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author:("like, Alan M.")
1.  High-Degree Neurons Feed Cortical Computations 
PLoS Computational Biology  2016;12(5):e1004858.
Recent work has shown that functional connectivity among cortical neurons is highly varied, with a small percentage of neurons having many more connections than others. Also, recent theoretical developments now make it possible to quantify how neurons modify information from the connections they receive. Therefore, it is now possible to investigate how information modification, or computation, depends on the number of connections a neuron receives (in-degree) or sends out (out-degree). To do this, we recorded the simultaneous spiking activity of hundreds of neurons in cortico-hippocampal slice cultures using a high-density 512-electrode array. This preparation and recording method combination produced large numbers of neurons recorded at temporal and spatial resolutions that are not currently available in any in vivo recording system. We utilized transfer entropy (a well-established method for detecting linear and nonlinear interactions in time series) and the partial information decomposition (a powerful, recently developed tool for dissecting multivariate information processing into distinct parts) to quantify computation between neurons where information flows converged. We found that computations did not occur equally in all neurons throughout the networks. Surprisingly, neurons that computed large amounts of information tended to receive connections from high out-degree neurons. However, the in-degree of a neuron was not related to the amount of information it computed. To gain insight into these findings, we developed a simple feedforward network model. We found that a degree-modified Hebbian wiring rule best reproduced the pattern of computation and degree correlation results seen in the real data. Interestingly, this rule also maximized signal propagation in the presence of network-wide correlations, suggesting a mechanism by which cortex could deal with common random background input. These are the first results to show that the extent to which a neuron modifies incoming information streams depends on its topological location in the surrounding functional network.
Author Summary
We recorded the electrical activity of hundreds of neurons simultaneously in brain tissue from mice and we analyzed these signals using state-of-the-art tools from information theory. These tools allowed us to ascertain which neurons were transmitting information to other neurons and to characterize the computations performed by neurons using the inputs they received from two or more other neurons. We found that computations did not occur equally in all neurons throughout the networks. Surprisingly, neurons that computed large amounts of information tended to be recipients of information from neurons with a large number of outgoing connections. Interestingly, the number of incoming connections to a neuron was not related to the amount of information that neuron computed. To better understand these results, we built a network model to match the data. Unexpectedly, the model also maximized information transfer in the presence of network-wide correlations. This suggested a way that networks of cortical neurons could deal with common random background input. These results are the first to show that the amount of information computed by a neuron depends on where it is located in the surrounding network.
PMCID: PMC4861348  PMID: 27159884
2.  Rich-Club Organization in Effective Connectivity among Cortical Neurons 
The Journal of Neuroscience  2016;36(3):670-684.
The performance of complex networks, like the brain, depends on how effectively their elements communicate. Despite the importance of communication, it is virtually unknown how information is transferred in local cortical networks, consisting of hundreds of closely spaced neurons. To address this, it is important to record simultaneously from hundreds of neurons at a spacing that matches typical axonal connection distances, and at a temporal resolution that matches synaptic delays. We used a 512-electrode array (60 μm spacing) to record spontaneous activity at 20 kHz from up to 500 neurons simultaneously in slice cultures of mouse somatosensory cortex for 1 h at a time. We applied a previously validated version of transfer entropy to quantify information transfer. Similar to in vivo reports, we found an approximately lognormal distribution of firing rates. Pairwise information transfer strengths also were nearly lognormally distributed, similar to reports of synaptic strengths. Some neurons transferred and received much more information than others, which is consistent with previous predictions. Neurons with the highest outgoing and incoming information transfer were more strongly connected to each other than chance, thus forming a “rich club.” We found similar results in networks recorded in vivo from rodent cortex, suggesting the generality of these findings. A rich-club structure has been found previously in large-scale human brain networks and is thought to facilitate communication between cortical regions. The discovery of a small, but information-rich, subset of neurons within cortical regions suggests that this population will play a vital role in communication, learning, and memory.
