Understanding dendritic branching statistics using maximum entropy models

Dendrite morphology is known to play an important role for neural computation and cells of the same class typically express characteristic properties in their dendritic structures, despite the fact that no two dendrites are exactly the same. In an attempt to capture those properties, a considerable number of different statistics for dendritic tree structures have been proposed over the last decades. Yet, their statistical power, e.g. for clustering neurons into well-known cell classes remained limited. Using a large data set of reconstructed dendritic trees from different species and brain regions, we give an overview of the commonly considered statistics and show that many of them are highly correlated, explaining their weak power in classification tasks. We furthermore devise simple maximum entropy null-models based on optimization principles already postulated by Ramon y Cajal that are able to explain in most cases both the observed distributions and pairwise correlations of common branching statistics. We conclude by presenting a number of novel statistics based on tree structure via centripetal branch orderings (Strahler numbers) and discuss what these

observations could mean for the configuration space occupied by dendritic trees.

This is joint work with Hermann Cuntz.