NMJiHaD:QuantalAnalysisProblems

Presentedby:AlasdairBall,AlistairRocke,RoryPiper

Problem1Inanexperimentonapar:allycurarisedfrogneuromuscularjunc:on,acetylcholine(ACh)wasappliedtotheendplatebyiontophoresis,using1nA,1mscurrentpulsesatafrequencyof2Hz.

Atrainoffiveendplatepoten:als(EPPs)wasthenevokedbys:mula:ngthemusclenerveat50Hz.

Theiontophore:cpulseswereresumedwithin20msoftheendofthes:mulustrain.

Problem1MeanAChresponsebeforeEPPtrain=1.53±0.12mV(mean±S.D.;n=10)

MeanAChresponseaVerEPPtrain=1.51±0.10mV(mean±S.D.;n=7)

EPPNumber

1 2 3 4 5

Amplitude(mV)

2.2 2.7 2.1 1.3 0.9

Problem1(a)

Calculatetheamountofchargedeliveredbyeachoftheiontophore:ccurrentpulses;

Q=It

=1x10‐9.1x10‐3

=1x10‐12C =1pC

?

Problem1(b)Sketchthecharacteris:cresponsestoAChandnerves:mula:onindica:ngthe:mecourseoftheresponses;

(fromphysiology/pathophysiologylecture)

Problem1(c)

Howmighttheiontophore:cresponsestoAChchange,ifalowconcentra:onofACh(1μM)werealsocon:nuouslypresentinthemedium?

DesensiFsaFon:‐Ini:alresponse(depolarisa:on)tosuchasolu:on‐In:me,furthers:mulusbyAChwouldhavealessereffect(thanbefore)

Problem1(d)Isthehypothesisthatshort‐termsynap:cdepressioniscausedbydesensi:sa:onofAChreceptorssupportedorrefutedbythesedata?Giveyourreasoning.

MeanAChresponsebeforeEPPtrain=1.53±0.12mV(mean±S.D.;n=10)MeanAChresponseaVerEPPtrain=1.51±0.10mV(mean±S.D.;n=7)

Refuted‐ Althoughthemeanvalueswouldbesupportthishypothesis…‐ …theSDshowsnosignificantdifference.

Problem2

Intracellularrecordingsweremadefromamouseneuromuscularjunc:on.

Thenervesupplywass:mulated150Fmesat1Hz.

ThemeansizeoftheEPPevokedwas1.00mV.

Fiveofthes:mulievokednoresponse(i.e.therewere5'failures').

Problem2(a)

Whatwasthemeanquantalcontentatthisneuromuscularjunc:on?

DIRECTMETHODm=meanEPP/meanmEPP✗

FAILURESMETHOD✓m=ln.(s:muli/failures)=ln(150/5)=3.40…VARIANCEMETHOD✗m=(meanEPPamplitude)2/(varianceofEPPamplitudes)

?Problem2(b)

Whatdoyoupredictforthequantalsize,theamplitudeoftheuniquantalevent(mEPP)?

DIRECTMETHOD✓

m=meanEPP/meanmEPP

3.4=1/meanmEPP

MeanmEPP=1/3.4=0.29mV

?

Problem2(c)

HowmanyoftheEPPswouldyoupredicttohavequantalcontentsof1,2,3and4quanta?

P(x)=mx.exp(‐m)/x!

P(1)=3.41.exp(‐3.4)/1=0.1134

P(2)=0.1928

P(3)=0.2186

P(4)=0.1859

x150

17

29

33

28

Problem2(d)

Whatdoyoupredictwouldbethestandarddevia:onoftheEPPamplitudes?

•AssumethemEPP(0.29mV)correlateswithP(1)

•Assume,linearsumma:on,P(2)…0.58mV…andsoon!

•UsetheSDequa:on:

Problem2(d)

UsetheSDequa:on:

+/‐0.5mV

P(x)

AssumedVoltage(mV)

Resultsfrom2(c)

E(x–x)2

0 0 0 0

1 0.29 17 8.5697

2 0.58 29 5.1156

3 0.87 33 0.5577

4 1.16 28 0.1024

5 1.45 19 3.8475

6 1.74 11 6.0236

7 2.03 5 5.3045

8 2.32 2 3.4848

9 2.61 1 2.5921

10 2.9 0 0

35.48…

Problem2(e)

Ifthebaseline‘noise’levelpeak‐to‐peakwas500μV,howwouldthisaffecttheaccuracyofyoures:mates?

