Polymer Physics-Based Classification of Neurons

Abstract

Recognizing that diverse morphologies of neurons are reminiscent of structures of branched polymers, we put forward a principled and systematic way of classifying neurons that employs the ideas of polymer physics. In particular, we use 3D coordinates of individual neurons, which are accessible in recent neuron reconstruction datasets from electron microscope images. We numerically calculate the form factor, F(q), a Fourier transform of the distance distribution of particles comprising an object of interest, which is routinely measured in scattering experiments to quantitatively characterize the structure of materials. For a polymer-like object consisting of n monomers spanning over a length scale of r, F(q) scales with the wavenumber $q(=2\pi /r)$ as $F(q)\sim q^{-\mathcal {D}}$ at an intermediate range of q, where $\mathcal {D}$ is the fractal dimension or the inverse scaling exponent ($\mathcal {D}=\nu ^{-1}$) characterizing the geometrical feature ($r\sim n^{\nu }$) of the object. F(q) can be used to describe a neuron morphology in terms of its size ($R_n$) and the extent of branching quantified by $\mathcal {D}$. By defining the distance between F(q)s as a measure of similarity between two neuronal morphologies, we tackle the neuron classification problem. In comparison with other existing classification methods for neuronal morphologies, our F(q)-based classification rests solely on 3D coordinates of neurons with no prior knowledge of morphological features. When applied to publicly available neuron datasets from three different organisms, our method not only complements other methods but also offers a physical picture of how the dendritic and axonal branches of an individual neuron fill the space of dense neural networks inside the brain.