCRF, and nomodel has been proposed to explain the phenomenon.

SequenceanalysisoftheB.subtilisprototrophsshowedthatonlyaminorityofthelate-appearingmutantswereactually causedby reversionof theauxotrophic alleles. Themajority weredue to external suppressors (possiblymutanttRNAs),andsomeofthesewerelate-appearingbecausetheygrewslowly(53)andmaythereforehavebeenpreexistinggrowth-associatedmutations.Theleakinessofthethreeauxotrophicalleleswasnottested,butnonsenseallelesinothersystemsarefrequentlyhighlyleakyandcouldplausiblysupportslowgrowth,especiallyifthemutantgeneswereamplifiedinasubpopulationofcells,asobservedinthelacsystem.Indeed,thetwoallelesforwhichthefrequencyof late-appearingprototrophswashighestarebothnonsensemutations.Notestsweremadeforgeneduplicationoramplification,orforthepresenceofgeneticheterogeneityinprototrophiccolonies.TCRFactivitywasonlyassociatedwiththeinfrequentreversionprototrophsandnotwiththemuchmorefrequentexternalsuppressorprototrophs.WedonotknowwhyTCRFshouldassociatewithasmallincreaseinthefrequencyofreversions:onepossibilitywesuggestisthatthenewDNAsynthesisfollowingnucleotideexcisionrepairiserrorprone,fortuitouslycausingoccasionalreversionmutations.Thishasnotbeentested.Insummary,asinothercasesdocumentedhere,theassumptionwasmadefromthebeginningthatstress-induced

increases in mutation rate were an established fact and alternative explanations (selection of slow-growingsubpopulations)werenot tested. Theexperimental systembreaks therulesof laboratoryselectionbynot clearly


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separatingselection fromgrowth. Theaccumulationof late-appearingprototrophs in thissystemcanplausiblybeexplainedbyselectionandgrowthofsubpopulationsofcellscarryingleakyalleles,possiblyassociatedwithgeneamplifications(Figure11). [[PPEE--QQ55::AAUU]] DDrr..AAnnddeerrssssoonn,,yyoouurr""TTaabbllee11""wwaasscchhaannggeeddttooaaffiigguurree((bbeeccaauusseeooffiittssggrraapphhiiccaallnnaattuurree))aannddnnuummbbeerreeddaassFFiigg..1111..FFiigg..1111((tthheeaaccttuuaallhhyyppeerrlliinnkk))nneeeeddssttoobbeecciitteeddaafftteerrFFiigg..1100iinnoorrddeerrffoorrtthheeiilllluussttrraattiioonnssttooaappppeeaarriinnoorrddeerr

iinntthheeppoosstteeddcchhaapptteerr..OOKKttoocciitteeiitthheerree??IIffnnoott,,pplleeaasseeiinnddiiccaatteeaassuuiittaabblleellooccaattiioonnaafftteerrtthheecciittaattiioonnooffFFiigg..1100..

FFIIGGUURREE1111Spontaneousmutationsastheyappearinagene.

AAddaappttiivveeRReevveerrssiioonnooffaaLLYYSS22FFrraammeesshhiiffttMMuuttaattiioonniinnSSaacccchhaarroommyycceesscceerreevviissiiaaee

A Cairns-type experiment was made to test whether the stress of stationary phase caused increased mutation rates alsoin eukaryotes (58). This experiment measured the accumulation of late-appearing prototrophs from a constructed lysframeshift mutation in S. cerevisiae and was, in design, methodology, and result, almost identical to the classicCairns-lac reversion experiment (8).

