We tested the binding-by-synchrony hypothesis which proposes that object representations are formed by synchronizing spike activity between neurons that code features of the same object. We studied responses of 32 pairs of neurons recorded with microelectrodes 3 mm apart in the visual cortex of macaques performing a fixation task. Upon mapping the receptive fields of the neurons, a quadrilateral was generated so that two of its sides were centered in the receptive fields at the optimal orientations. This one-figure condition was compared with a two-figure condition in which the neurons were stimulated by two separate figures, keeping the local edges in the receptive fields identical. For each neuron, we also determined its border ownership selectivity (H. Zhou, H. S. Friedman, & R. von der Heydt, 2000). We examined both synchronization and correlation at nonzero time lag. After correcting for effects of the firing rate, we found that synchrony did not depend on the binding condition. However, finding synchrony in a pair of neurons was correlated with finding border-ownership selectivity in both members of the pair. This suggests that the synchrony reflected the connectivity in the network that generates border ownership assignment. Thus, we have not found evidence to support the binding-by-synchrony hypothesis.

*Macaca mulatta*). The details of our general experimental methods have been described (Qiu & von der Heydt, 2005; Zhou et al., 2000). The animals were prepared by implanting, under general anesthesia, first three small posts for head fixation, and later two recording chambers (one over each hemisphere). Fixation training was achieved by controlling fluid intake and using small amounts of juice or water to reward correct responses. All animal procedures conformed to National Institutes of Health and USDA guidelines as verified by the Animal Care and Use Committee of the Johns Hopkins University.

^{2}was used, except for conditions in border ownership tests in which figure and background color were flipped (see below). Eye movements were recorded for one eye using an infrared video based system (Iscan ETL-200) with a resolution of 5120 (H) and 2560 (V). The eye was imaged through a hot mirror (selectively reflecting infrared), with the camera placed on the axis of fixation. The optical magnification in our system resulted in a resolution of the pupil position signal of 0.03 deg visual angle in the horizontal and 0.06 deg in the vertical. However, noise and drifts of the signal reduced its accuracy.

*SD*= 0.15–0.2 deg), and data from trials during which the fixation deviated from the target by more than 1 deg during 800 ms after stimulus onset were discarded.

^{2}gray were used for figure and background colors, otherwise white (53 cd/m

^{2}) and gray (16 cd/m

^{2}). Both configurations were also tested with the colors of figures and background reversed, so that one-figure and two-figure conditions in which the local edges in the receptive fields were identical could be compared. The four configurations (Figure 1) were presented in random order, one per trial (fixation period). The color of the blank screen shown between trials was intermediate between figure and background colors.

*B*

_{s}was defined as:

*n*

_{prefer}

^{i}and

*n*

_{null}

^{i}are the neuron's count of spikes for trial

*i*during the interval [60 ms, 800 ms] in response to the preferred and the nonpreferred sides of figure in the receptive field, respectively. The bracket 〈〉

_{i}denotes the average over all trials. The denominator

*σ*

_{r}is the square root of the residual variance calculated from a two-way ANOVA, in which the figure location (relative to the receptive field) is one factor and the local contrast polarity is the other factor. The ANOVA was performed on the squareroot-transformed spike counts,

*n*′ =

*pair*of neurons, we define

*B*

_{s1},

*B*

_{s2}are the border ownership selectivities computed from Equation 1 for the two individual neurons.

*B*

_{p}was not normally distributed, but inspection of quantile to quantile plots of various powers of

*B*

_{p}showed that the transformation using a power of 1/6 produced a normal distribution. We therefore used

*B*

_{p}

^{1/6}as the predictor for examining the correlation between synchronization and border ownership selectivity (Box & Cox, 1964).

*S*

_{j}

*(*

^{i}*n*), where

*n*is the bin index,

*j*is the number of the neuron, and

*i*is the trial number. The spike train,

*S*

_{j}

*(*

^{i}*n*), is a binary vector in which each component takes on either the value 0 if no spike is present in the interval [

*n, n*+ 1) ms in neuron

*j*during trial

*i,*or 1 if there is such a spike. Neurons typically responded to the stimuli with a fast transient response with a high, fast-changing instantaneous firing rate, followed by a period of sustained firing. We only analyzed the correlations during the sustained response period. To identify the latter, we fitted the function

*α*+

*β*exp(−

*kt*) to the average peri-stimulus time histograms (PSTH; Figure 2,

*α*= 23,

*β*= 120,

*k*= −0.019). The sustained response period was chosen to be the interval [160, 800] ms (right of vertical dashed line in the figure). We define a window function

*h*(

*n*) as

*h*(

*n*) = 1 if 160 ≤

*n*< 800 and

*h*(

*n*) = 0 otherwise.

