tuning dissimilarity explains short distance decline of spontaneous spike correlation in macaque v1

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Vision Research xxx (2014) xxx–xxx

VR 6773 No. of Pages 20, Model 5G

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Contents lists available at ScienceDirect

Vision Research

journal homepage: www.elsevier .com/locate /v isres

Tuning dissimilarity explains short distance decline of spontaneousspike correlation in macaque V1 q

0042-6989/$ - see front matter � 2014 The Authors. Published by Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.visres.2014.01.008

q This is an open-access article distributed under the terms of the CreativeCommons Attribution License, which permits unrestricted use, distribution, andreproduction in any medium, provided the original author and source are credited.⇑ Corresponding author at: Dept. of Neuroscience, Georgetown University, 3970

Reservoir Rd. NW, NRB EP-04, Washington, DC 20007, United States.E-mail address: [email protected] (C.P. Hung).

Please cite this article in press as: Chu, C. C., et al. Tuning dissimilarity explains short distance decline of spontaneous spike correlation in macaqVision Research (2014), http://dx.doi.org/10.1016/j.visres.2014.01.008

Cheng C. Chu a, Ping F. Chien a, Chou P. Hung a,b,⇑a Institute of Neuroscience and Brain Research Center, National Yang-Ming Univ., Taipei 112, Taiwanb Dept. of Neuroscience, Georgetown University, 3970 Reservoir Rd. NW, NRB EP-04, Washington, DC 20007, United States

a r t i c l e i n f o a b s t r a c t

2627282930313233343536

Article history:Received 4 October 2013Received in revised form 16 January 2014Available online xxxx

Keywords:Spike correlationCortical distanceCoincident spikingPrimary visual cortexReceptive field

37383940414243

Fast spike correlation is a signature of neural ensemble activity thought to underlie perception, cognition,and action. To relate spike correlation to tuning and other factors, we focused on spontaneous activitybecause it is the common ‘baseline’ across studies that test different stimuli, and because variations incorrelation strength are much larger across cell pairs than across stimuli. Is the probability of spikecorrelation between two neurons a graded function of lateral cortical separation, independent of func-tional tuning (e.g. orientation preferences)? Although previous studies found a steep decline in fast spikecorrelation with horizontal cortical distance, we hypothesized that, at short distances, this decline isbetter explained by a decline in receptive field tuning similarity. Here we measured macaque V1 tuningvia parametric stimuli and spike-triggered analysis, and we developed a generalized linear model (GLM)to examine how different combinations of factors predict spontaneous spike correlation. Spike correla-tion was predicted by multiple factors including color, spatiotemporal receptive field, spatial frequency,phase and orientation but not ocular dominance beyond layer 4. Including these factors in the modelmostly eliminated the contribution of cortical distance to fast spike correlation (up to our recording limitof 1.4 mm), in terms of both ‘correlation probability’ (the incidence of pairs that have significant fast spikecorrelation) and ‘correlation strength’ (each pair’s likelihood of fast spike correlation). We suggest that, atshort distances and non-input layers, V1 fast spike correlation is determined more by tuning similaritythan by cortical distance or ocular dominance.

� 2014 The Authors. Published by Elsevier Ltd. All rights reserved.

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1. Introduction

Fast spike correlation (‘synchrony’ or ‘coincident spiking’) isthought to be a code or signature of spiking ensembles, enablingthe brain to perform efficient computations relating to perceptionand behavior (Salinas & Sejnowski, 2001; Singer, 1999). Althoughthe functional roles of different timescales of spike correlation isunclear, synchrony within a narrow time window, approximatingthe temporal integration window of downstream neurons actingas coincidence detectors, is considered separately from slowerchanges in correlated excitability (noise correlation, ‘Rsc’, (Cohen& Kohn, 2011)). To develop computational models of spikingensembles, it is necessary to know which neurons fire coincidently(including before stimulus onset), and how much of the coincident

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firing is related to the neurons’ tuning properties vs. due to corticaldistance (Masquelier & Thorpe, 2007).

Previous studies of neural ensembles have been based on anal-ysis of relative spike times between two neurons or based on ana-tomical tracing (Gilbert & Wiesel, 1983; Malach et al., 1993;Toyama, Kimura, & Tanaka, 1981; Ts’o, Gilbert, & Wiesel, 1986).In cats and monkeys, spike correlation has been tied to tuning sim-ilarity for orientation (Ferster & Miller, 2000; Kohn & Smith, 2005;Nowak et al., 1995; Ts’o, Gilbert, & Wiesel, 1986), color processing(Roe & Ts’o, 1999), and disparity (Ts’o, Roe, & Gilbert, 2001), reveal-ing interactions between distant functionally related domainswithin and across cortical areas.

Although several reports have focused on the dynamic or con-text-dependent nature of spike correlations (Das & Gilbert, 1999;Gray et al., 1989; Hung, Ramsden, & Roe, 2007; Roelfsema et al.,1997; Stettler et al., 2002), here we focus on spike correlations dur-ing spontaneous activity because the variation in correlationstrength across cell pairs is typically many times larger than thevariation across stimulus conditions in the same pairs (Hung,Ramsden, & Roe, 2011; Luczak, Bartho, & Harris, 2009), suggestingthat the mechanism is mostly intrinsic (i.e. tied to the functionalarchitecture) rather than stimulus-dependent (Ringach, 2009).

ue V1.

http://dx.doi.org/10.1016/j.visres.2014.01.008

mailto:[email protected]


http://www.sciencedirect.com/science/journal/00426989

http://www.elsevier.com/locate/visres


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2 C.C. Chu et al. / Vision Research xxx (2014) xxx–xxx


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Although visual stimulation typically reduces neural variability(Churchland et al., 2010), correlations presented in both evokedand spontaneous activity are thought to share similar mechanisms(Jermakowicz et al., 2009). Understanding variability of spike cor-relations during spontaneous activity (i.e. whether this variabilityis random or systematic) is thus a necessary component to under-standing signal processing in basic cortical circuits. Also, identify-ing the factors underlying spontaneous correlations may providea fairer and more consistent baseline for comparing across studiesthat examine different stimuli and different mixtures of cells.Although new methods combining slice physiology, in vivo cal-cium imaging, and/or electron microscopy have been developedthat have enabled precise alignment between tuning, morphology,and circuitry in rodents and small animals (Bock et al., 2011; Koet al., 2011; Lefort et al., 2009; Shepherd et al., 2005), such meth-ods are extremely difficult to implement, especially in larger ani-mals such as macaque monkeys which are more similar tohumans. Analyses of spontaneous extracellular spiking may thusoffer an enormous advantage in studying coordinated assemblyactivity.

Although many studies have suggested that coincident spikingdeclines with cortical distance, it is unclear whether this distancedependency is simply due to examining too few factors. It is wellknown that different tuning factors are related, and that the inter-action of these factors may lead to a residual effect of cortical dis-tance when only single factors are examined (e.g. a study may findthat spike correlation depends on both orientation and distance,but the distance dependency may be due to an unexamined factorthat is co-linear with distance). However, no study has sampledsufficient tuning properties (typically no more than 2 or 3, ana-lyzed separately) and cell pairs to disentangle the effect of corticaldistance from the effect of the overall decline in tuning similarityacross combinations of tuning properties. Also, rather than sam-pling one site per penetration, it would be better to sample multi-ple sites per penetration (multiple pairs of neurons with equalhorizontal separation and the same topography) to disentangle thisrelationship.

Here, we asked what are the relative contributions of differenttuning properties to spike correlation, and whether horizontal cor-tical distance has a separate contribution, beyond that already pre-dicted by tuning dissimilarity. The standard hypothesis is thatspike correlation depends on horizontal cortical distance (Das &Gilbert, 1999; Gray et al., 1989; Hata et al., 1991; Hung, Ramsden,& Roe, 2007; Maldonado, Friedman-Hill, & Gray, 2000; Smith &Kohn, 2008; Toyama, Kimura, & Tanaka, 1981), in addition to tun-ing similarity (e.g. for orientation, ocular dominance, chromaticpreference, and spatiotemporal receptive field similarity (Das &Gilbert, 1999; DeAngelis et al., 1999; Engel et al., 1990; Hataet al., 1991; Nowak et al., 1995; Schwarz & Bolz, 1991; Ts’o & Gil-bert, 1988; Ts’o, Gilbert, & Wiesel, 1986)). However, whether if andto what extent spike correlations actually depend on cortical dis-tance is unclear, because not all factors were significant (Chiu &Weliky, 2002), including horizontal cortical distance (Samondset al., 2006; Schwarz & Bolz, 1991), and horizontal interactionscan be found at up to 4–7 mm (Engel et al., 1990; Smith & Kohn,2008), and even across hemispheres (Bosking et al., 2000; Engelet al., 1991; Nowak et al., 1999). We suggest an alternative hypoth-esis, that the decline of fast spike correlation with cortical distance,at least for short distances (<1.4 mm, about 1–2 hypercolumns),can be explained by the decline in tuning similarity with distance(this possibility was also mentioned in (Ts’o, Gilbert, & Wiesel,1986)). If so, it should be possible to use GLM to precisely quantifyweights (beta coefficients) for both spike correlation probabilityand correlation strength, and to determine whether cortical dis-tance is a significant predictor beyond that already predicted bytuning similarity.

Please cite this article in press as: Chu, C. C., et al. Tuning dissimilarity explainVision Research (2014), http://dx.doi.org/10.1016/j.visres.2014.01.008

2. Materials and methods

2.1. Animal preparation and surgery

We recorded from two 4–5 kg Formosan macaque monkeys(Macaca cyclopis). M. cyclopis is a member of the group M. mulattaalong with M. fuscata, and is paraphyletic to M. nemestrina andM. fascicularis based on mitochondrial DNA sequences (Li & Zhang,2005). All experimental procedures were performed in accordancewith the National Institutes of Health Guide for the Care and Use ofLaboratory Animals and were approved by the Institutional AnimalCare and Use Committee of National Yang-Ming University.

