1860 Received 15October 2013;Accepted11 February 2014 *Author ([email protected]) for correspondence Carolina,ChapelHill,NC27599,USA. Biology, North of University of Department animal, theearthworm. components ofthehydrostatic skeletonofaniconicsoft-bodied microscopic techniquestoexaminetheeffects ofsizeandscaleon little attention.Theaimofthisstudywastousehistological and scaling onsoft-bodiedanimalshave,however, receivedrelatively Biewener, 2005;Nudds,2007;ChiandRoth, 2010).Theeffects of the vertebratesandinsomearthropods(e.g.Schmidt-Nielsen, 1997; in formandfunctionduebodysize,hasbeenstudiedprimarily in Vogel, 2013;Biewener, 2005;Hilletal.,2012).Scaling,thechanges ecology andbiomechanics(Schmidt-Nielsen,1984;Quillin,1999; may beinfluencedbyitssize,includingphysiology, morphology, lifespan. Asaconsequence,almosteveryfacetofanorganism’s life including: geometry, metabolicrate,kinematics,mechanicsandeven A rangeofimportanttraitschangeasafunctionbodysize, fundamental effects onorganismal design(Schmidt-Nielsen, 1997). 1988). Sizealsoimposesphysicalconstraintsonorganisms, with environment aswelltheprocessesneededforsurvival(Vogel, organisms. Sizeaffects howanorganism interactswithits Body sizeplaysapivotalroleinthestructureandfunctionofall KEY WORDS:Scaling,Allometry, Ontogeny, Annelid,Burrowing of theearthwormLumbricusterrestris examine thescalingofmechanicallyimportantmorphologicalfeatures skeletons. We usedglycolmethacrylatehistologyandmicroscopyto relatively littleisknownaboutscaleeffects inanimalswithhydrostatic scale havebeenwellstudiedinanimalswithrigidskeletons,but The structuralandfunctionalconsequencesofchangesinsizeor Jessica A.Kurth*andWilliam M.Kier Lumbricus terrestris Scaling ofthehydrostaticskeletoninearthworm RESEARCH ARTICLE © 2014.PublishedbyTheCompanyofBiologistsLtd|JournalExperimentalBiology(2014)217,1860-1867doi:10.1242/jeb.098137 INTRODUCTION ABSTRACT from 0.03to12.89 burrowing mechanicswithsize. scaling ofearthwormsmayreflectchangesinsoilpropertiesand contraction scalesnearisometry. We hypothesize thattheallometric output generatedduringbothcircularandlongitudinalmuscle sectional areaandmechanicaladvantage,wecalculatethattheforce predicted byisometry. Bymodelingtheinteractionofmusclecross- ~0.8 poweracrosssegments,whichissignificantlyhigherthan of thecircularmusculature,however, scalesasbodymasstothe than the0.66powerpredictedbyisometry. Thecross-sectionalarea mass tothe~0.6poweracrosssegments,whichissignificantlylower cross-sectional areaofthelongitudinalmusculaturescalesasbody expansion, comparedwithhatchlingworms.We alsofoundthatthe mass, adultwormsgain~117% mechanicaladvantageduringradial length todiameterratiowithsizemeansthat,whennormalizedfor disproportionately longerandthinnerasitgrows.Thisincreaseinthe g. We foundthat over anontogeneticsizerange L. terrestris becomes aspects ofhydrostatic skeletonmorphology, usinganontogenetic properties (Piearce,1983;Quillin, 2000). area, skeletalleverage,burrowing kinematics,respirationandsoil size-dependent changesinmuscle stress,musclecross-sectional hydrostatic skeletonhavenot yet beentested,includingpossible Quillin, 2000).Inaddition,many hypothesesonthescalingof scaling inbothshapeandforceproduction(e.g.Piearce,1983; Quillin, 1998;1999),whileotherssuggestdisproportionate geometric andkinematicsimilaritywithchangeinbodysize (e.g. Some experimentsindicatethatthehydrostaticskeletonmaintains The resultsofseveralpreviousstudieswerealsocontradictory. circular musclecross-sectionalarea)(Quillin,1998;Quillin,2000). several mechanicallyrelevantaspectsofthemorphology (e.g. smallest specimensinthesizerange,andwereunabletomeasure issues remainunexplored,however. Priorstudiesdidnotsamplethe Che andDorgan, 2010;Lin etal.,2011). A numberofimportant skeletons (Piearce,1983;Quillin,1998;1999; 2000; a foundationforourunderstandingofthescalinghydrostatic et al.,2008;Daltorio2013). surface locomotionandforburrowing(e.g.Trimmer, 2008;Trivedi provide insightsusefulforthedesignofbiomimeticsoftrobots morphology andmechanicsofburrowers.Finally, thisresearchmay can onlybepredictedbyunderstandingthescalingof machinery couldimposesize-dependenteffects onburrowersthat induced changesinsoilpropertiesfromchemicalsandheavy bioturbation, ecosystemengineeringandsoilmaintenance.Human- environments, andareecologicallyeconomicallyimportantin these animalsaretaxonomicallydiverse,theyliveinmany soil–animal interactions.Further, thisworkisofinterestbecause soil onburrowingorganisms, orhowchangesinbodysizeimpact also knowlittleabouttheeffects ofthephysicalproperties poorly understoodcomparedwithotherformsoflocomotion.We animals burrow, andthescalingofburrowingmechanicsisalso through thisentiresizerangeandlarger. Inaddition,manyofthese of hydrostaticskeletontermedamuscularhydrostat,maygrow function. Indeed,manyindividualcephalopods,whichrelyonatype earthworms), yetlittleisknownaboutscaleeffects ontheirformand few millimeters(e.g.nematodes)toseveralmetersinlength 1958; Alexander, 1995;Kier, 2012). amplification andforcetransmission(Chapman,1950;Chapman, pressure allowsforsupport,muscularantagonism,mechanical significantly compressthefluid,andresultingincreaseininternal resist changesinvolume,muscularcontractiondoesnot surrounded byamuscularbodywall(Kier, 2012).Becauseliquids skeletons arecharacterizedbyaliquid-filledinternalcavity and nematodes)possessahydrostaticskeleton.Hydrostatic and marineworms,cnidarians,echinoderms,bivalves,gastropods In thisstudy, weinvestigatedthescalingoffunctionallyrelevant Previous researchonscalinginsoft-bodiedanimalshasprovided Animals supportedbyhydrostaticskeletonsrangeinsizefroma Many soft-bodiedorganisms orpartsoforganisms (e.g.terrestrial

