Restriction enzymes are naturally occurring enzymes found in bacteria, where they serve as a defense mechanism against viral DNA. Each restriction enzyme recognizes a unique palindromic DNA sequence, typically 4-8 base pairs long. Upon binding to its recognition site, the enzyme cleaves the phosphodiester bond in the DNA backbone. The cleavage can result in either 'blunt ends' or 'sticky ends'. Sticky ends have short, single-stranded overhangs that can readily base-pair with complementary sticky ends, facilitating ligation.

DNA ligase catalyzes the formation of a phosphodiester bond between the 3'-hydroxyl end of one nucleotide and the 5'-phosphate end of another. In rDNA technology, it is used to join the gene of interest (often with sticky ends) to a compatible vector molecule (also with complementary sticky ends). This enzymatic action creates a stable, continuous recombinant DNA molecule.

Plasmids contain an origin of replication (ori) that allows them to be replicated independently of the host chromosome. They also typically carry selectable marker genes, such as antibiotic resistance genes, which help in identifying bacterial cells that have successfully taken up the plasmid. Plasmids can accommodate DNA inserts of moderate size (up to ~15 kb).

Bacteriophage lambda (λ) vectors can accept DNA inserts up to 23 kb. Cosmids are artificial chromosomes that combine features of plasmids and bacteriophages, allowing for the cloning of very large DNA fragments (up to 45-50 kb). These vectors are crucial for constructing genomic libraries.

E. coli strains are genetically engineered to facilitate the uptake of foreign DNA (transformation) and to enhance the expression of cloned genes. Specific strains are chosen based on their ability to propagate certain types of plasmids or to express proteins efficiently. However, E. coli may not always be suitable for expressing complex eukaryotic proteins due to post-translational modification differences.

Common transformation methods include heat shock and electroporation. In heat shock, cells are treated with calcium chloride (CaCl2) to make their membranes permeable, and then exposed to a brief period of high temperature (e.g., 42°C). Electroporation uses a brief electric pulse to create temporary pores in the cell membrane, allowing DNA entry. The efficiency of transformation varies depending on the method and the host cell.

Selectable markers, such as antibiotic resistance genes, are commonly present on plasmids. Only bacteria that have taken up the plasmid will survive when grown on a medium containing the specific antibiotic. Further screening can be done using techniques like blue-white screening (if the vector contains the lacZ gene) or by probing for the presence of the inserted gene.