When lactose levels are low, what is the state of the lac repressor?

When lactose levels are low, the lac repressor is bound to the operator region of the lac operon. This binding is crucial for regulating the expression of genes involved in the metabolism of lactose. The presence of the repressor prevents RNA polymerase from accessing the promoter and transcribing the downstream genes, effectively inhibiting expression in the absence of lactose.

In conditions where lactose is scarce, the repressor remains attached to the operator, thereby blocking transcription. The repressor's role is to ensure that the operon is only activated when lactose is available, as the lac operon should only be expressed when its substrate is present.

With regards to the other options, when lactose is low, the repressor is in a functional state that actively inhibits transcription rather than being inactive or promoting transcription. It is also not the case that the repressor itself is synthesized in response to low lactose levels; instead, it is synthesized independently as part of the operon's regulatory mechanisms.