Precision and diversity in an odor map on the olfactory bulb

Transcription

1 ARTILES Preision nd diversity in n odor mp on the olftory bulb Edwrd R Souy,, Dinu F Albenu,, Antoniu L Fntn, Venktesh N Murthy & Mrkus Meister 9 Nture Ameri, In. All rights reserved. We explored the mp of odor spe reted by glomeruli on the olftory bulb of both rt nd mouse. Identified glomeruli ould be mthed ross nimls by their response profile to hundreds of odors. Their lyout in different individuls vried by only ~ glomerulr sping, orresponding to preision of prt in,. Aross speies, mouse nd rt shre mny glomeruli with pprently identil odor tuning, rrnged in similr lyout. In mpping the position of glomerulus to its odor tuning, we found only orse reltionship with preision of ~ spings. No hemotopi order ws pprent on finer sle nd nerby glomeruli were lmost s diverse in their odor sensitivity s distnt ones. This lol diversity of sensory tuning stnds in mrked distintion from other brin mps. Given the relible plement of the glomeruli, it represents feture, not flw, of the olftory bulb. In mny regions of the brin, neurons form n ordered representtion of the outside world, s exemplified by the homunulus of the somtosensory ortex, point-to-point topogrphi mp of the body surfe onto the brin surfe. There hs been gret interest in suh systemti reltionship between the funtion of neurons nd their ntomil rrngement, s the mp n suggest wht proessing the iruit performs,. Most brin omputtion is lol, relying on short onnetions between nerby ells. This is neessity, s the onnetions between neurons oupy most of the volume vilble to the brin, nd long-distne onnetions require more volume. onsequently, the rrngement of neurons in given brin region onstrins whih neuronl signls n be brought together in subsequent omputtions. Here we nlyzed sensory mp in the olftory system, nmely the two-dimensionl rrngement of glomeruli on the olftory bulb. lftion begins t the olftory epithelium, whih lines the upper region of the nsl vity, where millions of reeptor ells trnsdue the binding of odorous moleules into neurl signl. The genomes of the rt nd the mouse ontin B, genes for odornt reeptors, but eh sensory neuron is thought to express only one gene from this lrge set. This results in B, types of reeptor neurons tht re brodly intermixed on the epithelium. Reeptor neurons send their xons to the olftory bulb, where they undergo mrked resorting. Axons from prtiulr reeptor neuron type onverge onto tight fous nd their terminls form glomerulus. About, glomeruli line the outer shell of the left nd right olftory bulbs; generlly one finds two glomeruli for eh reeptor type,7. The positioning of glomeruli follows ertin generl rules. There is pproximte mirror symmetry between the left nd right bulbs, in tht glomeruli innervted by the sme reeptor neuron type pper to be refleted ross the sgittl midplne of the brin 8. Aross nimls, the lyout of glomeruli ppers to be similr, but not identil. Furthermore, there is some reltionship between the sptil position of glomerulus nd its odor sensitivity. ertin domins of the bulb respond preferentilly to speifi odor lsses 7. There hve been suggestions of even more detiled struture: in given odor lss, glomeruli tht re responsive to struturlly similr moleules hve tendeny to lie lose to eh other 9,,8. This hs been termed hemotopi mp. The gols of this study were twofold: to determine the preision of the olftory mp on the bulb nd to understnd how the mp reltes to odor proessing. We begn by identifying the funtionl properties of eh glomerulus, defined by its sensitivity spetrum to lrge pnel of odors. We found tht this funtionl identifition lone llowed us to uniquely tg mny glomeruli in both rt nd mouse. n tht bsis, we sked how reproduible the two-dimensionl rrngement of these glomeruli is, whih would revel the ury with whih Nture hs estblished this neuronl mp. We then tested whether there ws indeed systemti funtionl reltionship mong nerby glomeruli on the olftory bulb. RESULTS We mesured neurl tivity in glomeruli of the olftory bulb in response to lrge pnels of odors using two different optil reporters (Fig. ): the intrinsi signl nd synptophluorin (SpH). Both tehniques llow for extended reordings without degrdtion of the signl, s they require no exogenous inditors. The intrinsi signl n be used in ll speies, wheres the SpH method relies on geneti onstrut tht is urrently restrited to mie. n the other hnd, the SpH probe delivers muh stronger optil signls. Given these omplementry benefits nd Deprtment of Moleulr nd ellulr Biology nd enter for Brin Siene, Hrvrd University, xford Street, mbridge, Msshusetts 8, USA. These uthors ontributed eqully to this work. orrespondene should be ddressed to M.M. ([email protected]) or V.N.M. ([email protected]). Reeived September 8; epted 8 Deember 8; published online 8 Jnury 9; doi:.8/nn. VLUME [ NUMBER [ FEBRUARY 9 NATURE NEURSIENE

2 ARTILES 9 Nture Ameri, In. All rights reserved. b SpH IS df/f dr/r Number of glomeruli B B Air dor 7 nm 78 nm Time (s) SpH IS Glomerulus dor number %.% 8 our desire to ompre results from mie nd rts, we used both tehniques. In erly experiments, we pplied both methods simultneously to the sme glomeruli nd found tht they reported the sme spetrum of odor responses (see Methods nd Fig. ). Glomeruli n be identified relibly by their odor response Given lrge enough set of odornts, one expets tht eh glomerulus will hve unique response spetrum, governed by the ligndbinding ffinities of the orresponding olftory reeptor protein, with possible ontributions from lterl signl flow in the bulb. If so, one might be ble to reognize glomerulus with the sme reeptor type purely by its odor responses. The bilterl symmetry of reeptor neuron proetions to the two bulbs provides test of this proposition beuse one expets to find glomeruli with identil odornt sensitivity t pproximtely mirror-symmetri lotions ross the midplne. We exmined this mthing proess with smll pth of glomeruli in the two olftory bulbs of mouse (Fig. ). All of these were tivted by the sme odor, nd from this stimulus lone, it ws unler how glomeruli on the left bulb should be mthed with those on the right (Fig. b). Under stimultion with other odors, however, the glomeruli in this pth differed gretly in their responses nd eh hd unique odor spetrum. Moreover, eh odor spetrum on the left side hd ner perfet mth on the right side (Fig. ). n osion, we found severl possible mthes of equivlent qulity (Fig. ), perhps resulting from duplite glomeruli with the sme odornt reeptor. We voided suh mbiguous ssignments by requiring unique mth (see Methods) nd exluded the respetive glomeruli from further nlysis. 