© 2013 Nature America, Inc. All rights reserved. San San Francisco, San Francisco, California, USA. should Correspondence be addressed to J.H.R. ( 1 height that was in reduction an action-potential attention-dependent the that Wepredicted attention. with found decrease should also potentials of action height model firing The study. burst current in the reductions in the observed as well as reported previously rate in increases attention-dependent the both for accounts that model reduced. was it that found we attention, with increase should burst firing that hypothesis the to Contrary RFs. their from away or into directed was attention when (‘burstiness’) potentials of action bursts in selective attention implicated have studies recording unit single and studies lesion pr which stream, processing visual of ventral stage the in intermediate processing an V4, area macaque in responses recorded we hypothesis, this To test stimulus. a to directed is attention when increase to expected be might rate burst then information, sensory specific, highly detecting in events relevant role behaviorally a has firing burst that evidence provided have fish electric weakly the of neurons pyramidal the and plasticity and integration central role in communication selective (RF) field properties receptive spikes isolated than features stimulus to tuning sharper exhibit potentials of action bursts cortex, and summation linear exhibit better graded more are responses nonbursting whereas stimuli, incoming to sensitivity greater exhibit mode burst in neurons thalamus, In the potentials action individual than reliably more propagate and tion informa sensory carry to shown been have they sen as in encoding, role sory privileged a have may bursts that argued have studies Previous unknown. is processing sensory in firing burst of role The populations in mediating attention. modulation, two of them previously undescribed, and implicates scaling of the responses of excitatory and inhibitory input field, this reduces height. action-potential The model thus provided a unified explanation for three distinct forms of attentional increases in firing rate and made the surprising and correct prediction that when attention is directed into a neuron’s receptive model in which attentional modulation stems from scaling excitation and inhibition. The model exhibited attention-dependent among putative pyramidal neurons in macaque area V4. We accounted for this using a style Hodgkin-Huxley conductance-based an increase in burst firing to the attended stimulus. To the contrary, we found an reduction in attention-dependent ‘burstiness’ firing of action potentials in bursts. We tested the hypothesis that when spatial attention is directed to a stimulus, this causes Attention improves the encoding of visual stimuli. One mechanism that is implicated in facilitating sensory encoding is the Emily B Anderson action-potential height in macaque area V4 Attention-dependent reductions in burstiness and nature nature Received 16 January; accepted 12 June; published online 14 July 2013; corrected online 17 July 2013 (details online); The The Salk Institute for Biological Studies, San Diego, California, USA. We describe a conductance-based Hodgkin-Huxley style neuron neuron style Hodgkin-Huxley conductance-based a Wedescribe of transmission and encoding for important is firing burst If NEUR OSCI 10 EN , 1 1 . . We compared the propensity of neurons to fire C 1 E , 2

, , Jude F Mitchell 8 , advance online publication online advance 9 . Studies in the zebra finch song system system song finch zebra the in Studies . 1 . 3– 6 . . Burst in firing cortex may have also a 5 and make a larger contribution to to contribution larger a make and 2 . In primary visual . and visual auditory In primary 7 and in regulation of synaptic 1 & John H Reynolds

2 Center Center for Integrative Neuroscience and Department of Physiology, University of California, e vious vious 1 - - .

1 ditions, we examined ISI distributions of each neuron ( neuron each of distributions ISI examined we ditions, to Hz 7.1 from increased increase). the (69.8% Hz 12.1 of neuron second the of rate firing mean the and RF), the into directed attention with increase (33.6% mean rate firing of the first neuron from increased 36.2 Hz to 48.4 Hz The attention. rate with in firing a increase robust exhibited neurons Both burstiness. in reduction attention-dependent an exhibited that neurons pyramidal) (putative broad-spiking example two show we and of triplets spikes at short interspike (ISIs) intervals doublets firing often spiking, burst of degree larger much a exhibit neurons pyramidal of narrow-spiking interneurons, broad-spiking and studies have several found examples are (10–15%) neurons of fraction small A one. to one not class is identity cell and width spiking between relationship the because here fast-spiking neurons pyramidal putative and to interneurons corresponding categories, broad-spiking and narrow-spiking into separated be can neurons V4 task. tracking attention an using RFs, neurons’ individual from away or to directed was attention when responses neural of burstiness the To investigate the role of burst firing in macaque area V4, we compared Attention-dependent reduction in burstiness RESULTS conductance. synaptic inhibitory and tory in excita increase an attention-dependent mechanism: simple tively rela a on depends modulation attentional that suggests and height, the present findings show that attention reduces burst firing and spike comparable to the reductions predicted by the model. Taken together, We hypothesized that if burst firing were critical for sensory encoding, To quantify the degree of burst firing across To the two con attention across of burst firing the degree quantify with Consistent [email protected] in vitro in ) ) or E.B.A. ( physiology, putative pyramidal neurons neurons pyramidal putative physiology, doi:10.1038/nn.346 [email protected] 13– 1 2 . We use the term ‘putative’ term the use We . 1 5 . 3 t r a ). 1 6 . . In - demanding demanding Fig. 1a Fig. C I Figure Figure e l ,

b s 1 ). ).  - - - ,

© 2013 Nature America, Inc. All rights reserved. signed-rank signed-rank test, (Wilcoxon index in this reductions exhibited neurons broad-spiking (Online Methods). As with the burst ISI-based the metric, majority of of burst firing events at short delays from longer-timescale fluctuations effects of the low-frequency out fluctuations, subtracted thereby metric isolating second, This the contribution a metric. burst developed autocorrelation-based we fluctuations, low-frequency in reduction attention-dependent this of artifact an be might firing burst in tion attention by activity cortical of feature response in ability the V4 sustained (Mann-Whitney significant was populations two the of distributions index modulation attention test, signed-rank (Wilcoxon we did not see a reduction among significant narrow-spiking neurons ( rates firing lower with neurons see test, signed-rank (Wilcoxon index burst this in by their sum. Broad-spiking neurons exhibited a significant reduction of ISIs less than 4 ms the across two attention normalized conditions, attention modulation index, which was the difference in the percentage neurons ( narrow-spiking among burstiness in reduction significant a observe test, signed-rank (Wilcoxon tion the in ISIs short ­unattended condition, of indicating a reduction in burstiness with percentage These atten higher RFs. neurons’ significantly a the had into neurons directed was attention when firing and in population found of measure this a reduction burst systematic attention. with ISIs short of fraction the in tions reduc exhibited neurons both ISIs, short of fraction the an in in increase result to Despite expected be events. would which rate, burst firing of in increase the proportion the in reduction a reflecting neurons, example our of both for ms) (<4 ISIs short of proportion in the reduction we found an attention-dependent to prediction, this could measure as an increase in the percentage of short ISIs. Contrary we would see an attention-dependent increase in burstiness, which we ( attention with fraction burst in reduction attention-dependent significant indicating also sum, by normalized ( condition.) attention either in < 4 ms ISIs have not did (Two units attention. with bursts in potentials action of fraction the in reduction dependent attention- significant indicating neurons, broad-spiking 69 among sum, by normalized ( firing. burst in a reduction of indicative condition, unattended the to relative condition attended the in function autocorrelation the of b in neurons the for scale) (log lags time short at function autocorrelation normalized the ( trials. unattended the among ISIs short of fraction higher the Note superimposed. conditions attention two the with neurons, example ( burstiness. the 1 Figure t r a  We again found no for evidence changes in burst with firing e , respectively. Note the reduction in the peak peak the in reduction the Note , respectively.

