Mathematical model of nucleocytoplasmic transport and nuclear-to-cell ratio in a growing cell

It has been observed that the growth of the nucleus and the cytoplasm is coordinated during cell growth, resulting in a nearly constant nuclear-to-cell volume ratio (N/C) throughout the cell cycle. Previous studies have shown that the N/C ratio is determined by the ratio between the number of proteins in the nucleus and the total number of proteins in the cell. These observations suggest the importance of the nucleocytoplasmic transport process in nuclear size by regulating protein concentrations in the nucleus and cytoplasm. This paper combines a biophysical model of Ran-mediated nucleocytoplasmic transport and a simple cell growth model to provide insights into several key aspects of the N/C ratio homeostasis in growing cells. Our model shows that the permeability of the nuclear envelope needs to grow in line with the cell to maintain a nearly constant N/C ratio, that several parameters involved in the nucleocytoplasmic transport mechanism and gene translation significantly affect the N/C ratio, and that Ran may potentially compensate for the lack of NTF2 in the nucleocytoplasmic transport mechanism to maintain a viable N/C ratio. However, this compensation is possible only if RanGDP is allowed to translocate through the nuclear envelope independently of NTF2.