8 Rtio SpH/IS Glomerulus dor number 8 e f %.% Number of glomeruli 8 8 µm d SpH( df/f) Glomerulus + Glomerulus s = IS (dr/r) s = Similrity SpH versus IS Figure SpH nd intrinsi signl report the sme odor dependene. () Experimentl setup. The surfe of the olftory bulb ws imged with D mer. A dul bem illumintor llowed interleved illumintion with blue or red light to quire both SpH nd intrinsi optil signls during the sme odor response. (b) Mximumintensity proetion imges of odor responses on the olftory bulbs of SpH-trnsgeni mouse, probed by SpH fluoresene (left) nd the intrinsi signl (right). Eh pixel ws ssigned the highest signl mplitude eliited by ny of 88 odor stimuli. Approximtely 7 glomeruli were stimulted effetively in eh bulb. The sign of the intrinsi signls ws inverted for ese of omprison. Asterisks mrk referene points in the two imges. () omprison of responses from two glomeruli (left nd right) to 88 odors, mesured by the reltive fluoresene hnge of SpH (df/f) nd the reltive refletne hnge of intrinsi signls (dr/r). For odor identities, see Supplementry Tbles nd. (d) Stter plot of the dt shown in. Note tht SpH nd intrinsi signl vried proportionlly, but the slope is different for the two glomeruli. The orreltion oeffiient (s) between the two signls is listed for eh glomerulus. (e) The rtio of SpH to intrinsi signl, shown s histogrm for glomeruli. For eh glomerulus, the rtio ws determined from the slope in the plot of d. (f) Histogrm of the orreltion oeffiient (see d) for ll glomeruli. We tested whether this funtionl lbel for glomerulus orresponds to the moleulr lbel provided by its olftory reeptor type. A trnsgeni mouse line in whih the M7 olftory reeptor is fluoresently tgged showed single fluoresent glomerulus on the dorsl side of eh bulb (Fig. ). This glomerulus ws strongly tivted by severl tiglte odornts (Fig. b). ther glomeruli nerby shred some sensitivity to tigltes, but differed in other prts of the odor spetrum (Fig. b,). We used the mesured odor spetrum of M7 in one niml s templte to serh blindly for mth in other nimls. For every trget glomerulus, we omputed the orreltion between its odor spetrum nd the templte (eqution ()). The pek orreltion vlue relibly identified single glomerulus in eh niml (Fig. ) nd the fluoresene imge reveled tht this glomerulus ws indeed innervted by the M7 reeptor (onfirmed in out of pirs of bulbs). We onlude tht the odor spetrum is relible tg for the moleulr identity of glomeruli. A preise lyout of identified glomeruli in mouse nd rt We pplied the bove orreltion method to mth glomeruli in two olftory bulbs utomtilly by their odor spetr (see Methods). We mthed glomeruli between the two bulbs of the sme mouse (Fig. ). Even though the method ws entirely blind to the lotion of glomeruli, the resulting lyout of mthed glomeruli showed pproximte mirror symmetry ross the midline. To inspet the devitions from mirror symmetry, we overlid nd ligned the two ptterns (Fig. b). This reveled tht the shifts between the left nd right glomerulr lyouts were not isotropi (Fig. ). The displements of orresponding glomeruli were onsiderbly lrger in the nteroposterior diretion (r.m.s. displement ¼ 9 mm, pirs of glomeruli) thn in the medio-lterl diretion (9 mm). For referene, the verge sping between glomeruli in these nimls ws 8 mm. NATURE NEURSIENE VLUME [ NUMBER [ FEBRUARY 9

3 ARTILES 9 Nture Ameri, In. All rights reserved. We n oneive the tul lyout of glomeruli in ny given bulb s resulting from the prototype lyout, modified by errors in positioning tht our during development. When two suh lyouts re ligned, eh bulb is ffeted independently by the positioning error. Thus, the displement pffiffi between mthed glomeruli in the two lyouts hs s.d. tht is -fold lrger thn the error in eh individul lyout. From this, we found tht the developmentl vribility in glomerulr position reltive to the prototype mp ws 98 mm (r.m.s.), or.9 spings, in the ntero-posterior diretion nd 7 mm, or. spings, in the medio-lterl diretion (Tble ). When ompring the bulbs of two different nimls, the displements of mthing glomeruli were lmost identil to those mesured ross bulbs in the sme niml (Fig. d nd Tble ). We pplied the sme nlysis of developmentl preision to the rt (Supplementry Fig. online). Agin, the odor spetr of glomeruli were quite diverse, but glomerulus in one bulb often hd preisely mthing odor spetrum in the opposite bulb, llowing relible ssignment of orresponding glomeruli. The devitions from symmetry were mesured s before. As in the mouse, we found ler differene between the two ntomil xes, with Btwo-fold lrger displements long the ntero-posterior xis (Fig. e nd Tble ). Agin, we onverted the mesured displements to the developmentl µm µm 8 dor number b % Left Right Figure Glomeruli n be tgged by their odor responses. () The tivtion pttern in both bulbs of one mouse, indued by the odor ethyl tiglte nd mesured by SpH. (b) verly of the left bulb (green) nd right bulb (red) from. The left bulb imge ws refleted bout the midline nd shifted to lign the glomeruli lbeled. Arrows indite pirs of glomeruli with mthing odor response spetr (see Methods). () Responses to odors for the six pirs of glomeruli lbeled in b. The spetr for the right bulb glomeruli re inverted on the ordinte to filitte the omprison. Note the ssignment for glomeruli nd ws mbiguous, s ll four members hd very similr odor spetr. These ses did not pss the riterion for unique mth (see Methods) nd were not used in further nlysis (dshed rrows in b). For odor identities, see Supplementry Tble. error round the presumed prototype lyout. Aross nimls, this stter mounted to. glomerulr spings in the ntero-posterior diretion nd. spings in the medio-lterl diretion (Tble ). The verge sping between rt glomeruli ws mm. These mesurements of mp preision n provide onstrints on models of xon guidne in the olftory bulb. For exmple, two generl senrios ould explin the vribility in glomerulr plement. In one senrio, the globl grdients of xon guidne ues in the bulb vry from niml to niml, leding to slightly different lyouts. Alterntively, the grdients re very reproduible nd the noise rises when the reeptor xons red those ues. The former hypothesis predits tht nerby glomeruli should vry less in their reltive plement thn distnt glomeruli, s they trget similr levels of the guidne moleules. We tested this nd found no evidene for suh n A b L M P µm.% Figure A genetilly lbeled glomerulus vlidtes the tgging proedure. () Sensory xons with fluoresent M7-GFP olftory reeptor identified glomerulus on the posterior dorsl olftory bulb in two different mie (left nd right). (b) Intrinsi signl response to single odor (isopropyl tiglte) in the sme regions shown in (see sterisks for lignment). Severl glomeruli responded, inluding the M7 glomerulus (lbeled nd ). () Response spetr to 8 odors for the M7 glomerulus () nd neighboring ones in the sme niml ( ), s lbeled in b. In nother nlysis, we seleted n M7 glomerulus (spetrum ) s referene nd found the glomeruli with the best mthing response spetr in four other olftory bulbs (,, nd ). All four of these glomeruli were positive for M7-GFP. For odor identities, see Supplementry Tble. A, nterior; L, lterl; M, medil; P, posterior. 8 dor number VLUME [ NUMBER [ FEBRUARY 9 NATURE NEURSIENE

