We propose a spatio-temporal model of intracellular protein dynamics i.e. protein and mRNA transport, inside a cell, that takes into account active transport along microtubules in the cytoplasm as well as diffusion and is able to reproduce the oscillations in protein and mRNA levels observed in many experimental data. The mathematical model is generic, having in mind the possibility of future extension and modification to model and analyse specific signaling pathways. On the basis of our computational simulations, we formulate a new hypothesis that the oscillatory dynamics is controlled by the active transport of mRNA along the microtubules from the nucleus to distant locations.