Decoding thalamic afferent input using microcircuit spiking activity

Abstract

A behavioral response appropriate to a sensory stimulus depends on the collective activity of thousands of interconnected neurons. The majority of cortical connections arise from neighboring neurons, and thus understanding the cortical code requires characterizing information representation at the scale of the cortical microcircuit. Using two-photon calcium imaging, we densely sampled the thalamically evoked response of hundreds of neurons spanning multiple layers and columns in thalamocortical slices of mouse somatosensory cortex. We then used a biologically plausible decoder to characterize the representation of two distinct thalamic inputs, at the level of the microcircuit, to reveal those aspects of the activity pattern that are likely relevant to downstream neurons. Our data suggest a sparse code, distributed across lamina, in which a small population of cells carries stimulus-relevant information. Furthermore, we find that, within this subset of neurons, decoder performance improves when noise correlations are taken into account.

a key step in the process of extracting relevant information from sensory inputs and transforming it into a behavioral output is performed by the local cortical microcircuit. Much work has been done to characterize the direct representation of feed-forward inputs to primary sensory cortex. Comparatively little is known of how local recurrent circuitry transforms sensory information in the first of multiple stages of cortico-cortical processing that ultimately lead to behavioral output. Perhaps the most relevant aspect of this representation of information is the degree to which inputs can be read out by subsequent processing stages. Systematically quantifying the decodability of circuit activity distributed across columns and layers allows us to begin to identify what parts of a response can be used by downstream processors and ultimately drive behavior.

This paper describes decoding capabilities of local populations of neurons in the mouse primary somatosensory barrel cortex. Although barrel cortex is somatotopically organized, with each barrel column mapping to a principal whisker, sensory information from each whisker is represented in surrounding columns as well (Clancy et al. 2015; Drew and Feldman 2007; Elstrott et al. 2014; Jadhav et al. 2009; Jouhanneau et al. 2014; Kerr et al. 2007), indicating a distributed representation that would permit the rodent to integrate input from the full array of whiskers. Our study analyzes the decoding power of neuronal populations beyond the principal barrel columns. By focusing on activity outside of the principal columns, we deliberately emphasize that part of the code that is carried by recurrently generated activity in neocortex.

Specifically, we stimulate two distinct sets of thalamic relay cells in a thalamocortical slice and test how stimulus identity can be decoded from the response of indirectly stimulated circuits, those outside the directly activated columns. Previously, it was shown that such thalamically evoked activity occurs in specific ensembles of neurons that are also coactive in spontaneous events (MacLean et al. 2005). The relationship between stimulus-evoked and spontaneously occurring activity in cortex has also been established in vivo (Fiser et al. 2004; Kenet et al. 2003; Luczak et al. 2009; Luczak and MacLean 2012; Tsodyks et al. 1999). We aim to uncover how information about thalamic inputs can be determined from these cortical activity patterns. Our ex vivo experiment allows us to monitor the spiking activity of a large, densely sampled population of neurons, of which many are recurrently connected (Perin et al. 2011; Song et al. 2005), across columns and layers with high temporal resolution.

Serial recordings can be used to characterize information representation in neuronal populations, but this approach rests on the assumption that neuron-neuron correlations have a minimal role in sensory processing. In early sensory areas, such as retina, even weak neuron-neuron correlations shape the population response (Pillow et al. 2008; Schneidman et al. 2006; Shlens et al. 2006; Tkačik et al. 2010), although the degree to which this encoding structure affects decoding has only begun to be explored (Ganmor et al. 2011; Vidne et al. 2011). In contrast to the retina, where processing is largely feed-forward, cortical circuits have a high degree of recurrent connectivity (Song et al. 2005), the effect of which is difficult to predict. Recurrent connections may serve to decorrelate cortical activity (Renart et al. 2010), such that cortical neurons represent independent information. Alternatively, recurrence may actively suppress noise in cortical activity patterns, enhancing the decodability of encoded information (Pouget et al. 1998). A difficulty of directly assessing the representation of stimulus information from sparsely sampled cortical populations is that cortical connectivity is itself sparse, although synaptic connections are more probable between spatially proximate neurons (Fino and Yuste 2011; Ko et al. 2011; Lefort et al. 2009; Packer and Yuste 2011; Perin et al. 2011; Song et al. 2005; Thomson et al. 2002).

Decoding performance is quantified at the single-cell level across neuronal populations spanning multiple layers. We measure temporal aspects of the code and show that timing relative to the onset of population activity is sufficient to decode the stimulus identity. Finally, we quantified the representation built up by pairs and small groups of neurons, finding that noise correlations between neurons play a positive role in stimulus decoding. These data reveal insights into the cortical code defined at the level of the cortical microcircuit for somatosensation.

MATERIALS AND METHODS

Preparation of Slices for Two-Photon Imaging

Thalamocortical slices from somatosensory cortex (Agmon and Connors 1991) were obtained from C57BL/6 strain mice (N = 18) of either sex on postnatal days 15–17 using methods as previously described (Sadovsky et al. 2011; Sadovsky and Maclean 2013). Briefly, the brain was extracted, and, after 1 min in ice-cold solution [artificial cerebrospinal fluid (ACSF) with NaCl replaced by sucrose; contents as follows (in mM): 3 KCl, 26 NaHCO₃, 1 NaH₂PO₄, 0.5 CaCl₂, 3.5 MgSO₄, 25 dextrose, 123 sucrose], hemisected and blocked, then sliced with a Vibratome. Slices were placed in a 35°C incubation fluid (Incu-ACSF; contents contain the following, in mM: 123 NaCl, 3 KCl, 26 NaHCO₃, 1 NaH₂PO₄, 2 CaCl₂, 6 MgSO₄, 25 dextrose) for 30–45 min. Calcium dye loading was then achieved by placing all slices into a small Petri dish containing ∼2 ml of Incu-ACSF, an aliquot of 50 μg fura 2-AM (Invitrogen) in 13 μl DMSO and 2 μl of Pluronic F-127 (Invitrogen) and kept at 35°C for 25–27 min, with the shorter time used for the younger mice. Prior to experimentation, slices rested at room temperature in incubation fluid for a minimum of 40 min. ACSF solutions were continuously aerated with 95% O₂/5% CO₂ gas. All procedures were performed in accordance with and approved by the Institutional Animal Care and Use Committee at the University of Chicago.