SIGNIFICANCE STATEMENT Many studies have focused on communication networks between cortical brain regions. In contrast, very few studies have examined communication networks within a cortical region. This is the first study to combine such a large number of neurons (several hundred at a time) with such high temporal resolution (so we can know the direction of communication between neurons) for mapping networks within cortex. We found that information was not transferred equally through all neurons. Instead, ∼70% of the information passed through only 20% of the neurons. Network models suggest that this highly concentrated pattern of information transfer would be both efficient and robust to damage. Therefore, this work may help in understanding how the cortex processes information and responds to neurodegenerative diseases.
PMCID: PMC4719009  PMID: 26791200
effective connectivity; information transfer; microcircuits; rich club; transfer entropy
3.  Mapping nonlinear receptive field structure in primate retina at single cone resolution 
eLife  null;4:e05241.
The function of a neural circuit is shaped by the computations performed by its interneurons, which in many cases are not easily accessible to experimental investigation. Here, we elucidate the transformation of visual signals flowing from the input to the output of the primate retina, using a combination of large-scale multi-electrode recordings from an identified ganglion cell type, visual stimulation targeted at individual cone photoreceptors, and a hierarchical computational model. The results reveal nonlinear subunits in the circuity of OFF midget ganglion cells, which subserve high-resolution vision. The model explains light responses to a variety of stimuli more accurately than a linear model, including stimuli targeted to cones within and across subunits. The recovered model components are consistent with known anatomical organization of midget bipolar interneurons. These results reveal the spatial structure of linear and nonlinear encoding, at the resolution of single cells and at the scale of complete circuits.
eLife digest
Light that enters the eye begins the process of vision by activating two types of photoreceptors: rods, which support vision under low light levels, and cones, which are responsible for fine detail and color vision. Activation of either type of photoreceptor triggers responses in bipolar cells, which activate the ganglion cells that transmit visual signals to the brain.
Bipolar cells therefore belong to a class of cells called interneurons, which relay information from certain cell types to others. Interneurons play an important role in information processing throughout the brain, but directly accessing them or characterizing their role in neural computation is often difficult.
To address this problem, Freeman, Field et al. have developed a combined computational and experimental approach to describe the flow of sensory signals through the circuits within the retina of primates. Large arrays of electrodes were used to record the responses of many retinal ganglion cells in response to the activation or de-activation of pairs of cones. These experiments revealed that the responses of ganglion cells are not simply the sum of the inputs that they receive from cones; specifically, the activation of one cone is not cancelled by the deactivation of another. Instead, the data suggest that bipolar cells add cone inputs together and then pass on the total activation (but not deactivation) to ganglion cells.
By analyzing the responses of ganglion cells to numerous random patterns of cone activation, Freeman, Field et al. were able to estimate the locations and arrangements of bipolar cells that connect to them. These predicted patterns of connectivity agreed with observations from anatomical studies. This work provides detailed insights into how the primate retina works. It also suggests that similar approaches may be used to characterize how signals flow across other brain networks in which large-scale recordings are now possible.
PMCID: PMC4623615  PMID: 26517879
macaque; encoding models; nonlinearity; other
4.  Anatomical Identification of Extracellularly Recorded Cells in Large-Scale Multielectrode Recordings 
The Journal of Neuroscience  2015;35(11):4663-4675.
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.
PMCID: PMC4363392  PMID: 25788683
ganglion cells; immunohistochemistry; morphology; multielectrode array; retina; viral transfection
5.  High-Fidelity Reproduction of Spatiotemporal Visual Signals for Retinal Prosthesis 
Neuron  2014;83(1):87-92.
Natural vision relies on spatiotemporal patterns of electrical activity in the retina. We investigated the feasibility of veridically reproducing such patterns with epiretinal prostheses. Multielectrode recordings and visual and electrical stimulation were performed on populations of identified ganglion cells in isolated peripheral primate retina. Electrical stimulation patterns were designed to reproduce recorded waves of activity elicited by a moving visual stimulus. Electrical responses in populations of ON parasol cells exhibited high spatial and temporal precision, matching or exceeding the precision of visual responses measured in the same cells. Computational readout of electrical and visual responses produced similar estimates of stimulus speed, confirming the fidelity of electrical stimulation for biologically relevant visual signals. These results suggest the possibility of producing rich spatiotemporal patterns of retinal activity with a prosthesis and that temporal multiplexing may aid in reproducing the neural code of the retina.