) Changes in burst fraction (ISI < 4 ms), < 4 ms), (ISI fraction burst in ) Changes Slow fluctuations in firing rate in are firing of an source Slow the important vari fluctuations broad-spiking the across ISIs short of fraction the Wequantified Supplementary Fig. 1a Fig. Supplementary c ,

C I d Attention-dependent reduction in reduction Attention-dependent ) Attention-dependent reduction of reduction ) Attention-dependent P = 0.20, f ) Changes in burst index (BI), (BI), index burst in ) Changes e l 1 7 n . To rule out the possibility that the observed reduc observed the that possibility the out rule To . a = 71). , s b P ) ISI histogram for two two for histogram ) ISI < 0.0001, n = 47). For each neuron, we also computed a burst 18 ). This reduction tended to occur among among occur to tended reduction This ). U , Fig. Fig. 1 1 P 9 test, = 0.61). The difference between burst between difference The 0.61). = . These slow fluctuations are reduced reduced are fluctuations slow These . Supplementary Fig. 2 Fig. Supplementary f P ; ; see also P 1 = 0.00097, 0.00097, = a = 0.025). 7 and and that may reflect a that may more reflect general

Supplementary Fig. Supplementary 1b n P a e c = 71). We did not not did We 71). = = 0.0012, 0.0012, = Neurons Normalized Fraction of ISIs 0.25 autocorrelation 0.05 0.10 0.15 0.20 10 20 0 0 1 2 3 4 5 0 –0.8 ). In contrast, contrast, In ). 1 5 0 P =0.0012

attention (Attend fraction+unattendfraction) (Attend fraction–unattendfraction) Fig. 1 Fig. –0.6 10 e ). ). - - - - ; Attend awayfromRF Attend intoRF

15 –0.4 Time (ms) Time (ms) 10 among narrow-spiking neurons ( neurons narrow-spiking among examine examine how this modulates burst firing. We modeled synaptic inputs modulating in channels two neurons pyramidal in activity these bursting of role the work detail Previous in spiking. examined burst to contribute that channels sodium persistent and channels potassium muscarinic includes model The calcium-dependent adaptation. spike and several hyperpolarization after regulate as that channels well as potentials action drive that conductances voltage-dependent Hodgkin-Huxley–type including pyramidal CA1 neurons in firing burst of model single-compartment a on firing. burst its modulate might tion, in increases synaptic activity, resulting in mean depolariza increased attention-dependent how evaluated and model spiking burst exhibited that Hodgkin-Huxley–style conductance-based a developed this, we formalize To depolarization. neuronal in increase dependent attention- an from result potentially could observed we burstiness fulness to response in depolarization burstiness less exhibit neurons pyramidal Cortical attention of model conductance scaled The test, signed-rank (Wilcoxon metric ness bursti either with burstiness in reduction significant a observed we neurons, and broad-spiking of narrow-spiking population combined the Across rate. mean their in differences from stem classes between neurons, to broad-spiking it making out rule difficult that differences among than greater was neurons narrow-spiking among rate firing mean the Furthermore, burstiness. in reduction a observe to ability our limiting potentials, action of bursts fire to tend not do neurons narrow-spiking However, firing. burst of modulation attentional in difference a type–specific cell may reflect population neuron spiking ( metric either using narrow-spiking neurons showed modulation of significant burstiness each in collected ( metric either monkey, using individual neurons broad-spiking among significant were 20 We changes in inputsynaptic attention-dependent incorporated to ( attention of model conductance scaled The This reduction in burstiness among broad-spiking, but not narrow- –0.2 25 Example neuron 2 Example neuron 1 2 . This suggests that the attention-dependent reductions in in reductions attention-dependent the that suggests This . 2 advance online publication online advance . The model includes several active conductance channels, channels, conductance active several includes model . The 30 0 100 2 35 0 and during the transition from sleep to quiet wake quiet to sleep from transition the during and 0.2 1 40 1 P > 0.05, Wilcoxon signed-rank test). signed-rank Wilcoxon 0.05, > f d b Neurons Normalized Fraction of ISIs autocorrelation 0.02 0.04 0.06 0.08 1.00 10 15 0 2 4 6 0 0 5 –0.3 1 5 0 P <0.0001 P –0.2 = 0.67). Reductions in burstiness burstiness in Reductions 0.67). = (Attend BI+1unattend1) (Attend BI+1–unattend1) 10 –0.1 2 2 P . P

< 0.05). Neither monkey’s Neither < 0.05). 15 < 0.05). < Time (ms) nature nature Time (ms) 10 0 20 0.1 i. 2 Fig. 25 NEUR Example neuron Example neuron 0.2 30 a ) is based based is ) OSCI 0.3 100 35 EN 0.4 2 40 C 2 E - - -

© 2013 Nature America, Inc. All rights reserved. normalized by their sum. Among the broad-spiking neurons, neurons, broad-spiking with the burstiness of measure this in Among reduction significant a sum. found we their by conditions, attention two normalized the across ms <4 ISIs of percentage the in difference the calculated then and silence of ms 200 by preceded were that spikes identified we neuron, each For burst. to propensity to a yield ing change spike in rate the not neuron’swould be expected were zero,identically mechanisms that modulate burst firing by vary after of neurons periods of burstiness the modulated attention whether ined depolarization subthreshold reduce should the neuron’s to propensity burst. of To test we this, exam modulation attentional spiking no which occurred, in time of periods after to even that led This prediction the depolarization. by activated directly was model our in rate. burst in reductions and rate firing in increases attention-dependent for tion physiological the within explana unified a simple, change offers thus model The gain observed. we range a Hz, 39.9 to Hz 27.4 from 1c Fig. ( experimentally com observed we was what to parable that burstiness in reduction a to rise gave conductances neurons pyramidal in firing potassium burst reduce to shown been has which muscarine-sensitive channel, the rate. activated firing also in depolarization, increase Depolarization net attention-dependent a an in caused resulted which conductances synaptic inhibitory neurons inhibitory and excitatory both of activity the increases attention that posits which attention, of model malization activity increases neurons inhibitory attention and pyramidal both among spatial that evidence with consistent conductances, inhibitory and excitatory both increased portionally ‘Poisson-spiking’ of neurons and excitatory inhibitory populations across summed inputs synaptic conductances, inhibitory and excitatory fluctuating as condition. attended the and condition unattended the in height the between shift R ( inactivation sodium-channel on height spike of dependence this to addition In amplitude. higher of When channel. the blocking not is particle variable, inactivation a function as sodium the of plotted is action-potential Extracellular inactivation. sodium of levels matched for height action-potential in reduction attention-dependent Inset, ± 1 s.e.m. RF. the indicates into Shading directed was attention when curve height spike of shift downward the in reflected height, in reduction spike-independent predicted the Note height. action-potential extracellular in reduction ( condition. unattended the to relative condition attended the in function autocorrelation normalized the of peak the in reduction the by shown as neurons, V4 our in seen burstiness in reduction attention-dependent the reproduced Ca slow Ca high-threshold g conductance; conductance; sodium K rectified g (bottom). conditions (blue) unattended and (red) attended the in model the by produced traces intracellular example and (left), inputs synaptic fluctuating ( Figure 2 nature nature test, signed-rank (Wilcoxon attention c a Kca Na s ) Model prediction of an attention-dependent attention-dependent an of prediction ) Model and (right) neuron model of ) Schematic = 0.96 attended, attended, = 0.96 The voltage-dependent muscarine-sensitive potassium channel channel potassium muscarine-sensitive voltage-dependent The and excitatory in increases attention-dependent model, the In , transient Na , transient , fast Ca , fast 2+ ,

