Spike timing and the coding of naturalistic sounds in a central auditory area of songbirds

9 Pages·0.16 MB·English

by  Brian D. Wright

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Spike timing and the coding of naturalistic sounds in a
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central auditory area of songbirds

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J Brian D. Wright,1−3 KamalSen,1−3 WilliamBialek1,4,5 and AllisonJ. Doupe1−3
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1Sloan–Swartz CenterforTheoretical Neurobiology
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2DepartmentsofPhysiologyand3Psychiatry

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h UniversityofCaliforniaat San Francisco, San Francisco, California94143–0444
p 4NEC Research Institute,4 IndependenceWay,Princeton, New Jersey08540
o- 5DepartmentofPhysics,Princeton University,Princeton,New Jersey08544
bi {bdwright/kamal/ajd}@phy.ucsf.edu,[email protected]
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c February 2,2008
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Abstract
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[ Innature, animalsencounter high dimensional sensory stimulithat havecomplex statisticaland

dynamical structure. Attempts to study the neural coding of these natural signals face challenges
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both in the selection of the signal ensemble and in the analysis of the resulting neural responses.
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For zebra finches, naturalistic stimuli can be defined as sounds that they encounter in a colony of
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2 conspecific birds. We assembled an ensemble of these sounds by recording groups of 10-40 zebra
0 finches,andthenanalyzedtheresponseofsingleneuronsinthesongbirdcentralauditoryarea(field
1 L)tocontinuousplaybackoflongsegmentsfromthisensemble. Followingmethodsdevelopedinthe
0 flyvisualsystem,wemeasuredtheinformationthatspiketrainsprovideabouttheacousticstimulus
2 withoutanyassumptionsaboutwhichfeaturesofthestimulusarerelevant.Preliminaryresultsindicate
0 thatlargeamounts of informationarecarried byspike timing, withroughly half of the information
s/ accessibleonlyattimeresolutionsbetterthan10ms;additionalinformationisstillbeingrevealedas
c timeresolutionisimprovedto2ms. Informationcanbedecomposedintothatcarriedbythelocking
si ofindividualspikestothestimulus(ormodulationsofspikerate)vs. thatcarriedbytiminginspike
y patterns. InitialresultsshowthatinfieldL,temporalpatternsgiveatleast∼ 20%extrainformation.
h Thus,singlecentralauditoryneuronscanprovideaninformativerepresentationofnaturalisticsounds,
p inwhichspiketimingmayplayasignificantrole.
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X 1 Introduction
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Nearlyfiftyyearsago,Barlow[1]andAttneave[2]suggestedthatthebrainmayconstructaneuralcode
thatprovidesanefficientrepresentationforthesensorystimulithatoccurinthenaturalworld. Slightly
earlier, MacKay and McCulloch [3] emphasized that neurons that could make use of spike timing—
ratherthanacoarser“ratecode”—wouldhaveavailableavastlylargercapacitytoconveyinformation,
althoughtheyleftopenthequestionofwhetherthiscapacityisusedefficiently.Theoriesfortimingcodes
andefficientrepresentationhavebeendiscussed extensively,buttheevidenceforthese attractiveideas
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remainstenuous.Arealattackontheseissuesrequires(atleast)thatweactuallymeasuretheinformation
contentand efficiencyof the neuralcode understimulus conditionsthat approximatethe naturalones.
In practice, constructing an ensemble of “natural” stimuli inevitably involves compromises, and the
responsestosuchcomplexdynamicsignalscanbeverydifficulttoanalyze.
Atpresenttheclearestevidenceonefficiencyandtiminginthecodingofnaturalisticstimulicomes
from central invertebrate neurons [4, 5] and from the sensory periphery [6, 7] and thalamus [8, 9] of
vertebrates. Thesituationforcentralvertebratebrainareasismuchlessclear. Hereweusethesongbird
auditorysystemasanaccessibletestcasefortheseideas.Thesetofsongbirdtelencephalicauditoryareas
knownasthefieldLcomplexisanalogoustomammalianauditorycortexandcontainsneuronsthatare
stronglydrivenby naturalsounds, includingthe songsof birdsof the same species(conspecifics) [10,
11,12,13]. WerecordfromthezebrafinchfieldL,usingnaturalisticstimulithatconsistofrecordings
from groups of 10-40 conspecific birds. We find that single neurons in field L show robust and well
modulated responses to playback of long segments from this song ensemble, and that we are able to
maintain recordings of sufficient stability to collect the large data sets that are required for a model
independentinformationtheoreticanalysis. Herewegiveapreliminaryaccountofourexperiments.
