Static recipient cells as reservoirs of antibiotic resistance during antibiotic therapy

The many dimensions of combination therapy: How to combine antibiotics to limit resistance evolution

In combination therapy, bacteria are challenged with two or more antibiotics simultaneously. Ideally, separate mutations are required to adapt to each of them, which is a priori expected to hinder the evolution of full resistance. Yet, the success of this strategy ultimately depends on how well the combination controls the growth of bacteria with and without resistance mutations. To design a combination treatment, we need to choose drugs and their doses and decide how many drugs get mixed. Which combinations are good? To answer this question, we set up a stochastic pharmacodynamic model and determine the probability to successfully eradicate a bacterial population. We consider bacteriostatic and two types of bactericidal drugs-those that kill independent of replication and those that kill during replication. To establish results for a null model, we consider non-interacting drugs and implement the two most common models for drug independence-Loewe additivity and Bliss independence. Our results show that combination therapy is almost always better in limiting the evolution of resistance than administering just one drug, even though we keep the total drug dose constant for a 'fair' comparison. Yet, exceptions exist for drugs with steep dose-response curves. Combining a bacteriostatic and a bactericidal drug which can kill non-replicating cells is particularly beneficial. Our results suggest that a 50:50 drug ratio-even if not always optimal-is usually a good and safe choice. Applying three or four drugs is beneficial for treatment of strains with large mutation rates but adding more drugs otherwise only provides a marginal benefit or even a disadvantage. By systematically addressing key elements of treatment design, our study provides a basis for future models which take further factors into account. It also highlights conceptual challenges with translating the traditional concepts of drug independence to the single-cell level.

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.

Mathematical modelling to study the horizontal transfer of antimicrobial resistance genes in bacteria: current state of the field and recommendations

Antimicrobial resistance (AMR) is one of the greatest public health challenges we are currently facing. To develop effective interventions against this, it is essential to understand the processes behind the spread of AMR. These are partly dependent on the dynamics of horizontal transfer of resistance genes between bacteria, which can occur by conjugation (direct contact), transformation (uptake from the environment) or transduction (mediated by bacteriophages). Mathematical modelling is a powerful tool to investigate the dynamics of AMR; however, the extent of its use to study the horizontal transfer of AMR genes is currently unclear. In this systematic review, we searched for mathematical modelling studies that focused on horizontal transfer of AMR genes. We compared their aims and methods using a list of predetermined criteria and used our results to assess the current state of this research field. Of the 43 studies we identified, most focused on the transfer of single genes by conjugation in Escherichia coli in culture and its impact on the bacterial evolutionary dynamics. Our findings highlight the existence of an important research gap in the dynamics of transformation and transduction and the overall public health implications of horizontal transfer of AMR genes. To further develop this field and improve our ability to control AMR, it is essential that we clarify the structural complexity required to study the dynamics of horizontal gene transfer, which will require cooperation between microbiologists and modellers.

Herbicide ingredients change Salmonella enterica sv. Typhimurium and Escherichia coli antibiotic responses

Herbicides are frequently released into both rural and urban environments. Commercial herbicide formulations induce adaptive changes in the way bacteria respond to antibiotics. Salmonella enterica sv. Typhimurium and Escherichia coli were exposed to common co-formulants of formulations, and S. enterica sv. Typhimurium was exposed to active ingredients dicamba, 2,4-D and glyphosate to determine what ingredients of the commercial formulations caused this effect. Co-formulants Tween80 and carboxymethyl cellulose induced changes in response, but the pattern of the responses differed from the active ingredients, and effect sizes were smaller. A commercial wetting agent did not affect antibiotic responses. Active ingredients induced changes in antibiotic responses similar to those caused by complete formulations. This occurred at or below recommended application concentrations. Targeted deletion of efflux pump genes largely neutralized the adaptive response in the cases of increased survival in antibiotics, indicating that the biochemistry of induced resistance was the same for formulations and specific ingredients. We found that glyphosate, dicamba, and 2,4-D, as well as co-formulants in commercial herbicides, induced a change in susceptibility of the potentially pathogenic bacteria E. coli and S. enterica to multiple antibiotics. This was measured using the efficiency of plating (EOP), the relative survival of the bacteria when exposed to herbicide and antibiotic, or just antibiotic, compared to survival on permissive media. This work will help to inform the use of non-medicinal chemical agents that induce changes in antibiotic responses.