Electrophysiology

Cortical activity for decoding analysis was evoked by thalamic stimulation. Two platinum iridium CE2C55 stimulating electrodes (Frederick Haer, Bowdoinham, ME) were placed in the ventral posteromedial nucleus (VPm). Stimulating electrodes were placed with at least one complete barreloid, identified under bright-field illumination, between them. Across slices, this separation was at least 90 μm [mean 132 ± 33 μm (SE)], along the dorsal-ventral axis. Afferents from the central, unstimulated barreloid were visually tracked to cortex to obtain the optimal imaging field of view. Correct placement of the stimulating electrodes was confirmed by a response in patch-clamped cell, or, in the experiments in which electrophysiology was unavailable, by a population response from imaging data. Stimulation consisted of six 200-μs current pulses at 40 Hz with a minimal amplitude of 10–30 μA and was applied in one of the two locations every 20 s. Stimulation amplitude was set to the minimum level that evoked a cortical response, determined by monitoring a patched cell in cortex. If no cell was patched, a brief movie consisting of 2–5 trials at each location was taken, and the fluorescence traces visually checked for a population response to both stimuli.

Experimentation was performed in standard ACSF [containing the following, in mM: 123 NaCl, 3.5 KCl, 26 NaHCO₃, 1 NaH₂PO₄, 1.2 CaCl₂, 1 MgSO₄, and 25 dextrose (Shu et al. 2003), which was continuously aerated with 95% O₂/5% CO₂] flowing at 3 ml/min. Whole-cell current-clamp recordings were made using Multiclamp 700B amplifiers (Molecular Devices). Cells selected for patch-clamp recording were mostly in layer 4, with a few in lower layer 3 (3 cells) or upper layer 5 (2 cells). Only cells that were consistently responsive to both stimulation locations in an initial test period were monitored for the entirety of the experiment and included in the analysis.

Two-Photon Imaging

Rapid whole-field imaging of fura 2-AM loaded neurons was achieved using the Heuristically Optimal Path Scanning technique and microscopy setup, as previously detailed (Sadovsky et al. 2011), allowing us to monitor action potential generation within individual neurons over each 6-min movie. Dwell time was fixed at a value between 20 and 50 samples per cell per frame for each experiment.

Because of the importance of having highly stable neuronal recordings for each movie, regions of interest, corresponding to single cells, were extracted from the path scan by overlaying the average response along the path with the expected location of each putative cell. Within the expectation window, a cell mask was generated based on the smoothed (Gaussian filter, width of 5 samples, or 10% of on-cell samples) fluorescence profile. A cell mask was generated independently for each movie. To ensure recording stability, cell masks had to remain stationary across all movies, defined as better than 80% correlation between the smoothed cell masks of consecutive movies. Fluorescence traces for each cell were generated from the dot product between the cell mask and the path scan. In 3 of the 18 mice, multiple fields of view were used in recordings. Across a total of 22 fields of view, 3453 cells were identified. Spiking activity was inferred from fluorescence traces using a customized deconvolution method (Sadovsky and Maclean 2013; Vogelstein et al. 2009). This gives a measure of the likelihood of a spiking event in each frame, ranging from 0 to 1. Based on hand-scoring a subset of data and observing that even small values (0.03) were indicative of probable spiking events, while large values (>0.2) corresponded to multispike events, we use this activity probability measure directly, rather than setting a threshold, as the input to all decoding analyses.

Decoding Analysis

The decoder task is to identify which of the two thalamic locations was stimulated. We apply a linear decoder, implemented by a support vector machine (Boser et al. 1992; Cortes and Vapnik 1995) with a linear kernel (Matlab, The MathWorks, Natick, MA). Perfect separating hyperplanes did not exist for most datasets, so soft margins were used, parameterized by regularization parameter C. To set C, we tested logarithmically spaced values from 0.1 to 10 on a subset of data; values from 0.3 to 3 produced comparable classification success rates. C was fixed at 1 for all subsequent analyses.

A minimum of 20 total trials was required for inclusion in the decoding analysis. A trial consisted of a stimulus delivered at a single location. The number of trials was limited by dye responsiveness. Four experiments had 24 trials; 13 had between 30 and 50 trials; and 5 had 60 or more trials. Cross-validation is performed by dividing the trials into test (20% of trials) and training sets successively until all trials have been included in exactly one test set. Test sets are constrained to have equal number of trials for each stimulus. Decoding performance is the fraction of correctly identified test-set trials. We assess the quality of the decoder fit by comparing test set and training set performance. If the test set performance is higher than the training set performance by more than one trial, we conclude that there was too little data to fit the decoder and exclude the cell or cell set from decoding analysis. This occurs in <1% of all groups.

We decode activity pooled over a window of a fixed bin size starting a fixed time after the stimulus was delivered. For multicell decoders, the bin size and start time are the same for all cells. Because the number of cells prohibits exhaustive sampling of groups larger than 2, we randomly selected 2,000 sets from each experiment for all sets of 3 or larger. The bin size and start time are varied over a range from one frame (30–100 ms) to 500 ms. For each decoder, the optimal window (bin size and start time) for decoding is identified from performance on the training set. The reported decoding performance of the cell is the test-set decoding performance over that window.

To determine whether a cell decodes above chance levels, we run the decoder on data with stimulus labels shuffled (250 shuffles) and compare the measured decoding performance to the distribution of stimulus-shuffled decoding performances. Cells that decode above chance levels are defined as those that score at or above the 95th percentile of the shuffled distribution. With a small number of trials, it is possible that cells carrying a small amount of stimulus information would not be detected as decoding above chance levels. There was otherwise no relationship between the number of trials and decoder performance.

Shuffling Procedure for Noise Correlation Analysis

For the noise correlation analysis, we first identify the bin size and start time leading to the highest decoding performance for a given pair. For that combination of bin size and start time, we compose shuffled population responses for each stimulus by randomly drawing cell responses from different trials, thereby breaking trial-by-trial correlations between cells while keeping stimulus-driven correlation intact. The shuffled decoding performance is the mean decoding performance across 250 shuffles.

Statistical Tests

Shuffle test for pair separation significance.