2 A naturalistic ensemble
Auditoryprocessingof complexsoundsis criticalfor perceptionandcommunicationin manyspecies,
includinghumans,butsurprisinglylittleisknownabouthowhighlevelbrainareasaccomplishthistask.
Songbirdsprovideausefulmodelfortacklingthisissue,becauseeachbirdwithinaspeciesproducesa
complexindividualizedacousticsignalknownasasong,whichreflectssomeinnateinformationabout
thespecies’songaswellasinformationlearnedfroma“tutor”inearlylife. Inadditiontolearningtheir
ownsong, birdsuse the acoustic informationin songsofothersto identifymatesand groupmembers,
to discriminate neighbors from intruders, and to control their living space [14]. Consistent with how
ethologicallycriticalthesefunctionsare,songbirdshavealargenumberofforebrainauditoryareaswith
strong and increasingly specialized responses to songs [11, 15, 16]. The combination of a rich set of
behaviorallyrelevantstimuliandaseriesofhigh-levelauditoryareasresponsivetothosesoundsprovides
anopportunitytorevealgeneralprinciplesofcentralneuralencodingofcomplexsensorystimuli. Many
prior studies have chosen to study neuralresponses to individualsongs or altered versionsthereof. In
order to make the sounds studied increasingly complex and natural, we have made recordings of the
soundsencounteredby birdsin ourcolonyofzebra finches. To generatethe soundensemblethat was
used in this study we first created long records of the vocalizations of groups of 10-40 zebra finches
in a soundproof acoustic chamber with a directional microphone above the bird cages. The group of
birdsgeneratedawidevarietyofvocalizationsincludingsongsandavarietyofdifferenttypesofcalls.
Segmentsofthesesoundswerethenjoinedtocreatethesoundspresentedintheexperiment.Oneofthe
segmentsthatwaspresented(∼30sec)wasrepeatedinalternationwithdifferentsegments.
We recordedthe neuralresponsesin field L of one of the birds fromthe groupto the ensemble of
naturalsoundsplayedbackthroughaspeaker,atanintensityapproximatelyequaltothatinthecolony
recording. This bird was lightly anesthetized with urethane. We used a single electrode to record the
neuralresponsewaveformsandsortedsingleunitsoffline.Furtherdetailsconcerningexperimentaltech-
niquescanbefoundinRef.[13].
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Figure 1: A. Spike raster of 4 seconds of the responses of a single neuron in field L to a 30 second
segment of a natural sound ensemble of zebra finch sounds. The stimulus was repeated 80 times. B.
Peri-stimulustimehistogram(PSTH)with1msbins.C.Soundpressurewaveformforthenaturalsound
ensemble.D.BlowupofsegmentshownintheboxinA.Thescalebaris50ms.
3 Information in spike sequences
TheauditorytelencephalonofbirdsconsistsofasetofareasknownasthefieldLcomplex,whichreceive
inputfromtheauditorythalamusandprojecttoincreasinglyselectiveauditoryareassuchasNCM,cHV
andNIf[12, 17]andultimatelytothebrainareasspecializedforthebird’sownsong. FieldLneurons
respond to simple stimuli such as tone bursts, and are organized in a roughly tonotopic fashion [18],
butalso respondrobustlyto manycomplexsounds, includingsongs. Figure 1 shows4 secondsof the
responsesof a cell in field L to repeated presentationsof a 30 sec segmentfromthe naturalensemble
describedabove. Averagingoverpresentations,weseethatspikeratesarewellmodulated. Lookingat
theresponsesonafinertimeresolutionweseethataspectsofthespiketrainarereproducibleonatleast
a∼ 10mstimescale. Thisencouragesustomeasuretheinformationcontentoftheseresponsesovera
rangeoftimescales,downtomillisecondresolution.
