Spontaneous activity in cortical neurons is stereotyped and non-Poisson

Abstract

Neurons fire even in the absence of sensory stimulation or task demands. Numerous theoretical studies have modeled this spontaneous activity as a Poisson process with uncorrelated intervals between successive spikes and a variance in firing rate equal to the mean. Experimental tests of this hypothesis have yielded variable results, though most have concluded that firing is not Poisson. However, these tests say little about the ways firing might deviate from randomness. Nor are they definitive because many different distributions can have equal means and variances. Here, we characterized spontaneous spiking patterns in extracellular recordings from monkey, cat, and mouse cerebral cortex neurons using rate-normalized spike train autocorrelation functions (ACFs) and a logarithmic timescale. If activity was Poisson, this function should be flat. This was almost never the case. Instead, ACFs had diverse shapes, often with characteristic peaks in the 1–700 ms range. Shapes were stable over time, up to the longest recording periods used (51 min). They did not fall into obvious clusters. ACFs were often unaffected by visual stimulation, though some abruptly changed during brain state shifts. These behaviors may have their origin in the intrinsic biophysics and dendritic anatomy of the cells or in the inputs they receive.

Introduction

When cortical neurons are unstimulated, they generally fire at low rates, usually termed “spontaneous activity.” The intervals between spikes are erratic and, in the visual cortex, were initially thought to occur at random, where the times of successive spikes are independent, forming a Poisson process (Tomko and Crapper 1974; Burns and Webb 1976). These and subsequent studies of firing statistics, including those evoked by visual stimuli, used either the coefficient of variation (CV: the ratio of the standard deviation of the interspike interval [ISI] divided by the mean interval) or the ratio between the mean and the variance of spike counts taken over fixed intervals, known as the Fano factor. Both factors should be equal to 1 in the case of Poisson firing. The Fano factor will also equal 1 in the case of Poisson firing averaged over a variable firing rate caused by a more slowly varying stimulus, known as an inhomogenous Poisson process. These tests have been extensively applied to studies of stimulus-evoked firing, with the assumption that the stimulus merely modulates the firing rate on a timescale that is slow compared with the intervals between spikes. These tests have yielded variable results. Some studies reported Fano factors <1 in V1 (Gur et al. 1997; Kara et al. 2000; Gur and Snodderly 2006) and IT (Gershon et al. 1998). More commonly, variance has been found to be greater than the mean (Heggelund and Albus 1978; Tolhurst et al. 1983; Bradley et al. 1987; Skottun et al. 1987; Scobey and Gabor 1989; Vogels et al. 1989; Snowden et al. 1992; Swindale and Mitchell 1994; Geisler and Albrecht 1997; Bair and O’Keefe 1998; Scobey and Gabor 1989; Burac̆as et al. 1998; Shadlen and Newsome 1998; McAdams and Maunsell 1999; Maimon and Assad 2009). Variations between cortical areas have also been reported (Amarasingham et al. 2006; Maimon and Assad 2009) with the latter studies disagreeing on whether Fano factors are relatively low or high in V1. Mochizuki et al. (2016) studied various measures of ISI regularity in a variety of species and cortical areas and showed that firing was most regular in motor areas and near random in visual and prefrontal cortex (PFC). Theoreticians have generally assumed or pointed to advantages of Poisson firing (e.g. Gabbiani and Koch 1998; Dayan and Abbott 2001; Ma et al. 2006), although possible advantages of non-Poisson firing have been suggested (Koyama et al. 2013). It is common for neural models, such as the Linear-nonlinear-Poisson model, to implement Poisson firing at the output stage (e.g. Simoncelli et al. 2004). More to the point however, neither the Fano factor nor the CV is an ideal test of randomness as many different distributions can have a variance or a standard deviation equal to the mean (Kostal and Lánsky 2007). Even if the tests can show non-Poisson firing, they do not provide detailed information about the ways in which firing might deviate from that predicted by Poisson statistics.

In this paper, we report the results of a different test of the Poisson hypothesis. We computed the rate-normalized spike train autocorrelation function (ACF) using a logarithmic timescale. To the best of our knowledge, this analysis method is new. It shows the relative probability of firing as a function of time following a spike. Poisson firing will result in a flat function with a value of 1 beyond the refractory period, indicating no history dependence of one spike following another. The use of a logarithmic timescale can be justified by the fact that the temporal precision of potential signals is likely to be a constant fraction of the interval involved and hence to vary logarithmically. The ACF was used in preference to the interval distribution because it offers a richer description of temporal structure, giving the relative probability of occurrence of all the spikes that might follow a single spike, not just one. ACFs were calculated in this way for intervals between 1 and 1,000 ms, for units recorded with multi-electrode arrays (MEAs) in the cortices of primate, cat, and mouse. Recordings lasted from 15 to 51 minutes.

The results showed that almost no units passed a test for Poisson randomness. Instead, ACFs of spontaneous activity were diverse in shape across units, with characteristic peaks at temporal intervals over the range 1–700 ms. Functions were stable in shape over time, up to the longest recording periods used (51 min). There was little effect of physical separation in the cortex on the similarity in ACF shapes of unit pairs, measured using correlation. ACF shapes, as studied using a variety of methods, did not fall into obvious clusters. Shapes were variously impacted by visual stimulation and changes in brain state in the cat recordings, with some units changing and others remaining unaffected. The characteristic temporal firing patterns of different units may have their origins in the intrinsic biophysics of the cells, the inputs they receive, or in network dynamics.

Methods

Experimental details

Data were obtained from extracellular recordings made with multi-electrode array (MEA) electrodes in an awake macaque monkey (recordings R1 and R2), 5 anesthetized cats (recordings R3–R9), and 1 awake mouse (R10; Table 1). All procedures had been carried out in accordance with approved protocols at the institutions involved. The 2 monkey recordings were made using 96 channel Utah arrays (Blackrock) each spanning a 4 × 4 mm area of cortex with sites in the superficial layers. One electrode was in PFC and the other in area TEO (a region in temporal–occipital cortex). The recordings from cat were made from area 17 with the electrodes inserted vertically through the crown of the lateral gyrus. Anesthesia in these animals was either with 0.5%–1.5% isoflurane and 70% N₂O + 30% O₂ (recordings R3, R4, R8, and R9) or with continuously infused propofol (6–9 mg·k⁻¹g·h⁻¹) and fentanyl (4–6 μg·kg⁻¹·h⁻¹) (recordings R5–R7). The recording (R10) from the mouse was obtained at http://data.cortexlab.net/. It was made from an awake, head-fixed mouse with a Neuropixels phase3 array with a total of 384 channels. Because the electrode passed through structures other than the cortex, only the top 120 of the channels, which were judged to have been in the cortex (N. Steinmetz, personal communication), were used to isolate and sort units. The recording was divided into 2 periods. In the first, the animal received visual stimulation, and in the second, the animal was kept in nearly complete darkness. Local field potential (LFP) records suggested the animal remained awake during this period. Animals in recordings R1, R2, R3, R4, R6, R7, and R10 were male and in recordings R5, R8, and R9 were female. Further details of the procedures used in cats are given in Swindale and Spacek (2019). Details of the procedures used in monkeys are given in Krause et al. (2017). Signals from spikes in all the recordings were detected and sorted using the program “SpikeSorter” (https://swindale.ecc.ubc.ca/home-page/software/), which implements methods documented elsewhere (Swindale and Spacek 2014, 2015). Sorting was based on clustering of principal component distributions obtained from spike waveforms after carefully aligning waveforms to the mean. In order not to bias the results, we explicitly avoided using any aspect of the units’ spike train ACFs as a criterion for merging, or not merging, units with similar spike waveform shapes.