Physical separation between neuron pairs is not an independent quantity across the population, so significance for the observed differences in pair separation between the jointly decoding pairs and the general class of above-chance decoder pairs was determined by performing a shuffle test. We computed all pairwise separations between above-chance decoder pairs. From this set, we drew random subsets matched to the number of jointly decoding pairs. We then compare the distribution of mean separations, calculated over 1,000 random subsets, to the mean separation between jointly decoding pairs. The absolute difference is 5 μm (stimulus-locked) and 15 μm (population-locked), which is small relative to the mean separations (160 μm) but significant (stimulus-locked, P = 0.010; population-locked, P < 0.001).

Computing the Kullback-Leibler divergence.

To determine whether the best decoders were spatially distributed nonuniformly, we compared the distribution of distance from pia for the best decoders to the distribution of distance from pia of all recorded cells. We quantify this by computing the Kullback-Leibler (KL) divergence (D_KL):

$$D_{\text{KL}}\left(p;q\right)=\int \mathit{p}\left(\mathit{x}\right)\log \frac{p\left(x\right)}{q\left(x\right)}\text{d}x$$

where p(x) is the probability of a “best decoder” being located at position x and q(x) is the probability of a recorded cell being located at position x. We compute this using a nearest-neighbor estimate (Wang et al. 2006), which is an unbiased estimator of the divergence. To determine whether the measured D_KL was significant, we generated p^shuf(x) by drawing from all recorded cells [i.e., q(x)] using matched sample sizes. While D_KL ≥ 0, the shuffle distribution of D_KL values is expected to bracket zero, and so will contain negative values. We, therefore, use a two-sided test for significance. If the measured D_KL fell within the 95% confidence interval (2.5 to 97.5 percentile) of 0, it was deemed not significantly different from zero. Quoted P values are calculated from the percentile in the shuffle distribution; for example, the 90th percentile corresponds to a P value of 0.2.

Temporal Alignment for Cortex-Centric Decoding

An alternative to aligning activity relative to stimulus onset is to align based on the onset of population activity, determined across the full set of cells for each individual trial. For each trial, we took the activity across all neurons and set t = 0 to the frame at which at least three neurons were coactive, which is two standard deviations above the background activity rate of 0.36 ± 1.24 active cells per frame, measured over the 2-s period prestimulus. For population-locked alignment, a different start time relative to absolute start time is used in every trial. As with stimulus-locked activity, we performed the decoding analyses as described.

Simple Model of Gaussian Coding Units

To set expectations for a decoder with a linear kernel, we demonstrate the performance of this decoder in a simple model that is commonly used to illustrate principles of population coding (see, for example, Averbeck et al. 2006). Consider an independent collection of N Gaussian coding units, which each respond to two stimuli with mean μ = ±1 and variance σ². The population response distribution is

$$P\left(r\mid \mu =\pm 1\right)={\left(2\mathrm{\pi }{\sigma }^N\right)}^{-1/2}\exp \left[-\frac{1}{2}\left(r-\mu \right)C^{-1}{\left(r-\mu \right)}^T\right]$$

where diagonal elements of the covariance matrix are the variance (σ²) and off-diagonal elements are zero.

In this simple case, the optimal linear decoder is a plane P that is perpendicular to the vector 1. The success rate S of this decoder is

$$S={\displaystyle {\int }_P^{\infty }}{\text{d}}^{N}rP\left(r\mid \mu =\mathbf{1}\right)+{\displaystyle {\int }_{-\infty }^P}{\text{d}}^{N}rP\left(r\mid \mu =-\mathbf{1}\right)$$

The multidimensional integral is evaluated by rotating into the orthogonal coordinate system with z-axis along 1, so the plane P is simply z = 0, The distance from P to the mean response grows with N^1/2, while variance does not grow with N. The integrals in all dimensions except along z evaluate to 1. The remaining integral along the z-axis is

$$S={\displaystyle {\int }_0^{\infty }}{\left(2\pi {\sigma }^2\right)}^{-1/2}\exp \left[-\frac{{\left(r-\sqrt{N}\right)}^2}{2{\sigma }^2}\right]\text{d}r$$

$$=\frac{1}{\sqrt{2\pi {\sigma }^2}}{\displaystyle {\int }_{-\sqrt{N}}^{\infty }}\exp \left(-\frac{r^2}{2{\sigma }^2}\right)\text{d}r$$

$$=0.5\left[1+\text{erf}\left(\sqrt{N/2{\sigma }^2}\right)\right]$$

This function is curve-down and saturates at 1: with each additional decoder, the improvement to the group decoding performance decreases.

We can extend this to the case of covariance matrices with identical off-diagonal elements r (equivalent to the correlation coefficient between a pair of decoders). For example, if N = 3, this is:

$$C={\sigma }^2\left(\begin{array}{ccc}1& r& r\\ r& 1& r\\ r& r& 1\end{array}\right)$$

This either flattens or elongates the spherical response distribution into an ellipsoidal distribution with one principal axis along the vector 1. The normalized eigenvectors of C are

$$v_1=N^{-1/2}\mathbf{1}$$

with eigenvalue λ₁ and the vectors spanning the subspace (of dimension N − 1) orthogonal to v₁, with identical eigenvalues λ₀. The relationship between λ_0,1 and r is

$${\lambda }_1=1+\left(N-1\right)r$$

$${\lambda }_0=1-r$$

Because λ₁ ≥ 0, there is a lower limit on how negative correlation can be: r ≥ −(N − 1)⁻¹. Intuitively, this comes from the fact that it is impossible to have an arbitrary number of perfectly anti-correlated variables.

The effect of correlation is to constrict or expand the responses along the direction of discrimination (v₁), depending on whether λ₁ > 1 (r > 0) or λ₁ < 1 (r < 0). The decoding success rate is

$$S=\frac{1}{2}\left[1+\text{erf}\left(\sqrt{\frac{N}{2{\lambda }_1{\sigma }^2}}\right)\right]$$

$$=\frac{1}{2}\left[1+\text{erf}\left(\sqrt{\frac{N}{2\left(1+\left(N-1\right)r\right){\sigma }^2}}\right)\right]$$

This is in line with expectations: positive signal correlation (by assumption, since μ = +1) and negative noise correlation (r < 0, or λ₁ < 1) increase the decoding success by shrinking the variance along the discrimination dimension.