The Journal of Experimental Biology M will scaleas ( an earthwormscalesisometrically, lineardimensionssuchas length change withsize,themass( can betestedasfollows.Becausethedensityofananimaldoes not (Quillin, 1998).Thusournullhypothesisisisometricscaling,which in compressionandhavebeenhypothesizedtoscaleisometrically an increaseinmass.Hydrostaticskeletonslackrigidelementsloaded disproportionately inrelativecross-sectiontoavoidbucklingdue to common inanimalswithrigidskeletons,whichmustincrease (Huxley andTessier, 1936;Schmidt-Nielsen,1997).Allometryis growth, inwhichtherelativeproportionschangewithbody size body size,termedisometricgrowth,manyanimalsshowallometric Rather thanmaintainingsimilarrelativeproportionswithchange in and Lissman,1938;Quillin,1999). contraction alongthelengthofwormduringlocomotion(Gray one totwosimultaneouswavesofcircularandlongitudinalmuscle and pullingthemoreposteriorsegmentsforward.Therearetypically the segmentsradially, enlarging theburrow, anchoringtheworm, burrow inthesoil.Contractionoflongitudinalmusclesexpands contract, thesegmentsthinandarethrustforward,excavatinganew Lissman, 1938;SimsandGerard,1985).Whenthecircularmuscles length ofthebodyandtypicallyinvolve~30segments(Gray muscle contractionthatpassfromanteriortoposteriordownthe burrow usingalternatingwavesofcircularmuscleandlongitudinal shorten thewormandcauseradialexpansion.Earthwormscrawl radially thinthewormandelongateit,whilelongitudinalfibres circular andlongitudinal,arepresent.Thefibresactto hydraulic units(Seymour, 1969).Two orientationsofmusclefibres, muscular septae,allowingsegmentstoactasessentiallyindependent fluid thatislargely isolatedfromthefluidofadjacentsegmentsby (Piearce, 1983;Quillin,1998).Eachsegmentcontainscoelomic the numberofsegmentsremainsconstantduringdevelopment Earthworms haveasegmentedhydrostaticskeleton.In advantage, forceoutputandinternalpressureproduction. about theimplicationsofbodysizefordistanceandmechanical hydrostatic skeletonsandallowustomaketestablepredictions The resultsprovidenewinsightsintotheeffects ofscaleon size rangeoftheearthworm RESEARCH ARTICLE on theanimal as itchangesinsize.Suchfactors arepotentially scale allometricallyinresponse to selectivepressuresandconstraints Scaling of functionally relevant morphological features relevant morphological functionally Scaling of hydrostatic skeletonThe of L 1/3 ) ordiameter( Alternatively, wehypothesizethatthehydrostaticskeletonmay M reducedmajoraxis σ ordinaryleastsquares V RMA P OLS M L D C a b b A List of symbolsand abbreviations List of mech o m m , andanyarea,suchassurfacearea ormusclecross-sectionalarea, V 2/3 isometric musclestress pressure duetomusclecontraction mechanical advantage isometric scalingexponent volume body mass body length diameter projected coelomicarea scaling exponent muscle cross-sectionalarea D and thusM ) arepredictedtoscaletheanimal’s 2/3 M Lumbricus terrestris ) isproportionaltothevolume( (see T Lumbricus terrestris Lumbricus be1 able for terms). Linnaeus 1758. V L. terrestris, 1/3 and thus V ). If distance advantageofthelongitudinal musculature. mechanical advantageofthecircular musculatureanddecreasethe with sizebecauseboth reciprocal, anincreaseinthe Because mechanicaladvantageanddistance are advantage ofthismusculatureinradialexpansiontheworm. increase inthe muscle). Fromthestandpointoflongitudinalmuscles, an relatively greater(anincreaseindistanceadvantageforthecircular circular musclefibres,theelongationofalarge wormwouldbe during growthwouldmeanthatforagivenrelativeshortening of the scale as 1) (Fig. L musculature duringgrowth.Forinstance,anincreaseinthe however, couldaffect therelativeforceanddisplacementof muscle) comparedwithahydrostaticskeletonsmaller during lateralexpansion(duetoshorteningbythelongitudinal to shorteningbycircularmuscle)andgreatermechanicaladvantage more elongateandthushasalarger instance, iftwocylindricalbodieshaveidenticalvolume,butoneis in questionandthe distance advantage,dependingontheorientationofmusculature skeletons lackrigidlevers,theystillallowmechanicaladvantageor distance advantagearereciprocal.Althoughcylindricalhydrostatic (Kier andSmith,1985;Vogel, 1988).Mechanicaladvantageand input frommusclecontractionandthuspositivedistanceadvantage) mechanical advantage)oramplifydistance(distanceoutput> output >forceinputfrommusclecontractionandthuspositive animals withrigidskeletonsinwhichleversmayamplifyforce(force skeletal supportsystem.Thiscanbeunderstoodbyfirstreferringto length-to-diameter ( internal coelomicpressure.Forhydrostaticskeletons,achangeinthe including itskinematics,forceproduction,mechanicaladvantageand have importantimplicationsforthemechanicsoforganism, The scalingofthelineardimensionsandmusclecross-sectionalareas predation, competitionandfecundity. hydrostatic pressure,respiration,heatexchange,evaporation, diverse andinclude,forexample,burrowingmechanics,internal F σ P C A D Variable Symbol changes withsize, becauseforceduetomuscle contractionis determines howrelativeforce productionbythemusculature The scalingofmusclephysiological cross-sectionalarea( V exponents Table M Scaling of lineardimensions Scaling of Scaling of muscle cross-sectional areas and forceoutput muscle areas cross-sectional Scaling of L m m / D If ratio willshowgreaterdistanceadvantageduringelongation(due L. terrestris 1. Definitionofvariablesusedandtheirisometricscaling (Vogel, 2013). M 1/3 The JournalofExperimentalBiology(2014)doi:10.1242/jeb.098137 . Allometryintheoveralldimensionsof Force outputtoenvironment Projected coelomicarea Cross-sectional musclearea Diameter Muscle stress Pressure duetomusclecontraction Volume Body mass Body length L / scales isometrically, the D L ratio wouldresultinanincreasemechanical L / D / D ratio ofthebody(KierandSmith,1985).For ) ratioaffects theleverageprovidedby L and D are lineardimensionsandshould L L / / D D ratio, thebodywithlarger ratio woulddecreasethe L / D ratio willnotchange exponent ( Isometric scaling α α α α α α α α α M M M M M M M V M 2/3 0 0 2/3 2/3 1/3 1/3 L. terrestris, L L / / D D b 1861 o ratio ratio ) A )