*j, k*for the

*i*th trial is then calculated as

*t*is the time shift between the two spike trains (−

*w*≤

*t*≤

*w*). The parameter

*w*is the window of the cross-correlation function (

*w*= 100 ms in this study). Note that we omit the time argument in the ⊙ formulation here and everywhere below to alleviate notation. The cross-correlogram (see Figure 3A gray curve) of neurons

*j*and

*k*is the average of cross-correlation functions over all trials,

_{i}again denotes the average across trials

*i*.

*j, k*), referred to in the following as covariogram

*K*

_{j,k}, is thus

*j*during trial

*i*is,

*C*

_{j,k}(

*t*) is computed as:

*β*

_{j}

*=*

^{i}*β*

_{k}

*=*

^{i}*B*

_{j}and

*B*

_{k}, each of whose components is 〈

*c*

_{j}

*〉*

^{i}_{i}and 〈

*c*

_{k}

*〉*

^{i}_{i}, respectively, we can write Equation 8 as,

*a,b*) = 〈

*a*

^{i}

*b*

^{i}〉

_{i}− 〈

*a*

^{i}〉

_{i}〈

*b*

^{i}〉

_{i}denotes the covariance operation. The second term (see Figure 3A purple curve; note that this correction is usually very small) on the right hand side of Equation 9 is similar to the excitability covariogram proposed by Brody (1999), except that Brody used a more complicated neuronal model which includes a background term and a stimulus-induced term. However, since the background term is estimated from the activity recorded before the stimulus period, Brody's correction usually does not converge to exactly 0 if we integrate the excitability-corrected covariogram from −∞ to ∞.

*i*by

*t*

_{i}, and computed the ECCs

*C*

_{j,k}as described (Equation 8), now based on time-shifted versions of the spike trains,

*S*

_{j}

*(*

^{i}*t*−

*t*

_{i}), and

*S*

_{k}

*(*

^{i}*t*−

*t*

_{i}). We then quantified the strength of the synchrony (as defined later in Significance tests of synchrony and correlation section), i.e., the weight of any potential peak in the cross-correlation function around zero time lag with half integral width 20 ms, and determined its statistical significance as described below (Significance tests of synchrony and correlation section). The correlation functions will depend on the choice of the time shifts. If the synchrony were, in fact, due to a set of time shifts of the spike trains, say by

*τ*

_{i}, then it will disappear for the choice

*t*

_{i}= −

*τ*

_{i}since this would exactly compensate for the time shift that caused synchrony and thus make it disappear.

*t*

_{i}∈ [−10 ms, 10 ms] and used an optimization algorithm seeking to minimize the strength of synchrony with half integration width 50 ms. The minimization was performed by an exhaustive search for all time variables, first optimizing with respect to

*t*

_{1}, then

*t*

_{2}etc., and repeating this procedure until the synchrony strength reached a minimum. As discussed above, if the peak were due to a common shift in latency, it would disappear for some set of time shifts (which in general would be different for each trial), namely the one that compensates for the latency shift common for both neurons. Before the minimization, there are 8 pairs significantly synchronized (the test method is described in Significance tests of synchrony and correlation section) in the one-figure condition and 3 pairs significant in the two-figure condition. The minimization procedure is likely to result in a loss of some significance since a large number of changes was applied (20 different time shifts for each trial, thus thousands of shifts for every neuron pair), each in the direction that decreased significance if possible. As expected, the statistical significance of synchrony was lost for some pairs but even after the minimization, 5 pairs remained significant in the one-figure condition and 2 pairs remained significant in the two-figure condition. No neuron pair changed significance in both binding conditions (note that the latency effect is independent of the binding condition). Note that this is a conservative method since we compare the significance of a minimized test statistic (the integral over the peak) against the distribution of nonminimized values. We did the same regression analysis on the shifted spike trains as discussed later, and our conclusions did not change. We therefore concluded that latency covariation effects can be ignored in our data.

