lecture notes Module 4 part2.docx
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lecture notes Module 4 part2.docx
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lecturenotesModule4part2
LecturenotesforModule4Part2:
Inactivationmodels
TinyvanBoekel,PDQ
N.B.TheselecturenotesareadaptedfromChapter13fromthebookKineticmodellingofreactionsinfoods,M.A.J.S.vanBoekel,CRCPress,2008.
Introduction
Obviously,inactivationofmicro-organismsinrawmaterialsandfoodisnecessaryforfoodsafetyandfoodquality.Itisnocoincidencethatthefirstkineticprinciplesinfoodtechnologyweredevelopedwithrespecttoinactivationofmicro-organismsbecauseofitsimportance.Inthenineteen-twentiestheconceptofDandZvalueswasdevelopedbyEstyandMeyerandBigelow,andlatertakenupbyBallandStumboinF-values.Theterm‘thermobacteriology’wascoinedandpioneeredinthecanningindustryandthe‘12Dconcept’iswidelyaccepted.Thismeansthatsterilisedfoodshaveatleasta12decimallogreductionofthemostdangerous(becauseofitsverypotenttoxinbotuline)bacteriumClostridiumbotulinum,sothatsterilefoodisvirtuallyalwaysfreefromsporesofthisdangerousspecies.Theseideasarestillinusetoday.Herewefurtherelaborateonthismatterandinvestigatewhethertheclassicalfirst-orderinactivationkineticsapproachisstillavalidmethod.orthatalternativemethodsareneeded.Likethemicrobialgrowthkineticsissuediscussedinthepreviouschapter,thetopicofmicrobialinactivationisalsounderheavydebate.Moreover,non-thermaltreatmentsarebecominginvogueandtheconsequencesformicrobialactivityinfoodsneedtobeconsidered.
Kineticsofinactivationofvegetativecells
First-orderinactivationkinetics
SincethedevelopmentofthermobacteriologybyBigelowinthe1920s,itismorealesstakenforgrantedthatinactivationofmicro-organismscanbedescribedbyafirst-orderprocess.Inalmosteverystandardfoodtechnologyhandbookthefollowinganalysisisgiventhatthedecreaseinnumberofmicro-organismsNisafirst-orderreaction:
(1)
andso:
(2)
withNandN0thenumberofmicro-organismsattimetandtimezero,respectively.Inactualpractice,theso-calledsurvivalratio(
)isused:
(3)
or
(4)
withDthedecimalreductiontime(thetimeneededtoreducethenumbers/concentrationbyonedecimallogcycle):
(5)
AplotoflogS(t)versustimeiscalledasurvivalcurveanditshouldbelineariffirst-orderkineticshold.Theslopeofsuchalinearplotequals1/D.Theinactivationisthuscharacterisedbythedecimalreductiontimeor,equivalently,afirst-orderrateconstantk.Therewouldbesomemechanisticjustificationforfirst-orderbehaviourifitisacceptedthatmicrobialdeathiscausedbyinactivationofenzymes(usuallybyheatdenaturation,orbyhighpressure).(Inactivationofenzymescanoften,thoughnotalways,bedescribedasafirst-orderprocess)Thetheoryoffirst-orderinactivationcanbecheckedrigorouslybylookinguppublishedsurvivalcurves.Figure1givessometypicalexamples.
Figure1.SurvivalcurvesforinactivationofE.Coliinappleciderat52ºC,D=11.4min(A),55ºC,D=5.2min(B),58ºC,D=1.1min(C).Drawnlinesareregressionlinesassumingfirst-orderkineticsandDvaluesarecalculatedfromtheslopeoftheplots.
LookingattheplotsinFigure1,onewonderswhetherfirst-orderkineticsreallyappliesastwoofthethreesurvivalcurvesareclearlynonlinear(onereasonfortheapparentlinearityinFig.1Bcouldbethelimitednumberofdatapointsincomparisontotheothertwoplots).Ofcourse,threeexamplesarenotenoughtodisproveatheorybutinspectionoftheliteratureshowsthatnonlinearsurvivalcurvesareveryfrequentlyobserved.Surprisingly,nonlinearityismostlyneglectedandD-valuesaredeterminedbylinearregression,asshowninFigure1.Theexplanationsthatareofferedfortheobservednonlinearityofsurvivalcurvesisthatthereareseveralsubpopulationspresent,eachwithitsowninactivationcharacteristics.Also,theremaybeexperimentalartefactssuchasclumpedcellsthatarefallingapartduringheattreatment,thusgivingrisetoanomaliesincellcounts.Also,neglectofheating-upandcooling-downperiodsmaydisturbthepicture.However,apartfromthesubpopulationtheory,onecancorrectfortheothercausesandthennonlinearityisstillobserved.So,itseemsthatthepredictedlinearityisnotobservedinpractice,whichmakesitworthwhiletoreconsidertheclassicalfirst-orderinactivationtheory.
Aneedforalternativemodels?
