A polymerase is an enzyme (EC 2.7.7.6/7/19/48/49) that synthesizes long chains of polymers or nucleic acids. DNA polymerase and RNA polymerase are used to assemble DNA and RNA molecules, respectively, by copying a DNA template strand using base-pairing interactions or RNA by half ladder replication.
A polymerase from the thermophilic bacterium, Thermus aquaticus (Taq) (PDB 1BGX, EC 2.7.7.7) is used in the polymerase chain reaction, an important technique of molecular biology.

DNA polymerase

The enzyme synthesizes DNA from a DNA template. The intact enzyme purified from bacteria (termed the holoenzyme) has both synthetic and editing functions. The editing function results from nuclease activity.

Klenow fragment

A modified version of bacterial DNA polymerase has been modified so that only the polymerase function remains; the 5\’➝3\’ exonuclease activity has been eliminated.

Thermostable polymerases

The prototype polymerase, Taq, and newer versions such as Vent and Tth polymerase are derived from microorganisms that normally reside at high temperatures. Consequently, their DNA polymerase enzymes are quite stable to heat denaturation, making them ideal enzymes for use in the polymerase chain reaction.

RNA polymerase II

This enzyme is used by mammalian cells to transcribe structural genes that result in mRNA. The enzyme interacts with a number of other proteins to correctly initiate transcription, including a number of general factors, and tissue-specific and induction-specific enhancing proteins.

RNA polymerase III

The genes transcribed by RNA Pol III fall in the category of \”housekeeping\” genes whose expression is required in all cell types and most environmental conditions.
Other well-known polymerases include:

Terminal Deoxynucleotidyl Transferase (TDT)

Terminal deoxynucleotidyl transferase (TdT), also known as DNA nucleotidylexotransferase (DNTT) or terminal transferase, is a specialized DNA polymerase expressed in immature, pre-B, pre-T lymphoid cells, and acute lymphoblastic leukemia/lymphoma cells. It lends diversity to antibody-heavy chains.

Reverse Transcriptase

An enzyme used by RNA retroviruses like HIV is used to create a complementary strand to the preexisting strand of viral RNA before it can be integrated into the DNA of the host cell. It is also a major target for antiviral drugs.
References:
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