**Core Concept**
The question is testing the understanding of gene regulation in E. coli, specifically the concept of constitutive expression. Constitutive expression refers to the continuous production of a gene product, regardless of the presence of an inducer or repressor. This is often achieved through the use of promoters that are not regulated by external factors.

**Why the Correct Answer is Right**
In E. coli, the lac operon is a well-known example of a regulated gene expression system. However, the lac repressor protein can be overcome by the presence of a strong inducer like IPTG. In contrast, the gene constitutively expressed in E. coli is the lacZ gene, which encodes for beta-galactosidase. The lacZ gene is not part of the lac operon and is instead transcribed from a constitutive promoter, ensuring its continuous expression. This is crucial for the cell's ability to degrade lactose and other galactosides.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is not provided, so we cannot comment on it.
* **Option B:** This option is also not provided, so we cannot comment on it.
* **Option C:** This option is not provided, so we cannot comment on it.
* **Option D:** This option is not provided, so we cannot comment on it.

**Clinical Pearl / High-Yield Fact**
The lacZ gene's constitutive expression is a key factor in the development of beta-galactosidase assays, which are widely used in molecular biology to detect gene expression and protein activity.

**Correct Answer: lacZ. lacZ gene, which encodes for beta-galactosidase.**