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      Orientation Selectivity in Inhibition-Dominated Networks of Spiking Neurons: Effect of Single Neuron Properties and Network Dynamics

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      PLoS Computational Biology
      Public Library of Science

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          Abstract

          The neuronal mechanisms underlying the emergence of orientation selectivity in the primary visual cortex of mammals are still elusive. In rodents, visual neurons show highly selective responses to oriented stimuli, but neighboring neurons do not necessarily have similar preferences. Instead of a smooth map, one observes a salt-and-pepper organization of orientation selectivity. Modeling studies have recently confirmed that balanced random networks are indeed capable of amplifying weakly tuned inputs and generating highly selective output responses, even in absence of feature-selective recurrent connectivity. Here we seek to elucidate the neuronal mechanisms underlying this phenomenon by resorting to networks of integrate-and-fire neurons, which are amenable to analytic treatment. Specifically, in networks of perfect integrate-and-fire neurons, we observe that highly selective and contrast invariant output responses emerge, very similar to networks of leaky integrate-and-fire neurons. We then demonstrate that a theory based on mean firing rates and the detailed network topology predicts the output responses, and explains the mechanisms underlying the suppression of the common-mode, amplification of modulation, and contrast invariance. Increasing inhibition dominance in our networks makes the rectifying nonlinearity more prominent, which in turn adds some distortions to the otherwise essentially linear prediction. An extension of the linear theory can account for all the distortions, enabling us to compute the exact shape of every individual tuning curve in our networks. We show that this simple form of nonlinearity adds two important properties to orientation selectivity in the network, namely sharpening of tuning curves and extra suppression of the modulation. The theory can be further extended to account for the nonlinearity of the leaky model by replacing the rectifier by the appropriate smooth input-output transfer function. These results are robust and do not depend on the state of network dynamics, and hold equally well for mean-driven and fluctuation-driven regimes of activity.

          Author Summary

          It is not yet fully clear how sensory information is being processed when it arrives in primary cortical areas. We studied this general question in the context of rodent vision. We focused on the example of orientation selectivity, namely the selectivity of cortical neurons for specific orientations of an elongated stimulus. Our results show that a large body of experimental findings regarding the basic computations performed in early sensory processing can already be explained by linear processing of firing rates in neuronal networks with realistic parameters. The distribution of selectivity in our networks, as well as the exact shape of output tuning curves, including all details and inhomogeneities of structure and function, can be computed from the known connectivity matrix of the network and the known gain function of single neurons. A simple but essential form of nonlinearity, namely rectification of firing rates, accounts for sharpening of tuning curves and leads to some normalization of output modulation, even in networks without feature-specific connectivity. Our results and analyses demonstrate that none of these functional properties depend crucially on a fluctuation-driven or a mean-driven regime of activity, and that synchronous and asynchronous states of network dynamics can equally well serve these functions.

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          Most cited references32

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          Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons.

          N Brunel (2000)
          The dynamics of networks of sparsely connected excitatory and inhibitory integrate-and-fire neurons are studied analytically. The analysis reveals a rich repertoire of states, including synchronous states in which neurons fire regularly; asynchronous states with stationary global activity and very irregular individual cell activity; and states in which the global activity oscillates but individual cells fire irregularly, typically at rates lower than the global oscillation frequency. The network can switch between these states, provided the external frequency, or the balance between excitation and inhibition, is varied. Two types of network oscillations are observed. In the fast oscillatory state, the network frequency is almost fully controlled by the synaptic time scale. In the slow oscillatory state, the network frequency depends mostly on the membrane time constant. Finite size effects in the asynchronous state are also discussed.
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            Receptive fields and functional architecture of monkey striate cortex.