Table 1.

Spontaneous recording datasets.

ID	Species and cortical area	Anesthesia	Recording duration (mins)	No. of units	No. of units >2,000 spikes and SNR > 1.8
R1	macaque PFC	None	17.8	78	31
R2	macaque TEO	None	17.8	101	36
R3	cat area 17	iso/N2O	40.6	25	11
R4	cat area 17	iso/N2O	15.2	67	16
R5	cat area 17	prop/fent	45.1	25	10
R6	cat area 17	prop/fent	50.7	42	15
R7	cat area 17	prop/fent	15.6	43	13
R8	cat area 17	iso/N2O	21.4	69	21
R9	cat area 17	iso/N2O	45.0	46	14
R10	mouse V1	None	43	117	64

SNR = signal-to-noise ratio; iso = isoflurane; prop = propofol; fent = fentanyl.

Data preprocessing

To select units for further study, we used an exclusion criterion based on the signal-to-noise ratio (SNR) for which (i) the signal was defined as the peak-to-trough amplitude of the unit’s template (the average of all the individual, aligned, spike waveforms) taken on the channel for which the peak-to-trough value was a maximum, and (ii) the background noise was defined as the average of 1,000 randomly chosen peak-to-trough values for the voltage signals on the same channel, i.e. differences between the maximum and minimum voltage taken over a temporal window equal to that used to contain the template (typically around 1 ms in duration). Units with a SNR < 1.8 were excluded from analyses. Unless otherwise stated, units also had to fire more than 2,000 spikes during the period for which an autocorrelogram was calculated. These cut-off values represented a compromise between increasing the number of units in the study and including units that were likely poorly sorted or fired too few spikes to yield a well-defined ACF. The values were decided on after an initial set of data analyses and were not changed subsequently.

Calculation of the normalized ACF

ACFs for individual units were calculated using the following relation between the bin number, n, and the temporal interval, Δt ms, between a pair of spikes indexed by i and j, occurring at ordered times such that t_i + 1 > t_i ∀ i:

(1)

where α is a constant that determines the width ratio of successive bins, and int() denotes integer truncation. A raw count histogram, C(n), was first compiled by summing over pairs of spikes

(2)

The histogram was calculated using all pairs of spikes in the spike train, or the portion of it being analyzed, for a given unit, taking only intervals 1 ≤ Δt ≤ 1000 ms into consideration. The raw histogram counts were normalized to give a histogram A(n), first by dividing by the bin widths, given by 10^{α(n + 1)} −10^αn, and then further dividing by the total number of spikes, N, squared and multiplying by the recording duration T, where both bin widths and duration have the same units of time:

(3)

The rationale for this is that, for a given number of spikes, the raw bin counts will tend to increase as the square of the number and will decrease linearly as the recording duration increases. For a unit firing with a Poisson distribution, i.e. a fixed probability of firing in a given temporal interval, the values of A(n) in the limit of large numbers of spikes, will be flat, with a value of 1 in each bin. This can be taken as the null hypothesis, or Poisson limit, for each unit. Values shown in the graphs of the ACFs can hence be interpreted in terms of relative probability. For example, a value of 3 would indicate 3 times more spikes for that interval than expected on the basis of random firing. It can also be noted that because the bins are narrower for shorter temporal intervals, the number of observations in them will be smaller; hence the noise in the observations increases with smaller temporal intervals. It is convenient to index A by the value of Δt that would result in the given value of n according to Eq. (1) and to graph the histogram using logarithmic scaling on the x-axis, which will result in equally sized and spaced bins. For the analyses reported here, we used a value of α = 22.77, which gave a total of 69 bins in the range 1–1,000 ms. The choice of α reflected a compromise between temporal resolution in the histogram and noise resulting from the limited number of observations in each bin.

An empirical estimate of the error in each bin value was made by dividing each recording into m periods, each 1 min long, and calculating m histograms, one for each interval. Each of these histograms was further normalized by dividing by the sum of the bin values. This removed slow temporal variations common to all the bins (justification for this is given later on). The standard deviation, taken across the m samples, was then divided by √(m-1) (the Bessel correction) to give an estimate, after rescaling, of the standard deviation in each bin of the complete histogram. This value will be referred to as E(Δt_n).

Results

Each recorded unit had a characteristically shaped ACF, which was stable over the recording period. Figure 1 shows examples of functions from 4 different recordings. They are characterized by peaks with variable widths and positions in the range 1–1,000 ms. At intervals >100 ms, the functions tended towards the Poisson limit of 1, i.e. a fixed probability of firing, given by the rate averaged over the period of the recording. The functions often had values >1 for intervals <100 ms, indicating a tendency to fire in bursts. Plots of the ACFs as a function of time (Fig. 2) illustrate that the distinctive shapes were maintained over the periods of the recordings, which ranged from 18 to 51 min (Table 1). Some changes were observed. For example, Fig. 2D shows a slight decrease in peak intervals over the period of the recording. Many units showed variations in firing rate which were not directly manifest in the ACFs because of the normalization procedure (see Methods). However, periods of low firing rate usually gave rise to more noisy ACFs and/or missing detail in the plots. These variations are investigated in more detail later on.

Fig. 1.

Examples of log-time, rate-normalized autocorrelation functions (ACFs) from simultaneously recorded, spontaneously active units in 4 different animals: A is from a recording (R2) from area prefrontal cortex (PFC) in an awake macaque monkey; B and C are from recordings R2 and R9 in area 17 in anesthetized cats and D is from recording R10 in visual cortex of an awake mouse. Units were chosen to illustrate the diversity of ACF shapes. The dashed line shows the Poisson limit of 1, i.e. the value expected from random firing. Error bars in A and B show the s.d.s estimated as described in the Methods. They have been omitted from C and D for clarity.

Fig. 2.

Autocorrelation functions (ACFs) from different units calculated in 1-min long periods, shown as a function of time since the start of the recording period on the horizontal axis, and with temporal interval on the vertical axis. Pixel brightness is proportional to the ACF value. Examples were taken from 4 of the longer duration recordings: R5, R6, R9, and R10. Three of these units (D, E, and F) are also shown in Fig. 1. Note that a nonlinear (gamma function) ACF value to brightness scaling was used for the displays, with different scaling values for different units. These values were chosen to illustrate detail in different functions as clearly as possible. Hence, brightness should not be relied upon for quantitative information.

