Genetic regulation networks orchestrate many complex cellular behaviors. Dynamic operations that take place within cells are thus dependent on the gene expression machinery, enabled by powerful enzymes such as polymerases, ribosomes, or nucleases. These generalist enzymes typically process many different substrates, potentially leading to competitive situations: by saturating the common enzyme, one substrate may down-regulate its competitors. However, most theoretical or experimental models simply omit these effects, focusing on the pattern of genetic regulatory interactions as the main determinant of network function. We show here that competition effects have important outcomes, which can be spotted within the global dynamics of experimental systems. Further we demonstrate that enzyme saturation creates a layer of cross couplings that may foster, but also hamper, the expected behavior of synthetic biology constructs.