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Conceived and designed the experiments: HC FF AB. Performed the experiments: FF JH. Analyzed the data: HC FF. Wrote the paper: HC FF AB.

The authors have declared that no competing interests exist.

Dendrite morphology, a neuron's anatomical fingerprint, is a neuroscientist's asset in unveiling organizational principles in the brain. However, the genetic program encoding the morphological identity of a single dendrite remains a mystery. In order to obtain a formal understanding of dendritic branching, we studied distributions of morphological parameters in a group of four individually identifiable neurons of the fly visual system. We found that parameters relating to the branching topology were similar throughout all cells. Only parameters relating to the area covered by the dendrite were cell type specific. With these areas, artificial dendrites were grown based on optimization principles minimizing the amount of wiring and maximizing synaptic democracy. Although the same branching rule was used for all cells, this yielded dendritic structures virtually indistinguishable from their real counterparts. From these principles we derived a fully-automated model-based neuron reconstruction procedure validating the artificial branching rule. In conclusion, we suggest that the genetic program implementing neuronal branching could be constant in all cells whereas the one responsible for the dendrite spanning field should be cell specific.

Neural computation has been shown to be heavily dependent not only on the connectivity of single neurons but also on their specific dendritic shape—often used as a key feature for their classification. Still, very little is known about the constraints determining a neuron's morphological identity. In particular, one would like to understand what cells with the same or similar function share anatomically, what renders them different from others, and whether one can formalize this difference objectively. A large number of approaches have been proposed, trying to put dendritic morphology in a parametric frame. A central problem lies in the wide variety and variability of dendritic branching and function even within one narrow cell class. We addressed this problem by investigating functionally and anatomically highly conserved neurons in the fly brain, where each neuron can easily be individually identified in different animals. Our analysis shows that the pattern of dendritic branching is not unique in any particular cell, only the features of the area that the dendrites cover allow a clear classification. This leads to the conclusion that all fly dendrites share the same growth program but a neuron's dendritic field shape, its “anatomical receptive field”, is key to its specific identity.

Dendrite morphology is the most prominent feature of nerve cells, typically used by
neuroanatomists to discriminate and classify them

We studied inter-individual constancy and variability in four members of the LPTC
group: the equatorial and the northern cell of the horizontal system (HSE and HSN,

(A,B), Sketches showing HSE and HSN (A) and VS2 and VS4 (B) in the context of the lobula plate (gray). (C,D), Superimposed full anatomies of all individual cells sorted according to their respective cell type. Cells were aligned along their axonal axis (red lines). To the right, the corresponding dendrite spanning fields are outlined. (E–K) Statistics specifically related to dendrite branching. Statistics are represented as superimposed distribution histograms, filled squares show mean values and error bars correspond to standard deviation between individual dendrites: (E) path length to root values for all topological points; (F) ratios between direct and path distances from each topological point to the dendrite root; (G) topological point branching order values, a measure for the topological distance from the dendrite root; (H) length values of branch pieces between topological points; (I) branching angle values at all branching points between the two direct daughter branches within the plane in which they lay; (K) surface area values assigned to each topological point after Voronoi segmentation indicating topological point density and distribution homogeneity. (L) Sholl intersection plots: number of intersections of each tree with circles with increasing diameter. (M–R) Statistics describing the dendrite spanning field: (M) total surface value of spanning field; (N) percentage of the spanning field below the axonal axis; (O) convexity index of the spanning field; (P) ratio of width against height of the spanning field; (Q and R) horizontal and vertical coordinates of centre of mass of the dendrite spanning field.

Regarding branching-specific statistics (

(A) Dendrite spanning fields are readily separable into the individual cell
types at the example here of two parameters only: the convexity and the
relative location to the axonal axis (B) Cluster analysis using three
parameters of a generalized extreme value distribution fits for branching
properties from

In order to identify the critical impact of spanning field shape on branching
parameters, artificial dendrites were constructed covering the same region. Inside
the contours of the original cells, random points were distributed following their
respective density map. An iterative greedy algorithm was launched starting at the
coordinates of the real dendrite root. At each step, a connection was added from the
existing tree to one of the unconnected random points according to a cost function
which kept house of both total amount of wiring and total path length from the root
to each point

(A) Artificial dendrites: two examples of each cell type. Upper row: real
dendrites. Lower row, marked by preceding “m”:
artificial dendrites corresponding to each of the spanning field. (B)
Artificial dendrite parameter distributions as in

