© 2012 Nature America, Inc. All rights reserved. addressed to F.W.to addressed ([email protected]). France. Paris, Supérieure, Germany. Munich, University, Maximilians Ludwig Neurosciences, 1 beneficial be might correlations or negative positive SNR, and the the population level correlations in the of activity neurons affect the stimulus onencoding of how ideas have Many put forward or studies correlated. chronized syn be may activity their Consequently, cell. connected the of vity not depends only on potential its own rate, action firing but on also the acti­ an fire to neuron’sprobability each coupled, are interconnected cells two highly If are areas sensory in neurons Typically, the coupling strength lay in a range in which the information carried by single spikes is optimal. couplings, Vi benefited from inputs by H1 without a concomitant shift of its stimulus tuning. Second, at both low and high SNR, information about optic-flow in Vi. We identified two constraints confining the strength of the interaction. First, for weak coupling uni-directional from H1 to Vi. Especially at a low ratio signal-to-noise (SNR), the coupling strongly improved the between two optic-flow processing neurons (Vi and H1) in the fly ( understand how two neurons should be coupled to optimally process stimuli. We quantified the functional effect of an interaction a variety of single-cell properties, such as their stimulus tuning, firing rate or gain. All of these factors must be considered to Typically, neurons in sensory areas are highly Coupling interconnected. two neurons can synchronize their activity and affect Franz Weber connectivity between optic-flow processing neurons Disentangling the functional consequences of the nature nature Received 17 August 2011; accepted 10 January 2012; published online 12 February 2012; the contralateral side. contralateral the to axons their project and plate lobula one in dendrites vast their on motion receive neurons These lateral. cells tangential different the between connections lateral by and eye ipsilateral the motion by local output provided of the gration flow patterns plate lobula comprising about 60 one so possesses fly the of hemisphere brain Each tively. neurons (Vi and in H1) the located and left plate, lobula right respec ­sericata ( blowfly the of system visual the in neurons processing flow coupling. of their and directionality strength the governing ciples should be coupled to optimally process stimuli and to reveal the prin neurons two how understand to considered be must factors these of All cells. single of properties response the as well as correlations, as such level, computations population on a affects neurons connecting actions can influence the gain fields receptive can change tuning their neuron. For instance, connecting two neurons with a different stimulus their activity, but may also affect the response properties of each single Department of Systems and Computational Neurobiology, Max Planck Institute of Neurobiology, Martinsried, Germany. Martinsried, Neurobiology, of Institute Planck Max Neurobiology, Computational and Systems of Department e xmnd h efc o a itrcin ewe to optic two between interaction an of effect the examined We However, a coupling between two neurons may not only synchronize ). Both cells are individually identifiable, motion identifiable, individually are cells Both ). NEUR 13 OSCI , 4 1 1 , 4 15 , . Their receptive field properties . arise from Their receptive properties field the inte 2 , , Christian , K. Christian Machens 1 EN 6 6 , . A small subset of the tangential cells is hetero is cells tangential the of subset small A . 7 . . Depending on the similarity of receptive fields C 4 - E Present address: Champalimaud Neuroscience Program, Champalimaud Foundation, Lisbon, Portugal. Correspondence should be should Correspondence Portugal. Lisbon, Foundation, Champalimaud Program, Neuroscience Champalimaud address: Present called tangential cells tangential tuned optic to called specific

advance online publication online advance 1 1 or precision of single neurons 9 - , sensitive feedforward input input feedforward sensitive 1 0 . . Moreover, inter­synaptic - 3 sensitive elements of elements sensitive , 4 & Alexander Borst 3 Group for Neural Theory, INSERM Unité 960, Département d’Études Cognitives, École Normal Normal École Cognitives, d’Études Département 960, Unité Theory, INSERM Neural for Group

- sensitive sensitive 1 2 Lucilia Lucilia . . Thus, 1– 6 , 8 5 ­ ­ ­ ­ ­ - - . .

Lucilia Lucilia sericata induced by a self a by induced optic the resembled field receptive Vi’s Methods). ( fields receptive different exhibited H1 Viand Random rotation stimulus RESULTS systems. other in neurons of sensory the connectivity governing into the principles give insight also lateral might approach our areas, that sensory in abundant are Given interactions maximal. is spike per information the which in Vi of between the SNR, strength the and interaction H1 lay in a range high and low at both that, revealed analysis Further H1. from inputs enough that the shape of Vi’s stimulus tuning was nearly unaffected by ing in Vi. However, the connection between the neurons was still weak uni for a low the SNR, Especially encoding. and tuning stimulus rotation Vi’s on H1 of effect the estimate to GLM the Vi. We to H1 used then the GLM exhibited a purely excitatory, uni connectivity lateral and input feedforward of effects the includes explicitly that responses neural the to GLM) model, linear (generalized model generative a fitted we end, Tothis factors that the determine strength and of directionality the coupling. optic the improved connectivity their which to extent the studied we Next, coupling. their of dynamics ral the and describing tional strength, directionality connectivity tempo optic dynamic presenting while activity their recorded simultaneously we H1, Vi and between plate. of Tothe connectivity consequences the functional understand left the lobula plate, in and the right H1 cell, with its in dendrite located the right lobula dendrite its with cell, Vi left the neurons: lateral 1 We investigated the inter the Weinvestigated - directional interaction strongly improved the optic the improved strongly interaction directional doi:10.1038/nn.304 ). ). Using a generative model, we estimated a - rotation of the fly around an axis pointing to an an to pointing axis an around fly the of rotation 4 - flow stimuli. We then estimated the func the We estimated stimuli. then flow - hemispheric interaction of two hetero two of interaction hemispheric 2 Graduate School of Systemic Systemic of School Graduate - flow encoding to unravel the the unravel to encoding flow - directional coupling from directional 17– 1 Fig. 1a Fig. 9 . The parameters of of parameters The . t r a - flow pattern as as pattern flow , b - and Online Online and flow encod flow C I e l

s  ­ ­ ­ ­ © 2012 Nature America, Inc. All rights reserved. weakly visible on the contralateral (right) side of Vi’scross their receptive in field, ifdetectable at unknown. remain plate lobula eral synapses chemical via neuron H1 contralateral the from input excitatory receives and cells system horizontal to coupled the ipsilateral dCH is electrically cell (dCH) electrical horizontal via centrifugal dorsal the to connected synapses are which (VS7–VS10), cells system tical Vi.to projects H1 that indicates ( ms 3–4 of delay a with 3 about of factor a by increased was rate Vi’s H1, firing by fired spike a given correlated: clearly of Vi was H1 and activity spontaneous the overlap area of fields in part the frontal the receptive for except side, the binocular to on motion ipsilateral responses their strong showed only cells Both rotations. yaw to responded entially prefer therefore and motion horizontal to sensitive mainly was H1 degrees. −25 and −55 approximately of angle elevation and azimuth t r a  contralateral lobula plate are still unknown. still are plate lobula contralateral the in Vi of targets The cell. Vi left the with synapses electrical form which VS7–VS10, to coupled electrically is dCH synapses. chemical excitatory via dCH to connected is it where plate, lobula left the to axon its projects cell H1 right The previously. determined as H1 and Vi neurons ( flies over s.d. the shows shading gray The H1. by fired a spike of time the to relative ( activity ( cell. H1 a right of ( sensitivity. motion and direction preferred local the indicates arrow each of length and direction The plate. lobula left ( 1 Figure a

) Spatial receptive field of a left Vi cell with its dendrite located in the the in located dendrite its with cell Vi a left of field receptive ) Spatial The indirect, lateral interaction between Vi and H1 was clearly clearly was H1 and Vi between interaction lateral indirect, The ver caudal the to coupled Vi electrically is that shown been It has d c a f

Elevation (deg)