PMCID: PMC4465222  PMID: 24910077
6.  Retinal representation of the elementary visual signal 
Neuron  2014;81(1):130-139.
The propagation of visual signals from individual cone photoreceptors through parallel neural circuits was examined in the primate retina. Targeted stimulation of individual cones was combined with simultaneous recording from multiple retinal ganglion cells of identified types. The visual signal initiated by an individual cone produced strong responses with different kinetics in three of the four numerically dominant ganglion cell types. The magnitude and kinetics of light responses in each ganglion cell varied nonlinearly with stimulus strength, but in a manner that was independent of the cone of origin after accounting for the overall input strength of each cone. Based on this property of independence, the receptive field profile of an individual ganglion cell could be well estimated from responses to stimulation of each cone individually. Together these findings provide a quantitative account of how elementary visual inputs form the ganglion cell receptive field.
PMCID: PMC3951785  PMID: 24411737
7.  Spatially Patterned Electrical Stimulation to Enhance Resolution of Retinal Prostheses 
The Journal of Neuroscience  2014;34(14):4871-4881.
Retinal prostheses electrically stimulate neurons to produce artificial vision in people blinded by photoreceptor degenerative diseases. The limited spatial resolution of current devices results in indiscriminate stimulation of interleaved cells of different types, precluding veridical reproduction of natural activity patterns in the retinal output. Here we investigate the use of spatial patterns of current injection to increase the spatial resolution of stimulation, using high-density multielectrode recording and stimulation of identified ganglion cells in isolated macaque retina. As previously shown, current passed through a single electrode typically induced a single retinal ganglion cell spike with submillisecond timing precision. Current passed simultaneously through pairs of neighboring electrodes modified the probability of activation relative to injection through a single electrode. This modification could be accurately summarized by a piecewise linear model of current summation, consistent with a simple biophysical model based on multiple sites of activation. The generalizability of the piecewise linear model was tested by using the measured responses to stimulation with two electrodes to predict responses to stimulation with three electrodes. Finally, the model provided an accurate prediction of which among a set of spatial stimulation patterns maximized selective activation of a cell while minimizing activation of a neighboring cell. The results demonstrate that tailored multielectrode stimulation patterns based on a piecewise linear model may be useful in increasing the spatial resolution of retinal prostheses.
PMCID: PMC3972715  PMID: 24695706
8.  A Polyaxonal Amacrine Cell Population in the Primate Retina 
The Journal of Neuroscience  2014;34(10):3597-3606.
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.
PMCID: PMC3942577  PMID: 24599459
9.  Large-Scale, High-Resolution Multielectrode-Array Recording Depicts Functional Network Differences of Cortical and Hippocampal Cultures 
PLoS ONE  2014;9(8):e105324.
Understanding the detailed circuitry of functioning neuronal networks is one of the major goals of neuroscience. Recent improvements in neuronal recording techniques have made it possible to record the spiking activity from hundreds of neurons simultaneously with sub-millisecond temporal resolution. Here we used a 512-channel multielectrode array system to record the activity from hundreds of neurons in organotypic cultures of cortico-hippocampal brain slices from mice. To probe the network structure, we employed a wavelet transform of the cross-correlogram to categorize the functional connectivity in different frequency ranges. With this method we directly compare, for the first time, in any preparation, the neuronal network structures of cortex and hippocampus, on the scale of hundreds of neurons, with sub-millisecond time resolution. Among the three frequency ranges that we investigated, the lower two frequency ranges (gamma (30–80 Hz) and beta (12–30 Hz) range) showed similar network structure between cortex and hippocampus, but there were many significant differences between these structures in the high frequency range (100–1000 Hz). The high frequency networks in cortex showed short tailed degree-distributions, shorter decay length of connectivity density, smaller clustering coefficients, and positive assortativity. Our results suggest that our method can characterize frequency dependent differences of network architecture from different brain regions. Crucially, because these differences between brain regions require millisecond temporal scales to be observed and characterized, these results underscore the importance of high temporal resolution recordings for the understanding of functional networks in neuronal systems.
