Size tuning of neural response variability in laminar circuits of macaque primary visual cortex

Surround suppression and neural response variability are two widespread cortical phenomena thought to affect information processing and perception in seemingly opposite ways. Surround suppression is a non-linear neural response transformation consisting of suppression of a neuron’s response to a sensory stimulus presented inside its receptive field (RF) by a stimulus simultaneously presented in the RF surround (Hubel and Wiesel, 1965; Blakemore and Tobin, 1972; Nelson and Frost, 1978; Sceniak et al., 2001; Cavanaugh et al., 2002; Levitt and Lund, 2002; Angelucci and Shushruth, 2013). It is thought to facilitate information processing and the encoding of sensory stimuli, for example by facilitating visual perception (Knierim and van Essen, 1992; Lamme, 1995; Nothdurft et al., 2000), and reducing redundancies in sensory inputs (Vinje and Gallant, 2000; Schwartz and Simoncelli, 2001; Haider et al., 2010; Pecka et al., 2014). Neural response variability is the phenomenon in which repeated presentations of an identical visual stimulus produce neuronal spiking responses that differ from trial to trial (Tomko and Crapper, 1974; Vogels et al., 1989), and this trial-to-trial variability is correlated among neurons (Cohen and Kohn, 2011). Traditionally, neural response variability has been interpreted as ‘noise’ that impairs the fidelity of neural representations (Shadlen and Newsome, 1998; Abbott and Dayan, 1999; Averbeck et al., 2006; Moreno-Bote et al., 2014).

It has recently been hypothesized that response suppression (of which surround suppression represents a specific form) and neural variability are intimately connected and may share a common origin, as manipulations that elicit response suppression typically also quench variability (Goris et al., 2024). However, few studies have systematically examined the relationship between surround suppression and variability. Festa et al., 2021 reported that on average across a population of V1 cells, stimuli approximately twice the diameter of the neurons’ RF quench variability relative to variability measured for stimuli confined to the RF. However, in this study, individual V1 neurons showed a variety of effects of surround stimulation on variability, including increases, decreases, or no effect. A different study showed a decrease in correlated variability among V1 neurons following stimulation of the surround by large stimuli (12° diameter) (Snyder et al., 2014). However, experimental evidence indicates that surround suppression is mediated by multiple circuits and mechanisms, depending on stimulus size, spatio-temporal stimulus configuration, and cortical layer (Webb et al., 2005; Angelucci et al., 2017; Bijanzadeh et al., 2018; Henry et al., 2020). For example, small vs. large stimuli presented in the RF surround evoke distinct patterns of laminar activity (Bijanzadeh et al., 2018), consistent with the former engaging intrinsic horizontal connections, which extend into the ‘near’ RF surround of V1 neurons, and the latter corticocortical feedback connections, which are co-extensive with the ‘far’ RF surround of V1 neurons (Angelucci et al., 2002; Angelucci et al., 2017). As previous studies did not systematically address the relationship between stimulus size, single neuron variability, and correlated variability, it remains unclear whether near- and far-surround stimulation similarly affect variability, and whether their effects generalize to all cortical layers. Moreover, recent theoretical evidence has demonstrated that not all forms of variability are detrimental to encoding of sensory inputs and perception (Averbeck et al., 2006; Ruff and Cohen, 2014; Ruff and Cohen, 2016b; Haefner et al., 2016), and reports that variability is modulated by visual stimuli (Churchland et al., 2010; Ruff and Cohen, 2016b) have led some to suggest that variability may, instead, play a role in sensory information processing. For example, computational studies have assigned a role for variability in perceptual inference (Fiser et al., 2010; Pouget et al., 2013; Orbán et al., 2016; Hénaff et al., 2020), and suggested that cortical layers may play distinct roles in perceptual inference (Bastos et al., 2012). To obtain a comprehensive understanding of the relationship between surround suppression, variability, and laminar circuits, here we have used electrophysiological laminar recordings to examine how stimulus size affects changes in neural response variability and shared variability across the layers of macaque primary visual cortex (V1). Size tuning experiments allow us to isolate the driving feedforward thalamic inputs to the RF, from the modulatory inputs from the near and far RF surround, carried by intrinsic V1 and corticocortical feedback circuits, respectively (Angelucci et al., 2002; Angelucci et al., 2017; Nurminen et al., 2018). Understanding this relationship is important to constrain models of cortical circuits and the computations performed by networks of neurons.

We found that surround suppression does not always quench variability. Rather, both single neuron response variability and the shared variability among neurons are tuned for stimulus size, and this size tuning is layer dependent. In all layers, a stimulus matched to the RF size of the recorded neurons reduced both variability and shared variability compared to pre-stimulus baseline. However, modulation of variability by stimulation of the RF surround depended on both stimulus size and cortical layer. In infragranular (IG) layers, a stimulus involving the RF and the near surround decreased both response variability and shared variability, compared to their values for a stimulus matched to the RF size. Instead, in supragranular (SG) and granular (G) layers, near-surround stimulation had small or no effects on variability. A larger stimulus extending farther into the far-surround increased variability, relative to its value for stimuli matched to the RF size, in the SG layers, but either did not affect or reduced variability in G and IG layers. Interestingly, we found that in a subset of neurons, particularly in G and IG layers, stimuli smaller than the RF could increase variability compared to pre-stimulus baseline. Our results point to multiple laminar-specific circuits and mechanisms as the source of variability, likely affecting cortical processing and perception in distinct ways, and calling for new models of neural response variability.

We recorded visually evoked local field potentials (LFP), single-unit (SU) and multi-unit (MU) spiking activity, using 24-channel linear electrode arrays (100 µm electrode spacing) inserted perpendicularly to the surface of area V1 in two sufentanil-anesthetized macaque monkeys (see Methods). For accurate assignment of recorded responses to cortical layers, verticality of the electrode array was verified by the spatial overlap and similarity of orientation preference of the MUs’ minimum-response fields (mRFs) across the array, and confirmed by postmortem histology (as described in Bijanzadeh et al., 2018). Laminar boundaries were identified by current source density (CSD) analysis of LFP signals (Mitzdorf, 1985) averaged over all stimulus diameters used in this study. This allowed us to locate the G layer 4C as the site of the earliest current sink followed by a reversal to current source, the site of the reversal marking the bottom of the G layer; layers above and below G were defined as SG and IG, respectively. We used spiking activity in response to the same stimulus to identify the top and bottom of the cortex (Bijanzadeh et al., 2018).

