Neural population coding of sound level adapts to stimulus statistics

Transcription

1 COMPUTATION AND SYSTEMS 25 Nture Pulishing Group Neurl popultion oding of sound level dpts to stimulus sttistis Isel Den 1, Niol S Hrper 1,2 & Dvid MAlpine 1 Mmmls n her sounds extending over vst rnge of sound levels with remrkle ury. How uditory neurons ode sound level over suh rnge is unler; firing rtes of individul neurons inrese with sound level over only very limited portion of the full rnge of hering. We show tht neurons in the uditory midrin of the guine pig djust their responses to the men, vrine nd more omplex sttistis of sound level distriutions. We demonstrte tht these djustments improve the ury of the neurl popultion ode lose to the region of most ommonly ourring sound levels. This extends the rnge of sound levels tht n e urtely enoded, fine-tuning hering to the lol ousti environment. The uditory system is required to ode sounds tht vry enormously in level. Aurtely ssessing the overll level of sound hs importnt survivl vlue, for exmple, in judging the distne of sound soure, the urgeny of n lrm ll or the fitness of ompetitor. Furthermore, if sound level is represented urtely, then the levels within n ongoing sound n e etter disriminted, iding nlysis nd reognition of the sound. At the threshold of hering (pproximtely db sound pressure level (SPL) in humns), the er drum my move y only frtion of the width of n tom; some nturl environments re hrterized y similrly low levels of sound, verging only few db SPL 1. In omprison, groups of vol nimls n generte sounds of more thn 1 9 -fold higher verge intensity (9 db SPL) 1 3,wheres the upper limit of humn hering is met y sounds tht re twelve orders of mgnitude higher in intensity (12 db SPL) thn sounds tht re just udile. Over this vst rnge of levels, the uditory system hieves remrkle ury in deteting hnges in sound level: humns n her hnges in level of out 1 db ross most of the full rnge of hering 4 6. In order for sound level oding to e hieved using neurl firing rtes, firing rtes must hnge with level ross the full rnge of hering. However, the mjority of primry uditory nerve fiers hve low thresholds to sound stimultion, with firing rtes tht sturte t low to middle sound levels, giving neurl dynmi rnges (the rnge of levels over whih firing rtes hnge) of just 35 db or so 7,8.Eveny inluding the smller popultion of fiers with higher thresholds nd nonsturting responses, it does not seem tht neurl firing rtes n ount for the ury of oding over the full rnge of hering 9.As the limited neurl dynmi rnge does not over the rnge of levels over whih hering opertes (the so-lled dynmi rnge prolem 1 ) mehnisms must exist tht extend the rnge of oding eyond tht oserved in uditory nerve firing rtes. To this end, severl djunts to rte ode for sound level hve een onsidered 9. However, the mens y whih neurl responses re normlly ssessed s funtion of sound level ers little resemlne to the demnds pled on uditory neurons under nturl listening onditions. Trditionlly, firing rte versus sound level funtions re otined using sounds seprted y long silent intervls, rndomized in presenttion order, suh tht onseutive sounds n vry enormously in level Conversely, lthough nturl sound levels n vry extensively over the long term, over short time periods, within given environment, they more often flutute over reltively limited rnge 1. Neurons throughout the uditory system re sujet to dptive proesses, using hnge in response over time during sustined input to the neuron. A possile funtion of these dptive proesses is to tilor the neurl ode to mth the lol sensory environment. We hypothesize tht the neurl ode for sound level is flexile enough to tke ount of the time-vrying distriution of nturl sound levels, suh tht oding is ontext-dependent, llowing n effiient representtion of uditory stimuli. We hve exmined the ility of uditory neurons in the inferior olliulus, the mjor midrin nuleus in the sending uditory pthwy, to djust their oding for sound level to tke ount of stimulus sttistis. Our results show tht the responses of inferior olliulr neurons re rpidly djusted ording to the sttistil distriution of sound levels presented. These djustments lter the oding properties of the neurl popultion suh tht oding ury is inresed ner the most ommonly ourring sound levels. RESULTS We presented dioti (identil in eh er) white noise to nesthetized guine pigs for B7 