Intracellular transport in eukaryotic cells is a process in which cargo, carrying various materials and attached to molecular motors, moves around the cell. The cargos' transport consists of phases of passive, diffusion-based transport in the bulk cytoplasm and active, motor-driven transport along filaments that make up the cell's cytoskeleton. Because of it's role in the active phase of transport, the cytoskeletal geometry is an important factor. In this dissertation, we consider network parameters such as filament length, number, polarization direction, and location and examine their effect on the transport process. This can be achieved by computationally determining cargo transport through simulation and numerical analysis techniques.

We present this research by first demonstrating an approach that evolves a distribution of cargos in time using numerical integration. To do this, we use two coupled differential equations that enforce the distribution movement on and off filaments. An interesting finding here is that the distribution can become ``trapped" at what we consider intermediate filament lengths.

Although we mostly use a simplified model where normal diffusion governs the passive phase of transport, we also consider the effects of incorporating anomalous subdiffusion in the bulk. This means that the entire transport process can be described as anomalously diffusive, with the active transport phase being superdiffusive and the passive transport phase being subdiffusive. One thing we found by taking this approach is that filament length, rather than filament number, has a greater influence on the domination of overall superdiffusive transport at relatively early times compared to the domination of subdiffusive transport at later times. We were able to extend this observation to model the biphasic release of insulin out of cells in which there is a large spike in insulin release, followed by a slower, more sustained release.

In the final chapter, we consider the possibility of cargos capable of switching to different filaments. If multiple motors are attached to a cargo, it can switch from one filament to another, provided one is nearby. In this phase of our research, we took real images of networks of microtubule bundles and extracted network parameters from them in order to run our simulations. We compared our simulation data, where cargos had different switching probabilities, with experimental data, where cargos had different numbers of motors, and were able to draw a correlation between cargo switching probability and motor number. The network images and the experimental data were provided by our collaborator, Professor Jennifer Ross at UMass, Amherst.