*S*

_{j,k}

*measures the degree of synchronous firing. To compute it, we integrate the ECC of neurons*

^{s}*j, k*as defined in Equation 8, over the interval ±

*τ*ms around 0 ms time lag (Figure 3C, the area under the black curve in the interval quantified by vertical cyan lines). In our discretized data set, this integral is the finite sum

*A*

_{j}(Figure 3B black curve) of neuron

*j*as:

*S*

_{j,k}

*(*

^{s}*τ*) for neuron pair (

*j, k*) is then defined as:

*τ*is the half integration width for both ECC (Figure 3C marked by cyan dashed lines) and auto-correlogram (Figure 3B marked by cyan dashed lines). This definition

^{1}with auto-correlation normalization has the intuitively appealing property that

*S*

^{s}(

*τ*) will approach Pearson's cross-correlation coefficient of the two neurons trial-wise spike counts when

*τ*→ ∞ (Bair, Zohary, & Newsome, 2001; Roelfsema et al., 2004). In our case,

*S*

^{s}will approach 0 due to the excitability covariogram correction.

*not*simultaneously recorded. We do this by generating 10000 permutations of pairs of trial indices (drawn without replacement) and number them with the index

*p*= 1, 2, …, 10000. Let

_{j,k}

*be the ECC computed as in Equation 8 but using the*

^{p}*p*th permutation of the trial indices. The corresponding permuted strength of synchrony is

_{j,k}

*forms the null distribution. Given half integration width*

^{p}*τ,*we test the significance of the observed value for the integral around the peak, by using

*S*

_{j,k}

*(*

^{s}*τ*) from Equation 12 as the test statistic. If the value of

*S*

_{j,k}

*(*

^{s}*τ*) exceeds that of 95% of the values of

_{j,k}

*(at the*

^{p}*p*= 0.05 significance level), we will conclude that a significant peak is present in the ECC of neurons

*j*and

*k,*and the fraction of the distribution

_{j,k}

*with a value exceeding*

^{p}*S*

_{j,k}

*(*

^{s}*τ*) is the

*p*value of this test.

*S*

_{j,k}

*for neuron pair (*

^{c}*j, k*) is a more general measure used to quantify the correlations between the two neurons in the range of [−50, 50 ms], not necessarily at a time offset of zero. Such correlations would be manifested by peaks in the ECC. Let

*B*

_{10}() be a normalized Gaussian smoothing filter with standard deviation 10 ms around zero. The ECC is smoothed (Figure 3D blue curve) by convolving it with

*B*

_{10}, using the discrete convolution defined as,

*T*

_{peak}of the smoothed ECC in the interval [−50, 50 ms]. Note that

*B*

_{10}⊗

*C*

_{j,k}(

*T*

_{peak}) = max(

*B*

_{10}⊗

*C*

_{j,k}(

*n*)) where the max function always takes on the largest value of its argument for

*n*∈{−50, −49,…, 49, 50}. We thus obtain the strength of correlation for neuron pair (

*j, k*),

*τ*is the half integration width for both ECC (Figure 3D marked by two cyan dashed lines) and auto-correlogram. Comparing with Equation 12, correlation as defined here is equivalent to the strength of synchrony calculated around the peak of the ECC within the interval [−50, 50] ms rather than (always) around zero.

*p*th permuted smoothed ECC (

*B*

_{10}⊗

_{j,k}

*(*

^{p}*n*)) is

*T*

_{peak}

^{p}. Then given the half integration width

*τ,*the

*p*th permuted strength of correlation is

_{j,k}

*(*

^{p}*τ*) =

*O*

_{j,k}

*(*

^{p}*τ*) form the null distribution for the permutation test. Completely analogous to the synchrony test, the test statistic to be used now is

*S*

_{j,k}

*(*

^{c}*τ*).