min, during whih time the sound level ws set every 5 ms to new vlue drwn rndomly from defined distriution (Fig. 1,). The full rnge of sound levels presented ws db SPL. The distriution of sound levels onsisted of one or more regions of prole levels, referred to s stimulus high-proility regions, from 1 Deprtment of Physiology nd University College London Er Institute nd 2 Centre for Mthemtis nd Physis in the Life Sienes nd Experimentl Biology, University College London, Gower Street, London, WC1E 6BT, UK. Correspondene should e ddressed to I.D. (i.den@ul..uk). Reeived 14 April; epted 8 August; pulished online 6 Novemer 25; doi:1.138/nn VOLUME 8 [ NUMBER 12 [ DECEMBER 25 NATURE NEUROSCIENCE

2 Pressure Proility , 3, 5, Time (ms) Time (ms) Nture Pulishing Group d e 2 f 12 g whih levels were seleted with.8 overll proility (Fig. 1). The remining levels were seleted with n overll proility of.2. Adjustments of neurl responses to the men sound level We first exmined the effet of the men sound level on neurl rtelevel funtions, using sound-level distriution with single highproility region of width 12 db (Fig. 1). Neurl responses were reorded to level distriutions with four different high-proility regions, entered t 39, 51, 63 or 75 db SPL, referred to herefter s the 39-, 51-, 63- nd 75-dB stimuli. For eh level distriution, the men spike ount of the neuron to eh sound level ws lulted, nd the resulting rte-level funtion ws plotted. Bseline rte-level funtions (Fig. 1d g, gry) show the men spike ount to 5-ms noise ursts, seprted y 3-ms intervls, t sound levels rndomly seleted from flt distriution over db SPL. Sound stimultion of this form is typilly used to reord rte-level funtions of uditory neurons In ontrst, when rte-level funtions were reorded using the flututing noise stimuli, whih give eh sound level lol sttistil ontext, three oservtions were ommonly mde (Fig. 1d g). First, rte-level funtions shifted long the siss when the position of the high-proility region ws hnged. This shift resulted in hnge in the threshold sound level. The lrgest hnge in threshold from the seline funtion ws pproximtely 35 db. Notly, when the high-proility region ws positioned elow neuron s seline threshold, no neuron shifted its threshold to sound levels elow its seline threshold (see Fig. 1f). Seond, the shifts in rte-level funtions often resulted in neurons thresholds lying within the rnge of sound levels enompssed y the high-proility region of the stimulus. Third, inresing the men sound level often redued the mximum spike rte nd the slope of the rte-level funtions, prtiulrly over higher sound levels. Adpttion of the popultion ode to the men sound level We first investigted whether the djustments in rte-level funtions to different sound-level distriutions improve oding of those level Neuron 3 15 Neuron Figure 1 Adjustments in responses of inferior olliulr neurons to the men sound level. () Level vritions over 5 s of stimulus with high-proility region entered t 63 db SPL. () Stimulus wveform (2 ms shown). () Level distriution for stimulus with high-proility region entered t 63 db SPL. (d g) Eh pnel shows rte-level funtions of one neuron for four different sound level distriutions, plus the seline funtion (gry). Colored funtions in ll figures otined with high-proility regions t 39 db SPL (green), 51 db SPL (lue), 63 db SPL (red) nd 75 db SPL (yn). Filled irles nd thik lines on siss indite midpoint nd extent of the high-proility region of eh stimulus. distriutions y single neurons. We lulted the Fisher informtion, mesure of oding ury 15, for rte-level funtions of single neurons otined for different sound-level distriutions (Fig. 2). Assuming n optiml deoder, higher Fisher informtion reflets higher oding ury; tht is, more urte representtion of the sound level nd thus higher pity to disriminte nery sound levels. An intuitive pproximtion of Fisher informtion is the squre of the slope of the rte-level funtion divided y the spike ount vrine. Thus, Fisher informtion is high when the spike ount vrine is low nd when the spike ount hnges steeply with hnges in sound level. As the vrine in the neurl spike ounts tht we reorded from inferior olliulr neurons tended to e low when the spike ounts themselves were low, the mximum Fisher informtion ws typilly t sound levels just ove the threshold of the rte-level funtion. In some ses, this pled the pek Fisher informtion lose to the high-proility