C I n –4 The responses of the left Vi and right H1 cells are correlated. correlated. are cells H1 right and Vi left the of responses The = 8 flies). The cross-correlation depicts the firing rate of Vi of rate firing the depicts cross-correlation The = 8 flies). 48 R 8 0 –121 R e l – z R n Vi y = 8). ( = 8). R Azimuth (deg) x s R c y 2 ) Cross-correlation of Vi and H1 for spontaneous spontaneous for H1 and Vi of ) Cross-correlation 3 . The interaction partners of Vicontralat the in partners interaction . The 0 R d z R H1 rotationaxis Vi rotationaxis ) Physical connectivity of the two heterolateral heterolateral two the of connectivity ) Physical x - correlation ( correlation Fig. 1 Fig. Vi R 121 Strong stimulation Weak stimulation y c H1 H1 Vi Vi ). This lag in the cross the in lag This ). 0

Fig. 1 Fig. H1

0 50 100 Firing rate (Hz) rate Firing c b ). However, it was only only was it However, ). ) Spatial receptive field field receptive ) Spatial Time (s b Speed (deg s–1) –200 2 200 0 ) . Nevertheless, . Nevertheless, 0 0 H1 - 2 – correlation correlation 1 R ( y Fig. 1 Fig. R R R z y x R

d z R 0 2 ). ). .5 x 2 ­ ­ ­

Time (s) 0.25 with a regular grid of white dots ( what a fly would see if it randomly rotated in a big, black sphere painted random stimulus a rotationmimics This Methods). stimulus (Online straining the strength and directionality of the coupling, we presented con factors potential unravel to and H1 andVi between interaction all ( combination of the with Vi’s preferred rotation axis, whereas H1’s the that preferred such arranged was system coordinate The axis was a linear onto the stimulus device, which was faced by a real, fixed fly ( projected was fly’s eye virtual the by perceived image the point, time white rotation axis, whose changing steadily a about rotated fly virtual the point, time each At largesphere. the centerof the in fly virtual a placed we stimulus, tion R c a y e Firing rate of Vi (Hz) Elevation (deg)

SNR Fig. 1 100 –45 –15 0 1 2 50 15 45 –120 - 0 –50 noise profiles ( profiles noise Strong Weak Time relativetoH1spike(ms) * a –90 ** ). To study the functional effect of this weak inter advance online publication online advance 0 50 100 H1 Vi *

–60

** Firing rate (Hz) rate Firing Azimuth (deg) –30 0.5 0 x Vi x 3 0 and , , Fig. 2 Fig. y and specified by the the by specified was axis rotation three-dimensional the point, z ( shading). (gray mask a by blanked was field binocular frontal The half. right the via stimulated was H1 whereas device, stimulus the of half left the to restricted mainly was the of combination a was axis preferred H1’s axis. ( describe to axis rotation changing steadily a around sphere large a in rotated fly virtual a Left, stimulus. rotation random ( 2 Figure all flies ( flies all over averaging from obtained (right) H1 and ( s.e.m. ** ( ms 4 in binned rates firing for determined was SNR The stimulation. weak ( ms. 1 in binned were trains Spike spike. a of appearance the representing tick black each with plots raster as represented are segment stimulus short a to responses repeated The cell. H1 right and Vi left recorded simultaneously a of responses with along stimulus weak and strong the and 6 0 b R a axes as a function of time. At each time time each At time. of function a as axes z ) Scheme illustrating the generation of the the of generation the illustrating Scheme ) ) Rotation velocities around the the around velocities Rotation ) x P axes ( ) was aligned with Vi’s preferred rotation rotation preferred Vi’s with aligned was ) < 0.01, paired paired 0.01, < 9 0 b x R z 5 , , and components were given by independent 0 z y x ) describing the rotation velocity around around velocity rotation the describing ) 0 and and and and f

) Rotation tuning maps of Vi (left) (left) Vi of maps tuning Rotation ) Fig. 2 n Supplementary Supplementary Fig. 1c 120 Random rotation stimulus. stimulus. rotation Random e = 8). = Supplementary Fig. 1a Fig. Supplementary ) SNRs of Vi and H1 for strong and and strong for H1 and Vi of SNRs ) R z z was arranged such that the the that such arranged was axes. ( axes. axes. Right, Vi’s receptive field field receptive Vi’s Right, axes. –120 d a b ). To generate the random rota x , , –90 y

t and and Left eye test. Error bars represent represent bars Error test. c VS7–VS1 dCH nature nature , Vi –60 d R ) A single frame of the the of frame single A ) . The coordinate system system coordinate The . 0 z Azimuth (deg) –30 components ( components n Retina Lobula plate Electrical synapse Excitatory synapse x = 8). * 8). = H1 axis was aligned aligned was axis 3 0 NEUR Right eye ). x - 6 0 ? H1 , , hemispheric ). For each each For ). y P

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© 2012 Nature America, Inc. All rights reserved. are projected onto the receptive field of Vi or H1, yielding a one a yielding H1, dimensional time signal. This or as signal serves input Vi for a of GLM field receptive the onto projected are fly the in local detection for motion model algorithmic established an detectors, Reichardt by modeled detectors motion local tuned horizontally and vertically of array an through fed is stimulus visual the First, Methods). Online ( stages two comprises model generative The rate. firing neuron’s the on connections lateral and detectors motion local the input from feedforward of afferent effects the includes that explicitly model generative a fitted we Vi H1, and between connectivity the of dynamics and directionality strength, the describe functionally To Vi to projects H1 H1. from input the off turning by effect this observe to able be should we tuning, rotation Vi’s in shift a causes indeed H1 If axis. H1’s toward preferred tuning Vi’s shift Vi should to H1 from input excitatory an that implies This the toward shifted clearly was axis rotation preferred its tions, the around tions for rota responses Vistrongest the system, elicited of coordinate the ( sphere a of projection two resulting the represented Wethen angle. elevation and azimuth its by specified as axis, rotation each for rate firing mean the we calculated delay, response neural the Given neurons. both for tuning tion stimulation). (weak a with low one compared at stimulation) SNR a (strong high differed H1 Vi and between interaction the how study to able were we tions, condi stimulus both by Thus, comparing SNR for stimulation. weak 4 ms (ref. than Vi ( device. stimulus the of region frontal the we blanked area, overlap binocular the input from shared of grid dots ( sparse a with papered was of sphere the which grid in stimulation, dense weak and a dots, with painted was sphere the which in stimulation, strong conditions: stimulus two compared we H1, and Vi between s.e.m. represent bars Error ( rates firing predicted the by explained rates firing recorded the in variance the of percentage the indicate bars The (blue). H1 ( stimulus. strong the of segment a short of presentation repeated to H1 and Vi of responses ( shading. gray the ( flies all over averaged were correlations predicted and measured The cross-correlations. the in peak the depict insets The H1. by fired a spike of time the to relative Vi of rate firing the show correlations The activity. spontaneous for and stimulation, weak and strong for H1 and Vi between cross-correlations (yellow) ( model. the under trains spike recorded the of likelihood the maximizing by data the to fit directly were red) in (drawn GLM the of components unknown All filter. coupling and filter post-spike filter, stimulus filters: linear three via modeled is rate firing a neuron’s GLM, the In areas). shaded (gray H1 and Vi of GLM the for signal input the yielding H1, or Vi of field receptive spatial the with filtered then are detectors motion the of outputs The detectors. Reichardt of array a two-dimensional through fed first is stimulus visual 3 Figure nature nature of either Vi or H1 is modeled by three linear filters: a stimulus filter filter stimulus a filters: linear three by modeled is H1 Vi or either of rate firing the GLM, In the model. generative of the stage second the The random rotation stimulus allowed us to determine the rota the determine to us allowed stimulus rotation random The Under both stimulus conditions, H1 elicited more reliable responses interaction the influences strength stimulus the Towhether study - dimensional tuning maps for Vituning and H1 as a color dimensional

NEUR Fig. Fig. 2c Generative model for Vi and H1. ( H1. and Vi for model Generative 2 4 ) ) ( OSCI Fig. Fig. 2 , d e ), ), as by quantified the SNR for rates firing binned in x ) Recorded (black) and simulated (yellow) spiking spiking (yellow) simulated and (black) ) Recorded axis. Although H1 was also sensitive to to sensitive also was H1 Although axis. EN Fig. Fig. 2c e ). ). Moreover, both Vi and H1 exhibited a reduced f C ) Evaluation of the GLMs for Vi (green) and and (green) Vi for GLMs the of ) Evaluation E Fig. 2 Fig.

n , advance online publication online advance d = 8). For the data, the s.d. is depicted by depicted is s.d. the data, the For = 8). 4 b ). ). To from resulting correlations exclude , 25 – f d ). As expected from the arrangement arrangement the from expected As ). , 2 ) The measured (black) and predicted predicted and (black) measured ) The 6 . The outputs of the detector array array detector the of outputs The . a ) In the generative model, the the model, generative the ) In - coded planar planar coded n = 8). = 8). Fig. 3 Fig.

