A Map-like Micro-Organization of Grid Cells in the Medial Entorhinal Cortex.

How the topography of neural circuits relates to their function remains unclear. Although topographic maps exist for sensory and motor variables, they are rarely observed for cognitive variables. Using calcium imaging during virtual navigation, we investigated the relationship between the anatomical organization and functional properties of grid cells, which represent a cognitive code for location during navigation. We found a substantial degree of grid cell micro-organization in mouse medial entorhinal cortex: grid cells and modules all clustered anatomically. Within a module, the layout of grid cells was a noisy two-dimensional lattice in which the anatomical distribution of grid cells largely matched their spatial tuning phases. This micro-arrangement of phases demonstrates the existence of a topographical map encoding a cognitive variable in rodents. It contributes to a foundation for evaluating circuit models of the grid cell network and is consistent with continuous attractor models as the mechanism of grid formation.

Geometry of abstract learned knowledge in the hippocampus.

Hippocampal neurons encode physical variables1-7 such as space1 or auditory frequency6 in cognitive maps8. In addition, functional magnetic resonance imaging studies in humans have shown that the hippocampus can also encode more abstract, learned variables9-11. However, their integration into existing neural representations of physical variables12,13 is unknown. Here, using two-photon calcium imaging, we show that individual neurons in the dorsal hippocampus jointly encode accumulated evidence with spatial position in mice performing a decision-making task in virtual reality14-16. Nonlinear dimensionality reduction13 showed that population activity was well-described by approximately four to six latent variables, which suggests that neural activity is constrained to a low-dimensional manifold. Within this low-dimensional space, both physical and abstract variables were jointly mapped in an orderly manner, creating a geometric representation that we show is similar across mice. The existence of conjoined cognitive maps suggests that the hippocampus performs a general computation-the creation of task-specific low-dimensional manifolds that contain a geometric representation of learned knowledge.

Detecting and correcting false transients in calcium imaging.

Population recordings of calcium activity are a major source of insight into neural function. Large datasets require automated processing, but this can introduce errors that are difficult to detect. Here we show that popular time course-estimation algorithms often contain substantial misattribution errors affecting 10-20% of transients. Misattribution, in which fluorescence is ascribed to the wrong cell, arises when overlapping cells and processes are imperfectly defined or not identified. To diagnose misattribution, we develop metrics and visualization tools for evaluating large datasets. To correct time courses, we introduce a robust estimator that explicitly accounts for contaminating signals. In one hippocampal dataset, removing contamination reduced the number of place cells by 15%, and 19% of place fields shifted by over 10 cm. Our methods are compatible with other cell-finding techniques, empowering users to diagnose and correct a potentially widespread problem that could alter scientific conclusions.

Coarse Graining, Fixed Points, and Scaling in a Large Population of Neurons.

We develop a phenomenological coarse-graining procedure for activity in a large network of neurons, and apply this to recordings from a population of 1000+ cells in the hippocampus. Distributions of coarse-grained variables seem to approach a fixed non-Gaussian form, and we see evidence of scaling in both static and dynamic quantities. These results suggest that the collective behavior of the network is described by a nontrivial fixed point.

Anatomical identification of extracellularly recorded cells in large-scale multielectrode recordings.

This study combines for the first time two major approaches to understanding the function and structure of neural circuits: large-scale multielectrode recordings, and confocal imaging of labeled neurons. To achieve this end, we develop a novel approach to the central problem of anatomically identifying recorded cells, based on the electrical image: the spatiotemporal pattern of voltage deflections induced by spikes on a large-scale, high-density multielectrode array. Recordings were performed from identified ganglion cell types in the macaque retina. Anatomical images of cells in the same preparation were obtained using virally transfected fluorescent labeling or by immunolabeling after fixation. The electrical image was then used to locate recorded cell somas, axon initial segments, and axon trajectories, and these signatures were used to identify recorded cells. Comparison of anatomical and physiological measurements permitted visualization and physiological characterization of numerically dominant ganglion cell types with high efficiency in a single preparation.

Functional connectivity in the retina at the resolution of photoreceptors.

To understand a neural circuit requires knowledge of its connectivity. Here we report measurements of functional connectivity between the input and ouput layers of the macaque retina at single-cell resolution and the implications of these for colour vision. Multi-electrode technology was used to record simultaneously from complete populations of the retinal ganglion cell types (midget, parasol and small bistratified) that transmit high-resolution visual signals to the brain. Fine-grained visual stimulation was used to identify the location, type and strength of the functional input of each cone photoreceptor to each ganglion cell. The populations of ON and OFF midget and parasol cells each sampled the complete population of long- and middle-wavelength-sensitive cones. However, only OFF midget cells frequently received strong input from short-wavelength-sensitive cones. ON and OFF midget cells showed a small non-random tendency to selectively sample from either long- or middle-wavelength-sensitive cones to a degree not explained by clumping in the cone mosaic. These measurements reveal computations in a neural circuit at the elementary resolution of individual neurons.