If the decoders are synergistic, S(N) would grow super-linearly in N. Finding a combination of r, σ, and N that generates a synergistic curve S(N) amounts to finding a value of r, σ, and N for which:

$$S\left(N+2\right)-S\left(N-1\right)>S\left(N-1\right)-S\left(N\right)$$

Although N is discrete, S(N) is well-defined for continuous N, so we solve

$$\frac{{\partial }^{2}S}{\partial N^2}>0$$

and look for solutions with integer values of N. The condition is

$$f″\left(N\right)-{\left[f\prime \left(N\right)\right]}^2-\frac{{\left[f\prime \left(N\right)\right]}^2}{2f\left(N\right)}>0$$

where

$$f\left(N\right)=\frac{N}{2{\sigma }^2\left[1+\left(N-1\right)r\right]}$$

This amounts to solving a quadratic equation in N that is parameterized by r and σ. Solving numerically, we find that the synergistic regime corresponds to unrealistically large negative correlations (generally less than −0.2) and low single-cell decoding performances (<0.67).

RESULTS

To characterize the representation of thalamic afferent input at the level of the cortical microcircuit, we uniformly and densely sampled thalamically evoked neuronal activity in slices of mouse somatosensory barrel neocortex using high speed multiphoton calcium imaging (Sadovsky et al. 2011; Vogelstein et al. 2009). We imaged an average of 157 ± 60 (SE) (range = 40–267) neurons within a single field of view at 9–50 Hz and simultaneously patch-clamped individual neurons (n = 21, including 7 pairs), which provided 10-kHz sampling of recorded neurons (Fig. 1, A and B). Cortical circuit activity was evoked using minimal electrical stimulation (Beierlein and Connors 2002), consisting of 6 current pulses (200 μs) at 40 Hz, applied to one of two distinct locations in the VPm nucleus of thalamus (MacLean et al. 2005). Following the brief period of stimulation, a cortical response was triggered, characterized by an UP state in a single cell and a circuit event across the population. Stimulation locations were separated by at least 90 μm [mean, 132 ± 33 μm (SE)], approximately equivalent to one complete barreloid in the VPm (Van Der Loos 1976), and the imaged field of view corresponded to an indirectly stimulated barrel. In vivo, activity triggered by the principal whisker is only briefly (<20 ms) confined to the principal barrel before it spreads to adjacent barrels, and, even within the principal barrel, a subset of cells respond more strongly to neighboring whiskers (Clancy et al. 2015; Ferezou et al. 2007). By centering the imaging in the indirectly activated column, we specifically analyze the part of the code that arises from corticocortical synaptic interactions.

Fig. 1.

Experiment and overview of decoding analysis. A: thalamocortical slices including S1BF. Stimulating electrodes are placed in separate locations in thalamus [orange, stimulus a (stim a), and blue, stimulus b (stim b)], and cortical cells in barrel field (circle) are recorded using two-photon calcium imaging. For some experiments (N = 7), electrophysiology is also obtained from two cortical cells, indicated by patch pipettes over cortex. B: imaged field of view. Cells are loaded with fluorescent dye fura 2-AM. C: sample whole-cell patch-clamp recordings, population activity, and average population activity for responses to the two stimuli. Arrows mark time of stimulus delivery. Cells are sorted by onset time for stim a. Activation order is different for stim b. D: overview of decoder task. Stimulus location (a or b) is decoded from the activity of cells or groups of cells. We demonstrate the decoder performance in a simple model in which the stimulus-dependent response (orange, stim a, and blue, stim b) is Gaussian-distributed. E: decoding performance of a group of neurons depends on the number of cells in the group and on the correlations between cells. Pairwise correlation is illustrated by response density plots, with the 95% confidence region outlined. Negative correlation (black line) between cells improves the group performance relative to the independent (gray line) case, while positive correlation degrades group performance (light gray line).

We evaluated the representation of thalamic inputs by measuring the ability of cells and groups of cells to decode stimulus location (Fig. 1D) using a linear decoder, i.e., a binary classifier with a linear kernel. To establish performance expectations, we demonstrate how this decoder performs for a population of neurons whose responses are characterized only by mean and covariance. Such a simple model is a commonly used first approximation for characterizing the role of correlation in a population code (Averbeck et al. 2006). We first consider the decoding performance of a collection of independent, identical cells (Fig. 1D), with stimulus-dependent responses characterized by a Gaussian distribution. In this model, decoding performance increases sublinearly with each additional cell, and the rate of improvement is determined by the single-cell signal-to-noise ratio. Adding correlations between cells changes the multineuronal decoding performance (Fig. 1E). In this case, negative correlation between cells improves the decoding performance of a group over the independent condition, while positive correlation decreases performance (Fig. 1E). From the model, it is expected that we will find the largest gain in decoding performance derives from the first cell, with diminishing gains for each subsequent cell if each neuron is independent. Furthermore, the model indicates that we can expect either an increase or decrease in decoding performance when we shuffle the data, depending on whether noise correlations degrade or improve decoding accuracy.

Single-Cell Decoding from Patch-Clamped Cells

Thalamically evoked activity was characterized at the single-cell level by prolonged depolarizations, or UP states, in patch-clamped neurons and at the circuit level by a multineuronal response in the imaged field (Fig. 1B). If patch-clamped neurons did not reliably respond to the thalamic stimuli on every trial over an initial test period, then that neuron was not monitored, and another attempt was made to find a responsive cell. Overall, 21 patch-clamped neurons, including 7 pairs, reliably responded to thalamic input and were used for decoding analysis.

To fit a decoder to spike train data, we counted spikes in a fixed window of varying lengths (10 ms to 500 ms) and start times (0 to 500 ms) over the poststimulus period (Fig. 2A). Chance-level performance was computed from the distribution of decoding performance from stimulus-shuffled data; cells that scored at or above the 95th percentile of the shuffle distribution were considered above chance. Given the simplicity of the experimental design and the fact that we biased our sample to reliably responsive neurons, we expected that single neurons could easily decode the two-stimulus task. However, only a small minority of cells (N = 3 of 21) decoded with near-perfect (>0.9) performance (Fig. 2B). Although most patch-clamped neurons decoded at levels exceeding chance (N = 18/21), the mean decoding performance was only 0.78 ± 0.11 (SE) (Fig. 2B).