*j, k*) with spike trains

*S*

_{j}

*and*

^{i}*S*

_{k}

*, where*

^{i}*i*= 1, …,

*N*is the trial index and

*N*is the number of trials, we generate “artificial experiments” by drawing randomly, with replacement, numbers

*i*∈[1,

*N*] each of which corresponds to a trial index; thus, we draw a set of

*N*pairs of spike trains. Let

*R*

^{p}be the vector of length

*N*whose

*i*th component is the

*i*th number drawn, and

*p*∈[1, 10000] is the index in the set of trial indices. From this set of trial indices, we can find the geometrical mean firing rate

*F*

^{p}and compute the corresponding ECCs as in Equation 8, which we call

_{j,k}

*. We obtain for each of those the “bootstrapped strength of synchrony,”*

^{p}*S*

_{j,k}

^{p}*R*

_{j,k}

^{p}*T*

_{peak}was found from the smoothed ECC

_{j,k}

*as described previously. The variability (noise) of synchrony and correlation can be estimated from the distribution of*

^{p}*S*

^{p}and

*R*

^{p}.

*S*

_{i}and firing rate

*F*

_{i}and neuron pair BO selectivity

*B*

_{i}as independent variables, where

*i*is the index of the data point. There are 32 (

*i*= 1, …, 32) data points corresponding to the 32 neuron pairs. We draw, with replacement, 32 data points from the pool [

*F*

_{i},

*B*

_{i},

*S*

_{i}] and calculate the regression coefficient. Repeating this 10000 times, we obtain a distribution of the coefficients and we test the significance of the measured coefficient under the null hypothesis that there is no effect of the independent variable (coefficients are 0). To include the neuron's intrinsic noise, we change the pool into [

*F*

_{i}

*,*

^{p}*B*

_{i},

*S*

_{i}

*] where*

^{p}*S*

_{i}

*is the “bootstrapped strength synchrony” defined above (Equation 17) and*

^{p}*F*

_{i}

*is the corresponding firing rate. When we draw the*

^{p}*i*th neuron data, we choose one (index

*p*) of the bootstrapped synchrony

*S*

_{i}

*and corresponding firing rate*

^{p}*F*

_{i}

*randomly. Then the distribution of the coefficients contains the neuronal intrinsic noise.*

^{p}*w*= 100 ms (see Equation 3). In our parametrization, peak positions are integers ∈ [0, 99] corresponding to the position of the peaks in the strength of correlation (positive and negative integers are pooled since the sign only reflects the arbitrary ordering of neurons). The histogram of the peak positions (64 peaks in total, Figure 8) for both figure conditions was plotted in 5 bins, each 20 ms wide.

*k*in one bin of a histogram under the null hypothesis is a random number following the binomial distribution, namely the probability of

*k*counts is (

^{k}(1 −

^{64−k}. The

*p*value under the null hypothesis would be the probability (or

*p*value) that the number of the counts in one bin larger than the observed count

*o*:

*p*> 0.05). Therefore, results from the 32 pairs were pooled.

*t*test,

*p*= 0.397). These numbers are also close to what would be expected from independently firing neurons: given that their mean firing rate is 23.8 spikes/s (see Figure 2), an average of 23.8/1000 × 5 = 0.119 spikes in one neuron occur by chance within a ±2 ms window relative to a spike in the other neuron. By this simple measure, the neurons are therefore only weakly correlated.

*S*

^{s}(34), and correlation strength (normalized integral of the ECC around peak of the ECC),

*S*

^{c}(18), i.e., at their respective peaks shown in Figure 4. For strength of synchrony, we found that 5 pairs were significant in the one-figure condition only, 4 pairs were significant in both binding conditions (one-figure and two-figure conditions), and no neuron pair was significant in the two-figure condition only. For strength of correlation, 3 pairs were significant in the one-figure condition only, 4 pairs were significant in both binding conditions, and 3 pairs were significant in the two-figure condition. In the one-figure condition, both

*S*

^{c}(18) and

*S*

^{s}(34) were significant in 6 pairs of the neurons, while in the two-figure condition, both

*S*

^{c}(18) and

*S*

^{s}(34) were significant in 4 pairs of the neurons, as a result of the tendency of the peaks in the ECCs to be centered around 0 ms time lag.

*S*

^{s}(34) as the dependent variable and binding condition and the firing rate of a neuron pair (defined as the geometrical mean of the firing rates of the two neurons) as independent variables, plus one random intercept term which quantifies the neuron identity effects. We found a significant firing rate dependence (

*p*= 0.0003), but the effects of binding condition (

*p*= 0.661) and the interaction between rate and binding condition (

*p*= 0.088) were not significant. Thus, after removing the firing rate effects, the effect of the binding condition disappeared. Applying the same model to the strength of correlation

*S*

^{c}(18), we obtain a similar result. There was a significant firing rate effect (

*p*= 0.0335), but the effects of binding condition (

*p*= 0.735) and interaction (

*p*= 0.401) were not significant.

