The suppressive field of neurons in lateral geniculate nucleus

Abstract

The responses of neurons in lateral geniculate nucleus (LGN) exhibit powerful suppressive phenomena such as contrast saturation, size tuning, and masking. These phenomena cannot be explained by the classical center-surround receptive field and have been ascribed to a variety of mechanisms, including feedback from cortex. We asked whether these phenomena might all be explained by a single mechanism, contrast gain control, which is inherited from retina and possibly strengthened in thalamus. We formalized an intuitive model of retinal contrast gain control that explicitly predicts gain as a function of local contrast. In the model, the output of the receptive field is divided by the output of a suppressive field, which computes the local root-mean-square contrast. The model provides good fits to LGN responses to a variety of stimuli; with a single set of parameters, it captures saturation, size tuning, and masking. It also correctly predicts that responses to small stimuli grow proportionally with contrast: were it not for the suppressive field, LGN responses would be linear. We characterized the suppressive field and found that it is similar in size to the surround of the classical receptive field (which is eight times larger than commonly estimated), it is not selective for stimulus orientation, and it responds to a wide range of frequencies, including very low spatial frequencies and high temporal frequencies. The latter property is hardly consistent with feedback from cortex. These measurements thoroughly describe the visual properties of contrast gain control in LGN and provide a parsimonious explanation for disparate suppressive phenomena.

Figure 1.

Model of LGN responses. The model includes a receptive field and a suppressive field. The receptive field has the classical center-surround organization (difference-of-Gaussians). The suppressive field computes the SD of the outputs of a Gaussian-weighted bank of filters (FB) and sums the result to a constant, c₅₀. The signals from receptive field and suppressive field meet at a divisive stage. The output of the division is then rectified to yield positive firing rates.

Figure 2.

Masking experiments. Solid curves are firing rate responses of an example neuron. Dotted curves are predictions of receptive field followed by rectification. A, Responses to test grating presented alone. B, Same, but showing amplitude spectrum of responses. C, D, Measured and predicted responses to mask alone. E, F, Measured and predicted responses to sum of test and mask. Calibration bars in A and B indicate 50 spikes/s. Cell 44.4.2.

Figure 3.

Masking. Stimuli are sums of a test grating and a mask grating drifting with incommensurate temporal frequencies. Responses are measured at the frequency of the test, 7.8 Hz (test response; A-C) and at the frequency of the mask, 12.5 Hz (mask response; D, F). Unless otherwise stated, in this figure and in subsequent ones, the error bars indicate ±1 SD. Curves show model fit. Dashed lines indicate predictions of receptive field followed by rectification. A, D, Responses as function of mask contrast (V_max = 273; V₀ = -6). B, E, Responses as function of mask diameter (V_max = 242; V₀ = -6). C, F, Responses as function of mask spatial frequency (V_max = 275; V₀ = -4). Test and mask had spatial frequency of 0.24 cycles/deg (unless varied) and diameter of 1.4° and 14.1° (unless varied). Cell 33.1.3.

Figure 4.

Reliability of four estimated model parameters. To gauge the confidence with which the fits yield model parameters, we estimated fit quality while imposing a range of values on the parameter of interest. The overall responsiveness V_max was allowed to vary to yield the best fit. The other parameters were held at their optimal values, and, as usual, the resting potential V₀ was fixed based on the resting firing rate in each experiment. The results are shown for four key model parameters, for the example cell of Figures 3 and 5. A, Reliability of estimates for the width of the receptive field surround, σ_srd, which is obtained by varying grating spatial frequency (Fig. 8A). B, Reliability of estimates for the strength of suppressive field c₅₀, which is obtained by varying mask contrast (Fig. 3A). C, Reliability of estimates for the width of the suppressive field σ_SF, which is obtained by varying mask diameter (Fig. 3B). D, Reliability of estimates for the strength of the surround of the subunits that compose the suppressive field, k_d. This value is obtained by varying mask spatial frequency (Fig. 8B). Any value <0.8 would be approximately equally good at fitting those responses.

Figure 5.

Size tuning and contrast saturation. Stimuli are gratings varying in diameter and contrast. Curves are predictions of model with parameters held fixed from previous measurements (Fig. 3; V_max = 128; V₀ = -2). A, Responses as a function of diameter, for selected contrasts. B, Same data, plotted as a function of contrast, for selected diameters. Stimuli had optimal attributes: 0.24 cycles/deg and 7.8 Hz. Cell 33.1.3 (93.9% explained variance).

Figure 6.

Size tuning and contrast saturation in five additional cells. Details as in Figure 5. Gray areas indicate spontaneous response ± 1 SD. A, Responses as a function of diameter, shown here for two contrasts: the lowest one eliciting a reliable response (black), 40% (gray), and 100% (white). B, Responses expressed as a function of contrast, shown here for three diameters: the smallest diameter eliciting a reliable response (black), the optimal diameter (gray), and the largest diameter tested (white). Dotted lines indicate selected contrasts and diameters. Top to bottom, Cells 33.3.4 (OFF/X, 98.5% explained variance), 28.2.5 (ON/X, 91.8%), 31.3.3 (OFF/X, 98.7%), 35.3.3 (OFF/X, 93.7%), and 31.2.2 (OFF/Y, 93.3%).

Figure 7.

Spatial extent of receptive field and suppressive field. A, Comparison of extent of suppressive field and receptive field center obtained from model fits. Dashed line indicates linear regression. B, Same, for receptive field surround. C, Control measurements of spatial extent of receptive field surround and suppressive field. Filled symbols indicate responses to disks containing drifting gratings. Open symbols indicate responses to annuli containing a uniform field whose contrast is modulated in time. Arrows indicate estimated extents of receptive field surround (RF) and suppressive field (SF). Responses averaged across cells. We normalized the abscissa and the ordinate of each curve so that the size tuning curves peak at 1 with a value of 1. Error bars (invisible because smaller than symbols) indicate ± 1 SE (n = 15).

Figure 8.

Visual preferences of receptive field and suppressive field. A, Response of receptive field as function of spatial frequency. Curve is average across cells. Shaded areas indicate response scatter (±1 SD). The tuning of each cell was rescaled along the x-axis so that high-frequency cutoff of receptive field response equals 1. B, Same, for responses of suppressive field. C, Response of receptive field as function of temporal frequency. Dashed curve is average responses of LGN cells to single grating varying in temporal frequency. D, Same, for responses of suppressive field. E, F, Same, for responses as function of orientation. Responses were aligned so that maximum receptive field response is centered on 0°.