Fig. 2.

Decoding stimulus location with single neurons. A: spikes recorded from a patch-clamped cell in response to stim a (top) and stim b (bottom). Arrows indicate time at which the stimulus was delivered. B: histogram of decoding performances from patch-clamped cells performing above chance (black) and at chance (gray). Chance-level performance is determined by comparison with the stimulus-shuffled performance distribution. For details, see main text. C: for the cell shown in A, decoding performance of linear decoder fit to activity averaged over a bin size of 0.1 s (solid black) or 0.01 s (dashed black). Decoding performance was higher using the 0.1-s bin size. D: fluorescence trace from a single neuron with three detected events (orange bars). E: histogram of activity for a single cell. Activity values are obtained by averaging the deconvolved fluorescence trace over a window 450 ms wide, starting a time 390 ms after the stimulus onset. This cell had a higher response to stim a (orange) than to stim b (blue). a.u., Arbitrary units. F: for the cell shown in D and E, performance for multiple decoders over a range of poststimulus times and bin sizes. G: distribution of highest decoding performance found across all averaging windows for each imaged cell. Black bars indicate cells with decoding performances significantly above chance levels. H: distribution of optimal start times among all cells with decoding performance above chance and less than 0.8 (gray). Bars (green) superimposed show a histogram for the best decoders, with performances greater than 0.8. High decoding performances are associated with earlier start times. I: distribution of optimal bin sizes among all cells with decoding performance above chance and less than 0.8 (gray). Bars (green) superimposed show a histogram for the best decoders, with performances greater than 0.8.

Even for the best performing cells, there was a limit to the gains afforded by the high temporal resolution (10 kHz) provided by patch-clamp recording. For instance, averaging over a window of 100 ms could be more informative than a shorter time window of 10 ms (Fig. 2C). The most informative temporal window within any one neuron was highly variable within the tested range (mean start time = 190 ms, SE = 170 ms; mean bin size = 340 ms, SE = 170 ms). Importantly, this timescale is accessible to two-photon imaging of neuronal populations. That we rarely achieved perfect decoding using spike trains recorded from reliably responsive patch-clamped neurons indicated the importance of the population for the representation of the thalamic input. To characterize how information is represented across the population, we evaluated the decoding performance in the imaged population.

Decoding with Single Cells from Imaging

Of 3,453 imaged neurons, 3,326 (96%) had a detectable change in fluorescence within 1 s of the stimulus onset in at least one trial. We limited our decoding analysis to these neurons. Following thalamic stimulation, we found that the activity within this subset of neurons exhibited a range of reliability, with some neurons being consistently active [559 neurons (16%) active in >50% of trials] and others responding in only a few trials [818 neurons (24%) in < 10% of trials]. Across all imaging experiments (N = 22), the shortest latency to detectable activity in any one neuron was 49 ms ± 20 ms, and the subsequent propagation of activity through the local cortical circuits within each imaged field of view lasted 1–3 s [mean 2.1 ± 0.9 (SE)], as previously reported (MacLean et al. 2005; Watson et al. 2008). The mean latency preceding population activity across trials in which there was a detectable response was 600 ± 190 ms (mean ± SE, N = 22 experiments). This is longer than the decoding timescale from the patch-clamp recordings, but still consistent with intercolumnar activity propagation speeds (Wester and Contreras 2012). Thus we were able to reliably evoke activity, primarily through indirect cortico-cortical connectivity with thalamic stimulation applied to one of two locations, and image cortical circuit activity.

As with the patch-clamp data, we used a linear decoder over a variable peristimulus time window trained on the deconvolved fluorescence signal (Fig. 2, D and E). For imaging datasets, overlapping decoding time windows had lengths from 20–50 ms to 500 ms, and starting times ranging from 0 ms to 500 ms (Fig. 2F). We used the same criteria for decoding significance for the imaging data that we used for the electrophysiological data. Most neurons (N = 2,341/3,326, 70%) failed to decode above chance levels, performing below the 95th percentile in the stimulus-shuffled distribution. The remaining 985 cells, found across all 22 datasets, decoded the stimulus at higher than chance levels (Fig. 2G). Compared with the set of patch-clamp recorded cells, above-chance decoders were less common in the imaging dataset. However, patch-clamped cells were selected on the basis of stimulus responsiveness. Among the population of highly responsive cells (those active in >80% of trials, 119 cells total), most cells decoded above chance levels (N = 69 of 119, 58%), and the average decoding performance was 0.74 ± 0.09 (SE), which is comparable to the patch-clamped cell performance of 0.78 ± 0.11.

Among the imaged cells that decoded above chance, the optimal start time of the decoding window was distributed across the entire 500-ms range [mean, 280 ± 180 ms (SE), N = 985], while the distribution of optimal window lengths tended toward the longest tested windows (mean, 460 ± 130 ms, Fig. 2, H and I). The rate of frame acquisition, which ranged from 9 to 50 Hz, will affect the start time and window length analysis somewhat. However, even among experiments with the fastest frame rates (>20 Hz), start times were 240 ± 170 ms (N = 491), which corresponds to approximately five imaging frames. Increasing the frame rate further is therefore unlikely to reveal significantly earlier start times. The best decoders, those with decoding performance over 80%, had significantly earlier start times than other decoders (best decoders, mean, 190 ± 150 ms, N = 64; Wilcoxon rank sum, P = 1.5e-5). Bin sizes for cells achieving the highest decoding performances were not significantly different from those of the rest of the decoders (mean 430 ± 140 ms, N = 64; Fig. 2F). Thus the most informative cells decoded stimulus location sooner than other decoders, by starting at an earlier poststimulus time.

Setting t = 0

From trial to trial, there was a variable lag before the population became active. This latency was itself informative of the stimulus. However, for a single cell to read out this information, an additional “timekeeping” signal would be required. Whether such a signal is present can be debated, but it is clear that a single neuron receives a signal, in the form of synaptic input, indicative of activity in the surrounding population. We characterized whether neurons can decode stimulus location without explicit information about latency using instead timing relative to the population response.

