With this form, we point out the similarity of our combinatorial scheme to that of Mehrani et al. (2020), in which the input from cone-opponent V2 cells into hue tuning V4 cells is weighted as a function of the difference in their preferred hue angles. Most evidently, we differ from this model by first combining the cone-opponent signals in V1 rather than V4, in accordance with the above-mentioned studies. But beyond pointing to V1 as the origin of mixing, these exper-iments indicate that the combinatorial feedforward scheme is not sufficient to account forthe variability of neuronal hue preferences. Li et al. (2022) showed, for instance, that the con-tribution of signals isolating the S-(L+M) pathway is too small to explain the shifting of hue preferences away from the L-M axis by purely combinatorial means. As put forward by Shapley and Hawken (2011),Wachtler et al. (2003),a n d Lehky and Sejnowski (1999),a more complete understanding of neuronal hue encoding within V1 requires us to consider the nonlinear population dynamics therein. Recurrent Interactions We begin by characterizing the connectivity of the target hue tuning populations with a trans-lation invariant cortical connectivity function w(|x-x0|), such that the interactions between neurons in a single CO blob (length scale ∼0. 5 mm) depend only on the cortical distance between them ( Bullmore & Sporns, 2012 ;Salzmann et al., 2012 ). The network 's connectivity comprises the interactions of both its excitatory and inhibitory populations, wx-x0jjð Þ ¼ wexcþwinh; (7) each of which we model as a sum of an isotropic and distance-dependent term: wexc¼E0þ E1cos x-x0jjð Þ winh¼-I0-I1cos x-x0jjð Þ :(8) We set E0≥E1> 0 and I0≥I1> 0 so that wexcandwinhare purely excitatory and inhibitory, respectively, in accordance with Dale 's law ( Ben-Yishai et al., 1995 ;Dayan et al., 2001 ). Next, we map the weighting function onto hue space, drawing from the hue tuning micro-architecture revealed by the imaging studies of Liu et al. (2020) and Xiao et al. (2007). These studies point to a linear relationship between distance and hue angle difference, which min-imizes the wiring length of cells tuned to similar hues ( Liu et al., 2020 ). The hue-preferring cells inhabit the so-called “color regions, ”defined as such for their activation by red-green grating stimuli ( Liu et al., 2020 ). These regions predominantly overlap with the V1 CO blobs (Landisman & Ts 'o, 2002b ;Li et al., 2022 ) and are responsive to the full range of hues, much like the patchy distribution of orientation maps within the V1 hypercolumns. Thus, in a similarmanner to the local feature processing models of Bressloff and Cowan (2003b) and Ben-Yishai et al. (1995), we model the CO blob as a single color-processing unit consisting of Nneurons labeled by the continuous hue preference variable θ2[-π,π](Bressloff & Cowan, 2003b ). Figure 2 shows the distribution of hue-responsive neurons within a typical color region (Figure 2A ) as well as a more coarse-grained demarcation of peak activity within several of these regions ( Figure 2B ). To describe the spatial organization of their hue preference data, Xiao et al. (2007) and Liu et al. (2020) applied a linear fit to the cortical distance between two cell populations as a function of the difference in their preferred hue stimuli Δθ≡|θ-θ 0| apart in DKL space. Note, this implies a discontinuity between θ= 0 and θ=2π, allowing for the 2 πperiodicity of the hue preference label. Liu et al. (2020) report that the linear fit was able to capture the micro-organization of 42% of their tested hue maps, and a regression per-formed by Xiao et al. (2007) on an individual hue map gave a squared correlation coefficient of R2= 0. 91. Network Neuroscience 684Pattern forming mechanisms of color vision Downloaded from http://direct. mit. edu/netn/article-pdf/7/2/679/2118501/netn_a_00294. pdf by guest on 09 August 2024 