PMCID: PMC4134292  PMID: 25126851
11.  Properties and application of a multichannel integrated circuit for low-artifact, patterned electrical stimulation of neural tissue 
Journal of neural engineering  2012;9(6):066005.
Modern multielectrode array (MEA) systems can record the neuronal activity from thousands of electrodes, but their ability to provide spatio-temporal patterns of electrical stimulation is very limited. Furthermore, the stimulus-related artifacts significantly limit the ability to record the neuronal responses to the stimulation. To address these issues, we designed a multichannel integrated circuit for patterned MEA-based electrical stimulation and evaluated its performance in experiments with isolated mouse and rat retina.
The Stimchip includes 64 independent stimulation channels. Each channel comprises an internal digital-to-analog converter that can be configured as a current or voltage source. The shape of the stimulation waveform is defined independently for each channel by the real-time data stream. In addition, each channel is equipped with circuitry for reduction of the stimulus artifact.
Main results
Using a high-density MEA stimulation/recording system, we effectively stimulated individual retinal ganglion cells (RGCs) and recorded the neuronal responses with minimal distortion, even on the stimulating electrodes. We independently stimulated a population of RGCs in rat retina and, using a complex spatio-temporal pattern of electrical stimulation pulses, we replicated visually-evoked spiking activity of a subset of these cells with high fidelity.
Compared with current state-of-the-art MEA systems, the Stimchip is able to stimulate neuronal cells with much more complex sequences of electrical pulses and with significantly reduced artifacts. This opens up new possibilities for studies of neuronal responses to electrical stimulation, both in the context of neuroscience research and in the development of neuroprosthetic devices.
PMCID: PMC3551622  PMID: 23160018
12.  Focal Electrical Stimulation of Major Ganglion Cell Types in the Primate Retina for the Design of Visual Prostheses 
Electrical stimulation of retinal neurons with an advanced retinal prosthesis may eventually provide high-resolution artificial vision to the blind. However, the success of future prostheses depends on the ability to activate the major parallel visual pathways of the human visual system. Electrical stimulation of the five numerically dominant retinal ganglion cell types was investigated by simultaneous stimulation and recording in isolated peripheral primate (Macaca sp.) retina using multi-electrode arrays. ON and OFF midget, ON and OFF parasol, and small bistratified ganglion cells could all be activated directly to fire a single spike with submillisecond latency using brief pulses of current within established safety limits. Thresholds for electrical stimulation were similar in all five cell types. In many cases, a single cell could be specifically activated without activating neighboring cells of the same type or other types. These findings support the feasibility of direct electrical stimulation of the major visual pathways at or near their native spatial and temporal resolution.
PMCID: PMC3735130  PMID: 23616529
13.  Modeling the impact of common noise inputs on the network activity of retinal ganglion cells 
Synchronized spontaneous firing among retinal ganglion cells (RGCs), on timescales faster than visual responses, has been reported in many studies. Two candidate mechanisms of synchronized firing include direct coupling and shared noisy inputs. In neighboring parasol cells of primate retina, which exhibit rapid synchronized firing that has been studied extensively, recent experimental work indicates that direct electrical or synaptic coupling is weak, but shared synaptic input in the absence of modulated stimuli is strong. However, previous modeling efforts have not accounted for this aspect of firing in the parasol cell population. Here we develop a new model that incorporates the effects of common noise, and apply it to analyze the light responses and synchronized firing of a large, densely-sampled network of over 250 simultaneously recorded parasol cells. We use a generalized linear model in which the spike rate in each cell is determined by the linear combination of the spatio-temporally filtered visual input, the temporally filtered prior spikes of that cell, and unobserved sources representing common noise. The model accurately captures the statistical structure of the spike trains and the encoding of the visual stimulus, without the direct coupling assumption present in previous modeling work. Finally, we examined the problem of decoding the visual stimulus from the spike train given the estimated parameters. The common-noise model produces Bayesian decoding performance as accurate as that of a model with direct coupling, but with significantly more robustness to spike timing perturbations.
