Motivated by the melting transition of DNA, we study genuinely three-dimensional
models for two interacting open, flexible and homogeneous macromolecular
chains, bound or unbound to each other, at thermal equilibrium from
about room temperature up to about the denaturation temperature
(Tun). In each chain, angular constraints on bond angles (due to
covalent bonding) determine monomers: each monomer contains
ne nucleotides and has
an effective length de. These monomers could remain practically unaltered for temperatures in a range above and below
Tun, down to 300 K.
Estimates for ne
and de
are provided and justified. Upon proceeding from Quantum Mechanics to the
classical limit and using suitable large-distance approximations (partly, due to
those monomer configurations), we get a generalization of Edwards' model, which
includes effective potentials between monomers. The classical partition function for
the two-chain system is reduced to an integral of a generalized and discretized
two-chain Green's function. We analyse conditions for the denaturing transition.
The fact that each single chain is an extended one-dimensional system modifies
their mutual global interaction, in comparison with typical potentials between
nucleotides: this is simply illustrated by computing a global effective potential
between the two chains. Applications for Morse potentials are presented. Our
models seem to be physically compatible with some previous one-dimensional ones
and could allow us to efficiently extend the latter to three spatial dimensions.