A polyaxonal amacrine cell population in the primate retina.

Amacrine cells are the most diverse and least understood cell class in the retina. Polyaxonal amacrine cells (PACs) are a unique subset identified by multiple long axonal processes. To explore their functional properties, populations of PACs were identified by their distinctive radially propagating spikes in large-scale high-density multielectrode recordings of isolated macaque retina. One group of PACs exhibited stereotyped functional properties and receptive field mosaic organization similar to that of parasol ganglion cells. These PACs had receptive fields coincident with their dendritic fields, but much larger axonal fields, and slow radial spike propagation. They also exhibited ON-OFF light responses, transient response kinetics, sparse and coordinated firing during image transitions, receptive fields with antagonistic surrounds and fine spatial structure, nonlinear spatial summation, and strong homotypic neighbor electrical coupling. These findings reveal the functional organization and collective visual signaling by a distinctive, high-density amacrine cell population.

Efficient coding of spatial information in the primate retina.

Sensory neurons have been hypothesized to efficiently encode signals from the natural environment subject to resource constraints. The predictions of this efficient coding hypothesis regarding the spatial filtering properties of the visual system have been found consistent with human perception, but they have not been compared directly with neural responses. Here, we analyze the information that retinal ganglion cells transmit to the brain about the spatial information in natural images subject to three resource constraints: the number of retinal ganglion cells, their total response variances, and their total synaptic strengths. We derive a model that optimizes the transmitted information and compare it directly with measurements of complete functional connectivity between cone photoreceptors and the four major types of ganglion cells in the primate retina, obtained at single-cell resolution. We find that the ganglion cell population exhibited 80% efficiency in transmitting spatial information relative to the model. Both the retina and the model exhibited high redundancy (~30%) among ganglion cells of the same cell type. A novel and unique prediction of efficient coding, the relationships between projection patterns of individual cones to all ganglion cells, was consistent with the observed projection patterns in the retina. These results indicate a high level of efficiency with near-optimal redundancy in visual signaling by the retina.

Receptive fields in primate retina are coordinated to sample visual space more uniformly.

In the visual system, large ensembles of neurons collectively sample visual space with receptive fields (RFs). A puzzling problem is how neural ensembles provide a uniform, high-resolution visual representation in spite of irregularities in the RFs of individual cells. This problem was approached by simultaneously mapping the RFs of hundreds of primate retinal ganglion cells. As observed in previous studies, RFs exhibited irregular shapes that deviated from standard Gaussian models. Surprisingly, these irregularities were coordinated at a fine spatial scale: RFs interlocked with their neighbors, filling in gaps and avoiding large variations in overlap. RF shapes were coordinated with high spatial precision: the observed uniformity was degraded by angular perturbations as small as 15 degrees, and the observed populations sampled visual space with more than 50% of the theoretical ideal uniformity. These results show that the primate retina encodes light with an exquisitely coordinated array of RF shapes, illustrating a higher degree of functional precision in the neural circuitry than previously appreciated.

Correlated firing among major ganglion cell types in primate retina.

Retinal ganglion cells exhibit substantial correlated firing: a tendency to fire nearly synchronously at rates different from those expected by chance. These correlations suggest that network interactions significantly shape the visual signal transmitted from the eye to the brain. This study describes the degree and structure of correlated firing among the major ganglion cell types in primate retina. Correlated firing among ON and OFF parasol, ON and OFF midget, and small bistratified cells, which together constitute roughly 75% of the input to higher visual areas, was studied using large-scale multi-electrode recordings. Correlated firing in the presence of constant, spatially uniform illumination exhibited characteristic strength, time course and polarity within and across cell types. Pairs of nearby cells with the same light response polarity were positively correlated; cells with the opposite polarity were negatively correlated. The strength of correlated firing declined systematically with distance for each cell type, in proportion to the degree of receptive field overlap. The pattern of correlated firing across cell types was similar at photopic and scotopic light levels, although additional slow correlations were present at scotopic light levels. Similar results were also observed in two other retinal ganglion cell types. Most of these observations are consistent with the hypothesis that shared noise from photoreceptors is the dominant cause of correlated firing. Surprisingly, small bistratified cells, which receive ON input from S cones, fired synchronously with ON parasol and midget cells, which receive ON input primarily from L and M cones. Collectively, these results provide an overview of correlated firing across cell types in the primate retina, and constraints on the underlying mechanisms.