Consequently, one could consider that original raw fluorescent images containing a
labelled neuron would correspond to a distribution of interconnected points within a
spanning field. Then, if our assumptions about the branching rule are correct, one
should be able to apply it to obtain the branching model directly from the image
material. We therefore applied the same greedy algorithm describing our branching
rule for artificial dendrites on structural points extracted from the raw data via
image skeletonization. The results of such an attempt are shown at the examples of
an HSE dendrite (

Depicted at the example of an HSE dendrite (A,B) and of a VS2 cell (C,D). Left, maximum intensity projections of the image stacks containing fluorescent cells. Right, overlaid reconstructed branching in red.

In summary, we claim that all cells analysed here follow the same branching rule, and
that their morphological identifier is the shape of their dendrite spanning fields.
This claim is supported by the presented branching statistics, the previously
proposed branching rule

Female blowflies (

For simplification, the resulting generic directed graphs were transformed into
strict binary trees by substituting multifurcations with several bifurcations
after minimally shifting the branches on their parent cylinder. Region indices

Clustering (

Boundary-corrected density maps of dendrite topological points were derived from
real cell dendrites (

3D image stacks from one HSE dendrite and a full VS2 cell were submitted to 2D
anisotropic filtering, morphological closure and subsequent brightness level
thresholding. After 3D skeletonization and sparsening the carrier points, the
remaining points were submitted to the same greedy algorithm (started at a user
defined dendrite root location) as used for obtaining artificial dendrites
Quadratic diameter decay was mapped on the resulting trees

Sketches describing the manual cell reconstruction process and the subsequent
handling of dendrite morphology. (A) Assembled maximum Z-Projection of an
HSN with ten overlapping image stacks. (B) Example of a reconstructed
sub-tree of an HSN cell superimposed on a single slice from one image stack.
(C) Compromising effects of the maximum Z-Projection (right) compared to the
original slice (left, arrows show loss of branches). (D) Examples of
automatic diameter approximations. Normalized positions 0.25, 0.5 and 0.75
on the midline and 40 half pixels in orthogonal direction were used to
construct a sampling grid that covers a branch's thickness (first
panel). The average over the resulting sampling matrix was convolved with
the first derivative of a Gaussian distribution (little box) to emphasize
brightness changes. The diameter was obtained by the distance from the
centre of the maximum plateau in the mean signal to the null in the
derivative of the convolved signal. (E) Planar dendrites were mapped
entirely to two dimensional space (black original, red flattened dendrite).
(F) The dendrite spanning fields were determined by drawing a region at 25
μm away from any point on the dendrite. (G) Topological point density
distribution was obtained by Voronoi segmentation (green borders) with a
dendrite spanning field boundary. Shaded gray scale indicates surface area
of Voronoi pieces. Overlaid dendrite in red. (H–P) Steps in the
creation of artificial dendrites: (H) dendrite topological points were
morphologically closed (dilation followed by erosion) with a 25 μm
radius disc and the resulting binary image smoothened with a Gaussian filter
of 25 μm variance; (I) This was then cut out by the boundaries of the
closed image, representing for each location in the dendrite spanning field
the error made when smoothly averaging the density; (K) density estimation
of topological points by Gaussian filtering with a 25 μm variance.
(L) the density map in (K) was normalized by the estimation error obtained
in (I); (M) random points (green) were distributed according to the
corrected density distribution with sharp boundaries; (N) preliminary
artificial dendrite following the iterative greedy algorithm presented
previously

(4.55 MB TIF)

Supplementary information on cluster analysis. (A) Generalized extreme value
fits for the distributions shown in

(1.20 MB TIF)

Overview of all 45 reconstructed LPTC dendrites and their artificial
correlates. (A) Real manual dendrite reconstructions. (B) All constructed
artificial LPTC dendrites. The model dendrites were grown in the spanning
fields displayed in (A) in the same order. Diameter tapering was mapped here
onto the branching structures for visual aesthetic purposes

(2.02 MB TIF)

Demonstration of the artificial growth process. Dark red axonal arborizations
are randomly distributed and correspond to target points. Iteratively,
unconnected points are added to the tree (green). At each time step, for
visual purposes, diameter tapering was mapped onto the tree as in

(2.77 MB AVI)