  Renaturation and hybridization reactions lead to the pairing of complementary
single-stranded nucleic acids. We present here a theoretical investigation of
the mechanism of these reactions in vitro under thermal conditions (dilute
solutions of single-stranded chains, in the presence of molar concentrations of
monovalent salts and at elevated temperatures). The mechanism follows a
Kramers' process, whereby the complementary chains overcome a potential barrier
through Brownian motion. The barrier originates from a single rate-limiting
nucleation event in which the first complementary base pairs are formed. The
reaction then proceeds through a fast growth of the double helix. For the DNA
of bacteriophages T7, T4 and $\phi$X174 as well as for Escherichia coli DNA,
the bimolecular rate $k_2$ of the reaction increases as a power law of the
average degree of polymerization $<N>$ of the reacting single- strands: $k_2
\prop <N>^\alpha$. This relationship holds for $100 \leq <N> \leq 50 000$ with
an experimentally determined exponent $\alpha = 0.51 \pm 0.01$. The length
dependence results from a thermodynamic excluded-volume effect. The reacting
single-stranded chains are predicted to be in universal good solvent
conditions, and the scaling law is determined by the relevant equilibrium
monomer contact probability. The value theoretically predicted for the exponent
is $\alpha = 1-\nu \theta_2$, where $\nu$ is Flory's swelling exponent ($nu
approx 0.588$) and $\theta_2$ is a critical exponent introduced by des
Cloizeaux ($\theta_2 \approx 0.82$), yielding $\alpha = 0.52 \pm 0.01$, in
agreement with the experimental results.