d 20 Scaled conductance model of Scaled conductance attention. NEUR -activated K -activated ). At the same time, model neuron’s firing rate increased increased rate firing neuron’s model time, same the At ). + ,

conductance; conductance; 21 neuronal silence. As the firing rates during these periods periods these during rates firing the As silence. neuronal 2+ , 2 g -activated K -activated 5 Ka OSCI . The attention-dependent increase in model input input model in increase attention-dependent The . + , A-type K , A-type 2+ conductance; conductance; conductance; and and conductance; R g EN + g Leak s conductance. ( conductance. = 0.95 unattended), the modeled predicted an attention-dependent reduction in spike height. This can be seen by the vertical vertical the by seen be can This height. spike in reduction attention-dependent an predicted modeled the unattended), = 0.95 KM C E , leak conductance; conductance; , leak , muscarinic K , muscarinic g +

+ conductance; conductance; Nap conductance; conductance; advance online publication online advance , persistent , persistent g Kdr h , delayed , delayed 2 , 0.6 ms before the peak of the action potential. potential. action the of peak the before ms , 0.6 3 b . . We pro attention that assumed g ) Model ) Model sAHP + P

g h = 0.0061). = Ca , was large, more sodium channels were available to participate in the action potential, leading to spikes spikes to leading potential, action the in participate to available were channels sodium more large, was ,

Fig. 2 Fig. 1 2 a , and with the nor the with and ,

b 50 mV g g g g ; compare with with compare ; 11 50 ms e i e i I

, syn Synaptic currents representing representing 2 x 4 = g .

i Attention gain ( g t )( e Ref. 23 ( V t )( – 75) V – 0) ------+

reached during action-potential generation. action-potential during reached state depolarization maximum the below both are which potentials, which drove the neuron toward the and excitatory reversal inhibitory reduction increased excitatory reflected and inhibitory conductances, ( inactivation of sodium-channel independent was that in height a reduction However, observed attention. we with also tion inactivation of sodium channels stemming from increased depolariza additional from part, in resulted, amplitude spike in reduction This RF. the into directed was attention when curve spike-height of shift In attention. with height action-potential in decrease additional an of to this spike effect, the history–dependent model made the prediction studies intracellular of findings the with consistent potential, action preceding the during depolarization the by caused Na of inactivation the from arose height action-potential in reduction activity-dependent This potential. action prior a after immediately spikes for height action-potential in reduction a dicted pre model the conditions, attention of both In (preISI). ISI function preceding a as amplitude action-potential extracellular height neuron’s action-potential in ( reduction prediction attention-dependent novel an the made of model the modulation, attentional of firing. burst of reduction yield to sufficient is depolarization subthreshold which in proposal, our with consistent is result This mechanism. dependent test, signed-rank Wilcoxon silence; after −0.094 versus times all across −0.029 (median periods in enhancement quiescent during burstiness of significant modulation attention-dependent a this found we without Instead, periods activity. after spiking modulation a this of expect strength would the we in reduction, decrease this in essential were mechanisms the computing difference of these measures by divided by their sum. If spike-dependent quiescence, of ms 200 least at following periods versus periods time all across measure this of reduction dependent Fig. 2 Fig. In addition to providing a simple explanation for these two forms forms two these for explanation simple a providing to addition In We also compared, on a cell-by-cell basis, the strength of the attention- Figure 2 Figure g g g g g g g g g sAHP Ca Kc Ka KM Nap Kd Na Leak Model neuron c h a r ). This is illustrated in in illustrated is This ). corresponds to the probability that the sodium inactivation inactivation sodium the that probability the to corresponds Ref. 22 c , this additional reduction is reflected in the downward downward the in reflected is reduction additional this , P b c < 0.0001 (Spearman’s rank correlation), correlation), rank (Spearman’s < 0.0001 Normalized spike height Normalized 0.94 0.95 0.96 0.97 0.98 0.99 1.00 autocorrelation 0 2 4 1 Unattend P Unattend 000) agig gis a spike- a against arguing 0.0001), < Figure 2 Figure 10 Spike height 0. 0. 1. Attend 8 9 0 Probability 0.60 Attend 20 c , which shows the model model the shows which , 10 preISI (ms) Time (ms) ( h 0.65 ) Na + inactivationgateopen 30 t r a 26– Unattend 0.70 2 9 Fig. 2 Fig. . In addition addition In . Attend C I + 40 100 channels channels 0.75

