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Review
. 2013 Apr:103:156-93.
doi: 10.1016/j.pneurobio.2012.09.004. Epub 2012 Nov 1.

Population-wide distributions of neural activity during perceptual decision-making

Adrien Wohrer  1 , Mark D Humphries, Christian K Machens
Affiliations
Review

Population-wide distributions of neural activity during perceptual decision-making

Adrien Wohrer et al. Prog Neurobiol. 2013 Apr.

Abstract

Cortical activity involves large populations of neurons, even when it is limited to functionally coherent areas. Electrophysiological recordings, on the other hand, involve comparatively small neural ensembles, even when modern-day techniques are used. Here we review results which have started to fill the gap between these two scales of inquiry, by shedding light on the statistical distributions of activity in large populations of cells. We put our main focus on data recorded in awake animals that perform simple decision-making tasks and consider statistical distributions of activity throughout cortex, across sensory, associative, and motor areas. We transversally review the complexity of these distributions, from distributions of firing rates and metrics of spike-train structure, through distributions of tuning to stimuli or actions and of choice signals, and finally the dynamical evolution of neural population activity and the distributions of (pairwise) neural interactions. This approach reveals shared patterns of statistical organization across cortex, including: (i) long-tailed distributions of activity, where quasi-silence seems to be the rule for a majority of neurons; that are barely distinguishable between spontaneous and active states; (ii) distributions of tuning parameters for sensory (and motor) variables, which show an extensive extrapolation and fragmentation of their representations in the periphery; and (iii) population-wide dynamics that reveal rotations of internal representations over time, whose traces can be found both in stimulus-driven and internally generated activity. We discuss how these insights are leading us away from the notion of discrete classes of cells, and are acting as powerful constraints on theories and models of cortical organization and population coding.

