Searching for fat tails in CRISPR-Cas systems: Data analysis and mathematical modeling

Abstract

Understanding CRISPR-Cas systems—the adaptive defence mechanism that about half of bacterial species and most of archaea use to neutralise viral attacks—is important for explaining the biodiversity observed in the microbial world as well as for editing animal and plant genomes effectively. The CRISPR-Cas system learns from previous viral infections and integrates small pieces from phage genomes called spacers into the microbial genome. The resulting library of spacers collected in CRISPR arrays is then compared with the DNA of potential invaders. One of the most intriguing and least well understood questions about CRISPR-Cas systems is the distribution of spacers across the microbial population. Here, using empirical data, we show that the global distribution of spacer numbers in CRISPR arrays across multiple biomes worldwide typically exhibits scale-invariant power law behaviour, and the standard deviation is greater than the sample mean. We develop a mathematical model of spacer loss and acquisition dynamics which fits observed data from almost four thousand metagenomes well. In analogy to the classical ‘rich-get-richer’ mechanism of power law emergence, the rate of spacer acquisition is proportional to the CRISPR array size, which allows a small proportion of CRISPRs within the population to possess a significant number of spacers. Our study provides an alternative explanation for the rarity of all-resistant super microbes in nature and why proliferation of phages can be highly successful despite the effectiveness of CRISPR-Cas systems.

CRISPR-Cas Systems in Gut Microbiome of Children with Autism Spectrum Disorders

“…For example, for CRISPRCasMeta, an online service for systems identification in metagenomic data [ 55 ], main modules of CRISPRCasFinder are used in combination with the CRT program. In [ 56 ], a modified version of CRT, CRT-CLI [ 57 ], was used together with Piler-CR. Here, we used a slightly updated scheme based on all three original tools, CRISPRFinder, Piler-CR and CRT, suggested in [ 38 ].…”

CRISPR-Cas Systems in Gut Microbiome of Children with Autism Spectrum Disorders

“…For example, for CRISPRCasMeta, an online service for systems identification in metagenomic data [54], main modules of CRISPRCasFinder are used in combination with the CRT program. In [55] a modified version of CRT, CRT-CLI [56], was used together with Piler-CR. Here, we used a slightly updated scheme based on all three original tools, CRISPRFinder, Piler-CR and CRT, suggested in [36].…”

Dynamics of immune memory and learning in bacterial communities

“…However, we also observed rapid loss of previous spacer types as bacteria returned to the naive state before acquiring new spacers. In reality, bacteria can store multiple spacers in their CRISPR arrays [101, 90] and phages can have several hundred to several thousand protospacer sequences which are determined by a particular protospacer-adjacent motif (PAM) in type I and II CRISPR systems [102]. In S. thermophilus phage 2972 for example, there are about 230 protospacers that can be acquired into the CRISPR1 locus of S. thermophilus [23] and 465 that can be acquired into the CRISPR3 locus.…”

“…In S. thermophilus phage 2972 for example, there are about 230 protospacers that can be acquired into the CRISPR1 locus of S. thermophilus [23] and 465 that can be acquired into the CRISPR3 locus. Similarly, many bacteria can store tens to hundreds of spacers in their CRISPR arrays [101, 103, 104, 90]. Our single-spacer assumption is reasonable for the experimental systems we consider.…”