The Journal of Experimental Biology sectional areaand Quillin (Quillin,1998)]: remain constantunlessthe As statedabove,mechanicaladvantageinhydrostaticskeletonswill where where mechanical advantageproducedbytheskeletonitself: product bothoftheforcegeneratedbymusclesand on theforce-transmittingskeleton. however, dependsnotonlyontheforce-producingmuscles,butalso 1862 RESEARCH ARTICLE the projectedcoelomicareaoverwhichmusclesact[eqn stress inthemuscles,cross-sectionalareasofmusclesand The internalpressureduetomusclecontractionisafunctionofthe be proportionalto musculature scaleisometrically, thecross-sectionalareaofeachwill proportional tocross-sectionalarea.Ifthecircularandlongitudinal diameter cylinderandalowlengthtocylinder. Fig. contraction, Scaling of coelomicpressure Scaling of change andthusthefinalforceoutputwouldalsoscaleas ratio, themechanicaladvantageoftwomusclegroupswillnot terrestris AB Longitudinal log (length) (mm) contraction The forcetransmittedbytheskeletontoenvironmentisa Circular 15– 0500511.5 1 0.5 0 –0.5 –1 –1.5 10 Muscle

.Schematiccomparingskeletalleveragebetweenahighlengthto 1.

F

P is theforceoutputtoenvironment, m grows isometricallyandtherebymaintainsaconstant is thepressureincoelomicfluidduetomuscle σ log m 10 is themusclestressand (mass) (g) a 1.2 1.4 1.6 1.8 2.2 2.4 2.6 High lengthtodiameter mech 2 1 M Mechanical advantage Mechanical 2/3 Distance advantage b=0.397 is themechanicaladvantagefromskeleton. . Thefinalforceoutputtheanimalexerts, cylinder b P o F =0.333 m

L = (σ α / *

D A

(

m ratio oftheanimalchanges.If a A mech ) C ) −

1 (1) , C ,

D is theareaofcoelom.

15– 0500511.5 1 0.5 0 –0.5 –1 –1.5 log ( ) (mm) 10 middle

A is themusclecross- Lowto length diameter log cylinder 10 M (mass) (g) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 2/3 advantage Mechanical advantage 0

Distance 1 3 from . b L o

(2) =0.333

/ L. D

( scaled significantlygreater( with isometry( the anterior, middleandposteriorsegments,respectively)compared Table 3A, The cross-sectionalareaofthelongitudinalmusculature(Fig. 2,Table segments scaledallometrically(Fig. We foundthatbothbodylengthanddiameteracrossallmeasured the muscle( If Because oftheincreasein predicted ( posterior segments,respectively).Asaconsequence,the because theratioof (supplementary materialTable each peristalticwaveduringcrawlingwasindependentofbodysize ( segment didnotscalesignificantlydifferently fromisometry Table sectional areainthemiddleandposteriorsegments(Fig. segments exhibitedtheoppositetrend.Thecircularmusclecross- circular musclecross-sectionalareasofthemiddleandposterior Scaling of muscle area cross-sectional Scaling of lineardimensions Scaling of RESULTS Scaling of leverage andforceproduction Scaling of for themiddleandposteriorsegments,respectively).Forceoutput isometry forthemiddleandposteriorsegments( greater thanisometryintheanteriorsegments( 4)fromthelongitudinalmusclescales that theforceoutput(Table advantage andcross-sectionalareaofthemusculature,wecalculated the forceoutputisproportionaltoproductofmechanical that ofthelongitudinalmusculaturewillincrease( circular musculaturewilldecreasewithbodysize( 4).We calculatedthatthemechanicaladvantageof size (Fig. advantage anddistanceofthemusculaturechangeswith the caseforisometry( Table middle andposteriorsegments,respectively;supplementarymaterial increases withbodysize( size. allometrically ineither ( posterior segments,respectively)comparedwithisometricscaling b=0.278 b b b =0.690). o o L. terrestris =0.33), thediameterofallmeasuredsegmentsscaledlessthan =0.667). Circularmusclecross-sectionalareaintheanterior