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Figures

Figure 1
Figure 1. The statistical approach to population responses.
(a) We assume that data are recorded from awake behaving animals engaged in simple tasks. (Figure adapted from Feierstein et al. 2006). (b) The spike trains of a small subset of neurons in one area are recorded. (c) Recordings are sorted by trials over identical conditions. (d) For each neuron, we extract certain features from the spike trains, e.g., the stimulus-dependence of the firing rate or of the change in firing rate. (e) The distribution of these features across the recorded population leads to a probabilistic model of the population response. Such a model is usually generative, so that we can simulate data by randomly drawing neurons from the model (f), here depicted as an urn. (g) The simulated data should ideally be similar to the original data. This similarity is then quantified to evaluate the probabilistic model.
Figure 2
Figure 2. The effect of recording biases on the estimation of distributions.
(a) Statistical approaches rely on unbiased sampling. Within a population, neurons usually have different activity levels, here shown as different grey levels. Most extracellular recording techniques are more likely to find active cells, thus providing a biased sample (red box) as opposed to the desired unbiased sample of the population (green box). (b) A recording bias in single-cell recordings causes systematic errors in estimating population mean firing rates. Using a log-normal distribution of firing rates across neurons (see Section 3.1) to describe a simulated population, we took 500 samples of N individual firing rates; we repeated this for different levels of bias in the sample, by only taking samples above a certain firing rate, mimicking the bias in single-cell recordings. We plot the histograms of every sample’s mean rate, for a range of sample sizes and biases; the red line gives the mean value of the population distribution. The top row, with no bias, shows the central limit theorem in action: increasing the sample size causes the estimates of the mean firing rate to converge around the true mean value. However any bias in the sampling causes the convergence to occur around an incorrect mean firing rate for the population. (c) Increasing bias increases error in the estimate. We plot the mean ± s.d. of the error in estimating the true firing rate mean, taken over every sample for N = 1000 units. The error increases linearly, as expected, and is approximately twice the size of the recording bias.
Figure 3
Figure 3. Distributions of firing rates across neural populations in cortex.
(a) Violin plot (Allen et al., 2012) of firing rate distributions across cortical regions, in both spontaneous and task-aligned conditions. Width of bar is proportional to the fraction of neurons in that bin. Optimal histogram widths separately derived for each data-set (Wasserman, 2004). (b) Summary of data-sources in panel (a) and best-fit model to each data-set. Exponential, gamma, and log-normal distributions were fitted using maximum likelihood; best-fitting model was chosen using the Bayesian Information Criterion; p(best): the posterior probability of that being the best model within those tested (Wagenmakers and Farrell, 2004; Wasserman, 2004). The Session column indicates whether the data were from a single recording session or pooled across sessions and/or animals. (c) Probability-probability plots showing the correspondence between the cumulative probability distributions of the firing rate data and of the fitted models. A perfect fit would lie on the diagonal. Left: the V2 data was the only data-set best-fit by the exponential distribution; Middle: the prefrontal cortex data was best-fit by a log-normal distribution; Right: the orbitofrontal cortex data-set was best-fit by a gamma distribution. These examples show not only the best fitting model, but also that it was a good fit to the data. Data sources: A1, from (Otazu et al., 2009), data supplied by Gonzalo Otazu; V2: data recorded by Tim Blanche (see Blanche et al., 2005), available from crcns.org; PFC: from (Peyrache et al., 2009), data supplied by Adrien Peyrache; OFC, from (Feierstein et al., 2006), data supplied by Claudia Feierstein; M1, extracted from Figure 6A of (Goldberg et al., 2002); M2: data supplied by Masayoshi Murakami and Zach Mainen, unpublished.
Figure 4
Figure 4. Evoked changes from baseline firing-rate distributions are small.
(a) Distribution of spike counts across neurons in the auditory cortex (A1) of awake rats responding to a pure tone pip. Activity distributions are shown before (‘spontaneous’), during (‘early’, ‘late’) and after (‘offset’) the tone pip. Best model fits are provided, using respectively an exponential (gray) and a log-normal (black) distribution. The log-normal provides a markedly better fit. Loose patch clamp recordings, from Hromadka et al. (2008a). (b) Distribution of spike counts in the layers of barrel cortex (S1) of awake mice involved in a tactile detection task. The mean level of activity is plotted for each neuron against its cortical depth, both during (‘localization+response’) and between (‘intertrials’) periods of whisker contact with the stimulus. Loose patch clamp recordings from O’Connor et al. (2010). (c) Distribution of firing rates for spontaneous (baseline) activity in each layer of area V1 of monkeys observing a uniform-luminance screen; note firing rates are plotted on a log-scale (single extracellular micro-electrode recordings; adapted from Ringach et al., 2002). (d) Changes in mean firing rate distributions for two data-sets from Figure 3: stimulus-evoked changes in A1 (tetrodes; data from Otazu et al. 2009), and movement-evoked changes in OFC (tetrodes; data from Feierstein et al. 2006). Top: the empirical cumulative probability distributions for the baseline (‘spontaneous’) and task-aligned firing rates. Bottom: difference in probability distribution functions for the best-fitting models to spontaneous activity, p(r – baseline), stimulus-evoked activity, p(r – stimulus), or action-related activity, p(r – action) (the models are given in Figure 3b), showing the smooth extent of the increase in higher firing rates in both A1 and OFC. (e) From rat OFC data (Feierstein et al., 2006), the distribution of rate changes between baseline and movement for every sampled firing rate (every neuron in every trial): no change occurred between baseline and movement in 62.1% of samples. (f) From rat OFC data (Feierstein et al., 2006), the distribution of the proportion of trials on which each neuron showed a difference in rate between baseline and movement; median proportion was 0.42.
