Adaptation modulates correlated subthreshold response variability in visual cortex

Correlated response variability has profound implications for stimulus encoding, yet our understanding of this phenomenon is based largely on spike data. Here, we investigate the dynamics and mechanisms of membrane potential-correlated variability (CC) in visual cortex with a combined experimental and computational approach. We observe a visually evoked increase in CC, followed by a fast return to baseline. Our results further suggest a link between this observation and the adaptation-mediated dynamics of emergent network phenomena.

Abstract

Cortical sensory responses are highly variable across stimulus presentations. This variability can be correlated across neurons (due to some combination of dense intracortical connectivity, cortical activity level, and cortical state), with fundamental implications for population coding. Yet the interpretation of correlated response variability (or “noise correlation”) has remained fraught with difficulty, in part because of the restriction to extracellular neuronal spike recordings. Here, we measured response variability and its correlation at the most microscopic level of electrical neural activity, the membrane potential, by obtaining dual whole cell recordings from pairs of cortical pyramidal neurons during visual processing in the turtle whole brain ex vivo preparation. We found that during visual stimulation, correlated variability adapts toward an intermediate level and that this correlation dynamic is likely mediated by intracortical mechanisms. A model network with external inputs, synaptic depression, and structure reproduced the observed dynamics of correlated variability. These results suggest that intracortical adaptation self-organizes cortical circuits toward a balanced regime at which correlated variability is maintained at an intermediate level.

NEW & NOTEWORTHY Correlated response variability has profound implications for stimulus encoding, yet our understanding of this phenomenon is based largely on spike data. Here, we investigate the dynamics and mechanisms of membrane potential-correlated variability (CC) in visual cortex with a combined experimental and computational approach. We observe a visually evoked increase in CC, followed by a fast return to baseline. Our results further suggest a link between this observation and the adaptation-mediated dynamics of emergent network phenomena.

sensory cortex is not simply one layer in a feedforward network (Fig. 1A); although it receives strong inputs from thalamus, intracortical feedback dominates cortical circuitry (Fig. 1B). This tangle of cortical connections causes neural activity to be coordinated across multiple spatial and temporal scales (Ohiorhenuan et al. 2010; Panzeri et al. 2010). Moreover, in a given cortical network, the strength of this coordination can vary with activity level and network state (Doiron et al. 2016; Haider et al. 2016; Okun et al. 2015; Poulet and Petersen 2008; Renart et al. 2010; Schölvinck et al. 2015; Stringer et al. 2016), which is considered to have implications for cortical function (Averbeck and Lee 2004; Averbeck et al. 2006; Moreno-Bote et al. 2014; Zohary et al. 1994). For example, weak coordination corresponds to a larger “library” of words available to the spatiotemporal code, whereas stronger coordination supports signal propagation (Fig. 1C). The realized level of coordination in active cortical circuits is expected to represent a balance between such competing system needs. Two unanswered questions concerning coordination continue to block our path to understanding sensory processing in cerebral cortex. First, what are the levels of cortical coordination during sensory processing, and to what extent do these levels change with varying stimulus conditions (Fig. 1C)? Second, what mechanisms are responsible for the realized level of cortical coordination and its changes?

Fig. 1.

Investigating the dynamics of correlated variability in recurrent circuits of visual cortex. A: feedforward thalamocortical network subject to sensory inputs (magenta). Coordination between pairs of cortical neurons (black) is determined by convergence patterns in thalamic inputs (green). B: a more realistic, interaction-dominated thalamocortical network, in which the inputs to any one cortical neuron arise primarily from other cortical neurons. Coordination is thus a function of both feedforward and recurrent inputs. C: the level of cortical coordination affects cortical function, and it is unknown whether and how this changes with sensory stimulation. D: we simultaneously recorded the membrane potentials from pairs of cells during ongoing and visually evoked activity in a densely interconnected thalamocortical network. In some cases, we also recorded the nearby local field potential (LFP). E: pairwise membrane potential recordings provided a measure of cortical coordination across stimulus conditions that avoids the pitfalls of spike data. The LFP provided a measure of local population activity.

Correlated variability is one popular measure of coordination, which is due primarily to its potential implications for response fidelity of neuronal populations (Zohary et al. 1994). To calculate this measure, most studies use population-spiking activity (see Cohen and Kohn 2011, and Doiron et al. 2016 for reviews) in part because of the relative ease of obtaining spiking responses from pairs of neurons in intact brains. Although reported values of spike-based correlated variability tend to be significantly nonzero, results have varied across studies (Cohen and Kohn 2011; Doiron et al. 2016; Hansen et al. 2012; Schölvinck et al. 2015; Tan et al. 2014). Furthermore, the interpretation of spike data is littered with complications, including a spike rate dependence of correlated variability values (de la Rocha et al. 2007; Cohen and Kohn 2011), the underrepresentation of sparse-spiking neurons, and biases introduced by the spike-sorting process (Cohen and Kohn 2011; Ventura and Gerkin 2012; Schulz et al. 2015). Importantly, these complications make it difficult to infer state-dependent changes in underlying correlations from population spiking activity. In conclusion, the important study of correlated variability, including its relation to mechanisms and function, has been restricted by its focus on spike recordings and continues to represent an unmet challenge in systems of neuroscience.

In response to this need, we investigated the dynamics of correlated response variability at the level of the membrane potential by obtaining dual whole cell recordings from pairs of cortical pyramidal neurons during visual processing in the ex vivo turtle eye-attached whole brain preparation (Fig. 1, D and E). This preparation, which is useful for obtaining long-duration patch clamp recordings (Crockett et al. 2015), yields extracellular visual responses (see Fig. 1E and Shew et al. 2015) that are qualitatively similar to those in the anesthetized (Prechtl et al. 1997, 2000) and awake (Rutishauser et al. 2013) animal. We observed a high level of trial-to-trial membrane potential response variability. Furthermore, correlated variability in high-frequency (20–100 Hz) membrane potential fluctuations increased at stimulus onset but returned to prestimulus values during continued visual stimulation. A brief visual stimulus, triggering persistent cortical activity, elicited a similar dynamic of correlated variability, thus implicating an intracortical mechanism. A driven clustered network reproduced these empirical results and suggests crucial roles for synaptic clustering, synaptic depression, and network oscillations. Taken together, these results demonstrate early and late visual response phases characterized by elevated and baseline correlated variability levels, respectively, and suggest that adaptation toward an intermediate level of coordination is a fundamental principle of cortical organization during visual processing.

MATERIALS AND METHODS

Surgery.

