PLASMIDS AND EVOLUTIONARY RESCUE BY DRUG RESISTANCE

Limits to evolutionary rescue by conjugative plasmids

Plasmids may carry genes coding for beneficial traits and thus contribute to adaptation of bacterial populations to environmental stress. Conjugative plasmids can horizontally transfer between cells, which a priori facilitates the spread of adaptive alleles. However, if the potential recipient cell is already colonized by another incompatible plasmid, successful transfer may be prevented. Competition between plasmids can thus limit horizontal transfer. Previous modeling has indeed shown that evolutionary rescue by a conjugative plasmid is hampered by incompatible resident plasmids in the population. If the rescue plasmid is a mutant variant of the resident plasmid, both plasmids transfer at the same rates. A high conjugation rate then has two, potentially opposing, effects - a direct positive effect on spread of the rescue plasmid and an increase in the fraction of resident plasmid cells. This raises the question whether a high conjugation rate always benefits evolutionary rescue. In this article, we systematically analyze three models of increasing complexity to disentangle the benefits and limits of increasing horizontal gene transfer in the presence of plasmid competition and plasmid costs. We find that the net effect can be positive or negative and that the optimal transfer rate is thus not always the highest one. These results can contribute to our understanding of the many facets of plasmid-driven adaptation and the wide range of transfer rates observed in nature.

Linking within- and between-host scales for understanding the evolutionary dynamics of quantitative antimicrobial resistance

Understanding both the epidemiological and evolutionary dynamics of antimicrobial resistance is a major public health concern. In this paper, we propose a nested model, explicitly linking the within- and between-host scales, in which the level of resistance of the bacterial population is viewed as a continuous quantitative trait. The within-host dynamics is based on integro-differential equations structured by the resistance level, while the between-host scale is additionally structured by the time since infection. This model simultaneously captures the dynamics of the bacteria population, the evolutionary transient dynamics which lead to the emergence of resistance, and the epidemic dynamics of the host population. Moreover, we precisely analyze the model proposed by particularly performing the uniform persistence and global asymptotic results. Finally, we discuss the impact of the treatment rate of the host population in controlling both the epidemic outbreak and the average level of resistance, either if the within-host scale therapy is a success or failure. We also explore how transitions between infected populations (treated and untreated) can impact the average level of resistance, particularly in a scenario where the treatment is successful at the within-host scale.

A mathematician's guide to plasmids: an introduction to plasmid biology for modellers

Plasmids, extrachromosomal DNA molecules commonly found in bacterial and archaeal cells, play an important role in bacterial genetics and evolution. Our understanding of plasmid biology has been furthered greatly by the development of mathematical models, and there are many questions about plasmids that models would be useful in answering. In this review, we present an introductory, yet comprehensive, overview of the biology of plasmids suitable for modellers unfamiliar with plasmids who want to get up to speed and to begin working on plasmid-related models. In addition to reviewing the diversity of plasmids and the genes they carry, their key physiological functions, and interactions between plasmid and host, we also highlight selected plasmid topics that may be of particular interest to modellers and areas where there is a particular need for theoretical development. The world of plasmids holds a great variety of subjects that will interest mathematical biologists, and introducing new modellers to the subject will help to expand the existing body of plasmid theory.

Why are rhizobial symbiosis genes mobile?

Rhizobia are one of the most important and best studied groups of bacterial symbionts. They are defined by their ability to establish nitrogen-fixing intracellular infections within plant hosts. One surprising feature of this symbiosis is that the bacterial genes required for this complex trait are not fixed within the chromosome, but are encoded on mobile genetic elements (MGEs), namely plasmids or integrative and conjugative elements. Evidence suggests that many of these elements are actively mobilizing within rhizobial populations, suggesting that regular symbiosis gene transfer is part of the ecology of rhizobial symbionts. At first glance, this is counterintuitive. The symbiosis trait is highly complex, multipartite and tightly coevolved with the legume hosts, while transfer of genes can be costly and disrupt coadaptation between the chromosome and the symbiosis genes. However, horizontal gene transfer is a process driven not only by the interests of the host bacterium, but also, and perhaps predominantly, by the interests of the MGEs that facilitate it. Thus understanding the role of horizontal gene transfer in the rhizobium-legume symbiosis requires a 'mobile genetic element's-eye view' on the ecology and evolution of this important symbiosis. This article is part of the theme issue 'The secret lives of microbial mobile genetic elements'.

