Adaptation of the simple or complex nature of V1 receptive fields to visual statistics

Journal name:
Nature Neuroscience
Volume:
14,
Pages:
1053–1060
Year published:
DOI:
doi:10.1038/nn.2861
Received
Accepted
Published online

Abstract

Receptive fields in primary visual cortex (V1) are categorized as simple or complex, depending on their spatial selectivity to stimulus contrast polarity. We studied the dependence of this classification on visual context by comparing, in the same cell, the synaptic responses to three classical receptive field mapping protocols: sparse noise, ternary dense noise and flashed Gabor noise. Intracellular recordings revealed that the relative weights of simple-like and complex-like receptive field components were scaled so as to make the same receptive field more simple-like with dense noise stimulation and more complex-like with sparse or Gabor noise stimulations. However, once these context-dependent receptive fields were convolved with the corresponding stimulus, the balance between simple-like and complex-like contributions to the synaptic responses appeared to be invariant across input statistics. This normalization of the linear/nonlinear input ratio suggests a previously unknown form of homeostatic control of V1 functional properties, optimizing the network nonlinearities to the statistical structure of the visual input.

At a glance

Figures

  1. White-noise stimuli and second-order Volterra receptive field decomposition.
    Figure 1: White-noise stimuli and second-order Volterra receptive field decomposition.

    (a) Example of single-trial intracellular responses evoked in the same cell (cell 1) by sparse (SN, black), dense (DN, red) and Gabor noise (GBN, gray) stimuli. The visual stimulation period is indicated by the horizontal black line. Spike amplitudes have been cut off at −30 mV to facilitate the comparison between Vm fluctuation dynamics. (b) First- and second-order Volterra kernels were estimated using a least-squares method. In this decomposition, the h1st kernel linearly filters the stimulus contrast variations and can be considered to be the simple-like part of the receptive field in the strict sense. In contrast, the second-order diagonal h2Diag corresponds to the projection of the second-order receptive field nonlinearities in the first-order stimulus space, pooling receptive field components independent of the contrast sign, and can be considered as the complex-like part of the receptive field. The feature selectivity underlying this h2Diag complex-like component is provided by the off-diagonal terms of the second-order kernel h2nd. (c) Probability of stimulation (P(stim)) of the second-order kernel by sparse noise (left, 10 × 10 stimulation grid) and dense noise (right). In contrast with dense noise stimuli, pixels are activated one at a time in sparse noise condition. Consequently, off-diagonal components of the second-order kernel are barely stimulated by sparse noise compared to the diagonal elements, making their estimation irrelevant in sparse stimulation contexts.

  2. Stimulus dependence of simple-like and complex-like receptive field components.
    Figure 2: Stimulus dependence of simple-like and complex-like receptive field components.

    (a) First-order kernel (left column, simple-like, h1st) and second-order diagonal kernel (right column, complex-like, h2Diag) of subthreshold (Vm) and spiking (spikes) receptive field estimates for a typical V1 cell (cell 1). Kernels are depicted as spatial (X, Y) and two-dimensional spatiotemporal (Y, time (t)) z-scored maps. The X,Y spatial maps are shown for the lag time corresponding to their maximal spatial extent (indicated by the vertical black line in Y,t spatiotemporal profiles). The thin gray lines show the pixel size used for sparse and dense noise. (b) Examples of elementary responses corresponding to positions indicated in the inset, overlaid over the shaded responsive area. Note the differences of scale between sparse (black) and dense noise (red) waveforms, reflecting a divisive gain control of both simple-like and complex-like receptive field components when switching from sparse to dense visual stimulation. (c,d) Data are presented as in a,b for another example cell (cell 2).

  3. Receptive field Simpleness and gain control of simple-like and complex-like receptive field components.
    Figure 3: Receptive field Simpleness and gain control of simple-like and complex-like receptive field components.

    (a,b) Comparison over the population of recorded cells of the SI measured from synaptic (a) or spiking (b) receptive field estimates between sparse and dense noise conditions. All points lie above the identity line, indicating that all receptive fields underwent a systematic change in the balance between simple-like and complex-like receptive field components such that they appeared to be more simple in dense than in sparse noise conditions. The data points corresponding to the example cells (shown in Fig. 2) have been circled. (c,d) Comparison between the gainSN/DN measured for complex-like (h2Diag gainSN/DN) and simple-like (h1st gainSN/DN) receptive field components, at the subthreshold (c) and spiking (d) levels. The gain factors affecting the complex-like components were systematically higher and appeared to be linearly related to the amplitude of the gain controls measured from the first-order component h1st, except for two outliers (gray symbols) (blue regression lines; Vm: slope = +3.53, r2 = 0.98, P << 0.01, n = 30; spikes: slope = +1.81, r2 = 0.90, P << 0.01, n = 11). The vertical dotted line indicates the value that we would expect from perfectly adapting linear receptive field components; h1st gainSN/DN would correspond to the ratio of sparse and dense noise s.d. of luminance values (~8.16, see Online Methods).

  4. Spatiotemporal reconfiguration of simple-like and complex-like receptive field components.
    Figure 4: Spatiotemporal reconfiguration of simple-like and complex-like receptive field components.