OurapproachtoestimatingtheinformationcontentofspiketrainsfollowsRef.[4]. Atsometimet
(definedrelativetotherepeatingstimulus)weopenawindowofsizeT tolookattheresponse. Within
this window we discretize the spike arrival times with resolution ∆τ so that the response becomes a
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Total Entropy
Noise Entropy
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Mutual Info
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Figure2: Mutualinformationrateforthespiketrainisshownasafunctionofdatasizefor∆τ = 2ms
andT =32ms.
“word”withT/∆τ letters. Ifthetimeresolution∆τ isverysmall,theallowedlettersareonly1and0,
butas∆τ becomeslargeronemustkeeptrackofmultiplespikeswithineachbin. Examiningthewhole
experiment,wesampletheprobabilitydistributionofwords,PT(W),andtheentropyofthisdistribution
setsthecapacityofthecodetoconveyinformationaboutthestimulus:
Stotal(T;∆τ)=− PT(W)log2PT(W)bits, (1)
XW
wherethenotationremindsusthattheentropydependsbothonthesizeofthewordsthatweconsiderand
onthetimeresolutionwithwhichweclassifytheresponses. Wecanthinkofthisentropyasmeasuring
thesizeoftheneuron’svocabulary.
Becausethewholeexperimentcontributestodefiningthevocabularysize,estimatingthedistribution
PT(W) and hence the total entropy is not significantly limited by the problems of finite sample size.
ThiscanbeseeninFig.2inthestabilityofthetotalentropywithchangingthenumberofrepeatsused
intheanalysis. Hereweshowthetotalentropyasarateinbitspersecondbydividingtheentropybythe
timewindowT.
Whilethecapacityofthecodeislimitedbythetotalentropy,toconveyinformationparticularwords
inthevocabularymustbeassociated,moreorlessreliably,withparticularstimulusfeatures. Ifwelook
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atonetimetrelativetothe(long)stimulus,andexaminethewordsgeneratedonrepeatedpresentations,
we sample the conditional distribution PT(W|t). This distribution has an entropy that quantifies the
noiseintheresponseattimet,andaveragingoveralltimesweobtaintheaveragenoiseentropy,
Snoise(T;∆τ)=(cid:28)− PT(W|t)log2PT(W|t)(cid:29) bits, (2)
XW t
whereh···it indicatesatimeaverage(ingeneral,h···ix denotesanaverageoverthevariablex). Tech-
nically,theaboveaverageshouldbeanaverageoverstimulis,however,forasufficientlylongandrich
stimulus, the ensemble average over s can be replaced by a time average. For the noise entropy, the
problemofsamplingismuchmoresevere,sinceeachdistributionPT(W|t)isestimatedfromanumber
ofexamplesgivenbythenumberofrepeats. Still,asshowninFig.2,wefindthatthedependenceofour
estimateonsamplesizeissimpleandregular;specifically,wefind
A
S(T;∆τ;N )=S(T;∆τ;∞)+ +···. (3)
repeats
N
repeats
This is what we expect for any entropy estimate if the distribution is well sampled, and if we make
strongerassumptionsaboutthesamplingprocess(independenceoftrialsetc.) wecanevenestimatethe
correction coefficient A [19]. In systems where much larger data sets are available this extrapolation
procedure has been checked, and the observation of a good fit to Eq. (3) is a strong indication that
largersamplesizeswillbeconsistentwithS(T;∆τ)=S(T;∆τ;∞);further,thisextrapolationcanbe
testedagainstboundsontheentropythatarederivedfrommorerobustquantities[4]. Mostimportantly,
failuretoobserveEq.(3)meansthatweareinaregimewheresamplingisnotsufficienttodrawreliable
conclusionswithoutmoresophisticatedarguments,andweexcludetheseregionsofT and∆τ fromour
discussion.
