Hierarchical and nonhierarchical features of the mouse visual cortical network

Abstract

Neocortical computations underlying vision are performed by a distributed network of functionally specialized areas. Mouse visual cortex, a dense interareal network that exhibits hierarchical properties, comprises subnetworks interconnecting distinct processing streams. To determine the layout of the mouse visual hierarchy, we have evaluated the laminar patterns formed by interareal axonal projections originating in each of ten areas. Reciprocally connected pairs of areas exhibit feedforward/feedback relationships consistent with a hierarchical organization. Beta regression analyses, which estimate a continuous hierarchical distance measure, indicate that the network comprises multiple nonhierarchical circuits embedded in a hierarchical organization of overlapping levels. Single-unit recordings in anaesthetized mice show that receptive field sizes are generally consistent with the hierarchy, with the ventral stream exhibiting a stricter hierarchy than the dorsal stream. Together, the results provide an anatomical metric for hierarchical distance, and reveal both hierarchical and nonhierarchical motifs in mouse visual cortex.

Fig. 1. Identification of visual areas.

a Rostrocaudal series of coronal sections of the left hemisphere in which AM was injected with BDA. Dark-field images of anterogradely labeled axonal projections (yellow/orange) to distinct visual areas (white outlined boxes). Numbers denote the coronal plane corresponding to the respective rostrocaudal location shown in the inset. Fluorescent images of retrogradely labeled callosal neurons (cyan), after injection of bisbenzimide into the right hemisphere, aid in the identification of areal borders. For example, the column of callosal neurons (arrowheads in coronal sections) corresponds to the band shown in the inset (arrowheads). Inset, In situ image of left hemisphere, before coronal sectioning, showing retrogradely labeled callosally projecting neurons (cyan). Asterisk denotes injection site in AM. White arrowheads indicate a band of callosal neurons that form the boundary between V1 and an acalossal zone that includes LM, LI, and AL. Horizontal lines and numbers denote the coronal planes shown above. Scale bars, 1 mm. b Diagram of visual areas and a BDA injection into AM; a anterior, m medial, p posterior, l lateral. c High magnification images of regions within white boxes in Fig. 1a. Axonal projections from AM target the other nine areas with varying strengths and laminar patters, and are observed in all six layers. Arrowhead in the LI panel denotes boundary between LI and LM. Arrowhead in the A panel denotes boundary between A and AM. Scale bar, 200 µm.

Fig. 2. Dark-field images of coronal sections showing diverse laminar termination patterns and optical density ratios of intracortical axonal projections.

a Left. Representative termination patterns of the V1 → AL (top) and AL → V1 (bottom) pathways. Right. Histograms showing the distribution of pixel values in L1 (yellow) and L2-4 (blue) in the corresponding dark-field images. Only pixels within 70% of the highest pixel value were included for analyses, and plotted after subtraction of background intensity. Note the overall brighter pixels in L2-4 in the feedforward (FF) V1 → AL pathway (p < 10⁻¹⁶, K-S test) and the overall higher pixel values in L1 in the feedback (FB) AL → V1 pathway (p < 10⁻¹⁶, K-S test). Top inset. Diagram of an injection into V1 and the anterogradely labeled V1 → AL pathway (arrow). b. Laminar termination patterns of FF axonal projections in each higher visual area after injection of BDA into V1. The ratio of the average optical density of axonal projections in L2-4 to that in L1 + L2-4 (optical density ratio, ODR) for each pattern is presented in the respective panel. c. Laminar termination patterns of FB projections in V1 after injection of BDA into each of the nine higher visual areas. One injection was performed in each animal. The ODR for each pattern is indicated in the corresponding panel. Arrowhead in the AM → V1 panel demarcates the boundary between V1 and PM. d. Nine representative examples of higher visual cortico-cortical laminar termination patterns, for injections of BDA performed in areas P, AL, and AM. The ODR for each pattern is presented in each panel. Arrowheads in the P → LI, AL → LI, and AM → LI panels demarcate the boundaries of LI used for analysis. Scale bars (a–d), 200 µm.