*p*values,

^{2}summarized in Figure 5, confirm that, for the whole range of integration widths, synchrony and correlation significantly depend on the neuron pair firing rate but not on the binding conditions.

*S*

^{s}(34) and

*S*

^{c}(18) significantly depended on neuron pair BO selectivity and, furthermore, strength of both synchrony and correlation increased with the BO selectivity (coefficients are positive). Firing rate was found significant in the strength of synchrony and close to significant (

*p*= 0.076) in the strength of correlation. We did not find evidence of binding nor any significant interaction effects for either synchrony nor correlation.

Terms | Synchrony | Correlation | ||
---|---|---|---|---|

Coefficient | p value | Coefficient | p value | |

Intercept | −0.169 | 0.0172 | −0.114 | 0.044 |

Rate | 5.846 | 0.0388 | 4.048 | 0.076 |

Bos | 0.152 | 0.0467 | 0.151 | 0.017 |

Bind | 0.043 | 0.3270 | 0.040 | 0.287 |

Rate:bos | −2.082 | 0.4473 | −2.433 | 0.287 |

Rate:bind | −1.713 | 0.1143 | −0.671 | 0.463 |

Bos:bind | −0.043 | 0.3952 | −0.043 | 0.324 |

*p*values for the same linear model as discussed in the previous paragraph are summarized in Figure 6. Both synchrony and correlation depended significantly on BO selectivity for a range around the integration widths around 34 ms for synchrony and 18 ms for correlation, although significance is only marginal for the former. The effect of rate is only significant for the strength of synchrony, and correlation was found to be close to significant for some smaller choices of the integration width. Importantly, the binding condition did not have a significant effect, nor did any of the interactions.

^{3}The loss of statistical power was expected, because of the limited number of only 32 neuron pairs (the power of the bootstrap regression is limited by the number of data points) and because the bootstrapping procedure contributes additional “noise.” The evidence of a dependence on firing rate and neuron pair BO selectivity is thus weaker in these results than in the linear regression model. Nevertheless, the results of this test still convey the same message that there is little support for the BBS hypothesis.

^{4}We examined whether the strength of synchrony or correlation also depends on the directional selectivity. We selected border ownership selective neuron pairs if the border ownership selectivity was stronger than 0.2 for both of the neurons, resulting in 22 pairs with this property. This group was divided into 3 sub-groups: the 〉〈 group (5 pairs), in which the preferred sides of border ownership pointed towards each other; the 〈〉 group (4 pairs), in which the preferred sides of border ownership pointed away from each other; and the ≪ group (13 pairs), in which the preferred sides pointed in the same direction. Including this 3-level categorical variable in the analysis, we tested a new linear model by analysis of variance. Note that the neuron pair BO selectivity was eliminated as a dependent variable since only BO selective neurons were included in this analysis. The

*p*values are summarized in Figure 7. We found no evidence for a directional selectivity effect. Significance was only reached by rate. Again, we found no support of the BBS hypothesis.

*S*

^{c}(18) are summarized in Figure 8A. The peaks cover the whole [0 ms, 99 ms] range. However, for neuron pairs with significant strength of correlations (by randomization test

*p*< 0.05, large symbols in Figure 8A), the lags are mostly contained within the interval [0, 20] ms. Peaks for neuron pairs with smaller strength of correlations are spread more widely and their peak positions may be due to random effects. We fitted the strength of correlation

*vs*. peak position data with an exponential plus constant (

*α*exp(

*βx*) +

*c*) and found

*α, β,*and

*c*(

*α*= 0.104,

*β*= −0.105,

*c*= 0.0303) to be all significantly different from zero (

*p*< 0.05,

*t*test). In the peak histogram (Figure 8B), the first bin was significantly higher than expected by chance (

*p*= 0.042 binomial test), the other bins were not significant. Thus, we conclude that peaks in the correlation function are mostly found in the [0, 20 ms] interval.

*S*

_{j,k}

^{s}should not be confused with that for the spike trains which is

*S*

_{j}

^{i}(

*n*). The same applies for the symbol for the strength of correlation

*S*

_{j,k}

^{c}, introduced below in Equation 15.

*p*values for these tests do not need the further analysis for multiple tests.

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