Mathematical Models of Plasmid Population Dynamics

With plasmid-mediated antibiotic resistance thriving and threatening to become a serious public health problem, it is paramount to increase our understanding of the forces that enable the spread and maintenance of drug resistance genes encoded in mobile genetic elements. The relevance of plasmids as vehicles for the dissemination of antibiotic resistance genes, in addition to the extensive use of plasmid-derived vectors for biotechnological and industrial purposes, has promoted the in-depth study of the molecular mechanisms controlling multiple aspects of a plasmids' life cycle. This body of experimental work has been paralleled by the development of a wealth of mathematical models aimed at understanding the interplay between transmission, replication, and segregation, as well as their consequences in the ecological and evolutionary dynamics of plasmid-bearing bacterial populations. In this review, we discuss theoretical models of plasmid dynamics that span from the molecular mechanisms of plasmid partition and copy-number control occurring at a cellular level, to their consequences in the population dynamics of complex microbial communities. We conclude by discussing future directions for this exciting research topic.

Combining mutation and horizontal gene transfer in a within-host model of antibiotic resistance

Antibiotics are used extensively to control infections in humans and animals, usually by injection or a course of oral tablets. There are several methods by which bacteria can develop antimicrobial resistance (AMR), including mutation during DNA replication and plasmid mediated horizontal gene transfer (HGT). We present a model for the development of AMR within a single host animal. We derive criteria for a resistant mutant strain to replace the existing wild-type bacteria, and for co-existence of the wild-type and mutant. Where resistance develops through HGT via conjugation we derive criteria for the resistant strain to be excluded or co-exist with the wild-type. Our results are presented as bifurcation diagrams with thresholds determined by the relative fitness of the bacteria strains, expressed in terms of reproduction numbers. The results show that it is possible that applying and then relaxing antibiotic control may lead to the bacterial load returning to pre-control levels, but with an altered structure with regard to the variants that comprise the population. Removing antimicrobial selection pressure will not necessarily reduce AMR and, at a population level, other approaches to infection prevention and control are required, particularly when AMR is driven by both mutation and mobile genetic elements.

The Effect of Habitat Choice on Evolutionary Rescue in Subdivided Populations

AbstractEvolutionary rescue is the process by which a population, in response to an environmental change, successfully avoids extinction through adaptation. In spatially structured environments, dispersal can affect the probability of rescue. Here, we model an environment consisting of patches that degrade one after another, and we investigate the probability of rescue by a mutant adapted to the degraded habitat. We focus on the effects of dispersal and of immigration biases. We identify up to three regions delimiting the effect of dispersal on the probability of evolutionary rescue: (i) starting from low dispersal rates, the probability of rescue increases with dispersal; (ii) at intermediate dispersal rates, it decreases; and (iii) at large dispersal rates, it increases again with dispersal, except if mutants are too counterselected in not-yet-degraded patches. The probability of rescue is generally highest when mutant and wild-type individuals preferentially immigrate into patches that have already undergone environmental change. Additionally, we find that mutants that will eventually rescue the population most likely first appear in nondegraded patches. Overall, our results show that habitat choice, compared with the often-studied unbiased immigration scheme, can substantially alter the dynamics of population survival and adaptation to new environments.

Within-host bacterial growth dynamics with both mutation and horizontal gene transfer

The evolution and emergence of antibiotic resistance is a major public health concern. The understanding of the within-host microbial dynamics combining mutational processes, horizontal gene transfer and resource consumption, is one of the keys to solving this problem. We analyze a generic model to rigorously describe interactions dynamics of four bacterial strains: one fully sensitive to the drug, one with mutational resistance only, one with plasmidic resistance only, and one with both resistances. By defining thresholds numbers (i.e. each strain's effective reproduction and each strain's transition threshold numbers), we first express conditions for the existence of non-trivial stationary states. We find that these thresholds mainly depend on bacteria quantitative traits such as nutrient consumption ability, growth conversion factor, death rate, mutation (forward or reverse), and segregational loss of plasmid probabilities (for plasmid-bearing strains). Next, concerning the order in the set of strain's effective reproduction thresholds numbers, we show that the qualitative dynamics of the model range from the extinction of all strains, coexistence of sensitive and mutational resistance strains, to the coexistence of all strains at equilibrium. Finally, we go through some applications of our general analysis depending on whether bacteria strains interact without or with drug action (either cytostatic or cytotoxic).

