Final answer:
The Lac repressor's low copy number is adequate due to its high binding efficiency to the operator of the lac operon, controlling gene expression based on lactose availability and conserving cellular resources.
Step-by-step explanation:
The Lac repressor is present in only 10 copies per cell in E. coli because its role is to regulate the expression of the lac operon in response to the availability of lactose and glucose. In the absence of lactose, the Lac repressor binds to the operator region very efficiently, preventing RNA polymerase from transcribing the lac genes.
This system is highly sensitive to the presence of lactose, which acts as an inducer by binding to the repressor and causing its release from the operator, thereby allowing the transcription of the lac operon. The low number of repressor molecules is sufficient to control the transcription of the operon because of the high binding affinity of the Lac repressor to the operator.
This regulatory mechanism ensures that the lac genes are only expressed when needed, conserving energy and resources by not producing lactose metabolizing enzymes when lactose is not available and glucose is present. When glucose levels are low and lactose is available, the repressor is released from the operator, and the operon is expressed, facilitating the metabolism of lactose by producing the necessary enzymes.