All procedures were approved by Washington University’s Institutional Animal Care and Use Committees and conformed to the guidelines of the National Institutes of Health on the Care and Use of Laboratory Animals. Sixteen adult red-eared sliders (Trachemys scripta elegans, 150–1,000 g) were used for this study. Turtles were anesthetized with Propofol (2 mg/kg) and then decapitated. Dissection proceeded as described previously (Crockett et al. 2015; Saha et al. 2011). In brief, immediately after decapitation, the brain was excised from the skull, with the right eye intact, and bathed in cold extracellular saline (in mM: 85 NaCl, 2 KCl, 2 MgCl₂·6H₂O, 20 dextrose, 3 CaCl₂-2H₂O, and 45 NaHCO₃). The dura was removed from the left cortex and right optic nerve and the right eye hemisected to expose the retina. The rostral tip of the olfactory bulb was removed, exposing the ventricle that spans the olfactory bulb and cortex. A cut was made along the midline from the rostral end of the remaining olfactory bulb to the caudal end of the cortex. The preparation was then transferred to a perfusing chamber (Warner RC-27LD recording chamber mounted to PM-7D platform) and placed directly on a glass coverslip surrounded by Sylgard. A final cut was made to the cortex (orthogonal to the previous and stopping short of the border between the medial and lateral cortex), allowing the cortex to be pinned flat, with the ventricular surface exposed. Multiple perfusion lines delivered extracellular saline, adjusted to pH 7.4 at room temperature, to the brain and retina in the recording chamber.

Intracellular recordings.

For whole cell current clamp recordings, patch pipettes (4–8 MΩ) were pulled from borosilicate glass and filled with a standard electrode solution (in mM; 124 KMeSO₄, 2.3 CaCl₂-2H₂O, 1.2 MgCl₂, 10 HEPES, and 5 EGTA) adjusted to pH 7.4 at room temperature. Cells were targeted for patching using a differential interference contrast microscope (Olympus). Simultaneously recorded cells were located <300 μm apart. Intracellular activity was collected using an Axoclamp 900A amplifier, digitized by a data acquisition panel (National Instruments PCIe-6321), and recorded using a custom Labview program (National Instruments), with sampling at 10 kHz. We excluded cells that did not display stable resting membrane potentials. The visual cortex was targeted as described below.

Extracellular recordings.

Extracellular recordings were achieved with tungsten microelectrodes (MicroProbes heat-treated tapered tip), with ∼0.5 MΩ impedance. Electrodes were slowly advanced through tissue under visual guidance using a manipulator (Narishige) while monitoring for activity using custom acquisition software (National Instruments). The extracellular recording electrode was located within ∼300 μm of patched neurons. Extracellular activity was collected using an A-M Systems Model 1800 amplifier that was band-pass filtered between 1 and 20,000 Hz, digitized (NI PCIe-6231), and recorded using custom software (National Instruments).

Identification of visual cortex.

We used a phenomenological approach to identify the visual cortex, as described previously (Shew et al. 2015). In general, this region was centered on the anterior lateral cortex, in agreement with voltage-sensitive dye studies (Senseman and Robbins 1999, 2002). Anatomic studies identify this as a region of cortex receiving projections from lateral geniculate nucleus (Mulligan and Ulinski 1990).

Visual stimulation.

Whole field flashes were presented using either a red LED (Kingbright, 640 nm), mounted to a manipulator and positioned 1–5 cm above the retina or a projector lens system (described below). The mean LED light intensity (irradiance) at the retina was 60 W/m². For one turtle, we used these same LEDs in conjunction with 200-μm optical fibers (Edmund Optics) to project subfield flashes (1–200 ms) onto the visual streak. Other stimuli were presented using a projector (Aaxa Technologies, P4X Pico Projector) combined with a system of lenses (Edmund Optics) to project images generated by a custom software package directly onto the retina. The mean irradiance at the retina was 1 W/m². This system was used to present brief (100–250 ms) red whole field flashes, sustained (10 s) whole field illumination (gray screen), a naturalistic movie [“catcam” (Betsch et al. 2004)], a motion-enhanced movie (Nishimoto and Gallant 2011), and a phase-shuffled version of the same movie (courtesy of Jack Gallant and Woodrow Shew). In all cases, the stimulus was triggered using a custom Labview program (National Instruments).

The preparation was in complete darkness before and after each stimulus presentation. Flashes lasted between 1 and 150 ms, with ≥20 s between flashes. Movies lasted either 10 or 20 s and were presented ≥12 times. Stimulation trials were randomly interleaved with minutes-long recordings of spontaneous activity. Each visual stimulation trial was manually triggered by the experimenter. This approach resulted in semirandom intertrial intervals with a minimum duration of 30 s.

We presented continuous visual stimuli (movies or sustained whole field illumination) while recording from 19 pairs and brief flashes while recording from 16 pairs.

Signal processing.

In all analyses, only cells with 12 or more visual stimulation trials were included. Raw data traces were down-sampled to 1,000 Hz. Because action potentials in turtle cortical pyramidal neurons are relatively wide, spike waveforms still contributed to the band-pass-filtered intracellular recordings. To remove these, an algorithm was used to detect spikes, and the membrane potential values in a 20-ms window centered on the maximum of each spike were replaced via interpolation. For most analyses, the traces were then filtered (100 Hz low-pass or 20–100 Hz band-pass third-order Butterworth filter), and a sine wave removal algorithm was used to remove 60 Hz line noise. We used unfiltered traces (with spikes removed) when calculating power spectral densities.

We used a similar approach to process extracellular recordings: traces were down-sampled to 1,000 Hz and then filtered (100 Hz low-pass Butterworth), yielding the local field potential.

Cross-correlation analysis.

For each single-trial voltage trace, the residual (V_r or deviation from the average activity) was found by subtracting the across-trial average time series from the single-trial time series:

$$V_r=V-V_{trials}\mathrm{.}$$

Residuals were then separated into three epochs: the ongoing epoch (defined to be 1 s before the onset of visual stimulation), the transient epoch (1,200–2,200 ms after stimulus onset), and the steady-state epoch (2,400–3,400 ms after stimulus onset). For each pair of simultaneously recorded cells, the Pearson correlation between residual pairs was then calculated for each epoch and trial. The results were averaged across all trials, resulting in the trial-averaged correlated variability (CC) for each pair and epoch:

$$C{C}^{epoch}=cov\left(V_{r,1}^{epoch},V_{r,2}^{epoch}\right)/{[var(V_{r,1}^{epoch})var\left(V_{r,2}^{epoch}\right)]}^{1/\hspace{0.17em}2}{}_{trials}\mathrm{.}$$

Because the correlated variability of spike counts been shown to depend on the size of the window used for calculations (Schulz et al. 2015), we repeated the above process for three other sets of choices for epoch window sizes and gaps between epochs. The results presented here were largely robust to these choices (data not shown).

We also compared CC values for responses to brief and continuous visual stimulation. First, pairs were segregated according to the stimulus presented, resulting in 16 brief and 19 continuous-stimulation pairs. The two resulting sets of trial-averaged CC values were then compared using the Wilcoxon rank-sum test.

Power spectral analysis.

For each trial and cell, we extracted a 3.4-s window of activity (with epoch windows and gaps between epochs, as described above) and calculated the residual time series, as described above. For each residual trace, we calculated the power spectral density (psd) for each epoch using the multitaper psd function in the NiTime algorithms spectral module. We then calculated the transient (steady-state) relative power spectral density for each trial by dividing the transient (steady-state) psd by the ongoing psd. We averaged across trials for all frequencies <100 Hz, resulting in the relative power spectral density rP. For each pair, we also averaged across all frequencies in the 20–100 Hz range, resulting in rP_hf. We tested for significant changes in rP_hf across epochs for a given pair, and for the population as a whole, using the methods described below in Statistical analysis. Source code, binaries, and documentation for the NiTime library are freely available at http://nipy.org/nitime/.

