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}.Comment: Accepted for publication in Physical Review E (8 pages, including 6
figures
