Transport of intracellular material is a fundamental process observed within the cells of organisms across all realms of life. While the biology may be vastly different across species, the physical mechanisms underlying motion remain largely consistent. Tubular cells such as neuronal axons and fungal hyphae are excellent systems to study transport owing to their simple geometry, robust transport machinery, and experimental tractability. We combine mathematical and computational approaches to explore how transport processes contribute to intracellular organization and affect biological function. Imaging data from neuronal and fungal cells are leveraged to develop functional models and verify their predictions.

Neurons are large eukaryotic cells with high metabolic demands. Intracellular transport plays an important role in maintaining metabolic functioning in neurons despite heterogeneous spatio-temporal energetic demands. Mitochondria are the primary source of ATP in neurons and are distributed through motor-driven transport along neuronal cytoskeleton from the cell body of the neuron (soma) to long neuronal projections (axons and dendrites). Transport-based organization of mitochondria is regulated through a combination of mechanisms that control mitochondrial dynamics and its interplay with neuronal cytoskeleton.

One important regulatory mechanism is the control of mitochondrial motility through molecules such as glucose and Calcium that are localized to high metabolic activity regions in axons. In Chapter 2, we use a reaction-diffusion framework to analyze how glucose-regulated mitochondrial motility can be an effective mechanism within physiological limits to adapt metabolic organization to increase mitochondrial glucose turnover.

While local changes in motor activity of mitochondria create local stationary populations to service high-demand sites, there is still the issue of how mitochondrial populations across the long length scales of neuronal projections are maintained at varying distances from the soma throughout neuronal lifetimes. In Chapter 3, we develop a quantitative framework to understand how mitochondrial dynamics of transport, fusion-fission, and mitophagy, can be tuned to optimize the distribution of healthy mitochondria throughout interspersed sites located in long and occasionally branched axonal projections.

On longer length scales, axons and dendrites have interesting branched morphologies. Mitochondrial distribution patterns need to be robust to variations in subtree morphologies in dendrites so that distal branches with high metabolic activity have equitable but increased supply of mitochondria. In Chapter 4, we show that a combination of morphological scaling rules and mitochondrial transport behavior can explain how mitochondria are `equitably' distributed in a Drosophila HS dendritic tree yet still maintaining increased densities in distal tips. Our predicted laws are corroborated by experimental observations of dendritic morphology and mitochondrial motility.

This dissertation combines various quantitative models at different scales in neurons to understand how mitochondrial distribution patterns can lead to robust metabolic fulfillment in neurons.