Optimal Number Of Spacers In CRISPR Arrays

Abstract

We estimate the number of spacers in a CRISPR array of a bacterium which maximizes its protection against a viral attack. The optimality follows from a competition between two trends: too few distinct spacers make the bacteria vulnerable to an attack by a virus with mutated corresponding protospacers, while an excessive variety of spacers dilutes the number of the CRISPR complexes armed with the most recent and thus most effective spacers. We first evaluate the optimal number of spacers in a simple scenario of an infection by a single viral species and later consider a more general case of multiple viral species. We find that depending on such parameters as the concentration of CRISPR-CAS interference complexes and its preference to arm with more recently acquired spacers, the rate of viral mutation, and the number of viral species, the predicted optimal array length lies within a range quite reasonable from the viewpoint of recent experiments.\n\nAuthor summaryCRISPR-Cas system is an adaptive immunity defense in bacteria and archaea against viruses. It works by accumulating in bacterial genome an array of spacers, or fragments of virus DNA from previous attacks. By matching spacers to corresponding parts of virus DNA called protospacers, CRISPR-Cas system identifies and destroys intruder DNA. Here we theoretically estimate the number of spacers that maximizes bacterial survival. This optimum emerges from a competition between two trends: More spacers allow a bacterium to hedge against mutations in viral protospacers. However, keeping too many spacers makes the older ones inefficient because of accumulation of mutations in corresponding protospacers in viruses. Thus, fewer CRISPR-Cas molecular machines are left armed with more efficient young spacers. We have shown that a higher efficiency of CRISPR-Cas system allows a bacterium to utilize more spacers, increasing the optimal array length. On contrary, a higher viral mutation rate makes older spacers useless and favors shorter arrays. A higher diversity in viral species reduces the efficiency of CRISPR-Cas but does not necessary lead to longer arrays. We think that our study provides a new viewpoint at a huge variety in the observed array lengths and adds relevance to evolutionary models of bacterial-phage coexistence.