3) scaledgreaterthanexpected( 3) scaledlowerthanexpected(b S1) insteadofremainingconstantwithbodysizeaswouldbe * b The JournalofExperimentalBiology(2014)doi:10.1242/jeb.098137 σ =0.292, 0.278and0.283fortheanterior, middleand transformed graphcomparing graph comparingbodylengthwithmass.(B)Log- Fig. isometric scalingexponent( from theanterior)withbodymass.Regressionsdepict axis regression( scaling exponentfittoempiricaldatausingreducedmajor m ) remainsconstantwithbodysize, grows isometricallyandthepeakisometricstressin b o

.Scalingoflineardimensions.(A)Log-transformed 2. =0.667) forallsegmentsmeasured.However, the A to b A o C =0.00). Thenumberofsegmentsactivein or b =0.119, 0.138and0.140fortheanterior, would beunchanged.Ifthewormscales b C , solidline). b , thenpressurewillchangewithbody

S2). =0.39) thanpredictedforisometry L / D ratio withsize,themechanical b b o =0.815, 0.840formiddleand =0.620, 0.553and0.591for N , dashedredline)andthe D =25. middle

2). Whilebodylength (diameter ofsegment30, P b b b =0.653 and0.680 =0.724) andnear m =0.112). Because will beconstant b =–0.112) but L / D ratio

3B,

The Journal of Experimental Biology Asterisks indicatethattheCIsdonotoverlapwith muscle. body sizeforboththelongitudinal( measurement ofthecross-sectionalarealongitudinalmuscle sectioned inthesagittalplaneonly, whichcomplicatesthe both sagittalandtransverseplanes,whileQuillin(Quillin,1998) muscle andconnectivetissues.Finally, weusedserialsectionsin we employedselectivestainsthatallowedcleardifferentiation of tissues challenging,inparticularthesmallestspecimens.Instead, were unstained,whichmakesidentificationofthecomponents sections allowbetterresolutionofdetail.Inaddition,her shrinkage, comparedwithotherhistologicalmethods,andthinner procedures havetheadvantageofcausingverylittledistortionand methacrylate embedding.Glycolembedding significantly thickerthanthesectionsweobtainedusingglycol tend tobesubjectmuchgreaterdistortionandartefactare methods used.Quillin(Quillin,1998)usedfrozensections,which grow allometrically. We suspectthatthesedifferences reflectthe a numberofmechanicallyimportantdimensions of thehydrostaticskeletonshouldbeisometric,ourresultsshowthat Although previouswork(Quillin,1998)hadsuggestedthatscaling however, showedsignificantdifferences intheratioof 5,Table segments, respectively;Fig. circular muscles( 0.060 fortheanteriorandmiddlesegments,respectively) middle segmentsforboththelongitudinalmuscles( of theareasmuscleandcoelom( We didnotobserveadifference fromisometry( respectively). ( muscle ofthemiddleandposteriorsegmentsscalesnearisometry expected ( from thecircularmuscleofanteriorsegmentsscaleslessthan L D D D L Linear dimension( RESEARCH ARTICLE Table Scaling trends DISCUSSION pressure Scaling of A b , bodylength. 2 posterior middle anterior log10(muscle area) (mm ) =0.687 and0.696forthemiddleposteriorsegments,

17–. . 1.3 0.3 –0.7 –1.7 2. Hypothesistestingoflineardimensionsusing95%confidenceintervals(CI)

b log =0.561) forisometry, butthe force outputofthecircular D 10 anterior (body mass)(g) y Isometricscalingexponent( ) –0.5 –0.3 –0.1 0.1 0.3 0.5 0.7 0.9 1.1 , D b =0.044 and0.049foranteriormiddle middle b o =0.667 .3 .9*0330430.978 0.423 0.373 0.397* 0.333 0.333 0.333 0.333 b=0.553 and D

posterior * b =0.146) andcircular( refer tothediametersofsegments10,30and50,respectively, fromtheanterior. RMA,reducedmajoraxis.