For each cell and trial, we quantified the prevalence of low-frequency subthreshold fluctuations in prestimulus activity by averaging the Fourier transform for 1–5 Hz activity (similar to Sachidhanandam et al. 2013) in the 8 s preceding stimulus onset. We averaged this quantity across trials, resulting in <FFT_δ>. The Fourier transform was calculated using the numpy.fft routine. Source code, binaries, and documentation for the NumPy package are freely available at http://numpy.org.

Network models.

To investigate the roles of network properties in our experimental results, we implemented a series of model networks composed of 800 excitatory and 200 inhibitory single-compartment leaky integrate-and-fire neurons. In the model that reproduced our principal experimental results, excitatory-excitatory connections had clustered (or “small-world”) connectivity (with 3% connection probability) (Bujan et al. 2015; Litwin-Kumar and Doiron 2012; Watts and Strogatz 1998), and all other connections were random (with 3% excitatory-inhibitory and 20% inhibitory-excitatory and inhibitory-inhibitory connection probability). To implement the clustered excitatory-excitatory connectivity, we began by constructing a “ring network” of 800 excitatory nodes. Each node in the network was connected to its 24 nearest neighbors (reflecting 3% connection probability). The weight of each of these connections was drawn from a β-distribution with an average value 1.0. Finally, 1% of these connections were randomly rewired. That is, for each nonzero connection between a presynaptic and postsynaptic node, a different postsynaptic node was randomly selected from the excitatory network with a probability of 1%.

The dynamics of the membrane potential (V) of each node evolved according to

$${\tau }_m\frac{dV}{dt}=-\frac{1}{C}\left\{g_L\left[V\left(t\right)-E_L\right]+I_{syn}\left(t\right)\right\},$$

where the membrane time constant τ_m = 50 ms (25 ms) for excitatory (inhibitory) nodes, the membrane capacitance C = 0.4 nF (0.2 nF) for excitatory (inhibitory) nodes, and the leak conductance g_L = 10 nS (5 nS) for excitatory (inhibitory) nodes. The leak reversal potential E_L for each node was a random value between −70 and −60 mV, drawn from a continuous uniform distribution (to model the variability in resting membrane potentials observed across neurons in the experimental data). The reversal potentials for the synaptic current I_syn(t) were E_GABA = −68 mV and E_AMPA = 50 mV. The spike threshold for each neuron was −40 mV. A neuron was reset to −59 mV after spiking and was refractory for 2 (excitatory) and 1 ms (inhibitory).

The synaptic conductance g_YX(t) for each synapse type (between presynaptic neurons of type X and postsynaptic neurons of type Y) had three relevant time constants: delay (τ_LX, that is, the lag between presynaptic spike time and beginning of the conductance waveform), rise time (τ_RYX), and decay time (τ_DYX). Following a presynaptic spike at time 0, the synaptic conductance dynamics were described by a fast exponential rise and a slower exponential decay, or an “α-function”

$$g_{YX}\left(t\right)=g_{YX}^0\left(\frac{{\tau }_m}{{\tau }_{DYX}-{\tau }_{RYX}}\right)\left[exp\left(-\frac{t-{\tau }_{LX}}{{\tau }_{DYX}}\right)-exp\left(-\frac{t-{\tau }_{LX}}{{\tau }_{RYX}}\right)\right],$$

where $g_{YX}^0$ is the maximum synaptic conductance, and time constants (in ms) are τ_LE = 1.5, τ_REE = 0.2, τ_DEE = 1.0, τ_RIE = 0.2, τ_DIE = 1.0, τ_LI = 1.5, τ_RII = 1.5, τ_DII = 6.0, τ_REI = 2.25, and τ_DEI = 6.0. Maximum conductance values (in nS) were $g_{EE}^0$ = 3.0, $g_{IE}^0$ = 6.0, $g_{EI}^0$ = 30, and $g_{II}^0$ = 30. Thus, inhibitory synapses were in general stronger and slower than excitatory synapses.

All excitatory and inhibitory neurons received Poisson external inputs. During “ongoing” activity, the external input rate to each neuron was 50 Hz. The stimulus was modeled as an increase in the external input rate by a factor of 6. This increase was applied gradually in four equivalent steps over the course of 200 ms. This provided more realistic low-frequency membrane potentials than did a single-step function stimulus but did not qualitatively impact the results. The gating variables for external inputs had the same parameters as for excitatory-excitatory connections, and maximum conductances were $g_{EExt}^0$ = 6 nS and $g_{IExt}^0$ = 6 nS.

In response to a presynaptic spike in neuron j at time $t_j^{spk}$, the weight (W_ij) of a synapse connecting neurons j and i depressed and recovered toward the initial value ($W_{ij}^{\mathrm{\hspace{0.17em}0}}$) according to

$$\frac{d{W}_{ij}}{dt}=-\frac{W_{ij}\left(t\right)}{{\tau }_{depress}}\delta \left(t-t_j^{spk}\right)+\frac{W_{ij}^{\mathrm{\hspace{0.17em}0}}-W_{ij}\left(t\right)}{{\tau }_{recover}}\mathrm{.}$$

with depression time constant τ_depress = 15 ms and recovery time constant τ_recover = 2,500 ms. Depression and recovery time constants were chosen to give reasonable activity time courses for broadband (100-Hz low-pass) membrane potentials. Synaptic depression was applied only to external inputs after the stimulus onset (i.e., after the increase in external input rate). The synaptic weight matrix was reset to $W_{ij}^0$ at the start of each trial.

We repeated 15 trials for a single model network (defined by $W_{ij}^0$). Each trial was 4.4 s in duration, with stimulus onset at 1.7 s, and the time step was 0.05 ms. The ongoing epoch was defined to be 200 to 1,200 ms before stimulus onset, the transient epoch 0 to 1,000 ms after stimulus onset, and the steady-state epoch 1,200 ms to 2,200 ms after stimulus onset. The additional 500 ms at the beginning and end of each trial ensured there were no filtering artifacts in the ongoing and steady-state epochs.

We then randomly selected 20 excitatory nodes from a subpopulation of 100 neighboring excitatory nodes, and from these we generated 40 randomly selected node pairs. These choices for numbers of pairs and trials approximated our experimental conditions. Because action potential rates were higher in this model network than in the experiment [a common issue with small LIF networks (Dayan and Abbott 2001)], and because action potentials can affect high-frequency membrane potential correlated variability, we substituted “test” neurons for these network neurons before doing the calculation. Test neurons were identical to network neurons, but all synaptic conductances were multiplied by a factor of 0.5, and the spike threshold was removed. In other words, we used the model network to generate synaptic inputs to pairs of LIF neurons. For each such pair, we then calculated CC using the same methods described for our analysis of experimental data.

