Fig 1.
A. Receptor response curves as a function of odorant concentration. Solid circles correspond to effective threshold concentrations or inverse affinities: . For a certain concentration (dashed line), the ORs with a threshold below this concentration (solid red circles) are in an active state. These ORs form a primacy set with the primacy number p = 2 for this odorant. B. Representation of receptors in 2D space of affinities for odorants X and Y: KX and KY. C. An odorant X at concentration cX activates all receptors for which KrXcX>1 (red). For the given primacy number p = 2, the identity of odor X is defined by the two most sensitive receptors (red segment). D. The same for odor Y. E. A mixture of two odorants X and Y activates receptors, which are above the line perpendicular to the unit vector q = [cX, cY]/c, where
. F. Primacy sets for all possible mixture vectors q define a primacy hull (red), a 1D line in the 2D space. Receptors in the primacy hull (red) are retained in the genome. All other ORs (empty circles) are expected to be eliminated from the genome (pseudogenized).
Fig 2.
Primacy hull in higher dimensions.
A. Geometrical representation of primacy sets for different primacy numbers: p = 2: 1-simplex, a segment; p = 3: 2-simplex, a triangle; p = 4: 3-simplex, tetrahedron. B. An example of primacy hull for a random set of points in 2D (p = 2). A primacy hull is a set of simplexes that reside on the extremes of the given set of points. C. A primacy hull for D = 3, p = 3. A ~2D surface is tessellated by triangles, each of them representing an independent odor identity. D. The same for D = 6, p = 7. 6D manifold is projected onto 3D space for visualization. E. Decomposition of affinity matrix K into two low-dimensional matrices: Q is a low-dimensional matrix of basic odor features and R is a matrix of receptor affinities for these basic features.
Fig 3.
Suggested feedforward circuit which can process the primacy information.
A. Left: Primacy hull for D = 2 and p = 2; a, b, c, d are discriminable odor identities. Right: connectivity between ORs 1, 2, …5 and cortical cells (insect mushroom body cells) corresponding to different odor identities. The glomeruli from the same primacy sets converge to the same cortical cells. B. The same for D = 3 and p = 3. Only two example simplexes are shown. C. Subprime connectivity model. Individual cortical cells represent the faces of primacy simplexes (sides of the triangles). Individual odor identities are encoded by populations of neurons marked ‘a’ and ‘b’.
Fig 4.
Non-random low-dimensional structure in PN-KC connectivity that is conserved across animals.
A, B. Glomerulus-KC connectivity matrices from FlyEM and FAFB datasets. C, D: Glomerulus-glomerulus connectivity similarities (Pearson correlations of connectivities). E. Glomerulus-glomerulus connectivity similarities in two datasets against each other. The correlation in glomerulus-glomerulus connectivity similarities is r = 0.47 (p<0.01). F. Similarity between datasets disappears if one of the datasets is shuffled while preserving the connectivity matrix in- and out- degrees (right)[44]. We observed that the average correlations for bootstrapped connectivity data in which KCs were selected with repetitions is somewhat lower than for the intact data in panel E. G. Variance explained per dimension as a function of the PCA dimension (inset–total cumulative variance explained). PCA analysis shows that the first two linear dimensions are significantly different from random. H. Connectivity matrices in two datasets projected onto the first two dimensions. Points represent individual glomeruli. The same glomeruli in two datasets (different animals) are connected by black segments and reside near each other in the 2D embedding suggesting that the first two dimensions of the connectivity matrix are conserved across datasets. I, J. The same analysis using a non-linear low-dimensional embedding technique (Isomap) shows that the first two dimensions in the connectivity data are both different from random (I), explain more variance in the data than the linear algorithm (PCA), and are conserved across datasets (J). The number of nearest neighbors for the Isomap algorithm (inset) was chosen as described in Methods H in S1 Text.
Fig 5.
Comparing connectivity and affinity data.
A. OR-KC connectivity matrix (FlyEM dataset). B. Left: OR-odorant affinities (from DoORv2 dataset). Gray represents missing values of affinities. Right: OR-odorant primacy matrix for p = 5. C. OR-OR similarities (Pearson correlations) computed from connectivity data for 37 ORs represented in affinity data. D. OR-OR similarities (Pearson) computed from affinity data. The off-diagonal elements of matrices in C and D are correlated (R = 0.185, p < 10−4). E. Schematic showing the overlap matrix computed by matrix multiplication of connectivity and primacy matrices (p = 5). F. The difference in the number of actual overlaps of a given degree and the number of overlaps for a randomly shuffled connectivity matrix [44]. The difference is computed for different primacy numbers. Only the KCs with the highest overlap per odor (gKC) are considered. No statistically significant difference is observed. G. As in (F), but for the 10 topmost KCs per odor. Statistically significant differences are enclosed by a dashed red line (FDR<0.05). H. As in (G), but for the 50 topmost KCs per odor.