5). Theposteriorsegments, B 2 A

log (muscle area) (mm ) /

10 b 18–. . . 2.2 1.2 0.2 –0.8 –1.8 C o . N ) fortheanteriorand b=0.815 =25. b =0.00) intheratio log b o RMA scalingexponent( ) 10 (body mass)(g) b * L. terrestris =0.021 and –2.3 –1.8 –1.3 –0.8 –0.3 0.2 A b =0.378) / 0.283* 0.278* 0.292* C with b o =0.667 mass. Thisincreaseinthe muscle cross-sectionalareaincreasesataratethatisgreater than similar trend;inthemiddleandposteriorsegments,circular size (a M We foundthat in particular. by isometry(A longitudinal musclecross-sectionalareaincreaseslessthanpredicted scaling ofmechanicaladvantagetheskeleton.Although multiplied thescalingofmusclecross-sectionalareaby skeleton. Inordertopredictthescalingofforceoutput,we generated bythemusclesandtransmissionofthatforce Force outputtotheenvironmentisafunctionofbothforce isometric ( muscle cross-sectionalarea,andtheforceoutputisthusnearly mechanical advantagecompensatesfortheallometricscalingof increases withbodysize( advantage comparedwith0.01 expansion, weestimatethatadultshave117% greatermechanical musculature thatshortenstheanimalandtherebycausesradial allometrically withsize.Fromthestandpointoflongitudinal traveled duringoneperistalticwave)crawlingincreased 1999), whofoundthatL.terrestris’ stridelength (i.e.distance elongation isconsistentwiththeobservationsofQuillin(Quillin, with 0.01 ghatchlings.Thisincreaseindistanceadvantageduring body mass)havean~117% greaterdistanceadvantagecompared circular musculaturethatelongatestheanimal,adultworms(10 during elongationandshortening.Fromthestandpointof of distanceadvantageandmechanicalthemusculature musculature. We estimatedtheeffect ofthisallometryonthescaling L. terrestris observed byPiearce(Piearce,1983),whomeasuredformalin-fixed Mechanical anddistanceadvantage Force output 0.397 ) andthin(D mech b oe 5 IUpper95%CI Lower95%CI ) F The JournalofExperimentalBiology(2014)doi:10.1242/jeb.098137 α segment ( transformed graphofcircularmuscleareainthemiddle isometric scalingexponent( in themiddlesegment( transformed graphoflongitudinalmusclecross-sectionalarea Fig. regression ( exponent fittoempiricaldatausingreducedmajoraxis earthworms andnotedanincreaseinthe

l M α

l .Scalingofmusclecross-sectionalareas. 3. 0.112

L. terrestris α M

M 0.257 0.261 0.276 0.653–0.724 α ) duetotheincreasein A 0.553–0.620

M c,middle b , solidline). <0.30 ) andbodymass.Regressionsdepictthe L ). Thecircularmusculatureshowsa ), andthusthelength-to-diameterratio / L ), itgainsmechanicaladvantagewith D grows disproportionatelylong( /

D g hatchlings. ratio impactsthemechanicsof A l,middle N α =25.

b M o , dashedredline)andthescaling ) andbodymass.(B)Log- >0.10 0.312 0.296 0.309 ). Thistrendwasalso L / D . Theincreasein L / D (A) Log- ratio with 0.952 0.978 0.983 R 2 1863 L

α g

The Journal of Experimental Biology A A A A A decreases withsize( sampled. AsterisksindicatethattheCIsdonotoverlapwith 1864 RESEARCH ARTICLE travels downthelengthofbody, segmentsclosertothetailare in burrowing.Becausetheperistalticwaveoftendissipates asit may reflecttherelativeimportanceofdifferent portionsofthebody Several oftheallometrictrendsdiffered betweensegments,which cross-sectional areaandofthecoelom( We foundnosignificanttrendwithsizeoftheratiobetweenmuscle predicted byisometry( A A Muscle area( isometric ( Table of bodysize.Internalpressuremeasurements that thepressureproducedbymusculaturewillbeindependent the muscleisindependentofbodysize,thentheseresultspredict not beenmeasured,ifweassumethatthepeakisometricstressof Although thecontractilepropertiesofdevelopingmusclehave the sevensizeclassesofwormsanalyzed. which maynothavemeasuredanequivalentnumberofsegmentsin relative dimensionsoftheforcetransducersusedinherexperiments, our currentinvestigations.Anadditionalpossibilitymaybethe depend onthescaleofdeformation,issuesthatarefocus might changewithsize,andtheresistancetosoildeformation muscle stressmightvarywithbodysize,thekinematicsofburrowing area andofmechanicaladvantage.Inaddition,shesuggestedthat might beresponsibleforthediscrepancy, includingscalingofmuscle we wereabletoaddressseveralofthefactorsthatshesuggested earthworms crawlingthroughforcetransducers.Inthepresentstudy disproportionately lowscalingofforcemeasuredbyQuillinin (Quillin, 2000),ourforcecalculationsdonotresolvethe sectional areaareinagreementwithpriorresearchbyQuillin Intersegmental differences Intersegmental muscle from contraction Pressure (Quillin, 1998;KeudelandSchrader, 1999). consistent withthispredictionandexhibitnotrendbodysize

A l c,posterior c,middle c,anterior l,posterior l,middle l,anterior

a and A log10( mech,circular) While ourfindingsonthescalingofcircularmusclecross- 1–. . 1 0.5 0 –0.5 –1 3. Hypothesistestingofmusclecross-sectionalareasusing95%CI b o c =0 are thelongitudinalmuscleandcircularcross-sectionalareas,respectively. Thesubscriptsanterior, denotethelocations middleandposterior F y c Isometricscalingexponent( ) log α

M 10 –1.9 –1.8 –1.7 0.561–0.696 (mass) (g) –2 a mech 0.667 0.840* 0.667 0.815* 0.667 0.690 0.775 0.667 0.591* 0.748 0.630 0.667 0.553* 0.667 0.620* 0.535 0.508 0.580 A c α ). α

