Tuning curves vs. population responses, and perceptual consequences of receptive-field remapping

Abstract

Sensory processing is often studied by examining how a given neuron responds to a parameterized set of stimuli (tuning curve) or how a given stimulus evokes responses from a parameterized set of neurons (population response). Although tuning curves and the corresponding population responses contain the same information, they can have different properties. These differences are known to be important because the perception of a stimulus should be decoded from its population response, not from any single tuning curve. The differences are less studied in the spatial domain where a cell's spatial tuning curve is simply its receptive field (RF) profile. Here, we focus on evaluating the common belief that perrisaccadic forward and convergent RF shifts lead to forward (translational) and convergent (compressive) perceptual mislocalization, respectively, and investigate the effects of three related factors: decoders' awareness of RF shifts, changes of cells' covering density near attentional locus (the saccade target), and attentional response modulation. We find that RF shifts alone produce either no shift or an opposite shift of the population responses depending on whether or not decoders are aware of the RF shifts. Thus, forward RF shifts do not predict forward mislocalization. However, convergent RF shifts change cells' covering density for aware decoders (but not for unaware decoders) which may predict convergent mislocalization. Finally, attentional modulation adds a convergent component to population responses for stimuli near the target. We simulate the combined effects of these factors and discuss the results with extant mislocalization data. We speculate that perisaccadic mislocalization might be the flash-lag effect unrelated to perisaccadic RF remapping but to resolve the issue, one has to address the question of whether or not perceptual decoders are aware of RF shifts.

Keywords: FEF; LIP; corollary discharge; forward expansion; predictive remapping; space perception; transsaccadic visual stability.

Figure 1

Perisaccadic RF remapping, drawn on the display screen for the stimuli. The cross, square and arrow represent the fixation point (FP), saccade target (T), and saccade vector, respectively. cRF and fRF refer to a cell's current (pre-saccadic) and future (post-saccadic) RFs, respectively. In each panel, the region(s) enclosed by black curve(s) represent perisaccadic RF (pRF). (A) Forward jump to fRF. (B) Forward expansion toward fRF. Both (A) and (B) will be referred to as forward shift. (C) Convergent shift toward the target.

Figure 2

Simulations of the mirror relationship between the tuning curve of a cell preferring x_p = x_o (top row) and the population response to a stimulus x_s = x_o (bottom row), under the assumption of translational invariance. The mirror relationship is hidden when a symmetric response function is used (left column), but is revealed with an asymmetric function (right column).

Figure 3

Opposite shifts of tuning curves (here RFs) and the population response for unaware decoders (after figure 6 of Yao and Dan, 2001). (Top) RFs of three arbitrary cells before (solid) and after (dashed) a rightward translation (rightward arrows), similar to the forward pRF jump in Figure 1A. x_o indicates a specific stimulus position which evokes responses from the cells before (filled dots) and after (open dots) the shift. (Bottom) The population responses of all cells to x_o before (solid black) and after (dashed black) the RF shifts, plotted here at the cells' pre-shift preferred positions (unaware decoders). The three cells' responses from the top panel are indicated. If the cells' post-shift responses are plotted at their post-shift preferred positions (aware decoders), then the pre- and post-shift population responses are identical (both solid black).

Figure 4

The same-direction assumption is false for forward RF expansion as is for forward RF jump in Figure 3. (Top) RFs of three arbitrary cells before (solid) and after (dashed) a perisaccadic rightward expansion. (Bottom) The population responses of all cells to x_o = 0 before (solid) and after (dashed) the RF expansion. The dashed black and magenta curves are the post-expansion responses plotted against the pre- and post-expansion preferred positions, for the unaware and aware decoders, respectively.

Figure 5

Removing translational invariance does not change the conclusion that the same-direction assumption is false for forward RF shifts. This figure assumes that a cell's shifted RF size is determined by its pre-shift eccentricity. The x-axes measure position as eccentricity from fovea (0). (Top) RFs of three arbitrary cells before (solid) and after (dashed) a perisaccadic rightward jump. (Bottom) the population responses of all cells to a stimulus at x_o = 20 deg before (solid) and after (dashed) the RF shift. The dashed black and magenta curves are the post-shift responses plotted against the pre- and post-shift preferred positions, for the unaware and aware decoders, respectively.

Figure 6

Removing translational invariance does not change the conclusion that the same-direction assumption is false for forward RF shifts. This figure assumes that a cell's shifted RF size is determined by its post-shift eccentricity. The format is identical to that for Figure 5.

Figure 7

Convergent RF shift. (A) The direction of convergent RF shift. FP and T indicate the initial fixation point and saccade target, respectively. (B) Convergent RF shift as a function of the cRF-to-target distance used in the simulations of Figures 8–10. cRFs on the left and right side of the target (at 0) shift to the right (positive) and left (negative), respectively, as they converge to the target. (C) The cells' covering density before (top) and after (bottom) the convergent RF shifts toward the target in c, for aware decoders. The density stays the same (top) for unaware decoders. (D) The center/surround attentional modulation as a function of the cRF-to-target distance, used in the simulations of Figure 9. This curve is scaled by a factor of 4 in the simulations of Figure 10.

Figure 8

Perceptual consequence of convergent RF shifts. The target is at 0 deg. (A) (Top) RFs of five arbitrary cells before (solid) and after (dashed) the convergence. The “blue” cell tune to the target (0 deg) does not shift. (Bottom) the population responses of all cells to stimulus position x_o = −10 deg before (solid) and after (dashed) the RF convergence. The dashed black and magenta curves are the post-convergence responses plotted against the pre- and post-convergence preferred positions, for the unaware and aware decoders, respectively. (B) Perceptual mislocalization as a function of stimulus position relative to the target (0 deg). The results depend on whether the decoder is aware (magenta) or unaware (black) of the RF convergence, and whether the decoder uses the peak (dashed) or center-of-mass (solid) of population responses. The aware center-of-mass decoder (solid magenta) considers the change of the cells' covering density (see text); it predicts convergent mislocalization as stimuli to the left and right of the target (over a range of about 40 deg) have positive and negative mislocalization, respectively. The aware peak decoder (dashed magenta) predicts no mislocalization. The unaware center-of-mass and peak decoders (solid and dashed black) both predict divergent mislocalization.

Figure 9

Perceptual consequence of convergent RF shifts and response modulation. The target is at 0 deg. The maximum response enhancement (at the target) is 25%. The format is identical to that of Figure 8. For stimuli close to the target, the aware center-of-mass and peak decoders (solid and dashed magenta) and the unaware peak decoder (dashed black) all predict convergent mislocalization. The unaware center-of-mass decoder predicts divergent mislocalization. The unaware peak decoder also predicts divergent mislocalization for stimuli away from the target.

Figure 10

Perceptual consequence of convergent RF shifts and response modulation. The target is at 0 deg. The maximum response enhancement (at the target) is 100%. The format is identical to that of Figures 8, 9. For stimuli near the target, all the four decoders predict convergent mislocalization. Unaware decoders (solid and dashed black) still predict divergent mislocalization for stimuli away from the target.