Fig. 3. Mouse cortical network exhibits hierarchical features.

a 10 × 10 connection matrix of interareal connections between the 10 visual areas. Each block shows the ODR for the respective pathway in which the source and target areas are respectively denoted on the left of each row and the top of each column. Gray blocks represent pathways that could not be analyzed due to weak axonal projections in the target area. b Distribution of logit transformed values of the ODRs for all 80 pathways. A logit ODR value of zero indicates an ODR of 0.5. c Logit ODR for each pathway plotted against that of its reciprocal counterpart for all 74 pathways that have a dense reciprocal connection (see Fig. 3a). ‘Upper matrix’ and ‘lower matrix’ refer respectively to the ODR values in the upper/right and lower/left triangular halves of the matrix in Fig. 3a. The fit shows a significant negative association (slope = −0.53, p = 0.009, F-test, F-statistic: 7.54 on 1 and 35 degrees of freedom) indicating that the more FF a pathway is in one direction, the more FB is the reciprocal pathway. The identities of three representative reciprocal connections in the scatterplot are shown to illustrate the variation in asymmetry of ODRs for reciprocally connected areas. d. Scatterplots showing the correlation of logit ODR values in all shared targets of any two injected areas. The horizontal axis of each plot corresponds to the logit ODR of the pathway originating in the area indicated at the top of each column, and the vertical axis corresponds to the logit ODR of the pathway originating in the area indicated at the right of each row. Thus, each orange data point plots against each other the logit ODRs for pathways that terminate in a common target area for the corresponding two injected areas. Areas that exhibited weak or absent projections from one of the two injected areas (gray blocks in Fig. 3a) were excluded. Dotted lines, coordinate axes. A line of unit slope (blue) that best fit the points is plotted in each graph, and the absolute value of the y-intercept of this unit line provides a measure for hierarchical distance between the two injected areas. Two example graphs are shown at higher magnification with the injected areas indicated. Note that the absolute value of the y-intercept in the graph plotting pathways originating in RL and POR (y-intercept, −1.04) is greater than that in the graph for pathways from LI and POR (y-intercept, −0.33). This indicates that RL and POR are more hierarchically distant than are LI and POR when only projections emerging from these three areas are considered. The y-intercepts of each graph are plotted as a heat map on the right.

Fig. 4. Construction of mouse visual cortical hierarchy.

