Stable task information from an unstable neural population

Over days and weeks, neural activity representing an animal’s position and movement in sensorimotor cortex has been found to continually reconfigure or ‘drift’ during repeated trials of learned tasks, with no obvious change in behavior. This challenges classical theories, which assume stable engrams underlie stable behavior. However, it is not known whether this drift occurs systematically, allowing downstream circuits to extract consistent information. Analyzing long-term calcium imaging recordings from posterior parietal cortex in mice (Mus musculus), we show that drift is systematically constrained far above chance, facilitating a linear weighted readout of behavioral variables. However, a significant component of drift continually degrades a fixed readout, implying that drift is not confined to a null coding space. We calculate the amount of plasticity required to compensate drift independently of any learning rule, and find that this is within physiologically achievable bounds. We demonstrate that a simple, biologically plausible local learning rule can achieve these bounds, accurately decoding behavior over many days

Stable task information from an unstable neural population

Over days and weeks, neural activity representing an animal’s position and movement in sensorimotor cortex has been found to continually reconfigure or ‘drift’ during repeated trials of learned tasks, with no obvious change in behavior. This challenges classical theories, which assume stable engrams underlie stable behavior. However, it is not known whether this drift occurs systematically, allowing downstream circuits to extract consistent information. Analyzing long-term calcium imaging recordings from posterior parietal cortex in mice (Mus musculus), we show that drift is systematically constrained far above chance, facilitating a linear weighted readout of behavioral variables. However, a significant component of drift continually degrades a fixed readout, implying that drift is not confined to a null coding space. We calculate the amount of plasticity required to compensate drift independently of any learning rule, and find that this is within physiologically achievable bounds. We demonstrate that a simple, biologically plausible local learning rule can achieve these bounds, accurately decoding behavior over many days

Noise-Robust Modes of the Retinal Population Code have the Geometry of "Ridges" and Correspond with Neuronal Communities

An appealing new principle for neural population codes is that correlations among neurons organize neural activity patterns into a discrete set of clusters, which can each be viewed as a noise-robust population "codeword". Previous studies assumed that these codewords corresponded geometrically with local peaks in the probability landscape of neural population responses. Here, we analyze multiple datasets of the responses of ~150 retinal ganglion cells and show that local probability peaks are absent under broad, non-repeated stimulus ensembles, which are characteristic of natural behavior. However, we find that neural activity still forms noise-robust clusters in this regime, albeit clusters with a different geometry. We start by defining a soft local maximum, which is a local probability maximum when constrained to a fixed spike count. Next, we show that soft local maxima are robustly present, and can moreover be linked across different spike count levels in the probability landscape to form a "ridge". We found that these ridges are comprised of combinations of spiking and silence in the neural population such that all of the spiking neurons are members of the same neuronal community, a notion from network theory. We argue that a neuronal community shares many of the properties of Donald Hebb's classic cell assembly, and show that a simple, biologically plausible decoding algorithm can recognize the presence of a specific neuronal community

Noise-Robust Modes of the Retinal Population Code have the Geometry of "Ridges" and Correspond with Neuronal Communities

An appealing new principle for neural population codes is that correlations among neurons organize neural activity patterns into a discrete set of clusters, which can each be viewed as a noise-robust population "codeword". Previous studies assumed that these codewords corresponded geometrically with local peaks in the probability landscape of neural population responses. Here, we analyze multiple datasets of the responses of ~150 retinal ganglion cells and show that local probability peaks are absent under broad, non-repeated stimulus ensembles, which are characteristic of natural behavior. However, we find that neural activity still forms noise-robust clusters in this regime, albeit clusters with a different geometry. We start by defining a soft local maximum, which is a local probability maximum when constrained to a fixed spike count. Next, we show that soft local maxima are robustly present, and can moreover be linked across different spike count levels in the probability landscape to form a "ridge". We found that these ridges are comprised of combinations of spiking and silence in the neural population such that all of the spiking neurons are members of the same neuronal community, a notion from network theory. We argue that a neuronal community shares many of the properties of Donald Hebb's classic cell assembly, and show that a simple, biologically plausible decoding algorithm can recognize the presence of a specific neuronal community

Multi-electrode retinal ganglion cell population spiking data

The file contains spike time data from multi-electrode array recordings of salamander retinal ganglion cells under four stimulus conditions: a white noise checkerboard, a repeated natural movie, a non-repeated natural movie, and a bar exhibiting random one-dimensional motion. For each experiment, spike time data is provided in the file 'data.mat' and information necessary to reconstruct the stimulus and align to spike times is contained in 'aux_data' where relevant. All recordings were sampled at 10 kHz. Data is in Matlab .mat format

