Motivated by the desire to automate classification of neuron morphologies, we designed a topological signature, the Topological Morphology Descriptor (TMD), that assigns a so-called “barcode" to any geometric tree (i.e, any finite binary tree embedded in R^3). We showed that the TMD effectively determines reliable clusterings of random and neuronal trees. Moreover, using the TMD we performed an objective, stable classification of pyramidal cells in the rat neocortex, based only on the shape of their dendrites.
We have also reverse-engineered the TMD, in order to digitally synthesize dendrites, to compensate for the relatively small number of available biological reconstructions. The algorithm we developed, called Topological Neuron Synthesis (TNS), stochastically generates a geometric tree from a barcode, in a biologically grounded manner. The synthesized neurons are statistically indistinguishable from real neurons of the same type, in terms of morpho-electrical properties and connectivity. We synthesized networks of structurally altered neurons, revealing principles linking branching properties to the structure of large-scale networks. We have also successfully applied these classification and synthesis techniques to microglia and astrocytes, two other types of cells that populate the brain.
In this talk I will provide an overview of the TMD and the TNS and then describe the results of our theoretical and computational analysis of their behavior and properties.
This talk is based on work in collaborations led by Lida Kanari at the Blue Brain Project.