Figure 1.
Three layer visual pathway model.
(i) Layer 1: left and right retina/eye (each M x M overlapping ON and OFF retinal cells), (ii) Layer 2: left and right eye specific LGN layers (each M x M overlapping ON and OFF LGN cells), and (iii) Layer 3: IV layer of V1 in cat (N x N cortical cells). Each cortical cell in the model receives thalamic projections from each 13×13 left and right eye specific LGN cells centered at their retinotopic center. These thalamocortical connections define left and right RFs. We have used N = 50 and M = 30.
Figure 2.
Simple cell response characterization.
(A) Left and right 2D spatial (X-Y) RFs of a sample cortical cell from our 50×50 cortex. The ON and OFF subregions are shown in Grayscale with white (black) color representing strong synaptic connection from ON (OFF) LGN cells. The shading is proportional to the strength of the ON/OFF synaptic connections from LGN cells. (B) Left and right monocular OR tuning curves of the cell in ‘A’. Right eye response (maximum = 34 spikes/sec) dominates over left eye response (maximum = 17 spikes/sec). The OR preferences in left and right eyes are 122° and 124° (OR preference difference = 2°), with hwhh of 25° and 33° respectively. Eye preference i.e OD is 0.49. (C) Binocular OR tuning curve of the cell in ‘A’. The binocular OR preference is 120° with hwhh of 38°. (D) Left and right SF tuning curves of the cell in ‘A’. The optimal SF in left and right eye are 0.6 and 0.6 cycles/degree respectively. (E) Disparity tuning curve for the cell in ‘A’. The DP is −80° PA, DSen is 0.85 and S/N is 4.3. (F) 2D left and right spatial RFs of the cell in ‘A’ with X-axis transformation such that X-axis is orthogonal to cell's preferred orientation. 1D RF profiles is shown below the X-axis transformed 2D RFs. (G) 1D RF profiles marked with dark filled circles and fitted Gabor functions with solid curves for the cell in ‘A’. The positional disparity () is −0.18° VA and phase disparity (δφ) is: −113° PA and −0.87 VA. The overall RF spatial disparity is −87° PA (H) Summary of the characterization of the sample cell in ‘A’.
Figure 3.
Binocular interaction in almost monocularly driven simple cells shows robust disparity selectivity.
(A, B) Two sample cortical cells from our model cortex with left and right RFs along with their response characteristics and disparity values tabulated in table. (C, D) Phase disparity tuning curves for two sample cortical cells from our model. For both these cells, left monocular response (shown as ◂ L) dominates over the right monocular response (shown as ◂ R) with OD values of -1 and -0.83 respectively. The OD values closer to -1 categorize them as monocular left eye driven cells. These cells show robust binocular interaction with DSen (S/N) values of 0.52 (8.31) and 0.96 (8.19) respectively. The nature of binocular interaction is synergistic for the first cell (Figure 3C) and suppressive for the second cell (Figure 3D). (E, F) Phase disparity tuning curves for two sample monocular cortical cells with OD values close to +1. For both these cells, right monocular response (shown as ◂ R) dominates over the left monocular response (shown as ◂ L) with OD values of 0.92 and 0.84 respectively. These cells show robust binocular interaction with DSen (S/N) values of 0.72 (14.1) and 0.96 (7.56) respectively. The nature of binocular interaction is synergistic for the first cell (Figure 3E) and suppressive for the second cell (Figure 3F).
Figure 4.
IDPO, Dif-frequency, OD versus DP, and OD versus DSen.
(A) Histogram of interocular difference in preferred ORs. In our model cortex, 69.3% OR tuned cells (1200 out of total 1732) have IDPOs range of ±20° (S = 9°). Rest 30.7% of cells have significant IDPOs (>). (B) Histogram of Dif-frequency cells in cycles/degree. In our model cortex, 50.44% of cortical cells (1261 out of total 2500) have Dif-frequency range of ±0.05 cycles/degree. In remaining 1239 cells, 1179 (47.16%) cells have significant Dif-frequency (>
0.05 cycles/degree) and 60 (2.4%) cells are OR untuned in both eyes or have very weak responses from which we were not able to determined there SFs in left and right eyes. (C) Scatter plot of preferred binocular phase disparity (in −180° to +180° scale) and OD for all OR tuned cells. The plot shows almost no correlation (r = -0.05) between them at cell population level. (D) Scatter plot of disparity sensitivity (or selectivity) and OD for all OR tuned cells. The plot shows almost no correlation (r = 0.02) between them at cell population level. The red line represents the linear regression line and blue ellipse indicates 95% prediction interval in ‘B’ and ‘C’.