Anesthesia was induced with ketamine (10 mg/kg IM). Monkeyswere artificially respired and continuously monitored for EEG, EKG,body temperature, expired CO2, and pO2. Light anesthesia wasmaintained with sodium thiopental (Pentothal 2 mg/kg/h IV) andthe muscle relaxant rocuronium bromide (Esmeron 1.2 mg/kg/hIV), and anesthetic depth was maintained via custom software thatcontinuously measured delta vs. gamma EEG power. Pupils weredilated with atropine sulfate. The center of gaze was estimatedvia reverse ophthalmoscopy of the optic discs, and the eyes werefocused via contact lenses and converged upon the monitor at57 cm distance.

At the start of each session, the eyes were converged via rotat-ing wedge prisms (Thorlabs RSP1). Based on the alignment of small�0.2 deg receptive fields from the two eyes (three neurons permonkey), we estimate the precision of alignment to be less than0.1 deg. Except for ocular dominance (OD) measurements, all otherblocks were presented monocularly to avoid the possibility ofphase mis-alignment of receptive fields from the two eyes (phasemis-alignment alone could elevate OD as a factor). The longestblock, spatiotemporal receptive field (STRF) mapping, took25 min and yielded RFs as small as 0.44� wide with 0.22� wide sub-fields, indicating that the eyes were stable throughout the record-ing. The ‘‘orientation/SF/phase’’ recording block took 15 min andalso yielded reliable phase preference even at 2 cyc/deg (Fig. 2Eand F).

2.2. Electrophysiology

We inserted 64-site multi-electrode arrays (A8 � 8–5 mm200–200–413, 8 penetrations (‘shanks’), 8 sites per penetration,spanning 1.4 � 1.4 mm horizontally and in depth, 200 lm spacing,Neuronexus Technologies, Inc.) normal to the cortical surface,14 mm anterior of the occipital ridge and 10 mm lateral of midline(approximately 3–4 deg eccentricity). The width of the array wasthus sufficient to span two complete cycles of ocular dominancehypercolumns (as measured in a third monkey by aligning the ar-ray across OD columns). Cortical depth was assessed by DiI andcytochrome oxidase staining (Fig. S1A and B), current source den-sity analysis (Fig. S1C) and by the temporal frequency limit outsidelayer 4 (Fig. S1D–H). Spikes (400–5000 Hz) and local field poten-tials (LFPs, 1–300 Hz) were filtered (48 dB/octave) and continu-ously digitized at 24.4 kHz (RZ2, Tucker-Davis Technologies, Inc.).Single units were isolated offline via super-paramagnetic cluster-ing (Quiroga, Nadasdy, & Ben-Shaul, 2004). To avoid possible errorsfrom the unsupervised spike sorting algorithm, we rejected andmanually resorted all spike clusters (‘units’) if over 5% of interspikeintervals were <2.5 ms. Manual sorting was done by adjusting thetemperature of the annealing in the super-paramagnetic clusteringalgorithm. At low temperature, all spikes are assigned to the samecluster, whereas at high temperature, each spike forms a singlecluster. We chose an ‘optimal’ temperature by gradually increasingthe temperature until less than 5% of interspike intervals were<2.5 ms. This criterion is considered ‘good’ in extracellular

s short distance decline of spontaneous spike correlation in macaque V1.


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Fig. 1. Characterization of ocular dominance responses in macaque V1. (A–C) Spike rasters and peri-stimulus time histograms to drifting gratings in three example cells, 10repetitions. (A) Single unit preferring contralateral eye (left eye). (B) Single unit preferring ipsilateral eye (right eye). (C) Single unit preferring both eyes (binocular). (D and E)Distribution of ocular dominance vs. cortical depth in two monkeys M1 and M2. Ocular dominance index (OD index) is based on a contrast ratio (I � C)/(I + C) of meanbaseline-subtracted responses in the [0.05:2.05) s post-stimulus period and ranges from 1 (ipsilateral) to �1 (contralateral). The distribution was broad at each cortical depth(from 0.2 mm down to 1.6 mm, boxes show quartiles and extremes), with a bias towards contralateral units at 1.0–1.2 mm, consistent with monocular input to layer 4 andarray alignment along ocular dominance columns. (F) Distribution of OD similarities (N = 3503 pairs across two monkeys). OD similarity between each cell pair was defined as1 � abs(OD_index_1 � OD_index_2). Arrows indicate similarities for these example pairs.

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recordings (e.g. (Tolias et al., 2007) had 8% falsely assigned spikes).We matched the same neuron across different recording blocks bychoosing the waveforms that had the highest correlation. Becausetypically each channel only had 1 or 2 significant waveforms andthe match correlations were very high (r > 0.97, vs. �0.62 fornon-match), the matching was not difficult.

Multiple detection of the same unit across different channelswas tested via cross-correlation analysis with 1 ms histogram bins(Hung, Ramsden, & Roe, 2007). Of 3503 pairs tested, 101 (2.8%)were excluded as possible cases of multiple detection because theyhad narrow 1 ms peaks, defined by B0 > (B1 + B�1) and B0 > 0.05,where B0 is the height of the bin (in units of coincidences per spikepair) at 0, �1, or 1 ms (any of the 3) and B1, and B�1 are the heightsof the neighboring bins.

2.3. Visual stimulation

Stimuli were generated in Matlab (Mathworks Inc.) and Psycho-physics Toolbox 3 (Brainard, 1997) and displayed on a 21-in. cali-brated CRT monitor (ViewSonic pf227). Phosphor emission spectrawere measured via spectrometer, and stimuli were gamma cor-rected. Following hand mapping of receptive fields (RFs), all stimuliwere centered on the cluster of RFs. The most distant receptive fieldswere less than 1� apart. All stimuli were presented at an averageluminance of �27.8 cd/m2, about half the maximum luminance ofour monitor (Commission Internationale de l’Eclairage 1931; x,0.3106; y, 0.3261). Ocular dominance was measured via full contrast


chromatic drifting squarewave gratings (red, green, blue, and yellowinterleaved with black; 4 Hz, 2 color/black cycles per deg, i.e.0.25 deg per stripe, 4 orientations). Random monocular presenta-tion to left or right eye was controlled by eye shutters, with shuttersclosed between presentations. Other stimulus dimensions weretested via monocular presentation to the contralateral eye.

Orientation, spatial frequency, and phase tuning were deter-mined by flashing static Gabors (5 Hz, 94 ms ON, 106 ms OFF; fullcontrast grayscale; spatial frequencies 8, 4, 2, 1, 0.5, 0.25, 0.125,0.0625 cyc/deg; phases �3/4p �2/4p, �1/4p, 0, 1/4p, 2/4p3/4pp; and orientations 0, 45, 90, 135 deg). Sinusoidal gratingswere multiplied by a 2D Gaussian envelope (horizontal and verticalsize is 17 deg with r = 4 deg).

Spatiotemporal receptive fields were determined by spike-triggered analysis. Spike-triggered analysis was based onspike-triggered average (STA) and spike-triggered covariance(STC) analysis of random checkerboard patterns preceding eachspike. Stimuli were binary checkerboard m-sequence patternsextending 7.04� vertically and horizontally, a 32 � 32 grid of0.22� � 0.22� patches, updated at 42.5 Hz. We placed light anchors(4 � 4 deg, full luminance) at the four corners of the screen to sta-bilize brightness (Gilchrist et al., 1999).

Chromatic and luminance tuning were measured via flashedhomogenous color patches (5 Hz, 4 � 4 deg square) (Wachtler,Sejnowski, & Albright, 2003). The colors consisted of 8 hues withequal psychometric distance (based on the German Standard ColorChart) and 4 luminance levels (39.3, 33, 27.8, 23.4 cd/m2).



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Fig. 2. Characterization of spatial frequency, phase, and orientation tuning. Tuning to spatial frequency, phase, and orientation was determined by flashing static Gaborgratings (5 Hz, 17 deg Gaussian envelope with r = 4 deg). Stimuli included 8 spatial frequencies � 8 phases � 4 orientations. (A–F) Two example types of evoked responsepatterns. (A) A cell showing a phase selective response that depends on spatial frequency but not orientation. Darkness indicates average firing rate during [40:70) ms poststimulus (subtracted from baseline [0:30) ms). (B) Rasters and PSTHs at the cell’s preferred orientation (90 deg). Horizontal line below bottom right PSTH indicates [0:100] msstimulus presentation. (C) A cell showing a phase invariant response and narrow orientation and spatial frequency tuning. (D) Rasters and PSTHs at the cell’s preferredorientation (0 deg). (E) Another cell showing phase selective response like cell A but with narrower spatial frequency tuning. (F) Rasters and PSTHs at the cell’s preferredorientation (0 deg). (G) Distribution of tuning similarities (N = 3503 pairs across two monkeys). Tuning similarity between each cell pair was measured by Pearson correlation(R) between evoked (baseline-subtracted) response patterns. Arrow indicates R for pairwise similarities (RAC = �0.1, RCE = 0.43, RAE = �0.05).



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2.4. Data analysis

2.4.1. Selection criterion for neurons in GLMThe neurons were located across all cortical layers and most

recording sites (at least 41 out of 64 sites per monkey). We mea-sured neurons with at least 500 spikes during 15 min of spontane-ous activity (i.e. >0.56 Hz). This minimum spike count thresholdwas met by 107/117 units in M1 and 62/78 units in M2 (169 totalunits), yielding 5671 pairs in M1 and 1891 pairs in M2. This set wasfurther reduced to 118 units (68 in M1, 50 in M2) that had signif-icant receptive fields based on spike-triggered analysis (see spatio-temporal receptive field (STRF) similarity), yielding 3503 cell pairs(2278 in M1, 1225 in M2) in the final analysis.