c ). This ). This e l

s  - -

© 2013 Nature America, Inc. All rights reserved. interneurons has been shown to arise largely from the short duration short largely from the shown to arise been has interneurons cellular studies, this reduced adaptation among fast-spiking inhibitory than did narrow-spiking neurons, as a function of ISI ( height neurons stronger exhibited in also reductions action-potential broad-spiking The neurons)). (narrow-spiking 0.9726 and neurons) Whitney dependent height reduction than did narrow-spiking neurons (Mann- history– spike stronger significantly had neurons broad-spiking V4 hypothesis, this with neurons. Consistent do than tion broad-spiking adapta spike-height less exhibit therefore should they interneurons, If narrow-spiking neurons largely correspond to fast-spiking inhibitory interneurons inhibitory amongfast-spiking adaptation height neurons) pyramidal tive fast-spiking inhibitory interneurons) and broad-spiking neurons (puta neurons (putative narrow-spiking potentials: action duration of their neurons). narrow-spiking 52/67 (77.6%) broad-spiking neurons (2 excluded) and 22/43 (51.2%) test, signed-rank (Wilcoxon adaptation height significant test, bution of HAIs was less significantly than one (Wilcoxon signed-rank adaptation was also highly significant across the population: the distri test, signed-rank within 4 ms by another spike, which was highly (Wilcoxonsignificant preceded were that potentials action of height the in decrease 13% a neuron shown in example the For ms). (<4 preISIs short with potentials action all of height-adaptation index a (HAI), computed defined as then the we mean normalizedneuron, height each For unadapted. largely therefore by that were long preceded ISIs potentials ms) and (>100 action were the of height mean the by trough) to peak from difference (voltage height spike normalized we Here decreased. ISI the as amplitude in ( neuron V4 example an for observed we As primate. awake the in examined been not had edge condition. ­reduction in spike height attention predicted by the model, which to and our knowl ISI preceding We of first considered whether we would each observe the activity-dependent function of a potentials as action neuron measured we predictions, these test To history spike on depends shape potential Action (Mann-Whitney significant was neurons broad-spiking and narrow-spiking among adaptation height between difference The ( adaptation height significant with neurons to correspond circles, (orange neurons broad-spiking than squares, (green potentials action neurons’ spiking Narrow ms). (<4 preISIs short with potentials action all of height normalized mean the taking by computed was index adaptation height the correlation, rank (Spearman’s ( to correspond regions shaded Thin preISIs. shorter at reduced increasingly grew amplitudes Spike ms. > 100 ISIs by preceded spikes unadapted largely of amplitude the to normalized all were amplitudes Spike legend. the in indicated (preISI) ISI the following response, stimulus-evoked the of period sustained the during neuron example the by evoked potentials action all of waveform mean the to corresponds trace Each neuron. individual an for shape action-potential of dependence history spike Inset, 8 ms. to correspond regions Shaded height. spike unadapted the to normalized populations, spiking broad- and narrow for heights spike average population show lines yellow and Green neurons. broad-spiking and narrow- among adaptation height ( neurons. broad-spiking do than adaptation height 3 Figure t r a  sodium inactivated fewer in results which potentials, action their of b

) Significant correlation between mean waveform duration and spike HAI HAI spike and duration waveform mean between correlation ) Significant Two classes of neurons can be distinguished in area V4, based on the P << and 0.0001), 74/112 neurons exhibited (66.3%) individually

C I Narrow-spiking neurons show less spike history–dependent history–dependent spike less show neurons Narrow-spiking U test, test, e l s P Figure Figure 3 P << 0.0001). The effect of spike history–dependent of The << effect 0.0001). spike history–dependent 000; ein A: .36 (broad 0.9336 HAI: median 0.0001; < ± ± 1 s.e.m. of the interpolated waveform traces. traces. waveform interpolated the of 1 s.e.m. size, bin means; population the around 1 s.e.m. 1 2 a . Intracellular studies have found minimal minimal found have studies Intracellular . , , the HAI was 0.87, which corresponded to P Fig. 3 Fig. < 0.0001, < 0.0001, a ), action potentials were reduced reduced were potentials action ), n R = 43) were less adapted adapted less were = 43) n s = 69). Darker symbols symbols Darker = 69). = −0.39). For each neuron, neuron, each For = −0.39). a ) ) Timeof course U test, test, Fig. 3 P < 0.001). < 0.001). P a < 0.0001). P ). In intra < 0.001; 0.001; < - spiking spiking 28

,

30

, 3 1 - - - - - .

nels, nels, which deinactivate over time. During this recovery fewer period, chan sodium inactivate would potential action each because is This in rate increase firing would add to in this reduction spike amplitude. action-potential amplitude reduce would in turn which currents, cause in hyperpolarizing an increase would conductances synaptic in increase an result, a As tial. poten action the during reached depolarization peak the to relative hyperpolarized, are potentials reversal their because is This height. action-potential reduce to predicted con were activate, voltage-gated they as ductances well as conductances, These conductances. synaptic increase to assumed was attention First, both. for evidence observed we and mechanisms, attention-dependent distinct two by −0.0035, narrow −0.0034, = AHI median population, entire test; signed-rank (Wilcoxon attention with height cantly less than zero, corresponding to a reduction in action-potential signifi was distribution the population, the Across height). tended unat + height attended normalized height)/(normalized unattended normalized − height attended (normalized of: bins) preISI (across into RF.the was directed mean The the AHI was computed by taking attention when height spike in change the quantified which (AHI), index height attention an computed we population, the across effect attention this of distribution the examine To across bins. preISI condition, matched attended the in elicited those than amplitude in potentials elicited in the unattended condition were consistently larger spiking neuron ( broad- example an for We this attention. show action- with height in potential reduction small a found we model, our by predicted As height action-potential in reductions Attention-dependent ( height spike in reductions stronger exhibiting neurons broader with duration, action-potential mean and HAI between correlation cant channels Fig. 3 Fig. The proposed model predicted that be would spike reduced height predicted model The proposed b ; ; Spearman’s correlation, rank 3 b a 2 advance online publication online advance

. Consistent with this finding, we also observed a signifi a observed also we finding, this with Consistent . HAI Normalized spike height 1.00 0.95 0.96 0.97 0.98 0.99 1.00 1.01 0.75 0.80 0.85 0.90 0.95 1.05 Fig. 4 P P Significant correlation = 0.0041). = <0.0001 Broad a Narrow ). Consistent with the model prediction, action Narrow 200 50 R P 3 3 s = 0.00063; broad −0.0033, −0.0033, broad 0.00063; = Waveform duration =–0.39 . . In addition, the model predicted that an Normalized height –0.6 –0.4 –0.2 0.2 0.4 preISI (ms) 0 –200 300 100 P < 0.0001 < 0.0001 Duration 0