For each trial, we considered activity across all neurons and set t = 0 to the frame at which at least three neurons were coactive (Fig. 3A), which was two standard deviations above the background activity rate. We found that nearly as many cells decode above chance levels as in the stimulus-aligned data (N = 942 of 3,326; Fig. 3C). However, decoding performance was lower than with stimulus-locked alignment. We found a decrease of 4 to 8 percentage points in decoding performance among neurons that exhibited a minimum of 70% (stimulus-locked) decoding performance (Fig. 3D). Additionally, among population-locked decoders, there were fewer very accurate cells (N = 45 with ≥80% decoding performance) than there were among stimulus-locked decoders (N = 63 with ≥80% performance).

Fig. 3.

Decoding with single cells using population activity for temporal alignment. A: multitrial population activity raster. Solid horizontal lines separate single-trial responses of a subset of 40 cells from the population. Stimulus was delivered at t = 0; color indicates stimulus identity. Trials are sorted by stimulus identity, but were interleaved in the experiment. For population-locked decoding, activity is aligned based on the onset of population activity (vertical black lines) on a trial-by-trial basis. This is generally different from the stimulus delivery time. B: distribution of stimulus-specific latency to population activity across all trials. C: decoding performance of single cells using population-locked timing, with above-chance cells in black and at-chance cells in gray. D: difference in decoding performance between stimulus- and population-locked responses. Decoding performance typically decrease by 0.04 to 0.08 with population alignment. E: optimal start time distributions for above-chance cells (gray). Bars (green) superimposed show a histogram for the best decoders, with performances greater than 0.8. F: optimal bin size distributions for above-chance cells. Optimal start times and bin sizes are earlier and shorter with population-locked timing than stimulus-locked timing (cf., Fig. 2, H and I).

Because the delay between stimulus and activity onset was eliminated by activity alignment, the best start times for above-chance decoders were earlier than for stimulus-locked alignment [population-locked mean, 250 ± 7 ms (SEM) vs. 280 ± 4 ms (SEM) for stimulus-locked; Wilcoxon rank sum, P = 3.9e-5; Figs. 3E and 2H]. The optimal bin size was also smaller for decoders using population-locked alignment than stimulus-locked alignment [420 ± 5 ms vs. 460 ± 4 ms (SEM), Wilcoxon rank sum, P = 4.3e-5; Figs. 3F and 2I]. For the best decoders, window lengths were not significantly different from those of the other above-chance decoders [430 ± 20 ms (best decoders) vs. 420 ± 6 ms (rest), P = 0.82], but start times were earlier [160 ± 20 ms vs 237 ± 7 ms (SEM), P = 5.6e-5]. Thus temporal alignment to the population resulted in a small decrement in the quality, but not the number, of above-chance decoders and a shorter latency and time window for optimal decoding. In sum, these data suggest that the local population was capable of providing the information necessary to decode stimulus location and also tightened the temporal resolution necessary for optimal decoding.

Anatomical Distribution of Decoding Performance

Imaged neurons were located between 125 μm and 825 μm from the pial surface, spanning from pia to lower layer 5. To determine whether there was a relationship between decoding performance and cortical depth, we calculated the fraction of cells that decoded above chance as a function of distance from pia by counting above-chance decoders and total sampled cells in a sliding window of width 50 μm. Cells decoding above chance comprised between 20 and 25% of sampled cells, regardless of layer (laminar assignment based on distance from pia: L2/3: 128–418 μm; L4: 418–588 μm; L5, >588 μm; Lefort et al. 2009; stimulus-locked decoding, Fig. 4, A and B; mean ± SE across animals: layer 2/3, 21 ± 4%; layer 4, 27% ± 5%; layer 5, 22 ± 4%; for population-locked decoders, Fig. 5, A and B; mean ± SE: layer 2/3, 22 ± 4%; layer 4, 27% ± 5%; layer 5, 19 ± 4%). This range of decoding performances was within the variance across animals (±5%). To determine whether high-performance decoders (Figs. 4B and 5B) were distributed differently from the sampled population, we computed the D_KL between the spatial distribution of high-performance decoders and the spatial distribution of all imaged cells. We found no significant difference between the distributions (stimulus-locked, D_KL = 0.54, P = 0.11; population-locked, D_KL = 0.33, P = 0.37, two-sided shuffle test; see materials and methods). Thus we find that decoding performance at the single-cell level was not significantly associated with the cell's distance from pia.

Fig. 4.

Distribution of stimulus-locked decoders across lamina. A: fraction of recorded neurons that decoded above chance (stimulus-locked) as a function of distance from pia. Shaded region marks ±1 SE computed across experiments. B: locations and decoding performance of the best decoders (>80% success). Distribution is not significantly different from the overall distribution of sampled cells. Bars at right show approximate laminar boundaries. C: decoding performance for groups drawn from the core population of above-chance cells. Performance increases with the number of cells. D: fraction of each group of cells that decodes with 90% or higher decoding performance. E: group decoding performance relative to the best individual cell performance within the group. F–H: for stimulus-locked decoding, versions of C–E, respectively, with groups composed of cells located within a single layer. See Fig. 5 for population-locked decoders. No significant differences were found between any layers on any of these measures.

Fig. 5.

Distribution of population-locked decoders across lamina. A: fraction of neurons that decoded above chance (population-locked) as a function of distance from pia. Shaded region marks ±1 SE computed across experiments. B: locations and decoding performance of the best decoders (>80% success). Distribution is not significantly different from the overall distribution of sampled cells. Bar at right shows approximate laminar boundaries. C–E: decoding with groups composed of cells located within a single layer. C: decoding performance for groups drawn from the core population of above-chance cells. D: fraction of each set that decodes with 90% or higher decoding performance. E: group decoding performance relative to the best individual cell performance within the group. No significant differences were found between any layers on any of these measures.

Decoding with Larger Groups

Moving beyond single cells, we characterized decoding performance as cells are added to the decoding pool. Decoding groups were constructed by drawing neurons from the small set of cells with greater than chance decoding rates, the core decoder population. Depending on the information contributed by each cell, decoding performance may saturate at the level of the most accurate single cell or increase rapidly to the performance ceiling (Fig. 1E). For both stimulus-locked and population-locked alignment, the average decoding performance of a group of core neurons increased with the size of the group, from 65% (±1% SEM over N = 22 fields of view) for single neurons to 78% (±2% SEM, N = 21) for groups of eight using stimulus-locked alignment and from 63% (±1% SEM, N = 22) to 72% (±2% SEM, N = 22) using population-locked alignment (Fig. 4C).