2.4.2. Identification of cortical layersIdentification of cortical layers in V1 was based on several

methods. Cytochrome oxidase (CO) staining in M3 indicated the


location of color-sensitive blobs that mark output layers (Living-stone & Hubel, 1984; Lu & Roe, 2008). Current source density(CSD) analysis in M1 was calculated from the trial averaged LFPevoked with static gratings averaged across all orientations. CSDwas approximated by a 3-point formula to the second spatialderivative of the LFP:

CSD ¼ ½hðn� 1Þ þ hðnþ 1Þ � 2hðnÞ�=D2

where h(n) is the LFP signal on the nth electrode contact, h(n � 1)and h(n + 1) is the LFP signal of the immediately adjacent contactabove and below the nth contact on the same shank, and D is thespacing between contacts (0.2 mm). Layer 4 was determined bythe reversal of the CSD compared with superficial or deep layers(Kajikawa & Schroeder, 2011; Mitzdorf, 1985).

In addition, we tested gratings at several temporal frequenciesin V1 (1.7, 3.5, 7, 14, 28 Hz) and found a difference in the high tem-poral frequency cutoff between input and output layers, consistent



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with a previous report of a decrease of high-cutoff temporalfrequency of about 20 Hz between LGN and V1 output layers(Hawken, Shapley, & Grosof, 1996).

2.4.3. Spike correlationSpike correlation between cells was measured via cross-correla-

tion analysis (Ts’o, Gilbert, & Wiesel, 1986) from continuousperiods of spontaneous activity (15 min with the screen off). Toavoid the possibility of plasticity from stimulus presentation(Li & DiCarlo, 2010; Yao & Dan, 2001), spike correlations duringspontaneous activity were measured in a separate recording blockprior to measuring tuning properties. To avoid bias from spikecollisions (missing spike correlation on the same channel becausethey occur too closely or are overlapping in time), we only ana-lyzed pairs recorded from different channels, not pairs sorted fromthe same channel.

The ‘raw’ cross correlation histogram (CCH) was defined as

CCHðsÞ ¼PN1

i¼1

PN2j¼1SiðtÞSjðt þ sÞffiffiffiffiffiffiffiffiffiffiffiffi

N1N2p

where Si and Sj are binary values representing neuron 1’s ith spikeand neuron 2’s jth spike at a given temporal offset s (s’s are binnedin the CCH at 1 ms per bin), and their product indicates whether aninstance of a specific timing difference occurred (i.e. where neuron1’s spike preceded neuron 2’s spike by s). s is limited by the size ofthe convolution window (from �150.5 to 150.5 ms at 1 ms per bin,total 301 bins). The total is normalized by the number of spikes inthe two spike trains (N1 and N2) so that recording longer or shorterdurations does not alter the CCH.

Although previous studies corrected spike correlations for stim-ulus-locked responses, they only recently began controlling forslow correlations in spike timing (e.g. slow changes in excitabilitythat are driven by modulatory neurotransmitters, traveling waves,or large-scale coupling between distant areas) that are not stimu-lus-locked and that can distort the measurement of spike correla-tion (Brody, 1998; Sato, Nauhaus, & Carandini, 2012; Smith &Kohn, 2008). These limitations make it difficult to determine howdifferent factors relate to fast spike correlation, necessary to con-struct computational models of ensemble dynamics (Carandini &Ringach, 1997; Dehaene & Changeux, 2005; Goldberg, Rokni, &Sompolinsky, 2004; Grossberg & Williamson, 2001; Li, 1998;Masquelier & Thorpe, 2007; McLaughlin et al., 2000; Riesenhuber& Poggio, 2000).

We corrected the CCH for firing rate correlations slower than50 ms by using the jitter method (Smith & Kohn, 2008). This jitterwindow size was at the narrow end of those tested by Smith andKohn. This correction is more conservative than standard shift orshuffle predictors, because it is based on spontaneous activityand because it removes covariations in firing rate slower than50 ms (however, it cannot remove all sources of common input).

We measured the significance of the spike correlation based onthe [�50.5:50.5] ms interval. We permuted the spike train 2020times via the jitter method and defined the significance threshold(‘95%ile jitter predictor’) as the maximum (per bin) of the 2020permutations. We used 2020 permutations because there are 101bins in the [�50.5:50.5] ms interval, and so the likelihood thatany bin in the peak exceeds the significance threshold is 1/2020bin�1 � 101 bins (Bonferroni correction) = 101/2020, i.e. p = 0.05.We defined correlation significance as a binary value indicatingwhether the CCH passed the threshold.

We defined ‘correlation probability’ as the incidence of pairsthat had significant correlation (i.e. the total number of significantpairs, normalized by the number of tested pairs). We defined ‘cor-relation strength’ as the height of the jitter-corrected correlogram(i.e. CCH minus the 50%ile of the jitter predictor), also in the


[�50.5:50.5] ms interval, i.e. the strength of the spike correlationthat is faster than 50 ms.

2.4.4. Ocular dominance similarityOcular dominance was measured in response to chromatic

drifting squarewave gratings presented for 2 s ‘On’ and 2 s ‘Off’(see Section 2.3). For each cell, we calculated the ‘evoked’ (base-line-subtracted) responses in the [0.05:2.05] s interval after stimu-lus onset, averaged across 10 repetitions. The baseline was theaverage response in the [�150:�50] ms interval across all condi-tions, i.e. one number per cell, not stimulus-specific. The oculardominance index was defined as

ODindex ¼ rI � rCrI þ rC

where rI and rC are the evoked responses to the ipsilateral and con-tralateral eyes. We then defined ocular dominance similarity (ODS)as follows:

ODS ¼ 1� jODindexA � ODindexBj;

where A and B are the two cells. ODS ranges from 1 to �1. An ODS of1 indicates that both cells have exactly the same eye preference,whereas an ODS of �1 indicates that the cells have opposite eyepreferences (and that both are monocular).

2.4.5. Spatial frequency, phase, and orientation similarityWe measured each cell’s evoked (baseline-subtracted)

responses (mean of [40:70] ms) to phase, spatial frequency, andorientation, averaged across 20 repetitions of flashed achromaticsinusoidal gratings (94 ms On, 106 ms Off presentation, seeSection 2.3 and Fig. 2A, C, and E) and converted this 8 � 8 � 4 array(8 spatial frequencies � 8 phases � 4 orientations) to a 1 � 256array. The baseline was the [0:30] ms interval averaged across allconditions (one number per cell, not stimulus-specific). We thendefined Rsignal of each pair, i.e. their tuning similarity in terms ofspatial frequency, phase, and orientation, as their Pearsoncorrelation.

2.4.6. Spatiotemporal receptive field (STRF) similarityWe measured each cell’s spatiotemporal receptive field (STRF)

using spike-triggered analysis. Its advantage is that it makes fewerassumptions about the cell’s preferred stimulus and response pat-terns. We presented random binary checkerboard patterns (gener-ated via m-sequence, (Reid, Victor, & Shapley, 1997)). The STRF wasmeasured as spike-triggered average (STA), which captures theaverage pixel patterns preceding each spike, and as spike-triggeredcovariance (STC), which captures pixel covariation patterns pre-ceding each spike.

Spike-triggered analysis estimates the low dimensional linearsubspace of the full stimulus space (Chichilnisky, 2001; de Ruytervan Steveninck & Bialek, 1988; Paninski, 2003; Schwartz et al.,2006) and is similar to the Wiener/Volterra approach to determinethe firing rate function of a neuron (Korenberg, Sakai, & Naka,1989). Each spike provides a reference point for its preceding stim-ulus frames. We averaged all the spike-triggered stimulus framesin a defined temporal window preceding the spike across the entirestimulus space (spike triggered average, STA) as follows,

STA ¼ 1N

XN

i¼1

Si

where N is the total number of spikes recorded, and Si is the stim-ulus preceding the ith spike. We used a spike-triggered analysiswindow of 141 ms (23.5 ms per frame � 6 frames). In previousstudies, STA was used to map specific cone inputs to LGN receptivefields (Reid & Shapley, 2002) and receptive fields of simple cells in



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4 February 2014

the primary visual cortex (DeAngelis, Ohzawa, & Freeman, 1993;Jones, Stepnoski, & Palmer, 1987).

We used spike-triggered covariance (STC) to capture additionalfilters (low-dimensional subspaces), an approach that has beenused in many systems to characterize multidimensional modelsvia nonlinear combination rules (Rust et al., 2005; Touryan, Lau,& Dan, 2002). The spike-triggered covariance matrix, whichembodies the multidimensional covariance structure of a neuron’sreceptive field, is computed as follows:

STC ¼ 1N � 1

XN

i¼1

ðSi � STAÞ � ðSi � STAÞT

By applying eigenvalue decomposition, we identified significanteigenvectors from the STC matrix. The first eigenvector is the direc-tion in stimulus space along which the spike-triggered stimuli havethe greatest variance, and subsequent eigenvectors are orthogonaldirections in stimulus space explaining successively lower vari-ance. Typically, only the first one or two eigenvectors were signif-icant (exceeding the 95%ile of the explained variance of theshuffled distribution), based on shuffling the stimulus sequence(we ignored STCs higher than 2, see Selection criterion for neuronsin GLM). The STRF thus may contain 0 or 1 significant STAs and 0to 2 STCs.

We measured the similarity between STRFs in several ways. Asimple correlation coefficient was computed between the STAs ofeach pair of cells (DeAngelis et al., 1999). For each cell’s STA, weconcatenated the three consecutive frames (frame 2–4, i.e.[47:94] ms preceding the spike) that had the greatest spatialvariance.