Lys+coloniesappearedontheselectiveagarplatesafter3daysofincubationwithadditionalcoloniesappearingoneachofthefollowing5days.Thenumbersofcoloniesappearingfromindependentculturesshowedadistributionofmutantsthatfittedwelltoexpectationsforrandom(preexisting)mutationsonday3,calculatedaccordingtoLeaand


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Coulson(39).Atlatertimes(days5to8)thedistributionofmutantsfittedwelltoaPoissondistributionasexpectedformutationsoccurringafterplatingandinresponsetoselection.Geneticandphysicalanalysisof theLys+ mutantsshowed that 90% contained a compensating frameshift mutation within the LYS2 coding sequence, while theremaining10%wereapparentlyrevertants,aconclusionsupportedbydirectsequenceanalysisinalaterstudy(32).Aftertestingandrulingoutcross-feedingandslow-growingmutantsascausesofthelate-arisingLys+mutants,SteeleandJinks-Robertson (58) concluded that at least someof theevents leading to theLys+ phenotypemust haveoccurredafterselectiveplating.Theexperimentshowedthattherewasnosignificantincreaseintotalcellnumberasafunctionofthenumberof

daysaplatewasincubated.However,theseexperimentsdidnottestthepossibilitythatsubpopulationsofcellsweregrowing(thosethateventuallygaverisetoprototrophiccolonies),orthatwithinthosesubpopulationstheremighthavebeenamplificationoftheLYS2targetgene.Eitherorbothoftheseeventswouldhaveincreasedthegenetictargetforreversionorsuppressormutationswithoutnecessarilycausinganyappreciableincreaseinthesizeofthegeneralpopulationofplatedcells.ByanalogywiththeCairns-Fosterlacsystem,wesuggestthattheLYS2frameshiftmutationmightbeleaky,andthatitcouldbesubjecttoduplicationandamplificationunderselectionforlysinebiosynthesis.ToourknowledgenoonehascheckedthisexperimentalsystemforevidencethattheLYS2mutantalleleisleaky,orthatitisamplifiedduringthepostplatingselectionperiodbeforethevisiblegrowthoflate-appearingLys+revertants.

Interestingly,theauthorsdefinethelate-appearingLys+revertantsas"adaptive"becausetheyoccurspecificallyinresponsetolysinestarvation.Thus,ifcellswerestarvedforotheraminoacidsitdidnotselectforLys+revertants.Thisshowedthatstarvationdidnotinducegenome-widemutagenesis.ThisisinagreementwithdatathatstarvationinSalmonelladoesnotcauseageneralincreaseinmutationrates(33).

SteeleandJinks-RobertsonalsoselectedLys+revertantsfrompopulationsofcellsthatwereUV-irradiatedbeforeplating.Thenumbersofearly-andlate-appearingLys+revertantswerebothincreasedbytheirradiation,5.5-foldand~10-fold,respectively.Interestingly,the10-foldincreaseappliedtorevertantsappearingondays4,5,and6,whereasonday7itfellbacktoa6-foldincrease.Butifirradiatedcellswereallowedtogrowbeforeplating,orwereheldwithanotherstarvationbeforeplating,thenthenumberoflate-appearingLys+revertantswassignificantlyreducedrelativeto the numbers found when plating directly after irradiation. These data can easily be explained by the geneamplificationmodelbecauseUVirradiationwouldincreasethenumberofrecombinogenicDNAends,increasingtheprobabilityofduplicationandamplificationoftheLYS2allele.Thiswouldincreasethenumberofcellsinthepopulationthatcouldgrowslowlyintheabsenceoflysine,andbesubstratesforgeneamplificationandeventualselectionofareversionmutationintheLYS2gene.If,however,cellswerenotplatedontheselectivemediumdirectlyafterUVirradiation, thenDNArepair systemswouldhavetimetorepair lesions,unstableandnonselectedduplicationsoramplificationswouldbelost,andthenumberofcellsinthepopulationwithagenomeconfigurationsuitableforgrowthselectiontomakelysinewouldbereduced.

Ourconclusionisthatthelate-appearingLys+mutants,selectedintheabsenceoflysine,canbestbeexplainedwithintheparametersofthemodelforgrowthadvantageassociatedwithgeneamplification,essentiallyasdescribedforthelacsystem.ExperimentstotestthismodelhavenotbeenmadebutwewouldpredictthattheLYS2frameshiftallele is leakyandthatsomelate-appearingLys+ mutantcoloniesshouldbeheterogenousandcontaincellswithduplicationsandamplificationsofthemutantgene.