PMCID: PMC3560841  PMID: 22203465
Retina; Generalized linear model; State-space model; Multielectrode; Recording; Random-effects model
14.  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.
PMCID: PMC3537829  PMID: 23152609
15.  Extending Transfer Entropy Improves Identification of Effective Connectivity in a Spiking Cortical Network Model 
PLoS ONE  2011;6(11):e27431.
Transfer entropy (TE) is an information-theoretic measure which has received recent attention in neuroscience for its potential to identify effective connectivity between neurons. Calculating TE for large ensembles of spiking neurons is computationally intensive, and has caused most investigators to probe neural interactions at only a single time delay and at a message length of only a single time bin. This is problematic, as synaptic delays between cortical neurons, for example, range from one to tens of milliseconds. In addition, neurons produce bursts of spikes spanning multiple time bins. To address these issues, here we introduce a free software package that allows TE to be measured at multiple delays and message lengths. To assess performance, we applied these extensions of TE to a spiking cortical network model (Izhikevich, 2006) with known connectivity and a range of synaptic delays. For comparison, we also investigated single-delay TE, at a message length of one bin (D1TE), and cross-correlation (CC) methods. We found that D1TE could identify 36% of true connections when evaluated at a false positive rate of 1%. For extended versions of TE, this dramatically improved to 73% of true connections. In addition, the connections correctly identified by extended versions of TE accounted for 85% of the total synaptic weight in the network. Cross correlation methods generally performed more poorly than extended TE, but were useful when data length was short. A computational performance analysis demonstrated that the algorithm for extended TE, when used on currently available desktop computers, could extract effective connectivity from 1 hr recordings containing 200 neurons in ∼5 min. We conclude that extending TE to multiple delays and message lengths improves its ability to assess effective connectivity between spiking neurons. These extensions to TE soon could become practical tools for experimentalists who record hundreds of spiking neurons.
PMCID: PMC3216957  PMID: 22102894
16.  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 an unexpected relationship between the anatomical and functional architecture in the dominant circuits of the primate retina.
PMCID: PMC3202971  PMID: 19357292
17.  Functional connectivity in the retina at the resolution of photoreceptors 
Nature  2010;467(7316):673-677.
To understand a neural circuit requires knowing its connectivity. This paper reports measurements of functional connectivity between the input and ouput layers of the retina at single cell resolution and its implications for color vision. Multi-electrode technology was employed to record simultaneously from complete populations of the retinal ganglion cell types (midget, parasol, 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 exhibited 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.
PMCID: PMC2953734  PMID: 20930838
18.  Spatial-Temporal Patterns of Retinal Waves Underlying Activity-Dependent Refinement of Retinofugal Projections 
Neuron  2009;64(2):200-212.
During development, retinal axons project coarsely within their central visual targets before refining to form precisely organized synaptic connections. Spontaneous retinal activity, in the form of acetylcholine-driven retinal waves, is widely proposed to be necessary for establishing these precise projection patterns. In particular, both axonal terminations of retinal ganglion cells (RGCs) and the size of receptive fields of neurons in visual areas of the brain are larger in mice that lack the β2 subunit of the nicotinic acetylcholine receptor (β2KO). Here, using a large-scale, high-density multi-electrode array to record single-unit activity from hundreds of RGCs simultaneously, we present analysis of early post-natal retinal activity from both wild type (WT) and β2KO retinas. We find that β2KO retinas have correlated patterns of activity, but many aspects of these patterns differ from those of WT retina. Quantitative analysis of these differences suggests that wave directionality, coupled with short-distance correlated bursting patterns of RGCs, work together to drive refinement of retinofugal projections.
PMCID: PMC2771121  PMID: 19874788
19.  High sensitivity rod photoreceptor input to the blue-yellow color opponent pathway in macaque retina 
Nature neuroscience  2009;12(9):1159-1164.
