An enzyme that cleaves internal phosphodiester bonds of a DNA molecule is called an endonuclease.
Endonucleases are enzymes that specifically cleave DNA or RNA at internal sites, typically within the nucleotide sequence. These enzymes recognize specific DNA sequences, known as recognition sites or restriction sites, and cleave the phosphodiester bonds within those sites. Endonucleases play a crucial role in various molecular biology techniques, such as DNA digestion, restriction mapping, and cloning.
Option A, exonuclease, is an enzyme that cleaves nucleotides one at a time from the ends of a DNA or RNA molecule. Exonucleases can work in either the 5' to 3' direction (5' exonuclease) or the 3' to 5' direction (3' exonuclease).
Option C, ligase, is an enzyme that catalyzes the joining or ligation of DNA or RNA fragments by forming phosphodiester bonds between them. Ligases are commonly used in recombinant DNA technology to join DNA fragments, such as during cloning or the construction of recombinant molecules.
Option D, methylase, is an enzyme that adds a methyl group to specific nucleotides in DNA, typically for the purpose of regulating gene expression or protecting DNA from restriction endonucleases.
Therefore, the correct answer is B. Endonuclease.