Figure 5.
RF phase and positional disparities for 415 cells.
(A) Histogram of RF phase disparity in PA. 25% of cells have phase disparities in the range −10° to 10° PA. Rest 75° cells have broader range of phase disparities. Overall 95.7% of cells has phase disparity in the range −90° to 90° PA. The phase disparities lies in the range of −162° to 180° PA. (B) Scatter plot of RF position disparity versus phase disparity in VA and their respective histograms. The RF position and phase disparities show slight positive correlation between them (r = 0.35). The total range of phase disparities lie within ±1.4° VA (S = 0.39). Total range of position disparities lie within ±1° VA (S = 0.28).
Figure 6.
DP versus Overall RF spatial disparity for 415 cells.
Scatter plot of preferred binocular phase disparity versus overall RF spatial disparity and their respective histograms. The preferred binocular phase disparity and overall RF spatial disparity shows strong correlation of r = 0.91.
Figure 7.
OR map superimposed with OD map contours.
(A) Binocular OR map using color code scheme in 0° to 180° scale with superimposed OD map contours marked with thick black lines. The black color bars are oriented at cell's binocular preferred OR. The OD peak points are marked with white color circle markers. The pinwheel singularities are marked with: (i) white color up pointing triangle markers for positive pinwheel singularities and (ii) white color down pointing triangle markers for negative pinwheel singularities. The OD peak points appear on/near the pinwheel singularities. (B) Histogram of OD peak points to pinwheel separation across the model cortex. The mean separation is 2.2 units and median separation is 2 units.
Figure 8.
Disparity map and its organization.
(A) Disparity map using color code scheme in 0 to 360 scale. The black color filled circles represents cortical cells with DSen¡0.3. The white color cells are Dif-frequency disparity selective cells. The superimposed oriented black color bars depict binocular preferred OR for cells in the map. (B) Histogram of DP across the model cortex in −180 to 180 scale. (C) Here we explored the smoothness of the topographic organization of DP by finding similarity/smoothness in 3×3 neighborhoods in DP map. A sample 3×3 section of DP map is shown in Figure 8A marked with black square boundary. Figure 8C depicts the difference between neighborhood median DP and center DP for 56 possible 3×3 sections from our DP map. In 45 out of total 56 possible 3×3 sections difference is ≤45° threshold difference. This result suggests that DP values in disparity map are weakly clustered together.
Figure 9.
(A) Complex cell Cx built using four linear filters with spatial phases of −45°, 45°, −90° and 0°. (B) Binocular RF of complex cell Cx. (C) Complex cell C1 built using simple cell subunits with almost same disparity selectivity. The simple cell subunits are marked with black rectangular outlines in DP map patch. (D) Binocular RF of complex cell C1. (E) Complex cell C2 built using simple cell subunits exhibiting a systematic change in disparity selectivity. Subunits are marked with black rectangular outlines. (F) Binocular RF of complex cell C2. (G) Complex cell C3 built using simple cell subunits exhibiting a systematic change in disparity selectivity. Subunits are marked with black rectangular outlines. (H) Binocular RF of complex cell C3.
Table 1.
Modeled simple cell 1D RF profile phases for complex cell C1.
Table 2.
Modeled simple cell 1D RF profile phases for complex cell C2.
Table 3.
Modeled simple cell 1D RF profile phases for complex cell C3.
Figure 10.
LGN cell activity, RF from Reverse correlation and Effect of initial RF center distribution.
(A, B) 3×3 section of 2D left and right RFs from our model cortex. RFs are developed using the hypothesis that LGN cells are active during weight update. (C, D) 3×3 section of 2D left and right RFs from our model cortex. RFs are developed using LGN cell spontaneous activity as modeled by Goodhill [72]. (E) RF of a cortical cell as the set of LGN weights. (F) RF obtained using reverse correlation for the same cortical cell chosen in ‘E’. The RFs in ‘E’ and ‘F’ looks qualitatively similar. (G) Scatter plot of final versus initial shifts (horizontal and vertical) in VA of left and right RF centers for 50 cortical cells from our model cortex.
Table 4.
OR anisotropy.