a Estimated hierarchical levels obtained using a beta regression model such that the level value of V1 is set at 0, and differences between any two hierarchical level values best predict the ODR for pathways connecting the respective areas. Vertical lines demarcate 90% confidence intervals. The areas have been divided into previously described dorsal and ventral streams^,. b Hierarchical distance values between all pairs of areas estimated by the beta regression model show a high goodness of fit with the logit of the measured ODRs (r = 0.85). c The Akaike information criterion (AIC) values for eight models in which different combinations of areas were constrained to be part of the same level, and the beta regression fit performed for each such model. The lowest AIC value occurs for the model with five levels (V1, LM/RL, A/AL/PM/P, LI/AM, and POR), indicating that this is the hierarchical model with the best predictive power. Hierarchical models: 2, 2 levels (all higher-order areas combined into one level, and V1 as a separate level); 3a, 3 levels (V1, LM, all higher areas merged into one level); 3b, 3 levels (V1, LM–LI, POR); 4a, 4 levels (V1, LM, RL–LI, POR); 4b, 4 levels (V1, LM/RL, A–LI, POR); 5, 5 levels (V1, LM/RL, A–P, LI/AM, POR); 6, 6 levels (V1, LM, RL, A–P, LI/AM, POR); and 10, all 10 areas considered as separate levels. d Hierarchical levels similar to Fig. 4a, but scaled to values between 1 and 10. Black lines interconnect pairs of areas that show a significant difference in their hierarchical levels (p < 0.05, two-sided Wald test for multiple coefficients). Blue lines interconnect areal pairs that lack a statistical significance in their hierarchical level. e Illustration of the overlapping hierarchy of the network. All pairs of areas within each colored box lack a statistically significant hierarchical separation, and pathways interconnecting these areas can therefore be considered to be lateral (i.e. neither FF nor FB). f Frequency distribution of ODRs for FF, lateral, and FB pathways. p = 3 × 10⁻²⁴, one-way ANOVA; n = 161 laminar patterns from 20 injections. g. Box plots of ODR values for FF, lateral (‘LAT’), and FB pathways. FF vs LAT, p = 4 × 10⁻⁷; LAT vs FB, p < 2 × 10⁻¹⁶; one-way ANOVA with post-hoc Tukey’s range test; n = 44, 66, and 50 for FF, LAT, and FB pathways, respectively, from 20 injections. Box plots denote the median and are bound by the 25th and 75th percentile values, with whiskers denoting the 5th and 95th percentiles. h Receptive field diameters recorded in each area in anesthetized mice. Within each processing stream, RF diameters show an overall increase in areas at increasingly higher hierarchical levels for both dorsal and ventral streams (p < 2 × 10⁻¹⁶, one-way ANOVA; n = 142 and 164 neurons for the dorsal and ventral stream, respectively). This increase is more prominent in the ventral stream. Data are presented as mean values ± SEM. i Statistical significance of differences in RF diameters between all pairs of areas. *p < 0.05, **p < 0.01, ***p < 0.001, one-way ANOVA with post-hoc Tukey’s range test. Gray blocks indicate no statistical significance (n.s.). Text (asterisks and n.s.) colors indicate whether the corresponding areas are connected by either lateral (red) or FF/FB (blue) pathways based on the anatomical hierarchy (Fig. 4d, e). Text in black indicates areal pairs that lack a connection in both directions. j Hierarchical level values are significantly correlated with RF diameters (p = 0.001, r = 0.87, Pearson’s correlation; n = 308 neurons from 98 mice). Data are presented as mean values ± SEM.

Fig. 5. Construction of hierarchy after separation of dorsal and ventral streams.

a When pathways connecting areas belonging to the two different streams (dorsal and ventral) were eliminated from analysis, the plot of ODR values in one direction against that in the reciprocal direction shows a steeper slope compared to when all pathways are included (Fig. 3c; p = 0.009 for comparison between the two slopes, ANCOVA). b Estimated hierarchical levels obtained using a beta regression model after elimination of cross-stream pathways. Hierarchical level value of V1 was set at 0, and differences between any two hierarchical level values best predict the ODR for the pathways connecting the respective areas. c Hierarchical levels similar to Fig. 5b, but scaled to values between 1 and 10. Black lines interconnect pairs of areas that show a significant difference between their respective hierarchical levels (p < 0.05, two-sided Wald test for multiple coefficients). Blue lines interconnect areal pairs that lack a significant difference between their respective hierarchical levels. d Within-stream hierarchical distances estimated by the beta regression model plotted against the logit of the measured ODRs show a high goodness of fit (r = 0.90). e The AIC values for nine models in which different combinations of areas were constrained to be part of the same level, and the beta regression fit performed for each such model. The lowest AIC value occurs for the model in which the network is organized into five levels (V1, RL/LM, AL/A/PM, AM/P, LI/POR; model 5b), indicating this to be the model with the best predictive power. Hierarchical models: 2, two levels (V1, all higher-order areas merged into a second level); 3a, three levels (V1, RL/LM, all higher areas merged into a third level); 3b, three levels (V1, RL–PM, and AM–POR); 3c, three levels (V1, RL–LI, POR); 4, four levels (V1, RL–PM, AM/P/LI, POR); 5a, five levels (V1, RL/LM, AL/A/PM, AM/P/LI, POR); 6, six levels (V1, RL/LM, AL/A/PM, AM/P, LI, POR); and 10, all ten areas at different levels.