Figure 5
Figure 5. Distributions of spike train regularity in cortex.
(a) Distributions of rate-invariant irregularity measure CV2 in primate PFC during the fixation (top) and delay (bottom) period of an oculomotor task; neurons pooled over multiple single-unit recordings. Taken from Compte et al. (2003). (b) Distribution of CV2 in primate motor cortex, averaged over all task stages; neurons pooled over multiple single-unit recordings. Taken from (Hamaguchi et al., 2011). (c) Distribution of CV2 in a single tetrode recording from awake rat PFC. Data from study of (Peyrache et al., 2009). (d) Distribution of CV2 in a single polytrode recording from anaesthetised cat V2. Data recorded by Tim Blanche (see Blanche et al., 2005), available from crcns.org. (e) Correlation between mean firing rate and CV2 in primate motor cortex, calculated over all task stages. Note the lack of data-points below 10 Hz. Taken from (Hamaguchi et al., 2011). (f) Correlation between mean firing rate and CV2 in a single recording from awake rat PFC; data: black symbols; best-fit model: red line. The grey symbols and lines give the predicted relationship if each spike-train was a rate-varying Poisson process: each point is the mean predicted CV2 for a spike-train of that mean rate; 95% confidence intervals are too small to see on this scale. Data from study of (Peyrache et al., 2009). (g) Correlation between mean firing rate and CV2 in a single polytrode recording from anaesthetised cat V2. Grey lines and symbols as in panel e. Data recorded by Tim Blanche (see Blanche et al., 2005), available from crcns.org. (h) Distribution of coefficients r for the correlation between rate and CV2 for each neuron in a data-set of single-unit extracellular recordings from primate motor cortex during a joystick task. Taken from (Ponce-Alvarez et al., 2010). (i) Distribution of coeefficients r for the correlation between rate and CV2 for a population of neurons simultaneously recorded in awake rat PFC; the inset shows an example neuron that had a power-law relationship between rate and CV2. Data from study of (Peyrache et al., 2009). (j) Distribution of coecients r for the correlation between rate and CV2 for a population of neurons simultaneously recorded in anaesthetised cat V2. Data recorded by Tim Blanche (see Blanche et al., 2005), available from crcns.org.
Figure 6
Figure 6. Cortical receptive fields sizes are broadly distributed.
(a) Distribution of receptive field sizes (top curve, left ordinates) and inverse cortical magnification (bottom curve, right ordinates) in monkey V1 neurons as a function of retinal eccentricity; from Dow et al. (1981). (b) Top panels: sample responses of A1 neurons to pure tones, as a function of tone frequency, and intensity (measured in dB above the neuron’s threshold of response). Bottom panel: distribution of relative response bandwidths (best frequency divided by bandwidth) in cat A1 neurons, at respectively 10 dB and 40 dB above threshold; from Schreiner et al. (2000). (c) Distribution of receptive field sizes in monkey S1 neurons from the distal digit pads. From left to right, population histograms are shown for the excitatory subfields, inhibitory subfields, full receptive fields, and for the exc/inh ratio of areas; from DiCarlo et al. (1998).
Figure 7
Figure 7. Schematics for tiling of stimulus spaces by a neural population.
Each tile corresponds to the part of stimulus space to which a given neuron is responsive. (a,b) Representations of peripheral systems are often quite homogeneous. (c) Cortical representations appear usually more heterogeneous, resulting in broader population distributions. (d) In higher cortical areas, individual neurons may develop fragmented representations of the original stimulus space. Here, different neurons are depicted with different colors. For visual clarity, only a few neurons are shown.
Figure 8
Figure 8. Population-wide distributions of tuning parameters provide qualitative hints about the nature of feature encoding in different areas.
(a) Population response of V1 neurons to oriented gratings (anaesthetized cats, multi-unit electrode array). Left: Single neuron tuning curves to grating orientation. Right: Single neuron responses as a function of grating contrast. (b) Population distribution of two tuning features, namely sharpness of orientation tuning and contrast sensitivity, from the data in (a). Taken from (Busse et al., 2009). (c) Example of a “sharp” tuning curve for arm movement in primate M1 cortex. Symbols: the neuron’s mean firing rate as a function of the angular distance from the neuron’s preferred direction (at 0°). Black line: best-fit of a von Mises function; grey line: approximate fit of the classic cosine tuning curve for comparison. (d) Distribution of tuning curve width in primate M1 cortex, taken as the half-width of the von Mises function (blue lines in panel e). A half-width of σ = 90° is the cosine tuning curve assumed in (Georgopoulos et al., 1982). Taken from (Amirikian et al., 2000). (e) Population response of S1 neurons to vibratory