To understand how stimulus size modulates cortical response variability across V1 layers, we measured Fano-factor and the shared variability among simultaneously recorded units as a function of grating diameter for 82 visually responsive MUs and 60 spike sorted, visually responsive SUs. At the beginning of each penetration, we mapped the mRFs of the recorded MUs (see Bijanzadeh et al., 2018 for details). We next presented grating stimuli, centered on the aggregate mRF of the recorded MUs, to characterize the orientation, spatial frequency, and temporal frequency tuning of the recorded MU activity. We then selected the stimulus parameters that maximized the response of the majority of simultaneously recorded MUs across the array. Using these optimized parameters, we ran size tuning experiments in which the diameter of a drifting grating stimulus was varied from 0.1° (0.2° in one penetration) to 26°.

Layer-dependent modulation of neural response variability by stimulus size

Figure 1 shows size-tuning data for representative MUs recorded in SG, G, and IG layers. For all three example units, the Fano-factor decreased as the stimulus diameter was increased to fill the RF of the recorded neurons. However, for the SG layer MU (Figure 1A), increasing the stimulus diameter beyond the RF boundaries increased Fano-factor, relative to Fano-factor measured when the stimulus was matched to the size of the RF. In contrast, increasing the stimulus diameter beyond the RF boundaries did not affect Fano-factor for the G layer MU (Figure 1B). For the IG layer MU, increasing the stimulus diameter beyond the RF (here 0.5° diameter) led to a further decrease in Fano-factor when the stimulus was approximately twice the size of the RF (involving the ‘near’ RF surround), but for larger stimuli (involving the ‘far’ RF surround), Fano-factor increased back to approximately its value for a stimulus matched to the RF size (Figure 1C). Similar results were observed for the population of recorded MUs.

Figure 1

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Figure 2A shows Fano-factor and mean firing rate, both normalized to their value evoked by a stimulus diameter equal to the RF diameter (see Methods for definition), averaged over the population of MUs in our sample, separately for the different layers. In SG (n = 31 MUs), G (n = 15 MUs), and IG (n = 36 MUs) layers, increasing the stimulus size up to the RF diameter progressively decreased Fano-factor and increased firing rate.

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Large gratings extending into the RF surround of V1 cells are known to suppress the mean spiking response evoked by a stimulus confined to the cells’ RF, a phenomenon known as surround suppression (Sceniak et al., 2001; Angelucci et al., 2002; Cavanaugh et al., 2002; Levitt and Lund, 2002; Shushruth et al., 2009; Angelucci and Shushruth, 2013). Consistent with these previous reports, as the stimulus size was increased beyond that of the RF diameter, firing rate decreased across all layers, and this suppression was strongest in the SG layers. However, increasing the stimulus diameter beyond the RF of the recorded MUs had different effects on Fano-factor in different layers. In SG and G layers, the minimum Fano-factor was reached for a stimulus the size (or near the size) of the RF diameter; as the stimulus diameter was increased beyond the RF diameter, Fano-factor significantly increased relative to its value for a stimulus matching the RF diameter in SG layers (Figure 2A, left), and while it appeared to increase also in the G layers, this increase was not statistically significant (Figure 2A, middle). In contrast, in IG layers, the minimum Fano-factor was reached at a stimulus diameter approximately twice the RF diameter (we term this the ‘near surround’), and beyond this stimulus size, Fano-factor slowly increased back near its value for a stimulus matched to the RF diameter (Figure 2A, right). The size tuning of the Fano-factor for individual penetrations is shown in Figure 2—figure supplement 1A.

To quantify these observations, Figure 2B shows Fano-factor estimated at six different stimulus diameters individually for each MU (values were extracted from functions fit to the data; see Methods), normalized to its value at a stimulus size matching the RF diameter, and then averaged (geometric mean) over all MUs. Consistent with the population size-tuning curves in Figure 2A, this analysis also showed a laminar dependence of the impact of surround stimulation on Fano-factor.

In SG layers, the normalized Fano-factor was lowest for a stimulus matching the RF diameter, and it began to increase for stimuli larger than about twice the RF diameter, reaching its maximum (relative to the value at the RF) at the largest stimulus size tested (26°); in SG layers, Fano-factor at 4xRF diameter, 8xRF diameter, and 26° diameter was significantly higher than Fano-factor at a stimulus size matching the RF diameter (one sample t-test, p < 0.05). Moreover, the Fano-factor for a stimulus twice the RF diameter was significantly higher than the value measured at the RF diameter (one sample t-test, p = 0.015).

In IG layers, the Fano-factor reached its minimum at a stimulus twice the RF diameter, that is extending into the near surround. Fano-factor at 2xRF diameter was significantly lower than Fano-factor for a stimulus matching the RF diameter (one sample t-test, p = 0.019) and Fano-factors at 4xRF diameter, 8xRF diameter, and 26° diameter were not significantly different from Fano-factor for a stimulus the size of the RF (one sample t-test, p > 0.45).

In G layers, the Fano-factor decreased as a small stimulus was increased to fill the RF size and did not change significantly for larger stimuli (one-sample t-test, p > 0.19). Fano-factor for a stimulus twice the RF size was also not significantly different from Fano-factor for a 26° diameter stimulus (p = 0.16, t-test).