MMuuttaattiioonnuunnddeerrSSeelleeccttiioonnffoorrRReecceessssiivveeMMuuttaattiioonnssiinnaaCChhrroommoossoommaallGGeennee

This system resembles that of Cairns and Foster in that one selects for Lac+ revertants of a Lac− parent strain (64, 65).The system differs in that it does not involve an F′ plasmid and appears to demand recessive (loss of function)chromosomal mutations, while the Cairns-Foster system demands dominant (gain of function) mutations.

Thebasicsystemusesalacoperoninsertedwithinachromosomalpurinegene(purD)andtranscribedfromitspurine-regulatedpromoter.SincethepurD promoter isnormallyrepressedinthepresenceofexcesspurines,thestrain is phenotypically Lac− (andrequirespurinebecauseof thepurD disruption). When this strain is platedonminimallactosemediumwithaddedpurine(adenine),about100revertantcolonies(Lac+)ariseoverthecourseof6


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daysabovethelawnofplatedcells.Themostfrequentrevertantsareexpectedtobecommonrecessivemutationsinthegeneforthepurinerepressorprotein(purR-1,000bp)orraremutationsinthetinyPurR-bindingoperatorsequence(16bp)nearthepurDpromoter.EithertypeofmutationshouldactivatetranscriptionofpurDandallowexpressionoftheinsertedlacgenes,resultinginaLac+phenotype.

Intheinitialdescriptionofthissystem(65),thetesterlawnshowedverylittlegrowthandabout100Lac+revertantcoloniesaccumulatedoverthecourseof6daysofincubation.Resultswereinterpretedasevidenceforstress-inducedmutagenesisofnongrowingcells.ThisconclusionwassupportedbythefindingthattheratioofOctoR−mutantswasmuchhigherthanonewouldexpectbasedontheirtargetsizes.Amongday2revertants,Ocmutantswere34%oftotal.Amongday6revertantsOcmutantswere8%ofrevertants;theoperatortargetisonly1.6%ofthepurRtarget.ThehighrelativefrequencyofOcmutantsisinterpretedasevidencethatstressdirectsmutationstositesnearthosethatlimitgrowth(theunexpressedlacoperon);thehigherfrequencyonday2isnotexplained.Inthisexperiment,theabsolutefrequencyofOcmutantsisalsosurprising—approximately10per108platedcells—thisisapproximately100-to1,000-foldhigherthanonewouldexpectforatargetof10bp.Theconclusionthatthissystemreflectsstress-inducedmutationrestsonthepillarsoflaboratoryselection.Thatis,

growthoftheparentstrainispreventedbyselection,andthatrevertantcoloniesreflectsinglelarge-effectmutationsthatconferfullfitnessandarenotsubjecttofurtherimprovementduringmaturationofthecolony.RecentanalysisofthissystemsuggeststhatsubstantiallawngrowthoccursandtheprocessbywhichLac+coloniesariseisextremelycomplex—requiringmultiplemutationsthatariseasindividualstepsinapathwayofgeneticadaptationduringgrowthunderselection.Growthoftheparentonlactoseisrestrictednotonlybyrepression,butalsobypolareffectsofastem-loopstructurepresentupstreamoflacintheinsertedsequence.NeitherapurRnoranOcmutationaloneissufficienttoallowarevertantcolonytoappearunderselection.Allrevertantshave,inaddition,lostthestem-loopstructure.Thus,therecoveredrevertantshavegenotypesthatareexpectedtoariseatfrequenciesoflessthan10−15,yetabout100suchrevertantsarisefrom108 slow-growingplatedcells.Directtestsoftheserevertantsrevealnoevidencethattheyhaveexperiencedanyglobalmutagenesisduringselection.