17– x

z

rota a axis. axis. 19 and and , 2 7 ­ ­ ­ ­ - , multiplicative gain adjustment of neuron’s the adjustment gain rate ( multiplicative firing conductance acting as an effective gain control mechanism. these changes in the gain can be attributed to changes in the membrane dots, strongly modulates the gain of the tangentialwe foundcells that the stimulus strength, asstimulus controlled filter bywas theincreased density by ofa factormoving of about 10 ( reproduced 75% and 78% of the variance in the data ( data the in variance of and the 78% 75% reproduced rates firing for strong and the weak whereas stimulation, GLM recorded for H1 the in variance the of 60% and 72% for accounted trains) spike simulated the from (calculated Vi of rate firing predicted The ( counterparts recorded the resembled strongly trains spike characteristic sharp peak at 3–4 ms ( ous activity, reproduced the response observed correlations with their Methods). (Online uncorrelated are cell H1 right Vi the and left such that device the inputs from provided the and left eye right to the rotation independent stimuli on the left and right side of the stimulus To stimuli. two rotation we random end, presented this uncorrelated overlap binocular the blanked with obtained we the GLMs using recordings Second, trained region. we described, previously as First, approach. following the applied we correlations, stimulus or input Viaction between and H1 and does not shared reflect noise, common ( nonlinearity spiking the of approximation good a represents function exponential the H1, and exp( as outputs, filter exponentiated by the rate multiplying rate. can Equivalently, the be firing calculated neuron’s the yielding firing nonlinearity, an exponential through fed additional constant offset parameter. The an summed filter responses are introduced we rate, neuron’sfiring the Tomatch Vi). (or H1 by coupling filter capturing the dependency of Vi (or a H1) and on rate, a spike firing fired own its on neuron the by fired spike each of effect on the neuron’sdetectors rate, a firing post motion local the from input feedforward the of effect the describing b a e When exponentiated, the coupling filters can be interpreted as as interpreted be can filters coupling the exponentiated, When During weak stimulation for both Vi and H1, the amplitude (gain) of the The GLMs for strong and weak stimulation, as well as for spontane To ensure that an the coupling lateral inter existing describes filter Firing rate of Vi (Hz) H1 10 Vi Time relativetoH1spike(ms) 50 0 0 Stimulus –5 0 0 0 GL Data M Strong Reichardt detectors 100 0 4 1 8 50 fields Receptive 100 c Time (s) 50 Time relativetoH1spike(ms) 0 –50 Supplementary Fig. 2a Fig. Supplementary Weak filter Stimulus Fig. 3b Vi H1 0 a 100 + + 0 4 1 b Offse Offset – ) = exp( = ) - d + + 50 8 spike filter describing the describing spike filter ). Moreover, the predicted Nonlinearity t d exp( exp( 10 50 Time relativetoH1spike(ms) x x 0.5 0 ) 0 ) –50 Fig. 4a a t r a ) × exp( × ) 2 f 8 , b . We showed that Variance explained Spontaneou 0.2 0.4 0.6 0.8 Fig. 3 Fig. spiking Stochasti filters Couplin ). 0 , filter Post-spik b Strong ). Previously, 0 Fig. 4c Fig. C I b g f 100 H1 Vi c ). ). For Vi For ). Fig. 3 Fig. 0 e 4 1 s Weak e l 50 – 8 e e s ). ). ). ).  ­ ­

© 2012 Nature America, Inc. All rights reserved. In a control experiment, we ruled out the possibility that the small grat tunings closely overlapped for strong and weak stimulation ( H1’s( silenced activity presented a small grating moving in H1’s null direction ( decrease H1’s remaining activity during this unilateral stimulation, we ToMethods). H1’s(Online blankedto ingfurther was side ipsilateral correspond half right complete the whereas space, visual of side left We verified. tally presented random the rotation stimulus only on the conditions. stimulus both for tuning elevation and azimuth the that revealed the excitatory input from H1 the enhanced amplitude of tuning ( curves re then and Vi to H1 connecting filter stimulation coupling the weak and strong for ( tuning elevation and azimuth one a obtain to azimuth and elevation along averaged in data the for shown (as cell Vi of these spike trains, we calculated rotation tuning maps for the model and weak and stimulation spike generated several trains. On the basis the input from H1 ( Next, we the GLM used to study how Vi’s on rotation tuning depends tuning Vi’s rotation enhances H1 initiation. spike for likelihood the increasing period atory refractory period, H1 the showed for strong Following and weak stimulation a strength. facili stimulus increasing with shortened period ( spike a following period inhibitory an SNR. at high than SNR at low is stronger Vi on H1 of effect relative the that the suggesting reducing strength, when stimulus enlarged was strength coupling The Vi. to H1 uni a suggest strongly filters coupling the Thus, activity. spontaneous or stimulation weak stimulation, strong for 5.1 or 3.9 2.7, of factor a by ms 4 to up of delay a with rate firing Vi’s increased H1 by fired Vi. spike on A effect excitatory an had H1 ( H1 on Vi’sdependence capturing filter coupling the Contrarily, H1. on effect no had Vi is, that 1, approximately ( H1 on Vi of effect the describing filter the conditions, all For rate. firing own cell’s the on a spike of effect multiplicative the describe they that such exponentiated are filters The activity. spontaneous for and stimulation, weak and ( 1 8 to ms. from filters coupling the show insets The H1). (or Vi of rate firing the on Vi) (or H1 by fired a spike of effect multiplicative the depict they that such exponentiated are filters coupling The blue. in depicted is H1 to Vi connecting filter the and green in shown is Vi on H1’s effect describing filter coupling The conditions. all for filters ( s.e.m. the depict shadings blue and green the and flies, over average the indicate (different stimulation strong for than stimulation weak for larger tenfold about were amplitudes filter stimulus ( stimulation weak and ( strong for (blue) H1 and (green) Vi of filters 4 Figure t r a  ing had an inhibitory effect on Vi ( n Fig. Fig. 5a

= 8). A.u., arbitrary units. ( units. arbitrary A.u., = 8). Next, we tested whether these model predictions could be experimen post The

, C I b GLM components. ( components. GLM ). ). To estimate H1’s on effect Vi’s we tuning curves, cancelled - spike filters of both neurons exhibited for all conditions conditions all for exhibited neurons both of filters spike e l Fig. Fig. 5a f – s h ) Post-spike filters for strong strong for filters ) Post-spike Fig. y b axes). The solid lines lines solid The axes). i. 4c Fig. , ). Note that the the that Note ). b Fig. 5 Fig. 5 ). ). Comparison of the simulated tuning curves ). ). Using the GLM, we simulated Vi for strong Fig. 4c Fig. a c , f b – – ). The model predictions and measured and predictions model The ). e ) Stimulus ) Stimulus e ) Coupling ) Coupling ) was always always was ) – e

Supplementary Fig. 3a ) clearly peaked at 3–4 ms, that is, is, that ms, 3–4 at peaked clearly ) Fig. 2 Fig.

