Multiplexed computations in retinal ganglion cells of a single type

In the early visual system, cells of the same type perform the same computation in different places of the visual field. How these cells code together a complex visual scene is unclear. A common assumption is that cells of a single-type extract a single-stimulus feature to form a feature map, but this has rarely been observed directly. Using large-scale recordings in the rat retina, we show that a homogeneous population of fast OFF ganglion cells simultaneously encodes two radically different features of a visual scene. Cells close to a moving object code quasilinearly for its position, while distant cells remain largely invariant to the object’s position and, instead, respond nonlinearly to changes in the object’s speed. We develop a quantitative model that accounts for this effect and identify a disinhibitory circuit that mediates it. Ganglion cells of a single type thus do not code for one, but two features simultaneously. This richer, flexible neural map might also be present in other sensory systems.

To test the generality of our model, we displayed a randomly moving texture composed of a random alter-7 nation of black and white bars over half of the visual field (see methods). Ganglion cells with their receptive 8 field inside this half responded to the texture in a way that could be predicted by a LN model (supp. fig.   9 3A). However, cells far from the texture could not be predicted well (supp. fig. 3B). A subunit model similar 10 to the one used for the moving bar (with slight differences for the subunit filters and non-linearities, see 11 methods) could predict well these distant responses (supp. fig. 3C). This model architecture is therefore 12 able to predict the responses to stimuli more complex than a bar. Response (PSTH, black) of a ganglion cell whose receptive field center is stimulated by the texture, is predicted by the LN model (blue). r = 0.87. B: Response (PSTH, black) of the same ganglion cell when the texture is far from the receptive field center, is not predicted well by the LN model (blue). r = 0.04. C: Response (PSTH, black) of the same ganglion cell (as in B and C) to distant stimulation is predicted well by the subunit model (red). r = 0.76. D: Performance of the LN (blue) and subunit (red) models in predicting ganglion cell responses, as a function of the distance of the cell to texture border. Negative distances correspond to cells whose receptive field center is covered by the texture, while positive values correspond to the ones that are not covered by the texture. Note that here, in contrast with the case of the randomly moving bar, the performance of the subunit model decreased for central cells. This is because the subunit non-linearity employed here (see methods) did not allow this model to approximate a quasilinear behaviour with a combination of subunits. signal. This signal is then passed through the non-linearity to predict the firing rate. In this hypothesis, 23 the response to the distant bar is suppressed because, at the same time, the central bar triggers a negative 24 signal that cancels the activation due to the distant bar. We tested if this model of a linear summation of 25 inputs followed by a global nonlinearity could predict the responses to the two bars, and found that it did 26 not perform well at predicting the response to the two bars displayed simultaneously, compared to a model 27 fitted directly on the responses to the two bars (supp. fig. 6D). Moreover, it largely underestimated the 28 suppression index (see Eqs.12-13 in methods and supp. fig. 6E). We found similar results for the responses 29 to the texture (supp. fig. 6A,B,C).

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In particular, a consequence of this linear summation hypothesis is that a spiking response triggered by stimuli were presented simultaneously (supp. fig. 6A). To quantify this we measured the suppression index 37 only during periods where there was a minimal amount of spiking activity triggered by the central stimulus.

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We found that there was still a high suppression index in that case (supp. fig. 6F). We concluded that the 39 linear summation model could not account for the observed suppression. 40 We show here that the suppression index is mostly independent of the firing rate. Note that this  Figure 6: A: Response raster of a single cell to a randomly moving texture presented in and/or outside of its receptive field center. Each dot is a single spike from the recorded cell. Each line corresponds to a different repetition of the same stimulus. i: texture moving inside the receptive field center. ii: texture moving outside the receptive field center. iii: both textures displayed together. Red ellipses indicate examples where the response to the distant texture is strongly suppressed by the stimulus inside the receptive field center, while there was a moderate spiking response to the central texture alone. B: Performance of two models in predicting the responses to the two randomly moving textures. In the suppressive model, the model is fitted on the responses to the two textures. In the additive model, the prediction signal (before the last non-linearity) from the model fitted to the central texture responses, and the prediction from the model fitted to the distant texture responses, are summed and then passed through the non-linearity. Data are represented as mean ± SEM (n=12). Performance is significantly lower for the additive model (The three stars indicate that the p-value of a paired-sample t-test was lower than 0.001). C: Suppression index estimated on the data, or on the additive model described in B. Performance is significantly lower for the additive model (p ≤ 10 −3 , paired-sample t-test). Data are represented as mean ± SEM (n=12). D: Same as B, but for the bar stimuli (p ≤ 10 −3 , paired-sample t-test). E: Same as C, but for the bar stimuli (p ≤ 10 −3 , paired-sample t-test). F: Suppression index for the data and due to noise (see methods) estimated on cells responding to the texture stimuli, taking into account only the time bins with an average firing rate in response to the central texture above a threshold firing rate (x-axis). Data are represented as mean ± SEM.
absolute position 48 Our results show that cells close to the bar were much more sensitive to the bar position than distant cells.

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Here we show that the subunit model fitted on the cell responses also had this property. For this we directly 50 used our model to estimate the amount of information about a change in the absolute position of the bar 51 trajectory.

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To determine the sensitivity of each cell to a change in the absolute position we estimated the Kullback-

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Leibler divergence d KL (∆x) between the cell response to an initial trajectory x(t), and the response to the  To estimate d KL (∆x) we assumed that ∆x is small, so that we can expand the Kullback-Leibler divergence 61 up to the second order to obtain: where the matrix I t,t is the Fisher Information Matrix of the response distribution conditioned to the 63 stimulus: where x(t) is the position at time t and r(τ ) is the firing rate at time τ predicted by the subunit model in response to the stimulus. L = 0.5 s corresponds to the maximal latency of the response to the stimulus. 66 We then defined the sensitivity as d KL (∆x) for a normalized perturbation such that t ∆x(t) 2 = 1. We

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For cells close to the bar, sensitivity to changes in the absolute position of the bar was high and strongly 70 decreased for distant cells (supp. fig. 6A). We then asked if this decrease is specific to this uniform perturba-71 tion, or if it is a global decrease of sensitivity of distant cells to any perturbation. To test this we estimated 72 the maximal sensitivity of each cell, which is the largest eigenvalue of the Fisher information matrix I t,t . We 73 normalized the previous sensitivity values by this maximal sensitivity to obtain a "normalized sensitivity".

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Even after this, we observed a decrease of this normalized sensitivity with distance (supp. fig. 6B). These and after (C,D) adding strychnine, for OFF (A, C) and ON (B, D) subunits. The central ON subunits and the classical OFF inhibitory surround are suppressed by strychnine. Note that these changes are compatible with the preservation of the response to a bar flashed in the center that we observed above. The flashed bar elicits only OFF responses and thus should not be affected by the disappearance of ON negative weights in the center. Moreover, the OFF negative weights are not present in the center but only in the surround, so their disappearance should not affect the response either. Supplemental Figure 9: A: Raster of an OFF cell responding to a repeated sequence of random motion in the center of its receptive field, before and after adding LAP-4 to the bath B: Raster of an OFF cell in response to the same stimulus far away from its receptive field (central axis of the bar trajectory 300 microns away from the receptive field center of the cell), before (blue) and after (pink) adding LAP-4 to the bath. C: Distant response amplitude (see methods) for normal (blue) and LAP-4 (pink) condition (n=16 cells). The star indicates that the p-value of a two-sample t-test was lower than 0.05.