M

b=–0.112 M 0.69–0.840 -0.112

). Theforceoutputisthusnearly ), butitsmechanicaladvantage

log (a ) B 1–. . 1 0.5 0 –0.5 –1 10 mech,longitudinal

b b o o =0 RMA scalingexponent( ) P m L. terrestris b α o . N

log A =25. / C 10 1.7 1.8 1.9 (mass) (g) α 2

M are 0 ). b=0.112 disproportionately lowintheanteriorsegments( 1999). ahead oftheworm(GrayandLissman,1938;KeudelSchrader, laterally toenlarge theburrow, anchorthewormandrelievestress longitudinal musclesarethoughttobeimportantinmovingsoil middle andposteriorsegmentsscaledclosetoisometry. The to makedeepburrows. locomotion as anterior segmentsmayreflecttheincreasedimportanceofburrowing (Seymour, 1969).Thus,theallometrictrendsweobservedin recorded duringcrawlingresultfromcircularmusclecontraction forward. Indeed,incontrasttoburrowing,thehighestpressures on thesurfacebycausingsegmentstoelongateandmove circular musculatureplaysanimportantrolewhentheanimalcrawls scaled nearisometryforthemiddleandposteriorsegments.The at agreaterrate( as longitudinalforceproductionoftheanteriorsegmentsincreased (Yapp andRoots,1956).Ourdataareconsistentwiththisproposal likely oflessimportanceinburrowingthanthosenearthehead Many soils,includingloosegranularsoilsandconsolidatedclays, to reduce‘strainhardening’ duringburrowformation(Piearce,1983). As anearthwormgrows,selectionmightfavorathinnerbodyin order ongoing research. are notmutuallyexclusiveandtestingthemisafocusofour hypotheses fortheallometrictrendsobserved.These that growthwouldbeisometric.We brieflyoutlinebelowtwo environment, especiallybecausepreviousresearchhadpredicted selective pressuresthatmaybeactingontheseanimalsinthe patterns inL.terrestris Because weidentifiedseveralsignificantallometricgrowth Strain hardeninginsoil Potential for selective allometricgrowth pressures We alsofoundthatcircularmuscleforceproductionscaled

b Lwr9%C Upper95%CI Lower95%CI ) The JournalofExperimentalBiology(2014)doi:10.1242/jeb.098137 L. terrestris body mass. contraction ( mechanical advantagefromlongitudinalmuscle from circularmusclecontraction( advantage withbodymass.(A)Mechanical Fig. F l α

.Predictivemodelcomparingmechanical 4.

M 0.724 , itisofinteresttoconsiderthepotential develops, asonlyadultwormsarefound a ) thanexpectedfromisometry, whilethe mech , longitudinal ) asafunctionofearthworm 0.909 0.888 0.757 0.654 0.602 0.662 a mech , circular F c α ) and(B)

M 0.561 0.967 0.960 0.955 0.948 0.967 0.976 R ), but 2

The Journal of Experimental Biology size (A of longitudinalmuscleareatocoelomicdidnotchangewithbody (Che andDorgan, 2010)found thatsmallmarinewormsusethis 2005; Dorgan etal.,2007;Dorgan etal.,2008).Cheand Dorgan demonstrated innumerousburrowersmarinemuds(Dorgan etal., using amechanismtermed‘crackpropagation’,whichhasbeen also betheresultofselectivepressuresassociatedwithburrowing The increaseinthelengthtodiameterratioweobservedheremay ( was achievedbyreducingboththelongitudinalmusclecross-section ontogeny. Ourresultsindicatethattherelativereductionindiameter found that relatively thinnertoreducethiseffect. Thiswouldexplainwhywe the crevices,therecouldbeaselectiveadvantageinbecoming strain hardeningeffect. Asaburrowergrowsandexceedsthesizeof crevices, theymayavoiddisplacingthesoilandthereby 1965; Gerard,1967).Ifsmallwormscanindeedexploitthese through existingcracksandporesas‘creviceburrowers’ (Arthur, found nearthesoilsurfaceandhavebeenhypothesizedtosqueeze (including thehatchlingsofburrowingearthwormspecies)areoften in thestiffness ofthesoilsurroundingburrow. Smallworms section, itmustdisplacemoresoilradially, witharesultingincrease et al.,2012;Holtz2010).Asanearthwormgrowsincross- stiffness ofthesoilincreaseswithincreasingstrain(Chen,1975;Yong exhibit thisphenomenon,inwhichthemodulusofcompressionor RESEARCH ARTICLE denote thelocationssampled. force output,respectively. Thesubscripts anterior, middleandposterior Mechanical advantagewascalculatedbynormalizingthechangesin were multipliedwiththescalingexponentofmechanicaladvantage. The RMA regressionscalingexponentsforeachmusclecross-sectionalarea output (y Modeled force Table F F F F F F Crack propagation 25% radialstrain. ratios withmassandcalculatingthereciprocalofdistanceadvantageover A A c,posterior c,middle c,anterior l,posterior l,middle l,anterior

log 1.2 (A /C 0.2 ) –0.8 –1.8 10 l l,middle l α

M

4. Modelpredictingthescalingofforceoutput l / 0.553–0.620 exponent( ) C l b α L. terrestris o

=0 M log 0

). ) andthecross-sectionalareaofcoelom;ratio F 10 l –0.8 –0.7 –0.6 –0.5 –0.4 –0.3 –0.2 and F (mass) (g) c grew disproportionatelylongandthinduring b=0.06 refer tolongitudinalmuscleandcircular Isometric scaling 0.667 0.667 0.667 0.667 0.667 0.667

b o )