Split-period analysis

We characterized the consistency of ACF shape within units, relative to the variety among them, by splitting each recording period into 2 halves with equal numbers of spikes in each. In order to be included in the sample, the unit had to fire ≥2,000 spikes (i.e. ≥1,000 spikes in each half of the recording). For each qualifying unit in each recording, we calculated the Pearson correlation (r) between the ACF shapes (i) for halves belonging to the same unit and (ii) for different halves belonging to different units. For the latter case, correlating halves, rather than the entire period of the recording was done in order to avoid a possible bias resulting from increasing the number of spikes used in the cross-unit comparisons compared to the within-unit comparisons. Figure 3A shows the distributions of correlation values for within-unit and cross-unit comparisons as scatter plots with the number of spikes used for the comparison on the x-axis. Figure 3B shows the same data plotted as histograms. The cross-unit correlation values covered nearly the entire range of −1 to +1, with a mean of 0.24 ± 0.41 (n = 7,630). Some values were close to 1 though there was no clear evidence (Fig. 3B) that highly similar autocorrelograms formed a separate group, as might be expected if there was clustering of shapes. Within-unit correlations were high with a mean of 0.79 ± 0.24 and only 13.4% (31/231) units having values of r < 0.5. Units showing lower values tended to have lower spike counts, and it can be noted that noise in general will tend to systematically reduce absolute correlation values, rather than randomly perturb them. The difference in r-values between the 2 groups was highly significant with P < < 0.001 (Mann–Whitney U-test). These results demonstrate consistency of ACF shape over time within units, as well as diversity across units.

Fig. 3.

Results of the split-halves analysis. The correlation between the autocorrelation functions (ACFs) of different halves of the recordings was calculated. A) Scatter plots showing the correlation values for recording halves belonging either to the same unit (within-unit, black dots) or to different units (cross-unit, gray dots). The x-axis shows the number of spikes in both halves. B) The same data shown as distributions of within- and cross-unit correlation values.

Effects of physical separation

Units that are physically close together in the cortex might tend to have similar ACF shapes, indicating a systematic mapping of temporal properties. Unit positions were estimated by finding the spatial center-of-gravity of the spike template waveform, using the peak-to-peak amplitude on different electrode channels. Figure 4 is a scatter plot of cross-unit correlation values (taking the entire recording period into account) versus the spatial distance between units. Units had to fire ≥2,000 spikes to be included. The correlation was significant with r = − 0.081, n = 7,630, and P < 0.001; however, the percentage of the variance accounted for by the correlation (100r² = 0.66%) was small. This suggests that physical proximity makes a negligible contribution to the temporal properties of cell pairs as manifested by their ACFs.

Fig. 4.

The correlation between the autocorrelation functions (ACFs) of different units within the same recording, graphed as a function of the distance between them. The dashed line is the linear regression.

Effects of intrinsic changes in firing rate

Many units showed substantial variability in their spontaneous firing rates measured over time periods of seconds or minutes. This behavior is largely hidden in Fig. 2 (which shows how ACF structure varies on a comparably slow timescale) because of the normalization procedure applied to the ACFs. The effect of these slow variations in firing rate on the shape of the ACF was assessed by dividing each recording into time slices 1 min long, calculating the firing rate in each slice, and then calculating averaged ACFs for those sets of slices with rates either below or above the median rate. An example of a pair of ACFs obtained this way is shown in Fig. 5C. The correlation between each pair of ACFs was calculated and graphed against the ratio of the spike counts in the 2 conditions (Fig. 5A). This was done for all units in the data sets, excluding units with <2,000 spikes in the low firing rate periods. Figure 5B shows the resulting distribution of correlation (r) values for n = 125 units. The majority (82/125 or 66%) had r > 0.9 indicating a high degree of similarity in shape during high- and low-firing rate periods. Note that the normalization procedures applied to the calculation of the ACFs mean that the values will not scale in any particular way with the number of spikes (although multiplicative scaling of either of the ACFs would leave the correlation values unchanged in any case). The results suggest that variations in response rate, while they (by definition) change the overall probability of firing, have little effect on the conditional probability of firing at short intervals following a spike.

Fig. 5.

The correlation between the autocorrelation functions (ACFs) calculated separately from low- and high-firing rate periods of firing within individual units. A) Scatter plot showing the correlation values graphed against the count ratio (number of spikes fired in the low-firing rate periods divided by the number fired in the high rate periods). B) The distributions of the correlation values are shown in A. C) Example of a unit from dataset R9 (also shown in Fig. 2D) showing similar ACFs during low- and high-firing rate periods. The correlation was 0.98 and the low/high spike count ratio was 0.31.

Do the ACFs have stereotyped shapes?

We asked whether the ACFs fell into a continuum of shapes or whether different classes were present. While categorization into types is possible based on the temporal pattern of spiking responses to injected current (Nowak et al. 2003), it is possible that such categories might be less evident in the absence of injected current. A simple measure was tested based on the observation that some ACFs are relatively low in value (i.e. A < 1.0) up to around 10 ms, whereas others have values above 1.0 in that range. High values in this range indicate a tendency to bursting, which is thought to be characteristic of particular types of cortical neuron (Nowak et al. 2003). We calculated a value, here termed the “burst index,” which was the mean of the ACF values in the interval 1–10 ms. This was plotted it against the mean in the interval 10–1,000 ms. Although many other definitions of bursting behavior exist in the literature, this procedure is comparable to that used by others to define burstiness (e.g. Krause et al. 2019). Figure 6A shows the results which, although they might be used as an ad hoc basis for classification, do not provide clear evidence for distinct types.

Fig. 6.

Lack of clear evidence for clustering of autocorrelation function (ACF) shapes. Points are colored according to dataset, as shown in panel A. A) A plot of the sum of ACF values in the range <10 ms (referred to subsequently as the “burst index”) versus the sum above that range. B) Results of principal components analysis (PCA) of ACF shapes. Thirty-six out of 231 data points fell outside the graph axes and are not shown. C) The results of PCA applied to a log transform of the ACF values, done as described in the text. D) UMAP clustering of the data. The parameters were: n_neighbors = 3; min_dist = 0.3; n_components = 2; metric = Euclidian.

This analysis ignores many aspects of the shapes of the curves. Principal components analysis (PCA) was used in a more general attempt to classify shapes. The analysis was based on a single transformation of all the ACFs in the entire set of recordings, subject to the normal exclusion criteria. Different preprocessing strategies were used and gave different distributions but none revealed obvious clustering. If the raw ACFs were used, the distribution extended from the origin with many outliers and no sign of clustering (Fig. 6B). Standard PCA is sensitive to outliers and hence their presence might mitigate against finding clusters. To reduce the effects of outlying points, an initial log transform of the ACFs was applied, first setting any zero values (which were rare) to half the value of the smallest non-zero value in the ACF. The resulting PC distribution is shown in Fig. 6C. It was much more compact, without outliers. However, with the possible exception of a group of 4 points below the main group, clusters were not apparent. We also applied UMAP (McInnes et al. 2018) (Fig. 6D) and tSNE (Maaten and Hinton 2008) transformations. Neither method showed obvious clusters.

Peak intervals

Most, though not all, ACFs had one or more peaks in them, often for values of Δt < 10 ms and sometimes with more than one peak in that range. There was no obvious pattern to the peak values except that harmonically related peaks often occurred in obvious groups, e.g. at t, 2t, and 3t. On a log plot, these relationships result in peak pairs a fixed distance apart, independent of the implied frequency, e.g. peaks at intervals of t and 2t will be a distance of log(2) apart, which is roughly a third of the distance between intervals of 1 and 10 (or 10 and 100) as plotted on the graphs. They indicate a tendency to oscillatory firing, whereas peaks with no harmonic multiples present represent groupings of pairs of spikes at specific temporal intervals but lacking an oscillatory tendency. Examples of oscillatory firing could be found for very short temporal intervals, e.g. the units shown in Fig. 2E and F, fired at multiples of 1.35 and 2.03 ms, indicating brief oscillation frequencies of 740 and 490 Hz respectively (analyzed further below). Oscillatory firing was not further investigated as a separate phenomenon.