4 ARTILES 9 Nture Ameri, In. All rights reserved. Number of pirs e Number of pirs Displement (µm) f 8 A-P s.d. = 7 µm M-L s.d. = 8 µm, A-P M-L µm s.d. = 9 µm s.d. = 9 µm, Displement (µm) effet (Fig. f). This result fvors the ltter hypothesis, whih sttes tht the vribility rises t the red-out stge. Reent studies hve provided evidene tht two different mehnisms of xon guidne determine the ntero-posterior nd the dorso-ventrl oordintes of glomerulus,7. ur observtions of nisotropi preision suggest tht the ntero-posterior mehnism is less preise thn the orthogonl one. Some glomeruli hve identil odor responses ross speies Given the observed preision of glomerulr plement, we n speify wht the prototype mp is for the identifible glomeruli on the dorsl bulb (Fig. ). Some of these glomeruli were reognized in lmost every olftory bulb tht we inspeted, wheres others were reognized in only frtion. These differenes were prtly result of ntomil vrition in the dorsl viewing window nd of imging noise nd onservtive seletion proedure (see Methods). For the glomeruli tht were enountered repetedly, we determined the prototype lyout in the mouse ( glomeruli; Fig. ) nd the rt ( glomeruli; Fig. b) (the odor spetr tht tg the identity of eh of these nonil glomeruli re provided in Supplementry Figs. nd online). Among the nonil glomeruli in the prototype mps for mouse nd rt, we enountered ten whose odor spetr mthed very well ross speies: to within the onfidene limits developed for mthes within speies (Fig. ). For lmost ll of these (9 out of in mouse nd out of in rt), the mth to glomerulus in the other speies ws better thn to the most similr glomerulus in the sme speies. In less restritive proedure, we begn by mthing individul bulbs ross speies (see Methods). This method identified, in ddition to the bove b µm d 8 Reltive displement (µm) A-P M-L Displement (µm) µm s.d. = µm s.d. = 9 µm,,,, Pir seprtion (µm) Figure Mouse nd rt glomeruli re positioned preisely. () Lotions of odor-tivted glomeruli on the two olftory bulbs in one mouse. dor spetr on the left bulb were mthed with those on the right bulb nd the best mthes re shown with olored irles. (b) To lign the glomerulr lyouts in the two bulbs, we mirrored the left bulb onto the right, nd rotted nd trnslted the left bulb to minimize the displement of mthed pirs of glomeruli. Left, rrows indite the resulting displement vetors for ll pirs of glomeruli from the lotion in the right lyout to tht in the left lyout. Right, the sme displement vetors rooted on ommon origin. () Histogrm of glomerulr displements between left nd right bulbs of the sme mouse ( pirs in ten mie) mesured seprtely long the nterior-posterior (A-P) nd the medil-lterl (M-L) diretion. urves re Gussin fits entered on the origin, with s.d. s quoted. (d) A histogrm of glomerulr displements ross bulbs of different mie ( pirs in five mie) is shown, displyed s in. (e) A histogrm of glomerulr displements between left nd right bulbs of the sme rt ( pirs in seven rts) is shown, displyed s in. (f) We tested whether nerby glomeruli suffer similr displements in ompring the lyouts of two bulbs. Plotted long the bsiss is the seprtion of two glomeruli in one bulb nd long the ordinte is the hnge in this seprtion vetor in the other bulb ( glomeruli in seven rts; men ± s.e.m., see Methods). The stright line indites the verge reltive displement for ll pirs. ten, n dditionl six nonil glomeruli with ner-identil spetr in mouse nd rt (Supplementry Fig. online). These observtions suggest tht rt nd mouse shre substntil frtion of olftory reeptors with very similr odor-binding sites. Mouse nd rt re seprted by lrge evolutionry distne, but their olftory reeptor genes re unusully similr: About one third of the reeptor genes hve n ortholog in the other speies with 9% protein sequene identity, loser thn the nerest prlog in the sme speies. This suggests tht there is some degree of seletion pressure to mintin those sequenes. Whether the sequene similrity trnsltes to identil odor-binding spetr remins to be seen, but it is now possible to onnet the odor spetrum of glomerulus to the moleulr identity of the underlying reeptor nd this should llow further explortion of the onserved glomeruli nd their lignds. Notbly, the mthing glomeruli were lso loted t similr positions in the two speies. To llow for the different ntomil size of the bulbs, we normlized the two prototype lyouts by the verge glomerulr sping (AGS) in eh speies. After this sling, the lyouts of mthed glomeruli in the mouse nd rt differed by only B. AGS in the medio-lterl diretion nd.9 AGS in the ntero-posterior diretion (Fig. d nd Tble ). For omprison, if we hose pirs of glomeruli from the two mps t rndom, the stter would be muh greter:. AGS in medio-lterl nd 8.8 AGS in ntero-posterior. lerly there is strong orrespondene between the respetive mp positions of funtionlly relted glomeruli in mouse nd rt. This omprison of funtionl ntomy in the bulb ould be extended redily to other speies using the intrinsi signl method, whih requires no geneti modifition. NATURE NEURSIENE VLUME [ NUMBER [ FEBRUARY 9

5 ARTILES Tble Summry of preision in the glomerulr lyout on the olftory bulb Aross hemispheres Aross nimls Number of pirs Preision (mm) Reltive preision (AGS) Number of pirs Preision (mm) Reltive preision (AGS) Mouse A-P M-L 7.. Rt A-P. 8. M-L.8. Mouse-rt prototype A-P.9 M-L. The preision of plement of glomeruli is mesured s s.d. of the stter bout the verge position in the lyout nd reported in either bsolute units (preision) or multiples of the verge glomerulr sping (reltive preision). The results re reported seprtely by speies (mouse versus rt), by ondition (ompring two bulbs in the sme niml or ross nimls), nd by ntomil diretion (ntero-posterior (A-P) versus medio-lterl (M-L)), nd the number of glomerulr pirs ontributing is listed in eh se (number of pirs). The preision of lignment of the mouse nd rt lyouts is bsed on the ten nonil glomeruli in Figure. 