region of the relevnt stimulus distriution (Fig. 2), suggesting tht the funtion of the djustments in rte-level funtions might e to improve the ury of oding over this region. However, the rte-level funtions of different neurons were diverse, nd the pek Fisher informtion for individul neurons often did not over the entire high-proility region of the stimulus, nor ws it lwys djusted to e lose to tht region. To understnd the implitions of the djustments in rte-level funtions for sound-level oding, it is neessry to exmine responses ross popultions of neurons. Evidene from mny levels nd modlities of the verterte nervous system suggests tht informtion is represented y the tivity of neuronl popultions 16. An estimte of the oding ury for the neurl popultion ws otined y summing the Fisher informtion funtions of the individul neurons. This nlysis ssumes tht orreltion in spiking noise etween neurons is low. Although dt onerning suh orreltions in the uditory system re sre, orreltion in spiking noise is known to e low etween uditory nerve fiers 17, nd reent dt suggest this to e the se lso in the inferior olliulus 18 (see lso C.V. Seshgiri & B. Delgutte, Asso. for Reserh in Otolryngology Astr. 685, 23). NATURE NEUROSCIENCE VOLUME 8 [ NUMBER 12 [ DECEMBER

3 25 Nture Pulishing Group e g Fisher informtion We ompred the popultion Fisher informtion for neurons djusted to pirs of different sound-level distriutions (Fig. 2 g). Within eh omprison, the Fisher informtion ws otined for extly the sme popultion of neurons. Aross ll these pired omprisons, djustments of rte-level funtions to given distriution improved sound-level oding just ove the midpoint of the highproility region of tht distriution. For exmple, ompring the Fisher informtion urve for the 39-dB stimulus to tht for the 75-dB stimulus (Fig. 2), the most ommonly ourring sound levels in the 39-dB stimulus were oded est y responses djusted to tht stimulus. Conversely, for the 75-dB stimulus, the most ommonly ourring levels were oded est y responses djusted to the 75-dB stimulus. Finlly, we lulted the popultion Fisher informtion for 31 neurons from whih responses to ll four sound level distriutions were otined (Fig. 2h). Adpttion to stimulus vrine Nturl environments my present the uditory system not only with hnges in the men sound level ut lso with hnges in the extent of sound level flututions 1. Adpttion of inferior olliulr neurons to d f h Figure 3 Neurl djustments to stimulus vrine. () Level distriution for stimulus with wider (24 db) high-proility region (ompre to Fig. 1). (,) Eh pnel shows rte-level funtions of one neuron for two widths of the high-proility region of the stimulus, 12 db (gry) nd 24 db (lk). (d) Popultion Fisher informtion for stimuli entered t 63 db SPL, with high-proility regions of width 12 db nd 24 db (n ¼ 25). Figure 2 Adjustments in neurl responses improve popultion oding ury ner the men sound level. () Rte-level funtions of one neuron for stimuli with high-proility regions t 39 nd 63 db SPL, nd orresponding Fisher informtion funtions (dotted lines). ( h) Popultion Fisher informtion. In this nd ll figures, the totl popultion Fisher informtion hs een divided y the numer of neurons in the popultion to filitte omprison etween plots. () High-proility regions t 39 nd 75 db SPL (n ¼ 34 neurons); () 39 nd 63 db SPL (n ¼ 35); (d) 51nd 75 db SPL (n ¼ 5); (e) 63 nd 75 db SPL (n ¼ 42); (f) 51 nd 63 db SPL (n ¼ 54); (g) 39 nd 51 db SPL (n ¼ 38); (h) ll four sound level distriutions (n ¼ 31). sound level vrine of pure tones hs een reported in the t 19. However, the effet of sound level vrine on neurl rte-level funtions nd on the ury of the ode for sound level hs not een exmined. We therefore investigted the effet of extending the rnge of ommon sound levels in the distriution y ompring responses to sound-level distriutions with high-proility regions 12 db nd 24 db in width, entered t 63 db SPL (Fig. 3). The rte-level funtions of some neurons vried with the width of the high-proility region (Fig. 3). However, hnges in rte-level funtions with inresing width of the high-proility region were typilly not mrked (Fig. 3). Despite this, the Fisher informtion urve for the popultion of neurons ws slightly wider when neurl responses hd djusted to the wider (24 db) rnge of ommon sound levels (Fig. 3d). For oth widths, the region of highest oding ury ws positioned just ove the midpoint of the