Figure 2C plots for each layer the median percent change in Fano-factor, relative to baseline (pre-stimulus), evoked by a stimulus equal in size to the RF diameter of the recorded MUs. In all layers, presentation of visual stimuli in the RF significantly reduced Fano-factor relative to baseline (bootstrap test p < 0.03; median ± bootstrapped s.e. SG: –34.4 ± 7.55%, n = 31; G: –24.3 ± 7.84%, n = 14; IG: –13.7 ± 5.99%, n = 36). The median percent change in Fano-factor was significantly different in SG layers compared to IG layers (bootstrap test against the null hypothesis that the medians are equal: p = 0.024), but was not significantly different between the other layers (bootstrap test p > 0.25). The impact of near-surround (2xRF diameter) stimulation on Fano-factor was layer dependent. Figure 2D plots for each layer the median percent change in Fano-factor evoked by a stimulus matched to the near-surround of each MU, relative to a stimulus matched to the RF diameter. The dots in Figure 2D show this change for individual MUs. Whereas in SG and G layers, near-surround stimulation did not significantly change Fano-factor, relative to its value for a stimulus matching the RF diameter, in IG layers, the percent change in Fano-factor caused by a stimulus in the near surround was significantly different from zero (bootstrap test p = 0.010). While near-surround stimulation in all layers could either increase or decrease Fano-factor in individual MUs, in IG layers, a greater fraction of the MUs showed percent changes in Fano-factor below zero. We also analyzed the effect on the Fano-factor of stimulating the per-neuron surround (Figure 2E, see Methods for definition). Only in the IG layers did the median Fano-factor change evoked by stimulating the per-neuron surround compared to the Fano-factor evoked by RF stimulation differ significantly from zero (bootstrap test, p = 0.01; SG and G layers: bootstrap test, p > 0.17). Figure 2F plots for each layer the percent change in Fano-factor evoked by a 26° stimulus (the largest we used) relative to a stimulus matched to the RF diameter. As for the previous analysis, the impact of far-surround stimulation on Fano-factor was layer dependent. In G and IG layers, there was no statistically significant change in Fano-factor (median ± bootstrapped s.e. G: 7.15 ± 15.6%, bootstrap test median >0: p = 0.44; IG: –7.99 ± 3.73%, bootstrap test median <0: p = 0.055). In contrast, in SG layers, there was a significant increase in Fano-factor as the stimulus involved the ‘far surround’ (SG: 17.4 ± 11.3%, bootstrap test median >0: p = 0.04). One MU with extreme change in Fano-factor (564%), caused by dividing by a number close to zero, was removed from the analysis. In summary, near-surround stimulation evoked a significant decrease in Fano-factor relative to its value for a stimulus matching the RF in IG layers, but no change in SG and G layers. Instead, far-surround stimulation evoked a significant increase in Fano-factor relative to its value for a stimulus matching the RF in SG layers, but no change in G and IG layers.

Importantly, in all layers, individual MUs showed a variety of changes, including increases, decreases, or no change in Fano-factor, regardless of whether the near surround, the per-neuron surround, or the entire far surround (26° diameter stimulus) was stimulated; thus, differences in median Fano-factor observed across layers reflected the relative proportion of one vs. another MU type. Thus, for example, the SG layers contained a larger proportion of MUs with far-surround-induced increases in Fano-factor than the other layers, but such units were present in all layers. This is demonstrated by the single MU plots shown in Figure 2E, F.

Figure 2G plots the median normalized stimulus diameter at the lowest Fano-factor value (i.e. at max Fano-factor quenching) in different layers, and the dots indicate this value for each individual MU. Median stimulus diameter at max Fano-factor quenching normalized to the RF diameter was 1.14 (lower and upper bound of the 99% bootstrapped confidence interval of the median: 0.90, 2.42) in SG layers, 1.80 (0.91 19.41) in G layers, and 1.90 (1.32 6.21) in IG layers. The same data, color coded, for individual penetrations are shown in Figure 2—figure supplement 1B.

Figure 2H plots the smallest surround stimulus diameter at max Fano-factor value. For example, for a unit for which surround stimuli of any size reduced Fano-factor or did not change it relative to its value for a stimulus matched to the RF, the stimulus size at max Fano-factor value would correspond to the RF diameter. For SG and G layers, max Fano-factor value occurred when the stimulus diameter was approximately five times the RF diameter [median stimulus diameter normalized to the RF diameter and lower and upper bounds of bootstrapped 99% confidence interval, SG: 5.02 (2.93, 32.1); G: 4.84 (1.0, 67.2)]. In contrast, in IG layers, max Fano-factor value occurred at a stimulus diameter similar to the RF diameter [1.46 (1.0, 4.13)]. The same data, color coded, for individual penetrations are shown in Figure 2—figure supplement 1C. These data demonstrate that an increase in Fano-factor for stimuli larger than the RF, particularly prominent in the SG layers, is seen in cells across all penetrations.

To better understand the mechanisms that underlie the effects of surround stimulation on Fano-factor, we investigated whether the surround-induced percent change in Fano-factor linearly depends on the strength of surround suppression. We plotted percent Fano-factor change against suppression index (see Methods) and computed the Pearson’s correlation between the two (Figure 2I–K). For near-surround stimulation, the correlation between percent Fano-factor change and suppression index was not significantly different from zero in any of the layers (SG: r = 0.25; G: r = 0.15; IG: r = 0.02; p > 0.16; Figure 2I). When the per-neuron surround was stimulated, the correlation was significant in SG layers (r = 0.37, p = 0.04), but not in G or IG layers (r = 0.08 -G-, r = 0.22 -IG-, p > 0.2; Figure 2J). For far-surround stimulation with a 26° diameter stimulus, the correlation was significant in SG and IG (r = 0.48 -SG-, r = 0.50 -IG-, p < 0.006), but not G (r = 0.30, p = 0.30), layers (Figure 2K). In summary, strength of surround suppression was positively correlated with percent change in Fano-factor only for far-surround stimulation in SG and IG layers. We also found that surround suppression was stronger in the MUs in which Fano-factor was increased by a 26° diameter grating relative to Fano-factor measured in the RF (one-way ANOVA, strength of surround suppression conditioned on whether RF surround increased, decreased, or had no effect on Fano-factor relative to RF stimulation, p = 0.001, n = 82). Specifically, for the MUs in which surround stimulation increased Fano-factor relative to RF stimulation (n = 21), the strength of surround suppression was 74.1 ± 2.91%, while it averaged 54.7 ± 3.47% for the MUs in which surround stimulation did not affect variability (n = 49), and 51.8 ± 5.63% for the MUs in which surround stimulation reduced variability (n = 12).

