Final answer:
The lac operon in bacteria is an inducible operon activated in the presence of lactose through the inactivation of the lac repressor and the enhancement of RNA polymerase binding by the cAMP-CAP complex. Conversely, the trp operon is a repressible operon that is inactivated in the presence of high levels of tryptophan, preventing transcription of tryptophan synthesis genes.
Step-by-step explanation:
Gene Regulation in Prokaryotes: The lac and trp Operons
Prokaryotic cells such as bacteria have evolved intricate systems to regulate gene expression in response to environmental changes. An example of such regulation is seen with the lac operon in the presence of lactose. When lactose is added to the environment of a bacterial cell, it induces the expression of the genes necessary for its metabolism. This cascade involves the inactivation of the lac repressor by lactose, which prevents the repressor from binding to the operator. Subsequently, RNA polymerase can bind to the promoter and initiate transcription of the lactose metabolism genes. Simultaneously, if glucose levels are low, cyclic AMP (cAMP) binds to the catabolite activator protein (CAP), and the cAMP-CAP complex then binds to the promoter to enhance RNA polymerase activity, increasing the efficiency of transcription initiation.
Comparatively, the trp operon functions via repressible control, which operates in a manner that is inversely related to the abundance of tryptophan. When tryptophan levels are high, it binds to the trp repressor protein, which then binds to the operator region, preventing RNA polymerase from transcribing the tryptophan synthesis genes. Thus, the operon is repressed when the end product, tryptophan, is plentiful, and it is not economical for the cell to synthesize more.
Overall, the lac operon is an example of an inducible operon that is turned on by the substrate it catabolizes (lactose), while the trp operon is a repressible operon that is turned off by the product it synthesizes (tryptophan).