A C B log10( c/ c,middle ) –2

b –1 Modeled scaling 0.696 0.687 0.561 0.680 0.653 0.724 exponent ( o =0 log 10 –1.8 –1.6 –1.4 –1.2 –0.8 –0.6 (mass) (g) L –1 b / D 0 )

b=0.049 oatmeal (Burchetal.,1999). humus andpeatmoss)at17°C(BerryJordan,2001)feddriedinfant were housedinplasticbinsfilledwithmoisttopsoil(composedoforganic from cocoonsdepositedbyadultsbredinthelaboratorycolony. Allworms from purchasedjuvenilesorcolonyhatchlings.Hatchlingswereraised mechanics. general principlesofscalinginhydrostaticskeletonsandburrowing bodied invertebrates.Usingthisapproach,wehopetoidentify the taxonomicdiversityandrangeofhabitatsecologysoft- scaling ofhydrostaticskeletonsinothertaxa,takingadvantage important. We intendtotestthesehypothesesandalsoexplorethe changes insoilpropertiesandburrowingmechanicswithsizeare force productionoftheanteriorsegments.We hypothesizethat responsible fortheincreasein Additional workisneededtoinvestigatetheselectivepressures shape oftheanimalandcross-sectionalareamusculature. aspects ofthemorphologyscaleallometrically, includingtheoverall isometric scalingduringgrowth.A numberoffunctionallyrelevant work, thehydrostaticskeletonof Our analysisindicatesthat,contrarytoexpectationsfromprevious mechanism (Molles,2009). possess mechanicalpropertiesamenabletothisburrowing future researchbecauseavarietyofterrestrialsoilenvironments worms hasnotyetbeeninvestigated.Thisisanimportantareafor may fracture,butthepossibilityofcrackpropagationbyterrestrial earthworm androotgrowthliterature,proposethatterrestrialsoils worms. Dorgan etal.(Dorgan etal.,2005),basedonareviewof L. terrestris, withsmallwormsbeingrelativelythickerthanlarge show allometryinbodydimensionssimilartothatobservedherefor required stresstopropagateacrackaheadoftheworm.Thus,they burrowing andexertrelativelyhigherforcesinordertoapplythe of thebodytofracturemud,arerelativelythickerwhen mechanism, whichinvolveslateralexpansionoftheanteriorportion (v/v) untilquiescent,patteddryandweighed.Thelengthwasobtained after Each wormwasanaesthetizedina10%ethanolsolutiondistilledwater the laboratory. Adultworms(3–10 MI, USA)aswellraisedfromhatchlingsbredinacolonymaintained Juvenile (1–3 g)wormsweresuppliedbyKnutson’s LiveBait(Brooklyn, Conclusions Anaesthetization, and dissection lengthmeasurements terrestris Lumbricus MATERIALS ANDMETHODS 1

The JournalofExperimentalBiology(2014)doi:10.1242/jeb.098137 body mass. ( Fig. A longitudinal andcircularmuscles,respectively. (A)Plotof contraction isapplied. A l / ) toprojectedcoelomicarea( C

l,middle .Scalingoftheratiomusclecross-sectionalareas 5. relative tobodymass.(B)Plotof collection andmaintenance N =25.

g) werepurchasedlocallyandraised The subscriptslandcreferto L L. terrestris / D ratio andallometryinthe C ) wheremuscle A does notexhibit c / C c,middle relative to 1865

The Journal of Experimental Biology that theCIsdonotoverlapwith during longitudinalandcircularmusclecontraction,respectively. Thesubscriptsanterior, sampled.Asterisksindicate middleandposteriordenotethelocations 1866 A A A A A A A Ratio RESEARCH ARTICLE Fig. muscle cross-sectionalarea( USA) tomakemorphologicalmeasurementsonmicrographs.Longitudinal of coverslips.We usedSigmaScan(SystatSoftware,Inc.,SanJose,CA, at 60°Cfor1–2 Rojkind, 1985).We adaptedtheprotocoltoglycolmethacrylatebystaining in ordertodifferentiate musclefromconnectivetissue(López-DeLeónand thickness werecutwithaglassknife.We usedaPicrosirius/FastGreenstain Wehrheim, Germany)tominimizetissuedistortion.Sectionsof3–7 in glycolmethacrylateplastic(Technovit 7100,HeraeusKulzerGmbH, The tissueblockswerepartiallydehydratedin95%ethanolandembedded transverse andsagittalsectionscouldbeobtained from eachlocation( middle andposteriorsegmentswerethencutinhalftransverselysothatboth segments 29–34as‘middle’ Theanterior, andsegments49–54as‘posterior’. (segments 9–14,29–34and49–54).We refertosegments9–14as‘anterior’, 24–48 half ofthewormisoftenpassivelydraggedalong)(Yapp andRoot,1956). of thewormbecauseitisgreatestimportanceinlocomotion(theposterior worm, althoughparticularattentionwaspaidtosegmentsintheanteriorhalf these threeareastodocumentpotentialvariationalongthelengthof (segments 1–20,21–40and41–60,numberingfromanterior).We examined killed andthreeblocksoftissuecontaining20segmentseachwereremoved length oftheentirebody(Piearce,1983;Quillin,1998).Thewormwasthen Because straighten thebodyandextendsegmentstoaconsistentrestinglength. pulling thewormbyanteriorendalongbenchsurfaceinorderto during longitudinalmusclecontraction( Table Histology andmorphometrics Histology musculature. LM, longitudinal muscle;CM,circularmuscle. ofthelongitudinal (C) Parasagittalsection throughtheanteriorsegments. (D)Insetoftransversesectionshows highermagnificationviewofcross-section musculature. section throughtheanteriorsegments. (B)Insetofsagittalsectionshowshighermagnificationviewcross-section ofthecircular l c c c l l l / / / / / / The tissueblockswerefixedin10%formalindistilledwater(v/v)for C C C and A C C C