In all layers, statistically significant increases in variability (as determined by bootstrapping; see Methods) induced by surround stimulation had larger magnitude than decreases in variability (increase vs. decrease SG: 103 ± 18.9% vs. −36.5 ± 6.10%; G: 68.1 ± 14.4% vs. −40.1 ± 20%; IG: 91.6 ± 31.0% vs. −36.5 ± 6.09% independent samples t-test pooled over layers and computed over the absolute value of the Fano-factor change induced by RF surround, p = 0.002).

To rule out that changes in Fano-factor with stimulus size are trivially related to changes in firing rate, we performed a ‘mean-matched’ analysis (Mitchell et al., 2009; Churchland et al., 2010) (see Supplementary Methods, Supplementary Results, and Figure 2—figure supplement 2). This analysis showed similar results as described above for the non-mean-matched analysis. One difference between the two analyses was that the mean-matched analysis demonstrated a small but significant decrease in Fano-factor for near-surround stimulation, relative to its value for RF stimulation, also in the G layers (vs. no change in Fano-factor for the non-mean-matched analysis; Figure 2B, D). Moreover, the mean-matched analysis demonstrated a significant decrease in Fano-factor for far-surround stimuli relative to Fano-factor for a stimulus matched to the RF in both the G and IG layers (see Supplementary Results), while there was no difference in Fano-factor between these two stimulus sizes in these layers for the non-mean-matched analysis (Figure 2B, F).

We also replicated this analysis on a smaller population of spike-sorted SUs from SG and IG layers (see Supplementary Methods, Supplementary Results, and Figure 2—figure supplement 3). Similar to the MU analysis, the SU analysis demonstrated a diversity of responses in all layers (Figure 2—figure supplement 3A). As in MUs, a larger fraction of SUs in the SG layers than in the IG layers showed max Fano-factor facilitation for stimuli larger than the RF size (Figure 2—figure supplement 3D). In Figure 2—figure supplement 3B, however, this increase in Fano-factor for large stimuli in the SG layers did not reach statistical significance, due to the small SU sample size. The analysis in panel D, however, is more sensitive, because it does not perform measurements at predefined stimulus sizes (as in panel B), but searches for Fano-factor increases at any stimulus size for each individual cell.

A larger fraction of SUs in both SG and IG layers showed a decrease in Fano-factor for near-surround stimuli, relative to Fano-factor for a stimulus matched to the RF diameter (Figure 2—figure supplement 3B, C); this was in contrast to the MU data in which this decrease in Fano-factor for near-surround stimulation was only observed in the G and IG layers (Figure 2B, D, G). This was because our larger population of MUs in SG layers contained a larger fraction of individual MUs with lowest Fano-factor value for stimuli matched to the RF size, compared to our smaller population of SUs.

Amplification of cortical response variability by small stimuli

It has been previously reported that the onset of a visual stimulus reduces cortical response variability relative to pre-stimulus baseline (Churchland et al., 2010). However, previous studies used relatively large stimuli, and the impact of stimulus size on response variability has not been explored. Previous experimental studies (Ichida et al., 2007) have shown, and several models of cortical dynamics predicted, that when the cortex is weakly driven (e.g. by a small stimulus), the cortical state is dominated by excitation, whereas it is dominated by inhibition when the cortex is strongly driven, for example, by a large stimulus (Schwabe et al., 2006; Schwabe et al., 2010; Rubin et al., 2015; Hennequin et al., 2018). In an excitation-dominated cortical state, stochastic supralinear stabilized networks predict amplification of response variability relative to pre-stimulus baseline (Hennequin et al., 2018). To test this model’s prediction, we examined the impact of small stimuli on response variability.

Figure 3A shows the response of three example MUs to small gratings (0.1–0.6° diameter) centered on the RF. In all three MUs, this small stimulus-evoked firing rates and Fano-factors values higher than those measured during the pre-stimulus baseline.

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Amplification of variability for small stimuli was seen also at the population level. Figure 3B compares Fano-factor evoked by a 0.1° diameter grating with that evoked by a grating of diameter equal to the RF diameter of the recorded MUs, normalized to the pre-stimulus baseline, and averaged over the population of SG (n = 31, left), G (n = 15, middle), and IG (n = 36, right) MUs. Presentation of the small stimulus significantly increased Fano-factor relative to pre-stimulus baseline in G and IG (p < 0.05, one-sample t-test, n = 15 and 36, respectively), but not SG (p = 0.14, n = 31), layers. Consistent with previous studies (Churchland et al., 2010), in all layers, the larger stimulus instead decreased Fano-factor relative to baseline. There was no obvious difference in firing rates across the layers that could have explained the increase in Fano-factor in G and IG layers for smaller stimuli, but not in SG layers.

To provide a better understanding of variability amplification across layers, we performed an MU-by-MU analysis. This revealed significant variability amplification for small stimuli in all layers. We included in this analysis only MUs showing statistically significant increase and decrease (see Methods) in Fano-factor relative to baseline for at least one data point. While all MUs in our sample showed statistically significant stimulus-evoked decreases in Fano-factor, 67% of these units (55/82) also showed statistically significant increases in Fano-factor for presentation of small stimuli. The proportion of MUs showing both increases and decreases in stimulus-evoked Fano-factors was fairly constant across layers (SG, 61%; G, 67%; IG, 72%).