Curves from particular groups have a diversity of shapes, however. A substantial fraction of groups of four or more neurons achieved near-perfect decoding performances (>90% correct): 7% (±3% SEM, N = 22 fields of view) of groups of four above-chance decoders, and 14% (±5% SEM, N = 21 fields of view) of groups of eight (Fig. 4D). With population-locked alignment, fewer individual cells achieved near-perfect decoding compared with stimulus-locked alignment, and only 2% (±1% SEM, N = 21 fields of view) of four-cell groups of above-chance decoders achieved near-perfect decoding performance (Fig. 4D). To determine whether this difference between stimulus-locked and population-locked alignment derived from differences in the single-cell performance or differences in how information was combined across neurons, we computed the relative decoding performance of the group, the ratio of group decoding performance to the performance of the best cell in the group (Fig. 4E). Relative decoding performance for both temporal alignments is significantly larger than one, indicating that in both scenarios groups do improve over the best-cell performance by integrating information from the other members of the decoding pool. The relative performance of small groups was slightly higher with stimulus-locked decoding than with population-locked decoding [groups of 4: 5.4% ± 0.6% (SEM) for stimulus-locked groups, vs. 2.7% ± 0.8% (SEM) for population-locked, N = 22 slices; rank sum tests: 2 neurons, P = 0.042; 3 neurons, P = 0.053; 4 neurons, P = 0.023; 5 neurons, P = 0.020; 6 or more neurons, P > 0.05]. However, we did not find a consistent significant difference. Thus the lower incidence of near-perfect decoder groups for population-locked alignment appears to be a consequence of drawing from a less informative pool of single cells than the stimulus-locked decoding groups did, not from a difference in how decodable information is built up within the group.

We also analyzed whether decoding performance depended on the location of the group members. Using published laminar boundaries for somatosensory cortex (Lefort et al. 2009), we classified cells by lamina and measured the decoding performance of groups confined to a single layer. We find no significant difference between any pair of layers for any size of group (all P > 0.05, rank sum with Bonferroni correction; Fig. 4, F–H, and Fig. 5, C–E).

Role of Noise Correlation in Decoding

As suggested by the model (Fig. 1E), group decoding performance typically increased with added cells, and the overall performance level was strongly dependent on the decodable information carried by the most accurate single cell. Using the imaging data, we examined the role correlation plays in representation of stimulus information by dissecting the performance of pairs of cells. We illustrate the strong potential effect of noise correlation with an example from our data in Fig. 6A. These two cells displayed strong positive noise correlation that allowed for decoding of the stimulus identity. We found no significant difference in the pair-decoding performance of the stimulus-locked vs. population-locked responses (Fig. 6B).

Fig. 6.

Role of noise correlation in decoding performance. A: plot of pairwise activity, with cell 1 and cell 2 responses on x- and y-axes, respectively, and histograms (as in Fig. 2E) of single-neuron activity off axis. For this cell pair, the activity pattern across the two cells could be decoded with 90% success. Individual cells were only 60–65% successful. B: decoding performance of pairs drawn from the core above-chance population using stimulus-locked (top) and population-locked (bottom) timing. C: histogram of performance gain from the first and second cell using stimulus-locked (top) and population-locked (bottom) timing. First-cell gain is the difference between single-cell performance and chance (0.5), and second-cell gain is the difference between pair performance and single cell performance (see text). As expected from the model (Fig. 1E), the first-cell gain is generally higher than the second-cell gain. D: histogram of effect of noise correlation on decoding performance, measured as the difference between true decoding performance and trial-shuffled decoding performance. Positive values indicate an improvement in decoding when correlations are taken into account. Pairs with significant second-cell gains in decoding performance showed on average a positive effect of correlation. Filled gray outline shows zero-mean normal distribution with matched variance, a null model for no overall effect of noise correlation. E: box plot of correlation effect for stimulus-locked decoders (as in D) and population-locked decoders. Both show a significant positive effect of correlation.

Because we were able to image neurons immediately adjacent to one another, we did not expect that every neuron would carry independent information, and so not every set of two cells will decode significantly better than one (as in Fig. 1E). The gain in decoding performance from adding a second cell was significantly greater than zero on average (Fig. 6C; mean 0.033, SEM 0.001, pairs drawn from N = 985 cells with above-chance performance), although a small fraction (14% stimulus-locked; 20% population-locked) of pairs had negative gains. This apparent decrement in decoding performance was used as a measure of the noise around the no-gain condition (Fig. 6D). We identified jointly decoding pairs, i.e., pairs in which decoding performance substantially improved when using the joint activity pattern, to be those above a threshold set by comparing with a zero-mean distribution of equal variance (Fig. 6D, gray distribution). The same threshold (gain > 0.09) was used for stimulus-locked and population-locked alignment.

Among jointly decoding pairs, each neuron contributed a “piece” of information. To determine the role of correlated activity in decoding the stimulus, we compared the pair decoding performance to the trial-shuffled performance. If cells operate independently, then shuffling will have no effect on decoding performance. Shuffling will increase decoding performance if trial-by-trial correlations are detrimental, while it will decrease if correlated variability served as an additional information channel (Figs. 1E and 6D). We found that shuffling tended to decrease decoding performance, indicating a positive effect of correlation (Fig. 6D; mean 0.028, SEM 0.002, pairs drawn from N = 419 unique cells, P < 1e-10, signed rank), for both stimulus-locked and population-locked alignment (Fig. 6E; for population-locked alignment, mean correlation effect, +0.034, SEM 0.002, pairs drawn from N = 373 unique cells, P < 1e-10, signed rank). These pairs were slightly closer in space than other pairs [160 μm ± 90 μm (SE) vs. 165 μm ± 90 μm (SE), P < 0.01, shuffle test]. We also analyzed peristimulus lag, intercellular difference in lag, and fraction of trials active, but found no systematic difference.

