Part of Advances in Neural Information Processing Systems 14 (NIPS 2001)

*Giorgio Ascoli, Alexei Samsonovich*

Visual inspection of neurons suggests that dendritic orientation may be determined both by internal constraints (e.g. membrane tension) and by external vector fields (e.g. neurotrophic gradients). For example, basal dendrites of pyramidal cells appear nicely fan-out. This regular orientation is hard to justify completely with a general tendency to grow straight, given the zigzags observed experimentally. Instead, dendrites could (A) favor a fixed (“external”) direction, or (B) repel from their own soma. To investigate these possibilities quantitatively, reconstructed hippocampal cells were subjected to Bayesian analysis. The statistical model combined linearly factors A and B, as well as the tendency to grow straight. For all morphological classes, B was found to be significantly positive and consistently greater than A. In addition, when dendrites were artificially re-oriented according to this model, the resulting structures closely resembled real morphologies. These results suggest that somatodendritic repulsion may play a role in determining dendritic orientation. Since hippocampal cells are very densely packed and their dendritic trees highly overlap, the repulsion must be cell- specific. We discuss possible mechanisms underlying such specificity.

1 Int r oduc t i on

The study of brain dynamics and development at the cellular level would greatly benefit from a standardized, accurate and yet succinct statistical model characterizing the morphology of major neuronal classes. Such model could also provide a basis for simulation of anatomically realistic virtual neurons [1]. The model should accurately distinguish among different neuronal classes: a morphological difference between classes would be captured by a difference in model parameters and reproduced in generated virtual neurons. In addition, the model should be self-consistent: there should be no statistical difference in model parameters measured from real neurons of a given class and from virtual neurons of the same class. The assumption that a simple statistical model of this sort exists relies on the similarity of average environmental and homeostatic conditions encountered by individual neurons during development and on the limited amount of genetic information that underlies differentiation of neuronal classes.

Previous research in computational neuroanatomy has mainly focused on the topology and internal geometry of dendrites (i.e., the properties described in “dendrograms”) [2,3]. Recently, we attempted to include spatial orientation in the models, thus generating

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virtual neurons in 3D [4]. Dendritic growth was assumed to deviate from the straight direction both randomly and based on a constant bias in a given direction, or “tropism”. Different models of tropism (e.g. along a fixed axis, towards a plane, or away from the soma) had dramatic effects on the shape of virtual neurons [5]. Our current strategy is to split the problem of finding a statistical model describing neuronal morphology in two parts. First, we maintain that the topology and the internal geometry of a particular dendritic tree can be described independently of its 3D embedding (i.e., the set of local dendritic orientations). At the same time, one and the same internal geometry (e.g., the experimental dendrograms obtained from real neurons) may have many equally plausible 3D embeddings that are statistically consistent with the anatomical characteristics of that neuronal class. The present work aims at finding a minimal statistical model describing local dendritic orientation in experimentally reconstructed hippocampal principal cells.

Hippocampal neurons have a polarized shape: their dendrites tend to grow from the soma as if enclosed in cones. In pyramidal cells, basal and apical dendrites invade opposite hemispaces (fig. 1A), while granule cell dendrites all invade the same hemispace. This behavior could be caused by a tendency to grow towards the layers of incoming fibers to establish synapses. Such tendency would correspond to a tropism in a direction roughly parallel to the cell main axis. Alternatively, dendrites could initially stem in the appropriate (possibly genetically determined) directions, and then continue to grow approximately in a radial direction from the soma. A close inspection of pyramidal (basal) trees suggests that dendrites may indeed be repelled from their soma (Fig. 1B). A typical dendrite may reorient itself (arrow) to grow nearly straight along a radius from the soma. Remarkably, this happens even after many turns, when the initial direction is lost. Such behavior may be hard to explain without tropism. If the deviations from straight growth were random, one should be able to “remodel” th e trees by measuring and reproducing the statistics of local turn angles, assuming its independence of dendritic orientation and location. Figure 1C shows the cell from 1A after such remodeling. In this case basal and apical dendrites retain only their initial (stemming) orientations from the original data. The resulting “cotton ball” s uggests that dendritic turns are not in dependent of dendritic orientation. In this paper, we use Bayesian analysis to quantify the dendritic tropism.

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