9 Nture Ameri, In. All rights reserved. A orse-sle mp from odor spe onto the olftory bulb Above, we hve disussed the developmentl preision in the lyout of glomeruli; we move now to the funtionl logi of their rrngement. Speifilly, we would like to find systemti reltionship between the hemil sensitivity of glomerulus nd its position on the olftory bulb. The prototype lyouts desribed bove (Fig. ) provide look-up tble between odor spetrum nd sptil lotion, but onvey no understnding of the rules behind the lyout. Perhps the simplest hypothesis for mpping rule is liner reltionship between odor responses nd position (eqution ()). In this mp, eh odor is ssigned one lotion on the bulb. A hypothetil glomerulus tht responds exlusively to one odor would be mpped to tht odor s lotion. A glomerulus tht responds to severl odors is mpped to n intermedite position, determined by weighting eh single-odor lotion with the response to tht odor. This type of reltionship between the responses nd lotions of neurons pplies, t lest lolly, in mny somtotopi or visuotopi mps in the brin. Given the mesured odor spetr nd lotions for ll glomeruli, we derived the optiml liner mp between the two (see Methods). To explore its utility, we begn by fousing on the rt, s the lrger bulb llows more preise position mesurement nd prior work hs elborted odor mps extensively in this speies 7,. We found tht the liner mp did provide some predition s to where glomerulus lies on the bsis of the odor spetrum lone, but it ws inomplete nd orse (Fig. ). Along the ntero-posterior xis, the predited position ws orrelted with the true position, but the disrepny hd s.d. of B mm, muh greter thn the inherent ntero-posterior vribility in the lyout of glomeruli ( mm; Tble ). Thus, the liner mp does not ount for the lotion of glomeruli to the ury with whih they re rrnged. Along the medio-lterl xis, whih hs muh shorter extent, the liner mp ws not useful t ll: the errors in the predited positions were lmost s lrge s the rnge of positions. How is the predition of ntero-posterior lotions hieved? Inspetion of the oeffiients in the liner fit showed tht only smll number of odors ontributed to this (Fig. b). Furthermore, the subsets of odors tht were ssigned very nterior or very posterior positions eh shred strong struturl similrity. Among the pure ompounds tht predited nterior plement of the glomerulus, liphti ldehydes mde up four of the seven odors. All were stright-hin moleules ontining double-bonded oxygen speies M A P AGS L b Figure Prototype lyout of glomeruli in mouse nd rt. () Prototypil glomerulr lyout for the mouse. irles indite the verge lotion on the bulb for glomeruli tht were relibly identified ross experiments (bsed on eight bulbs). irle dimeter is equl to the verge glomerulr dimeter. Ellipses indite s.d. of the stter in position bout the men lotion. olored irles nd numbers lbel glomeruli tht hd mthing odor spetr in mouse nd rt (the odor spetr of these glomeruli re plotted in Supplementry Fig. ). (b) Prototypil glomerulr lyout for the rt, identifying glomeruli (bsed on four bulbs), displyed s in, with the sptil sle normlized to the AGS. The odor spetr of these glomeruli re plotted in Supplementry Fig.. () dor spetr of ten nonil glomeruli (olored dots in nd b) whose responses re lmost identil in the mouse nd rt. Glomerulr tivity ws reorded using the SpH probe in the mouse nd intrinsi signls in the rt. For odor identities, see Supplementry Tble.(d) Displement vetors between mthed glomeruli in the mouse nd rt lyouts, rooted to ommon origin nd sled in terms of the AGS dor number d SpH mouse IS rt AGS s.d. A-P.9 M-L.9 VLUME [ NUMBER [ FEBRUARY 9 NATURE NEURSIENE

6 ARTILES 9 Nture Ameri, In. All rights reserved. Fit position (µm),,, b Most nterior, H,, Rel A-P position (µm) A-P oeffiient normlized dor rnk In ontrst, the odors tht predited posterior plement were, with single exeption, thizoles. Given tht this odor set (Supplementry Tble online) ontined mny other ompounds, these struturl similrities lerly stnd out. Moreover, seond odor set (Supplementry Tble ) tht did not ontin these moleules llowed no systemti predition of ntero-posterior position. Thus, mong the lsses of odornts tht we tested, the stright-hin hydrorbons nd the thizoles produed responses tht were lerly lolized to one portion of the dorsl bulb. We onlude tht liner mp between odor spetrum nd lotion of glomerulus n ount for orse positioning to within B glomerulr spings, but not on the finer sle of the nturl preision of the lyout. This nlysis is onsistent with previous reports tht responses to ertin odors n be preferentilly lolized to domin or module of the dorsl bulb, typilly B mm in size,7,,. Fine-sle diversity in the odor mp loser inspetion of the domins identified by the ldehydes or thizoles showed tht they still ontined glomeruli with gret Rel M-L position (µm) S Most posterior S S N N N S S N N Figure A orse mp reltes the lotion of glomerulus to its odor spetrum. () The optiml liner odor mp for the rt olftory bulb. The glomerulr position s predited by the optiml mp (eqution ()) is plotted ginst the tul position. Solid line denotes the identity. Dotted lines represent the stter (± s.d.) expeted from the mesured ury of glomerulr plement, if the liner reltionship ounted entirely for the hemotopi mp. Note the tul stter ws muh greter. Left, ntero-posterior position; the fit hs orreltion oeffiient of r ¼.9. Right, medio-lterl position; r ¼.. Dt re from four bulbs in two rts. (b) The weighting oeffiient (A in eqution ()) for eh odor response in fitting the ntero-posterior position of the glomerulus. The odors re ordered by the strength of their oeffiient. A few odors emerged with unusully strong nterior (negtive) or posterior (positive) weights (outside dotted lines). Their hemil strutures re shown on the left nd right, respetively. For odor identities, see Supplementry Tble. diversity of hemil spetr. For exmple, s in previous studies,9 we enountered some lol lusters of glomeruli tht were responsive to ldehydes (Fig. 7). However, two glomeruli with similr responses over the ldehyde series often hd very different responses to the reminder of the odor set (Fig. 7b,). Furthermore, interspersed mong the glomeruli responsive to ldehydes were glomeruli tht were entirely insensitive to this lss of odors (Figs. nd 7b,). Similr heterogeneity ws found in the domin ssoited with thizoles. Is there ny systemti odor dependene in these fine-sle rrngements? The reltionship between odor spetrum nd the lotion of glomerulus my oneivbly be very onvoluted nd nonliner, in whih se globl liner fit to the mp (Fig. ) will be only modertely suessful. To the extent tht there is systemti reltionship, however nonliner, we still expet to find lol order in the mp: nerby glomeruli should hve similr odor sensitivity spetr. We tested