  DNA renaturation is the recombination of two complementary single strands to
form a double helix. It is experimentally known that renaturation proceeds
through the formation of a double stranded nucleus of several base pairs (the
rate limiting step) followed by a much faster zippering. We consider a lattice
polymer model undergoing Rouse dynamics and focus on the nucleation of two
diffusing strands. We study numerically the dependence of various nucleation
rates on the strand lengths and on an additional local nucleation barrier. When
the local barrier is sufficiently high, all renaturation rates considered scale
with the length as predicted by Kramers' rate theory and are also in agreement
with experiments: their scaling behavior is governed by exponents describing
equilibrium properties of polymers. When the local barrier is lowered
renaturation occurs in a regime of genuine non-equilibrium behavior and the
scaling deviates from the rate theory prediction.