Fig. 4f Fig. f a - ). For simplicity, we then then we simplicity, For ). ) directional coupling from from coupling directional – h ). This refractory refractory This ). filters Stimulus filters Coupling filters Post-spike - Fig. 5 calculated the the calculated - dimensional dimensional , b Fig. 5a ). e ), which c a Gain f Gain Amplitude (a.u.) 0 1 2 1 3 5 0 2 4 , 0 2 0 b ). ­ ­ ­ ­ –60

5 1 4 1 Time (ms) Time (ms) Time (ms) (Online Methods). (Online tion gave a lower bound on the information carried by spikes the gave tion carried a on lower bound information the Viof of Comparison the power the spectra stimulus and the reconstruc of spikes simulated) (or recorded the from filter linear a by reconstructed be could stimulus rotation random the of the which to extent the tested Vi,we by (encoding) representation stimulus the Tomeasure H1. from input the of ence depend in Vi by fired spikes the by represented is profile rotation self the well how on Vi,of H1 asked we effect the To quantify better information spike single the maximizes coupling The main Vi’s plate. lobula is contralateral the from H1 partner interaction regions, stimulated the and stimuli presented the model for that, suggests the curves tuning that measured the reproduced accurately finding our Hence, plate. lobula right of the from partners Vi interaction potential further of influence the diminish H1. from by inputs unaffected Viof nearly ing was tun that stimulus the verifying unchanged, were nearly components linear the conditions, both For stimulation. unilateral and bilateral in Vi’s preferred rotation axis by comparing the linear components for recorded firing rates ( three the mapping models unaffected. nearly tuning only H1 of Vi’samplitude of the shape the the leaving from increased while tuning, input lateral the tuning, their in differed H1 and Vi although Thus, small. very only was effect this significant, although lation overlapped for positive angles larger than 40 However,degrees. stimu and for unilateral tunings bilateral both the elevation whereas ( increased significantly were rates firing the degrees, 40 ( H1 from input the of result a as shift asymmetric an revealed tunings elevation measured and Vi’srecorded Indeed, angles. negative toward tuning elevation ( tuning elevation their in differed H1 Viand as However, tuning. elevation and muth Strong –40 20 Presenting no stimulus on the right side of visual space might also also might space of visual side right on the no stimulus Presenting linear estimated we finding, this validate further To Vi’s of azi amplitude the increased H1 from input the Generally, 4 0 8 –20 advance online publication online advance 40 0 0 b d g Gain Gain Amplitude (a.u.) 20 40 0 1 2 1 3 5 0 i. 5a Fig. 2 0 2 0 Supplementary Fig. Supplementary 4 – Fig. 5a Fig. 60 1 5 Time (ms) Time (ms) Time (ms) 4 1 – Weak –40 d - dimensional rotation profile onto the the onto profile rotation dimensional , n nu fo H sol sit Vi’s shift should H1 from input an ), 4 0 4 0 , 8 b –20 ). For elevation angles smaller than than smaller angles elevation For ). 0 0 0 h e Gain Gain ). ). We the assessed change nature nature 1 3 5 0 1 2 Spontaneous 2 0 2 0 5 1 4 1 Time (ms) Time (ms) x NEUR Vi H1 29– , , Vi H1 Vi H1 y 4 0 4 0 or or 3 8 1 - ( OSCI P nonlinear nonlinear z Fig. 6 Fig. < 0.01), 0.01), < Vi H1 profiles profiles EN 0 0 24 a C , 2 ). ). E 9 ­ ­ ­ ­ ­ -

© 2012 Nature America, Inc. All rights reserved. increase in information suggests that Vi benefits more from inputs inputs from more benefits Vi that suggests information in increase ( stimulation weak during 55% improved Vi’s by encoding 33% stimulus ( ( pre a its for around rotations ( about axis ferred spikes recorded Vi’s by ­carried (see stimulation ablated. Experimentally, the latter case was using measured unilateral 1 to corresponds for the whereas strength, measured 0 the coupling is is, that decreased, or increased was filter coupling the of amplitude the which by factor the as defined was H1 and Vi between strength ( Vi to H1 connecting filter coupling (non the of amplitude the varied we strength, pling over a strength the coupling large range of Tovalues. change the cou the about information representation. At the same time, however, the coupling also transmits tion about two these axes ( 1c Fig. the of combination a is axis preferred ferred rotation axis corresponding to the curves. tuning or correlations predicted the affect not did tude 5 Fig. Supplementary and Methods (Online GLM the in parameter offset the reducing by the amplitude of the stimulus filter and matched increased the mean rates firing slightly the we bias, by this for carried Tocompensate spikes. information recorded the underestimated data, the from fit (gray). Errors bars represent s.d. ( H1 for bilateral (black) and unilateral stimulation on the right side. ( grating moving in H1’s null direction was presented and weak stimulation (right). To silence H1, a smallstimulation. ( elevation tuning (right) of H1 for strong and weak and gray. ( unilateral stimulation ( tuning curves for bilateral weak stimulation and ablating H1 in the model (pale blue). The measured for weak stimulation before (dark blue) and after elevation tuning (right) of Vi predicted by the GLM represent s.d. ( ** stimulation closely overlap. * where the tuning curves for bilateral and unilateral ( lines depict the tunings for unilateral stimulationfor the recorded data is shown in black. Theelevation gray and azimuth. The averaged tuning curveas depicted in elevation tuning were calculated from tuning maps,rotation tuning was reduced. The azimuth and red. Without input from H1, the amplitude of H1 thein the model are depicted in dark and pale predicted by the GLM before and after ablating (right) of Vi for strong stimulation. The tunings ( rotation tuning without affecting the tuning shape. Figure 5 nature nature SNR. at high than SNR at low by H1 provided e a Fig. , left). The arrows indicate elevation angles ) Averaged azimuth (left) and elevation tuning P First, we tested whether the GLM reproduces the information information the reproduces GLM the whether tested we First, pre its around rotations about information only Vi’scarry spikes directly as GLM, a by generated trains spike the that found We < 0.001, paired x

axis and affect its rotation tuning. To test this intuition, we varied

coupling strength of 0 and 1 matched the experimental values values experimental the matched 1 and 0 of strength coupling 6 d ), this neuron provides information about rotations around around rotations about information provides neuron this ),

). During strong stimulation, the input strong ). stimulation, from During H1 significantly H1 enhances the amplitude of Vi’s NEUR c , x d e rotations, coupling H1 to Vi should improve Vi’s stimulus ) Measured azimuth (left) and ) Unilateral stimulation for strong (left) Figure 2 x b axis). The information rates predicted by the GLM GLM the by predicted rates information The axis). OSCI ) Averaged azimuth (left) and Fig. Fig. 6 f ) Mean firing rates of Vi and Fig. 5 Fig. t test ( z EN e f , by averaging along the rotations, which might impair Vi’s encoding of of Vi’s impair encoding might which rotations, , right) are shown in black b C ). The adjustment of the stimulus filter ampli filter stimulus of the adjustment The ). e ). ). Given informa that independent H1 carries E ). n

= 8). Error bars P advance online publication online advance < 0.01, n = 8). P < 0.00001). This difference in the the in difference This 0.00001). <

Fig. 6 Fig. x and and x axis ( P < compared with 0.0001) c

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b Elevation exponentiated) exponentiated)

). ). Because H1’s Firing rate (Hz) Firing rate (Hz) 20 40 60 20 40 60 0 0

–90 –90 Azimuth (deg) Azimuth (deg) Azimuth * Str Da GLM -str GLM -str ** ong 0 9 0 ta ** ** ­ ­ ­ ­ ­

