Statistical Physics of DNA melting: Unveiling the artificial corrections for self-complementary sequences

Abstract

DNA hybridization is at the heart of countless biological and biotechnological processes. Its theoretical modeling played a crucial role, since it has enabled extracting the relevant thermodynamic parameters from systematic measurements of DNA melting curves. However, in its current state, hybridization modelling requires introducing an extra entropic contribution in self-complementary sequences that lacks any biophysical meaning. In this article, we propose a framework based on statistical physics to describe DNA hybridization and melting in an arbitrary mixture of DNA strands. In particular, we are able to analytically derive closed expressions of the system partition functions for any number N of strings, and explicitly calculate them in two paradigmatic situations: (i) a system made of self-complementary sequences and (ii) a system comprising two mutually complementary sequences. We derive the melting curve in the thermodynamic limit (N [->] {infty}) of our description, which differs from the expression commonly used to evaluate the melting of self-complementary systems in that it does not require correcting terms. We provide a thorough study comprising limit cases and alternative approaches showing how our framework can give a comprehensive view of hybridization and melting phenomena. SIGNIFICANCEIn this study, we provide a transparent derivation of the melting curves of DNA duplexes using basic tools of statistical mechanics. We find that in the case of self-complementary sequences, our expression differs from the one used in literature, which is generally amended by the introduction of a phenomenological correction which in our approach becomes unnecessary. By offering a clean formal description of DNA hybridization, our approach sharpens our understanding of DNA interactions and opens the way to study the pairing of DNA oligomers away from any thermodynamic limit.