# Optimal number of spacers in CRISPR arrays

## TL;DR

This paper models the optimal number of spacers in CRISPR arrays to maximize bacterial defense, balancing protection against viral mutations and the efficiency of recent spacers, with results aligning with experimental data.

## Contribution

It introduces a theoretical framework for determining the optimal CRISPR spacer count considering multiple viral species and biological parameters.

## Key findings

- Optimal spacer number depends on viral mutation rate and CRISPR complex concentration.
- Predicted array lengths match observed experimental ranges.
- Model applies to both single and multiple viral species scenarios.

## 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.