Step-by-step explanation:
Three enzymes for lactose metabolism are grouped in the lac operon: lacZ (β-galactosidase), lacY (permease) and lacA (trans-acetylase). The transcription of this operon occurs only when lactose is available to digest, presumably to avoid wasting energy. Apart from these protein-coding genes we have P(promoter), O(operator and CBS(Cap-binding site), sequences that work as binding sites for transcriptional regulation.
Negative components: An important regulator is lacI when four of these molecules assemble they form a repressor, this will bind to the promoter, this won't allow the operon to be transcribed as long as the operator is occupied by a repressor. LacI can also prevent lactose to bind to the operator by binding with it and changing its shape.
Positive components: cAMP binding protein is another molecule that when is bound to CBS improves the chance of RNA polymerase to bind to the promoter to initiate transcription.
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I adden an image that ilustrates what I explained.