Clustering and spatial distribution of mitochondria in dendritic trees

Highly extended neuronal cells face the challenging task of distributing their organelles, including the mitochondria which provide a source of energy for neuronal function. In dendrites, mitochondria form a ”social network” of variable-size clusters whose dynamic fusion and fission are thought to contribute to mitochondrial maintenance by helping spread mitochondrial material through the cell. 

Inspired by experimental measurements of mitochondrial transport and localization in Drosophila visual system neurons, we introduce a mass-aggregation model to describe the spatial distribution of mitochondrial clusters within dendritic arbors. Our model incorporates mitochondrial production, fusion, fission, and motor-driven transport, as well as the topology of the dendritic trees. We demonstrate that the steady-state cluster distributions arising in stochastic agent-based simulations can be predicted from an analytically tractable mean-field model.

We show that enhanced fusion probabilities at narrow distal branches are necessary to enable the formation of substantial mitochondrial clusters at distal tips. A fusion probability that scales steeply with branch radius gives rise to the experimentally observed distal enrichment of mitochondria. This steep scaling in turn engenders a high sensitivity to the mitochondrial production rate, such that small increases in production are predicted to greatly enhance dendritic mitochondrial content. Our results highlight the importance of branching tree topology in determining both the spatial distribution and size distribution of mitochondrial clusters. 

This modeling and simulation framework can also be expanded to explore the dynamic mixing and transport of mitochondrial material throughout the dendritic tree, demonstrating asymmetric spreading arising from the arbor geometry.