Quantal Analysis Presentation€¦ · Quantal Analysis Problems Presented by: Alasdair Ball,...
Transcript of Quantal Analysis Presentation€¦ · Quantal Analysis Problems Presented by: Alasdair Ball,...
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?