l,posterior l,middle l,anterior .Photomicrographs (brightfieldmicroscopy)of7-μ 6. c,posterior c,middle c,anterior A 5. Hypothesistestingofmuscleandcoelomareausing95%CI h. Afterfixation,theblockswerefurtherdissectedforembedding / C c L. terrestris are thelongitudinalmuscleandcircularcross-sectionalareas,respectively; ( y Isometricscalingexponent( ) h followedbyadistilledwaterrinse,dryingandmounting does notaddsegmentswithgrowth,wemeasuredthe 0 0.378* 0 0.049 0 0.044 –0.100 0 0.146* –0.126 0 0.060 0 0.021 –0.043 –0.004 A l ), projectedareaofapplicationinthecoelom b o . N =25. C l ) anddiameter( b o Measuredscalingexponent( ) D m-thick sectionsofLumbricusterrestris ) weremeasured i.6). Fig. μm in diameterthatistypicalof calculated astheabsolutevalueofdecreasebodylengthworm Likewise, themechanicaladvantageoflongitudinalmusclewas contraction usingEqn ellipse andthencalculatedthediameterofacirclesamearea. measurements ofthemajorandminoraxestocalculatearea section. To determineanequivalentdiameterofacircularcylinder, weused prepared inthiswaywereflattenedslightlyandthushadanellipticalcross- contraction wascalculatedusing body length( ( circular musculatureastheabsolutevalueofdecreaseinbodydiameter using transversesections.Circularmusclecross-sectionalarea( As wedescribeabove,the muscle contractionwascalculatedusing contraction ( projected areaofapplicationinthecoelomduringcircularmuscle isometric stressofthemuscle and sagittalsections,withtheassumptionofnochangesizeinpeak Calculation of mechanical andforceoutput advantage Calculation of distance advantage,wecalculatedthemechanicaladvantage( during growth.Becausethemechanicaladvantageisreciprocalof of sizeandthusthemechanicaladvantagemusculaturechanges D We estimatedthescalingofinternal pressureproducedbymuscle ) duringcircularmusclecontractiondividedbytheresultingincreasein b C oe 5 IUpper95%CI Lower95%CI ) l The JournalofExperimentalBiology(2014)doi:10.1242/jeb.098137 C L and C c ), asafunctionofthe ) weremeasuredusingsagittalsections.Theearthworms c are theprojectedareasofapplicationincoelom 0.253 0.061

stained withPicrosirius/FastGreen. (A)Transverse 2 andmeasurementsofcoelomicareafromtransverse P P m,longitudinal m,circular L / L. terrestris D ratio wasobservedtochangeasafunction σ = (σ A m = (σ l . Pressurefromlongitudinalmuscle L and m / D A m A during movement(Quillin,1999). A c C ratio, forthe25%decreasebody ) c l C ) l and , whilepressurefromcircular C c 0.560 0.228 0.269 0.265 0.200 0.050 − l − 1 1 . C , c (Quillin, 1998): a mech A ) ofthe 0.556 0.020 0.014 0.305 0.055 0.105 R c ) and 2 (3) (4)

The Journal of Experimental Biology er,E n odn D. Jordan, and E. Berry, rhr D. Arthur, uc,S . izarc,L . oe,A . eals .J n igea,M.A. Giggleman, and B.J. Venables, A.J., Goven, L.C., Fitzpatrick, S.W., Burch, A. Biewener, isometric scalingexponent the scalingexponent calculated the95%confidenceintervalsofslopetodeterminewhether the independentvariable,whileRMA regressiondoes(Rayner, 1985).We the morphologicaltraitsofinterest, http://jeb.biologists.org/lookup/suppl/doi:10.1242/jeb.098137/-/DC1 Supplementary materialavailableonlineat W.M.K.]. This studywasfundedbytheNationalScienceFoundation[grantIOS-0951067to manuscript andassistedwithdataanalysis. and analyzedthedata,draftedinitialmanuscript.W.M.K. revisedthe Both authorswereinvolvedintheplanningofexperiments.J.A.K.collected The authorsdeclarenocompetingfinancialinterests. Purdue forhelpwithhistology. We thankBrinaM.Montoya forherinsightsintosoilpropertiesaswellTony transformed scalingdatafittothepowerfunction squares (OLS)andreducedmajoraxis(RMA)regressiononthelog- Team, 2013)forstatisticalanalysis.We performedbothordinaryleast We usedthe divided bytheresultingincreaseinbodydiameter, asafunctionofthe RESEARCH ARTICLE regressions arereported. of thesimilarityandagreementbetweenmodels,onlyRMA consistent indistinguishingsignificantdifferences fromisometry. Because and RMA regressionfitsimilarscalingexponentsinouranalysisandwere O’Reilly, 2006;Nudds,2007;ChiandRoth,2010).BothOLSregression lxne,R.McN. Alexander, hpa,G. Chapman, and both thelongitudinalandcircularmusculatureasafunctionofsize. These calculationsthusprovidedestimatesofthemechanicaladvantage ratio: References Supplementary material Funding Author contributions Competing interests Acknowledgements Statistical analysis hpa,G. Chapman, conditions. growth ofLumbricusterrestris worms. Viewpoints Biol. Mucchi. 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