Ideally,tomeasurethespiketraintotalandnoiseentropyrates,wewanttogotothelimitofinfinite
word duration. A true entropy is extensive, which here means that it grows linearly with spike train
worddurationT,sothattheentropyrateS =S/T isconstant. Forfiniteworddurationhowever,words
sampled at neighboring times will have correlations between them due, in part, to correlations in the
stimulus(forbirdsongthesestimulusautocorrelationtimescalescanextendupto∼100ms). Sincethe
wordsamplesarenotcompletelyindependent,therawentropyrateisanoverestimateofthetrueentropy
rate. Theeffectislargerforsmallerworddurationandtheleadingdependenceoftherawestimateis
B
S(T;∆τ;∞)=S(∞;∆τ;∞)+ +···, (4)
T
whereB > 0 andwe have alreadytaken the infinite datasize limit. We cannotdirectlytake the large
T limit, since for large word lengths we eventually reach a data sampling limit beyond which we are
unabletoreliablycomputetheworddistributions. Ontheotherhand,ifthereisarangeofT forwhich
the distributions are sufficiently well sampled, the behavior in Eq. (4) should be observed and can be
usedtoextrapolatetoinfinitewordsize[4]. Wehavecheckedthatourdatashowsthisbehaviorandthat
it sets in for word sizes below the limit where the data sampling problemoccurs. For example, in the
caseofthenoiseentropy,for∆τ = 2ms,itappliesforT belowthelimitof50ms(abovethiswerun
intosamplingproblems).Thetotalentropyestimateisnearlyperfectlyextensive.
Finally,wecombineestimatesoftotalandnoiseentropiestoobtaintheinformationthatwordscarry
aboutthesensorystimulus,
I(T;∆τ)=S (T;∆τ)−S (T;∆τ)bits. (5)
total noise
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Figure2showsthetotalandnoiseentropyratesaswellasthemutualinformationrateforatimewindow
T = 32 msandtime resolution∆τ = 2 ms. Theerrorbarsonthe raw entropyand informationrates
wereestimatedtobeapproximately±0.2bits/secusingasimplebootstrapprocedureovertherepeated
trials. The extrapolation to infinite data size is shown for the mutual information rate estimate (error
barsintheextrapolatedvalueswillbe< ±0.2bits/sec)andisconsistentwiththepredictionofEq.(3).
Sincethetotalentropyisnearlyextensiveandthenoiseentropyratedecreaseswithworddurationdue
tosubextensivecorrectionsasdescribedabove,themutualinformationrateshowninFig.2growswith
word duration. We find that there is an upward change in the mutual information rate (computed at
∆τ = 2 msand T = 32ms) of∼ 7%, in the largeT limit. For simplicity in the following, we shall
lookatafixedworddurationT = 32msthatisinthewell-sampledregionforalltimeresolutions∆τ
considered.
Themutualinformationratemeasurestherateatwhichthespiketrainremovesuncertaintyaboutthe
stimulus. However,themutualinformationestimate doesnotdependonidentifyingeithertherelevant
featuresofthestimulusortherelevantfeaturesoftheresponse,whichiscrucialinanalyzingtheresponse
to such complex stimuli. In this sense, our estimates of information transmission and efficiency are
independentofanymodelforthe code, andprovidea benchmarkagainstwhichsuchmodelscouldbe
tested.
OnewaytolookattheinformationresultsistofixourtimewindowT andaskwhathappensaswe
changeourtimeresolution∆τ. When∆τ = T,the“word”describingtheresponseisnothingbutthe
numberofspikesinthewindow,sowehavearateorcountingcode. Aswedecrease∆τ,wegradually
distinguish more and more detailin the arrangementof spikes in the window. We chose a range of T
values from 30−100 ms in our analyses to cover previously observed response windows for field L
neurons and to probe the behaviorally relevant time scale (∼ 100 ms) of individual song syllables or
notes. For T = 32 ms, we show the results (extrapolated to infinite data size) in the upper curve of
Fig.3. Thespiketrainmutualinformationshowsaclearincreaseasthetimingresolutionisimproved.
Inaddition,Fig.3showsthatroughlyhalfoftheinformationisaccessibleattimeresolutionsbetterthan
10msandadditionalinformationisstillbeingrevealedastimeresolutionisimprovedto2ms.
