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Spike-triggered covariance: geometric proof, symmetry properties, and extension beyond Gaussian stimuli
Full text linkThe space of sensory stimuli is complex and high-dimensional. Yet, single neurons in sensory systems are typically affected by only a small subset of the vast space of all possible stimuli. A proper understanding of the input–output transformation represented by a given cell therefore requires the identification of the subset of stimuli that are relevant in shaping the neuronal response. As an extension to the commonly-used spike-triggered average, the analysis of the spike-triggered covariance matrix provides a systematic methodology to detect relevant stimuli. As originally designed, the consistency of this method is guaranteed only if stimuli are drawn from a Gaussian distribution. Here we present a geometric proof of consistency, which provides insight into the foundations of the method, in particular, into the crucial role played by the geometry of stimulus space and symmetries in the stimulus–response relation. This approach leads to a natural extension of the applicability of the spike-triggered covariance technique to arbitrary spherical or elliptic stimulus distributions. The extension only requires a subtle modification of the original prescription. Furthermore, we present a new resampling method for assessing statistical significance of identified relevant stimuli, applicable to spherical and elliptic stimulus distributions. Finally, we exemplify the modified method and compare it to other prescriptions given in the literature.Fil: Samengo, Ines. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comision Nacional de Energia Atomica. Gerencia del Area de Investigaciones y Aplicaciones no Nucleares. Gerencia de Fisica (CAB); Argentina. Comisión Nacional de Energía Atómica. Gerencia del Area de Energía Nuclear. Instituto Balseiro; ArgentinaFil: Gollisch, Tim. Universitat of Gottingen; Alemani
Nonlinear Spatial Integration Underlies the Diversity of Retinal Ganglion Cell Responses to Natural Images
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Nonlinear Spatial Integration in the Receptive Field Surround of Retinal Ganglion Cells
No full textThroughout different sensory systems, individual neurons integrate incoming signals over their receptive fields. The characteristics of this signal integration are crucial determinants for the neurons' functions. For ganglion cells in the vertebrate retina, receptive fields are characterized by the well-known center-surround structure and, although several studies have addressed spatial integration in the receptive field center, little is known about how visual signals are integrated in the surround. Therefore, we set out here to characterize signal integration and to identify relevant nonlinearities in the receptive field surround of ganglion cells in the isolated salamander retina by recording spiking activity with extracellular electrodes under visual stimulation of the center and surround. To quantify nonlinearities of spatial integration independently of subsequent nonlinearities of spike generation, we applied the technique of iso-response measurements as follows: using closed-loop experiments, we searched for different stimulus patterns in the surround that all reduced the center-evoked spiking activity by the same amount. The identified iso-response stimuli revealed strongly nonlinear spatial integration in the receptive field surrounds of all recorded cells. Furthermore, cell types that had been shown previously to have different nonlinearities in receptive field centers showed similar surround nonlinearities but differed systematically in the adaptive characteristics of the surround. Finally, we found that there is an optimal spatial scale of surround suppression; suppression was most effective when surround stimulation was organized into subregions of several hundred micrometers in diameter, indicating that the surround is composed of subunits that have strong center-surround organization themselves
Features and functions of nonlinear spatial integration by retinal ganglion cells
No full textAbstractGanglion cells in the vertebrate retina integrate visual information over their receptive fields. They do so by pooling presynaptic excitatory inputs from typically many bipolar cells, which themselves collect inputs from several photoreceptors. In addition, inhibitory interactions mediated by horizontal cells and amacrine cells modulate the structure of the receptive field. In many models, this spatial integration is assumed to occur in a linear fashion. Yet, it has long been known that spatial integration by retinal ganglion cells also incurs nonlinear phenomena. Moreover, several recent examples have shown that nonlinear spatial integration is tightly connected to specific visual functions performed by different types of retinal ganglion cells. This work discusses these advances in understanding the role of nonlinear spatial integration and reviews recent efforts to quantitatively study the nature and mechanisms underlying spatial nonlinearities. These new insights point towards a critical role of nonlinearities within ganglion cell receptive fields for capturing responses of the cells to natural and behaviorally relevant visual stimuli. In the long run, nonlinear phenomena of spatial integration may also prove important for implementing the actual neural code of retinal neurons when designing visual prostheses for the eye
Throwing a glance at the neural code: Rapid information transmission in the visual system
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