Final answer:
DNA polymerase I is required for the in vitro reaction that involves both the removal of RNA primers from Okazaki fragments and the synthesis of DNA to fill in those gaps on the lagging strand during DNA replication.
Step-by-step explanation:
In the context of DNA replication and repair enzymes, the in vitro reaction that requires full length DNA polymerase I (DNA pol I) is the reaction in which DNA pol I binds to the 5' end of the primer and adds deoxynucleotide monophosphates (dNMPs) to the 3' end of a new Okazaki fragment while simultaneously hydrolyzing nucleotide monophosphates (NMPs) from the 5' to 3' direction on the previous Okazaki fragment. This process is essential for removing the RNA primers used during DNA synthesis and for filling in the resulting gaps with DNA. In contrast, DNA pol II and DNA pol III do not have the same 5'→3' exonuclease activity that DNA pol I possesses.
Specifically, DNA pol I's 5'→3' exonuclease activity makes it unique among the E. coli DNA polymerases. Following the removal of RNA primers by this exonuclease activity, the DNA pol I enzyme fills in the gaps with DNA nucleotides. Finally, DNA ligase is responsible for forming the phosphodiester bonds that link the Okazaki fragments, completing the replication process on the lagging strand.