high-proility region; the djustments of neurl responses to the wider high-proility region resulted in mrked inrese in Fisher informtion t the edges of the region of high oding ury. The high-proility region ws widened on oth sides y 6 db, nd the resulting Fisher informtion urve widened y similr mgnitude. No hnge ws oserved in the Fisher informtion urve when the width of the highproility region ws inresed for the stimulus entered t 51 db SPL (dt not shown), possily euse the wider rnge of (lower) sound levels in this stimulus extended the distriution signifintly elow the neurons seline thresholds. Adpttion to stimulus imodlity Finlly, we exmined how inferior olliulus neurons enode stimuli with more omplex sound level distriutions. In imodl stimuli, sound levels were seleted from distriution with two highproility regions, entered t 51 nd 75 db SPL or t 39 nd 63 db SPL (Fig. 4). Proility d Men Fisher informtion VOLUME 8 [ NUMBER 12 [ DECEMBER 25 NATURE NEUROSCIENCE

4 25 Nture Pulishing Group Proility Men Fisher informtion Individul rte-level funtions did not show ny ovious tendeny to djust to oth high-proility regions in response to imodl stimuli. However, when the popultion Fisher informtion for imodl stimuli ws ompred with tht for the orresponding unimodl stimuli, we found tht the region of highest oding ury ws djusted so s to inorporte oth high-proility regions. In the se of the 51- to 75-dB SPL stimulus, two regions of high ury were pprent in the popultion Fisher informtion, with dip in ury etween them; these regions of high ury orresponded to the louder ends of eh of the two high-proility regions (Fig. 4). This doule-peked Fisher informtion urve ppered to result, lrgely, from some neurons positioning the thresholds of their rte-level funtions ner one of the high-proility regions, nd others positioning their thresholds ner the other high-proility region, therey dividing the neurl popultion s resoures. These divisions were oserved within nimls (Fig. 4). Rte-level funtions of neurons with high seline thresholds tended to shift to the louder high-proility region; rtelevel funtions of neurons with low seline thresholds tended to shift to the quieter high-proility region (dt not shown). Most sound levels presented t high proility within imodl stimulus were oded less urtely thn the sme sound levels presented t high proility within unimodl stimulus. However, most sound levels presented t high proility within imodl stimulus were oded more urtely thn the sme sound levels presented t low proility within unimodl stimulus. These results indite tht the neurl popultion did not simply dpt to the men sound level (whih ly etween the two high-proility regions of the imodl stimuli) ut rther ould pportion its oding resoures so s to tke ount of more omplex stimulus distriution. Time ourse of neurl dpttion The time ourse of neurl oding djustments ws exmined y plotting rte-level funtions seprtely for onseutive 5-s segments of the 63-dB (12-dB width) stimulus. For most neurons, rte-level funtions were djusted rpidly to finl, stle position, reproduile in response to susequent stimulus segments. The time tken for the rtelevel funtion to stilize ws ssessed y lulting the root-men-squred (r.m.s.) differene etween the rte-level funtion from eh 5-s segment nd the verge rtelevel funtion from the finl 5 s of the stimulus (Fig. 5,). Single exponentil dey funtions were fitted to the r.m.s. dt for eh neuron (Fig. 5). The time tken for neurl responses to stilize vried etween neurons (Fig. 5), with medin time onstnt of 3.2 s (n ¼ 5). Most neurons rte-level funtions First 5-s segment 1 Figure 4 Neurl djustments to stimulus imodlity. () Level distriution for imodl stimulus entered t 51 nd 75 db SPL. () Popultion Fisher informtion for imodl stimulus shown in (n ¼ 46). () Rte-level funtions from two neurons, from one niml. Filled irles on funtions indite point of eh neuron s mximum Fisher informtion. Top nd enter: responses to unimodl stimuli; ottom: responses to imodl stimulus shown in. lerly differed from their seline funtion within the first 5 s of presenting the stimulus (Fig. 5); for 2/5 neurons, the rte-level funtion from the first 5 s ws lredy very similr to the verge funtion from the finl 5 s, suh tht the r.m.s. dt showed no pprent dey. The rte-level funtion of only one neuron did not stilize ut ws ontinully djusted throughout the 7 min of stimulus presenttion. Neurl