            1. The striate cortex was studied in lightly anaesthetized macaque and spider monkeys by recording extracellularly from single units and stimulating the retinas with spots or patterns of light. Most cells can be categorized as simple, complex, or hypercomplex, with response properties very similar to those previously described in the cat. On the average, however, receptive fields are smaller, and there is a greater sensitivity to changes in stimulus orientation. A small proportion of the cells are colour coded.2. Evidence is presented for at least two independent systems of columns extending vertically from surface to white matter. Columns of the first type contain cells with common receptive-field orientations. They are similar to the orientation columns described in the cat, but are probably smaller in cross-sectional area. In the second system cells are aggregated into columns according to eye preference. The ocular dominance columns are larger than the orientation columns, and the two sets of boundaries seem to be independent.3. There is a tendency for cells to be grouped according to symmetry of responses to movement; in some regions the cells respond equally well to the two opposite directions of movement of a line, but other regions contain a mixture of cells favouring one direction and cells favouring the other.4. A horizontal organization corresponding to the cortical layering can also be discerned. The upper layers (II and the upper two-thirds of III) contain complex and hypercomplex cells, but simple cells are virtually absent. The cells are mostly binocularly driven. Simple cells are found deep in layer III, and in IV A and IV B. In layer IV B they form a large proportion of the population, whereas complex cells are rare. In layers IV A and IV B one finds units lacking orientation specificity; it is not clear whether these are cell bodies or axons of geniculate cells. In layer IV most cells are driven by one eye only; this layer consists of a mosaic with cells of some regions responding to one eye only, those of other regions responding to the other eye. Layers V and VI contain mostly complex and hypercomplex cells, binocularly driven.5. The cortex is seen as a system organized vertically and horizontally in entirely different ways. In the vertical system (in which cells lying along a vertical line in the cortex have common features) stimulus dimensions such as retinal position, line orientation, ocular dominance, and perhaps directionality of movement, are mapped in sets of superimposed but independent mosaics. The horizontal system segregates cells in layers by hierarchical orders, the lowest orders (simple cells monocularly driven) located in and near layer IV, the higher orders in the upper and lower layers.
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              Highly selective receptive fields in mouse visual cortex.

              Genetic methods available in mice are likely to be powerful tools in dissecting cortical circuits. However, the visual cortex, in which sensory coding has been most thoroughly studied in other species, has essentially been neglected in mice perhaps because of their poor spatial acuity and the lack of columnar organization such as orientation maps. We have now applied quantitative methods to characterize visual receptive fields in mouse primary visual cortex V1 by making extracellular recordings with silicon electrode arrays in anesthetized mice. We used current source density analysis to determine laminar location and spike waveforms to discriminate putative excitatory and inhibitory units. We find that, although the spatial scale of mouse receptive fields is up to one or two orders of magnitude larger, neurons show selectivity for stimulus parameters such as orientation and spatial frequency that is near to that found in other species. Furthermore, typical response properties such as linear versus nonlinear spatial summation (i.e., simple and complex cells) and contrast-invariant tuning are also present in mouse V1 and correlate with laminar position and cell type. Interestingly, we find that putative inhibitory neurons generally have less selective, and nonlinear, responses. This quantitative description of receptive field properties should facilitate the use of mouse visual cortex as a system to address longstanding questions of visual neuroscience and cortical processing.
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                Author and article information

                Contributors
                Role: Editor
                Journal
                PLoS Comput Biol
                PLoS Comput. Biol
                plos
                ploscomp
                PLoS Computational Biology
                Public Library of Science (San Francisco, USA )
                1553-734X
                1553-7358
                January 2015
                8 January 2015
                : 11
                : 1
                : e1004045
                Affiliations
                [1]Bernstein Center Freiberg & Faculty of Biology, University of Freiberg, Freiberg, Germany
                Université Paris Descartes, Centre National de la Recherche Scientifique, France
                Author notes

                The authors have declared that no competing interests exist.

                Conceived and designed the experiments: SS SR. Performed the experiments: SS. Analyzed the data: SS. Contributed reagents/materials/analysis tools: SS SR. Wrote the paper: SS SR.

                Article
                PCOMPBIOL-D-14-01594
                10.1371/journal.pcbi.1004045
                4287576
                25569445
                b91f807b-3b76-48f6-b5a0-1645a9782c11
                Copyright @ 2015

                This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                History
                : 29 August 2014
                : 14 November 2014
                Page count
                Pages: 17
                Funding
                Funding by the German Ministry of Education and Research (BMBF, grant BFNT 01GQ0830) and the German Research Foundation (DFG, grant EXC 1086) is gratefully acknowledged. The article processing charge was covered by the open access publication fund of the University of Freiburg. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
                Categories
                Research Article
                Biology and Life Sciences
                Computational Biology
                Computational Neuroscience
                Coding Mechanisms
                Neuroscience
                Sensory Systems
                Visual System
                Neuronal Tuning
                Custom metadata
                The authors confirm that all data underlying the findings are fully available without restriction. All relevant data are within the paper and its Supporting Information files.

                Quantitative & Systems biology
                Quantitative & Systems biology

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