The intervals at which peaks occurred were measured by first calculating smoothed functions that approximated the raw data. To preserve the shapes of the sharper peaks, a sixth-order Savitzky–Golay smoothing filter (Press et al. 1992) with a width ±7 was applied to the raw data, treating the Δt_n values as equally spaced. Spline interpolation was then used to construct a smoothed function, Â, with 10 times the number of points as the raw data. In addition, a smoothed set of error values, Ê, was obtained using Gaussian smoothing applied to the raw error values, determined as described in the Methods. Peaks and troughs in  were determined, and peaks were counted if, for a peak indexed by j with neighboring troughs at points i and k, all of the following were true:

(4)

These criteria ensured, in turn, that selected peaks were not extremely narrow, that peak points were more than 10% higher than their neighboring troughs, and that peak points were more than one estimated standard deviation apart on one side and more than 2 standard deviations on the other.

Visually obvious peaks were occasionally missed by this procedure if, for example, a probably spurious trough was present on one side close to a peak. However, an automated method of identifying peaks that matched visual judgment in all cases was not found.

Figure 7A shows the distribution of peak intervals, plotted against their height (i.e. the normalized smoothed count, Â). The observations showed that peak heights mirrored the general tendency of the ACFs to have high count values at intervals <10 ms and to approach a value of 1 at intervals >100 ms. Peaks covered the entire range of intervals between 1 and 700 ms. With the exception of a clustering of peak intervals around 80 ms in the monkey data, there were no obvious differences in the distributions for the 3 species (monkey, cat, and mouse). Overall, however, the distribution was not uniform (Fig. 7B), showing a tendency to cluster at around 3 ms, 8 ms and, weakly, over a range of 30–700 ms. Note that because individual units often had peaks at intervals both below and above 10 ms, such clustering as is evident in Fig. 7A does not reflect a clustering of units but a clustering of behaviors within individual units. Figure 7C shows the distribution of the number of detected peaks per unit. Many units had no detectable peaks; others had as many as 5. Note that different detection criteria would likely have yielded different numbers.

Fig. 7.

The intervals at which peaks in the autocorrelation functions (ACFs) occurred. A) A scatter plot of peak intervals graphed against their height (normalized count value) with different symbols representing each of the 3 species in the study. B) The frequency distribution of the intervals. C) The distribution of the number of detected peaks per unit. D) Example of a train of spikes occurring at intervals of about 1.5 ms. The vertical lines in the figure are 1 ms apart.

The significance of peaks for inter-spike intervals as short as 1.5 ms might be questioned. However, the majority of cortical spikes are less than 0.5 ms in width, and spikes as little as 1.5 ms apart are not uncommon. Recordings were frequently checked by eye to make sure that short intervals were real. As an example, Fig. 7D shows a group of 5 spikes occurring at intervals of about 1.5 ms, which was mirrored by a corresponding peak in the autocorrelogram (Fig. 1C). Intervals as short as 1 ms have been reported in previous studies (DeBusk et al. 1997; Reich et al. 2000).

Spike widths

Spike width is a parameter that correlates with cell type defined according to spiking pattern (McCormick et al. 1985, 2015; Nowak et al. 2003; Mitchell et al. 2007). These include fast-spiking (FS), chattering (CH), intrinsic bursting (IB), and regular spiking (RS) types. FS and CH types have been shown to have narrow spike widths, and IB and RS types to have broad widths. Although, as shown above, ACFs do not appear to fall into a small number of types, some relationship between spike width and ACF properties might nevertheless be expected. The relationship might not be straightforward however, as bursting types (CH and IB) include both narrow and broad spike types. We first asked whether the similarity of ACF pairs, measured by their correlation, was greater in unit pairs that had similar spike widths. Spike width was measured as the interval between the peak and the trough of the averaged spike waveform, independently of which came first. We chose a threshold of 0.38 ms to divide units into narrow and wide spike categories, based on the observed bimodal distribution of widths in the mouse (Fig. 8B). Eligible unit pairs were placed in 3 groups: (i) where both spikes were narrow, (ii) where the categories were different, and (iii) where both units had wide spikes. The distribution of correlations was similar in each group, with means and standard deviations of r = 0.25 ± 0.44 (both narrow; n = 1,966 pairs), 0.25 ± 0.43 (mixed; n = 544), and 0.28 ± 0.43 (both wide; n = 1,305). Hence, there was no evidence that ACFs are more or less similar on average in unit pairs with similar spike widths. It should be noted that many (2,016/3,815) of the pair comparisons in this analysis came from a single dataset R10 (mouse) since this dataset had more eligible units than the others.

Fig. 8.

Relationship between spike width and (A) peak interval; (B) burst index. Note that not every unit had a peak that could be included in A, hence the slightly wider range of spike widths (one per unit) shown in B. Note that clear bimodality in widths is largely confined to the mouse data.

We also examined the relationship between the peak intervals found in the ACFs and spike width (Fig. 8A). There was no indication that particular peak intervals were more common in units with narrow versus broad widths. We also looked at the relationship between spike width and the burst index (Fig. 8B). There was little indication that the burst index was different overall in narrow versus broad spikes. This would however be consistent with the observation that bursting types of neuron (CH and IB) can have narrow or broad spikes, respectively. We also observed that no mouse neurons had a burst index >10; those neurons that did, all had narrow spike widths. This is consistent with the observation that the CH cell type is absent in rodents (McCormick et al. 2015).

Effects of visual stimulation

We examined the changes in the ACF that might be caused by visual stimulation. Temporal frequencies above the flicker fusion frequency (of around 50–60 Hz) might not be expected to be transmitted by the retina to the cortex and hence it might be expected that regions of the ACF below 16–20 ms would not be directly affected by stimulation. In addition to that, stimuli were normally delivered at a frame rate of 30 Hz meaning that frequencies above 15 Hz would not (barring aliasing) have been present in the stimulus in any case. However, frequencies below 15 Hz might have been present (corresponding to intervals of 66 ms and longer) and hence regions of the autocorrelogram above this interval might potentially be directly affected by the stimulus. Other stimulation-dependent neural mechanisms of course might potentially change the temporal properties of spike trains, e.g. the induction of gamma-frequency oscillations, or an increased tendency to fire spikes at short intervals (bursting behavior).

In order to answer this question, we chose pairs of recordings, which will be referred to individually as “epochs,” that were made consecutively (i.e. one started a few minutes after the other ended), and where one epoch consisted of spontaneous activity and the other was a recording of responses to visual stimulation. In 7 of 8 selected cat recordings, the visual stimulus was a natural scene movie (details given in Spacek and Swindale 2016); in the other case, it was a 32 × 32 m-sequence stimulus lasting 40 min. In the mouse recording, the visual stimulus was sparse noise (details given at http://data.cortexlab.net/singlePhase3/). Further details of the recordings are given in Table 2. Note that the spontaneous recordings from cats in this dataset are not the same as the ones analyzed in the preceding sections.