this predition for the rt s glomerulr lyout by nlyzing the reltionship between physil distne nd funtionl similrity mong pirs of glomeruli. To mesure the funtionl similrity of two glomeruli, we used the sme quntity tht llowed their identifition ross nimls, nmely the orreltion oeffiient of their response spetr to lrge set of Figure 7 Lol diversity in the mp of glomeruli. () Detil of odor responses in smll region of the rt olftory bulb. In eh pixel, the response mplitudes to liphti ldehydes of three different hin lengths (pentnl, hexnl nd heptnl) re enoded with the red, green nd blue olor hnnels. The lol lusters of glomeruli tht re eh tuned shrply to dent hin lengths should be noted. (b) Glomeruli on one olftory bulb of rt. Sensitivity to liphti ldehydes is mrked in red (left) nd sensitivity to thizoles in green (right). () dor response spetr of seleted glomeruli lbeled in b; note the sensitivity to ldehydes in the nterior nd to µm Pentnl Hexnl Heptnl thizoles in the posterior bulb. Adent glomeruli n hve nonoverlpping odor spetr (for exmple, nd ). The ldehyde domin inluded glomeruli with no sensitivity to those odors (for exmple, ). Glomeruli with overlpping sensitivity to ldehydes my hve entirely different responses to other odors (for exmple, nd ). For odor identities, see Supplementry Tble. b Aldehydes Thizoles Aldehydes Ethyl esters Tigltes Thizoles dor number 8.% NATURE NEURSIENE VLUME [ NUMBER [ FEBRUARY 9

7 ARTILES 9 Nture Ameri, In. All rights reserved. Figure 8 Lk of lol hemotopy. () Reltionship between the odor response similrity (ordinte, eqution ()) of two glomeruli nd their sptil seprtion (bsiss) in the rt. The nlysis extended over, pirs of glomeruli in olftory bulbs from..8. >..8. > 7 rts. Eh pir of glomeruli ontributed one.. ount in this histogrm nd the gry sle reports the number of ounts in eh bin. Red.. lines indite men (solid) nd medin (dshed) similrity versus distne, obtined by binning.. the distne. Blue lines indite men (solid),,,,,,, nd medin (dshed) distne versus similrity, obtined by binning the similrity. For odor identities, see Supplementry Tble. (b) Under the null hypothesis in whih there b..8 e..8 is no hemotopy whtsoever, the response.. similrity of pir of glomeruli should hve > > the sme probbility distribution t ll distnes... Therefore, the oint distribution of similrity nd distne should equl the produt of the two mrginl distributions (see Methods). This predition is plotted here; note the lose.... resemblne to the mesured distribution ().,,,,,,, () Differene between the mesured distribution () nd the distribution expeted in the bsene of ny hemotopy (b), plotted on n expnded grysle. The region with the strongest devition..8 f..8 from the null hypothesis inluded the pirs.. seprted by o mm (vertil line) with similrity of. (horizontl line). (d) Distribution of.. response similrity nd sptil seprtion for glomeruli in the mouse, presented s in. Dt re from,9 pirs of glomeruli in bulbs from mie. For odor identities,.... see Supplementry Tble. (e) Distribution,,,,,,, expeted under the null hypothesis of no hemotopy, presented s in b. (f) Differene Seprtion (µm) Seprtion (µm) between the mesured distribution (d) nd the distribution expeted in bsene of ny hemotopy (e), presented s in. The strongest devition ppered for pirs of glomeruli seprted by o.7 mm (vertil line) with similrity of. (horizontl line). odors (eqution ()). This is nturl hoie beuse it diretly mesures the overlp between the moleulr reeptive rnges of the two glomeruli; in turn, the reeptive rnge overlp hs been ited s riterion for hemotopi order on the olftory bulb. Furthermore, very similr orreltion oeffiient hs been in ommon use for ssessing the similrity of odor response ptterns. With this similrity mesure in hnd, we plotted similrity ginst distne for more thn, pirs of glomeruli in the rt (Fig. 8). At ny given distne, we found bout the sme distribution of similrities. Even t the smllest distnes there ws no shortge of nerby glomeruli tht hd strongly differing or nonoverlpping response properties (Figs. nd 7b,). The verge similrity hd lmost no systemti dependene on distne (Fig. 8). If there were no hemotopi order on the bulb, then the distribution of similrities should be stritly identil t ll interglomerulr distnes (Fig. 8b). We ompred the observed distribution to this null hypothesis nd resolved some smll differenes tht refleted wek tre of hemotopy (Fig. 8): At short interglomerulr distnes o mm, omprble to the size of orse odor domins, we found n exess of highly similr pirs nd derth of dissimilr pirs. This exess ws smll effet: It mounted to only.7% of ll pirs of glomeruli seprted by o mm nd.7% of ll glomerulr pirs inspeted. A seond series of experiments, using different odor set, rehed the sme onlusions (Supplementry Fig. online). Similrity Similrity Similrity d We repeted this nlysis in the mouse with more thn, pirs of glomeruli nd it yielded very similr results (Fig. 8d f). Agin, similrity nd distne were nerly independent of eh other, with smll devition t short distnes; here, the exess mounted to.7% of glomerulr pirs seprted by o.7 mm nd % of ll glomerulr pirs onsidered. We onluded tht on blne there is very little systemti mpping of glomeruli on sle finer thn the orse domins. Furthermore, even the orse domins do not impose strong orgniztion on the odor mp. If one onsiders the response spetrum to brod pnel of odors, two glomeruli from the sme domin, with o mm seprtion, re in most ses s dissimilr s those from different domins (Fig. 8,d). DISUSSIN ur study ws onerned with the funtionl ntomy of the olftory bulb. We nlyzed the sptil lyout of glomeruli in reltion to their odor sensitivity nd found tht mny glomeruli ould be identified uniquely nd relibly by their odor sensitivity spetrum lone (Figs. ). In both mouse nd rt, the lyout of glomeruli ws notbly preise, to within.. glomerulr spings, nd the vrition ws lrgest in the nterior-posterior diretion (Fig. nd Tble ). Some glomeruli ppered to be funtionlly identil in mouse nd rt nd were even loted t orresponding positions on the bulb in both speies (Fig. ). There ws only orse reltionship between the odor VLUME [ NUMBER [ FEBRUARY 9 NATURE NEURSIENE

