Statistical mechanics of homologous pairing of long double-stranded DNA

Abstract

The ability of homologous dsDNA to recognize and attract each other is a fundamental feature in DNA recombination and repair. A major unresolved question is how homologous genes initially locate and position themselves in front of each other—whether they do so at a distance without the use of proteins or unzipping their strands. One hypothesis suggests that such recognition is an innate property of DNA’s structure. DNA is not a perfect double-helix and distortions from helical structure are correlated with the sequence of base pairs. These distortions influence the patterns of charge distribution along the molecules. Those with identical sequences exhibit matching patterns of distortion, allowing them to align in a one-to-one register, which facilitates more favorable interactions. Conversely, uncorrelated sequences are unlikely to align perfectly, resulting in weaker attraction or greater repulsion. Consequently, the pairing of homologous sequences (i.e., positioning homologous genes in front of each other at a distance corresponding to free energy minimum) is more favorable than that of heterologous sequences. But how complete and stable would the pairing be? To address this, we present a model mapped on an Ising-like framework, which provides insight into the extent of pairing and its robustness. Our findings suggest that homologous dsDNAs, spanning multiple Kuhn lengths, can pair with some “bubbles”—regions of less tightly coupled sections. We compute the fraction of these unpaired sections and analyze the stability conditions to demonstrate that under physiological salt concentrations, heterologous double-stranded DNA cannot sustain long paired segments beyond the helical coherence length, further supporting the advantage of homologous pairing.