4 Information in rate modulation
Knowing the mutualinformationbetween the stimulus and the spike train (defined in the window T),
we would like to ask whether this can be accounted for by the information in single spike events or
whetherthereissomeadditionalinformationconveyedbythepatternsofspikes. Inthelattercase, we
havepreciselywhatwemeanbyatemporalortimingcode:thereisinformationbeyondthatattributable
totheprobabilityofsinglespikeeventsoccurringattimetrelativetotheonsetofthestimulus. Byevent
at time t, we meanthat the eventoccursbetweentime t and time t+∆τ, where ∆τ is the resolution
atwhichwearelookingatthespiketrain. Thisprobabilityissimplyproportionalto thefiringrate(or
peri-stimulustimehistogram(PSTH))r(t)attimetnormalizedbythemeanfiringrater¯. Specificallyif
thedurationofeachrepeatedtrialisT wehave
repeat
r(t)∆τ
′
P(1spk@t|s(t))= , (6)
r¯T
repeat
wheres(t′)denotesthestimulushistory(t′ <t).Theprobabilityofaspikeeventatt,aprioriofknowing
the stimulus history, is flat: P(1spk@t) = ∆τ/T . Thus, the mutual information between the
repeat
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Spike Train
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∆τ (ms)
Figure3: Informationratesforthespiketrain(T =32ms)andsinglespikeeventsasafunctionoftime
resolution∆τ ofthespikerasters,correctedforfinitedatasizeeffects.
stimulusandthesinglespikeeventsis[20]:
I(1spike;∆τ) = S[P(1spk@t)]−hS[P(1spk@t|s)]i
s
r(t) r(t)
= log bits, (7)
(cid:28) r¯ 2(cid:18) r¯ (cid:19)(cid:29)
t
where r(t) is the PSTH binned to resolution ∆τ and the stimulus average in the first expression is
replacedby a time averagein the second (as discussed in the calculationof the noise entropyin spike
train wordsin the previoussection). We find that this informationis approximately1 bit for ∆τ = 2
ms. Supposingthattheindividualspikeeventsareindependent(i.e.nointrinsicspiketraincorrelations),
theinformationrateinsinglespikeeventsisobtainedbymultiplyingthemutualinformationperspike
(Eq. 7) by the mean firing rate of the neuron (∼ 3.5 Hz). This gives an upper bound to the single
spike event contribution to the information rate and is shown in the lower curve of Fig. 3 (error bars
are again < ±0.2 bits/sec). Comparing with the spike train information(uppercurve), we see that at
a resolution of ∆τ = 2 ms, there is at least ∼ 20% of the total information in the spike train that
cannot be attributable to single spike events. Thus there is some pattern of spikes that is contributing
synergisticallytothemutualinformation.Thefactdiscussed,intheprevioussection,thatthespiketrain
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informationrategrowssubextensivelywiththetheworddurationouttothepointwheredatasampling
becomesproblematicis furtherconfirmationof the synergyfromspike patterns. Thuswe haveshown
model-independentevidenceforatemporalcodeintheneuralresponses.
5 Conclusion
Untilnow,fewexperimentsonneuralresponsesinhighlevel,centralvertebratebrainareashavemea-
suredtheinformationthattheseresponsesprovideaboutdynamic,naturalisticsensorysignals. Asem-
phasizedin earlier workon invertebratesystems, informationtheoreticapproacheshavethe advantage
thattheyrequirenoassumptionsaboutthefeaturesofthestimulustowhichneuronsrespond.Usingthis
method in the songbirdauditory forebrain, we found that patterns of spikes seem to be special events
intheneuralcodeoftheseneurons,since theycarrymoreinformationthanexpectedbyaddingupthe
contributionsofindividualspikes. Itremainstobedeterminedwhatthesespikepatternsare,whatstim-
ulusfeaturestheymayencode,andwhatmechanismsmayberesponsibleforreadingsuchcodesateven
higherlevelsofprocessing.
Acknowledgments
Work at UCSF was supported by grants from the NIH (NS34835) and the Sloan-Swartz Center for
TheoreticalNeurobiology.BDWandKSsupportedbyNRSAgrantsfromtheNIDCD.WethankKatrin
SchenkandRobertLiuforusefuldiscussions.
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