We modeled the LFP as the sum of all synaptic currents (similar to Atallah and Scanziani 2009; Destexhe 1998) to 100 neighboring neurons multiplied by a factor of −1 (to mimic the change in polarity between voltages measured intracellularly and extracellularly). The contribution of each neuron to the LFP was not distance dependent.

In addition, we implemented three alternate model versions: 1) a clustered network identical to that described above, but without synaptic adaptation; 2) a network identical to that above, but with random excitatory-excitatory connectivity, $g_{EE}^0$ = 2.5 nS, and $g_{IExt}^0$ = 4 nS (i.e., a randomly connected network tuned to oscillate in response to strong external drive); and 3) a randomly connected network with $g_{EE}^0$ = 2.5 nS, $g_{IExt}^0$ = 4 nS, τ_RII = 0.2 ms, τ_REI = 0.3 ms, τ_RIE = 0.2 ms, τ_REE = 0.2 ms, τ_LX = 1.5 ms, andτ_DYX = 1.0 ms for all X and Y (i.e., a randomly connected network that did not oscillate). For both randomly connected networks, we used an ongoing external input rate of 65 Hz, and the stimulus was modeled as an increase by a factor of 4.5.

Statistical analysis.

For a given trial-averaged quantity Y^epoch calculated from the data (e.g., CC^ongoing for a pair of cells), we determined the significance of the value relative to zero by bootstrapping; Y^epoch was considered to be significantly nonzero if the average value ± the 95% confidence level from bootstrapping did not include zero. Similarly, Y for two epochs (e.g., CC^ongoing and CC^transient) was considered to be significantly different from one another if the bootstrapping intervals did not overlap.

For a population of data values (e.g., 35 values of CC^ongoing), we determined the significance of the population average value for a given epoch using the one-sample t-test (that is, by comparing to a zero mean normal distribution with the same standard deviation). We tested for a significant change in the population of values across two epochs by applying the Wilcoxon signed-rank test to the two sets of values. In several analyses, we checked for linear relationships between two sets of quantities using linear regression. These three statistical tests were implemented using the ttest_1samp, wilcoxon, and linregress functions in the stats module from Scipy. Source code, binaries, and documentation for Scipy can be downloaded from https://scipy.org/.

For the full population of 35 pairs, we tested for a linear relationships between <FFT_δ> (see above) and CC values in each epoch and then compared the resulting r values using “Steiger’s method” for testing the equality of multiple interdependent correlations (Steiger 1980). This tested the null hypothesis that the three r values were the same. This two-tailed t-test was implemented in python using the dependent_corr function in the CorrelationStats script written by Phillip Singer (Singer et al. 2013), which is freely available on github (https://github.com/psinger/CorrelationStats/blob/master/corrstats.py).

In general, when making multiple comparisons, we Bonferroni-adjusted the threshold P values for significance.

Code and data.

All code used to generate the results presented here is available on GitHub (https://github.com/nathanielcalebwright/wessel-lab-correlated-variability), and the data are available upon request.

RESULTS

To quantify response variability and its correlation across neurons, we recorded the membrane potential (V) from 35 pairs of pyramidal neurons in the visual cortex of the turtle ex vivo eye-attached whole brain preparation during visual stimulation of the retina (Fig. 1D). In some cases, we simultaneously recorded the nearby local field potential (LFP; Figs. 1, C and D, and 2, A and B). For this analysis, we considered three windows of activity: the ongoing (1,000 to 0 ms before stimulus onset), transient (200–1,200 ms after stimulus onset), and steady-state (1,400–2,400 ms after stimulus onset) windows (Fig. 2, A and B). These epoch choices were motivated by the results of an earlier study (Shew et al. 2015) in this same preparation, which uncovered an early supercritical visual response phase, and a later critical phase.

Fig. 2.

Dynamics and complexity of trial-to-trial response variability. A: single-trial responses (low opacity) and across-trial average responses (high opacity) for 2 simultaneously recorded neurons (top black middle red traces), and the nearby LFP (bottom black traces). Stimulus is naturalistic movie (see materials and methods). Single-trial membrane potentials for each cell have been vertically aligned for clarity. B: same as in A, but for a different pair of cells, and stimulus is 150 ms red (640 nm) whole field flash, with onset at magenta arrow (see materials and methods). C: average membrane potential values for all 55 cells during each epoch. Each dot represents the across-trial average value of the broadband (0–100 Hz) membrane potential ($\overline{V}$) for 1 cell for that epoch. High-opacity lines connecting pairs of dots indicate significant changes in values across epochs (assessed comparing bootstrap intervals; see materials and methods). The triple asterisks (***) above line connecting 2 epochs indicate results of Wilcoxon signed-rank significance test (corrected for three comparisons) for difference in populations of values for those epochs (***P < 0.00033). D: single-trial response from cell in A. Expanded view (gray window): high-frequency activity nested within the broader depolarization. E: average relative power spectrum (rP; evoked power divided by ongoing) of residuals for red traces in A for the transient (blue) and steady-state (green) epochs. Shaded regions indicate ±95% confidence intervals by bootstrapping method. F: trial-averaged high-frequency (20–100 Hz) relative power (rP_hf) for all 55 cells for brief and continuous visual stimulation. Each dot represents the across-trial average high-frequency power for 1 cell for that epoch. Connecting lines as in C; ***P < 0.001. One outlier (rP_hf = 377.5 during transient epoch) has been truncated for clarity.

Ongoing activity in turtle visual cortex was largely quiet (Fig. 1E), although we did observe large, spontaneous depolarizations on a subset of visual stimulation trials (Fig. 2A). The frequency of occurrence of these spontaneous events varied across turtles (Fig. 2B) and recording sessions in a given turtle (Wright NC and Wessel R, in press).

Visual stimuli evoked barrages of postsynaptic potentials in cortical pyramidal neurons (Figs. 1E and 2, A and B), which caused them to depolarize by several millivolts (grand average membrane potential $\overline{V}$ = −65.4 ± 6.9 mV ongoing, −58.1 ± 8.5 mV transient, −61.8 ± 7.6 mV steady state; means ± SE, 55 neurons in 16 turtles; Fig. 2C; also see materials and methods). These synaptic barrages coincided with large fluctuations in the nearby LFP (Figs. 1E and 2, A and B), and previous work (Shew et al. 2015) has shown that these broadband LFP oscillations extended across large regions of cortex. Thus, visually evoked intracellular activity was accompanied by synchronous local and global network activity.

Pyramidal neuron membrane potential visual responses are highly variable.

We recorded from 19 pairs of pyramidal neurons (generated from 26 cells in 10 turtles) while presenting continuous visual stimulation and from 16 pairs (generated from 21 cells in seven turtles) while presenting brief whole field flashes (see materials and methods). Single-neuron membrane potential responses to repeated presentations of continuous stimuli varied from trial to trial, with a response variability magnitude that was comparable with the trial-averaged mean response (Fig. 2A). Importantly, the magnitude of the response variability was qualitatively unchanged when the visual stimulus consisted of brief flashes, which evoked long-lasting responses in visual cortex (Fig. 2B). This stimulus invariance suggests an intrathalamocortical origin of the trial-to-trial response variability.