( µ s) nature nature 400 >100 ms, <4 ms, ( 200 4–32 ms, 32–100 ms, µ s) 150 R

Broad n s = −0.39). 400 = 3,175

n n NEUR = 25 = 470

n = 1,958 500 5 P OSCI = 0.019; 0.019; = EN C E ------

© 2013 Nature America, Inc. All rights reserved. cant (Wilcoxon signed-rank test, test, signed-rank (Wilcoxon cant signifi was height spike in We ms. 100 and reduction the that found ms 50 ms, 25 ms, 10 adaptation of periods shorter over count spike We at longer intervals. to equate the analysis occurring thus repeated to than spikes more contribute reduction be to expected spike-height would intervals shorter within occurring spikes additional window, ( in monkey each significant tion (Wilcoxon signed-rank test, ( neuron example the for both AHI, in reduction attention-dependent significant a find to continued we ( ditions con attention two the across distribution spike-history the matched which spikes, more had condition attention whichever from spikes discarded randomly we bin, each Within follows. as conditions, tion atten across history spike equated then We attention. with higher to condition shifted the right with attention, rates firing because were attention each during window adaptation the within falling rates ing ( window adaptation 200-ms a in potential action each of we number the that preceded spikes counted to potentials action by caused from recover the the adaptation prior spike ( observed we which over period the exceed to conservative estimate of the spike-adaptation window, which we chose window, adaptation Weattention conditions. across 200 ms used as a this within of spikes number the to equate designed analyses control relatively short time periods ( attention conditions. Spike history–dependent adaptation occurs over action-potential equate to designed methods several spike in reduction amplitude. To attention-dependent control for of spike history–dependent adaptation, we sources used hypothesized adaptation. spike-height in increase an via indirectly, height action-potential reduce also would attention conductance, synaptic to amplitude by caused anyin increases in reduction action-potential addition in that predicted model the rate, firing As window. increases attention adaptation this within fall to spikes more causing average ISI, the reduce would rate firing Increasing spike- adaptation. as height known is phenomenon This amplitude. its reducing tial, poten action next the to contribute to available be would channels ( right. the on shown are adaptation history–dependent spike in differences for control to procedure, matching spike-history this applying after conditions, attention across equated counts, spike of Distributions history. spike preceding in matched were that potentials action compare to us allowed This spikes. more had condition attention whichever from spikes discarded randomly we bin, each within conditions, attention across history To spike equate attention. with higher were rates firing because attention with right the to shifted was distribution The (left). conditions (blue) in shown neuron example the for conditions, to correspond regions Shaded bins. preISI matched across 4 Figure nature nature history–dependent spike measurable observed we which over c ) Action-potential height after the application of the spike-history–matching procedure illustrated in in illustrated procedure spike-history–matching the of application the after height ) Action-potential To test the model, it was therefore essential to isolate these two two these isolate to essential therefore was it model, the test To The above analysis equated spike count across the prespike period period prespike the across count spike equated analysis above The

Fig. NEUR Attention-dependent reduction in action-potential height. ( height. action-potential in reduction Attention-dependent

4 OSCI b ). After equating recent spike history in this manner, this in history spike recent equating After ). EN C E advance online publication online advance Figs. 2c P < 0.05). Within the 200-ms adaptation adaptation Within < 200-ms the 0.05). P P = 0.0044). Reductions in AHI were Fig. 4 Fig. < 0.05) across all windows. all across 0.05) < and Fig. 4 Fig. 3 b a a ). The distribution of fir of distribution The ). c . Firing rates during the 200-ms period preceding each spike in the attend RF (red) and attend away away attend and (red) RF attend the in spike each preceding period 200-ms the during rates . Firing ). Therefore, we conducted ), and across the popula the across and ),

± history across across history Fig. Fig. 3 1 s.e.m.; bin size, 4 ms. ( 4 ms. size, bin 1 s.e.m.;

a ). ). First, a ) Action potentials elicited in the attended and unattended condition, condition, unattended and attended the in elicited potentials ) Action ------

rate could have contributed to spike-height adaptation over longer longer over adaptation spike-height to contributed firing have could mean rate in differences that possible is it However, ­adaptation. observed reduction in burstiness with attention contradicts the the contradicts attention with burstiness in The reduction burstiness. of observed modulation attention-dependent an for dence evi first the provides It ways. several in attention underlying nisms mecha neural of the understanding our advances study present The DISCUSSION model. by the predicted as height, action-potential reduced attention adaptation, history–dependent spike in differences ms, for ing account 25 after that, ms, conclude Wethus 10 ms). 200 of and ms bins 100 ms, 50 for test, signed-rank Wilcoxon one-tailed all For windows, spike windows. height was significantly reduced spike-adaptation by attention of ( range full the across analysis test, signed-rank Wilcoxon (one-tailed attention by reduced significantly was height action-potential that found we control, spike-history and firing-rate combined this performing a After window. in spikes spike-adaptation 200-ms preceding of number the in matched exactly were that spike history by from selecting recent subsets these trials of action potentials equated then we trials, of subset rate-matched this selecting After conditions. attention two the across rates to firing match procedure exactly rate-matching the performed test, we First, controls. two signed-rank Wilcoxon (one-tailed P magnitude in significantly reduced still were heights action-potential that found we ner, man this in rates matching After data. AHI trial-matched resulting the averaged and times 100 process selection random this repeated we neuron, For each trials. rate-matched resulting the from AHI the computed Wethen conditions. attention across distributions count this spike for counts, matching all thereby observed spike- identically Werepeated conditions. attention across identical was count spike from at the more of the number until each numerous trials condition trials other, the discarded than we randomly condition one attention in count spike given a with trials more had frequently we As tions. of numbers matched with spike counts in attention trials condi both attended or unattended stimulus paused with the RF. We the then when selected occurred that potentials action of number the counted we First, rate conditions. attention als that across were in matched firing Wetime periods. controlled for this by recomputing the AHI over tri = 0.023; median AHI of −0.0016). As a final test, we combined the the combined we test, final As a −0.0016). of AHI median 0.023; = b ) Method for equating recent spike history across attention attention across history spike recent equating for ) Method P = 0.023, median AHI −0.0021). We repeated this this We repeated −0.0021). AHI median 0.023, = b . t r a

C I

P < 0.05, e l s  ------

© 2013 Nature America, Inc. All rights reserved. tory conductances (whose reversal potentials are more hyperpolar more are potentials reversal (whose conductances tory inhibi in increases conjoint However, increased. are conductances excitatory only which in model a in reduction observed be can the firing and burst in height spike in reduction attention-dependent necessary: strictly not is This tandem. in inhibition and excitation tasks demanding of attention- in the during performance monkeys methods recording intracellular using directly tested be could prediction this difficult, technically Though depolarization. subthreshold heightened of ods peri from result firing burst in reductions attention-dependent that propose we Rather, burstiness. in reductions for account to models these in featured mechanism burst spike-dependent the of necessity to necessary not are generate reduction the in activity observed burstiness. This argues against the spiking in of differences periods Thus, after silence. undiminished were that burstiness in reductions attention-dependent significant However, we observed our findings. compartments dendritic and somatic between potentials action of back-propagation incorporate system oculomotor by the generated as such those signals, feedback selective by spatially mediated is attention, selective of case the in that, depolarization in increase an common in have arousal and attention that hypothesize arousal in changes mediating those with part, in shared, are attention selective of mechanisms that hypothesis the support thus arousal of levels elevated with reduced be depolarized are they when bursty less become neurons pyramidal cortical that finding the with muscarinic channels, reducing burst these firing. This proposal is activate consistent depolarization in increases attention-dependent that channels sodium persistent and fast ductances con potassium muscarinic voltage-gated between on the interaction was inspired by a in part, where previous model burst depends, firing of model attention. This conductance model the scaled we developed adopted. analyses the of sensitivity the in differences from the stems likely of difference the differ, studies conclusions two the although Thus, metric. second we this when applied firing burst in reduction observed the detect not did We here. we used comparison within-cell the than sensitive is less which the relationship between raw burst rate and firing rate across neurons, study that in used metric the applied we when Indeed, firing. burst in a reduction with attention-dependent increases in firing rate, potentially masking the raw rate of spikes with short ISIs. This would be for a expectedchange evidence and not did find tofiring increase computation. cortical of aspects these for consequences important have to likely are study current the in observed firing burst in changes attention-dependent integration in other of aspects computation, cortical including plasticity implicated been also has firing Burst stimuli. attended of sig naling neuronal improve to as so reduced is that variability response of source a are bursts that view the with consistent instead is firing task- are stimuli ­relevantwhen and attention is directed increase toward them. The to reduction in burst bursts expect would we spikes, than isolated fidelity nel. greater with If information conveyed bursts chan communication privileged a are bursts that view held widely t r a  in strongly contribute did conductances) excitatory are than ized

