Error correction during DNA replication

DNA polymerase (DNAP) is a dual-purpose enzyme that plays two opposite roles in two different situations during DNA replication. It plays its normal role as a {\it polymerase} catalyzing the elongation of a new DNA molecule by adding a monomer. However, it can switch to the role of an {\it exonuclease} and shorten the same DNA by cleavage of the last incorporated monomer from the nascent DNA. Just as misincorporated nucleotides can escape exonuclease causing replication error, correct nucleotide may get sacrificed unnecessarily by erroneous cleavage. The interplay of polymerase and exonuclease activities of a DNAP is explored here by developing a minimal stochastic kinetic model of DNA replication. Exact analytical expressions are derived for a few key statistical distributions; these characterize the temporal patterns in the mechanical stepping and the chemical (cleavage) reaction. The Michaelis-Menten-like analytical expression derived for the average rates of these two processes not only demonstrate the effects of their coupling, but are also utilized to measure the extent of {\it replication error} and {\it erroneous cleavage}.