To compute the correlation between the STA of one cell vs. theSTC of another cell, we applied two methods, one based on RF en-ergy and the other based on the STC kernel itself or its negative (forcells with only one significant STC) or Procrustes transformation ofthe STC kernel (for cells with two significant STCs). Because the RFenergy and Procrustes transformation methods yielded similar re-sults, we report only the RF energy results.

The RF energy method was based on the correlation betweenthe energy of receptive fields (receptive field overlap). Receptivefield energy is defined as follows:

ERF ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXn

i¼1

RF2i

vuut

where RF could be any significant STA or STC kernel.We tried several variations of computing a summary score of

STRF correlation, e.g. by taking the maximum Pearson correlationvalue across these methods (i.e. Max of STA vs. STA, STA vs. STC,and STC vs. STC comparisons). However, in reporting GLM results,the functional similarity of STRF was based on only the STA-STAsimilarity measure, because it explained better than STA-STC andSTC–STC combinations, including RF energy (RF overlap, seeresults).

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2.4.7. Full field color similarityWe flashed homogenous color patches at 5 Hz (94 ms ON,

106 ms OFF, (Wachtler, Sejnowski, & Albright, 2003)). For each cell,we measured color responses across 32 conditions (8 hues � 4luminances) and converted these evoked responses (mean of[40:130] ms, averaged across 20 repetitions, minus baseline inthe [0:30) ms interval, one baseline value per cell) to a 1 � 32 ar-ray. We then defined the color tuning similarity of each cell pairas the Pearson correlation of their arrays.


2.4.8. Generalized linear modelsTo quantify the relationship between spike correlation (correla-

tion probability or correlation strength) and tuning similarity, wedeveloped a generalized linear model (GLM) with the tuning sim-ilarity measurements and cortical distance as factors.

For correlation probability, we used a logistic regression form ofthe GLM, because correlation significance is a binary (not continu-ous) measure of the presence (1) or absence (0) of spike correlationfaster than 50 ms. We began with a column vector Z, consisting ofbinary numbers Zi, i = 1,2, . . .,N, indicating whether a particular cellpair i had a significant correlogram peak. This was matched to a de-sign matrix X, composed of N rows and K + 1 columns, where K isthe number of factors in the model. For each row of the design ma-trix, the first element xi0 = 1. Logistic GLM was defined as follows:

logpi

1� pi

� �¼ f ðxÞ ¼

XK

k¼0

xikbk; i ¼ 1;2; :::;N; ð1Þ

where f(x) is computed for each pair as a continuous variable, usingbeta coefficients bk learned from the training population.pi = P(Zi = 1) estimates the probability that a particular pair i hassignificant correlation. xik is cell pair i’s tuning similarity for factork, bk is the coefficient for that factor, with K total factors and N totalpairs. b0 is the offset for each monkey. The large difference in b0

across monkeys appears to be related to a difference in averagefiring rate (9.9 sp/s for M1, 4.3 sp/s for M2) and does not appearto affect the beta coefficients. The intuition behind this regressionis to use a linear combination f(x) of multiple tuning similarity mea-sures (x) to predict whether a pair’s spike correlation is significant(Z = 1) or not (Z = 0).

Fig. 9A and C shows the relationship between the data and thefitted model. The pairs are sorted along the abscissa according tof(x). Although Eq. (1) (solid lines) was fitted to the binary (peak)significance data, because the binary data are difficult to see, weplot the binary significance data of nearby pairs by applying asmoothing window of 15 pairs (dotted lines) to the binary data.

For correlation strength (the jitter-subtracted correlogram peakheight of significantly correlated pairs), we used a logarithmicregression form of the GLM because the peak height distributionwas normally distributed after logarithmic transformation (as ver-ified via quantile–quantile plots and Komolgorov-Smirnov testing).The GLM for correlation strength was as follows:

LogðYiÞ ¼XK

k¼0

xikbk; i ¼ 1;2; . . . ;N; ð2Þ

where Yi is the correlation strength for one cell pair, xik is cell pair i’sfunctional tuning similarity for factor k, bk is the coefficient for thatfactor, with K total factors and N total pairs. b0 is the offset for eachmonkey. For computing R2 during cross-validation (Eq. (6)), pi isdefined as exp

PKk¼0xikbk.

2.4.9. Model selectionWe screened factors to include in the combined model by iden-

tifying factors that were significant at p < 0.2 with single-factormodels. Screened factors were then included in our final (reduced)model. We then sequentially reduced the number of factors in themodel, by removing the factor with the highest p-value, until onlysignificant (p < 0.05) factors remained. Finally, because some fac-tors were co-linear, we used the log likelihood ratio test to verifythat the reduced model was not significantly less likely than thefull model.

The standard equation for computing likelihood (L) for logisticregression is as follows:

LðbjyÞ ¼YNi¼1

ni!

yi!ðni � yiÞ!pyi

i ð1� piÞni�yi ð3Þ



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4 February 2014

where yi is the number of pairs with significant correlogram peaksin a given population, and ni is the number of total pairs in thatpopulation.

Because we only have a single population, ni = 1 and yi = Zi is abinary value (either 0 or 1, indicating whether a pair has a signif-icant correlogram peak). The equation simplifies to the following:

LðbjyÞ ¼YN

i¼1

pyii ð1� piÞ1�yi ð4Þ

The likelihood (L) for logarithmic regression is as follows:

LðbjYÞ ¼YN

i¼1

1rLogðYÞ

ffiffiffiffiffiffiffi2pp e

�12

LogðYiÞ�EðLogðYi ÞÞrLogðYÞ

� �2

ð5Þ

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2.4.10. Evaluation of model performanceTo evaluate the GLM performance, we calculated explained var-

iance (average R2 ± SEM � 100%) based on repeated cross-valida-tions (N = 200) within each animal. We based our conclusions oncross-validation across cells because it is more conservative, butwe also show the cross-validation across cell-pairs for complete-ness. For ‘cell cross-validation’, model coefficients were first esti-mated with the pairs formed by half of the cells and then testedon pairs among the remaining cells (i.e. no re-use of the samecells). For ‘pair cross-validation’, model coefficients were first esti-mated with 70% of total pairs and then tested on the remaining30%.

More specifically, we estimated beta coefficients (bk) and offset(b0) using a subset of data (‘‘training’’). Based on those weights andoffsets (learning the hyperplane), we evaluated the model perfor-mance on the remainder of the data (‘‘testing’’). The testing wasbased on Eq. (1) for binary logistic regression and Eq. (2) for loga-rithmic regression. The goodness of fit (GOF) of the logistic modelwas assessed with Hosmer–Lemeshow test (Hosmer et al., 1997).

Model performance was assessed via R2, which indicates thepercent of variance in the data that is explained by the model.However, because R2 is not frequently used in logistic regression,we adopted the definition of pseudo R2 in Efron (1978), whichhas a similar formula as in linear regression. Both R2 and pseudoR2 were computed as follows:

R2 ¼ 1�PN

i¼1ðYi � piÞ2PNi¼1ðYi � YÞ2

ð6Þ

where Yi are the dependent variables in the regression model, pi arethe predicted values based on Eqs. (1) and (2), N is the total numberof pairs in the model testing. Because pseudo R2 is not a standardmeasure of model performance of logistic regression, we also com-puted the ROC (receiver operating characteristic) curve. The curve isbased on the true positive vs. false positive distribution betweenactual pairwise correlation significance (Y) and model predictedprobability (p).

Model performance was then assessed as AUC (area under ROCcurve). To determine the significance of the AUC vs. 0.5, we carriedout a z-test where the z-score is the AUC minus expected chance0.5, divided by the standard deviation of the AUC (across 20resamples of cell or pair cross-validation).

2.4.11. Vertical (within-penetration) and horizontal (within-row)shuffling

To test whether the model results were due to a sampling biasdue to the relationship between the array and the local topography(i.e. simply due to vertical (columnar) organization), we appliedwithin-penetration shuffling, computed 20 cross-validations ofeach, then applied a t-test to the two distributions. ‘Within-penetration shuffling’ was done by randomly replacing, for each


pair, its correlation significance value (0 or 1) and correlationstrength with that of a different pair of neurons. Each replacementneuron was chosen from the same or adjacent electrode shank(horizontal separation 6 0.2 mm) as its original and had averagefiring rate within ±5 sp/s of the original. As a separate control,we also shuffled ‘within-row’ (vertical separation 6 0.2 mm),which should further dilute the influence of topographic organiza-tion and result in AUC closer to chance (0.5).

These results are reported as p-values in Results: Correlationprobability and correlation strength.

3. Results

We measured the tuning and spontaneous spike correlation of118 V1 single units in two monkeys (68 in M1, 50 in M2), afterselecting for cells that were active at >0.56 Hz and that hadsignificant receptive fields based on spike-triggered analysis (seeSections 2 and 4). This yielded 3503 cell pairs (2278 in M1, 1225in M2) in the final analysis. Spike correlation strengths were highlycorrelated between visually evoked and spontaneous conditions(M1: r = 0.67, p < 10�10; M2: r = 0.54, p < 10�10, Pearson correlationof log spike correlation strengths, Fig. S2), indicating that variationsin spike correlations are much larger across pairs than acrossconditions.