On average, the largest stimulus-evoked increase in Fano-factor for the cells that showed variability amplification relative to baseline was observed for stimulus diameters smaller than the RF of the recorded MU (Figure 3C; median stimulus diameter normalized to the RF diameter at the largest increase in Fano-factor relative to baseline ± s.d. of the bootstrapped distribution: SG, 0.33 ± 1.20; G, 0.67 ± 0.52; IG, 0.63 ± 0.26). We found that stimulus-evoked increases in Fano-factor were smaller in magnitude than stimulus-evoked decreases in Fano-factor. The difference between the magnitude of maximum variability quenching and magnitude of maximum variability amplification was statistically significant in SG and IG layers (Figure 3D; mean ± s.e.m. quenching vs. amplification: SG, 1.85 ± 0.37 vs. 0.89 ± 0.14, t-test, p = 0.01; IG, 0.93 ± 0.12 vs. 0.67 ± 0.06, p = 0.03), but not in G layers (G, 1.14 ± 0.21 vs. 0.93 ± 0.19, p = 0.23). For this analysis, we removed outlier data points that were at least 2.5 absolute median deviations above or below the median.

Across the entire population, the MUs showing variability amplification for small stimuli (here termed ‘amplifiers’) had a significantly lower baseline Fano-factor than the MUs in which a stimulus always reduced variability (termed ‘quenchers’) (mean baseline Fano-factor ± s.e.m.: 3.44 ± 0.33 for quenchers vs. 1.90 ± 0.13 for amplifiers, t-test, p = 0.000001). However, this varied by layer (Figure 3E); in SG and IG layers, baseline Fano-factor was significantly higher for the quenchers than for the amplifiers (mean baseline Fano-factor ± s.e.m.: SG, quenchers 4.70 ± 0.39, n = 12, vs. amplifiers 2.30 ± 0.29, n = 19, t-test, p = 0.00023; IG, quenchers 2.82 ± 0.40, n = 10, vs. amplifiers 1.65 ± 0.14, n = 26, t-test, p = 0.0013). Instead, in the G layer, baseline Fano-factor did not differ significantly between these two groups (quenchers 1.65 ± 0.14, n = 5, vs. amplifiers 1.77 ± 0.19, n = 10, t-test, p = 0.68). Moreover, baseline firing rate was significantly lower in the amplifiers compared to the quenchers (mean ± s.e.m. baseline firing rate: 4.1 ± 0.4 vs. 6.0 ± 0.7 Hz, t-test, p = 2^–12). Importantly, however, all amplifiers also showed variability quenching for larger stimuli. This suggests that a floor effect, for example, due to low baseline firing rates, cannot explain the variability amplification in our data (see Discussion). Variability amplification for small stimuli could potentially arise as a result of slow drifting eye movements which can occur under anesthesia. However, we controlled for eye movements by frequent remapping of the mRF location (see Methods). Figure 3—figure supplement 1 rules out eye movements as a potential cause of increased variability for stimuli smaller than the RF size. This figure shows an example penetration in which amplification of variability for small stimuli was seen in 12 MUs, and this amplification could not be explained by eye movements. Because our penetrations were nearly perfectly vertical to the cortical surface (as assessed by alignment of RF location and similarity of tuning functions; see Bijanzadeh et al., 2018 for quantification), eye movements would be expected to cause a decrease in firing rate in some trials across the entire cortical depth, that is across all contacts in a penetration; this was not observed in the penetration shown in Figure 3—figure supplement 1.

Layer-dependent size tuning of network variability

The results presented above indicate that the response variability of visual cortical neurons is modulated by stimulus size. However, the impact of neural response variability on visual processing also depends on how strongly variability is shared across neurons (Shadlen and Newsome, 1998; Bair et al., 2001). To determine the impact of stimulus size on shared variability, we exploited the covariance of simultaneous recordings obtained with electrode arrays.

The left panels in Figure 4A–C show raster plots of spiking activity of simultaneously recorded MUs in a single example penetration spanning all layers (SG, n = 4 units, Figure 4A; G, n = 3, Figure 4B; IG, n = 7, Figure 4C), in response to presentation of gratings of three different diameters (0.1° top, 0.5° middle, 26° bottom). Qualitative inspection of these raster plots reveals that, following presentation of the 0.1° stimulus, the responses of the entire neuronal population waxed and waned in unison. In some trials, all MUs spiked vigorously, whereas in other trials, the entire population was silent. However, the population responses appeared less coordinated following presentation of the 0.5° diameter grating. The covariation in population responses to presentation of the 26° diameter grating, instead, appeared to be layer dependent. In all layers, responses to a 26° stimulus were reduced compared to those to a 0.5° diameter grating. However, compared to the responses to the 0.5° stimulus, neural activity in response to the 26° stimulus appeared more strongly coordinated in SG layers but remained relatively uncoordinated in G and IG layers.

Figure 4

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To quantify these observations, we used Factor Analysis (see Methods). This allowed us to isolate the network variability (i.e. the variability that is shared across MUs) from the private spiking variability (i.e. the variability that is private to each recorded MU) (Churchland et al., 2010). Factor analysis decomposes the measured covariance matrix into a low-rank network covariance matrix and a diagonal matrix that holds the private variances for each MU. Using cross-validated leave-unit-out predictions, we determined that a single-latent dimension was sufficient to model the current data; therefore, we modeled the network covariance matrix with a single factor and took the diagonal of the network covariance matrix as the shared variance (Churchland et al., 2010). A separate single-factor model was learned for each layer, stimulus condition, and penetration. Importantly, the results of this analysis do not imply that V1 activity is one-dimensional, but rather reflect the sampled V1 activity. Because we used linear arrays with 100 µm contact spacing, and we factored our analyses based on layer, our sample consists of nearby neurons, at most 700 µm apart. Moreover, to maximize the similarity of the RFs of the recorded neurons, we ensured that the recording probe was inserted vertically into the cortex; this was determined based on the overlap in RF locations and similarity of the orientation preferences of neurons recorded in a single penetration (for an example penetration, see Figure 1 in Bijanzadeh et al., 2018).