For any given trial of visual stimulation, the evoked membrane potential fluctuations were large and consisted of high-frequency fluctuations nested within broader deflections (Fig. 2D). To quantify the frequency content of the single-trial fluctuations from the mean response, we first calculated the membrane potential residual (V_r), which is the single-trial membrane potential recording from which the trial-averaged membrane potential time series has been subtracted. We then divided the residuals into the epochs defined above. Finally, we calculated the relative power spectral density (rP) for each evoked epoch (Fig. 2E), which is the power spectral density of the membrane potential residual for the transient or steady-state window divided by its trial-averaged counterpart from the ongoing window (see materials and methods).

This analysis revealed four important features concerning the spectral content of the residual membrane potential fluctuations and of the trial-to-trial response variability. First, evoked power of residual membrane potential fluctuations in the 0- to 100-Hz range typically increased by two orders of magnitude compared with ongoing activity (Fig. 2E). Second, the frequency content of the membrane potential residuals varied across trials (as demonstrated by the broad confidence bands in Fig. 2E). Third, the relative power spectral density typically consisted of a prominent peak located approximately in the 4- to 10-Hz theta range and a broader but distinct distribution in the 20- to 100-Hz range. Fourth, for both movies and flashes, high-frequency (20–100 Hz) power increased from the ongoing to the transient window (as indicated by rP_hf, the total relative power in the 20- to 100-Hz range) and significantly decreased from the transient to steady state (transient rP_hf = 55.6 ± 56.2, steady-state rP_hf = 17.7 ± 18.0, means ± SE; 55 cells in 15 turtles, P = 1.11 × 10⁻¹⁰ for transient vs. steady-state comparison, Wilcoxon signed-rank test; Fig. 2F). High-frequency power of the transient activity varied drastically across cells in terms of both the relative power (Fig. 2F) and the details of the power spectra (data not shown).

Together, these data establish that cortical pyramidal neuron membrane potential visual responses 1) have complex temporal dynamics, 2) are highly variable from trial to trial, and 3) differ from neuron to neuron (Fig. 2).

Correlated variability adapts during visual stimulation.

The complex and extensive variability of membrane potential visual responses (Fig. 2) and the interconnected nature of cortical circuits (Fig. 1B) raised the question of to what extent the response variability is correlated across pyramidal neurons. To address this question, we calculated the Pearson correlation coefficient between residual membrane potential fluctuations for each trial and window of interest, i.e., the ongoing, transient, and steady-state windows. We focused on high-frequency (20–100 Hz) activity, which captures the fast, nested membrane potential fluctuations [Figs. 2D (expanded view, gray window) and 3A). This band of activity is thought to be associated with narrow “windows of opportunity” for spiking, determining the precise timing of spikes within a broader depolarization (see Haider and McCormick 2009 for a review). Trial-averaged correlation coefficients (CC) for ongoing activity were broadly distributed across pairs of pyramidal neurons (Fig. 3B), and the population average (CC) was significantly nonzero (CC  = 0.019 ± 0.042; 19 pairs in 10 turtles, P = 0.037, 1-sided t-test). In response to continuous visual stimulation, trial-averaged correlation coefficients increased significantly compared with ongoing values (Fig. 3B) to an elevated population average of CC  = 0.064 ± 0.055 (P = 0.016 for ongoing transient comparison, Wilcoxon signed-rank test). In the steady-state period, i.e., during continued stimulus presentation, trial-averaged correlation coefficients returned to near-ongoing values (CC = 0.026 ± 0.040, P = 8.4 × 10⁻⁴ for transient vs. steady-state comparison, P = 0.52 for ongoing – steady-state comparison).

Fig. 3.

Evoked high-frequency correlated variability appeared to be modulated by internal mechanisms. A: examples of high-frequency (20–100 Hz) residual membrane potential pairs for several trials (same pair as in Fig. 2A). B: trial-averaged CC values for each of 19 pairs, 20–100 Hz, continuous visual stimulation (see materials and methods). Each dot represents the across-trial average CC value for 1 pair for that epoch. Colored (white) dots represent values (not) significantly different from zero (1-sided t-test). Stimulus is naturalistic movie. High-opacity lines connecting pairs of dots indicate significant changes in values across epochs (assessed comparing bootstrap intervals, see materials and methods). Single (*) and double asterisks (**) above the line connecting 2 epochs indicate results of Wilcoxon signed-rank significance test (corrected for three comparisons) for difference in populations of values for those epochs (*0.003 ≤ P < 0.017 and **0.00033 ≤ P < 0.0033). C: same as in B, but for 16 pairs, and brief visual stimulation (see materials and methods).

These results were largely robust with respect to choices of window sizes and gaps between windows, provided the transient and steady-state epochs qualitatively captured the “early” and “late” response phases, respectively (data not shown).

Correlated variability is partially determined by internal variables.

The observed dynamics of high-frequency correlated variability in response to continuous visual stimulation could be imposed by the spatiotemporal structure of the stimulus, or alternatively, they could be intrinsic to the thalamocortical system. To distinguish between these two hypotheses, we recorded from 16 pyramidal neuron pairs while presenting brief flashes (1–200 ms) of light, which evoked cortical responses that persisted for up to several seconds (Fig. 2B). We found that across the population of all pairs, CC values for responses to these brief flashes were not significantly different from those for responses to continuous stimuli (P > 0.05, Wilcoxon rank-sum test, for all epochs; data not shown). Importantly, we also observed a similar dynamic of correlated variability for responses to brief stimuli (ongoing CC = 0.028 ± 0.038, transient CC = 0.093 ± 0.056, steady-state CC = 0.032 ± 0.035; P = 0.0027 for ongoing vs. transient comparison, 16 pairs from 7 turtles, P = 0.0013 transient vs. steady-state comparison, P = 0.64 ongoing vs. steady-state comparison, Wilcoxon signed-rank test, Fig. 3C). The similarity of the dynamics of correlated variability for brief and continuous stimuli implicates a mechanism that is possibly stimulus-invariant and intracortical in origin, with intracortical connectivity being a reasonable candidate mechanism (MacLean et al. 2005; Luczak et al. 2009; Okun et al. 2015).

Correlated variability is related to prestimulus fluctuations.

Next, we noted that CC values were reordered to some degree across stimulus conditions (as indicated by the crossing of lines in Fig. 3, B and C). Furthermore, CC values changed significantly across epochs for several pairs and for the population as a whole. Thus, anatomic connectivity alone could not explain the empirical CC dynamics. What other factors might have been involved?

First, it should be noted that the Pearson correlation coefficient is independent of the amplitudes of the two signals used to calculate CC. Thus, the CC dynamics were not trivially related to the dynamics of high-frequency subthreshold power (Fig. 2F). Second, although it is possible that the CC dynamics for high-frequency activity were influenced by the stimulus modulation of the average membrane potential (Graupner and Reyes 2013; Salkoff et al. 2015), we found no relationship between $\overline{V}$ (Fig. 2C) and CC for any epoch (P > 0.05, linear regression; data not shown). This suggests that the CC dynamic observed here reflected changes in synaptic current correlations across epochs, and that some (likely internal) variables determined the degree to which these correlations changed across epochs for a given pair.