Data from: Error-robust modes of the retinal population code

Across the nervous system, certain population spiking patterns are observed far more frequently than others. A hypothesis about this structure is that these collective activity patterns function as population codewords–collective modes–carrying information distinct from that of any single cell. We investigate this phenomenon in recordings of ∼150 retinal ganglion cells, the retina’s output. We develop a novel statistical model that decomposes the population response into modes; it predicts the distribution of spiking activity in the ganglion cell population with high accuracy. We found that the modes represent localized features of the visual stimulus that are distinct from the features represented by single neurons. Modes form clusters of activity states that are readily discriminated from one another. When we repeated the same visual stimulus, we found that the same mode was robustly elicited. These results suggest that retinal ganglion cells’ collective signaling is endowed with a form of error-correcting code–a principle that may hold in brain areas beyond retina

Data from: Error-robust modes of the retinal population code

Across the nervous system, certain population spiking patterns are observed far more frequently than others. A hypothesis about this structure is that these collective activity patterns function as population codewords–collective modes–carrying information distinct from that of any single cell. We investigate this phenomenon in recordings of ∼150 retinal ganglion cells, the retina’s output. We develop a novel statistical model that decomposes the population response into modes; it predicts the distribution of spiking activity in the ganglion cell population with high accuracy. We found that the modes represent localized features of the visual stimulus that are distinct from the features represented by single neurons. Modes form clusters of activity states that are readily discriminated from one another. When we repeated the same visual stimulus, we found that the same mode was robustly elicited. These results suggest that retinal ganglion cells’ collective signaling is endowed with a form of error-correcting code–a principle that may hold in brain areas beyond retina

Discriminability of modes.

<p>(A,B) Discriminability of some example modes. For each mode, we collected all response words assigned to that mode (A-B, <i>top</i>). Words that occurred within one time bin of a transition between two modes were omitted. For each pair of modes, we then carried out Fisher’s linear discriminant analysis (LDA) to find the one-dimensional projection of the two word populations that maximized their discriminability (quantified by <i>d</i>′). A and B each summarize this analysis for an arbitrarily chosen example mode (black) and its nearest-neighbor (the mode with smallest <i>d</i>′), in red. <i>Top</i>: Rasters of unique words assigned to each of the two modes (rows indexing words, columns cells). <i>Bottom</i>: Distribution of LDA projections of the words shown above. (C) Blue points: <i>d</i>′ of nearest-neighbor modes. Discriminability is high and increases with <i>⟨k⟩</i>, consistent with the suggestion of panels A and B. Gray points: results of the same analysis carried out on shuffled data in which words were randomly assigned to modes, keeping the same number of words in each mode. Shuffled modes are highly overlapping, even though the LDA projection maximizes <i>d</i>′. (D) Blue: distribution of <i>d</i>′ for all mode pairs, not just nearest neighbor. Gray: result on shuffled data, as in (C).</p

Organization of ganglion cells within collective modes.

<p>(A) Average number of cells within a given mode (red) and average number of modes containing a given cell (blue) plotted as a function of the firing threshold, <i>θ</i>. (B) Histogram of the number of cells within a given mode for <i>θ</i> = 3. (C) Histogram of the number of modes containing a given cell for <i>θ</i> = 3.</p

Visualization of model structure.

<p>(A) Overall mode weight, <i>w</i>_<i>α</i>, versus mode index. (B) The mean spiking probability of each mode, <i>m</i>_<i>iα</i>, projected into two dimensions by multidimensional scaling (MDS). The color of each point indicates that mode’s log probability (as in A) while the size scales with the mode’s average population spike count, ⟨<i>k</i>⟩. Modes with higher ⟨<i>k</i>⟩ pack response space less densely. (C) Entropy rate of mode emission distribution, <i>S</i>_<i>α</i> (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005148#sec014" target="_blank">Methods</a>), plotted against average population spike count of the mode. Dashed gray line: <i>Smax</i>, the maximum entropy for fixed <i>k</i>; i.e. the entropy of the uniform distribution over all <i>k</i>-spike words (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005148#sec014" target="_blank">Methods</a>). <i>Inset</i>: the ratio of maximum entropy to mode entropy. (D) Schematic representation of the structure of the response probability distribution. Each lump represents one mode, with the overall amplitude decreasing and width increasing with average response magnitude, <i>m</i>. The tall, narrow, central peak corresponds to the silent and near-silent words near <i>m</i> = 0.</p