3.1. Characterization of tuning similarity

3.1.1. Ocular dominanceWe presented full contrast color squarewave drifting gratings

on separate trials to each eye. Cells responded vigorously andshowed clear periodic response modulation. Three example cells(Fig. 1A–C) show typical responses, preferring either one eye(Fig. 1A and B) or both eyes (Fig. 1C). Grating responses appearedhalf-wave rectified (Fig. 1A and C) or full-wave rectified (Fig. 1B).We quantified ocular dominance preference via a contrast measure(OD index) ranging from �1 (contralateral eye) to 1 (ipsilateral).OD indices were widely distributed and varied with cortical depth(Fig. 1D: M1; Fig. 1E: M2). OD was biased contralaterally in bothmonkeys, consistent with the alignment of our electrode arraysanterior-posteriorly along OD columns (guided by optical imagingin M1) to reduce the association between ocular dominance simi-larity and distance (we confirmed these results by aligning the ar-ray across OD columns in a third monkey, see below). The depth ofmaximum contralateral response was �1–1.2 mm, consistent withmonocular input to layer 4 and with DiI, cytochrome oxidasestaining, current source density analysis, and temporal frequencyanalysis (Fig. S1, see Section 2). OD similarity (ODS, see Methods)was skewed toward 1 (both cells had similar OD) but included abroad range of similarities across the two monkeys (Fig. 1F).

3.1.2. Spatial frequency/phase/orientationWe characterized the cells’ preferred spatial frequency, phase,

and orientation by flashing static Gabor gratings (see Section 2).Most cells showed transient and robust responses. Response pat-terns ranged between two types. Cells that exhibited simple cell-like behavior were selective for different phases at different spa-tial frequencies, typically showing diagonal bands in the phase/frequency/orientation plot (Fig. 2A, B, E and F). Cells that exhib-ited complex cell-like behavior were selective for a particular ori-entation and spatial frequency regardless of phase (Fig. 2C andD). Fig. 2G shows the unimodal distribution of pairwise similari-ties (measured as Pearson correlation between baseline-sub-tracted response patterns; arrow indicates similarity for thispair).



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4 February 2014

3.1.3. Spatiotemporal receptive field (STRF)We mapped each cell’s STRF via spike-triggered averaging (STA,

‘reverse correlation’) and spike-triggered covariance (STC) analysis(Schwartz et al., 2006). Fig. 3A, C, and E shows STRFs of three exam-ple units (different cells than in Fig. 2). In all examples, the STRFpattern was strongest at �70.5 ms before the spike (stimulusframes are 23.5 ms apart, i.e. 2 video frames at 85 Hz), beginningas early as 47 ms.

Of the 70% of cells that showed either significant STA or STC ker-nels, 69% (81/118) were cells with no significant STC (e.g. Fig. 3B,see Section 2) and 31% (37/118) were cells with at least one signif-icant STC (e.g. Fig. 3D and F) (Rust et al., 2005; Touryan, Lau, & Dan,

STA

STC1

STC2

STA

STC1

STC2

STA

STC1

STC2

23.5 47 70.5 94 117.5

23.5 47 70.5 94 117.5

23.5 47 70.5 94 117.5

A

C

E

G

−1 -0.5 0 0.50

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600

Fig. 3. Characterization of spatiotemporal receptive fields (STRF). (A and B) Example cellno spike-triggered covariation (STC), consistent with ‘simple cells’. Scale bar = 1 deg. (Bsequence shuffling, indicating that all STCs were non-significant. (C) Example cell showsignificant eigenvalues for STC1 and STC2. (E and F) Example cell with one significant STreceptive fields in the [47:94] ms period (see Section 2). By this measure, the pairwise STdistribution of STRF similarities (N = 3503 pairs).


2002). As with spatial frequency/phase/orientation, the distribu-tion of STRF similarities was unimodal and broad (Fig. 3G, seebelow and Section 2).

3.1.4. Chromatic and luminance preferenceWe tested 8 hues having equal psychometric distance (Richter,

1955; Xiao, Wang, & Felleman, 2003) and 4 luminances per hue.These hues are plotted in CIE 1931 space in Fig. 4A. Testing withequal psychometric distance reduces bias from unbalanced activa-tion of LGN cone responses (Mollon, 2009).

The example cell in Fig. 4B and C was narrowly tuned for redacross a range of luminances, whereas the example cell in Fig. 4D

(msec)

141

141

141

(msec)

(msec) 1 10

Eige

nval

ue

STC1

Rank

1 10Rank

Eige

nval

ue

1 5 10

STC1

STC2Ei

genv

alue

B

D

F

1

showing clear spike-triggered average (STA) pattern, with ON and OFF subfields, but) STC eigenvalues (open circles) and their 5–95%ile CI (dotted lines) after stimulus

ing clear STA and STC, consistent with ‘complex cells’. (D) Filled circles indicateC. STRF similarity of each cell pair was based on STA-to-STA Pearson correlation ofRF similarities among these 3 cells are A–C: �0.15, A–E: �0.13, C–E: �0.03. (G) The



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4 February 2014

and E was broadly tuned to hue. Fig. 4F shows the distribution ofhue preferences, based on cosine fitting of hue responses at eachcell’s preferred luminance. This distribution is consistent with pre-vious reports (Wachtler, Sejnowski, & Albright, 2003), including abias toward darker colors (Fig. 4G) (Yeh, Xing, & Shapley, 2009).Both chromatic and luminance histograms were similar acrossthe two monkeys. Overall, 36/118 cells (31%) were tuned to hue,38/118 cells (32%) to luminance, and 7/118 cells (6%) to the inter-action of hue and luminance, ANOVA). As with other tuning prop-erties, the distribution of color tuning similarities, based onPearson correlation of hue and luminance responses, was unimodaland broad (Fig. 4H).

3.1.5. Horizontal distanceHorizontal cortical distance between cell pairs ranged from

0 mm (same penetration, different electrode contacts) to 1.4 mm(first and last penetrations) in 0.2 mm steps. On average, tuningsimilarity declined with distance for all functional properties ex-cept ocular dominance (OD), which did not vary with distance(Fig. 5) because the arrays were aligned along ocular dominancecolumns. Because each distance had a wide variation in OD prefer-ence, we were still able to assess the effect of OD similarity via theGLM.

3.2. Conversion to tuning similarity indices for the GLM

Ocular dominance similarity was calculated as 1 minus theabsolute difference of the OD indices (0–2) and so ranged from 1(similar) to �1 (dissimilar) (Fig. 1F). Other functional similaritieswere measured as the Pearson correlation of the tuning properties,thus also ranging from 1 (similar) to �1 (dissimilar). Overall, thesetuning similarity indices were unimodally distributed. A few wereskewed due to the placement of the electrode array along OD col-umns (Fig. 1F) or due to the quantification of similarity (Figs. 2Gand 3G).

3.3. Characterization of spike correlation

We used cross-correlation analysis to measure the precise spiketiming differences of pairs of spike trains (Fig. 6A, black solid line:Raw cross-correlation histogram, ‘CCH’). Recent reports have high-lighted differences between fast and slow correlations (Benucci,Frazor, & Carandini, 2007; Kenet et al., 2003; Smith & Kohn,2008; Xu et al., 2007). To focus on fast correlations that have beenlinked to both tuning similarity and cortical distance and that aremore likely to trigger coincidence detection by downstream neu-rons, we used jitter analysis to estimate and remove correlationsslower than 50 ms (Smith & Kohn, 2008). We report these jitter-corrected results as correlation probability (‘CP’) and correlationstrength (‘CS’). CP is the incidence of pairs with significant spikecorrelation (see Section 2: Spike correlation). CS is measured forsignificant pairs only and is based on correlations faster than50 ms, i.e. the height of the raw cross-correlation peak minus the50%ile of the jitter predictor (see Section 2). Correlations slowerthan 50 ms are postulated to be due to non-specific factors liketraveling waves or top-down feedback.

Example correlograms and rasters (black and gray dots, Fig. 6B–G) indicate that the sharp peaks were not simply due to artifacts ofslowly covarying firing rate, e.g. due to slow covariations in excit-ability (Fig. 6C, E, and G). Although correlation significance and cor-relogram peak height are not entirely separate (weakercorrelogram peak heights are also more likely to be non-signifi-cant), the transition was smooth across a wide range of peakheights (Fig. 7).

Decline in correlation probability with horizontal cortical distance.Consistent with previously reports, raw CCH peak height declined


with horizontal cortical distance (Fig. 6H and I). This decline in rawspike correlations contains a mixture of both fast and slow correla-tions. Correlation probability and correlation strength focus on thefast correlations that are postulated to be more focal and linked totuning and possibly distance (Benucci, Frazor, & Carandini, 2007;Kenet et al., 2003; Smith & Kohn, 2008; Xu et al., 2007).

Correlation probability declined with distance in both monkeys(Fig. 6J and K, for M1 and M2 resp., both R = �0.9, p < 0.001 basedon mean correlation probability), whereas correlation strengthweakly declined with distance in M1 (p = 0.02) but not M2(Fig. 6L and M). This weaker decline for correlation strength be-came non-significant upon cross-validation, and the decline forcorrelation probability became non-significant when receptivefield tuning dissimilarity was included in the GLM (see belowand Section 4).

The magnitudes of correlation probability differed across thetwo monkeys. We speculate that this is due to a difference in theirsensitivity to anesthesia rather than a difference in sampling, be-cause it coincided with a difference in the mean firing rates(9.9 ± 0.1 sp/s in M1, 4.3 ± 0.1 sp/s in M2). The higher firing rateof M1 produces higher jitter predictors, which elevates the signif-icance threshold for calculating correlation probability. Despitethese differences, the model beta coefficients and explained vari-ances were similar across the two monkeys (see below).

