The gene that specifies a protein that binds to an operator and physically blocks RNA polymerase from binding the promoter site is called the repressor gene.

Here's a breakdown:

* Operator: This is a short sequence of DNA located near the promoter.

* Repressor protein: This protein is encoded by the repressor gene. It binds to the operator, physically blocking RNA polymerase from accessing the promoter.

* Promoter: This is the region of DNA where RNA polymerase binds to initiate transcription.

How it works:

1. The repressor protein is usually bound to the operator, preventing RNA polymerase from accessing the promoter and transcribing the genes in the operon.

2. When a specific signal (like the presence of a molecule the cell needs) is detected, it binds to the repressor protein, changing its shape and causing it to release from the operator.

3. This allows RNA polymerase to bind to the promoter and begin transcribing the genes in the operon.

Example:

A classic example is the lac operon in bacteria. The repressor protein for the lac operon binds to the operator and blocks transcription of the lac genes unless lactose is present. When lactose is present, it binds to the repressor, causing it to release from the operator, allowing transcription of the lac genes.

Let me know if you'd like to know more about specific operons or the mechanisms of gene regulation!