90 * ong w/oH1 ong 0 Supplementary Fig. 6 Fig. Supplementary ( optimal is spike per information the which in range a in lay strength coupling measured the stimulation, weak and for strong the bymeasure quantifies resulting information carried a spike. single Notably,The rate. firing mean the by second per bits in measured rate information the divide to is reconstruction, stimulus the of ity qual the measuring when cost, energy the include to way One sive. expen more energetically became encoding stimulus the that such coupling both neurons between led to rates firing increased ( information an from fly the in coupled optimally be to seem Vinot did H1 tion, and two negligible linear The simplified a by reproduced shifted. be Vi’scan on H1 tuning clearly of effect tuning the was Vi on effect large a had strengths H1 when Only coupling affected. slightly for only was Vi’s tuning 1.5, to However, up angles. negative toward tuning ( strength coupling the on depending tuning elevation the simulated about information no nearly Vi contained ( about information the around rotations about information provided y gain) are only shifted downward by a constant offset ( information rate curves predicted by the original GLM adjustment(withoutbythe stimulusenced thementioned filtersof above. The adjusted ( strength a coupling strength about 2.5 the fly, the information keeps increasing until it reaches a maximum at Fig. 6 Fig. axis, irrespective of the coupling strength ( strength coupling the of irrespective axis, Str Although the input from H1 improved Vi’s stimulus representa Vi’sstimulus improved H1 from input the Although we tuning, Vi’s in stimulus reflected is effect this whether Totest the around rotations about information no had Vi model, the In couplingmodeled thatfoundstrengthbeyondin the increase weIf ong -

neuron model ( model neuron Elevation (deg) Elevation (deg) –45 6 –45 45 g f 45 0 ). Increasing input from H1 was expected to shift Vi’s elevation ). However, for weak coupling strengths (from 0 to 1.5), 1.5), to 0 (from strengths coupling weak for However, ). 0 2 0 2 0 Fig. 6 Fig. Fi Fi r r ing ra ing ra 4 0 * * 4 0 - d Azimuth 0 te 0 theoretic perspective ( perspective theoretic te W * * ). This general trend of the information is not influ notinformation is the of trend general This ). (Hz) (Hz) eak 60 60 * * Supplementary Results Supplementary z rotations only for large coupling strengths strengths coupling large for only rotations ). b Firing rate (Hz) d 20 40 60

Firing rate (Hz) 0 20 40 60 - 0 fold greater than the measured coupling –90 Azimuth (deg) –90 Azimuth (deg) f * Mean firing rate (Hz) Da GLM -weakw/oH1 GLM -weak * 40 20 ta 9 0 0 ** 9 0 ** Fig. 6 Fig. Vi * 0 Str 0 z ong rotations. d ). H1 W Fig. 6 Fig. ). However, a stronger stronger However, a ). Elevation (deg) eak Elevation (deg) –45 –45 45 t r a 45 0 0 z 2 0 e 2 0 Fig. 6 axis, Vi carried carried Vi axis, ). Although H1 H1 Although ). Fi Fi Vi r r * W ing ra ing ra 4 0 4 0 eak Fig. 6 Fig. C I d * ). H1 0 0 te te Unilat Bilat * Fig. Fig. 6 * (Hz) (Hz) 60 60 e l eral i eral and h s ), ),  ­ ­ ­ ­

© 2012 Nature America, Inc. All rights reserved. was clearly deteriorated for increasing increasing for strengths. ­coupling deteriorated clearly was about spike per information the eye. For ipsilateral their of this type from input stimulus uncorrelated received H1 and Vi that such device, stimulus the of side right and left the on rotations random (uncorrelated) different two presented we ( ing encod Vi’s of stimulus improvement the lie from (resulting to shared sensitivity their H1 and Vi between tions ( model captured by two linear the simplified is SNR the on information the and strength coupling of the dependence This at H1 low SNR. with an interaction from most benefits spike of a content single information the that ing ( stimulation for strong than for weak is larger spike for the rate information ( single spikes more informative. Moreover, make as we to had already observed required are strengths coupling larger SNR, low a for that, Vi increased with decreasing stimulus strength ( tive as possible. The amplitude of the coupling filter H1 connecting to were as informa spikes single that such to a value adjusted therefore t r a  optic the improve might Vi H1 to from

g d a Finally, we studied whether a coupling coupling a whether studied we Finally, correla stimulus the whether asked We For each stimulus condition, the amplitude of the coupling filter was Elevation (deg) –1

–50 Information rate (bits s ) upeetr Fg 7 Fig. Supplementary 50 20 30 10 0 0 0 1 0 C I Supplementary Results Supplementary **** R *** elativ Fi Stimulus: ri e l Vi spik ng ra e couplingstr 50 2 s te es R

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Information rate (bits s ) e Information rate (bits s ) stimulus, stimulus, Mean firing rate (Hz) 20 30 10 10 - 20 30 10 50 0 neuron neuron 0 0 0 1 0 1 0 - R flow flow R R elativ * * elativ x R ­ ­ ­ e couplingstr y e couplingstr 2 R Fig. 4c 4 2 the coordinate system was arranged such that the the that such arranged was system coordinate the its preferred axis axis preferred its ( s.e.m. denote bars Error axis. by (denoted axis preferred its around rotations about ( unchanged. left was Vi to H1 from connection The Vi. to H1 from connection the for fit as filter coupling same the by H1 to Vi coupled we encoding, H1’s stimulus affect would 7 Figure R z a y 20 30 Relative coupling strength 10 H1 0 Vi Fig. 6 Fig. 0 1 1 0 – Vi ength R 4 e ength

x ), ), suggesting Effect of a fictive coupling from Vi to H1. ( H1. to Vi from coupling a fictive of Effect R i Co ), indicat ), y T ime (ms) 2 0 upling R i Information per spike z R –1 –1 f

Vi (bits spike ) Information rate (bits s ) ′ x 0.2 0.4 0.6 c 0 H1 . Error bars represent s.e.m. represent bars . Error 20 30 10 0 0 ­ ­ 1 0 0 Relative coupling strength R 0 1 R H1 0 elativ elativ explaining why H1 profits much less from Vi than vice versa is the the is versa factor vice than Vi important from less much one profits H1 Thus, why explaining responses. simulated the of SNR the determined strongly filter stimulus the of gain The versa. vice H1 and from benefits Vi which to degree the reversed also GLM the in ( versa vice than Vi by provided inputs from less much benefited H1 carried by the H1 model neuron increased with the coupling strength, ( GLM the in H1 Vito from encoding in H1. To this end, we introduced a (nonzero) coupling filter Vi 2 1 Figs. 6d 6d Figs. b Reversing the gain (amplitude) of the stimulus filters of Vi filters and H1 of stimulus the (amplitude) gain the Reversing e couplingstr e couplingstr

–1 Co n Information rate (bits s ) T 10 4 2 ime (ms) = 8). ( = 8). 20 30 10 upling R 0 z R 1 0 Or Da GLM -weak GLM -str x and advance online publication online advance ig R ta Vi 20 elativ . c GLM H1 ength 4 ) Information per spike carried by H1 about rotations around around rotations about H1 by carried spike per ) Information ength 7 b ong e couplingstr H1 ). 2 R ′ x x axis was aligned with H1’s preferred rotation rotation H1’s preferred with aligned was axis we examined the extent to which the the to which extent the we examined by Vi, Toencoding stimulus the quantify ( representation. 6 Figure *** ( data recorded the for differences significant indicate Asterisks amplitude. filter stimulus adjusted without GLM original the by predicted information the represent lines dotted The stimulation). (weak points gray and stimulation) (strong as black 1 and depicted are of 0 strength a for coupling rates information measured experimentally The line. solid blue and red by the is shown GLM by the as predicted stimulation weak and strong during information the about ( strength. coupling relative the defines is changed amplitude the by which H1’sfactor The on Vi. effect describing filter coupling (non-exponentiated) of the amplitude the we changed GLM, the ( s.e.m. ( stimulation the about filter. ( a linear using spikes the from reconstructed or represent s.e.m. represent of Vi about spike per information t (* strength coupling of the ( black. in H1’sis shown tuning strength. coupling of the of Vi in dependence tuning elevation by Vi about carried ( s.e.m. represent bars Error a test). Error bars represent s.e.m. ( s.e.m. represent bars Error test). R ength ) To quantify how a coupling from Vi to H1 to Vi from a coupling ) Tohow quantify 4 z ′ x P rotation velocity ( velocity rotation ). To quantify the information carried by H1, H1, by carried information Tothe ). quantify < **** 0.0001, Fig. 7 Fig. b h c ) Information encoded by H1 Vi and encoded ) Information