Table 2.

Datasets used for examining the effects of visual stimulation.

ID	Species	Epoch 1 (mins)	Interval (mins)	Epoch 2 (mins)	Epoch 1 stimulus	Epoch 2 stimulus	# eligible/# units
PE1	cat area 17	26.9	0.4	40.6	Movie	Spont	6/22
PE3	cat area 17	37	0.3	5.2	Movie repeats	Spont	8/60
PE4	cat area 17	45.1	5.9	22.9	Spont	Movie	7/33
PE5	cat area 17	38.8	0.3	10	Movie repeats	Spont	4/44
PE6	cat area 17	43.8	5.0	50.7	Mseq	Spont	4/38
PE7	cat area 17	38.8	0.4	15.6	Movie repeats	Spont	11/62
PE8	cat area 17	38.8	0.6	21.4	Movie repeats	Spont	12/71
PE9	cat area 17	45.0	2.1	38.8	Spont	Movie repeats	11/55
PE10	mouse V1	17.6	2.4	43	Sparse noise	Spont	85/142

spont = spontaneous activity, i.e. no stimulus; Mseq = M-sequence stimulus. The movie stimuli were natural scene movies described in more detail in Spacek and Swindale (2016).

As in the split-halves analysis described above, we calculated the correlation between the ACFs obtained for spontaneous and stimulus-driven activity within single units. This distribution was compared with that obtained for pairs taken across units. Cross-unit pairs could be taken in different ways: cross-epoch types, where one epoch consisted of spontaneous activity and the other had a visual stimulus (so 2 possible pairs per unit pair), and within-epoch types, where both members of the pair were spontaneous or both members were stimulus driven. All of these cross-unit comparisons gave similar results and only the cross-epoch subset of comparisons will be presented here.

The results showed that the distinctiveness of the ACF shapes was often maintained in the presence of visual stimulation, with ACFs from the same unit being similar to each other (Fig. 9A). However, the distribution of correlation values was somewhat broader than for the split-half within-unit comparisons of spontaneous activity (cf Figs 3B and 9B). Thus, 24.4% (39/160) of cross-epoch pairs had correlation values <0.5, whereas for the within-unit, split-halves comparison, only 13.4% (31/231) units had values of r < 0.5. The mean correlation values for these 2 cases were 0.69 ± 0.36 and 0.79 ± 0.24, respectively.

Fig. 9.

Effects of visual stimulation on the autocorrelation functions (ACFs). A) The vertical axis shows the distribution of correlation values for ACF pairs calculated during spontaneous and visually driven firing (cross-epochs) within the same unit. The horizontal axis shows a comparative measure of the mean firing rate during the 2 epochs. A value of zero indicates the same mean rate; values greater than zero indicate a higher rate of firing during the epoch where visual stimulation was present, and vice versa. Arrows (a, b) indicate the points that came from the units shown in panels C and E, respectively. B) Upper panel shows the distribution of correlation values for the points in A; lower panel show the distribution for ACFs taken from different units and different epochs. C) Example of a unit where visual stimulation had a marked effect on the ACF shape, with the transition in shapes coinciding exactly with the transition between epochs. The oscillatory behavior only occurred when the unit was not being visually stimulated. D) Spike rasters from the unit, showing responses during 15 movie repeats (rasters wrap from line to line). E) Example of a unit where stimulation had little effect on ACF shape. In order to better show the similarity in shape, the ACFs have been normalized so the area under each = 1. F) Spike rasters from the same unit during the stimulation epoch, showing responses to multiple repeats of the same ~5 s long movie.

Comparison of stimulated versus unstimulated ACF pairs showed that visual stimulation often increased the height of the ACF for intervals <10 ms, i.e. the burstiness, even though the functions remained generally similar in shape. This contradicts the above suggestion that visual stimulation might leave short-interval ACFs unchanged. It was further investigated by calculating (as in Fig. 6A) the mean ACF value in the interval 1–10 ms (the burst index) and plotting the value in the stimulus condition against the value in the unstimulated (spontaneous) condition (Fig. 10). This was done for all qualifying units in the 9 paired-epoch datasets. The stimulus condition had a mean burst index of 5.4 ± 9.3 and the spontaneous condition had a mean of 4.8 ± 11.0 (Fig. 10). The difference (Wilcoxon matched pairs test; n = 143) was significant at P < 0.001.

Fig. 10.

Values of the burst index, i.e. the mean autocorrelation function (ACF) value in the interval 1–10 ms (c.f. Figure 6A), in the stimulation condition (horizontal axis) versus the spontaneous condition (vertical axis) for individual units in the 9 paired-epoch datasets. The solid line shows equality. Values are greater in the stimulation condition indicating a greater tendency to fire in bursts. The distribution of values for the spontaneous condition can be compared with that shown in Fig. 6A, which shows the same measure for a different set of data.

Effects of brain state

Brain state can change under anesthesia, affecting the structure of responses to visual stimuli (Goard and Dan 2009; Hirata and Castro-Alamancos 2011; Marguet and Harris 2011; Zagha et al. 2013; Pachitariu et al. 2015; Spacek and Swindale 2016) as well as spontaneous activity (Swindale and Spacek 2019). Such changes often manifest as a sudden change in LFP structure (Fig. 11D), which may reverse after a period of several minutes. Changes in brain state were observed during some of our recordings of spontaneous activity, and we asked whether or not ACF structure also changed. Four recordings (RSC1–4: Table 3) from penetrations in 3 animals were selected as showing clear changes between synchronous and desynchronous states with each state lasting several minutes or more. The start times of the change, and in one case the end time (followed by a reversal to the initial state), were noted and used to divide the recording into 2 periods referred to here as blocks. As with the preceding paired analyses, ACFs were calculated separately for the 2 blocks and the correlations between ACF pairs from the same unit (within-unit, cross-state) were compared with the correlations obtained for different blocks in different units (cross-unit, cross-state). The minimum number of spikes required to be present in each block was set at 1,000 (rather than 2,000 for the other analyses) in order to increase the number of units. Figure 11A shows the distribution of correlation values for within- and cross-unit comparisons. As with the effects of visual stimulation, the distribution of correlation values was significantly higher for the within-unit comparisons (P < 0.005; Mann–Whitney non-parametric test, one-tailed). However, many units showed changes and 33% (9/27) had correlation values <0.5. Figure 11B shows an example of a unit whose ACF shape changed abruptly at the start of the transition period, but was stable within each period. The correlation between the 2 ACFs (right panel of Fig. 11B) was −0.73. Similar abrupt and well-defined changes in ACF structure were common among units showing changes. However, many units were unaffected by the transition. Figure 11C shows one such example, with a correlation between ACFs of 0.99.

Fig. 11.