RevertantcoloniesincludecellswithanunstableLac+ phenotype.Thesecellshaveanamplificationofthe lacoperonduetorecombinationbetweentherrnHandrrnEloci–5kbdirectsequencerepeatsthatflankthepurD::lacregion.TheyieldofrevertantsinthissystemisreducedaboutfivefoldbyarecAmutation.Whilemanydetailsofthereversionprocessremaintobeelucidated,it isclearthattheexcessofOcmutationsandfrequencyofstem-loopdeletionscanbeexplainedbyamplificationofthepurD::lacregionunderselectionduringgrowthofthedevelopingrevertant colonies. This amplification allows growth and provides additional copies of the growth-rate-limiting lacregion,therebyenhancingthelikelihoodofmutationsthatimprovegrowthunderselection

CCOONNCCLLUUDDIINNGGRREEMMAARRKKSS

Publication of the Cairns system in 1988 (8) has sparked renewed interest in the process by which mutations arise. Workfollowing up on this initial report has revealed methodological pitfalls associated with measuring mutation rates and thedifficulty of unambiguously separating the effects of mutation and selection. Thus, as outlined in this chapter, theinference that stress induces mutagenesis can generally be explained by an inability in the different experimental setupsused to completely prevent the effects of growth when applying nonlethal selections; i.e., the claims of stress-inducedmutagenesis have not strictly excluded the influence of growth and selection in increasing mutant frequencies. Insteadmany of these observations can be explained by the ability of selection to detect and amplify small differences in growthrate caused by common small-effect mutations. One very common class of mutations that will be important during anyadaptive response in which increased activity of some gene can enhance growth is gene amplification. In the widelystudied lac system of Cairns, amplification of lac and occasional coamplification of the nearby dinB (coding for theerror-prone DNA polymerase, PolIV), can account for the apparent increase in number of Lac+ revertants without anyneed to invoke an increased mutation rate.

Fromamoregeneralperspective,geneamplificationsareexpectedtobeamajorimmediateresponsewhenevergrowthislimitedbyanexternalfactor(e.g.,lownutrientlevelsorthepresenceofatoxicfactor)oraninternalfactor


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(e.g.,adeleteriousmutation)andwhenincreasedlevelsofageneproductmightmitigatetheproblem.Furthermore,geneamplificationcouldfacilitatetheprocessofacquiringstableadaptivemutationsby increasingthenumberofselectedtargetgenesinthepopulation.Thesestablechangescouldoccuroutsideoftheamplifiedregionandincreaseinfrequencybypopulationexpansionalone,ortheycouldaffecttheamplifiedgenes,inwhichcasetargetnumberisincreasedbybothcellgrowthandaddedcopiespercell.Sincetheamplificationmaybedispensableafterastablemutationalimprovementoccurs,itisconceivablethattheintermediateamplificationsleavenotraceinthegenome.Thus,wesuggestthatmanyadaptivephenomenainfactoccurwithamplificationsbeingtransientintermediatesthat,becauseoftheir intrinsicinstability,arerapidlylostandthereforeeasilyunderestimatedduringstudiesofadaptiveevolution. Apart from the lac system, recently described examples of such amplification processes of medicalsignificanceareprovidedbythesequentialevolutionofcephalosporinresistancebyTEMβ-lactamases(S.Song,O.G.Berg,J.R.Roth,andD.I.Andersson,unpublisheddata),resistancetothetRNAsynthetaseinhibitormupirocin(49)andresistanceoftumorcellstocytostaticdrugs(15).Similarprocessesofsequentialselectionofcommonmutationsof small effect (including gene amplification) are likely to apply also for malignant transformations, where cellssuccessivelyescapethevariousspatialandtemporalcontrolmechanismsthatkeepgrowthofindividualcellsincheck(2).

RReeffeerreenncceess [[CCEE--QQ66::AAUU]]OOrriiggiinnaallrreeffeerreenncceess99,,4466,,aanndd5599hhaavveebbeeeennddeelleetteeddbbeeccaauusseetthheeyywweerreedduupplliiccaatteessooffoorriiggiinnaallrreeffeerreenncceess88,,4455,,aanndd5588..TThheerreemmaaiinniinnggrreeffeerreenncceesshhaavveebbeeeennrreennuummbbeerreedd,,aannddtthheecciittaattiioonnssiinntthheetteexxtthhaavveebbeeeennuuppddaatteedd

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http powerxeditor.aptaracorp.com ecosal DashBoard Homerothlab.ucdavis.edu/publications/ASMProofs2010.pdffundamental to the whole ﬁeld of bacterial genetics. The experiments also