8 ARTILES 9 Nture Ameri, In. All rights reserved. sensitivity of glomerulus nd its lotion on the bulb (Fig. ). Nerby glomeruli tended to hve very diverse odor sensitivities (Figs., 7 nd 8). Here, we briefly disuss the bsis for these onlusions nd their implitions. Preision of the glomerulr lyout By loting the orresponding glomeruli in different bulbs nd superposing their lyouts, we obtined both the men lotion of eh glomerulus nd the vrition bout the men (Figs. nd, nd Tble ). We n piture this vrition s rising from developmentl proess tht ples eh glomerulus t its intended lotion modified by rndom positioning error. In the mouse, tht error region orresponded to -s.d. ellipse ontining B.8 glomeruli (p..9; Tble ). Beuse the mouse bulb hs B,8 glomeruli, this mounts to n impressive trgeting preision of prt in,. For the rt, the orresponding number ws B prt in. In ontrst, severl previous reports on this subet hve emphsized the high vribility of the glomeruli plement 7,,. This disrepny hs two soures. First, some glomeruli seem to split into multiple opies nd one prominent study inluded the positions of severl suh duplites in its estimte of vribility. ur nlysis ws restrited to single glomeruli with unique odor spetrum in the dorsl bulb. Seond, some prior studies mesured the bsolute position of glomeruli with respet to ntomil lndmrks,, wheres we foused on the reltive plement of glomeruli on the bulb surfe. Any interindividul vrition in the globl lyout of the bulb, suh s slight shift or rottion, will ffet the bsolute oordintes, but for the logi of lterl intertions, only reltive plement mtters. A renlysis of published dt onfirms tht the reltive positions of glomeruli re in ft reprodued with high fidelity: For exmple, the medio-lterl displement of two glomeruli (lbeled E nd M in Fig. S of ref. ) vried ross nimls with s.d. of only 88 mm, whih ompres well to our vlue of 9 mm (Fig. ). Another study diretly inspeted the reltive plement of two moleulrly tgged glomeruli on the bulb nd found tht shifts by or rry positions re most ommon, onsistent with our results. orse hemotopy nd lol diversity in the odor mp hemotopy refers to the notion tht hemilly similr odors re mpped to nerby lotions on the olftory bulb. This ide fes some diffiulty from the outset, s single odor generlly tivtes mny olftory reeptors 8 nd the glomeruli driven by those reeptors tend to be loosely dispersed,,9,9. ur study onfirmed this result. n verge, single odor stimulted 7 glomeruli spred over region B glomeruli in dimeter in the rt ( in n re B glomeruli in dimeter in the mouse; Supplementry Fig. online). The size of these regions of tivtion is muh greter thn the vribility tht we mesured in glomerulr positioning (s.d. of. or less; Tble ). Thus, the brod dispersion of glomeruli tivted by single odor is not used simply by developmentl noise in the odor mp, but insted represents reproduible feture of the mp, nd should not be ignored. n the lrge sle of these single-odor ptterns, the olftory bulb does show systemti hemotopi orgniztion, in tht ertin hemilly relted odors tend to tivte glomeruli in the sme orse domin of the bulb 7,8,. Two suh domins on the dorsl bulb were pprent in our study: n nterior re responsive to ldehydes nd posterior re responsive to thizoles (Figs. b nd 7b). These regions probbly orrespond to lusters A nd D identified in ref. nd the domins for ldehydes nd romti hydrorbons in ref. 7. Notbly, these two odor lsses emerged here from n unbised nlysis tht simply looked for systemti odor mp on the bulb, entirely blind to the identity of the odors (Fig. b). The mp tht we found ws rther orse: Knowing the odor spetrum of glomerulus determined its position only to within ± mm, omprble to the B-mm size of the reported odor domins. Agin, the orse resolution of the hemotopi mp nnot be sribed to developmentl noise beuse the positioning of individul glomeruli ws, in ft, muh more preise (Tble ). It hs been suggested tht there is lol hemotopy on fine sle in the odor domins nd tht ertin struturl fetures of odornts re mpped ontinuously ross neighboring glomeruli 7,,. We sw some inditions of this, suh s lol lusters of glomeruli tuned to liphti ldehydes of different lengths (Fig. 7). However, these strutures re pprent only if one fouses on speifi moleulr feture nd ignores others. In generl, glomeruli tht re sensitive to one odor lss tended to be interspersed by glomeruli tht responded to entirely different odors (Figs. nd 7b), s seen in erlier studies,8,9,9. The question rises how prevlent suh lol hemotopy relly is nd whether it n be ssessed in n unbised wy tht does not dust the riteri to eh neighborhood of glomeruli. For this purpose, we sked whether nerby glomeruli systemtilly hve similr odor sensitivity spetrum (Fig. 8). We found tht the hemil similrity of two glomeruli ws lmost entirely independent of their proximity. A smll enhned similrity mong nerby glomeruli deyed with distne on the sle of B mm(fig. 8,d) nd thus reflets the orgniztion of the orse odor domins. This deprture from independene ffeted only few glomerulr pirs (rt, o%; mouse, o7%). Thus, the dominnt hrteristi of the olftory mp seems to be lol diversity: ny mitrl ell finds itself surrounded by glomeruli with mny different odor sensitivity spetr. Beuse glomerulr plement is so preise, this lol diversity is relible feture rther thn rndom flw of the odor mp. Wht does the olftory bulb ompute? The bsi iruit of the olftory bulb follows simple sheme. Mny prllel exittory pthwys re linked by lterl inhibition.ineh glomerulus, the sensory fferents mke exittory synpses onto mitrl ells, whih in turn send their xons to higher olftory enters. These through-pthwys intert vi two networks of interneurons, in the glomerulr lyer nd in the externl plexiform lyer. Both networks re predominntly inhibitory, lthough there is evidene for lterl exittion s well,. Therefore, the individul mitrl ell reeives exittion from reeptor fferents in its primry glomerulus nd potentil ontributions from other glomeruli in lrge region extending to -mm rdius. lerly the nture of mitrl ell s omputtion depends on whih of the surrounding glomeruli ontribute nd wht odor signls they rry. In one prominent proposl, the mitrl ell ollets inhibition from ll glomeruli in brod surrounding region, leding to enter-surround orgniztion of sensitivity nlogous to visul reeptive fields in the retin. Given the lol diversity of odor spetr doumented here, the glomeruli in suh brod surround region will olletively spn vst rnge of odor stimuli. If so, then lterl inhibition might implement nonspeifi gin ontrol, suh tht ny odor presented to the nose trnsiently lowers the sensitivity of ll mitrl ells. This ould well serve for rpid dpttion by whih mitrl ell proessing beomes independent of bsolute odor onentrtions. In ontrst, suh nonspeifi surround would not be useful for shrpening mitrl ell sensitivity long speifi hemil xis. In very different senrio, mitrl ell ollets inputs from ust smll number of sprsely distributed glomeruli. In tht se, the lterl iruits serve to perform speifi omprison of few omponents of NATURE NEURSIENE VLUME [ NUMBER [ FEBRUARY 9 7