Recent experimental and computational work (employing a variety of coordination measures) suggests that network state strongly influences the level of coordination between pairs of neurons (Poulet and Petersen 2008; Renart et al. 2010; Okun et al. 2015; Schölvinck et al. 2015; Doiron et al. 2016; Haider et al. 2016; Stringer et al. 2016). Therefore, we asked how well a measure of network state (calculated from spontaneous activity) could explain the CC values we observed. In searching for a measure, we noted that the prevalence of large-amplitude, low-frequency fluctuations during prestimulus activity varied across turtles and recording sessions (Figs. 2, A and B, and 4, A and B). We quantified the prevalence of these fluctuations by calculating the average low-frequency (1–5 Hz) FFT (<FFT_δ>, similar to Sachidhanandam et al. 2013; Fig. 4, A and B; see materials and methods). Matching our qualitative observations, <FFT_δ> varied considerably across cells (Fig. 4C). Furthermore, for a given pair of neurons, CC during the steady-state epoch was significantly related to the larger of the <FFT_δ> values for the two neurons (Fig. 4F). Importantly, <FFT_δ> and CC were calculated for different frequency bands, using different windows of activity (Fig. 4, A and B); the two quantities are not trivially related.

Fig. 4.

The prevalence of low-frequency prestimulus fluctuations is related to high-frequency CC values in the steady state. A: multiple trials for a single neuron demonstrating relatively few low-frequency prestimulus events. The across-trial average low-frequency integrated FFT <FFT_δ> is calculated for an 8-s window (indicated by red arrow) preceding the ongoing epoch. Yellow, blue, and green regions indicate the ongoing, transient, and steady state used to calculate CC for high-frequency (20–100 Hz) activity. Stimulus is motion-enhanced movie. B: same as in A, but for a different cell (from a different turtle) demonstrating prominent prestimulus fluctuations. Stimulus is naturalistic movie. C: distribution of <FFT_δ> values for all 55 cells. D–F: absolute value of CC (20–100 Hz) for each pair vs. the geometric mean of <FFT_δ> values for the neurons comprising the pair for the ongoing (D), transient (E), and steady-state (F) epochs. Red lines, r values, and P values indicate results of linear regression analysis. The 3 r values were not significantly different (P = 0.19, t-test for comparison of interdependent correlations; see materials and methods).

Together, these results suggest that in addition to connectivity, the network state (as indicated by the prevalence of low-frequency fluctuations in prestimulus activity) influenced high-frequency subthreshold CC values during the steady-state epoch.

The dynamics of correlated variability are related to emergent network phenomena and are shaped by synaptic properties.

What biophysical mechanisms could mediate the experimentally observed response properties [i.e., high-frequency membrane potential fluctuations (Figs. 2D and Fig. 3A), broadband LFP oscillations (Fig. 2, A and B), the dynamics of correlated variability (Fig. 3), and the apparent relationship to stimulus-independent variables (Figs. 3, D–H, and 4)]? As a starting point, we considered a randomly connected network of 800 excitatory and 200 inhibitory single-compartment leaky integrate-and-fire neurons, with Poisson process external inputs to all neurons (Fig. 5A). We used an increase in the external input rate to mimic the stimulus. (see materials and methods for model details). Motivated by previous experiments (Chung et al. 2002) and models (Levina et al. 2007), we used synaptic adaptation (i.e., short-term synaptic depression with recovery) to modulate network activity levels. We performed 15 simulations using this network and then calculated subthreshold correlated variability for 40 pairs of “test” neurons (see materials and methods for model details). This simple network, which effectively tested for a relationship between CC and network activity levels, did not reproduce our principle empirical result; although overall activity levels qualitatively agreed with the experiment (Fig. 5A), CC values did not change significantly across epochs (ongoing CC = 0.021 ± 0.027, transient CC = 0.010 ± 0.034, steady-state CC = 0.006 ± 0.051; P = 0.12 for ongoing – transient comparison, P = 0.66 for transient vs. steady-state comparison, P = 0.15 for ongoing vs. steady-state comparison, Wilcoxon signed-rank test; Fig. 5B).

Fig. 5.

A model network strengthens the “internal mechanism” hypothesis, suggesting crucial roles for network oscillations and connectivity. A: example traces for a randomly connected network of LIF neurons tuned to remain “asynchronous” after stimulus onset (see materials and methods). Top: representative spike trains for 20% of all excitatory (black rasters) and inhibitory (blue rasters) nodes. Middle: high-frequency (20–100 Hz) membrane potentials for a pair of “test” neurons (see materials and methods). Bottom: single-trial “LFP” generated by summing the synaptic currents to 100 excitatory nodes (see materials and methods). B: trial-averaged CC values for each of 40 test neuron pairs, 20–100 Hz (see materials and methods). Each dot represents the across-trial average CC value for one pair for that epoch. Colored (white) dots represent values (not) significantly different from zero (1-sided t-test). High-opacity lines connecting pairs of dots indicate significant changes in values across epochs (assessed comparing bootstrap intervals; see materials and methods). Low-opacity lines above plot indicate insignificant changes in populations of values across epochs (see materials and methods). C and D: same as in A and B, but for randomly connected network tuned to oscillate in response to strong external drive (see materials and methods). Scale bars same as in A. D: triple asterisks (***) above the line connecting 2 epochs indicate results of Wilcoxon signed-rank significance test (corrected for three comparisons) for difference in populations of values for those epochs (**0.00033 ≤ P < 0.0033 and ***P < 0.00033). E and F: same as in C and D, but for clustered network. Scale bars same as in A and C.

The results of this first model suggested to us that the empirical CC dynamic either was imposed by external inputs or reflected an internal mechanism. Given that we observed relationships between CC values and properties of cortical activity that were unrelated to the stimulus (Fig. 4), we investigated the latter possibility. From the perspective of network activity, the most obvious difference between the model and experimental evoked activity involved network oscillations, which were clearly present in visual responses (Figs. 1B and 2, A and B; also see Shew, et al. 2015) but were conspicuously absent in the simulated responses (Fig. 5A). Such oscillations are known to correspond to elevated synaptic input correlations (Atallah and Scanziani 2009; Salkoff et al. 2015), and, therefore, were likely relevant to our empirical results. As such, we selected a set of synaptic rise and decay times (Brunel and Wang 2003; Wang 2010) that were consistent with high-frequency (20–100 Hz) oscillations in the instantaneous network firing rate in response to strong external drive (Fig. 5C). This network reproduced the empirical CC dynamic (ongoing CC = 0.069 ± 0.032, transient CC = 0.16 ± 0.034, steady-state CC = −0.0009 ± 0.037; P = 3.57 × 10⁻⁸ for ongoing vs. transient comparison, P = 3.57 × 10⁻⁸ for transient vs. steady-state comparison, P = 8.18 × 10⁻⁸ for ongoing vs. steady-state comparison, Wilcoxon signed-rank test; Fig. 5D), suggesting that the visually evoked oscillations were indeed related to pairwise membrane potential-correlated variability. In addition, we found that sparse connectivity and broad synaptic weight distributions were crucial to reproducing the broad CC distributions across pairs for a given epoch (data not shown). Importantly, however, it was necessary to abolish the model network oscillations during the transient epoch (via synaptic depression) to significantly reduce CC values from transient to steady-state (data not shown). This was in contrast to the experimental result; visually evoked oscillations continued in the steady state (as indicated by the LFP; Figs. 1D and 2, A and B; also see Shew et al. 2015), whereas CC values decreased (Fig. 3, B and C). In other words, the experimental results suggested that transient and steady-state oscillations were different in some manner that was manifested in membrane potential correlated variability. The model network did not capture this interesting feature of evoked activity.

