Gene Regulation:
Gene regulation refers to the mechanisms by which cells control the expression of their genes. It involves the processes that turn genes on and off, as well as those that determine the amount of gene product (protein or RNA) that is produced.

Lac Operon:
The lac operon is a classic example of gene regulation in bacteria. It consists of three structural genes (lacZ, lacY, and lacA) that are involved in the metabolism of lactose, as well as regulatory elements (promoter, operator, and regulator gene) that control the expression of these genes.

Diagram:
Here is a diagram illustrating the lac operon:

```
___________
mRNA ->| |
| lacZ |
| |
| lacY |
| |
| lacA |
|___________|
| |
| Operator |
| |
| Promoter |
|___________|
| |
| Regulator|
| Gene |
|___________|
```

Explanation:
The lac operon is responsible for the metabolism of lactose in bacteria, such as Escherichia coli. It consists of three structural genes: lacZ, lacY, and lacA. The lacZ gene encodes the enzyme β-galactosidase, which breaks lactose down into glucose and galactose. The lacY gene encodes the lactose permease, which transports lactose into the cell. The lacA gene encodes transacetylase, which is involved in the removal of toxic intermediates.

The expression of the lac operon is regulated by the presence or absence of lactose in the environment. When lactose is not available, the lac repressor protein binds to the operator region of the operon, preventing the RNA polymerase from transcribing the structural genes. This is known as repression.

When lactose is present, it is converted into allolactose, which binds to the lac repressor protein and causes it to dissociate from the operator. This allows the RNA polymerase to bind to the promoter and initiate transcription of the structural genes. This is known as induction.

The lac operon also demonstrates the concept of negative regulation. The lac repressor protein is encoded by the regulator gene, located upstream of the operon. In the absence of lactose, the lac repressor is active and inhibits gene expression. In the presence of lactose, the lac repressor is inactivated, allowing gene expression to occur.

In summary, the lac operon is a classic example of gene regulation in bacteria. It demonstrates how the expression of genes can be controlled in response to environmental conditions, such as the presence or absence of specific molecules.