3.4. Dependence of spike correlations on ocular dominance, colorsensitivity, and cortical depth

Because the main analysis is based on measures of similarity, itdoes not specifically analyze interactions such as those betweenbinocular vs. monocular cells, color sensitive vs. color insensitivecells, or interactions that are specific to layer 4. Fig. 8 shows howthe number of significant pairs, correlation probability (CP), andcorrelation strength (CS) of significant pairs vary across a widerange of tuning interactions. As expected from the higher numberof contralateral OD cells sampled, many significant pairs are con-tra–contra, with slightly more contra–binoc pairs than binoc–binocpairs (Fig. 8A). CP corrects for this sampling bias by normalizing forthe number of pairs tested for each type of interaction. CS exam-ines significant pairs only. Neither CP nor CS varied strongly acrossthe range of OD interactions tested. However, all three measuresare clearly dominated by the contralateral OD input to layer 4,showing both contra–contra and contra–binoc interactions(Fig. 8B, G and L). We confirmed these results for OD similarityin a third monkey in which the array was placed across OD col-umns (Fig. S3).

The prevalence of color-insensitive (‘gray’) cells explains thehigher number of significant pairs for gray–gray interactions(Fig. 8C). CP is higher for color–color pairs (Fig. 8H), and CS is sim-ilar across the range of color–gray interactions (Fig. 8M). These pat-terns are similar in layer 4 (Fig. 8D, I, and N). All three measures ofspike correlation are higher for pairs of neurons at similar depths,particularly near layer 4 (Fig. 8E, J, and O).

3.5. Generalized linear model

We used a generalized linear model (GLM) to relate tuning sim-ilarity to spike correlation, using the pairwise similarity of eachtuning property and horizontal distance as regressors (X) to ex-plain spike correlation (Y or Z). We generated two types of GLMs,a logistic model for correlation significance (Z = 0 or 1) and a loga-rithmic model for peak height (Y) (see Section 2). In both cases, weprimarily report results based on cell-wise cross-validation. Com-pared to cell-wise cross-validation, pair-wise cross-validation (i.e.training on some pairs, testing on other pairs, but allowing forre-use of the same cells) only slightly increased performance.



204060

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Please cite this article in press as: Chu, C. C., et al. Tuning dissimilarity explains short distance decline of spontaneous spike correlation in macaque V1.Vision Research (2014), http://dx.doi.org/10.1016/j.visres.2014.01.008


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4 February 2014

3.5.1. Correlation probabilityFig. 9A and C shows the smoothed and predicted correlation

probabilities based on logistic regression for the two monkeys.The GLM predicted about 13.6 ± 0.5% of the variance in correlationprobability in M1 and 8.6 ± 0.3% in M2 (Efron’s pseudo R2, see Sec-tion 2). Although correlation probability was higher in M2 than inM1, the goodness of fit (GOF) was similar across the two monkeys(v2 11.38, p = 0.18 for M1; v2 13.34, p = 0.10 for M2; non-signifi-cance indicates good fit, Hosmer–Lemeshow test for logisticregression (Hosmer et al., 1997).

Because explained variance is not commonly used for logisticregression, we also measured performance based on signal detec-


tion theory. We plotted the receiver operating characteristic(ROC) curve for each monkey based on the binary correlation sig-nificance and predicted correlation probability (Figs. 9B and D).The area under the curve (AUC) was significantly higher thanchance (M1: 0.69 and 0.70 for cell- and pair-wise cross-validation,respectively; M2: 0.63 and 0.65, resp.; p < 10�5 in all cases, z-testvs. chance 0.5). It was also significantly higher than expected fromcolumnar or layer-specific organization, based on vertical (within-penetration) and horizontal (within-row) shuffling (M1: 0.57 and0.53 for vertical and horizontal, resp.; M2: 0.54 and 0.52, resp.;p < 10�10 in all cases, based on n = 20 cell-wise cross-validations,two-tailed t-test).



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Fig. 6. Distance dependence of spike correlation (correlation probability and correlation strength). (A) Example cell pair with significant coincident spiking duringspontaneous activity. Abscissa indicates time interval between spikes from two cells. The peak of the cross correlation histogram (CCH) exceeds the jitter predictor 95%ilesignificance threshold (upper gray line, see Section 2). (B) The same pair’s correlogram, defined as CCH – jitter predictor 50%ile. (C) Raster pairs (black and gray dots) showingthat coincident spiking was not slow correlations in excitability. Periods are 1-s snippets from 15 min of continuous recording. (D–G) Two more example pairs. (H and I) RawCCH peak height declined with horizontal cortical distance for both monkeys. Plots include significant pairs only. (J and K) Correlation probability (significant pairs/testedpairs) decreased with horizontal cortical distance in both monkeys. Based on random subsamples of 64 pairs per distance for M1, 40 pairs per distance for M2. (L and M)Correlation strength (correlogram peak height) was weakly correlated with distance in M1 (p = 0.02) but not M2 (p = 0.11). Boxes/crosses indicate quartiles, extremes, andoutliers.



4 February 2014

3.5.2. Correlation strengthFor correlation strength (M1 404 pairs, M2 778 pairs, significant

pairs only), the total explained variance (R2 ± SEM � 100%) was14.2 ± 0.5% in M1 and 12.9 ± 0.3% in M2, cross-validated acrosscells.

The model performance was not simply due to vertical (colum-nar) organization (i.e. not because neurons along the same pene-tration are similarly tuned or because of biased sampling of ourarray). Within-penetration shuffling (see Section 2) reduced theprediction to near chance (total explained variance = 0.46% and0.48% for M1 and M2, resp.) and was significantly worse than mod-el performance with actual tunings (p < 10�30 and 10�18, resp.).


3.5.3. Beta coefficientsTable 1 shows the beta coefficients and explained variances

when factors were tested individually (regular font) or combined(bold face font) in the GLM. In both monkeys, ocular dominance(OD) was the least predictive of all factors tested and was non-sig-nificant for both correlation probability and correlation strength(b1, regular font). This factor dropped out upon initial screening.The weakness of OD was not simply because the arrays werealigned along ocular dominance columns. We confirmed this byrecording from a third monkey in which the array was alignedacross OD columns. In that monkey, we found no significant rela-tionship between OD and correlation probability (p = 0.2) and a



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Fig. 7. Correlogram peak height distribution vs. binary correlation significance. Distribution of correlogram peak heights for significant pairs (filled bars) and all tested pairs(open bars) across two monkeys. Correlogram peak height and correlation significance were more strongly associated in M1 than in M2. However, model results wereconsistent across the two monkeys (Tables 1 and 3). Generalized linear model (GLM) of correlation strength was based on jitter-subtracted correlogram peak height and soincluded significant pairs only (M1: 404/2278 pairs, 18%; M2: 778/1225, 64%), whereas GLM of correlation probability included all tested pairs.

A B C D E

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K L M N O

Fig. 8. Dependence of spike correlations on ocular dominance, color sensitivity, and cortical depth. (A–E) Number of significant pairs for each type of pairing of tuningpreferences or cortical depth. Layer 4 corresponds approximately to depths 1.0 and 1.2 mm, based on the lack of responses in other layers at high temporal frequencies (notshown). Marginals show sums along columns. Color sensitivity is determined by contrast ratio responses to achromatic vs. isoluminant drifting gratings. Color sensitivityblock was tested in only one monkey. (F–J) Correlation probability, calculated as number of significant pairs/number of pairs tested in each bin. (K–O) Correlation strength,defined as jitter-corrected correlogram peak height.



4 February 2014

weak but significant relationship for correlation strength(R2 = 0.008, p = 0.017, see Section 4).

Correlation probability was significantly associated with otherreceptive field properties including spatial frequency, phase, orien-tation, STRF, and full field color similarity, explaining 2.2–6.5% of


the variance (b2–4, regular font). Correlation probability was moreassociated with STRF similarity, whereas correlation strength wasmore associated with spatial frequency/phase/orientation similar-ity. For STRF, STA–STA similarity alone predicted better than thecombination of STA and STC, including models based on receptive



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k¼0xikbk),i = 1,2, . . .,N pairs, learned from the ‘training’ pairs only (no ‘testing’ pairs). xik indicates tuning similarity of factor k (K = 5) for pair i. pi is defined as P(Zi = 1), where Zi is binary0 or 1 depending on correlation significance. Because Z is difficult to visualize, we plotted a smoothed version of Z (dots, ‘testing’ pairs only) by convolving Z with a slidingwindow (width = 15). Although correlation probability differed across monkeys, the beta coefficients were similar across monkeys (Table 1). Goodness-of-fit measures werecomputed for each model by cross-validating across cells. (B and D) Model performance was assessed as area under ROC curve (thick curve: cross-validated across cells; thinsolid curve: cross-validated across pairs). Axes indicate how the true and false positive rates for predicting correlation significance vary as a function of p, where ground truthis based on the correlation significance of independent data (‘test’ cells or pairs) not used to calculate p. In both cases, performance was significantly higher (p < 10�10, pairedt-test, two-tailed, n = 20 cross-validations) than chance that is expected from columnar or laminar organization, modeled by vertical (within-penetration) and horizontal(within-row) shuffling (dashed and dotted curves, resp.).

Table 1GLM beta coefficients and explained variance.

b Coefficients Explained variance of single factorMean ± SEM

CP CS CP CS

Ml M2 Ml M2 Ml M2 Ml M2

b1 (OD) Single factor 0.2 0.2 0.09 0.08 n.s. n.s. n.s. n.s.Combined factors 0.3 0.4 0.11 0.13

b2 (SF/phase/Ori) 1.4 1.4 0.52 0.71 2.2 ± 0.1 2.5 ± 0.2 4.4 ± 0.8 4.8 ± 0.30.7 1.2 0.47 0.60

b3 (STRF) 3.3 3.2 0.45 0.56 6.5 ± 0.3 4.0 ± 0.2 3.2 ± 0.7 3.8 ± 0.42.7 1.6 0.28 0.35

b4 (Colors) 3.7 1.8 0.84 1.10 4.6 ± 0.4 3.2 ± 0.2 8.0 ± 0.8 5.6 ± 0.53.0 1.7 0.73 0.94

b5 (Horiz. distance) �0.7 �0.4 �0.16 �0.10 0.8 ± 0.1 0.6 ± 0.1 n.s. n.s.�0.3 �0.2 0.00 �0.01

Generalized linear model beta coefficients based on tuning similarity and horizontal cortical distance (x1 to x5) were used to predict correlation probability (CP) andcorrelation strength (CS) measured during spontaneous activity. The beta coefficient of each factor is shown for the single-factor model (regular font) and for the combined-factors model (boldface font, five factors). Model performance is cross-validated across cells and shown as percent explained variance (mean ± SEM) for the two monkeys.