Of150….can’tseeEPP(1)/mEPPs…underthenoisethreshold.

Overes:ma:onofmEPPs.

Problem3Inanexperimentonanisolatedflexordigitorumbrevisnerve‐muscleprepara:ondissectedfromamouse,intracellularmicroelectroderecordingsweremadeofspontaneousminiatureendplatepoten:als(MEPP).

Endplatepoten:als(EPP)werethenevokedbynerves:mula:onatafrequencyof1Hz.Intotal,97ofthes:muliappliedtothenerveevokedanEPPbut3s:mulifailedtoevokeanyEPP.

Thefollowingmeandatawiththeirstandarddevia:onswereobtained:MeanMEPPamplitude(±SD):1.20±0.72mVMeanEPPamplitude(±SD):4.25±2.42mV

Problem3

a)Speculateonthera:oofCa2+toMg2+ionsinthemediumbathingthisprepara:on.

b)CalculatethemeanquantalcontentoftheEPPusingtheDirect,VarianceandFailuresMethods.

c)Whatdoesthestandarddevia:onoftheMEPPamplitude(quantalsize)indicateandhowmightthisaffectthees:ma:onofmeanquantalcontent?

d)Giveoneotherpossiblereasonforalowquantalcontent,inthecontextsofhealthanddisease.

Problem3(a)SpeculateontheraFoofCa2+toMg2+ionsinthemediumbathingthispreparaFon.

‘’Intotal,97ofthes1muliappliedtothenerveevokedanEPPbut3s1mulifailedtoevokeanyEPP.’’

• Inaperfectsolu:on,failuresshouldnotoccur.

• Mg2+‐Decreasesthepresynap:creleaseofAchbyantagonisingCa2+,andreducesthesensi:vityofthepostjunc:onalmembrane.

• Ca2+‐entryintothenerveterminalcausesAchcontainingvesicleexocytosis.

• Thismedium‐↑[Mg2+]and/or↓[Ca2+].

Problem3(b)

CalculatethemeanquantalcontentoftheEPPusingtheDirect,VarianceandFailuresMethods.

DIRECT VARIANCE MofFailures

( )( )

quanta m

m

MEPP

EPPm

54.3

2.1

25.4

=

=

=( )

quanta m

m

EPP of Variance

EPPm

09.3

42.2

25.4

2

2

2

=

=

=

quanta m

Logm

failures

stimuliLnm

e

51.3

3

100

=

=

=

Problem3(c)WhatdoesthestandarddeviaFonoftheMEPPamplitude(quantalsize)indicateandhowmightthisaffecttheesFmaFonofmeanquantalcontent?

• MeanMEPPamplitude(±SD):1.20±0.72mV

• Broadrange

• Skewanycalcula:onofEPP

• BothMEPP/EPPpresentinDirectmethodofquantalcontentes:mate

• Errorinmcouldendupverylarge

What does the standard deviation of the MEPP amplitude (quantal size) indicate and how might this affect the estimation of mean quantal content? What does the standard deviation of the MEPP amplitude (quantal size) indicate and how might this affect the estimation of mean quantal content?

Problem3(d)

Giveoneotherpossiblereasonforalowquantalcontent,inthecontextsofhealthanddisease.

• LEMS–IgtoCa2+channelsleadstoreducedCa2+

influx,hencesmallerevokedresponseandreducedquantalcontent.

Problem4

InastudybyWood&Slater(1997)itwasfoundthattheac:onpoten:alfiringthresholdinratsoleusmusclefibresisreachedbyanendplatepoten:al(EPP)withameanquantalcontentofabout15.

Quantalsizedidnotvarysubstan:allybetweenmusclefibresineithersoleusorextensordigitorumlongusmusclesinthisstudy.

Problem4(a)Explainwhatismeantbytheterms‘quantalcontent’and‘quantalsize’

QUANTALCONTENT‐Numberofeffec:vevesiclesreleasedinresponsetoanerveimpulse.

QUANTALSIZE–The‘synap:cresponse’tothereleaseofAChfromsinglevesicle.

