Diffusive spreading across dynamic mitochondrial network architectures

In eukaryotic cells, mitochondria form networks that range from highly fused interconnected structures to fragmented populations of individual organelles that undergo transient interactions. These structures can be described as temporal networks of physical units, whose dynamic topology is determined by fusion, fission, and motion of the mitochondria through intracellular space. The heterogeneity of the mitochondrial population is governed by diffusive transport and interunit exchange of proteins, lipids, ions, and RNA within these networks. We present a unifying framework for the dispersion of material within temporal networks of spatially embedded units that span across a broad connectivity range. Specifically, we consider filling of the networks with a locally produced but globally consumed material, demonstrating that the steady-state content is determined by the balance of timescales for spatial encounter between clusters, local fusion, fission, and diffusive transport within a cluster. As the connectivity increases, filling behavior transitions from three-dimensional spread through a "social network" limited by cluster interactions to low-dimensional transport through a largely stationary "physical network" limited by material diffusivity. We extract parameters for mitochondrial networks in three human cell lines, demonstrating that different cells can access both the social and the physical network regimes. These results provide a quantitative basis for predicting the homogenization of biomolecules through a mitochondrial population. Our framework unifies a variety of temporal network structures into an overarching theory for transport through populations of interacting and interconnected units.