Down the Penrose stairs: How selection for fewer recombination hotspots maintains their existence

In many species, meiotic recombination events tend to occur in narrow intervals of the genome, known as hotspots. In humans and mice, double strand break (DSB) hotspot locations are determined by the DNA-binding specificity of the zinc finger array of the PRDM9 protein, which is rapidly evolving at residues in contact with DNA. Previous models explained this rapid evolution in terms of the need to restore PRDM9 binding sites lost to gene conversion over time, under the assumption that more PRDM9 binding always leads to more DSBs. In recent experimental work, however, it has become apparent that PRDM9 binding on both homologs facilitates DSB repair, and moreover that, in the absence of enough symmetric binding, meiosis no longer progresses reliably. We therefore consider the possibility that the benefit of PRDM9 stems from its role in coupling DSB formation and efficient repair. To this end, we model the evolution of PRDM9 from first principles: from its binding dynamics to the population processes that govern the evolution of the zinc finger array and its binding sites in the genome. As we show, the loss of a small number of strong binding sites leads to the use of a greater number of weaker ones, resulting in a sharp reduction in symmetric binding and favoring new PRDM9 alleles that restore the use of a smaller set of strong binding sites. This decrease in PRDM9 binding symmetry and in its ability to promote DSB repair drive the rapid zinc finger turnover. These results imply that the advantage of new PRDM9 alleles is in limiting the number of binding sites used effectively, rather than in increasing net PRDM9 binding, as previously believed. By extension, our model suggests that the evolutionary advantage of hotspots may have been to increase the efficiency of DSB repair and/or homolog pairing.