• Quantalsize=Effectofonevesiclerelease(MEPC/MEPP)

• Quantalcontent=Numberofvesiclesreleased(EPC/EPP)

Problem4(b)‘Explainbrieflyhowrecordingsofendplatecurrentscouldbemadefromthisfibre,whyendplatecurrentssumlinearlywithincreasingquantalcontentbutEPP’ssumnon‐linearly,andhowEPP‐amplitudemeasurementsmaybecorrectedfornon‐linearsumma1on.’

• i‐Howareendplatecurrentrecordingsmade?

• ii‐Whydoendplatecurrentssumlinearlywithincreasingquantalcontent?

• iii‐WhydoEPP’ssumnon‐linearlywithincreasingquantalcontent?

• iv‐Howdoyoucorrectfornon‐linearsummaFon?

Problem4(b)iHowareendplatecurrentrecordingsmade?

Endplatecurrentrecordingsaremadeusingthevoltageclamp.

Nega:vefeedback.Membranepoten:alamplifiermeasuresmembranevoltageandsendsoutputtofeedbackamplifier;thissubtractsthemembranevoltagefromthecommandvoltage,whichitreceivesfromthesignalgenerator.

Thissignalisamplifiedand

outputissentintotheaxon

viathecurrentelectrode.

Eg. Problem4(b)ii

Whydoendplatecurrentssumlinearlywithincreasingquantalcontent?

• Theendplatecurrentistherateofflowofchargethroughtheendplatemedium.

dt

Qdcurrent =

Problem4(b)iiiWhydoEPP’ssumnon‐linearlywithincreasingquantalcontent?

• Asthequantalcontentincreases,theamountofoveralldepolarisa:onbecomesgreater.

• However,eachsuccessivequantalcomponenthasaweakereffectonfurtherdepolarisa:on.

• ‘Reversalpoten:al’ofmembranemet≈(‐5mV).

• Currentthroughopenchannelsbecomesv.small.

• Ifm.p>(‐5mV)outwardcurrentproduced.

• EPPreverses.

Problem4(b)ivHowdoyoucorrectfornon‐linearsummaFon?

V’–predictedamplitude

V–observedamplitude

E–differencebetweenres:ng

m.pandreversalpoten:al

f–‘fudgefactor’(varieson

length,diameter,membrane/

cytoplasmicelectricalresistance)

egL=0.8andS=0.3

fVE

VEV

E

fV

VV

!=

"#$

%&' !

=

'

1'

Problem4(c)Predictthenumberof‘failures’inatrainof100EPC’sifthemeanquantalcontentbecamereducedto2quanta.

( )

( )

failures

failures

m

stimulifailures

failures

stimulim

failures

stimuliLogm e

14

2exp

100

exp

exp

!

=

=

""#

$%%&

'=

=

Problem4(d)UsetheFailuresMethodtocalculatetheprobabilityof‘failures’inatrainofEPC’sevokedbyrepeFFvesFmulaFonwhenthemeanquantalcontentis15.

71006.3

15

exp

!"=

=

=

=

Failure ofy Probabilit

m

mfailures

stimuli

failures

stimuliLogm e

Problem4(d)CalculatethepredictedvarianceandstandarddeviaFonofquantalcontentsinatrainofEPPsofthesamemeanquantalcontent(ie15).

?!=m)exp(

!)( !

!"=

xxP

x

22 ))(()()var( xxx µµ !=)(

2

µ! "##$

%&&'

(= )

n

x

Problem4(e)DiscussbrieflywhatexperimentalorclinicalcondiFonsleadtoareducFonofquantalcontentandthemechanismsthatcanenhancethe‘safetyfactor’forneuromusculartransmission.

• DecreaseCa2+infuxleadstodecreasedquantalcontent

• Cause–LEMS,Hypocalcaemia,botulinumtoxin

SafetyFactor

• Increasedatareasofjunc:onalfolds.

• Increasedresistancewithincytoplasmofjunc:onalcells,increaseddepolarisa:onlowerinthefoldwherethereisanabundanceofNa+channels.

Problem5

•Intracellularrecordingsofendplatepoten:als(EPPs)andminiatureendplatepoten:als(MEPPs)wereobtainedfromamusclefibreinanisolatedmouseskeletalmusclebathedinnormalphysiologicalsalinebutinwhichtheCa2+concentraFonwasreducedfrom2mMto1mMandtheMg2+concentraFonwasincreasedfrom1mMto4mM.

