Dynamics of adaptive immunity against phage in bacterial populations

The CRISPR (clustered regularly interspaced short palindromic repeats) mechanism allows bacteria to adaptively defend against phages by acquiring short genomic sequences (spacers) that target specific sequences in the viral genome. We propose a population dynamical model where immunity can be both acquired and lost. The model predicts regimes where bacterial and phage populations can co-exist, others where the populations exhibit damped oscillations, and still others where one population is driven to extinction. Our model considers two key parameters: (1) ease of acquisition and (2) spacer effectiveness in conferring immunity. Analytical calculations and numerical simulations show that if spacers differ mainly in ease of acquisition, or if the probability of acquiring them is sufficiently high, bacteria develop a diverse population of spacers. On the other hand, if spacers differ mainly in their effectiveness, their final distribution will be highly peaked, akin to a “winner-take-all” scenario, leading to a specialized spacer distribution. Bacteria can interpolate between these limiting behaviors by actively tuning their overall acquisition probability.Author summary: The CRISPR system in bacteria and archaea provides adaptive immunity by incorporating foreign DNA (spacers) into the genome, and later targeting DNA sequences that match these spacers. The way in which bacteria choose spacer sequences from a clonal phage population is not understood. Our model considers competing effects of ease of acquisition and effectiveness against infections in shaping the spacer distribution. The model suggests that a diverse spacer population results when the acquisition rate is high, or when spacers are similarly effective. At moderate acquisition rates, the spacer distribution becomes highly sensitive to spacer effectiveness. There is a rich landscape of behaviors including bacteria-phage coexistence and oscillations in the populations.