The right panels in Figure 4A–C show the network covariance matrices for the same MUs and three stimulus diameters used for the raster plots. In all layers, shared variance was highest when the smallest of the three stimuli was presented and dropped to near zero in response to the 0.5° stimulus (0.1° vs. 0.5° mean ± s.e.m.: SG, 1.53 ± 0.18 vs. 0.48 ± 0.08, n = 4; G, 1.07 ± 0.18 vs. 0.16 ± 0.02, n = 3; IG, 0.74 ± 0.21 vs. 0.30 ± 0.06, n = 7). The impact of larger stimuli on shared variance, instead, depended on layer. Compared to shared variance in response to the 0.5° stimulus, shared variance in response to the 26° stimulus increased in SG layers (0.5° vs. 26° mean ± s.e.m.: 0.48 ± 0.08 vs. 0.74 ± 0.20, n=4), did not change in G layers (0.16 ± 0.02 vs. 0.14 ± 0.05, n = 3), and decreased in IG layers (0.30 ± 0.06 vs. 0.14 ± 0.04, n = 7). The bottom panel of Figure 4A–C shows, for the same example MUs, shared variance as a function of stimulus diameter for all diameters used in our study (0.1–26°).

Figure 5A shows size tuning of firing rate and shared variance for the population of MUs recorded in SG, G, and IG layers. Shared variance was tuned for stimulus size in a manner that resembled the size tuning of Fano-factor (compare with Figure 2A). In all layers, increasing the stimulus diameter from 0.1° to a size equal to the aggregate RF diameter of the recorded MUs progressively increased firing rate but decreased shared variance (Figure 5A, B). Shared variance also decreased relative to baseline for a stimulus matched to the RF diameter; the percent change in shared variance was similar across layers and there were no obvious differences across the two animals used in this study (Figure 5C; median percent change in shared variance ± s.d. of the bootstrap distribution, SG: –47.5 ± 11.2%, G: –29.6 ± 18.9%, IG –31.9 ± 17.7). The median percent change in shared variance was significantly below zero in all layers (one-tailed bootstrap test, p < 0.02). In contrast, the effect on shared variance of stimulating the RF with larger stimuli extending beyond the RF, into the RF surround, differed across layers. Near-surround stimulation (2xRF diameter) significantly reduced shared variance compared to its value for a stimulus matched to the RF, only in IG layers, but not in G and SG layers (Figure 5D; median percent change in shared variance ± s.d. of the bootstrapped distribution, SG: –4.60 ± 9.58%, G: –8.31 ± 11.11%, p ≥ 0.21, IG: –28.8 ± 7.01%, p < 0.015). Stimulating the per-neuron surround did not affect the shared variance in any layer (Figure 5E; median percent change in shared variance ± s.d. of the bootstrap distribution, SG: 4.55 ± 20.6%, G: 10.1 ± 20.2%, –37.4 ± 15.5%, p ≥ 0.12). The effect on shared variance of stimulating the far surround with a 26° stimulus differed across layers (Figure 5F). In SG and G layers, the percent change in shared variance was not significantly different from zero (Figure 5F; median percent change in shared variance ± s.d. of the bootstrapped distribution, SG: 6.35 ± 16.97, G: 7.62 ± 36.43, one-tailed bootstrap test p > 0.18). However, in IG layers, the 26° diameter stimulus significantly decreased shared variance compared to its value for a stimulus matched to the RF (median percent change in shared variance ± s.d. of the bootstrapped distribution –33.7 ± 10.99%, one-tailed bootstrap test p < 0.001; Figure 5F).

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The median stimulus diameter at the lowest shared variance (i.e. at maximum shared variance quenching) normalized to the RF diameter was 1.86 (1.30, 14.7, 99% CI) in SG layers, 2.22 (1.40, 14.9) in G layers, and 6.59 (2.06, 19.9) in IG layers (Figure 5G).

The median surround stimulus diameter evoking the highest shared variance, normalized to the RF diameter, was 5.8 (1.0, 24.4) in SG, 9.4 (2.27, 45.0) in G, and 1.49 (1.0, 6.60) in IG (Figure 5H).

To better understand the connection between shared variance and changes in firing rate related to stimulus size, we computed the average shared variance following the same mean-matching procedure performed for Fano-factor (see Methods). This analysis showed similar results to those of the non-mean-matched analysis (see Supplementary Methods, Supplementary Results, and Figure 5—figure supplement 1).

Using laminar multi-electrode array recordings, we have studied how single neuron response variability and the shared variability among neurons are modulated by stimulus size across the layers of macaque V1. We found that both forms of variability are size-tuned, and this tuning is layer dependent. In all layers, variability declined as a stimulus was progressively increased in size from 0.1° to the diameter of the RF. However, as the stimulus was enlarged beyond the RF, variability changed in a layer and stimulus-size-dependent manner. Stimuli involving the near surround decreased variability and shared variability relative to their values for a stimulus the size of the RF, mainly in the IG layers. In contrast, larger stimuli extending into the far surround increased both single neuron and shared variability in SG layers (relative to their value for a stimulus matched to the RF diameter), but did not change them or reduced them in G and IG layers. Given the hypothesized influence of variability on visual information processing and the encoding of sensory inputs, these laminar differences suggest that the different layers employ different strategies for coding large stimuli. Moreover, given known laminar differences in connectivity, these laminar-specific effects of stimulus size on variability suggest different underlying circuit mechanisms.

