Pseudo-chaotic oscillations in CRISPR-virus coevolution predicted by bifurcation analysis

Cost and benefits of clustered regularly interspaced short palindromic repeats spacer acquisition

Clustered regularly interspaced short palindromic repeats (CRISPR)-Cas-mediated immunity in bacteria allows bacterial populations to protect themselves against pathogens. However, it also exposes them to the dangers of auto-immunity by developing protection that targets its own genome. Using a simple model of the coupled dynamics of phage and bacterial populations, we explore how acquisition rates affect the probability of the bacterial colony going extinct. We find that the optimal strategy depends on the initial population sizes of both viruses and bacteria. Additionally, certain combinations of acquisition and dynamical rates and initial population sizes guarantee protection, owing to a dynamical balance between the evolving population sizes, without relying on acquisition of viral spacers. Outside this regime, the high cost of auto-immunity limits the acquisition rate. We discuss these optimal strategies that minimize the probability of the colony going extinct in terms of recent experiments.

This article is part of a discussion meeting issue ‘The ecology and evolution of prokaryotic CRISPR-Cas adaptive immune systems’.

How adaptive immunity constrains the composition and fate of large bacterial populations

Features of the CRISPR-Cas system, in which bacteria integrate small segments of phage genome (spacers) into their DNA to neutralize future attacks, suggest that its effect is not limited to individual bacteria but may control the fate and structure of whole populations. Emphasizing the population-level impact of the CRISPR-Cas system, recent experiments show that some bacteria regulate CRISPR-associated genes via the quorum sensing (QS) pathway. Here we present a model that shows that from the highly stochastic dynamics of individual spacers under QS control emerges a rank-abundance distribution of spacers that is time invariant, a surprising prediction that we test with dynamic spacer-tracking data from literature. This distribution depends on the state of the competing phage-bacteria population, which due to QS-based regulation may coexist in multiple stable states that vary significantly in their phage-to-bacterium ratio, a widely used ecological measure to characterize microbial systems.

Optimal number of spacers in CRISPR arrays

Prokaryotic organisms survive under constant pressure of viruses. CRISPR-Cas system provides its prokaryotic host with an adaptive immune defense against viruses that have been previously encountered. It consists of two components: Cas-proteins that cleave the foreign DNA and CRISPR array that suits as a virus recognition key. CRISPR array consists of a series of spacers, short pieces of DNA that originate from and match the corresponding parts of viral DNA called protospacers. Here we estimate the number of spacers in a CRISPR array of a prokaryotic cell which maximizes its protection against a viral attack. The optimality follows from a competition between two trends: too few distinct spacers make host 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 useful 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 number of spacers lies within a range that agrees with experimentally-observed values.

CRISPR-Cas systems provide adaptive immunity defense in bacteria and archaea against viruses. They function by accumulating in prokaryotic genome an array of spacers, or fragments of virus DNA from previous attacks. By matching spacers to corresponding parts of viral DNA called protospacers, a CRISPR-Cas system identifies and destroys intruder DNA. Here we theoretically estimate the number of spacers that maximizes prokaryotic host cell survival. This optimum emerges from a competition between two trends: More spacers allow a prokaryotic cell to hedge against mutations in viral protospacers. However, the older spacers loose efficiency as corresponding protospacers mutate. For a limited pool of CRISPR-Cas molecular machines, keeping too many spacers leaves fewer of such machines armed with more efficient young (most recently acquired) spacers. We have shown that a higher efficiency of CRISPR-Cas system allows a prokaryotic cell to utilize more spacers, increasing the optimal number of spacers. 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. Our study provides a new viewpoint at a variety of the observed array spacer number and could be used as a base for evolutionary models of host-phage coexistence.

[Why so rare if so essentiel: the determinants of the sparse distribution of CRISPR-Cas systems in bacterial genomes]

CRISPR-Cas (Cluster of Regularly Interspaced Short Palindromic Repeats) systems confer bacteria and archaea an adaptative immunity against phages and other invading genetic elements playing an important role in bacterial evolution. However, despite the protection they generate and high rate of horizontal transfer, less than 50% of bacterial genomes harbor a CRISPR-Cas system. As a comparison, 90% of archaea encode a CRISPR-Cas system and a bacterial genome codes for two restriction modification systems on average. This review describes CRISPR-Cas systems distribution in bacterial genomes and then details the different hypotheses put forward to explain the relative scarcity of CRISPR-Cas systems. More specifically, phage escape mechanisms, ecological factors such as phage diversity and abundance and intrinsic costs, such as maintenance or autoimmunity, are discussed. Overall, a better understanding of the downsides of encoding CRISPR-Cas systems is essential to explain their evolutionary dynamics and their relative success in different environments and clades.

Evolution of the CRISPR-Cas adaptive immunity systems in prokaryotes: models and observations on virus-host coevolution

CRISPR-Cas is an adaptive immunity system in prokaryotes that functions via a unique mechanism which involves incorporation of foreign DNA fragments into CRISPR arrays and subsequent utilization of transcripts of these inserts (known as spacers) as guide RNAs to cleave the cognate selfish element genome. Multiple attempts have been undertaken to explore the coevolution of viruses and microbial hosts carrying CRISPR-Cas using mathematical models that employ either systems of differential equations or an agent-based approach, or combinations thereof. Analysis of these models reveals highly complex co-evolutionary dynamics that ensues from the combination of the heritability of the CRISPR-mediated adaptive immunity with the existence of different degrees of immunity depending on the number of cognate spacers and the cost of carrying a CRISPR-Cas locus. Depending on the details of the models, a variety of testable, sometimes conflicting predictions have been made on the dependence of the degree of immunity and the benefit of maintaining CRISPR-Cas on the abundance and diversity of hosts and viruses. Some of these predictions have already been directly validated experimentally. In particular, both the reality of the virus-host arms race, with viruses escaping resistance and hosts reacquiring it through the capture of new spacers, and the fitness cost of CRISPR-Cas due to the curtailment of beneficial HGT have been reproduced in the laboratory. However, to test the predictions of the models more specifically, detailed studies of coevolving populations of microbes and viruses both in nature and in the laboratory are essential. Such analyses are expected to yield disagreements with the predictions of the current, oversimplified models and to trigger a new round of theoretical developments.