Effects of brain state changes on the autocorrelation functions (ACFs). A) Correlations in ACF shape calculated for (left panel) within-unit, cross-state ACF pairs and (right panel) cross-unit, cross-state pairs. B) Example of a unit showing a change in ACF structure coinciding with a state change, as determined from separate examination of the LFP spectral pattern (the arrow at the top of the left panel marks the state change); the right panel shows the 2 ACFs, with spikes no longer being preferentially fired at intervals of around 4 ms. C) Example of a unit from the same recording as B showing little or no impact of the state change on its firing pattern. The difference between the 2 ACFs can be largely accounted for by a multiplicative change in height. D) The state change from desynchronous (first 34 minutes) to synchronous activity in recording RSC3 as indicated by the change in the LFP power spectrum (arrow). Brightness values are proportional to the log of spectral intensity.

Table 3.

Datasets used for examining the effects of cortical state.

ID	Anesthesia	Total duration (mins)	Duration of synchronized state (mins)	# of units/# eligible
RSC1	iso/N2O	40	9	42/5
RSC2	iso/N2O	45	8.7	75/6
RSC3	prop/fent	54	20	35/12
RSC4	iso/N2O	29	11	24/4

Recordings were divided into synchronized versus desynchronized blocks based on the local field potential (LFP) spectrum (Spacek and Swindale 2016). All recordings were from anesthetized cat area 17. iso = isoflurane; prop = propofol; fent = fentanyl.

Are any units Poisson?

We asked whether any units in the sample of recordings of spontaneous activity satisfied reasonably unrestrictive criteria for firing randomly, i.e. with a Poisson distribution. Though most clearly do not, it is possible that some do. It is also possible that lower firing rate units, which were excluded from the above analyses, might be more Poisson in their firing. A Poisson distribution arguably means that the normalized ACF, calculated as described in the Methods, should not be significantly different from 1, excluding short intervals where the probability of firing would likely be impacted by refractory behavior. (It is probably the case that non-random spiking patterns can be contrived that would give rise to flat distributions, but these seem unlikely to occur.) To test this, we calculated, for each ACF, a goodness-of-fit measure, g, defined as

(5)

where A_n is the value of the normalized ACF for bin n, (Eq. 3) with k = int[αlog₁₀(3)] and K = int[αlog₁₀(1000)], and σ_n is the estimated standard deviation of A_n. Thus, g is the average squared deviation of A from the Poisson limit of 1, taken over a range of intervals of 3–1,000 ms, in units of standard deviation. The first 3 ms of the range was excluded in order not to include effects that might simply be the result of refractoriness in firing. Rather than apply statistical tests of the values of g, we compared them with a control where the spike train of each unit was replaced by one in which the spike times were random, i.e. with uniform probability over the recording period. No allowance for refractory firing was made in doing this. Every unit satisfying the SNR inclusion criterion (n = 461) was included in the analysis, including units with low numbers of spikes.

Figure 12A graphs values of g versus the number of spikes for each unit in the test and control conditions. Figure 12B shows the same data graphed against firing rate. The control (Poisson) values were mostly ~1 with a variability which decreased with larger numbers of spikes. In contrast, real units generally showed much larger (i.e. worse) fit values. The values tended to increase linearly (dashed line) with the number of spikes as well as firing rate. A linear increase is expected given that the standard deviation of the ACF count value, C_i, (Eq. 2) is likely to equal the square root of the count in each bin, which in turn will tend to be proportional to the total number of spikes. Thus, the 2 distributions converge as the number of spikes decreases, and the test loses power, as would be expected, for small numbers of spikes. Almost all units firing more than 1,000 spikes had values of g that were well outside of the range of the controls. Only one unit firing more than 2,000 spikes had a value of g that fell into the Poisson range. Examination of its ACF confirmed that it was similar to the control one.

Fig. 12.

Open circles show the goodness-of-fit values (g) of units to an ideal Poisson distribution of inter-spike intervals (A = 1) plotted against A: the number of spikes fired by the unit in the recording period (which varied across units) and B: the firing rate in spikes/second (i/s). The dashed line in A was obtained by linear regression to the logs of the data values. Black dots show the corresponding fit values for simulated Poisson distributions where the spike times for a given unit were replaced with random ones.

There is little evidence in Fig. 12 to support the possibility that Poisson firing is more prevalent among low-firing rate units. An increased prevalence of Poisson firing in low firing rate units should be manifest as a downward trend (below linear) of g for lower spike counts. However, the finding, if anything, suggests the opposite—although the relationship is approximately linear, the lowest firing rate units tend to have values of g that are higher rather than lower than expected and tend to fall above the solid line.

Discussion

The present study used log-interval, rate-normalized autocorrelograms to characterize temporal structure in the spontaneous activity of simultaneously recorded cortical neurons in a variety of cortical areas and species (Table 1). Autocorrelograms were used in preference to ISI histograms because they offer a potentially richer description of temporal structure, giving the relative probability of occurrence of all the spikes that might follow a single spike, not just one. The interval distribution is also strongly affected by firing rate, whereas the shape of the normalized ACF is relatively independent of it. The normalized ACF shape is easily interpretable, given that a Poisson distribution will result in a flat function with a value of 1 beyond the refractory period. The use of logarithmically spaced bins can be justified by the fact that temporal precision of potential signals is likely to be a constant fraction of the interval involved and hence to vary in a logarithmic way. The use of even a relatively narrow bin width of 10 ms for a linear histogram would have obscured all of the structure observed at <10 ms in the present study and much of it above that interval. The advantages of a logarithmic time scale were also pointed out by Reich et al. (2000), who used ISI distributions to study responses to visual stimuli. Power spectral analysis was avoided in the present study because, although ideal for demonstrating sustained oscillatory behavior, it is less able to reveal structure in very short bursts of only 2 or 3 spikes. Such bursts will have a very narrow envelope in the time domain, leading to a broad one in the frequency domain and are likely to pass undetected.

The results of the present study revealed that almost no units satisfied a statistical test for Poisson spiking (Fig. 12). Because the test was insensitive for units firing at low rates and consequently lower numbers of spikes, it is possible that, had more spikes been recorded over a longer period, more units would have passed it. However, the significance of demonstrating Poisson firing for rates of 0.1 Hz and lower might be questioned. The deviations from Poisson firing that were observed were often large, with units firing at rates that were up to 100 times more probable than expected for specific intervals (Fig. 7A). These extreme deviations only occurred for intervals <10 ms; however, up to 10-fold deviations could be found above this interval (Fig. 7A).

Our results provide partial support for claims for the presence of distinctive short intervals and ordered sequences of intervals (Strehler and Lestienne 1986; Abeles 1991; Oram et al. 1999; Ikegaya et al. 2004, 2008). However, the present study only provides information about the relative prevalence of inter-spike intervals and does not say anything about structured sequences of intervals. It can also be noted that Baker and Lemon (2000) failed to confirm the presence of repeating sequences of spikes in monkey motor cortex. DeBusk et al. (1997) reported peaks in the ISI distributions of units in cat visual cortex between 3–5 ms and at 10–30 ms, with intervals in some cases as short as 0.73 ms. Individual differences between units were apparent in this study though the authors did not comment on them. Reich et al. (2000) reported distinctive ISI differences between visually stimulated macaque V1 neurons, which could have between 1 and 3 peaks in ISI histograms. Units lacking peaks were not reported. Our results suggest that similar peaks would have been found in recordings of spontaneous activity by these authors and in fact an example of a structured ISI histogram of spontaneous activity is shown in Fig. 1 of Reich et al. (2000). We did not however find evidence that peaks occupied the same temporal ranges as reported by Debusk et al. (1997) and Reich et al. (2000).

