Mixing and Transport in Dendritic Mitochondria

Abstract

Neurons contain long, branched projections (axons and dendrites) whose distal tips play an important role in cell growth and signal transmission, requiring high rates of energy consumption. Mitochondria are localized throughout these projections in order to supply energy and buffer calcium levels. These dynamic organelles undergo continuous fusion and fission events, facilitating the delivery of newly synthesized proteins and the homogenization of mitochondrial contents. Our work focuses on the mathematical modeling of mixing through mitochondrial populations in complex neural geometries. We use a combination of agent-based simulations and mean-field modeling to probe the key physical features that govern the dispersion and turnover of mitochondrial material in dendritic trees. Our results demonstrate that the spreading of mitochondrial contents depends on a three key timescales - the turnover timescale, the spreading timescale, and the exchange timescale. Model predictions are compared against experimental data quantifying the dynamics of photoconverted mitochondrial protein in Drosophila sensory dendrites, with and without perturbed expression of the mitochondrial fusion factor Marf. Marf overexpression is observed to enhance protein dispersion without substantially altering the mitochondrial transport flux, consistent with a model that incorporates upregulated exchange between stationary and dynamic mitochondria. Overall, mixing in the mitochondrial population is found to be governed by a complex interplay of directed transport and interactions between individual organelles. The model can be extended to other systems with mixing and transport, as demonstrated by the axonal model for mitochondrial dynamics.