) To vary the coupling strength in ) To strength coupling the vary ) Mean firing rates of Vi in dependence of Vi in dependence rates firing ) Mean The coupling improves Vi’s stimulus improves coupling The c x x rotation velocity velocity rotation , Information per spike a y n –1 rate information the Although ). and and

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© 2012 Nature America, Inc. All rights reserved. were previously applied in studies on populations of retinal ganglion ganglion of retinal on populations in studies applied were previously connectivity. neural the role of gave and us therefore into a functional the insight more direct the modifying turn, coupling filters allowed us to In study their oneffect stimulus processing connections. lateral the of dynamics poral and tem the size, quantify directionality The coupling directly filters rate, including the stimulus, spiking dynamics and lateral connectivity. that explicitly accounts for various factors affecting the neuron’s firing trains spike recorded the to model generative a We fitted approach. model a pursued we correlations, noise with problems these for account and detect to difficult often are that changes firingrates it over which is computed scale as temporal the such factors, various by influenced is correlation noise the of value ity of the coupling between the correlated neurons. However, the exact quantity can be used to study the size, temporal and scale directional the so removed, yielding are typically tivity connec underlying the of dynamics and structure the inferring and with the aim of understanding their effect on stimulus retina, the and cortex processing sensory the in particularly studied, intensively been have neurons recorded simultaneously between Correlations models generative and correlations Noise data interaction. the neural a of effect to functional the fit analyze to us allowed directly are components whose model generative a with neurons simulating Thus, maximal. is spike single a by carried information the which in range a in lay the strength coupling SNR, measured high and low both at Second, tuning. rotation its of shift weak constraints the determining strength of the First, connection. only for potential two of revealed GLM the investigation at Further low SNR. advantageous especially is coupling the that suggesting stimulation, tion bycarried Vi’s spikes. The information increase is larger for weak informa the increased strongly GLM the in coupling the that found the tested we of dependence Vi’s Next, stimulus representation on the input direction. from H1. We null H1’s in moving grating small a this prediction by stimulating Vi while eliminating H1’s activity using H1 ablating of amplitude the only reduce Vi’sshould that We tuning. rotation verified predicts model This strength. stimulation the on excitatory, uni an revealed GLM the of filters coupling The their responses. to GLM a fitted and stimuli rotation random of during presentation activity spiking their recorded simultaneously we neurons, optic of encoding the on lobula right and left plate of the the fly and tested the of effect this in inter located H1) right and Vi heterolateral (left two ­neurons of connectivity functional the characterized We DISCUSSION neuron. each for optic the improves H1 and Vi between coupling the of directionality and strength found the Hence, Vidisadvantageous. from be would to H1 ( Vi from input increasing with decreased clearly which H1, of spike two linear ( simplified the by captured also is effect (see H1 and Vi of SNRs the between difference large nature nature cells Supplementary Results Supplementary Fig. 7 Fig. Model - directional coupling from H1 to Vi whose strength depended depended strength whose Vi to H1 from coupling directional 17

- 34– couplings Vi benefited from inputs by H1 without a concomitant flow encoding such that the information per spike is maximal maximal is spike per information the that such encoding flow , c 42 ). Thus, according to the single spike information, a coupling spike information, to single the ). Thus, according 3 , NEUR - 4 7 based approaches to understanding the role of correlations role the of correlations to approaches understanding based 3 . Correlations resulting from similar stimulus selectivity selectivity stimulus similar from resulting Correlations . 4 . These studies effectively described correlations by fitting correlations described effectively . studies These 0 , the behavioralthe, state animalofthe OSCI EN C E

- ). ). Finally, we the per information quantified flow. To characterize the coupling of these these of coupling the flow.To characterize advance online publication online advance - called noise correlation called - 37 hemispheric coupling hemispheric 3 , 9 4 , the , neurons’ the mean 1 andglobalactivity - neuron model model neuron Fig. 2 Fig. 3 8

. To . avoid e 3 - ). This This ). 8 17 based based . . This , 3 2 , 3 3 ­ ­ ­ ­

existent synaptic interaction of two neurons and captures the direc the captures and neurons two of interaction synaptic existent to Vi by a filter.single However, this can filter related be directly to an H1 from coupling indirect an replaces it that sense the in functional purely also is correlations response the underlying identi connectivity The fied eye. right and left the via stimulated independently be could that hemispheres brain opposite in located neurons identified of a pair chose we explicitly To problem, this processing. circumvent on stimulus effect and their couplings physical existent between link noise or shared fields tive recep overlapping input, feedforward common by also but actions, inter lateral by only not induced correlations reflected connectivity functional the Instead, couplings. synaptic to specific activity related However,models these previous model generative of components the constrain effectively to us allows interactions functional of organization and structure the ing areas upstream in possi performed computations outlines ble therefore and activity population the strategies decoding optimal for on constraints of formulation the permits code of the neural structure the Knowing in correlational the retina. codes population underlying connectivity functional the of structure the identified thereby and activity population neural on the correlations of effect functional the of exploration direct more a allowed models pair for account that models ­representation in single neurons. Indeed, in the visual cortex, neurons might improve the stimulus selectivity stimulus ­neurons with similar two coupling positively Moregenerally, unchanged. nearly is ­tuning tuning. Vi’s rotation improves However,Vi’scoupling the although its shift encoding, stimulus to optic assumed be might Vi different to H1 ­coupling to correspondingly, and, preferentially fields receptive respond different have H1 and Vi areas sensory in couplings positive of role The ing optic turns) show a correlation between yaw and roll rotations ous maneuvers flight (as stereotyped for example, or saccades banked self from the described mechanism during free flight, flies must experience tion that is to similar also Vi’s preferred rotation axis. Thus, to benefit stimulus representation in Vi if increased activity in H1 implies a rota stimuli. encoded the of statistics the reflects prior the if beneficial only is a Such mechanism increases. input the in noise the as increases neuron’s a on response organs from the sensory evidence might be as interpreted nectivity a prior that accounts for the missing con lateral the regime, SNR low a in Thus, connections. lateral on about is stimuli less clear, neurons more of depend responses sensory information where SNR, low at However, input. feedforward direct on more relies neurons sensory of activity the stimulus, external the about evidence strong is there which in conditions under that, cate coupling the of gain filter is reduced with stimulus These results increasing strength. indi the that finding our with consistent is which connections, lateral by than input feedforward by more driven are cortex visual the in neurons conditions, stimulus strong under that, contrast stimulus increasing with reduced is the distance traveled by a field wavepotential local induced by a spike strength stimulus the on depend cortex visual the have studies Previous found neurons that in the between correlations SNR on strength coupling of Dependence interaction. this of dependence stimulus and dynamics tionality, For the fly, the coupling filter Vibetween and H1 only improves the - rotations that simultaneously drive both neurons. Indeed, vari Indeed, neurons. both drive simultaneously that rotations - flow patterns induce correlated responses in Vi responses correlated induce patterns flow and H1. 4 3 . Thus, these studies could not establish a not establish could studies . these Thus, - wise neural interactions. The resulting resulting The interactions. neural wise - based based studies could not relate the cor 8 . The effect of the prior (coupling) of . (coupling) the prior The effect - 4 flow patterns. Thus, Thus, patterns. flow 5 . This effect suggests suggests effect This . 1 7 . Moreover, know Moreover, . t r a 35 , 4 5 . For instance, instance, For . 4 6 . . The result C I e l 4 s 4  ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ . © 2012 Nature America, Inc. All rights reserved. 9. 8. 7. 6. 5. 4. 3. 2. 1. reprints/index.html. http://www.nature.com/ at online available is information permissions and Reprints Published online at http://www.nature.com/natureneuroscience/. The authors declare no competing interests.financial and analyzed the data. F.W., C.K.M. and A.B. wrote the manuscript. F.W., C.K.M. and A.B. the designed study. F.W. performed all of the experiments Agence National de la Recherche. through the Emmy Research Training Group 1091) and the Max Planck Society. C.K.M. is funded F.W. is supported by a grant from the Deutsche Forschungsgemeinschaft (DFG, for help with the experiments and H. Eichner for reading critically the manuscript. We thank M. Walter for improving the offunctionality the LED arena, F. Schwarz Methods in Computational Neuroscience course in Woods Hole, Massachusetts. We thank E. Schneidman and G. Tkacik for important discussions during the Note: Supplementary information is available on the of the paper at http://www.nature.com/natureneuroscience/. Methods and any associated references are available in M the online version systems. sensory of variety a in connectivity specific the of consequences functional the of standing and partners analysis using generative our models will deepen under interacting of stimulation targeted stimuli, sensory chosen carefully neurons of to inputs the for Vicase as the was manipulation or and H1, direct either allows separate activation of feedforward and lateral input lines, negative such potentially as effects correlated noise. This requires a systems approach that against computations beneficial resulting the trade and connectivity underlying on the focus directly should tions correla of effects the of discussion thorough more a Thus, unclear. and precision, or rates improvepotentially these effects whether stimulus processing remain firing mean tuning, stimulus their as such neurons, single of properties the affects correlations the underlying inter­ lateral of connectivity the to which strength however, extent the cases, In most actions. the limiting factor a represent therefore might and disadvantageous to be appear neurons between couplings information of amount population whole the total by carried the restrict also neurons ­correlated stimuli preferred nected con be to likelihood higher a have tuning orientation similar with t r a  COM AU Acknowledgment