9 ARTILES 9 Nture Ameri, In. All rights reserved. the odor stimulus. Given the lol diversity of odor spetr tht we found mong glomeruli, every mitrl ell ould perform unique omputtion, even those neurons shring the sme prinipl glomerulus. There re some strong inditions in fvor of this theory. Nerby mitrl ells do indeed hve quite different odor sensitivity, espeilly with regrd to their inhibitory inputs 7. Antomil tring suggests tht the lterl networks leding to individul mitrl ells re sprse 8 nd omprison of mitrl ell responses to those of surrounding glomeruli diretly showed tht the mitrl ell ollets sprse set of inputs 9. If eh mitrl ell indeed ombines different set of olftory signls from the lol field of glomeruli, then the number of different output hnnels of the bulb gretly exeeds the number of odornt reeptors. This mounts to substntil revision of how the olftory bulb opertes. METHDS Subets. The niml subets onsisted of dult rts (femle Wistr or Long- Evns, B g) nd dult mie (mles nd femles, mp-sph heterozygous, d old, g). Eh niml ws prepred for surgery with tropine ( mg per kg, intrperitonel inetion), nesthetized with urethne (.% intrperitonel inetion, finl dose B. g per kg) or oktil of ketmine/xylzine (initil dose of either or mg per kg), nd mounted in stereotxi frme. The skull ws thinned or removed ompletely to revel the dorsl surfe of both olftory bulbs. Low melting point grose (.%) ws poured over the thinned bone nd topped with over slip. All niml proedures onformed to US Ntionl Institutes of Helth guidelines nd were pproved by Hrvrd University s Animl re nd Use ommittee. Stimultion. dornts were delivered to the niml using either of two utomted olftometers (desribed in the Supplementry Methods online). For severl odornts representing different hemil lsses, we used flme ioniztion detetor to mesure the finl vpor onentrtion: typilly. % of the sturted vpor t. These onentrtions re low enough to void sturtion of most reeptors. A list of ll of the odors nd the odor sets used in eh figure re provided in Supplementry Tbles nd online. Imging. An instrument ws developed to mesure intrinsi signls nd SpH signls in prllel. A dul illumintor, using bright light-emitting diodes, delivered either blue light (B7 nm for SpH, Luxeon V LED, Lumileds) or deep red light (B78 nm for intrinsi signl, Roithner Lser Tehnik) tht ws swithed rpidly under omputer ontrol (Fig. ). Imges were quired with D mer (Vosskühler -D) t -bit resolution, with frme rte of frmes per s (intrinsi signl) or frmes per s (SpH). Two photo lenses oupled front to front were used to imge the olftory bulb surfe onto the D rry, with pixel size of mm (mouse)ormm (rt). Some intrinsi signl dt were reorded in similr mnner using n erlier quisition system (Imger, ptil Imging). Imge quisition typilly begn s before odor delivery nd ontinued for nother s during odor presenttion. The interstimulus intervl ws s of fresh ir. Eh stimulus ws presented four to ten times, interleved with other odor trils. For eh odor, rtio imge ws omputed by dividing the verge imge during odor exposure by the imge during the preeding ir exposure. Signls were verged further over trils with the sme odor. For intrinsi signls, the rtio imge ws filtered to remove ontmintion from lrge-sle hemodynmi signl by subtrting opy onvolved with Gussin sptil kernel (s.d. ¼ mm). Delivery of n odor often produed spots in the rtio imge tht orresponded to the tivtion of individul glomeruli,. For eh distint spot, the intensity profile ws pproximted with two-dimensionl Gussin. The response strength of the glomerulus to ny given odor ws mesured s the best-fit mplitude of its Gussin to tht odor s intrinsi imge. For disply, we inverted the intrinsi signl imges to show bright spots (Figs. nd b nd Supplementry Fig. ). omprison of intrinsi signl nd SpH. The two optil probes, intrinsi signl nd SpH, report neurl tivity vi different mehnisms. By its design, the SpH reporter is linked to presynpti relese of trnsmitter from reeptor neuron terminls. The ellulr origin of the intrinsi signl is somewht less understood nd there hs been debte bout whether its origins in the glomerulus re presynpti or postsynpti,. If there is postsynpti omponent from mitrl ells or periglomerulr ells, then the odor response reorded from given glomerulus my inlude signls trnsmitted lterlly from other glomeruli, whih ould lter the odor sensitivity spetrum. Therefore, we begn by testing whether the two methods reported the sme odor spetrum. In reordings from mouse olftory bulb, the illuminting light ws swithed rpidly every. s between blue (SpH) nd red (intrinsi signl), llowing for interleved mesurement of both signls during the sme odor response (Fig. ). Aross pnel of 88 odors, bout 7 glomeruli per bulb ould be tivted using SpH nd similr number ould be tivted using intrinsi signl (Fig. b). By grphing the intensity of single glomerulus for ll the odors, we obtined response spetrum. The spetr derived from SpH nd intrinsi signl were often very similr (Fig. ), exept tht the SpH response ws muh lrger thn tht of the intrinsi signl (Fig. d). Furthermore, this rtio between SpH nd intrinsi signls vried gretly mong glomeruli (rnge ¼ B ; Fig. e). After sling the SpH nd intrinsi signls of given glomerulus for this reltive gin, the two odor response spetr beme indistinguishble. We mesured their similrity by the orreltion oeffiient of the two signls (eqution ()). These orreltions were very high (men ross glomeruli,.89 ±.; Fig. f), inditing tht, for the vst mority of glomeruli, the sled SpH nd intrinsi signl signls vried proportionlly, t lest over the odor onditions in our experiments. The ft tht SpH nd intrinsi signls hve different reltive gin ross glomeruli probbly results from their distint biophysil origins. For exmple, the SpH signl will be ffeted by the resting tivity of reeptor neurons, the rtio of synpti to other membrnes in the glomerulus nd the mount of overlying nerve lyer. Presumbly suh glomerulus-speifi sling of signls would lso be benefiil in ompring intrinsi signl to intrellulr lium responses. The ft tht the two signls hve identil odor dependene is onsistent with prior suggestions tht the intrinsi signl is strongly linked to presynpti glutmte relese, perhps vi the effets on nerby stroytes. For the present purpose, we tke dvntge of the ft tht the normlized odor spetr re identil nd use the two imging methods interhngebly. Mthing glomerulr response spetr. To formlize the mthing of glomeruli tht re driven by the sme odornt reeptor, we used simple mesure of similrity between two odornt spetr: the unentered orreltion oeffiient mong their two responses ross the different odors, r ðaþ r ðbþ s ða;bþ ¼ ¼ similrity of glomeruli A nd B ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P n r ðaþ r ðaþ P n r ðbþ r ðbþ ¼ P n ¼ eqution ðþ where r ðaþ ¼ response of glomerulus A to odor, ndn ¼ number of odors. Two glomeruli with the sme odornt sensitivity hve similrity of, wheres glomeruli tht respond to nonoverlpping odor sets hve similrity of. To mth glomeruli in one bulb with those in nother, we omputed the similrity for every inter-bulbr pir. The pir with the highest similrity ws epted s being mth nd ws removed from onsidertion. This proess ws repeted until ll possible pirings ourred. We tested more omplex lgorithms tht optimize overll similrity over severl simultneous mthes, but they lwys yielded results tht were omprble to this simple seril method. To redue the effets of noise on this nlysis, we set responses of very low mplitude (o. for SpH or o. for intrinsi signl) to (Supplementry Fig. 7 online). Furthermore, to ept mth, we generlly imposed two onditions: strong similrity (.7) nd uniqueness (similrity. for the next best mth). Alignment of mps. In ompring the lyouts of glomeruli on two bulbs, we strted with the two sets of lotions of mthed glomeruli. We refleted left 8 VLUME [ NUMBER [ FEBRUARY 9 NATURE NEURSIENE

10 ARTILES 9 Nture Ameri, In. All rights reserved. bulbs ross the ntero-posterior xis. We then shifted nd rotted the first bulb to lign optimlly with the seond bulb. Speifilly, we minimized the squred distne between the lotions of orresponding glomeruli, Pm, x ðiþ y ðiþ i¼ where m is the number of mthed glomeruli in eh bulb, x (i) is the lotion of glomerulus i in the first bulb fter rottion nd trnsltion, nd y (i) is the lotion of glomerulus i in the other bulb. Subsequent nlysis of this lignment foused on the residul shift vetors x (i) y (i) nd their extent in the ntero-posterior nd medio-lterl diretions. In Figure f, we ompred the lyout of two bulbs to test whether nerby glomeruli suffered similr displements. onsider n identified glomerulus i, with lotions x (i) nd y (i) in the two bulbs, nd nother glomerulus, loted t x () nd y (). We mesured their seprtion vetor in the first bulb, Dx (i) ¼ x (i) x (), nd their seprtion vetor in the other bulb, Dy (i) ¼ y (i) y ().The grph shows the reltive displement of the two glomeruli Dy ðiþ Dx ðiþ s funtion of their seprtion Dx ðiþ. Prototype mps nd mthes ross speies. To find set of nonil glomeruli in eh speies, we strted with ll glomeruli in eight mouse bulbs nd four rt bulbs. The nlysis ws restrited to glomeruli whose odor spetrum ould be mthed to glomerulus in nother individul of the sme speies. We required this mth to be both relible (similrity.7) nd unique (. differene from seond best mth). We then subeted this set of glomeruli to luster nlysis on the bsis of the similrity between spetr (verge linkge lustering, utoff t similrity ¼.7). Eh luster with three or more members ws tken to represent nonil group of identil glomeruli. We verged the lotion nd the odor spetrum ross members of the luster (plotted in Fig. ). To identify funtionlly similr glomeruli ross speies, we pired the nonil glomeruli in mouse nd rt using the sme mthing lgorithm desribed for individul glomeruli. This strtegy gve rise to ten pirs of nonil glomeruli with ner identil funtion in the mouse nd rt (Fig. ). An lternte strtegy reveled nother six suh shred glomeruli (Supplementry Fig. ). Liner mp of spetrum to lotion. We performed liner regression to find the best liner mp between the odor response vetor r nd the glomerulr position on the bulb x: where x A r " # x " # ntero-posterior position x ¼ ¼ x medio-lterl position " A #... A n A ¼ ¼ mtrix of mp oeffiients A... A n r r ¼.. 7 ¼ spetrum of responses to n odors r n eqution ðþ We first normlized eh response vetor r so tht its omponents summed to unity, P n ¼ r ¼. By doing this, two glomeruli with the sme reltive odornt sensitivity, but different overll response mplitude, will mp to the sme lotion. We then determined the mtrix A to minimize the squred error, P m,wherem x ðiþ A r ðiþ is the number of glomeruli. When n m, the i ¼ problem is underdetermined, with more unknowns thn mesurements. Thus, we begn by reduing the dimensionlity of the odor response spetr. From the set of n-dimensionl vetors r, we determined the first five prinipl omponents, proeted eh r onto those diretions nd pplied the fit to the resulting five-dimensionl response vetors. For the nlysis in Figure, the glomerulr position in eh bulb ws mesured reltive to the verge position of ll observed glomeruli. Similrity nd distne for pirs of glomeruli. As mesure of funtionl similrity of two glomeruli (Fig. 8), we hose gin the orreltion of the two odor spetr s (A,B) (eqution ()). To retin mximl sensitivity to ny lol hemotopi order, we nlyzed only pirs of glomeruli in the sme olftory bulb, whih elimintes the effet of developmentl vrition ross bulbs or individuls. For eh pir, we plotted similrity versus distne between the enters of the two glomeruli nd reted histogrm of the result, yielding oint probbility distribution (Fig. 8). By proeting this grph onto either xis, we obtined the mrginl distributions of distne nd of similrity. To test whether similrity nd distne re t ll relted, we omputed the produt of the two mrginl distributions (Fig. 8b). This produt is the oint distribution expeted under the null hypothesis tht similrity nd distne re sttistilly independent. Finlly, we subtrted this expettion from the observed oint distribution (Fig. 8) to highlight ny devitions from independene (Fig. 8). Note: Supplementry informtion is vilble on the Nture Neurosiene website. AKNWLEDGMENTS We thnk P. Momberts for providing M7-EGFP mie nd R. Wilson nd N. Uhid for helthy ritiques. AUTHR NTRIBUTINS E.R.S., D.F.A., V.N.M. nd M.M. designed the study, E.R.S., D.F.A. nd A.L.F. performed experiments nd nlysis, E.R.S., D.F.A. nd M.M. wrote the mnusript, nd V.N.M. nd M.M. supervised the proet. Published online t Reprints nd permissions informtion is vilble online t reprintsndpermissions/. Ks, J.H. Topogrphi mps re fundmentl to sensory proessing. Brin Res. Bull., 7 (997).. Knudsen, E.I., du L, S. & Esterly, S.D. omputtionl mps in the brin. Annu. Rev. Neurosi., (987).. hklovskii, D.B. & Koulkov, A.A. Mps in the brin: wht n we lern from them? Annu. Rev. Neurosi. 7, 9 9 ().. Serizw, S., Miymihi, K. & Skno, H. ne neuron one reeptor rule in the mouse olftory system. Trends Genet., 8 ().. Momberts, P. Moleulr biology of odornt reeptors in vertebrtes. Annu. Rev. Neurosi., 87 9 (999).. Imi, T. & Skno, H. Roles of odornt reeptors in proeting xons in the mouse olftory system. urr. pin. Neurobiol. 7, 7 (7). 7. Momberts, P. Axonl wiring in the mouse olftory system. 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