To address this final problem, we again considered the results of our previous investigation of large-scale evoked activity (as measured via extracellular multielectrode arrays) in this same preparation (see Shew et al. 2015). In this previous work, we found that the early “supercritical” visual response was dominated by large-amplitude, long-lasting events that spanned large regions of the cortex, whereas the later response obeyed event size and duration distributions consistent with a more balanced (“critical”) network. That is, correlated fluctuations were present in the late response, but were more spatially confined. We asked whether there was a relationship between this earlier result and the CC dynamics we observed here. To address this question, we introduced clustered (or “small-world”) connectivity to our model network (Fig. 5E; also see materials and methods) (Bujan et al. 2015; Litwin-Kumar and Doiron 2012; Watts and Strogatz 1998). This connectivity structure is motivated by cortical anatomy (Perin et al. 2011; Song et al. 2005), and it has been shown that groups of nearby neurons in clustered model networks can exhibit slow, coordinated spike-rate fluctuations (Litwin-Kumar and Doiron 2012). We repeated the simulations described above and calculated CC for pairs of nearby nodes (see materials and methods). We found that our clustered network reproduced the experimentally observed CC dynamics (ongoing CC = 0.070 ± 0.068, transient CC = 0.112 ± 0.098, steady-state CC = 0.021 ± 0.056; P = 7.8 × 10⁻⁴ for ongoing vs. transient comparison, P = 1.1 × 10⁻⁷ for transient vs. steady-state comparison, P = 2.3 × 10⁻⁵ for ongoing vs. steady-state comparison, Wilcoxon signed-rank test; Fig. 5F) and also gave qualitative agreement with the population dynamics (Fig. 5E). In other words, a model constrained to qualitatively reproduce the meso-scale spatiotemporal network response profile also recovered the empirical CC dynamic. Importantly, this model did not reproduce the decrease in CC from transient to steady state when synaptic adaptation was removed (ongoing CC = 0.152 ± 0.068, transient CC = 0.198 ± 0.113, steady-state CC = 0.0206 ± 0.092; P = 5.0 × 10⁻⁴ for ongoing vs. transient comparison, P = 0.41 for transient vs. steady-state comparison, P = 1.4 × 10⁻⁵ for ongoing vs. steady-state comparison, Wilcoxon signed-rank text).

Taken together, the results of our model investigation suggest a close relationship between the emergent network phenomena detailed in our previous study and the subthreshold CC dynamics observed here for pairs of nearby neurons. Moreover, these results identify synaptic time constants, synaptic depression, and synaptic clustering as key anatomic properties that determine CC values and dynamics for pairs of nearby neurons by modulating network-wide spatiotemporal response patterns.

DISCUSSION

To study how cortical coordination evolves during visual processing, we measured correlated variability between the membrane potentials of pyramidal neuron pairs in turtle visual cortex during ongoing and visually evoked activity. We supplemented our experimental approach with a model network investigation, which allowed us to infer the relative contribution of the cortical network to the dynamics of correlated variability and identify potentially relevant network variables.

Most such studies to date have focused on spike correlations. This is reasonable given that spikes are likely the fundamental unit of the neural code. This body of work has revealed many important insights into the variables that shape spike-count correlations and the mechanisms underlying changes in correlations across stimulus conditions. For instance, it is often observed that spike-count correlations decrease with sensory stimulation (Churchland et al. 2010; Snyder et al. 2014). Network models suggest that this may be due to strong feedforward inhibition that is correlated with excitatory inputs (Ly et al. 2012; Middleton et al. 2012). Yet other experimental and computation work suggests that this “linear, feedforward” framework provides an incomplete picture of cortical correlations across all conditions. First, spike-count correlations in a driven network can depend on the structure of intracortical connectivity (Litwin-Kumar and Doiron 2012), suggesting that recurrent inputs should be considered as well. Second, correlations in these recurrent inputs are not necessarily fixed but can change spontaneously and/or in response to sensory stimulation. For example, sensory input can trigger emergent phenomena (e.g., oscillations), during which synaptic input correlations are elevated (Atallah and Scanziani 2009; Salkoff et al. 2015). In such regimes, the linear approximation does not hold. Importantly, the confounds associated with using spikes to measure correlations (Cohen and Kohn 2011; de la Rocha et al. 2007; Schulz et al. 2015; Ventura and Gerkin 2012) make it difficult to infer such changes in input correlations. Thus, it is crucial to supplement the vast literature on spike-count correlations with an investigation of the dynamics of subthreshold-correlated variability during sensory processing (Doiron et al. 2016). Furthermore, these results should be interpreted using network models that incorporate the nonlinearities and strong feedback typical of the cortex (Stringer et al. 2016). We designed this study to address this need.

We found that both continuous and brief visual stimulation evoked large, low-frequency membrane potential fluctuations (Figs. 1E and 2, A and B) with nested high-frequency (20–100 Hz) oscillations (Figs. 2D and 3A), both of which varied considerably from trial to trial (Figs. 2, A and B, and 3A). In a given window of activity, this high-frequency variability was significantly correlated across the population of pairs (Fig. 3, B and C). Several observations suggested to us that the CC values were influenced by network connectivity and ongoing network state. First, CCs were broadly distributed in each epoch (Fig. 3, B and C), consistent with previous measurements of spike (Ecker et al. 2014; Kohn and Smith 2005; Ruff and Cohen 2014; Snyder et al. 2014) and subthreshold (Cohen-Kashi Malina et al. 2016; Haider et al. 2016; Lampl et al. 1999; Poulet and Petersen 2008; Yu and Ferster 2010; Tan et al. 2014) correlations. This was the case despite the fact that all pairs were separated by <300 μm and, therefore, likely received similar feedforward sensory inputs (Mulligan and Ulinski 1990). Such variability is thought to reflect sparse cortical connectivity (Renart et al. 2010), and accordingly, our model network required sparse connectivity to reproduce this across-pair variability (results of alternate models with dense interconnectivity not shown). Second, steady-state CC values for high-frequency fluctuations were significantly related to the prevalence of spontaneous low-frequency fluctuations (Fig. 4E). Recent work investigating a similar phenomenon in spiking activity implicates the cortical inhibitory population (Stringer et al. 2016). Together, these results contribute to the emerging view that cortical correlations are largely determined internally (Cohen-Kashi Malina et al. 2016; Okun et al. 2015; Schölvinck et al. 2015; Stringer et al. 2016).