Theoretical work has shown that correlated variability can be detrimental for sensory processing (Abbott and Dayan, 1999; Averbeck et al., 2006). Consistent with this idea, a number of top–down modulations thought to improve sensory processing and perception tend to reduce spike-count variability (Fano-factor) and correlated variability. For example, attention directed toward a visual stimulus reduces Fano-factor and correlated variability in primate areas V4 (Cohen and Maunsell, 2009; Mitchell et al., 2009) and V1 (Herrero et al., 2013), decorrelation is induced by perceptual learning in area MSTd (Gu et al., 2011), and surround suppression reduces Fano-factor (Festa et al., 2021) and correlated variability (Snyder et al., 2014) in V1. However, theoretical and experimental work has also indicated that not all correlations impede encoding (Averbeck et al., 2006), that the strength of variability and correlations depends on stimulus, cognitive factors, cortical layers, and area (Hansen et al., 2012; Smith et al., 2013; Ruff and Cohen, 2016a; Ruff and Cohen, 2016b), and that some form of correlations can facilitate, rather than impede, perception (Ruff and Cohen, 2014; Haefner et al., 2016). In line with these later studies, we find that the effects of surround suppression on variability and correlated variability depend on stimulus size and cortical layer. Our results in IG layers that near and far-surround stimulation reduce Fano-factor and correlated variability are consistent with previous reports (Snyder et al., 2014; Orbán et al., 2016; Festa et al., 2021) (although we used factor analysis as a measure of shared variability, unlike Snyder et al., which instead measured correlations). However, we have additionally shown that the effect of surround suppression on Fano-factor and shared variability depends on both the size of the surround stimulus (near vs. far) and cortical layer. Unlike in IG layers, in G and SG layers, near-surround stimulation did not decrease Fano-factor or shared variability below their values measured for a stimulus matched to the RF size, while far-surround stimulation increased variability in SG layers, but decreased it (or had no effect) in IG layers. As near- and far-surround suppression are thought to be mediated by different circuits (intra-areal horizontal and inter-areal feedback connections, respectively), and different layers have distinct connectivity, these results suggest that different circuits affect variability in different ways. In particular, they suggest that increased activity of long-range intra-areal or inter-areal feedback connectivity in IG layers quenches variability. In contrast, corticocortical feedback connections to the SG layers may be a source of variability and correlated variability in these layers, and enhancing their activity amplifies variability and correlations. It is unlikely that the increased variability in SG layers induced by presentation of large stimuli is detrimental for visual processing. The impact of surround modulation on visual processing ultimately depends on the way neuronal responses are read out, which may vary with cortical layer. It is also possible that variability increases in SG layers and decreases in IG layers induced by surround stimulation both facilitate encoding and perception. Additional studies are necessary to determine how these laminar-specific modulations of variability affect perception and behavioral performance, but these laminar differences are consistent with mounting evidence that SG and IG layers represent functionally distinct processing streams. For example, SG and IG layers show distinct dynamics and spectral behavior (Maier et al., 2010; Wang, 2010; Buffalo et al., 2011; Mendoza-Halliday et al., 2024), which are thought to underlie functional and computational asymmetries (Bastos et al., 2012; Shipp, 2016).

It has recently been suggested that variability and response suppression share a common origin, as manipulations that increase response suppression typically quench variability (Goris et al., 2024). Our results, however, indicate that surround suppression is not always associated with variability quenching, as far-surround stimulation in the SG layers increased both variability and shared variability, and instead suggest multiple circuits and mechanisms as the source of variability.

It is often assumed that the trial-to-trial variability of neural responses follows Poisson statistics (Simoncelli et al., 2004). Under Poisson statistics, variability does not depend on firing rate; rather, the Fano-factor remains constant (=1) regardless of mean firing rate. In contrast, we found that, across all layers, firing rate increased, and Fano-factor decreased as the stimulus diameter was increased from 0.1° to a diameter equal to that of the RF. These results are inconsistent with the Poisson model of neural response statistics. An extension of the Poisson model, the modulated Poisson model (Goris et al., 2014), augments the Poisson model by a stochastic gain variable. With this addition, the model captures overdispersion (Fano-factor >1) of neural responses in a physiologically and statistically meaningful way. The modulated Poisson model predicts that Fano-factor increases as firing rate increases (Goris et al., 2014). In contrast to this prediction, our data show that for stimuli within the RF, Fano-factor decreases as mean firing rate increases. Our results for small stimuli resemble those of Coen-Cagli and Solomon, 2019 who showed that, in macaque V1, Fano-factor decreased as stimulus contrast (and firing rate) increased. These authors also concluded that their data was incompatible with the modulated Poisson model and suggested that neural response statistics in macaque V1 are better captured by stochastic normalization models.

A different class of models is based on the idea of perception as probabilistic inference (Knill and Pouget, 2004). In these models, spikes represent samples from probability distributions, and neural response variability reflects the uncertainty of the inferences (Hoyer and Hyvärinen, 2003; Fiser et al., 2010; Orbán et al., 2016; Echeveste et al., 2020; Festa et al., 2021). The model by Festa et al., 2021 predicts a decrease in Fano-factor induced by surround stimulation relative to its value for a stimulus matched in size to the RF. These authors’ neural recording results confirmed the model predictions for stimuli extending into the near surround (2xRF size), but for larger stimuli involving the far surround, Fano-factor increased back to its value at the RF size. However, these authors did not examine laminar differences, and the use of 1 mm shank length Utah electrode arrays in their study suggests they may have sampled neurons primarily from the G layer. Our mean-matched analysis confirmed the result of Festa et al. that near-surround stimulation reduces Fano-factor, but we found this to occur only in G and IG layers; we additionally showed that in G and IG layers, as the stimulus was extended into the far surround, Fano-factor either increased back to its value at the RF size (non-mean-matched analysis) or remained at its value for a stimulus in the near surround (mean-matched analysis). This points to the intriguing possibility that in G and IG layers, a significant proportion of neurons serves to perform probabilistic inference. Festa et al., 2021 also presented a version of their model in which global context had an additive, instead of multiplicative, effect on neural responses. Interestingly, the additive version of their model predicted that stimulating the RF surround should increase variability, as we found in many cells, particularly in the SG layers.