Small bistratified cells (SBCs) in the primate retina carry a major blue-yellow opponent signal to the brain. Here we show that SBCs also carry signals from rod photoreceptors, with the same sign as S cone input. SBCs exhibited robust responses under low scotopic conditions (<0.01 P*/rod/s). 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. We discuss three implications of these findings. First, more retinal circuits than previously thought may multiplex rod and cone signals, efficiently exploiting the limited number of optic nerve fibers. Second, signals from AII amacrine cells may diverge to most or all of the <20 RGC 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.
PMCID: PMC2789108  PMID: 19668201
20.  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 ~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.
PMCID: PMC2678680  PMID: 19369571
Retinal Ganglion Cell; Synchrony; Information Theory; Sensory Neurons; Network; Correlated variability
21.  Direction selectivity in the retina is established independent of visual experience and early cholinergic retinal waves 
Neuron  2008;58(4):499-506.
Direction-selectivity in the retina requires the asymmetric wiring of inhibitory inputs onto four subtypes of On-Off direction selective ganglion cells (DSGCs), each preferring motion in one of four cardinal directions. The primary model for the development of direction selectivity is that patterned activity plays an instructive role. Here we use a unique, large scale multielectrode array to demonstrate that DSGCs are present at eye-opening, in mice that have been reared in darkness, and in mice that lack cholinergic retinal waves. These data suggest that direction selectivity in the retina is established largely independent of patterned activity, and is therefore likely to emerge as a result of complex molecular interactions.
PMCID: PMC2474739  PMID: 18498732
22.  Spatio-temporal correlations and visual signalling in a complete neuronal population 
Nature  2008;454(7207):995-999.
Statistical dependencies in the responses of sensory neurons govern both the amount of stimulus information conveyed and the means by which downstream neurons can extract it. Although a variety of measurements indicate the existence of such dependencies1–3, their origin and importance for neural coding are poorly understood. Here we analyse the functional significance of correlated firing in a complete population of macaque parasol retinal ganglion cells using a model of multi-neuron spike responses4,5. The model, with parameters fit directly to physiological data, simultaneously captures both the stimulus dependence and detailed spatio-temporal correlations in population responses, and provides two insights into the structure of the neural code. First, neural encoding at the population level is less noisy than one would expect from the variability of individual neurons: spike times are more precise, and can be predicted more accurately when the spiking of neighbouring neurons is taken into account. Second, correlations provide additional sensory information: optimal, model-based decoding that exploits the response correlation structure extracts 20% more information about the visual scene than decoding under the assumption of independence, and preserves 40% more visual information than optimal linear decoding6. This model-based approach reveals the role of correlated activity in the retinal coding of visual stimuli, and provides a general framework for understanding the importance of correlated activity in populations of neurons.
PMCID: PMC2684455  PMID: 18650810
23.  Receptive Fields in Primate Retina Are Coordinated to Sample Visual Space More Uniformly 
PLoS Biology  2009;7(4):e1000063.
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°, 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.
Author Summary
All visual information reaching the brain is transmitted by retinal ganglion cells, each of which is sensitive to a small region of space known as its receptive field. Each of the 20 or so distinct ganglion cell types is thought to transmit a complete visual image to the brain, because the receptive fields of each type form a regular lattice covering visual space. However, within each regular lattice, individual receptive fields have jagged, asymmetric shapes, which could produce “blind spots” and excessive overlap, degrading the visual image. To understand how the visual system overcomes this problem, we used a multielectrode array to record from hundreds of ganglion cells in isolated patches of peripheral primate retina. Surprisingly, we found that irregularly shaped receptive fields fit together like puzzle pieces, with high spatial precision, producing a more homogeneous coverage of visual space than would be possible otherwise. This finding reveals that the representation of visual space by neural ensembles in the retina is functionally coordinated and tuned, presumably by developmental interactions or ongoing visual activity, producing a more precise sensory signal.
Receptive fields in primate retina have irregular shapes, but they interlock like puzzle pieces to provide highly uniform coverage of visual space.
PMCID: PMC2672597  PMID: 19355787

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