Stability of ACF shape

ACF shapes were stable over the recording periods, which could last up to 50 min (Fig. 2). Spontaneous firing rates, averaged over seconds or longer, could be much more variable over these periods, and our findings (Fig. 5) suggest that ACF shapes were relatively unaffected by these changes. This could be because the factors that affect overall firing rate multiplicatively scale the probability of firing, leaving the relative probability of firing as a function of time following a spike unchanged. This would be consistent with observations showing that slow firing rate variations multiplicatively scale tuning curves (Carandini 2004; Swindale and Spacek 2012 and unpublished observations) as does attention (e.g. McAdams and Maunsell 1999). A possible mechanism for making membrane potential variations multiplicatively change stimulus responses has been suggested by Carandini (2004). Multiplicative interactions between signals originating in apical and basal dendrites have been demonstrated physiologically (Larkum et al. 1999, 2004). The reasons why firing rates are modulated in this way are not well understood but can be categorized as resulting from variations in cortical state (Arieli et al. 1996; Burac̆as et al. 1998; Tsodyks et al. 1999; Kenet et al. 2003). These variations may be responsible for the large values of Fano factor observed in previous studies.

While ACF shapes tended to be stable over time, changes did occur in some units as a result of visual stimulation, or a change in brain state. The changes induced by visual stimulation could be relatively subtle, as shown in Fig. 10, or in some cases quite large, as shown in Fig. 9C. Changes caused by changes in brain state could likewise be relatively slight (Fig. 11C) or substantial (Fig. 11B). While the ACFs of many units appeared little affected by either visual stimulation or changes in brain state, it is not known if the susceptibility to change might vary in magnitude and type over time within individual neurons, or whether stability in shape in general persists over periods of hours or days or even longer. Stability in ACF shape during stimulation would be consistent with the findings of Oram et al. 1999) who showed that groups of spikes forming particular temporal patterns simply increased in frequency of occurrence as a result of stimulation.

These changes, and ACF properties in general, might be caused by variations in intrinsic neuronal properties such as dendritic architecture, channel kinetics, and/or plasticity in the nonlinear integration of signals by dendrites (Hodassman et al. 2022). They could also reflect the presence of thalamic inputs with specific temporal structures or they could be the result of network dynamics. These possibilities are considered in more detail in the following sections.

Intrinsic factors that might cause variations in ACF shape among neurons

Static properties intrinsic to the neuron might have to do with the shape of the cell, its channel properties, or more likely both. A rich variety of channels with different temporal properties is known to be present in cortical neurons (Cauli et al. 1997, 2000; Mainen and Sejnowski 1998; Zeisel et al. 2015; Tasic et al. 2018). Intrinsic neuronal variability, over and above genetic influences on channel expression, also should be taken into account (Marder and Taylor 2011). Cellular morphology is another potential factor, since modeling shows it can influence the temporal characteristics of spiking independently of membrane channel properties (Mainen and Sejnowski 1996). Both factors are supported by numerous experimental findings showing a relationship between morphology and spiking patterns (e.g. Chagnac-Amitai et al. 1990; Connors and Gutnick 1990; Mason and Larkman 1990; Kasper et al. 1994; Chen et al. 1996; Gray and McCormick 1996; Nowak et al. 2003). Since cellular morphology and, in the short term, biophysical channel characteristics are relatively stable characteristics of cells, this could account for the stability of the ACF shapes. However if the variety is intrinsic in origin, the lack of clustering (Fig. 6) has to be reconciled with the evidence (McCormick et al. 1985, 2015; Nowak et al. 2003; Mitchell et al. 2007) that cortical cells fall into regular spiking (RS), fast-spiking (FS), intrinsic bursting (IB), and chattering (CH) types. FS and RS neurons might be expected to give rise to peaks in the ACFs at different and distinctive intervals; however, in the present study, peak intervals were spread over a wide range with, at best, ambiguous evidence for clustering of values (Fig. 7B). The classes observed by Nowak et al. (2003) as well as in the earlier studies were based on the responses to steady current injection, and it is not implausible that the distinctions would be less evident when cells were not being stimulated. However, as shown here, bursting behavior, defined as an excess of short (< 10 ms) spike intervals over the average expected on the basis of random firing, was present in spontaneous activity. It appeared to vary continuously among the population of cells studied (Fig. 6A) and so this behavior is also inconsistent with the standard grouping of cells into 4 types. We additionally failed to find any clear relation between spike width, which is known to correlate with cell type, and ACF structure (Fig. 8). Nowak et al. (2003) mention that subtypes and transitional behaviors could be observed in the 220 cells in their sample, and it is possible that a different study might not identify the same classes, or as clearly.

Regarding cortical cell types, it is currently estimated on the basis of mRNA classification studies that there are as many as 133 genetically distinct types in cerebral cortex (Tasic et al. 2018). If these have distinct temporal properties, many more than the relatively limited number of neurons studied so far by current injection, or in the present study, might be required before distinct clusters became apparent. It is possible that discrete classes of spiking behavior might be more evident in stimulus-evoked spike trains. For example, Gray and McCormick (1996) mention that chattering behavior is much less obvious during periods of spontaneous activity in cat visual cortical neurons. Visual stimulation did increase the overall degree of bursting behavior in the cells in our study, but it did not reveal obvious subclasses based on bursting behavior (Fig. 10).

Network dynamics

Independent of intrinsic neuronal properties, network properties are also a potential cause of varied temporal patterns of spiking. This would require networks to be capable of generating and preserving very short temporal intervals of only a few ms. For this to be possible, very narrow temporal integration windows would need to be present. However, the extent to which integration windows in cortical neurons are narrow or broad, and can support timing as opposed to rate codes, remains a topic of debate. It has been argued (Softky and Koch 1992, 1993) that a broad integration window would cause cortical neurons to fire regularly, which they clearly do not. Hence, they argued, integration windows are more likely to be narrow. A counter-argument to this was presented by Shadlen and Newsome (1994, 1998) who demonstrated irregular firing in an integrate-and-fire-model with both excitatory and inhibitory inputs to neurons. It has also been argued that randomly connected networks of neurons, and possibly structured networks as well, have chaotic dynamics at small timescales and therefore cannot produce spikes at deterministic short intervals (Latham et al. 2006; London et al. 2010). This prediction is contradicted by the results of the present study; however, it does not establish that short intervals convey information. While there is abundant evidence for the importance of latency, i.e. the timing of individual spikes in neural signaling (e.g. Usrey and Reid 1999; Thorpe et al. 2001; Van Rullen and Thorpe 2002), this is not the same as showing that intervals have a particular significance (Oram et al. 2002). However, conditions where cortical neurons have very narrow temporal integration windows may exist (Softky 1994) while delays or resonant or damped resonant behaviors might also be capable of endowing very narrow temporal windows with information. In this vein, it has been argued that neural circuitry is capable of generating information-rich, fine-scale temporal structure in groups of cells (Harris 2005; Luczak et al. 2007), in line with Hebb’s cell assembly hypothesis. This view requires cells to be capable of generating a variety of temporally structured firing motifs. The firing patterns observed in the present study might be a result of this. It can be noted that the individual ACFs do not necessarily reflect single stereotyped spike sequences but might be the sum of a smaller number of distinct patterns. This possibility might be investigated further by searching for repeating motifs in spike trains of individual units (using the ACF structure to narrow down the possibilities) and seeing if they can be classified into a small number of types.