In the scaled conductance model of attention, attention increases increases attention attention, of model conductance scaled the In that such as ‘ping-pong’ models of burst firing, models Alternative burstiness, in reduction attention-dependent this for Toaccount burst of modulation attentional examined study previous One C I 1 , e l 9 3 and communication to select subpopulations 4 , we did not detect a reduction. They reduction. a detect not did we , s 4 0 . 3 6 . 20 37– , 2 1 3 . Burstiness has also been found to to found been also has Burstiness . 9 , could also potentially account for account potentially also could , 2 3 1 4 . The present findings findings present The . . That study measured . measured That study 2 2 . Our model posited posited model . Our 3 4 also examined examined also 8 , 7 9 . . Thus the , , synaptic 3 5 . We . ------

6. 5. 4. 3. 2. 1. reprints/index.htm very-low level phenomenon, action-potential shape, to a high-level high-level a to shape, action-potential phenomenon, level a link very-low finding this does only Not neurons. V4 narrow-spiking and broad both among height attention- action-potential in measurable reduction yet dependent small a height. found we action-potential this, with in Consistent reduction attention-dependent an prediction novel of the made model our Specifically, state. cognitive unde mechanisms neural about inferences make to the first study in the nonhuman primate to use changes in spike shape cellular action-potential height in the rat tude provide a ‘window’ into the state that variables modulate spike ampli to models conductance-based with coupled shape, action-potential neurons inhibitory) (putative and narrow-spiking excitatory) (putative rates of broad-spiking both firing the in increases causes attention that finding by the supported neurons inhibitory drive neurons excitatory that fact the from expected be might as inhibition, in changes corresponding by accompanied be to found often are excitation in changes that ing show experiments with consistent also is inhibition in increases by observed accompanied experimentally are excitation in the increases that assumption The in range. rate spike in increase dependent attention- the keep helped and reduction height spike to model the Reprints and permissions information is available online at at online available is information permissions and Reprints The authors declare no competing interests.financial J.H.R. wrote the manuscript. physiology data and contributed to the burst-reduction analyses. E.B.A., J.F.M. and E.B.A. analyzed the data and built the model. J.F.M. most collected of the help with animal care. We thank K. Sundberg for help in data andcollection, C. Williams and J. Reyes for (J.F.M. and J.H.R.) and The Gatsby Charitable Foundation (E.B.A. and J.H.R.). This work was supported in part by US National Eye Institute grant EY13802 Note: Supplementary information is available in the the pape the of in version available are references associated any and Methods M attention. of understanding toward the longstanding goal of a achieving mechanistic, reductionist step an important takes therefore study This empirically. to tested be attention of model channel-level first the is which model, proposed phenomenon, attention, it is a specific and surprising prediction of the COM AU Acknowledgment

ethods The second The innovation second in our study was the use of the extr T Reich, D.S., Mechler, F., Purpura, K.P. & Victor, J.D. Interspike intervals, receptive Mechler,intervals, F.,D.S., K.P.Interspike Victor,Reich, Purpura, J.D. & by representation stimulus Improved C.E. Schreiner, & C.A. Atencio, J.Y., Shih, coding cortical in differences angle: another From A.B. Bonds, & J.M. Samonds, and simple of discharge the in Patterns C. Morrone, & L. Maffei, A., Cattaneo, relay. thalamocortical of modes dual firing: burst Tonicand S.M. Sherman, systems. sensory in firing Burst F. Gabbiani, & R. Krahe, fields, and information encoding in primary visual cortex. inprimary (2000). encoding 1964–1974 information and fields, cortex. auditory primary in (2011). 1908–1917 intervals interspike short oforientation. discrimination (2004). coarse 1193–1202 and fine between (1981). cells. cortical visual complex Neurosci. (2004). 13–23 H 26– P O ET 31 R R I , CONT NG 4 advance online publication online advance 2

24 . Although a few studies have examined changes in changes extra have a examined . few studies Although FI , 122–126 (2001). 122–126 , N l RIBU . A NC r . T IA s I ON L I NTE S rc R Sc Ln. Bo. Sci. Biol. B Lond. Soc. R. Proc. R 1 2 E . S T S 42– online version of the pape

