Modeling bacterial immune systems: strategies for expression of toxic - but useful - molecules

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.

Understanding key features of bacterial restriction-modification systems through quantitative modeling

Background

Restriction-modification (R-M) systems are rudimentary bacterial immune systems. The main components include restriction enzyme (R), which cuts specific unmethylated DNA sequences, and the methyltransferase (M), which protects the same DNA sequences. The expression of R-M system components is considered to be tightly regulated, to ensure successful establishment in a naïve bacterial host. R-M systems are organized in different architectures (convergent or divergent) and are characterized by different features, i.e. binding cooperativities, dissociation constants of dimerization, translation rates, which ensure this tight regulation. It has been proposed that R-M systems should exhibit certain dynamical properties during the system establishment, such as: i) a delayed expression of R with respect to M, ii) fast transition of R from “OFF” to “ON” state, iii) increased stability of the toxic molecule (R) steady-state levels. It is however unclear how different R-M system features and architectures ensure these dynamical properties, particularly since it is hard to address this question experimentally.

Results

To understand design of different R-M systems, we computationally analyze two R-M systems, representative of the subset controlled by small regulators called ‘C proteins’, and differing in having convergent or divergent promoter architecture. We show that, in the convergent system, abolishing any of the characteristic system features adversely affects the dynamical properties outlined above. Moreover, an extreme binding cooperativity, accompanied by a very high dissociation constant of dimerization, observed in the convergent system, but absent from other R-M systems, can be explained in terms of the same properties. Furthermore, we develop the first theoretical model for dynamics of a divergent R-M system, which does not share any of the convergent system features, but has overlapping promoters. We show that i) the system dynamics exhibits the same three dynamical properties, ii) introducing any of the convergent system features to the divergent system actually diminishes these properties.

Conclusions

Our results suggest that different R-M architectures and features may be understood in terms of constraints imposed by few simple dynamical properties of the system, providing a unifying framework for understanding these seemingly diverse systems. We also provided predictions for the perturbed R-M systems dynamics, which may in future be tested through increasingly available experimental techniques, such as re-engineering R-M systems and single-cell experiments.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-016-0377-x) contains supplementary material, which is available to authorized users.

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.