The laminar differences in variability found in our study suggest different underlying circuit mechanisms and potentially different computational functions. One plausible hypothesis is that laminar-specific inhibitory circuits underlie the different effects of surround stimulation on variability. This hypothesis is based on the assumption that inhibition plays an important role in modulating cortical response variability, as postulated by several models (Stringer et al., 2016; Hennequin et al., 2018; Huang et al., 2019), and the well-established laminar differences in the distribution of inhibitory neuron types (Tremblay et al., 2016). In macaque sensory-motor cortex, somatostatin-positive inhibitory interneurons predominate in SG layers (Hendry et al., 1984; Gielow et al., 2025). In mouse cortex, these interneuron types subtractively control the gain of their target neurons (Sturgill and Isaacson, 2015), by hyperpolarizing the dendrites of pyramidal cells (Markram et al., 2004; Pouille et al., 2013), and mediate surround suppression (Adesnik et al., 2012). This subtractive inhibition counteracts the excitatory feedforward drive (Pouille et al., 2013), thus, ultimately affecting neural responses in a manner resembling reduced feedforward input. Because reduced feedforward input to the cortex increases neural response variability (e.g. Churchland et al., 2010; Festa et al., 2021, this study), activation of somatostatin neurons ultimately would lead to increased neural response variability. This hypothesis predicts that neurons in which variability is increased by surround stimulation, which are present in all layers but dominate in the SG layers, are those in which surround suppression is mediated by somatostatin cells. Alternatively, reduced feedforward drive induced by surround stimulation, leading to increased variability, may result from withdrawal of feedforward excitation from surround-suppressed excitatory neurons in the thalamus or cortex itself, a mechanism that is consistent with a recent model of neural response variability (Bressloff, 2019). This hypothesis predicts that neurons in which variability is increased by surround stimulation are those inheriting surround suppression from other suppressed excitatory neurons. In contrast, neurons for which surround stimulation does not affect or decreases variability (more numerous in G and IG layers) may be surround suppressed via different circuit mechanisms; for example, via inhibitory cells that track the activity of excitatory cells (such as parvalbumin interneurons). This mechanism quenches variability in a stochastic inhibition-stabilized network model (Hennequin et al., 2018).

Quenching of cortical response variability by stimulus onset is considered to be a universal property of the cortex (Churchland et al., 2010). In line with this idea, we showed that presenting a stimulus most commonly quenched variability compared to pre-stimulus baseline. However, in addition to variability quenching, we found that, for a substantial fraction of neurons in all layers, but predominantly in G and IG layers, small stimuli amplified variability relative to pre-stimulus baseline. The use of very small stimuli and a unit-by-unit analysis were the key differences between our study and previous studies that did not observe amplification of variability by small stimuli. Amplification of cortical response variability by small visual stimuli relative to pre-stimulus baseline was predicted by a supralinear stabilized network model of cortical response variability (Hennequin et al., 2018). This model predicts variability amplification when the stimulus-evoked response is of comparable magnitude to spontaneous activity. However, in our data, variability amplification was observed also when neural responses were significantly above the spontaneous baseline. Thus, the prediction of supralinear stabilized network models of cortical response variability may not be in quantitative agreement with the results of this study. Variability amplification can trivially arise in units with close to zero baseline firing rates, as it is often the case for anesthetized primate V1, because the variance of a spike train with zero mean is necessarily zero and can only increase as the firing rate increases. In our dataset, the cells that showed variability amplification had lower baseline firing rates and Fano-factor values, but also showed variability quenching for larger stimuli. Thus, a floor effect due to low baseline firing rates cannot explain the variability amplification in our data. A potential caveat of our dataset is that even though the animals were anesthetized and paralyzed, small eye movements can still occur, causing a small stimulus to move in and out of the RF. This could cause amplification of variability. While we cannot rule out this explanation for all penetrations, we found amplifying units in penetrations in which eye movements could be confidently ruled out. Thus, we conclude that small, weak stimuli can amplify trial-to-trial variability relative to baseline.

A number of different dynamical models have been proposed to explain various aspects of stimulus-dependent variability. In models with multi-stable dynamics, response variability arises from the stochastic wandering across the cortex of spontaneously formed tuning curves or bumps (Ponce-Alvarez et al., 2013; Bressloff, 2019; Huang et al., 2019). In these models, increased stimulus drive reduces wandering of the activity patterns, locking the stimulus-driven bump in place, and as a consequence, quenching variability. Recently, one such model explicitly predicted an increase in variability by surround stimulation (Bressloff, 2019). This prediction is consistent with our results in SG layers, but not in G and IG layers, although this model captures well the experimentally observed differences in the magnitude of variability across cortical layers in the spontaneous state (Smith et al., 2013). In a different class of models, instead, variability results from fluctuations about a single, stimulus-driven attractor in a stochastic stabilized supralinear network (Hennequin et al., 2018). In these models, when stimulus drive increases, the balanced network causes an increase in inhibition which leads to reduced variability. Thus, in these models, variability quenching results from increased inhibition, as opposed to the multiple-attractor models described above in which variability quenching results from increased excitation. Although the effects of surround suppression on variability have not been explicitly studied in stabilized supralinear network models, they would seem consistent with our results in G and IG layers, that is a reduction or saturation of variability by surround stimulation, but not in SG layers.

In summary, existing models of cortical response variability are either inconsistent or only partly consistent with our results, capturing the effects on variability of stimulus size we have observed for some, but not all, layers. We suspect that both kinds of mechanisms may occur, depending on particular cortical operating conditions and the specific layer. Therefore, our results call for the extension of these existing models or the development of new models that can capture the laminar differences in the stimulus-dependent modulation of cortical response variability we have observed in our study.

Upon acceptance of the study, the data will be available without restrictions at https://doi.org/10.5061/dryad.hqbzkh1x4. The codes used for this study are available at https://github.com/nurminenlab/variability-sizetuning-analysis, copy archived at nurminenlab, 2026.

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Author details

1. Lauri Nurminen

   Department of Ophthalmology and Visual Science, Moran Eye Institute, University of Utah, Salt Lake City, United States

   Present address

   College of Optometry, University of Houston, Houston, United States

   Contribution

   Conceptualization, Data curation, Software, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing – original draft, Writing – review and editing

   Competing interests

   No competing interests declared

2. Maryam Bijanzadeh

   Department of Ophthalmology and Visual Science, Moran Eye Institute, University of Utah, Salt Lake City, United States

   Present address

   Department of Neurology, UCSF Weill Institute for Neurosciences, University of California San Francisco, San Francisco, United States

   Contribution

   Data curation, Software, Validation, Investigation, Methodology

   Competing interests

   No competing interests declared

3. Alessandra Angelucci

   Department of Ophthalmology and Visual Science, Moran Eye Institute, University of Utah, Salt Lake City, United States

   Contribution

   Conceptualization, Resources, Data curation, Software, Supervision, Funding acquisition, Investigation, Visualization, Methodology, Project administration, Writing – review and editing

   For correspondence

   alessandra.angelucci@hsc.utah.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-1957-2231

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