Sufficient minimal model for DNA denaturation: Integration of harmonic scalar elasticity and bond energies

Abstract

We study DNA denaturation by integrating elasticity -- as described by the Gaussian network model -- with bond binding energies, distinguishing between different base-pair and stacking energies. We use exact calculation, within the model, of the Helmholtz free-energy of any partial denaturation state, which implies that the entropy of all formed bubbles ("loops") is accounted for. Considering base-pair bond removal single events, the bond designated for opening is chosen by minimizing the free-energy difference for the process, over all remaining base-pair bonds. Despite of its great simplicity, for several known DNA sequences our results are in accord with available theoretical and experimental studies. Moreover, we report free-energy profiles along the denaturation pathway, which allow to detect stable or meta-stable partial denaturation states, composed of "bubbles", as local free-energy minima separated by barriers. Our approach allows to study very long DNA strands with commonly available computational power, as we demonstrate for a few random sequences in the range 200-800 base-pairs. For the latter we also elucidate the self-averaging property of the system. Implications for the well known breathing dynamics of DNA are elucidated.