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© 2013 Nature America, Inc. All rights reserved. in the stimulus-free fixation toperiod reduce the effects of long-timescale drift normalized these measures by the mean height or duration of action potentials 0.05 25 fromwaveforms the spline-interpolated we duration, we subtracted the trough from the peak of the waveform. To calculate waveform digitized the waveforms to 25 which system, ProcessorAcquisitionMultichannel Plexon the from obtained M the targets resulted in a liquid reward. of identification Correct balanced. symmetrically were stimulinontarget and target the forpositions ending and starting the biases, spatial developmentof Totarget. the cued minimize each to saccade a make to monkey the signaling eccentricpositionsstopping.and Atfixationpoint, pointthethis disappeared, RF. The stimuli then paused for 1,000 ms before moving to a final set of equally and unattended trials, and by preventing all but one stimulus from entering the twoattentionthe conditions, by usingidentical the trajectories attendedthe in outside the RF. The trajectories wereneuron’sothers the the designedof andcenter RF the at stimulito the ofmatch one placed This stimulation history across trajectoriesthat positioned stimulithe at four new, equallyeccentric positions. luminance. All four stimuli then moved along independent, randomly generated neurons’ RFs. One or two stimuli were then cued as targets by a brief elevationringof equaleccentricity, in suchselected that of stimuli theall fell outside of the positions of the stimuli were selected to fall at regular intervals along an invisible based on the subspace reverse correlation map to produce a strong response.(40% The luminance contrast). The color and appearedstimuli orientation Gabor identical four ms, 200 After trial. of the of theseend the until stimuli were chosen The monkeys began each trial by fixating a central point and maintained fixationhas been used to study attention in humans T (240 Hz, ETL-400; ISCAN, Inc.). NIMH Cortex software. tion, 120 Hz) placed 57 cm from the eye. Experimental control was handled by ona computer monitor (Sony Trinitron Multiscan, TC, 640 × 480 pixel resolu Stimulus presentation and eye movement monitoring. selected to excite the best-isolated units. rons were recorded simultaneously, the features and location of stimulusthe locationstimulus that wouldwere elicit a robust visual response. When multiple neu single a determineto flashedwere GaussianGabor2°)degree, half-width, per Gabor stimuli (eight orientations, six colors, 80% luminance contrast, 1.2 cycles mappedusing subspacea reverse correlation procedure cluster from noise and other units. After isolating one or more neurons,three principal componentsRFs were of their waveform shape formed a clearly separable identifiedisolatedasanalysisSorter, offline in (Offline Plexon, Inc.)firstthe if which was set to exclude noise, were stored for later off-line analysis. Units were Processor system (Plexon, Inc.). Spike waveforms crossing a negative threshold, cutoffsatHz 154andkHz), 8.8 and stored usingMultichannel the Acquisition 3-db filter,6-pole, (Butterworth extracellularly,filteredrecorded were signals neurons could be isolated based on action-potential waveform shape. Neuronal tungsten(FHC)electrodesthat were advanced untilpotentialsaction ofsingle ing following procedures as described previously care and use of animals in research. Monkeys were prepared for humaneNationalthe neuronal InstitutesforUS guidelinesHealth conformedto ofand record CommitteeUse and Care InstituteInstitutionalAnimal Salk the approvedby E similar to those used in previous publications. statistical tests were run to determine sample size a priori. The sizes we chose are P tests were performed and the results in each were significant at the ent in parametric tests. Statistical analysis. ONLINE METHODS nature nature in action-potential shape ( ask and stimuli. values greater than 0.0001 have been rounded to two significant digits. No digits. significant two to rounded been have 0.0001 than greater values lectrophysiology and receptive field characterization. field receptive and lectrophysiology aueet f cinptnil shape. action-potential of easurement Eye position was continuously monitored with an infrared eye tracking system µ s and then calculated the time from the trough to the peak the to trough the from time the calculated then and s NEUR OSCI Two monkeys performed a multiple-object tracking task that Nonparametric tests were used to avoid assumptions inher EN P values are reported for each test, except where multiple C Supplementary Fig. 3 E µ s. To calculate the height of an action potential, 47 cin oeta wvfrs were waveforms potential Action , 4 8 and nonhuman primates 1 ). Two broad-spiking neurons 2 . Recordings were made from 12 Stimuli were presented , All procedureswere All 4 µ 6 s to a resolution of resolution a to s . In. thisprocedure, P < 0.05 level. 1 2 . We then . 12 , 16 , 1 7 - - - - . In addition, four units were excluded because their waveforms did not have the (Mann-Whitney stimuliGabor the ofonset beforethe ms 250 rateaveragedoverthe firing ous spontane mean the than greatersignificantly was and period pause stimulus directed away from the RF exceeded 5 Hz, averaged over the final 500 ms of the attentionwas when trials on response whose units to analyses patterncharge adultmacaques ( Inclusion criteria. from 225 120 fromduration in ranging those as narrow-spiking defined neuronswith tion, based on the trough between the two modes of the waveform duration distribu Hartigan’s dip test, and also across the subset of these cells with significant visual responseswaveforms( spikebiphasic ( with cells bution of spike-waveform duration was significantly bimodal across all isolated neurons from putative fast-spiking interneurons in the neocortex basis of studies showing that this measure best distinguishes putative pyramidal waveformaverage the of peak the to trough on waveform duration. We defined waveform duration to the be time from the dividedneurons into narrow-spiking andbroad-spiking subpopulations based Broad-spiking and narrow-spiking classification. HAI analyses. did not have any action potentials with a preISI < 4 ms and were excluded from fluctuations, we also applied a spike-jitter analysis ( analysis to further isolate attention-dependent reductionsnormalizedautocorrelationadditionalcontrolwithanfilter above.As defined in burst firing from slow The burstiness index (BI) was computed as the sum of the product of the described Fourier transform of the following equation: ing rate over the neuronal population rangehavetheHz,where we10 previously reportedshared fluctuations fir in autocorrelationbelowfluctuationsrate the contributionsfromeliminate toto changes in low-frequency fluctuations in firing rate, we defined examplea neuronsfilter in that served for depicted function, autocorrelation normalized the defined This lag. time After this subtraction, we normalized the result by the shuffle predictor at each stimulus. the presentationofrepeated from result that spiking in fluctuations trial-locked anyremovedpredictor, we the subtracting By neuron. individual predictor is defined as the mean cross-correlation across all pairs of trials of an shuffle condition.Thethatpredictor for shuffle Wethe subtracted trials. then neuron separately for each attention condition for the correctmetric. two Forof thefour secondtracking measure, we calculated the autocorrelation function­calculated the ofpercentage the of ISIs < 4 ms, and an autocorrelation function–based analysis. Burst thus the mean firing rate was relatively stationary. excludedoftransient periods response stimulias entered orexitedRF,the and restricted to the final 800 ms of the pause period (the ‘sustained period’), which not be determined. Unless otherwise specified, analysis of spiking statistics was and the other four were excluded as the peak of many of their waveforms could waveformavailable,weremeandataonly Two excluded werebecause these of neurons.112 in neurons,resultingadditional six excluded we analyses, tation resulted in 118 neurons that met these selection criteria. For the waveform adap could they not therefore classified be as narrow-spiking or broad-spiking. This typical µ s to 224

biphasic shape, with a trough followed by a clearly defined peak, and peak, defined clearly a by followed trough a with shape, biphasic µ s to 500 µ s and broad-spiking neurons defined as those ranging in duration We computed two burst measures: an ISI-based metric that metric ISI-based an measures: burst two computedWe n U P = 53 monkey53 = B, if otherwis We recorded from 206 well-isolated neurons from two male test, µ < 0.01). Narrow- and broad-spiking neurons were separated Figure 1c freq s. P < < 0.05). This resulted in 84 neuronsresultedThis84 0.05).excluded. inbeing < e 22       , . , 1 1 5 d . To further isolate changes in burst firing from + th e en − + n . ( = 153 monkey153= We M). restricted our dis 1 freq n       7 . It was created by taking the inverse fast = 202, Hartigan’s202, = test, dip 7 0 . + 5 e 33 − − 1 2 . ( 5 freq . We selected this metric on the on metric this We selected . ) 7 0       . − As described previously Supplementary Fig. 4 1 5 11 5 )       doi: − 1 10.1038/nn.3463 4 9 P . The distri < 0.0001), < n ) = 118, 1 1 9 2 . , we ------

