  Renaturation of complementary single strands of DNA is one of the important
processes that requires better understanding in the view of molecular biology
and biological physics. Here we develop a stochastic dynamical model on the DNA
renaturation. According to our model there are at least three steps in the
renaturation process viz. incorrect-contact formation, correct-contact
formation and nucleation, and zipping. Most of the earlier two-state models
combined nucleation with incorrect-contact formation step. In our model we
suggest that it is considerably meaningful when we combine the nucleation with
the zipping since nucleation is the initial step of zipping and the nucleated
and zipping molecules are indistinguishable. Incorrect-contact formation step
is a pure three-dimensional diffusion controlled collision process. Whereas
nucleation involves several rounds of one-dimensional slithering dynamics of
one single strand of DNA on the other complementary strand in the process of
searching for the correct-contact and then initiate nucleation. Upon
nucleation, the stochastic zipping follows to generate a fully renatured double
stranded DNA. It seems that the square-root dependency of the overall
renaturation rate constant on the length of reacting single strands originates
mainly from the geometric constraints in the diffusion controlled
incorrect-contact formation step. Further the inverse scaling of the
renaturation rate on the viscosity of the reaction medium also originates from
the incorrect-contact formation step. On the other hand the inverse scaling of
the renaturation rate with the sequence complexity originates from the
stochastic zipping which involves several rounds of crossing over the
free-energy barrier at microscopic levels.