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© 2012 Nature America, Inc. All rights reserved. LED arena. Each dot was represented by a two relies on a Brownian motion stimulus in which 20 dots randomly moved on the previouslyusingmethoda cell H1rightdescribed the Receptive fields. luminance of all stimuli was comparable. The luminance intensity of the mask was adjusted to a value such that the mean elevation of the LED arena and ranged from −30 to 30 degrees alongentirehomogeneouslythe spanned apositioned itthat illuminated such mask the azimuth. was repeatedly presented during one recording. the azimuth (unilateral stimulation). Each stimulus condition lasted for 30 s and alongdegrees100 elevationto alongdegreesthefromand50 7.5 to from−7.5 direction (front to back) at a temporal frequency of 1.5 Hz. The grating ranged presented a small sine grating with a wavelength instead andof side right the rotationrandom20stimuluson the blankedVi, weon degrees moving in H1’s null were presented on the left and right side (correlated condition). Toandright side of the LED arena, respectively. test Consequently, H1’sthe same rotations effect displayed the left and right half of the same random rotation stimulus on the left visual space are uncorrelated (uncorrelated condition). For testing the GLMs, we the right side. Consequently, the rotations presented on the left and right side of sideleftofthe LEDthearena and rightthe halfof secondthe stimulus only on random rotation stimuli and displayed the left half of the first stimulus only on tions. For training the generalized linear models, we generated two independent stimulation.weak For strong and stimulation,weak wecompared threecondi for dots 21 with andstimulationstrong for grid spherical regular a on placed was aligned with the orthogonal coordinate system was rotated such that Vi’s preferred rotation axis response filter with a cutoff frequency of 37.5 Hz ( R from a mean zero Gaussian noise with an s.d. of 228 deg s other ( separate white the for profiles velocity The point two a bysented reprewas dot Each dots. white of grid regular a with paintedroom spherical large a of center the in placed was which sphere, small a by fly’seye the eled Random rotation stimulus. n random rotation stimuli. To estimate receptive fields, we recorded Vi and H1 in noise. We simultaneously recorded Vi and H1 in Gaussian mixture model to these waveforms to separate spikes of Vi or H1 from waveforms whose negative peak exceeded a sensitive threshold. We then fitted a potential all isolated first Towe spikes,kHz. detect 10 atsampled and filtered band amplified,were signals measured Thehemisphere. brain right and neurons was recorded using two 1 pupils. To get access to the brain, we opened the head werecapsule. fixed Thewith activitywax and of theirboth heads were aligned by means of theThe frontalexperiments pseudowere performed in 5–10 lobula plate) and the right H1 neuron (with its dendrite in the right lobula plate).of two lobula plate tangential cells, the left Vi neuron (with its dendrite in the Preparationleft and recording. azimuth and elevation coordinates of 0 degrees. were placed in the center of the arena with their eye facing the center point with the receptive field estimation) or 250 Hz (for the random rotation stimuli). Flies presented on a sphere. All stimuli were presented at a frame rate of 200 Hz (for along the elevation, we distorted the stimuli along the vertical axis as resolutionif spatialthey werea with 32.2 cm, the LED arena has a horizontal and vertical extend of ing242 for 16and different 96luminance degreesintensities. Given a radius of 14 cm and height of arena composed of 240 × 128 LEDs along the horizontal and vertical axis, allow Visual stimulation. ONLINE METHODS doi:10.1038/nn.3044 = 5 flies each. x , Tooverlapwebinocularspace, visualtheoffrontalblank thepart region in We compared two stimulus conditions. The sphere was painted with 256 dots R y and t Supplementary Fig. 1a i , the virtual fly rotated fly virtual the around, randomlya changing rotation axis R z werelow - noise profiles and are therefore statistically independent of each - dimensional Gaussian with a s.d. of 1.5 degrees. At each time Ateach degrees. 1.5 of s.d. a Gaussiandimensionalwith We estimated the spatial receptive fields of the left Vi cell and For stimulus presentation, we used a cylinder x axis ( - pass filtered using a 50 filteredusinga pass ≤ 1.03 degrees. To account for the missing curvature missing the forTo account degrees. 1.03 Supplementary Fig. 1c To generate the random rotation stimulus, we mod We simultaneously recorded the action potentials x ). The value of the , y and - M Ω z tungsten electrodes inserted into the left components of components - d - old blowflies ( - dimensional Gaussian with a s.d. th x - n orderlow Supplementary Fig. 1b component = 8 flies while presenting the ). 2 8 . In short, this method Inshort,this . R Lucilia sericata −1 ( t - i . The time series of pass finite impulsefinitepass ) are generated by generated are ) R x ( t - i shaped LED ) was drawn ). Flies ). The R - pass ( t i ). - ­ ­ ­ ­ estimate for log the with of the entire spike train of duration vector The k neuron and spikes on the firing rate, where of the second neuron. These dependences are expressed via linear filters by The instantaneous firing rate Poisson distribution. Thus, the spiking probability a one a detector array onto the spatial receptive Reichardt field of the correspondingthe cell yielding of output the projected we H1, or Vi to input the To estimate location ( motion predictions in each square grid. The horizontal andReichardt detector verticalarray to a motion 14 × 6 grid by atsumming all horizontalgrid and vertical by the LED arena. For further computation, we reduced the dimensionalitytotal, a 39 of× 98 thearray of Reichardt detectors covering the visual space stimulated in detector,yielding, Reichardt tuned vertically or horizontally a implements 2.5 degrees. pair Each of horizontally orneighboring photoreceptorsvertically ing starts with an array of linear photoreceptors separated by a sampling base of detectors, an algorithmic model for local motion detection Second, this signal serves as input for a GLM modeling Vi’s or H1’s spiking. onto the spatial receptive field of Vi or H1 yielding adimensional one array of Reichardt detectors. The outputs of this array are projected or H1 comprises two stages. First, the luminance stimuli are fed through a two G spatial receptive field, which we represented as vector field. arena was discretized to a 14 × 6 grid. Using linear regression, we estimated the vector describing the velocity of a single dot. The visual space coveredThe stimulus was parameterizedby as a temporalthe series of vector fields,LED with each loworder white of1.5 degrees. The velocity profile of each dot was given by a two ity of observing (at least) one spike at a Bernoulli distribution, states: in bins of duration 8 ms and 800 ms, respectively. low for optimal was performance recorded firing rates of Vi or H1 while varying both time constants. The model the performance of a linear on the contralateral side of Vi’s and H1’s receptive field were set to zero. ­sensitivity of the averaged receptive fields of Vi or H1. The motion sensitivities where time comprises enerativemodel. All visual stimuli were first fed through a two To model Vi’s and H1’s responses, we used a GLM To determine the optimal low x i = [ t θ - - k r dimensional time signal used as input for the GLM. The input signal at inputsignal The GLM. inputthe for as used signal time dimensional k noise profile with a s.d. of 20 deg s deg 20 ofs.d. a profilewithnoise = { = is denoted by i H = 0 (no spike) or - is a stimulus filter, x likelihood with respect to to respect with likelihood 1 az H x φ - ,…, k pass finite impulse response filter with a cutoff frequency of 20 Hz. 20 of frequency cutoff a with filterresponseimpulse finite pass a k i ( , , , s φ µ θ m denotes the spike train of the second neuron.second the of train spike the denotes θ h = L i is a constant offset to match the neuron’s firing rate. Assuming that . To avoid over , j , x θ ) ) and time point | ( elements, ∑ j i i x r c , j ], the neuron’s spiking up to time point ) and and ) , µ dt }. The optimal model parameters are found byparametersfoundaremodel optimal The }. ) , The generative tomodel used predict thespike trains of Vi q = 1 ms. The response z x l , ( k i − = q f k p H and is given by r L r j i + = c i − = | ( i ∑ k el = 1 (at least one spike). Thus, the likelihood for is a coupling filter quantifying the effect of the second = n h - exp( i i ( · 1 x nonlinear model mapping the input signal φ is a post r i - a ( ) i is a shorthand notation for i λ p p , fitting, we added the regularizing term V θ log( | ( i depends on the input signal preceding az x k ∑ ∑ ∑ ( ) j t ) denote the horizontal and vertical motion motion vertical and horizontal the denote ) - i k − = and high ⋅ ⋅ is denoted by 1 q f - i j i pass and high and pass - n dt i r i ) , spike filter describing the effect of preceding i t exp( | | i θ r h 1 . The number of spikes fired at + + , yielding the maximum a posteriori posteriori a maximum the yielding , , is given by t i e k i i - p − − −1 r − − pass filter time constant, we evaluated i i l 1 1 at time point + ) c h , which was convolved50 was a whichwith , 1 i + + i dt − H | | r s c i p - )) V , where ⋅ dimensional array of Reichardt i l i is given by az , ( - i q f pass filter time constants of constants time filter pass nature nature 17– ( i ∑ = n φ 1 i 19 i , , - ) ( t e j |) dimensional time signal. p 1 i θ , ( ) m and the spiking history 2 ∑ V j i m j 7 t − describes the probabil 4 = ) , , i . Time was discretized . The motion process can take two possible 1 t d r i l k i i x k p ) ) and The log The q f NEUR j i l − = ) , j i + − e 1 k j t - , V

