A simplified mathematical model of directional DNA site-specific recombination by serine integrases

Serine integrases catalyse site-specific recombination to integrate and excise bacteriophage genomes into and out of their host's genome. These enzymes exhibit remarkable directionality; in the presence of the integrase alone, recombination between attP and attB DNA sites is efficient and irreversible, giving attL and attR products which do not recombine further. However, in the presence of the bacteriophage-encoded recombination directionality factor (RDF), integrase efficiently promotes recombination between attL and attR to re-form attP and attB. The DNA substrates and products of both reactions are approximately isoenergetic, and no cofactors (such as adenosine triphosphate) are required for recombination. The thermodynamic driving force for directionality of these reactions is thus enigmatic. Here, we present a minimal mathematical model which can explain the directionality and regulation of both ‘forward’ and ‘reverse’ reactions. In this model, the substrates of the ‘forbidden’ reactions (between attL and attR in the absence of RDF, attP and attB in the presence of RDF) are trapped as inactive protein–DNA complexes, ensuring that these ‘forbidden’ reactions are extremely slow. The model is in good agreement with the observed in vitro kinetics of recombination by ϕC31 integrase, and defines core features of the system necessary and sufficient for directionality.