Towards a supervised classification of neocortical interneuron morphologies

Abstract

Background: The challenge of classifying cortical interneurons is yet to be solved. Data-driven classification into established morphological types may provide insight and practical value.

Results: We trained models using 217 high-quality morphologies of rat somatosensory neocortex interneurons reconstructed by a single laboratory and pre-classified into eight types. We quantified 103 axonal and dendritic morphometrics, including novel ones that capture features such as arbor orientation, extent in layer one, and dendritic polarity. We trained a one-versus-rest classifier for each type, combining well-known supervised classification algorithms with feature selection and over- and under-sampling. We accurately classified the nest basket, Martinotti, and basket cell types with the Martinotti model outperforming 39 out of 42 leading neuroscientists. We had moderate accuracy for the double bouquet, small and large basket types, and limited accuracy for the chandelier and bitufted types. We characterized the types with interpretable models or with up to ten morphometrics.

Conclusion: Except for large basket, 50 high-quality reconstructions sufficed to learn an accurate model of a type. Improving these models may require quantifying complex arborization patterns and finding correlates of bouton-related features. Our study brings attention to practical aspects important for neuron classification and is readily reproducible, with all code and data available online.

Keywords: Feature selection; Martinotti; Morphometrics.

Fig. 1

Examples of the eight morphological types from [6] for which we learned supervised models. The types are: bitufted (BTC); chandelier (ChC); double bouquet (DBC); large basket (LBC); Martinotti (MC); nest basket (NBC); small basket (SBC), and the compound basket (BA) type, composed of NBC, LBC, and SBC cells. Neurogliaform (NGC) and bipolar (BP) types not shown as we omitted them from supervised classification, because we had only three cells of each. Typical features, according to [6], include: bitufted dendrites (BTC); sharply branching axons and low bouton density (LBC); and axons with spiny boutons, reaching L1 (MC); and vertical rows of boutons (ChC). Axons are drawn in blue with dendrites and somata in red. Dashed green lines indicate layer boundaries from the rat hind-limb somatosensory cortex. There are 100 μm between consecutive grid lines

Fig. 2

Frequencies of interneuron types in our data: overall (left) and per cortical layer (right). This figure shows the 217 cells used for supervised classification, with the SBC, NBC, and LBC types also shown in the bar corresponding to BA (i.e., the BA bar does not contribute to total cell count)

Fig. 3

Custom-implemented morphometrics for an L4 MC (top panel: left; bottom panel: red), an L2/3 NBC (top: middle; bottom: green), and an L2/3 SBC (top: right; bottom: blue) interneuron. The bottom panel shows standardized values, with black dots indicating minima and maxima (extrema outside (−2.5,2.5) not shown). The axon of the MC cell originates from the upper part of the soma (axon_origin), grows along a radial axis (eccentricity, radial; axis drawn with the orange line), radially far from the soma (y_mean, center of mass shown with orange dot) and above it (y_std_mean), covers a small surface (grid_area), and its branches are not clustered together (grid_mean). It is translaminar (translaminar) and there is just a moderate (around 30%) probability of it reaching L1 (l1_prob) because, even with its soma vertically in the middle of L4, it only touches the bottom of L1. Low l1_prob and arbor width produce a low estimate of width (l1_width), bifurcations count (l1_bifs), and horizontal fanning out (l1_gxa) in L1. The dendritic arbor of the MC cell is displaced (d.displaced) from the axon and the dendrites stem from opposite ends of the soma (d.insert.eccentricity), located along a radial axis (d.insert.radial). The NBC cell’s axonal arbor is circular (radial), with closely grouped branches (grid_mean)) and a number of short vertical terminals (short_vertical_terminals). The axon of the SBC cell is intralaminar, tangentially oriented, with closely grouped branches, while both cells’ dendrites are spread out (multipolar) and colocalized with the axons. Dashed green lines indicate layer boundaries from the rat hind-limb somatosensory cortex, assuming that the somas are located in the middle of their layer. Axon is shown in blue with dendrites and somata in red. The grid lines are at 100 μm from each other. Dendritic morphometrics are prefixed with d.. Axon terminal branch morphometrics, not shown here, are prefixed in the remainder of the text with t