Thefirstreasontoreconsider,asmentioned,isthataninspectionoftheliteratureoninactivationofmicro-organismsrevealsthatalinearsemi-logarithmicfirst-orderplotismoretheexceptionthantherule.Inotherwords,thehypothesishasbeenfalsifiedinanoverwhelmingnumberofcases,whichimpliesthatanalternativehypothesisformicrobialkineticsneedstobefound.Thesecondreasontoreconsideristhatfromamechanisticpointofviewkineticsofmicrobialinactivationisnotthesameaschemicalkinetics.Mostlikely,thereisamultitudeofpossiblechemicalreactionsleadingtocellinactivationanditisanoversimplificationtotreatthisasasingleelementaryreaction.
Thereadermightask:
ifthisistrulyanoversimplification,whythenhastheclassicalapproachbecomesosuccessful?
Indeed,thesafetyrecordofthefoodindustrysincetheintroductionofthisclassicalinactivationkineticsisimpressive.However,thissuccessisnotaproofofthevalidityofthescientificbackground.Onemayask,inresponse,whetherornotitisimportanttohaveabettertheoryforaprocessthatweapparentlymasterinpractice.Intheauthor’sview,itwillpayofftolookforabettertheory.Firstofall,itisscientificallyandintellectuallymorerewardingtoupdateaquestionabletheory.Second,wearenowinanerawhereothertechnologiesthanheattreatmentbecomemoreprominentanditmaybehelpfulifweareequippedwithabettertheorytohandlethesesituations.Third,itmaywellbethatwiththecurrentlyappliedheattreatmentsfoodisactuallyoverprocessed(tosafeguardfoodsafety),inotherwords,wemaybegivinginonquality(lossofnutrients,sensorialproperties,formationofundesiredheat-inducedcompounds)whilethereisperhapsnoneedforitbecauseweareoverestimatingtheheattoleranceofmicro-organisms.Theheateddebatesthatarecurrentlyappearinginliteratureprobablyindicateaparadigmcrisis.Therearescientistsstickingtotheestablishedparadigmoffirst-orderinactivationkineticsandthereareothersrejectingthisparadigm,andasthesciencephilosopherKuhnhasshown,thiswillleadtoheavyandemotionaldebatesthatarenotalwaysscientific.Also,foodsafetyauthoritiesmayberesistanttoanewviewbecausetheyarenowworkingwithinacontextthatmoreorlessguaranteesfoodsafety,soifitworksinpractice,whybother?
Thelargevariabilityanduncertaintyinrelationtomicro-organismsisnotmakingiteasier.
Incidentally,itisnotonlynowthatfirst-orderkineticshasbeenquestioned.Alreadyfiftyyearsagoaso-called‘vitalistic’theoryhasbeenputforward,butthistheorywas,apparently,notabletoexistnexttothedominantfirst-orderkineticsassumption.
Modelsfornonlinearsurvivalcurves
Whatalternativetheorycanbeputforward?
Intheauthor’sview,kineticsofcellinactivationshouldbeconsideredasastochasticprocessandnotasachemicalreaction.So,whatweobserveexperimentallyasadecreaseinnumberofcellsbystudyingapopulationisareflectionoftheresponsesofindividualcellstoanappliedstress,whetherthatisheat,highpressure,electricfields,orchemicalagents.Lethaleventsaretobeconsideredasprobabilities,ratherthanasdeterministicevents.Anindividualmicro-organismiseitheraliveoritdiesbecauseofsomeappliedstress.Weneglectforamomenttheexactmechanismwhyitdies.Thesurvivalcurveofasinglemicro-organismisthusastepfunction:
Si(t)=1(celliisalive)fort
seeFigure2.
Figure2.Stepfunctionforfourcellseachhavinganindividualinactivationtime.St=1:
cellisalive,St=0:
cellisdead.
Ofcourse,inpracticewecannotobservethebehaviourofindividualcells,butweobservethebehaviourofthewholepopulationunderstudy.Theindividualbehaviourisreflectedinthechangeinnumberoftotalcellsthatwecount.Thestepthatwetakenowisthatthedistributionofindividualcriticalinactivationtimesisreflectedintheexperimentallyobservedsurvivalcurve.Ifthenumberofcellsishigh(whichisusuallythecase)thiscanbetakenasacontinuousdistribution.Consequentlytheinactivationtimesdescribingthewholepopulationwillvaryaroundsomecharacteristicvalue,andthiscanbedescribedbyadistributionfunction,forinstance,asinFigure3.
Figure3.Apossiblefrequencydistributionforinactivationtimesofapopulationofmicrobialcellsunderlethalstress.
Consequently,thesurvivalcurveisacumulativeformoftheunderlyingdistribution.Ofcourse,thereisafundamentalmechanismatthemolecularlevelbehindtheeventualdeath(suchastheinactivationofcertainvitalenzymes,orDNAdamage)butthepointisthatthismayvaryfromcelltocell.Itisquestionablethatsuchamechanismwouldhavethesameeffectineachandeverycell;rather,onemayexpectthatonecellismoreresistantthananotherone.Hence,atthe
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