sensitivity to hnges in sound level Our dt demonstrte the extent to whih neuron s stimultion history influenes its response to the urrent stimulus. Thus, the neuron s response will e funtion of the urrent sound level nd pst sound levels. One of the simplest possile funtions tht might provide for the shifting rte-level funtions is one in whih neurl responses re determined not y the solute sound level, ut y the differene etween the urrent nd immeditely preeding sound level (the step size ), regrdless of the sound level distriution. For this reson, we exmined whether firing rte versus step size funtions were invrint with sound level distriution (Fig. 6 ). We found tht few neurons firing rtes were dependent on step size in mnner independent of the distriution of sound levels. The rte versus step size funtions of suh neurons were rodly ligned ross different sound level distriutions, lthough never invrint (Fig. 6). However, for most neurons, rte versus step size funtions differed onsiderly in threshold nd shpe etween sound level distriutions (Fig. 6,), s did the rte-level funtions. Thresholds of individul neurons to step size vried y up to 3 db etween different sound level distriutions (Fig. 6), nd, for some distriutions, firing rtes were reltively insensitive to step size (Fig. 6). Thus, simple dependene of neurl responses on level step size, suh tht responses were invrint with the sound level distriution, did not ount for the neurl dpttion we oserved. Bseline R.m.s. differene (spikes/s) 1 Averge from finl 5 s 5 Seventh 5-s segment Tu = 4.7 s Time (s) Numer of neurons Dey time onstnt (s) Figure 5 Time ourse of neurl dpttion. () Rte-level funtions of one neuron for high-proility region of stimulus only, from 5-s segments of stimulus, ompred with verge funtion from finl 5 s of stimulus nd seline funtion. () Sme neuron s : root-men-squred (r.m.s.) differenes etween rte-level funtion from eh 5-s segment nd verge funtion from finl 5 s of stimulus. Times on siss: segment numer multiplied y the 5-s segment durtion, minus 2.5 s. Dshed line: single exponentil dey; t ¼ 4.7 s. () Histogrm of t vlues for ll neurons for whih t o 4 s (n ¼ 46/51 neurons). NATURE NEUROSCIENCE VOLUME 8 [ NUMBER 12 [ DECEMBER

5 25 Nture Pulishing Group Neuron Step size (db) Step size (db) 1 DISCUSSION Our dt demonstrte tht lthough uditory rte-level funtions show restrited dynmi rnge, the rnge of sound levels over whih the dynmi rnge lies is mutle. Neurl responses were rpidly djusted in mnner tht tended to improve oding of the most prole sound levels y the neurl popultion. There ws slight is of oding ury towrds levels louder thn those ourring most ommonly. This my rise euse the rin needs not only to enode the ongoing noise stimulus, or the mient environment, ut lso to e prepred for enoding ny dditionl stimuli tht my e enountered. Further, lthough rte-level funtions shifted in n pproximtely prllel mnner over some men sound levels, prllel shifts were not mintined ross ll men levels. This suggests tht the neurl ode is not invrint with men sound level, ut rther tht it retins some informtion out overll level, whih is onsistent with evolutionry demnds for some representtion of overll level. It is possile tht men sound level independent representtion ours t stges in the uditory pthwy higher thn the inferior olliulus, suh s uditory ortex. A numer of mehnisms, possily ting in omintion, might underlie the dptive effets we hve desried. It is unlikely tht the middle-er musle reflex is involved, s this reflex is only wekly tive in guine pigs 2, is intive in nesthetized nimls 21 nd predominntly ffets trnsmission of very high intensity, low-frequeny sounds 22. A more likely ontriuting mehnism is the tion of the medil olivoohler system, whih feeds k diretly to the reeptor hir ells of the inner er, using suppression; however, the time onstnt of tion of this efferent system is pproximtely 1 ms (ref. 23), preluding it from fully ounting for the dptive effets reported here, whih hve time onstnt of severl seonds. A further ontriuting mehnism is likely to e neurl spike-frequeny dpttion, or the deline in firing rte over time during sustined stimulus. Suh dpttion my rise through mehnisms intrinsi to the neuron, through synpti depression or through network intertions. Spike-frequeny dpttion is hrteristi of primry uditory nerve fiers 24,25 s well s of higher-level uditory neurons 26.Thus,it is possile