Uniform signal redundancy of parasol and midget ganglion cells in primate retina.

The collective representation of visual space in high resolution visual pathways was explored by simultaneously measuring the receptive fields of hundreds of ON and OFF midget and parasol ganglion cells in isolated primate retina. As expected, the receptive fields of all four cell types formed regular mosaics uniformly tiling the visual scene. Surprisingly, comparison of all four mosaics revealed that the overlap of neighboring receptive fields was nearly identical, for both the excitatory center and inhibitory surround components of the receptive field. These observations contrast sharply with the large differences in the dendritic overlap between the parasol and midget cell populations, revealing a surprising lack of correspondence between the anatomical and functional architecture in the dominant circuits of the primate retina.

The structure of large-scale synchronized firing in primate retina.

Synchronized firing among neurons has been proposed to constitute an elementary aspect of the neural code in sensory and motor systems. However, it remains unclear how synchronized firing affects the large-scale patterns of activity and redundancy of visual signals in a complete population of neurons. We recorded simultaneously from hundreds of retinal ganglion cells in primate retina, and examined synchronized firing in completely sampled populations of approximately 50-100 ON-parasol cells, which form a major projection to the magnocellular layers of the lateral geniculate nucleus. Synchronized firing in pairs of cells was a subset of a much larger pattern of activity that exhibited local, isotropic spatial properties. However, a simple model based solely on interactions between adjacent cells reproduced 99% of the spatial structure and scale of synchronized firing. No more than 20% of the variability in firing of an individual cell was predictable from the activity of its neighbors. These results held both for spontaneous firing and in the presence of independent visual modulation of the firing of each cell. In sum, large-scale synchronized firing in the entire population of ON-parasol cells appears to reflect simple neighbor interactions, rather than a unique visual signal or a highly redundant coding scheme.

CaImAn an open source tool for scalable calcium imaging data analysis.

Advances in fluorescence microscopy enable monitoring larger brain areas in-vivo with finer time resolution. The resulting data rates require reproducible analysis pipelines that are reliable, fully automated, and scalable to datasets generated over the course of months. We present CaImAn, an open-source library for calcium imaging data analysis. CaImAn provides automatic and scalable methods to address problems common to pre-processing, including motion correction, neural activity identification, and registration across different sessions of data collection. It does this while requiring minimal user intervention, with good scalability on computers ranging from laptops to high-performance computing clusters. CaImAn is suitable for two-photon and one-photon imaging, and also enables real-time analysis on streaming data. To benchmark the performance of CaImAn we collected and combined a corpus of manual annotations from multiple labelers on nine mouse two-photon datasets. We demonstrate that CaImAn achieves near-human performance in detecting locations of active neurons.

Spatial properties and functional organization of small bistratified ganglion cells in primate retina.

The primate visual system consists of parallel pathways initiated by distinct cell types in the retina that encode different features of the visual scene. Small bistratified cells (SBCs), which form a major projection to the thalamus, exhibit blue-ON/yellow-OFF [S-ON/(L+M)-OFF] light responses thought to be important for high-acuity color vision. However, the spatial processing properties of individual SBCs and their spatial arrangement across the visual field are poorly understood. The present study of peripheral primate retina reveals that contrary to previous suggestions, SBCs exhibit center-surround spatial structure, with the (L+M)-OFF component of the receptive field approximately 50% larger in diameter than the S-ON component. Analysis of response kinetics shows that the (L+M)-OFF response in SBCs is slower than the S-ON response and significantly less transient than that of simultaneously recorded OFF-parasol cells. The (L+M)-OFF response in SBCs was eliminated by bath application of the metabotropic glutamate receptor agonist L-APB. These observations indicate that the (L+M)-OFF response of SBCs is not formed by OFF-bipolar cell input as has been suspected and suggest that it arises from horizontal cell feedback. Finally, the receptive fields of SBCs form orderly mosaics, with overlap and regularity similar to those of ON-parasol cells. Thus, despite their distinctive morphology and chromatic properties, SBCs exhibit two features of other retinal ganglion cell types: center-surround antagonism and regular mosaic sampling of visual space.

Identification and characterization of a Y-like primate retinal ganglion cell type.