Problem5

•Theprepara:onwasthens:mulatedwith100trains‐of‐fournervesFmuli,deliveredat50Hzwithintervalsof10sbetweeneachs:mulustrain.Eachs:mulustrainevokedacorrespondingtrainoffourEPPs(EPP1‐EPP4).TheacetylcholinesteraseinhibitorneosFgmine(finalconcentraFon3µM)wasthenaddedtothephysiologicalsaline.Aner20minutes,recordingswereresumedfromthesamemusclefibreandafurther100trains‐of‐foursupramaximalnervesFmuliwereappliedtothenerve.

Problem5

•Othercons:tuentsofthebathingsolu:onwereunalteredfromthatofnormalphysiologicalsaline.TheresFngmembranepotenFalofthemusclefibreremainedsteadythroughoutat‐72mV.ThefollowingdatawereobtainedbeforeandaneraddingneosFgmine.

Problem5

Problem5

•(a)Describeandexplaintheresponsestonerves:mula:onandtheeffectsofneos:gmineonamplitudeand:mecourseoftheEPPs.Sketchtheirappearanceinthetrains‐of‐fourbeforeandaVerthechangeinbathingsolu:on.

Problem5

S:mula:oncausedanendplatepoten:al.

Rise:mesaround1.5ms.

Halfdecay:mesaround2.5ms.

Synap:cfacilita:onwasobserved(anincreaseinamplitudeoverthetrains‐of‐four).Residualcalciumhypothesis?

Problem5

Neos:gmineincreasedtheamplitudeoftheEPP(slightly).

Normallyacetylcholine(ACh)ishydrolysedassoonasitleavesitsreceptor.However,neos:gmineimpairsthishydrolysis,leavingAChfreetoac:vateanotherreceptor,allowingagreaterinfluxofNa+.

Problem5

Neos:gmineincreasedtherise:meoftheEPP(byabout60%).

AChshuwlingbetweenreceptorstakes:me.

Problem5

Neos:gmineincreasedthehalf‐decay:me.Thehalfdecay:mealsoincreasedoverthetrains‐of‐four.

NotalltheAChwashydrolysedbeforethenextEPPcamealong.IttooklongertoclearACheach:me.

Problem5

Sketch.

Problem5

•(b)Whatwouldyouconcludefromaquantalanalysisofthesedataandshouldcorrec:onfornon‐linearsumma:onofEPPsbeconsidered?

Problem5

Failuresmethod.

Theaddi:onofneos:gminedidnotchangethequantalcontent.

Theeffectsofneos:gminearebewerexplainedbyanincreaseintheeffec:vequantalsize.

EPP1 EPP2 EPP3 EPP4Quantal content 3.51 3.91 3.91 4.61 before neostigmineQuantal content 3.21 3.51 3.91 4.61 after neostigmine

Problem5

Non‐linearsumma:on?

No.Thequantalcontentsaresufficientlysmallthatthisisnotanissue.

Problem5

•(c)An:cholinesterasesmayhaveaddi:onaldirecteffectsonproper:esofpresynap:corpost‐synap:cacetylcholinereceptors.Formulatehypothesestoexplaintheeffectsofneos:gmineontheamplitudeand:mecourseofthesynap:cpoten:als,withjus:fica:onofyourreasoning.

Problem5

Neos:gminemayitselfbindtoandac:vateacetylcholinereceptors(AChRs)onthepost‐synap:cmembrane.

Neos:gminemaybindtopresynap:cAchRs,butnotac:vatethem,increasingthesynthesisofAch.

Others?

Problem5

•(d)Suggesthowthehypothesesyouhaveproposedmightbetestedexperimentallyandwhatalterna:veoutcomesoftheseexperimentswouldimply.

Problem5

Co‐precipitateneos:gmineandAChRs?

Iftheydidn'tco‐precipitatetheirwouldbeevidenceofnointerac:on.

Problem5

PatchclampnAChRsinthepresenceandabsenceofneos:gmine.

Increasedprobabilityofopeninginthepresenceofneos:gminewouldindicatethatneos:gminecouldopenAChRs.

Problem5

Otherideas?