tht neurl sustrtes for the hnges in oding we oserved originte t low levels of the uditory system. Previous studies hve shown tht rte-level funtions to pure tones shift to higher sound levels if the tones re presented in onstnt level of kground noise. These effets re oserved t ll levels of the uditory system tht hve een exmined 12 14,27,28. This phenomenon my shre some mehnisms with the shifts in rte-level funtions tht we oserved, lthough the effet of suh hnges in rte-level funtions on the popultion oding ury for sound level hs not een mesured. At suortil levels, noise-indued hnges in rte-level funtions to tones re thought to result lrgely from ohler, or two-tone, suppression 12, Step size (db) Figure 6 Responses of inferior olliulr neurons to hnges in sound level. ( ) Eh pnel shows firing rtes of neuron during the urrent 5-ms epoh of the stimulus, s funtion of the differene in sound level etween the urrent epoh nd the previous 5-ms epoh, for different sound-level distriutions. Two-tone suppression is dependent on nery frequenies in the kground noise suppressing the response to the tone on the silr memrne. As the reltive power of our widend stimulus ws onstnt ross ll frequeny omponents for ll sound level distriutions, we n disount two-tone suppression s potentil mehnism ontriuting to the djustments in oding tht we desrie. Our dt hve shown tht, despite the diversity of dptive mehnisms tht re likely to shpe inferior olliulus responses, the onerted tion of suh proesses seems to funtion so s to improve the ury of the neurl ode for sound level. Neurl dpttion hs een ttriuted numer of funtions. For exmple, there is evidene tht dptive proesses in uditory ortex filitte novelty detetion y single neurons 3. The dpttion tht we hve desried my e the uditory nlogue of gin ontrol proesses in the visul system These proesses hve een suggested to improve oding y djusting neurl responses to the sttistis of visul stimuli. An improvement in oding resulting from neurl dpttion hs reently een demonstrted for single neurons in the lowfly visul system 34,35. Our study is the first demonstrtion of neurl dpttion, dependent on stimulus sttistis, tht improves the oding ury of neurl popultion; we hve shown tht the popultion ode dpts to the men sound level, the vrine nd even imodlity. The pity of the uditory rin to fine-tune to the lol ousti environment llows high ury in level disrimintion to e mintined over wide rnge of sound levels, despite the limited dynmi rnge of individul neurons. METHODS Physiologil reordings. Extrellulr reordings were mde from the right inferior olliuli of urethne-nesthetized guine pigs, using stndrd tehniques 26 pproved y the UK Home Offie. Single neuron responses were reorded using glss-oted tungsten miroeletrodes (Tuker Dvis Tehnologies System III). White noise (o25 khz) ws presented diotilly vi seled, lirted erphones. Only integer db vlues of sound level, etween db SPL, were used, giving 76 sound level vlues in totl. For given sound-level distriution, the level sequene nd noise token were the sme for ll neurons. For seline rte-level funtions, noise ursts were seprted y 3-ms intervls; levels were seleted rndomly from flt distriution, nd eh level ws presented ten times. For ll other stimuli, sound ws presented in 5-s segments, seprted y o.4 s. All rte-level funtions were plotted from the men numer of spikes ourring during the 5-ms epohs orresponding to given sound level. We used stndrdized neurl lteny of 8 ms, the minimum lteny mesured, so we do not ssume the opertion of system tht n ount for differing neurl ltenies. The first nd seond 5-s segments of eh stimulus were exluded from ll nlyses, exept nlyses of the time ourse of hnges in neurl responses. For time ourse nlyses, we lulted the r.m.s. differene etween the rte-level funtion from eh 5-s segment nd the verge funtion from the finl 5 s of the stimulus. This nlysis ws performed for the high-proility region of the stimulus only, euse other sound levels were presented too few times within eh 5-s segment. We then fitted the r.m.s. dt for eh neuron with single exponentil dey (Fig. 5) nd otined dey time onstnt. For 2/5 neurons, the r.m.s. dt were etter fitted y flt line thn y n exponentil dey (F-test, P o.5 to ept exponentil fit), inditing tht the rte-level funtion hd lredy, within the first 5 s, rehed the position oupied in the finl 5 s of the stimulus; the time onstnt of these neurons ws designted s. The time onstnt of one neuron ws 46 s, inditing tht the rte-level funtion hd not stilized within the time of reording VOLUME 8 [ NUMBER 12 [ DECEMBER 25 NATURE NEUROSCIENCE