Fig. 4

Effects of under- and over-sampling the full dataset with the chosen rates. Each bar represents a one-versus-all classification task (e.g., the leftmost bar is for ChC versus rest). ‘Positive‘ denotes the examples of the class of interest (e.g., ChC in the leftmost bar), ‘Synthetic‘ are the artificial SMOTE examples of the positive class (i.e., the class of interest), while ‘Negative‘ are the kept examples of all remaining classes. The horizontal line shows the size of the original data set (217 examples). For ChC (leftmost bar), for example, applying our sampling method to the full data set containing seven ChC cells (red segment of the bar), would retain 105 (blue segment) out of 210 non-ChC cells and add 14 synthetic ChC cells (green segment), yielding a data set of size 126 (hence the bar is lower than the horizontal line at 217). Except for BA, in all cases the class of interest was the minority class. For BA we performed no undersampling

Fig. 5

Possible class label and reconstruction issues. Left panel: cells C050600B2 (left), C091000D-I3 (middle), and C150600B-I1 (right) from Table 3, labelled as MC and ChC, respectively, yet only one, three, and one (out of 42) neuroscientists in [14], respectively, coincided with those labels, assigning them instead to the LBC, CB, and CT types. Note that we did not know the location of soma inside their layers; for the MC cells, a soma closer to L1 would mean more extensive axonal arborization in that layer. Axons are drawn in blue with dendrites and somata in red. Dashed green lines indicate layer boundaries from the rat hind-limb somatosensory cortex; L6 is only partially shown. There are 100 μm between consecutive grid lines. Right panel: newer reconstructions, whose IDs do not begin with a C, had thinner and shorter segments

Fig. 6

MC cells that were classified as non-MC by the two most accurate models. Cells C050600B2, C260199A-I3, and C230998C-I4 were classified as MC by only one, three, and 13 neuroscientists in [14], respectively. Cells C260199A-I3 and C230998C-I4 do not reach L1 unless their actual soma was located near the top of L4, although tissue shrinkage may have reduced their height by around 10%. Axons are drawn in blue with dendrites and somata in red. Dashed green lines indicate layer boundaries from the rat hind-limb somatosensory cortex. There are 100 μm between consecutive grid lines

Fig. 7

Relevant morphometrics for the BA type. Top left: per-type boxplots for the six morphometrics selected with RF BVI (RF BVI values shown, in blue, to the right). The most relevant morphometrics, mean arborization distance to soma (path_dist.avg), and mean remote bifurcation angle (remote_bifurcation_angle.avg), are shown in the upper part of the panel. Top right: a biplot of these six morphometrics, with the data projected onto the two principal components, found with principal component analysis (vectors represent morphometrics and the angles between them are indicative of their pairwise correlation). All morphometrics were correlated with either path_dist.avg or remote_bifurcation_angle.avg. Bottom left: the ten most relevant morphometrics according to KW, after removing those with absolute correlation >0.90 with a better ranked morphometric, with the KW p-values shown, in blue, to the right of the boxplot. These morphometrics included those relative to arborization distance from soma (e.g., euclidean_dist.avg, path_dist.avg), remote bifurcation angles (t.remote_bifurcation_angle.avg), the number of dendritic trees (d.N_stems), and axonal arborization along the radial direction (ratio_y). In addition to having sharper bifurcation angles and arborizing closer to the soma, especially in the radial direction, BA cells had more dendritic trees than non-BA cells

Fig. 8

CART model (F-measure value of 0.85) for BA derived from the six morphometrics selected with RF BVI. Most of the BA cells (i.e., those contained in the two rightmost tree leaves) have a path_dist.avg <414 and either y_mean_abs <133 or remote_bifurcation_angle.avg <75°, meaning that they arborize close to the soma, especially vertically, whereas if they do arborize further vertically (as some LBC cells do), they have sharper bifurcation angles. Each box represents a split in the data set, indicating: (a) its majority type (BA is the majority type overall and hence it is shown in the root node of the tree (i.e., the initial split)); (b) proportion of positive examples (BA cells represent 57% of the data set and hence 0.57 in the root node; they present 95% of the samples in the rightmost node); and (c) the percentage of the data set reaching the split (100% of the data passes through the root split; 44% of the data set reaches the rightmost node)