Our principal result was that CC values transiently increased with visual stimulation before relaxing to prestimulus values. What was responsible for this dynamic? We first address two possible explanations that, although relatively simple (and therefore attractive), are not supported by these and/or previous results. First, it is possible that during the early response, CC values were determined largely by feedforward inputs, and steady-state values were influenced by strong cortical feedback. Because we did not directly measure thalamic inputs, we cannot rule out this possibility. However, if such a shift does take place, it is unlikely to evolve over the course of hundreds of milliseconds, given the extremely short latencies between thalamic inputs and cortical feedback (Li et al. 2013; Lien and Scanziani 2013; Cohen-Kashi Malina et al. 2016). Second, these changes in high-frequency membrane potential correlations may have simply reflected shifting activity levels, with static underlying correlations. For instance, previous work has shown that for a given level of synaptic input correlations, the resulting membrane potential correlations depend on the level of the membrane potential relative to synaptic reversal potentials. One study (Salkoff et al. 2015) suggests that the CC dynamic should follow the $\overline{V}$ dynamic we observed (Fig. 2C), whereas another predicts the opposite trend (Graupner and Reyes 2013). We, however, observed no relationship between the average membrane potential and CC. Furthermore, our model results demonstrated that qualitatively reproducing the dynamics of total activity level (Fig. 5A) was not sufficient to reproduce the CC dynamic (Fig. 5B). These considerations collectively motivated the search for an alternative explanation.

Our experimental results, interpreted in the context of previous work, hinted that an evolving network state was involved. Specifically, evoked activity was dominated by LFP fluctuations (Figs. 1E and 2, A and B), which were larger and more coordinated across the cortex in the early response than in the late response (Shew et al. 2015). Previous studies that relate network state to the coherence of oscillations (Yang et al. 2012) and spike correlations (Gautam et al. 2015) suggest that the CC dynamics we observed here were consistent with a cortical network adapting from a “disinhibited” to a “balanced” state. Our model results strengthened this “cortico-centric” hypothesis by showing that the dynamics of membrane potential-correlated variability followed those of the network spike-rate oscillations (Fig. 5, C–F). Thus, constraining the model network (driven by random external inputs that were uncorrelated across nodes) to qualitatively reproduce experimental observations related to network state (i.e., the spatiotemporal dynamics of network-wide activity) also recovered the dynamics of correlated variability. This is consistent with previous experimental work suggesting that coordination in cortical spiking activity (Okun et al. 2015; Schölvinck et al. 2015; Stringer et al. 2016), synaptic inputs (Atallah and Scanziani 2009; Haider et al. 2016), and membrane potentials (Yu and Ferster 2010) are related to network state.

What are the implications of this CC dynamic for cortical function? The elevated levels in the early response may promote robust drive of downstream cortical targets (Fig. 1C), and the large-scale correlated activity (see Shew et al. 2015) may be well-suited for stimulus detection (Ollerenshaw et al. 2014). In contrast, the smaller-amplitude and more spatially confined correlations in the steady state may strike a more even balance between the needs listed above and those that theoretically benefit from lower coordination levels, such as response fidelity (Zohary et al. 1994) and stimulus discrimination (Gutnisky and Dragoi 2008; Ollerenshaw et al. 2014). As such, these results suggest that during visual processing, adaptation mechanisms mediate a transition between cortical coding schemes and maintain correlated variability at an intermediate level (i.e., less than that during the initial response phase, but larger than zero) that represents the ideal balance between competing cortical needs (Fig. 1C).

It is important to note that we investigated only a simple synaptic adaptation mechanism in our model. There are a variety of other mechanisms that may have influenced CC values by modulating network oscillations, including inhibitory feedback (Bernacchia and Wang 2013; Tetzlaff et al. 2012), thalamic adaptation (Ollerenshaw et al. 2014; Wang et al. 2010), unequal adaptation of excitatory and inhibitory cortical synapses (Heiss et al. 2008), and the (time-varying) statistics of neuronal activity in the early visual pathway [e.g., correlations across thalamic inputs (Bujan et al. 2015; Whitmire et al. 2016)].

In our experimental approach, we made use of an ex vivo preparation that is particularly well suited to obtaining long-duration multi-whole cell recordings of cortical visual responses. This added convenience comes at a price; the three-layer reptilian visual cortex is not directly analogous to the six-layer mammalian visual cortex, and so a one-to-one relationship is not to be expected. Still, the turtle visual thalamocortical system possesses many properties that make it a useful tool for understanding thalamocortical function generally (Shepherd 2011) [e.g., a diversity of morphological and electrophysiological cortical cell types (Mancilla and Ulinski 2001; Crockett et al. 2015), feedforward inhibition (Mancilla and Ulinski 2001), large-scale broadband cortical oscillations (Shew et al. 2015), and an architecture similar to the mammalian olfactory system and hippocampus (Fournier et al. 2015)].

Despite these similarities, we do not suggest that visually evoked CC dynamics in mammalian V1 are necessarily uniformly the same as those described here. Indeed, recent work in (awake) mammals provides conflicting reports; whereas a study in primate V1 described a stimulus-induced decrease in low-frequency V-LFP correlated variability, with no change in higher-frequency activity (Tan et al. 2014), recordings in mouse V1 indicate a stimulus-induced increase in fast V-LFP “coupling” (Haider et al. 2016). Pairwise membrane potential recordings in cat V1 reveal a simultaneous decrease in low-frequency correlations and increase in high-frequency correlations with visual stimulation (Yu and Ferster 2010). This variability does not necessarily arise from differences in preparations or experimental approaches, as cortical population-spiking dynamics and correlations can vary across identical recording conditions (Okun et al. 2015) and even across recording sessions in a given animal (Schölvinck et al. 2015). This may instead reflect the relative influence of feedforward and recurrent inputs on cortex or the cortical “operating mode” (Sachidhanandam et al. 2013; Stringer et al. 2016; Supèr et al. 2001). Therefore, we suggest a more general principle; membrane potential CC dynamics during sensory stimulation will 1) be determined by the operating mode of the cortex, 2) follow those of the cortical spike-rate oscillations (which will in turn be shaped by those variables identified by our model) when the cortex is in “recurrent” mode, and 3) be maintained (by adaptation mechanisms) at an intermediate level during visual processing. As dual whole cell recordings in awake, behaving preparations (possibly combined with other recording modalities across multiple areas) become increasingly common, future experiments can be designed to assess the generality of these results and identify intracortical and extracortical modulators of correlated variability.

GRANTS

This research was supported by a Whitehall Foundation grant (no. 20121221; R. Wessel) and a National Science Foundation Collaborative Research in Computational Neuroscience grant (no. 1308159; R. Wessel).

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

N.C.W., M.S.H., and R.W. conceived and designed research; N.C.W. performed experiments; N.C.W. analyzed data; N.C.W., M.S.H., and R.W. interpreted results of experiments; N.C.W. prepared figures; N.C.W., M.S.H., and R.W. drafted manuscript; N.C.W., M.S.H., and R.W. edited and revised manuscript; N.C.W., M.S.H., and R.W. approved final version of manuscript.