DISCUSSION

The classical approach to characterizing the cortical code has been to record the responses of single cells and map out such properties as receptive fields and tuning curves. While informative, this approach has proven difficult to extend to a coding scheme utilized by local cortical microcircuit composed of interconnected neurons. Considering the strong influence of connectivity on cortical information processing, investigation at the level of the microcircuit is necessary to begin to generate a general framework for the input-output function of the brain.

Here, we have presented a careful quantification of decoding of thalamic inputs in large cortical populations extending across layers and columns. We focus on decoding, rather than a generalized measurement of encoded information, which permits us to characterize what information is accessible to downstream neurons via a plausible biological mechanism based on the linear decoder (Seung and Sompolinsky 1993). Additionally, a decoding approach has the advantage of higher robustness to data limitations (Averbeck et al. 2006) than directly measuring encoded information.

While the decoding task is simple, it is not trivial: the majority of single cells do not decode stimulus information at levels exceeding chance. By contrast, cells selected for reliable stimulus response, including those both imaged and recorded intracellularly, exhibited a much higher decoding performance, reflecting how strongly selection bias can affect measured decoding performance. These data would suggest that there is a subset of neurons that are the key to encoding each “piece” of information in cortex. This is consistent with the finding that only a specific subset of cortical neurons is reliably responsive to whisker stimulation (Yassin et al. 2010) and with sparse coding theories in barrel cortex (Crochet et al. 2011; Ganguli and Sompolinsky 2012; O'Connor et al. 2010). While categorical differences in stimulus-specific responsiveness exist, the majority of decoders responded to both stimuli, and much of the decoding power of a cell derives from a difference in lag in stimulus-driven activity, which is consistent with studies showing a latency code in barrel cortex (Bale and Petersen 2009; Petersen et al. 2001). Previous experiments, including single-unit recordings, have shown that the latency to first spike in vivo is on the order of tens of milliseconds (Drew and Feldman 2007; Jadhav et al. 2009; Swadlow 1995). When we broadly sample a cortical population outside of the primary column, we find that the first spikes of the population response appear within 50 ms of stimulus onset. Regardless of the exact latency, we found that decoding and discrimination of the stimulus require further computation, namely, a comparison between the responses, and the best decoders discriminated the stimulus within 200 ms of onset. Over a longer time window (up to 500 ms), many additional cells were capable of decoding stimulus identity at levels exceeding chance. An important future direction will be to conduct a similar analysis of cortical circuit activity driven by temporally extended stimuli that fluctuate on naturalistic timescales, reflecting the characteristics of whisking behavior.

Cells in the brain may not have independent access to stimulus onset times and must, therefore, compute time zero from locally available measures. We reanalyzed the data using the timing of activity relative to the population onset instead of the stimulus. While it is not clear what exactly sets the clock in cortex, information about population activity is locally available to an individual cell as total synaptic drive, making it a plausible candidate variable. Some of the high-performance decoders lost decoding power when population activity was used for temporal alignment. Among the decoders that remained, the maximally informative window for stimulus discrimination immediately followed population onset. For a single cell, the difference in lags between the two stimuli reflects a different position of that cell in multineuronal spatiotemporal sequence triggered by the stimulus. In other words, the stimulus-dependent pattern of circuit activity sets a stimulus-dependent lag at the level of the single cell, so this lag may be used to determine the stimulus identity that in turn reflects stimulus location. The partial loss of decoding power when absolute temporal information is removed is consistent with previous reports (Arabzadeh et al. 2006; Panzeri and Diamond 2010).

The role of noise correlation in the cortical code is a topic of much theoretical speculation (Abbott and Dayan 1999; Averbeck et al. 2006; Ecker et al. 2011; Latham and Nirenberg 2005; Schneidman et al. 2003) and little experimental consensus (Cohen and Kohn 2011; Ecker et al. 2010; Hansen et al. 2012; Nirenberg and Latham 2003; Osborne et al. 2008; Smith and Kohn 2008; Snyder et al. 2014). On the basis of multiunit recordings, noise correlations have not been found to increase the information carried by populations of neurons. However, cells in these recordings are typically separated by hundreds of microns (Adibi et al. 2014; Ince et al. 2013) significantly diminishing the likelihood of synaptic connectivity between units. In contrast, here we do find a significant effect of noise correlation in decoding, among a specific set of pairs: those that decode better than either constituent cell. Such pairs are rare among all recorded pairs (<1% of 306,456), but comprise about 12% of the pairs drawn from the core population of above-chance decoders. It is not possible to know a priori which subset of cells form the “core” decoding population, and so discovering these pairs requires dense sampling of a sufficiently large population.

Finally, we evaluated decoding performance as we built up groups of up to eight above-chance decoders. Regardless of how we temporally aligned the data, there is an increase in decoding performance with each cell added to the group. However, improvements saturate quickly: the third cell in the group improves the performance much less than the second cell did, the fourth less than the third, and so on. On average, combining more than five cells no longer improved the group performance. This saturation is partially due to the growing fraction of groups that have achieved near-perfect performance, and, along those lines, a natural next step is to make the decoding task more challenging by increasing the complexity of the stimulus space. By this logic, the 84% of groups that do not reach near-perfect decoding are simply lacking some stimulus information. Alternatively, this saturation may be a limitation of the type of decoder we used. Our simple model demonstrated that, typically, decoding performance would saturate as cells are added to the pool. Other decoders, which permit XOR-type logic, might display supralinear scaling with N, indicating a set of neurons that are individually uninformative about the stimulus, but have a highly informative joint activity pattern. In this case, the helpful effect of correlation we observed among some pairs might be a suggestion of truly synergistic decoding at the population level.

GRANTS

This work was supported by the DANA Foundation (A. J. Sederberg, J. N. MacLean), the National Science Foundation CAREER Award 0952686 (J. N. MacLean), and the Mary-Rita Angelo Fellowship (A. J. Sederberg).

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).

AUTHOR CONTRIBUTIONS

Author contributions: A.J.S., S.E.P., and J.N.M. conception and design of research; A.J.S. performed experiments; A.J.S. analyzed data; A.J.S., S.E.P., and J.N.M. interpreted results of experiments; A.J.S. prepared figures; A.J.S. drafted manuscript; A.J.S., S.E.P., and J.N.M. edited and revised manuscript; A.J.S., S.E.P., and J.N.M. approved final version of manuscript.