The primate retina communicates visual information to the brain via a set of parallel pathways that originate from at least 22 anatomically distinct types of retinal ganglion cells. Knowledge of the physiological properties of these ganglion cell types is of critical importance for understanding the functioning of the primate visual system. Nonetheless, the physiological properties of only a handful of retinal ganglion cell types have been studied in detail. Here we show, using a newly developed multielectrode array system for the large-scale recording of neural activity, the existence of a physiologically distinct population of ganglion cells in the primate retina with distinctive visual response properties. These cells, which we will refer to as upsilon cells, are characterized by large receptive fields, rapid and transient responses to light, and significant nonlinearities in their spatial summation. Based on the measured properties of these cells, we speculate that they correspond to the smooth/large radiate cells recently identified morphologically in the primate retina and may therefore provide visual input to both the lateral geniculate nucleus and the superior colliculus. We further speculate that the upsilon cells may be the primate retina's counterparts of the Y-cells observed in the cat and other mammalian species.

A Dedicated Population for Reward Coding in the Hippocampus.

The hippocampus plays a critical role in goal-directed navigation. Across different environments, however, hippocampal maps are randomized, making it unclear how goal locations could be encoded consistently. To address this question, we developed a virtual reality task with shifting reward contingencies to distinguish place versus reward encoding. In mice performing the task, large-scale recordings in CA1 and subiculum revealed a small, specialized cell population that was only active near reward yet whose activity could not be explained by sensory cues or stereotyped reward anticipation behavior. Across different virtual environments, most cells remapped randomly, but reward encoding consistently arose from a single pool of cells, suggesting that they formed a dedicated channel for reward. These observations represent a significant departure from the current understanding of CA1 as a relatively homogeneous ensemble without fixed coding properties and provide a new candidate for the cellular basis of goal memory in the hippocampus.

The structure of multi-neuron firing patterns in primate retina.

Current understanding of many neural circuits is limited by our ability to explore the vast number of potential interactions between different cells. We present a new approach that dramatically reduces the complexity of this problem. Large-scale multi-electrode recordings were used to measure electrical activity in nearly complete, regularly spaced mosaics of several hundred ON and OFF parasol retinal ganglion cells in macaque monkey retina. Parasol cells exhibited substantial pairwise correlations, as has been observed in other species, indicating functional connectivity. However, pairwise measurements alone are insufficient to determine the prevalence of multi-neuron firing patterns, which would be predicted from widely diverging common inputs and have been hypothesized to convey distinct visual messages to the brain. The number of possible multi-neuron firing patterns is far too large to study exhaustively, but this problem may be circumvented if two simple rules of connectivity can be established: (1) multi-cell firing patterns arise from multiple pairwise interactions, and (2) interactions are limited to adjacent cells in the mosaic. Using maximum entropy methods from statistical mechanics, we show that pairwise and adjacent interactions accurately accounted for the structure and prevalence of multi-neuron firing patterns, explaining approximately 98% of the departures from statistical independence in parasol cells and approximately 99% of the departures that were reproducible in repeated measurements. This approach provides a way to define limits on the complexity of network interactions and thus may be relevant for probing the function of many neural circuits.

Collective Behavior of Place and Non-place Neurons in the Hippocampal Network.

Discussions of the hippocampus often focus on place cells, but many neurons are not place cells in any given environment. Here we describe the collective activity in such mixed populations, treating place and non-place cells on the same footing. We start with optical imaging experiments on CA1 in mice as they run along a virtual linear track and use maximum entropy methods to approximate the distribution of patterns of activity in the population, matching the correlations between pairs of cells but otherwise assuming as little structure as possible. We find that these simple models accurately predict the activity of each neuron from the state of all the other neurons in the network, regardless of how well that neuron codes for position. Our results suggest that understanding the neural activity may require not only knowledge of the external variables modulating it but also of the internal network state.

High-sensitivity rod photoreceptor input to the blue-yellow color opponent pathway in macaque retina.

Small bistratified cells (SBCs) in the primate retina carry a major blue-yellow opponent signal to the brain. We found that SBCs also carry signals from rod photoreceptors, with the same sign as S cone input. SBCs exhibited robust responses under low scotopic conditions. Physiological and anatomical experiments indicated that this rod input arose from the AII amacrine cell-mediated rod pathway. Rod and cone signals were both present in SBCs at mesopic light levels. These findings have three implications. First, more retinal circuits may multiplex rod and cone signals than were previously thought to, efficiently exploiting the limited number of optic nerve fibers. Second, signals from AII amacrine cells may diverge to most or all of the approximately 20 retinal ganglion cell types in the peripheral primate retina. Third, rod input to SBCs may be the substrate for behavioral biases toward perception of blue at mesopic light levels.