Evolutionary Rescue and Drug Resistance on Multicopy Plasmids

Bacteria often carry "extra DNA" in the form of plasmids in addition to their chromosome. Many plasmids have a copy number greater than one such that the genes encoded on these plasmids are present in multiple copies per cell. This has evolutionary consequences by increasing the mutational target size, by prompting the (transitory) co-occurrence of mutant and wild-type alleles within the same cell, and by allowing for gene dosage effects. We develop and analyze a mathematical model for bacterial adaptation to harsh environmental change if adaptation is driven by beneficial alleles on multicopy plasmids. Successful adaptation depends on the availability of advantageous alleles and on their establishment probability. The establishment process involves the segregation of mutant and wild-type plasmids to the two daughter cells, allowing for the emergence of mutant homozygous cells over the course of several generations. To model this process, we use the theory of multitype branching processes, where a type is defined by the genetic composition of the cell. Both factors-the availability of advantageous alleles and their establishment probability-depend on the plasmid copy number, and they often do so antagonistically. We find that in the interplay of various effects, a lower or higher copy number may maximize the probability of evolutionary rescue. The decisive factor is the dominance relationship between mutant and wild-type plasmids and potential gene dosage effects. Results from a simple model of antibiotic degradation indicate that the optimal plasmid copy number may depend on the specific environment encountered by the population.

Gene mobility promotes the spread of resistance in bacterial populations

Theory predicts that horizontal gene transfer (HGT) expands the selective conditions under which genes spread in bacterial populations. Whereas vertically inherited genes can only spread by positively selected clonal expansion, mobile genetic elements can drive fixation of genes by infectious HGT. We tested this using populations of Pseudomonas fluorescens and the conjugative mercury resistance (Hg^R) plasmid pQBR57. HGT expanded the selective conditions allowing the spread of Hg^R: Chromosomal Hg^R only increased in frequency under positive selection, whereas plasmid-encoded Hg^R reached fixation with or without positive selection. Tracking plasmid dynamics over time revealed that the mode of Hg^R inheritance varied across mercury environments. Under mercury selection, the spread of Hg^R was driven primarily by clonal expansion while in the absence of mercury Hg^R dynamics were dominated by infectious transfer. Thus, HGT is most likely to drive the spread of resistance genes in environments where resistance is useless.

Lytic phages obscure the cost of antibiotic resistance in Escherichia coli

The long-term persistence of antibiotic-resistant bacteria depends on their fitness relative to other genotypes in the absence of drugs. Outside the laboratory, viruses that parasitize bacteria (phages) are ubiquitous, but costs of antibiotic resistance are typically studied in phage-free experimental conditions. We used a mathematical model and experiments with Escherichia coli to show that lytic phages strongly affect the incidence of antibiotic resistance in drug-free conditions. Under phage parasitism, the likelihood that antibiotic-resistant genetic backgrounds spread depends on their initial frequency, mutation rate and intrinsic growth rate relative to drug-susceptible genotypes, because these parameters determine relative rates of phage-resistance evolution on different genetic backgrounds. Moreover, the average cost of antibiotic resistance in terms of intrinsic growth in the antibiotic-free experimental environment was small relative to the benefits of an increased mutation rate in the presence of phages. This is consistent with our theoretical work indicating that, under phage selection, typical costs of antibiotic resistance can be outweighed by realistic increases in mutability if drug resistance and hypermutability are genetically linked, as is frequently observed in clinical isolates. This suggests the long-term distribution of antibiotic resistance depends on the relative rates at which different lineages adapt to other types of selection, which in the case of phage parasitism is probably extremely common, as well as costs of resistance inferred by classical in vitro methods.

Why There Are No Essential Genes on Plasmids

Mobile genetic elements such as plasmids are important for the evolution of prokaryotes. It has been suggested that there are differences between functions coded for by mobile genes and those in the "core" genome and that these differences can be seen between plasmids and chromosomes. In particular, it has been suggested that essential genes, such as those involved in the formation of structural proteins or in basic metabolic functions, are rarely located on plasmids. We model competition between genotypically varying bacteria within a single population to investigate whether selection favors a chromosomal location for essential genes. We find that in general, chromosomal locations for essential genes are indeed favored. This is because the inheritance of chromosomes is more stable than that for plasmids. We define the "degradation" rate as the rate at which chance genetic processes, for example, mutation, deletion, or translocation, render essential genes nonfunctioning. The only way in which plasmids can be a location for functioning essential genes is if chromosomal genes degrade faster than plasmid genes. If the two degradation rates are equal, or if plasmid genes degrade faster than chromosomal genes, functioning essential genes will be found only on chromosomes.