© 2013 Nature America, Inc. All rights reserved. calcium concentration inside the compartment are: g paper original the g in used parameters of range the V c ( I ioniccurrentsbelow).Thecurrentare: (see where quency adaptation. In total, the current balance equation is: K ( rent ( model behavior, we included the other currents found in the full nonzero [Ca cortical layers some of the variability in burstiness seen across pyramidal neurons in different Na persistent the of expression in differences neuron, intrinsicmodelburstiness currentstheconductances the variesof thethese of scale of the transient and persistent Na the slow timescale of the muscarinic-sensitive K analysisdemonstrateto interplayfromthearises thatmodel bursting ofthe in ( neurons, including the transient Na of the currents known to exist in the soma and proximal dendrites of pyramidal tionsaccording Hodgkin-Huxley–typetoa scheme. includesThemodel many a temporal resolution of 0.02 ms, and was constructedFigure 2 of coupled differential equa previousworkin described model Single compartment model. doi: C Nap I I V ( Ca NaP Kca + K Kdr V dv dt − Althoughfourthese currents are sufficienttomost togiveofmodel rise the current ( = −90 mV and mV −90 = = 0.02mS/cm= − 10.1038/nn.3463 ( 03 mS/cm 0.3 = ), which contribute to rapid spike repolarization and the slow Ca ) that generate spikes. In the original paper original the In spikes.generate that ) V I − = V V Ca 2 ) = C K 2 K . This includes an A-type K ), and two Ca a = 1 = ), ), V g . The model was implemented using Matlab software (Mathworks) with g L L I I Nap sAHP M ) ( I sAHP µ ( 5 p V F/cm − − 0  . ( , I V ( V z ), which mediates a slow after-hyperpolarization and spike fre V 2 ) = ) , , )( q 2 2 g , , ) = V V , Kca 2+ g g g Ca − Kdr M L activated K Na g = 10 mS/cm10 = = 0.05 mS/cm 0.05 = = 120 mV. All conductances are equal to or within within or to equal are conductances mV.All 120 = z sAHP V d ( 6 mS/cm 6 = Na V − − [C − dt ), We implemented the Golomb single-compartment I I q ] a Na ( I 2 V V Kdr + K p − K ), ( + 2 − = + V V + current ( 2 currents: the fast Ca g . A schematic of the model can be seen in seen be can model the schematicof A . current ( 2 , K Ca and n + dr ). The reversal potentials are vI 2 2 currents ( ) = r , , , 2 Ca − − V ( g V g A g L I I Kdr A M sAHP = −70 mV,−70 = and 14 mS/cm 1.4 = − − I I Na Na I [C n A V ( + ) the delayed rectifier K t 4 ), the high-threshold Ca V = 5 mS/cm5 = current ( Ca ( ] a 2 Ca I V 2 2 , Na , the authors use a fast-slow a authors use the , ), + h − − − and ) = ) I I I V Kca Ca + K 2 channel may underlie may channel 2+ g ( ), 2 I Na V : : I Nap -activated K I M 2 , A m g , , 2 ) and the fast time Kca I Na c ( . Thedynamics. of ) syn  V ) = ) g 2 M 3 3 mS/cm 35 = 2 , ( . Just as varying is the synapticthe is b 1 mS/cm 1 = + − V g ) V ) C I I = h 2+ sA 2+ d Na

( g  -activated V NP ] Golomb A = 55 mV, + ([Ca + − a current current  2+ 3 V cur ( 2+ V Na sy ] ) n 2 2 ), i b - - - ­ ) , ,

the mean (s.d. proportional to the square root of the mean). Thus, the scaling scaling the Thus,mean). the ofroot square the proportionalto (s.d. mean the to proportional is that variance a and inputs of number the to equal mean a a large population of Poisson inputs results in a Gaussian random variable with these processes by the square root of inhibitoryandconductances attentionalanby factor, Weaccomplished this by proportionally increasing the means of the excitatory varied the relative balance of these conductances. we when resultsqualitatively similarobtained we conductance,butexcitatory respectively. The mean of the inhibitory conductance was twice as strong as the stants for the excitatory and inhibitory conductances were 2.71 ms and 10.49 ms, manyPoissonconstant.synapticcon timetime a byprocessesThesmoothed process Ornstein-Uhlenbeck an to similar processes stochastic one-variable by described is conductances these of Each of independent excitatory and inhibitory conductances, approximate fluctuating synaptic activity seen ( of Poisson synaptic inputs. applied here is equivalent to scaling of the rate parameters of a large population Golomb model by replacing the applied current with a synaptic current, synaptic a with current applied the replacing by model Golomb model. to input Synaptic as the first derivative of the intracellular voltage. to those used in the original paper where 50. 49. 48. 47. 46. Fig. 2 To simulate attentional modulation, we scaled the synaptic inputs to the model.

rci P. Aracri, P.Barth, attention. multifocal with targets multiple Tracking G.A. Alvarez, & P. Cavanagh, for evidence targets: independent in multiple TrackingR.W. Storm, & Z.W. tuning Pylyshyn, orientation of Dynamics R. Shapley, & M.J. Hawken, D.L., Ringach, sensorimotor cortex. sensorimotor (2004). features. extracellular and interactions network Sci. TrendsCogn. mechanism. tracking parallel a macaque primary visual cortex. visual primary macaque a ν ). This synaptic current was generated by a point-conductance model to = 0.13 cm et al. et t al. et Characterization of neocortical principal cells and interneurons by interneurons and cells principal neocortical of Characterization 2 Layer-specific properties of the persistent sodium current in current sodium the persistent of properties Layer-specific ms

9 g I , 349–354 (2005). 349–354 , sy −1 J. Neurophysiol. J. e n

µ − = A o iuae conditions simulate To −1 , ) ( τ V t Ca Spat. Vis. Spat. 1 Nature ) ( 5 = 13 ms. The kinetics equations are identical . Extracellular action potentials were modeled A

95 . By the central limit theorem, summing

0 387 , 3460–3468 (2006). 3460–3468 ,

− + 3 2 , 281–284 (1997). 281–284 , , 179–197 (1988). 179–197 , t g 3 , and is equivalent to the sum of sum the to equivalent is and , i ) ( in vivo ) ( V . Neurophysiol. J. nature nature 2 n vivo in 3 A 7 . This current is the sum 5 , and scaling the s.d. ofs.d. the scalingand , g e ( t ) and , we modified the the modified we , NEUR

g 92 i ( OSCI t ): 600–608 , EN I C syn E -

ERRATA

Erratum: Attention-dependent reductions in burstiness and action-potential height in macaque area V4 Emily B Anderson, Jude F Mitchell & John H Reynolds Nat. Neurosci.; doi:10.1038/nn.3463; corrected online 17 July 2013

In the version of this article initially published online, burstiness was defined on p. 1 as the prosperity of neurons to fire rather than the ­propensity, and model neuron firing rates were given on p. 3 in nHz rather than Hz. The errors have been corrected for the print, PDF and HTML versions of this article. © 2013 Nature America, Inc. All rights reserved. America, Inc. © 2013 Nature npg

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