Three-dimensional models for homogeneous DNA near denaturation

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