6 25 Nture Pulishing Group Mesuring the Fisher informtion of the neurl popultion. The popultion Fisher informtion funtion F(s) ws used to mesure the ury with whih sound level s ws enoded y the spike ounts of the reorded neurl popultion when s ws presented in given sound level distriution. In the limit of lrge numer of neurons, the reiprol of the Fisher informtion equls the vrine of the representtion of s y the neurl popultion. The squre root of this vrine is proportionl to the just-notiele differene, nother ommon mesure of oding ury. Correltion in spike ount of neuron pirs due to shred stimulus history ws smll for ll stimuli. The men orreltion oeffiient verged over sound levels, for ll neuron pirs nd ll stimuli, ws.56 (s.d. ross pirs ¼.13). Furthermore, there is some suggestion tht orreltion in intrinsi spiking noise etween inferior olliulr neurons is low 18 (see lso C.V. Seshgiri & B. Delgutte, Asso. for Reserh in Otolryngology Astr. 685, 23). Thus, it is resonle to pproximte the Fisher informtion y ssuming tht the neurons generte spikes independently, giving FðsÞ ¼ X f ðsþ where f (s) is the Fisher informtion funtion of eh neuron, for the sound level distriution of interest. The Fisher informtion funtion of neuron is lulted from the proility P [r s] ofneuron giving r spikes when sound level s is presented. Hene, f ðsþ ¼ X r dln P ½rjsŠ 2 P ½rjsŠ ds where the differentil ws performed y five-point entered numeril lgorithm. To otin P [r s] for the stimulus with the level distriution of interest, the numer of spikes ws ounted during eh 5-ms epoh, with stndrdized 8-ms neurl lteny. F(s) ws lso lulted using eh neuron s mesured lteny, rther thn the 8-ms lteny; this hd no qulittive effet on the results. For eh sound level, s, histogrm ws onstruted of the numer of epohs in the stimulus ontining r spikes. This gve n R 76 mtrix, where R is the mximum numer of spikes in ny epoh. For the high-proility region of the stimulus, only rndom smple of the epohs ws used so tht the verge numer of epohs per db ws the sme in the high-proility region s elsewhere. For the unimodl stimuli, the numer of epohs used for eh sound level verged t Owing to the smpling, eh neuron s Fisher informtion funtion is the medin of 2 funtions, where eh funtion ws otined using different smple. The mtrix ws onvolved with Gussin kernel with.5 spikes stndrd devition nd 4 db stndrd devition, in order to remove spurious flututions. Finlly, the mtrix ws onverted into proility mtrix of spike ount given sound level, P [r s], y normlizing the sum of eh sound level olumn to 1. In ddition, F(s) ws lulted using n pproximtion of the single neuron Fisher informtion f (s) ¼ y (s) 2 /s (s) 2,wherey (s) is the differentil of the spline fit to the rte-level funtion, nd s (s) is the spline fit to the stndrd devition s funtion of sound level, for neuron. The splines were fitted using the BARS lgorithm 36. This lterntive method hd no qulittive effet on the results. ACKNOWLEDGMENTS We thnk P. Lthm nd J. Linden for disussions nd C. Miheyl, T. Mrqurdt nd J. Ashmore for ritil reding of the mnusript. This work ws supported y the Royl Ntionl Institute for Def People nd the Medil Reserh Counil (UK). COMPETING INTERESTS STATEMENT The uthors delre tht they hve no ompeting finnil interests. Pulished online t Reprints nd permissions informtion is ville online t reprintsndpermissions/ 1. Christopher Kirk, E. & Smith, D.W. Protetion from ousti trum is not primry funtion of the medil olivoohler efferent system. J. Asso. Res. Otolryngol. 4, (23). 2. Auin, T. & Jouventin, P. Coktil-prty effet in king penguin olonies. Pro. R. So. Lond. B 265, (1998). 3. Simmons, J.A., Wever, E.G. & Pylk, J.M. Periodil id: sound prodution nd hering. Siene 171, (1971). 4. Houtsm, A.J., Durlh, N.I. & Brid, L.D. Intensity pereption XI. Experimentl results on the reltion of intensity resolution to loudness mthing. J. Aoust. 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Firhll, A.L., Lewen, G.D., Bilek, W. & de Ruyter Vn Stevenink, R.R. Effiieny nd miguity in n dptive neurl ode. Nture 412, (21). 36. DiMtteo, I., Genovese, C.R. & Kss, R.E. Byesin urve-fitting with free-knot splines. Biometrik 88, (21). NATURE NEUROSCIENCE VOLUME 8 [ NUMBER 12 [ DECEMBER