stimulation on the fingertip (awake macaques, multi-electrode recordings). S1 neurons can display tuned responses to the vibration frequency, either through conservation of the stimulus periodicity (“periodic” neuron), or through their overall amount of firing (“rate” neuron). (f) Joint distribution of these two forms of tuning across recorded S1 neurons. Rate tuning is not correlated with periodic tuning, supporting a plausible specific role of the former in tactile perception. Taken from (Hernández et al., 2000). (g) Trial-to-trial distributions of activity for an MT cell conditioned on the animal’s subsequent decision, when the stimulus is ambiguous (0% binocular disparity). Choice probability quantifies the amount of separation between the two distributions. (h) Choice probability and neuronal sensitivity are correlated at the population level, indicating that the animal’s ultimate decision correlates more with neurons tuned to the stimulus. Macaque MT during a binocular discrimination task, taken from (Uka and DeAngelis, 2004).
Figure 9
Figure 9. Theories of feature encoding yield predictions for population-wide distributions of activity or tuning.
(a) Receptive fields of V1 cells are fitted by Gabor functions, and plotted in the “shape domain” consisting of each field’s length and width divided by its characteristic spatial frequency. Receptive fields with a single bump fall near the origin, while receptive fields with several oscillations fall away from the origin. Taken from (Ringach, 2002). (b) Distribution, in the same shape domain, of receptive fields predicted by the sparse coding model of Olshausen and Field (1997) (red dots); blue dots are the experimental data from (Ringach, 2002). (c) Same as (b), but red dots are receptive fields predicted by the “hard” sparse coding model of Rehn and Sommer (2007). Panels b and c taken from (Rehn and Sommer, 2007). (d) Transfer filters measured from cat auditory nerve fibers (blue) have similar shapes as the transfer filters predicted by a sparse analysis of natural auditory signals (red). Gray bars represent 5 ms. (e) Population distribution of centre frequency and bandwidth for cat auditory nerve fibers (blue dots) and for sparse kernels learned from natural auditory signals (red dots). Panels d and e taken from (Smith and Lewicki, 2006). (f) Evolution of population activity in a probabilistic population code model of sensory integration in area LIP. Population sparseness is predicted to increase as a result of the inferred distribution over stimuli becoming sharper. Taken from (Beck et al., 2008).
Figure 10
Figure 10. Distribution of response latencies across cortical areas.
(a) Cumulative distributions of (minimum) response latencies in several areas of the visual system of anaesthetized monkeys. Taken from (Schmolesky et al., 1998). (b) Latencies and choice probabilities in different areas involved in a tactile discrimination task. Latencies and choice probabilities increase along the putative processing pathway of information. Taken from (de Lafuente and Romo, 2006).
Figure 11
Figure 11. The temporal structure of the population response to sensory stimuli.
(a) Principal Component Analysis (PCA) of insect antennal lobe principal neurons responding to two odors. From Mazor and Laurent (2005). B: baseline, bold traces: stimulus onset, FP: fixed point (persistent activity), thin traces: stimulus offset. (b)-(c) Population dynamics of rat auditory cortex responding to tone pips is visualized thanks to PCA (panel b) and Linear Discriminant Analysis (panel c, segregates responses to different stimuli). From Bartho et al. (2009). (d)-(i) Population dynamics (determined using PCA) of macaque S2 neurons responding to a vibratory frequency on the fingertip. Colors from blue to orange indicate increasing frequency values. (d): First 10 eigenvalues of signal covariance matrix. (e): Population activity in the 2 first Principal Components (PC). (f),(g): Temporal activity in the first two PCs. (h),(i): Population histograms of neural factor loadings on the two first PCs. CV+ and CV– are the respective coefficients of variation for the positive and negative parts of the distributions. Reanalysis of published data (Hernández et al., 2010).
Figure 12
Figure 12. Temporal dynamics of trial-to-trial variance and stimulus discriminability.
(a)-(b) Mean firing rate and Fano Factor amongst LIP neurons with a given preferred direction, responding to a random dot motion stimulus. The Fano Factor is not constant as predicted by Poisson-like statistics (panel b). Instead, it reveals variance quenching at stimulus onset and offset, and a rise of variance during the course of sensory stimulation. Taken from (Churchland et al., 2011). (c)-(e) Causal influence of stimulus and choice probabilities in area V2, in macaques during a binocular disparity discrimination task. The psychophysical kernel for the animal (panel c, overall amplitude in panel d), which reflects the causal influence of stimulus disparity across time on the animal’s ultimate decision, has a different temporal evolution than choice probability signals (panel e, average CP in the V2 population). This is inconsistent with a purely bottom-up interpretation of choice probability signals. Taken from (Nienborg and Cumming, 2009). (f)-(h) Temporal evolution of neurometric thresholds and other spiking statistics in macaque MT neurons during a binocular depth discrimination task. (f): Overall scheme of the analysis. A neuron responds to two possible stimuli with different binocular depths (stimulus 1: plain red curves, mean response plus trial-by-trial standard deviation, stimulus 2: dashed blue curves). From its spike counts on a trial-by-trial basis, a neurometric threshold (TH) can be derived measuring the neuron’s sensitivity to the stimulus, based either on the neuron’s spike count over the whole stimulation period (1500 ms), or