t dimensional maximizing OSCI 1 el - xp . x t ( t likelihood likelihood i i k follows a , denoted φ r onto the ) ( i i follows − , , θ EN l j i , , d t (3) (2) (1) C th k t ). ). E - ­ - ­ .

© 2012 Nature America, Inc. All rights reserved. bu te tmls ( stimulus the about from the data under correction. Bias where ­according to eral stimulation), the coupling filter from H1 to Vi was set to zero. simulate the condition in which H1 was inhibited by a small sine grating (unilat simultaneously to account for the fictive reciprocal coupling of both neurons. To stimulus and the recorded spikes of H1. For in shown 7 Figure results Supplementary the for responses Vi’s predict To under a homogeneous Poisson process with rate with units of bits per spike. condition). The prediction accuracy is given by related condition), we calculated the log M algorithm. dataset. To maximize the penalized log We chose the parameter nature nature odel evaluation. h cross The 〈 · 〉 denotes averaging over trials. NEUR - L orltos ewe V ad 1 ee optd n 1 in computed were H1 and Vi between correlations sp OSCI ik The spike trains predicted by a GLM as directly estimated estimated directly as GLM a by predicted trains spike The e To evaluate the GLM estimated on the training dataset (uncor r C | ( - x r ) ( estimate estimate the amount by of carried information the spikes t upeetr Fg 5c Fig. Supplementary EN ) , 〈 = α q C , we modeled the cell’s spiking given the presented the given cell’sspiking the modeled we , such that it maximizes the log L E ∑ ∑ = ho i ( ( m lo i i ) ( ) ( ( g Vi r L denotes the log r x r − - , | likelihood, we applied a gradient - t likelihood on the test dataset (correlated ) ( H H q 1 1 l ) Figure − ) / / og ). This is likely a result of an an of result a likely is This ). i l L d r i = ) ( - h 7 likelihood of the spike train om , Vi and H1 were simulated ∑ 〉 ) ( i Figures 5 5 Figures r n r - i likelihood on the test ) /( t /

∑ dt i i ) r (ref. 17). and - - ms bins bins ms descent

6 and ­ ­

mal linear filter mapping filter linear mal of decoding linear used we L amplitudes. adjusted with GLMs the by generated were data simulated presented all differently, mentioned not If (strong stimulation) and 1.15 (weak stimulation). For H1, For the the chose sum value that of spikes. minimized both errors. For Vi, we recorded set the by encoded information the from deviates of error, decoding a and GLM, original the of accuracy, prediction the which of rate. We the mean firing two errors in dependence preserving calculated then cross spike bits in (measured spike per information the of estimate an gives rate firing mean is, is, gives a lower bound on the information, stimulus the of spectra power the of Comparison of value each For likelihood models. the resulting all calculated for and offset and amplitude the varied first we end, offset constant the reducing while tude more the that revealed input 5a Fig. under na decoding. inear A A R I LB k k ( - the percentage by which the information carried by the predicted spikes by the predicted carried by the information which the percentage : an encoding error, encoding an : t A y validation validation on single trials. - ) denoted by denoted ) , , provided by presynaptic elements to the modelled neuron. Simulations estimate of the amplitude amplitude the of estimate k , = b will be under be will ). The input signal input signal The ). ∫ −1 0 ∞ ). The information values were evaluated by means of a fivefold fivefold a of means by evaluated were values information The ). lo ( g 2 P For stimulus reconstruction and information estimates, estimates, information and reconstruction stimulus For v v v ) ( can be reconstructed given the spike train train spike the given reconstructed be can P f - estimated. To account for this bias, we increased increased we bias, this for account To estimated. ( / y 24 deviates from from deviates Err ˆ , r 29– onto x f enc to the GLM is only an estimate of the unknown unknown of the an estimate only is GLM the to )) 3 1 . We tested how well the the well how We tested . , quantifying for a given given a for quantifying , df L spike A . Dividing Dividing . v k was determined using linear regression. regression. linear using determined was µ of the stimulus filter filter stimulus the of , deviates from the prediction accuracy accuracy prediction the from deviates , to match the mean firing rate. To this Tothis rate. firing mean the match to x I LB , the more the stimulus filter ampli filter stimulus the more the , , , transmitted by the spikes A Err I k LB we determined the value of of value the determined we (quantified in bits s bits in (quantified dcd P , quantifying as a function function a as quantifying , v ( f ) and the estimate the and ) A A x doi:10.1038/nn.3044 k , , k k the percentage by percentage the was 1.15 and 1.35. y ( or Supplementary Supplementary z component r . The opti The . −1 24 A ) by the the by ) , k 2 A to 1.2 9 f P k , , that v ˆ , we we , ) ( A µ ­ ­ k