A different possibility is that ACF shape reflects the presence of inputs from particular subcortical sources which themselves produce spikes with characteristic temporal intervals. In the visual system, the possibilities include ON and OFF center LGN neurons and their lagged counterparts (Saul and Humphrey 1990) as well as X and Y (or magno- and parvocellular) subtypes. Differences in the temporal structure of different classes of inputs might explain the observations of Reich et al. (2000) who were able to correlate different aspects of receptive field structure (e.g. the magnitudes of ON and OFF subregions) with different intervals between spikes. This could happen if intervals between ON LGN spikes were different from those of OFF cells and these differences were passed on to their post-synaptic targets. Showing that temporal patterns in thalamic inputs to cortical neurons were (or were not) passed on to their post-synaptic targets could be an important test of the ability of cortical neurons to transmit temporal interval codes.

Significance of idiosyncratic temporal spike train structure

Leaving aside the question of how it is produced, what functions might temporal structure in spontaneous activity serve? The spike trains studied here have been classed as “spontaneous” and so one possibility is that they have no functional significance. It is possible, however, that information is always being passed between neurons and “resting state” might be a better term to use than “spontaneous.” There have been many fMRI studies of resting state brain activity in humans though its functional significance remains obscure (Northoff et al. 2010; Snyder 2016). Some 20% of cardiac output supports resting brain activity so it is unlikely that the brain is literally doing nothing in such states. The present observation that spike train temporal structure in the visual cortex is not greatly changed by visual stimulation suggests that if temporal structure in the spike train is conveying information, as opposed to firing rate, it is not specifically about the visual stimulus. It might be noted that messages devised by humans frequently contain meta-information not directly related to the overt content, such as information about the message source or its intended destination, or both. The brain might employ the same strategy. It might be important, for example, to signal whether activity in a neuron had been evoked by thalamic input or by top-down signals. Information about the destination, that is changes which allowed post-synaptic neurons to be differentially targeted, might possibly change with brain state. It is possible that these signals, or versions of them, are still present, even in the absence of a stimulus. However, their complexity, or entropy, might be expected to increase in the presence of visual stimulation. This possibility has not yet been tested. Contextual information about a localized stimulus might also be provided this way. Whether part of a stimulus is “bound” to other stimuli or not is one possibility that has been extensively explored (Singer and Gray 1995) but there could be many others.

Many studies have shown that bursting behavior can be induced by visual stimulation (Cattaneo et al. 1981a, 1981b; Bair et al. 1994; Livingstone et al. 1996; DeBusk et al. 1997; Kepecs et al. 2002; Martinez-Conde et al. 2002) and that bursts convey different information than the overall rate (Kepecs and Lisman 2003; Zeldenrust et al. 2018). However, one might not have expected bursts to be so widely present in spontaneous activity or for their temporal structure to be stereotypically different in different neurons. While it has been proposed (Lisman 1997) that bursts facilitate synaptic transmission, increasing the probability of synaptic vesicle release, this does not explain why specific temporal intervals would differ among neurons. A different rationale is that specific temporal intervals might be used to target different post-synaptic cells (Markram et al. 1998; Izhikevich et al. 2003). There are 2 mechanisms that might do this. One depends on the properties of pre- and post-synaptic receptors and is based on a combination of short-term depression and longer-term facilitation. These can combine to create a preferred temporal interval for transmission across the synapse. This interval can be different for different neurons, allowing a cell to selectively target different post-synaptic neurons without changing synaptic connections (Markram et al. 1998). The second mechanism (Izhikevich et al. 2003) depends on the intrinsic membrane properties of the post-synaptic neuron and the dynamics of persistent low-threshold Na⁺ and K⁺ currents. These can create membrane oscillations in the 10–80 ms range and have been demonstrated to occur in cortical neurons (Llinás et al. 1991). Either mechanism might allow, or cause, synapses to be pruned if they targeted cells with the wrong post-synaptic properties. Alternatively, cells might dynamically change their preferred spike intervals, or the post-synaptic cell might change its channel properties, allowing selective communication. The present findings support these suggestions inasmuch as they show that cortical neurons produce spikes at well-defined temporal intervals which differ from cell to cell.

While a function of precisely timed spike intervals might be to regulate burst communication, bursting behavior was absent in many cells. Figure 6A, for example, shows that 32% (74/231) of units fired with a relative probability <1 for intervals <10 ms. Bursting is more prevalent with visual stimulation (Fig. 10) and perhaps all cells are capable of it. Figure 11 shows a unit that converted from non-bursting to bursting during a state change and perhaps other non-bursting cells can do the same.

Practical applications

Independent of functional implications, the present findings have some practical applications. During spike sorting, similarity between ACFs is sometimes used as a criterion for deciding that 2 weakly separable clusters of spikes might actually be from the same unit, justifying merging. The present study provides a more principled basis for such a practice. For this purpose, the ACF should ideally be calculated using log time scaling as this will reveal relevant detail on both short and long timescales. Although it has not been done here, distributions like those shown in Fig. 3B could be used to estimate the probability that 2 putatively different units, with a given correlation between their ACFs, are, or are not, likely to be the same unit. The accuracy of this can of course be increased above that provided in Fig. 3B by excluding unit pairs that are physically far apart and pairs that have very differently shaped spike waveforms. (Note that, as detailed in the Methods, the ACFs were not used as a criterion for merging during sorting of the units used for this study.)

ACF structure also appears to be a sensitive indicator of cortical state. The changes that occurred in some units were abrupt and easy to identify (e.g. Figure 11B). It should not be hard to identify correlated changes in structure across units and use these as state indicators. Further work would be required however to characterize the relation between ACF structure and specific states, e.g. synchronized versus desynchronized, or to define additional states or substates.

Timing versus rate codes

In summary, the present findings show that cortical spontaneous activity is not random but is structured on very short timescales from 1 ms up to intervals of many hundreds of milliseconds. Furthermore, these structures vary idiosyncratically from cell to cell. While these behaviors could be a hallmark of an information-rich temporal code, they could also be an epiphenomenon reflecting a combination of the effects of cellular geometry and channel properties whose effects on spike timing might have a limited impact on neural communications. In fact, brain communication might have evolved to mitigate their effects. Dismissing a finding as an epiphenomenon however is arguably unwise as it will discourage searches that might reveal a possibly unsuspected function. Further investigations might usefully be made, comparing log-interval ACFs in different brain structures to see if specific patterns characterize structures like retina, thalamus, hippocampus, and elsewhere. Recordings should be made over longer periods of time to investigate stability. Examination of the effects of anesthesia versus wakefulness, spontaneous changes in brain state, and a search for correlations with behavioral states in appropriate cortical areas are all likely to prove informative.

Funding

This work was supported by grants from the Canadian Institutes of Health Research (CIHR) numbers MOP-15360 (to NVS) and MOP-115178 (to CP).

Conflict of interest statement: None declared.

Data availability statement

Data are available on request to the corresponding author (NVS).