Homeostasis of protein concentrations in cells is crucial for their proper functioning, and this requires concentrations (at their steady-state levels) to be stable to fluctuations. I will present a minimal gene expression model to capture the homeostasis of protein and mRNA concentrations in growing cells. Notably, the model predicts that the exponential growth of cell volume can be violated as the cell volume exceeds a threshold, which has recently been experimentally observed. We will show how fluctuations of protein concentrations provide additional information on the nature of gene expression. Using this model, we explore factors affecting the stability of the gene regulatory network. We find that the system goes unstable if the regulation strength or system size becomes too large, and that other global structural features of actual transcriptional networks can dramatically enhance stability. Contrary to what one might expect from random matrix theory, mRNA degradation rate does not affect system stability. Our findings suggest that constraints imposed by system stability may have played a role in shaping the existing regulatory network during evolution.