Fig. 9

CART model for MC, with an F-measure value of 0.75. Most MC cells (rightmost leaf) have a y_mean ≥132 (their axons mainly arborize above the soma), remote_bifurcation_angle.avg ≥ 74°, l1_width ≥0.27 and dendritic terminal degree <2.1. Each box represents a split in the data set, indicating: (a) its majority type (Non-MC is the majority type overall and hence it is shown in the root node of the tree (i.e., the initial split), whereas MC is the majority type in the rightmost split); (b) the proportion of positive examples (MC cells represent 23% of the whole data set and hence 0.23 in the root node; they present 95% of the samples in the rightmost node); and (c) the percentage of the data set reaching the split (100% of the data passes through the root split; 18% of the data set reaches the rightmost node)

Fig. 10

Relevant morphometrics for the MC type. Left: ten morphometrics with strongest β in the KW + RMLR model (β shown, in blue, to the right of the boxplot; full model in Additional file 1, Table 6). Largely positive y_std_mean (top of the boxplot) indicates that MC cells preferentially arborized above the soma. Having longer dendritic arbors (d.total_length) but less dendrites (d.N_stems) means that MC cells had longer individual dendritic trees; these arbors were displaced from the axonal ones (d.displaced), which were often radially oriented (radial). Right: MC cells mainly arborize above the soma (y_std_mean) and have wide bifurcation angles (remote_bifurcation_angle.avg)

Fig. 11

Relevant morphometrics for the NBC type. Left: per-type boxplots for the nine morphometrics selected with RF BVI (RF BVI values shown, in blue, to the right). For most NBC cells, the axon never arborized far from the soma (low euclidean_dist.max; top part of the panel) nor outside of its cortical layer (low translaminar). Although selected by RF BVI, length.avg and density_bifs, the box-plots (bottom part) show that these morphometrics were not univariately useful. Right: the nine selected morphometrics separate the NBC cells from non-NBC ones. The biplot shows the data projected onto the two principal components, found with principal component analysis, with the vectors representing the morphometrics and the angles between them indicative of their pairwise correlation. Besides branch length (length.avg), translaminar reach (translaminar), and arborization density (density_bifs), all selected morphometrics are related to arborization distance from soma. They correspond to the vectors pointing towards the right; only euclidean_dist.avg is annotated to avoid overlapping

Fig. 12

Relevant morphometrics for the DBC (above) and SBC and LBC (below) types. Top left: per-type boxplots for the morphometrics selected with RF BVI (RF BVI values shown, in blue, to the right). The axonal arbor of a typical DBC cell was radially oriented (high radial and eccentricity values), rather than circular, it did not spread far tangentially (low x_sd and width), and was mainly located below the soma (low y_std_mean and y_mean). Top right: the ten most relevant morphometrics according to KW, after removing those already shown in the left panel and those with an absolute correlation >0.90 with a better ranked morphometric (KW p-values shown, in blue, to the right). DBC cells’s dendrites were bipolar/bitufted (d.insert.radial, not shown), arborized along the radial axis (d.radial) and reached far radially (d.y_sd), while their axonal arbors were short (total_length), with wide terminal bifurcation angles (t.remote_bifurcation_angle.avg). Bottom left: per-type boxplots for the morphometrics selected with RF BVI for SBC (RF BVI values shown, in blue, to the right). SBC cells had short branches (low length.avg) and dense, local arbors (low density_bifs and euclidean_dist.avg). Bottom right: per-type boxplots for the morphometrics selected with RF BVI for LBC (RF BVI values shown, in blue, to the right). LBC cells had sharp bifurcation angles