    (a) Comparison between dense noise and sparse noise conditions of the maximal spatial extents of significant responses measured in simple-like (h1st, top) and complex-like (h2Diag, bottom) receptive field components (units, visual degree of apparent diameter). Although simple-like receptive field components appeared to be significantly larger in the dense noise than in the sparse noise condition (paired Student's t test, P < 0.01), the complex-like receptive field components were significantly smaller (paired Student's t test, P << 0.01). (b) Comparison of onset latencies of simple-like (h1st, top) or complex-like (h2Diag, bottom) receptive field components between dense noise and sparse noise conditions. (c) Comparison of peak latencies of simple-like (h1st, top) or complex-like (h2Diag, bottom) receptive field components between dense noise and sparse noise conditions.

  5. V1 receptive field simpleness adapts to visual statistics.
    Figure 5: V1 receptive field simpleness adapts to visual statistics.

    (a) In each stimulus condition, the simpleness was measured in two ways: by the SI, which compares the relative power of the simple-like (h1st) and complex-like (h2Diag) components of receptive field estimates (RF, middle), and by the SI*, which measures the balance between simple-like and complex-like synaptic contributions once the stimulus-dependent receptive fields have been convolved with the corresponding stimulus sequences (RF * Stim, right). In sparse stimulation conditions, as the pixels are activated one at a time, the nonlinear contributions conveyed by the off-diagonal terms of the h2nd kernel have barely any weight in the response, and the output of the h2Diag filter provides an almost complete estimate of the complex-like synaptic contributions. In contrast, in the dense noise condition, as multiple pixels are activated at the same time, the dynamics of the evoked complex-like response also relies on the selectivity of the h2Diag receptive field components to the spatiotemporal patterns that are presented. We thus computed the convolution of the stimulus with the full second-order kernel estimate h2nd to reconstruct the complex-like synaptic contributions evoked by dense noise stimuli. (b) Comparison of SI values between sparse and dense noise conditions. Left, graph shown in Figure 3a. Right, comparison of SI* values. Note that over the population the SI* values are much more aligned along the identity line than the SI values. (c) Data are presented as in b for the comparison of the Gabor noise and dense noise conditions.

  6. Simpleness in non-adaptive receptive field models.
    Figure 6: Simpleness in non-adaptive receptive field models.

    (a) Parallel LN cascade receptive field architecture in which linear filter outputs corresponding to different stimulus feature selectivities are passed through a second-order polynomial nonlinearity (one linear branch and several quadratic branches). In this model architecture, the linear component provides simple-like contributions, whereas the quadratic components contribute in a complex-like manner to the cell response. By keeping the same receptive field structure while imposing the relative weights of these two types of afferent components, we simulated a set of receptive fields, each expressing a fixed degree of simpleness, and simulated their responses to sparse noise, Gabor noise and dense noise stimulus sequences. (b) Left, comparison of the SI between sparse and dense noise conditions when considering the receptive fields estimated from the responses of the non-adaptive model depicted in a. Right, comparison of the SI* (measured directly from the receptive field model outputs) between sparse and dense noise conditions. (c) Data are presented as in b for the comparison of the Gabor noise and dense noise conditions.

  7. Simpleness in gain control receptive field models.
    Figure 7: Simpleness in gain control receptive field models.

    (a) Differential gain control model. The adaptation of V1 receptive field simpleness can be explained by adding two separate gain control processes (α and β) to the receptive field models depicted in Figure 6a. These processes respectively divide simple-like and complex-like receptive field components when switching from sparse to dense noise. (b) Shown is the graph depicted in Figure 5b. (c) Shown is the graph depicted in Figure 3c. The colors of the symbols correspond to three different ranges of value for the SI values measured in the sparse noise condition. (d) Post-NL gain control model (GC1). A gain control process γ acts post-NL and normalizes the variance of the evoked response across stimulus conditions. (e) SI (left) and SI* (right) measured from GC1 receptive field model responses in sparse and dense noise conditions. (f) GainSN/DN measured from the h1st and h2Diag kernels estimated from the GC1 receptive field responses. Dark and light colors of the symbols indicate low and high values of γ, respectively. (g) Pre-NL gain control model (GC2). A gain control process g acts pre-NL and results in a division of linear filter outputs by g when switching from sparse noise to dense noise, independently of the receptive field simpleness. (h) SI (left) and SI* (right) measured from GC2 receptive field model responses in sparse and dense noise conditions. (i) GainSN/DN measured from the h1st and h2Diag kernels estimated from the GC2 receptive field responses. The purple curve indicates the quadratic relationship. Dark and light colors of the symbols indicate low and high values of g, respectively. g* corresponds to the value for which we observed a complete adaptation of the receptive field simpleness between sparse noise and dense noise conditions (SI*DN = SI*SN). (j) Hybrid gain control model (GC3), a combination of the GC1 and GC2 models (with g = g*). (k) SI (left) and SI* (right) measured from GC3 model responses in sparse and dense noise conditions. (l) GainSN/DN measured from the h1st and h2Diag kernels estimated from the GC3 responses. The slope of the regression line (blue) corresponds to g*. Note that this model is mathematically equivalent to the differential gain control model (a) considering α = g* × γ and β = g*2 × γ. Dark and light colors of the symbols indicate low and high values of γ, respectively.

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Affiliations

  1. Unité de Neuroscience, Information et Complexité (CNRS-UNIC), UPR CNRS 3293, Gif-sur-Yvette, France.

    • Julien Fournier,
    • Cyril Monier,
    • Marc Pananceau &
    • Yves Frégnac
  2. Université Paris-Sud, Orsay, France.

    • Marc Pananceau

Contributions

The study was conceived by J.F., C.M. and Y.F. The experiments were performed by J.F., C.M. and M.P. J.F. performed the data analysis and model simulations. J.F., C.M. and Y.F. wrote the paper.

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The authors declare no competing financial interests.

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