4 February 2014

field energy (1.5% and 2.3% for M1 and M2, resp.) and Procrustestransformation of STC components. Tuning similarity for spatialfrequency or orientation alone was predictive of spike correlation,but phase alone was not (orientation: 7.4% and 4.1% for M1 andM2, resp.; spatial frequency: 3.6% and 2.8% for M1 and M2, resp.;phase was not significant: p = 0.26 M1, p = 0.09, M2). Color tuning


was the best predictor of correlation strength (5.6–8.0% explainedvariance) and the second-best predictor of correlation probability(3.2–4.6%).

Consistent with previous reports, spike correlation declinedwith distance (i.e. negative beta coefficients) when horizontal dis-tance was tested as a single factor without cross-validation (Fig. 6J



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4 February 2014

and K). With cross-validation, this relationship was weakly signif-icant (p = 0.02 and 0.04 for M1 and M2) for correlation probabilitybut was non-significant for correlation strength (p = 0.07 and 0.21for M1 and M2, single-factor GLM, Table 1). The relationshipbecame non-significant for multiple-factors GLM.

We considered whether these results might be biased byuneven sampling with fewer pairs at larger distances. When themodel was based on the same number of pairs at each distance(i.e. 64 pairs per distance for M1, 40 pairs per distance for M2),the beta coefficients for both distance and ocular dominance wereweak and non-significant with cross-validation, for both correla-tion probability and correlation strength. Additionally, verticaldistance and diagonal (contact-to-contact) distance were alsonon-significant factors in both monkeys (p > 0.1). Thus, theweakness of distance and ocular dominance in the model is notdue to uneven sampling in distance.

3.5.4. Additivity/co-linearity of functional propertiesBecause some of these properties are related (e.g. STRF and SF/

phase/orientation), we wondered whether separating the factorsindividually or examining particular combinations of factors wouldlead to a different interpretation. We examined pair-wise correla-tion coefficients (R) between tuning similarities of these factors foreach monkey (Fig. 10A and B, for M1 and M2 respectively). Theoverall pattern showed that ocular dominance similarity wasuncorrelated with other factors. STRF, color, and SF/phase/orienta-tion similarity were positively correlated. STRF similarity andhorizontal distance were negatively correlated (Fig. 5E and F).

We also considered whether co-linearity may have resulted innon-stationary beta coefficients, e.g. between STRF and horizontaldistance. However, varying these beta coefficients (varying b3 andb5 while keeping other beta coefficients constant) resulted inworse cross-validated performance (not shown). Thus, althoughthe collinearity of STRF and horizontal distance resulted in some

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Fig. 10. Interactions across tuning properties in the GLM. (A and B) Correlation coefficicorrelation probability (CP) and correlation strength (CS), collinearity between propertiebars, summed across single models), vs. when factors are ‘combined’ in the model (ope


instability in the beta coefficients, it was still possible to obtainstable values for both b3 and b5.

Logically, collinearity should cause the total explained varianceof combined factors (‘Combined’) to be less than the sum of theexplained variances of individual factors (‘Single’). Fig. 10C and Dshows the summed explained variance for single factors, vs. theexplained variance for the combined factors. As expected, collin-earity reduced the additivity of these factors, resulting in lower(by 10–20%) explained variance for combined factors.

Next, we examined how different combinations of factors af-fected GLM performance (Fig. 11A–D). The additional contributionsof individual factors varied depending on whether it was the onlyfactor included in the model (slope of lines between 0 and 1 factor)or if it was the last factor added to the model (slope of lines be-tween 4 and 5 factors). The ordering had little effect on the addedcontribution of most factors, but appeared to affect the contribu-tion of horizontal distance (yellow). To quantify this additionalcontribution, we compared the performance of GLM when individ-ual factors were left out of the combination (e.g. a 4-factor model),vs. when all 5 factors were combined. The additional contributionof each factor to performance (delta explained variance) is shownin Fig. 11E and 11F for M1 and M2, respectively, for both correla-tion probability (CP) and correlation strength (CS) (unpaired t-test,N = 20). Based on this test of additional contribution, horizontalcortical distance does not provide significant contributions beyondthose provided by other factors, for both correlation probabilityand correlation strength (p > 0.1). We note that OD also does notprovide an additional contribution, but it was already non-signifi-cant as a single factor upon cross-validation.

Finally, we considered informative predictors in our final mod-el. During the model selection (see Section 2), only ocular domi-nance was removed during the initial screening due to its non-significance in the single factor model (p > 0.2). When we ran acombined factors model based on the remaining four factors, hor-

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ents (R) between tuning similarity properties in two monkeys. (C and D) For boths significantly reduced the performance between models with ‘single’ factors (filledn bars) (unpaired t-test, n = 20 repeats). ��p < 0.01, ��p < 0.001.



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Fig. 11. Contributions of combinations of GLM factors. Tree graphs show cell-wise cross-validated performance for all possible permutations of five factors (N = 5!) forcorrelation probability (A and B) and correlation strength (C and D) across the two monkeys. Starting from the left, the GLM’s explained variance generally increases withincreasing the number of factors, depending on the combination of factors included (e.g. blue line at arrowhead indicates how adding color improves the GLM performancebeyond just including STRF). Note that in every case, adding STRF (red) improved performance, whereas adding horizontal distance resulted in negligible improvement after�3 factors are included. (E and F) The additional contribution of each factor was measured as the difference in explained variance when all 5 factors were combined in themodel, vs. when that factor was dropped (4 factor model). ��p < 0.01, ��p < 0.001, n.s. p > 0.05.

Table 2Likelihood ratio test between 3 vs. 5 factor model.

CP CS

Loglikelihood3 Factor model �2054.8 �1110.25 Factor model �2056.1 �1111.2

Likelihood ratio test (v22) 2.6 2.11

p 0.14 0.17



4 February 2014

izontal distance was non-significant (p > 0.05) and so was dropped.Reducing the combined factors model from 5 factors to theremaining 3 factors was also supported by likelihood ratio test be-tween the two models (Table 2).

The reduced GLM contained only three remaining factors (x2–x4), SF/phase/orientation, STRF, and color. Table 3 shows the betacoefficients, tuning similarity scores used as factor values (see tun-ing similarity histograms in Figs. 2G, 3G, and 4H), and total ex-plained variance for this reduced model. Beta coefficients in the3-factor model were also compared with those of the 5-factormodel (unpaired t test). Notably, all beta coefficients were not sig-nificantly different across the two models, except for STRF (b3).This further indicates substantial collinearity between STRF andcortical distance. We suggest that these beta coefficient valuesmay be useful for developing computational models of V1.


4. Discussion

Our results show that, for short distances up to 1.4 mm (abouttwo V1 hypercolumns), tuning dissimilarity is better than cortical



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Table 3Reduced model.

P coefficients Tuning similarity scores (xk)Mean ± SD

CP CS

Ml M2 Ml M2 Ml M2

b2 (SF/phase/Ori) 0.79n.s. 1.34n.s. 0.48n.s. 0.62n.s. 0.17 ± 0.2 0.33 ± 0.2b3 (STRF) 3.18* 1.77* 0.28n.s. 0.57n.s. 0.2 ± 0.25 0.2 ± 0.26b4 (Colors) 2.96n.s. 1.72n.s. 0.73n.s. 0.95n.s. 0.07 ± 0.2 0.08 ± 0.1

Total EV (%) 12.9 ± 0.6 8.5 ± 0.5 14.2 ± 1.0 13.2 ± 0.3

Reduced model, combining only 3 factors without OD and horizontal cortical distance. Model performance is cross-validated across cells and shown as percent explainedvariance (Total EV: mean ± SEM). Although the precise beta coefficients varied across monkeys, their relative magnitudes across tuning factors were consistent. Betacoefficients were mostly unchanged between 3 factor model vs. 5 factor model. Significant difference for STRF is likely due to collinearity with horizontal distance.* p < 0.05, unpaired t-test.



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distance at predicting the steep decline in fast spike correlations.Although spike correlation does decline with cortical distance, thiscan be explained at short distances by the decline in tuning simi-larity, without requiring an additional factor for cortical distanceitself. Thus, measuring combinations of tuning similarities may benecessary to model ‘‘distance’’ in the cortex, at least for short cor-tical distances.

Also, previous studies showed that different tuning propertiespredict spike correlation, but it was unclear what was the relativecontribution of these properties. Our model suggests that color(and luminance) tuning similarity is the strongest predictor, fol-lowed by spatiotemporal receptive field similarity. Surprisingly,ocular dominance was not a significant predictor beyond layer 4.We report these factor weights (Tables 1 and 3) and are placingthis data in a public database (http://crcns.org/). This data is likelyto be useful for constructing computational models of ensembledynamics.

4.1. Why was horizontal distance non-significant?

Consistent with previous reports, raw spike correlations did de-cline with horizontal distance (Fig. 6H–I). The steep decline in rawcorrelations is associated with a decline in the incidence rate of fastcorrelations (Fig. 6J and K), and a shallower decline in the strengthof fast correlations (Fig. 6L and M). This dependency on distancedisappeared after a combination of tuning similarity factors wasincluded. In summary, both the focus on fast correlations (byapplying jitter correction) and the combination of multiple factors(Fig. 11) in a generalized linear model contributed to exclude shortcortical distance as an explanatory factor.

