Localization of messenger RNA (mRNA) at the vegetal cortex plays an important role in the early development of Xenopus laevis oocytes. While it is known that molecular motors are responsible for the transport of mRNA cargo along microtubules to the cortex, the mechanisms of localization remain unclear. We model cargo transport along microtubules using partial differential equations with spatially-dependent rates. A theoretical analysis of reduced versions of our model predicts effective velocity and diffusion rates for the cargo and shows that randomness of microtubule networks enhances effective transport. A more complex model using parameters estimated from fluorescence microscopy data reproduces the spatial and timescales of mRNA localization observed in Xenopus oocytes, corroborates experimental hypotheses that anchoring may be necessary to achieve complete localization, and shows that anchoring of mRNA complexes actively transported to the cortex is most effective in achieving robust accumulation at the cortex.
Keywords: 35B40; 35K57; 92C15; 92C40; anchoring; intracellular transport; long-time dynamics; microtubules; reaction-diffusion model.