over the sole initial response (first 300 ms). Candidate statistics influencing the value of the threshold are: neural tuning (TU) to the stimulus, variance-to-mean ratio (Fano Factor, FF), and noise autocorrelation (AC) for the neuron on a trial-by-trial basis. (g): Population mean across neurons for the three statistics. The mean amount of tuning is constant across the response, as well as the mean noise autocorrelation (with a value around 0.1). The Fano Factor increases in the second half of the stimulation, indicating a global divergence of the population response on a trial-by-trial basis. (h) Correlation analysis for early/late ratios across the population. Different symbols indicate the two animals in the experiment. The dashed line is the predicted threshold ratio (THr) for homogenous Poisson processes. The whole analysis hints at a progressive loss of sensitivity to the stimulus in the neural population, as resulting from the influence of internally generated dynamics on a trial-by-trial basis (see main text). Taken from (Uka and DeAngelis, 2003)—panel h, unpublished recomputation from the data.
Figure 13
Figure 13. Population statistics of delay activity.
(a) Rotation of the population vector in monkey PFC during an oculomotor-delayed-response task. Shown is the angle of the population vector over time with respect to the population vector at time t = 0 (adapted from Takeda and Funahashi 2004). (b) Rotation of neural tuning in monkey PFC during the delay period of a somatosensory discrimination task. The left panel shows the population activity during the delay period for different stimuli (colored). Shown is the activity of the recorded population (N = 842 neurons) projected onto the two response modes with the strongest stimulus tuning. The right panel shows the angle between the original direction of tuning at time t = 0, and subsequent tunings. (c) Demixed principal components of PFC population activity during a delay period, from a monkey performing a working memory task. The components show that temporal and stimulus-related activities can be separated (demixed) into orthogonal subspaces. Inset numbers are the percentages of total variance accounted for by each mode. Adapted from (Machens et al., 2010). (d) Factor loadings for the principal components from above. The factor loadings show that there are no clear separate classes of cells. For instance, the first panel shows that some cells have large positive loadings (and hence firing rates that ramp up according to the first panel in (c)), some cells have large negative loadings (thereby ramping down), but most cells cluster around zero, so that their firing rates ramp neither up or down (adapted from Machens et al. 2010).
Figure 14
Figure 14. Population distributions of correlations.
(a) Distribution of signal correlations in IT neurons responding to various visual objects. Each blue cross depicts a pair of recording sites at the same cortical depth (ordinate), with the abscissa encoding signal correlation strength (similarity of tuning to a set of 60 objects) between multiunit activities at the two sites. The black curve and bars are mean and standard deviation of pairwise tuning similarity. The red line is the p = 0.05 significance threshold. The clear dependency between cortical depth and signal correlations is the mark of “activity spots”, whose neurons have broadly similar tuning and which are located mostly in the upper layers of cortex. Taken from (Sato et al., 2009). (b) Average pairwise noise correlation strength in macaque V1, plotted as a function of distance and tuning similarity (orientation) between the recorded neurons (Smith and Kohn, 2008). (c) Joint population distribution of signal correlation and noise correlation coefficients between pairs of neurons in secondary somatosensory cortex of macaques during a tactile discrimination task. The signal correlation between two neurons is computed as the overall similarity of their trial-averaged firing rates across time and stimuli (as in (Wohrer et al., 2010)). Blue histograms on the sides are marginalized distributions. Red curves represent conditional mean and standard deviation of noise correlation value at a given level of signal correlation. The width of the standard deviation plays an active role in estimating the overall sensitivity to stimulus in the population. Adapted from (Wohrer et al., 2010), a re-analysis of data from (Hernández et al., 2010). (d)-(g) Statistics of coupling strengths in an Ising model fit to cat V1 neurons. Coupling strengths relate, but are not equivalent, to classical noise correlation coefficients (panel d). Coupling is higher for similarly tuned neurons (orientation, panel e) and for nearby neurons (panel g). Taken from (Yu et al., 2008). (h)-(i) Statistics of coupling strengths in a Generalized Linear Model fit to retinal ganglion cell activity. On and Off cells are mostly interacting through mutual inhibition, whereas cells of the same polarity are positively coupled. Mean coupling strength decreases with interneuronal distance. Taken from (Pillow et al., 2008).
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References

    1. Abbott LF, Dayan P. The effect of correlated variability on the accuracy of a population code. Neural computation. 1999 Jan;11(1):91–101. - PubMed
    1. Abeles M. Corticonics: Neural circuits of the cerebral cortex. Cambridge Univ Pr; 1991.
    1. Adrian E. The basis of sensation. WW Norton & Co; 1928.
    1. Aertsen aM, Gerstein GL, Habib MK, Palm G. Dynamics of neuronal firing correlation: modulation of ”effective connectivity”. Journal of neurophysiology. 1989 May;61(5):900–17. - PubMed
    1. Afshar A, Santhanam G, Yu BM, Ryu SI, Sahani M, Shenoy KV. Single-trial neural correlates of arm movement preparation. Neuron. 2011 Aug;71(3):555–64. - PMC - PubMed

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