Although this may appear to contradict a previous report thatfound that shuffle-subtracted spike correlations decreased withdistance independent of orientation similarity (Das & Gilbert,1999), we suggest that orientation similarity is only one of manytuning similarities (e.g. spatial frequency, phase, motion, ocularpreference) that combine to determine spike correlation. In ourfactor permutation analysis (Fig. 11), distance is significant unlessmultiple factors are included.

An important facet of these findings is that they are based on ar-rays aligned along OD columns, and that anisotropy of horizontalprojections may lead to different results for arrays aligned acrossOD columns. Unfortunately, currently available electrode arraysdo not enable sufficiently dense and unbiased sampling of combi-nations of factors (ideally one would sample multiple depths per80 lm horizontal distance, (Nauhaus et al., 2008)), and aligningour electrode arrays across OD columns tends to miss color blobsand oversample iso-orientation domains, resulting in fewer col-or-sensitive cells and stronger spike correlation strength at shortdistances due to the orthogonality of orientation and ocular dom-inance maps. These results are also limited to the short distances


examined (up to 1.4 mm) and do not include factors that mayapply at longer distances, e.g. long-distance patchy connectionswithin V1. Longer distance interactions may be specific for partic-ular properties (e.g. orientation, color) and may be associated withcontextual effects (e.g. co-linearity, co-circularity) that are beyondthe scope of this study.

4.2. Why was ocular dominance similarity non-significant?

Our ocular dominance (OD) results are also surprising, becausesome reports suggest that OD and spike correlations are linked.Three reasons may explain the apparent discrepancy of our OD re-sults. First is that correlation probability (CP) and correlationstrength (CS) are not the same as counting the number of signifi-cant pairs, which was often the basis of reports in physiologicaland anatomical studies (Hata et al., 1991; Yoshioka et al., 1996).OD is a significant factor when we simply analyze based on numberof significant pairs, instead of CP or CS (see Fig. 8 and Results).

Second is that our analysis spans most cortical layers, whichemphasizes common input that is possibly local, rather than thal-amocortical inputs that arrive in layer 4. When we analyzed onlylayer 4 (both cells within layer 4), OD was clearly a factor for thenumber of significant pairs (Fig. 8B), CP (Fig. 8G), and CS (Fig. 8L).

Third is that we did not exclude binocular cells from the ODanalysis. Previous studies excluded binocular cells (Hata et al.,1991; Ts’o, Gilbert, & Wiesel, 1986), which may have elevatedthe importance of OD or the contribution of layer 4.

We considered that the weakness of OD might be because thearrays were aligned along OD columns. In a third monkey, wealigned the array across alternating OD columns. We found no sig-nificant relationship between OD and correlation probability(p = 0.2) and a weak but significant relationship for correlationstrength (r2 = 0.008 cross-validated across cells, p = 0.017, single-factor GLM). As with the first two monkeys, spike correlationsdepended more on OD when the analysis was restricted to layer4 (Fig. S3).

Our results agree with a previous report (Chiu & Weliky, 2002),that correlated spontaneous activity in ferret V1 (P24–P29) doesnot solely reflect the pattern of segregated eye-specific LGN inputs.Like us, they found non-significant relationship between oculardominance similarity and spontaneous correlations within thesame contralateral band. In regions of alternating ocular domi-nance patches, they did find a weak link (r2 = 0.06) between spon-taneous correlations and ODSI. Ts’o, Gilbert, and Wiesel (1986) alsoreported weak but non-significant relationship for OD (p < 0.06).This weakness is consistent with previous anatomical reports(Malach et al., 1993; Yoshioka et al., 1996) that horizontal axonstarget freely across ocular dominance columns and are not con-fined to columns from the same eye. Thus, local circuits appearto largely dilute the effect of eye-specific thalamocortical inputs.


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Additional factors may also explain the stronger link betweenOD and spike correlations. In previous studies, visual stimulation(i.e. during strong thalamocortical input) may have elevated thelink between synchrony and ocular dominance similarity,especially if synchrony was measured during effectively monocu-lar visual presentation (Kruger & Aiple, 1988), if the receptive fieldsfrom the two eyes were not precisely aligned (e.g. a separate barshown to each eye, resulting in asynchronous input) (Ts’o, Gilbert,& Wiesel, 1986), or if OD was collinear with other factors likedistance (Hata et al., 1991).

4.3. Color (and luminance) best predict correlation strength

Although STRF was the best predictor of correlation probability,color (including luminance) was the best predictor of correlationstrength (Table 1 explained variance values). Why was color sucha strong predictor, given that V1 is full of orientation selectivecells? One possible explanation is that because color cells are lessselective for orientation (Lu & Roe, 2008), the explanatory power ofcolor is particularly strong for such pairs. This is consistent withseveral studies that reported a significant association betweenchromatic preference and spike correlations (Roe & Ts’o, 1999;Ts’o & Gilbert, 1988). It is possible that aligning our arrays alongOD columns may also have increased the proportion of the popula-tion that was color-selective, due to the tendency of color blobs toalign along OD columns (Lu & Roe, 2008). The predictive power ofcolor similarity may be even stronger if color subfields were tested,instead of the full-field color patches we tested here.

Because our measure of full field color similarity is based onboth hue and luminance, it is reasonable to ask whether most ofit is due to hue or due to luminance? The answer is, ‘‘both’’. Whenassessed individually, neither hue nor luminance was a significantpredictor, and it was only in combination that they were signifi-cant. We previously reported that spike correlation depended onluminance edge contrast similarity (Hung, Ramsden, & Roe,2007), so there is good reason to suspect that luminance tuningmay predict spike correlations. The results here suggest that hueand luminance act in combination to determine spike correlations,consistent with the integration of these cues in V1 (Clifford et al.,2003).

4.4. Generalizability of these results across cell tuning strength andanimal state

Besides tuning similarity, spike correlation is also related to thedegree to which the cells are tuned for particular factor (tuningstrength). Like OD, the strength of color tuning is stronger in layer4. However, we did not see an obvious difference in the number ofsignificant pairs, CP, and CS for layer 4 vs. other layers (compareFig. 8C,H, and M with Fig. 8D, I, and N). Instead, the main differencewas a higher number of significant correlations between gray–grayneurons due to the prevalence of such neurons (Fig. 8C), but higherCP and CS between color–color pairs (Fig. 8H and M). There alsoappears to be some dependency on cortical depth (Fig. 8E, J, andO), as well as on asymmetric properties (e.g. simple vs. complex,low vs. high spatial frequency tuning). We did not add these factorsto the model because they were peripheral to the question ofwhether (short) cortical distance or tuning dissimilarity betterexplained spike correlations, and because they greatly increasedthe number of factors and added the complication of temporal se-quence, while only modestly increasing performance. Overall,spike correlations are more complicated than we have describedwith this simple model, and other tuning properties are alsoimportant factors that are not included in our model.

Because spike correlations also depend on stimulus condition,we also examined spike correlation acquired from one monkey


(M1) during the OD block. We chose the OD block because it acti-vated most cells, including cells that preferred color, and also be-cause we wanted to confirm the lack of relationship with ODduring spontaneous activity. The results of the GLM were essen-tially the same, with only slightly lower explained variance inthe OD block compared to spontaneous activity (logistic: 12.7%,logarithmic: 11.7%, cross-validated across cells). Specifically, ODremained non-significant, and horizontal distance was alsonon-significant when other factors were included. SF, phase, andorientation remained highly significant. Color tuning similarity re-mained significant for CS, but it was non-significant for CP, possiblydue to different tuning for full-field color vs. the OD color gratings.

Finally, measurements of spike correlations may depend on thestate of the animal. Spontaneous synchrony in barbiturate anesthe-sia, particularly at concentrations many times higher than we haveused here (Contreras & Steriade, 1997), is qualitatively and quanti-tatively different from recordings in awake animals. Interactionsunder anesthesia reflect more the cumulative weight of commoninput and similarly tuned connections (Kenet et al., 2003; Tsodykset al., 1999), whereas dynamic effects such as attention (Roelfsemaet al., 1997; Singer, 1999) may emerge or dominate during naturalvision. On the other hand, recordings in awake animals rely moreon eye-segregated thalamocortical input and may be affected bythe different microsaccades of the two eyes (Hermens & Walker,2010), which may artificially elevate the dependence of synchronyon ocular dominance similarity. Spike synchrony and local fieldpotentials are time-locked to saccades and microsaccades (Bosmanet al., 2009; Ito et al., 2011; Rajkai et al., 2008). Recording underlight anesthesia and muscle relaxation, as in this study, avoids thispotential confound. In summary, combining multiple tuning prop-erties measured during spontaneous activity can be useful to iden-tify ‘baseline’ spike correlations to compare across studies, to avoidpotential confounds, and to improve sensitivity for discoveringwhat are the other non-similarity interactions (e.g. co-circularity)that are learned from natural image statistics.

Acknowledgments

We thank Yueh-peng Chen, Nicole Rust, and Manabu Tanifujifor helpful discussions. Supported by the Taiwan Ministry of Edu-cation Five Year Aim for the Top University Plan, Taiwan NationalScience Council Grants NSC-96-2811-B-010-501 and NSC-97-2321-B-010-007, and by the Georgetown University MedicalCenter Grant GD4235619. The authors have no competing inter-ests. C.H. and C.C. conceived the experiment and designed the dataanalysis. All authors carried it out. C.C. and C.H. wrote the paper.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.visres.2014.01.008.

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tuning dissimilarity explains short distance decline of spontaneous spike correlation in macaque v1

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