A theoretical study of cell evolution is presented here. By using a toolbox containing an intracellular catalytic reaction network model and a mutation-selection process, four distinct phases of self-organization were unveiled. First, the nutrients prevail as the central substrate of the chemical reactions. Second, the cell becomes a small-world. Third, a highly connected core component emerges, concurrently with the nutrient carriers becoming the central product of reactions. Finally, the cell reaches a steady configuration where the concentrations of the core chemical species are described by Zipf's law.