Mathematical modeling of the intracellular protein dynamics: The importance of active transport along microtubules

In this paper we propose a mathematical model of protein and mRNA transport inside a cell. The spatio-temporal model takes into account the active transport along microtubules in the cytoplasm as well as diffusion and is able to reproduce the oscillatory changes in protein concentration observed in many experimental data. In the model the protein and the mRNA interact with each other that allows us to classify the model as a simple gene regulatory network. The proposed model is generic and may be adapted to specific signaling pathways. On the basis of numerical simulations, we formulate a new hypothesis that the oscillatory dynamics is allowed by the mRNA active transport along microtubules from the nucleus to distant locations.