Conjugative plasmids enable the maintenance of low cost non-transmissible plasmids

Some plasmids can be transferred by conjugation to other bacterial hosts. But almost half of the plasmids are non-transmissible. These plasmid types can only be transmitted to the daughter cells of their host after bacterial fission. Previous studies suggest that non-transmissible plasmids become extinct in the absence of selection of their encoded traits, as plasmid-free bacteria are more competitive. Here, we aim to identify mechanisms that enable non-transmissible plasmids to persist, even if they are not beneficial. For this purpose, an individual-based model for plasmid population dynamics was set up and carefully tested for structural consistency and plausibility. Our results demonstrate that non-transmissible plasmids can be stably maintained in a population, even if they impose a substantial burden on their host cells growth. A prerequisite is the co-occurrence of an incompatible and costly conjugative plasmid type, which indirectly facilitates the preservation of the non-transmissible type. We suggest that this constellation might be considered as a potential mechanism maintaining plasmids and associated antibiotic resistances. It should be investigated in upcoming laboratory experiments.

Fitness costs associated with the acquisition of antibiotic resistance

Acquisition of antibiotic resistance is a relevant problem for human health. The selection and spread of antibiotic-resistant organisms not only compromise the treatment of infectious diseases, but also the implementation of different therapeutic procedures as organ transplantation, advanced surgery or chemotherapy, all of which require proficient methods for avoiding infections. It has been generally accepted that the acquisition of antibiotic resistance will produce a general metabolic burden: in the absence of selection, the resistant organisms would be outcompeted by the susceptible ones. If that was always true, discontinuation of antibiotic use would render the disappearance of resistant microorganisms. However, several studies have shown that, once resistance emerges, the recovery of a fully susceptible population even in the absence of antibiotics is not easy. In the present study, we review updated information on the effect of the acquisition of antibiotic resistance in bacterial physiology as well as on the mechanisms that allow the compensation of the fitness costs associated with the acquisition of resistance.

Sublethal exposure to commercial formulations of the herbicides dicamba, 2,4-dichlorophenoxyacetic acid, and glyphosate cause changes in antibiotic susceptibility in Escherichia coli and Salmonella enterica serovar Typhimurium

Biocides, such as herbicides, are routinely tested for toxicity but not for sublethal effects on microbes. Many biocides are known to induce an adaptive multiple-antibiotic resistance phenotype. This can be due to either an increase in the expression of efflux pumps, a reduced synthesis of outer membrane porins, or both. Exposures of Escherichia coli and Salmonella enterica serovar Typhimurium to commercial formulations of three herbicides-dicamba (Kamba), 2,4-dichlorophenoxyacetic acid (2,4-D), and glyphosate (Roundup)-were found to induce a changed response to antibiotics. Killing curves in the presence and absence of sublethal herbicide concentrations showed that the directions and the magnitudes of responses varied by herbicide, antibiotic, and species. When induced, MICs of antibiotics of five different classes changed up to 6-fold. In some cases the MIC increased, and in others it decreased. Herbicide concentrations needed to invoke the maximal response were above current food maximum residue levels but within application levels for all herbicides. Compounds that could cause induction had additive effects in combination. The role of soxS, an inducer of the AcrAB efflux pump, was tested in β-galactosidase assays with soxS-lacZ fusion strains of E. coli. Dicamba was a moderate inducer of the sox regulon. Growth assays with Phe-Arg β-naphtylamide (PAβN), an efflux pump inhibitor, confirmed a significant role of efflux in the increased tolerance of E. coli to chloramphenicol in the presence of dicamba and to kanamycin in the presence of glyphosate. Pathways of exposure with relevance to the health of humans, domestic animals, and critical insects are discussed.

IMPORTANCE

Increasingly common chemicals used in agriculture, domestic gardens, and public places can induce a multiple-antibiotic resistance phenotype in potential pathogens. The effect occurs upon simultaneous exposure to antibiotics and is faster than the lethal effect of antibiotics. The magnitude of the induced response may undermine antibiotic therapy and substantially increase the probability of spontaneous mutation to higher levels of resistance. The combination of high use of both herbicides and antibiotics in proximity to farm animals and important insects, such as honeybees, might also compromise their therapeutic effects and drive greater use of antibiotics. To address the crisis of antibiotic resistance requires broadening our view of environmental contributors to the evolution of resistance.

Antibiotic resistance: from Darwin to Lederberg to Keynes

The emergence and spread of antibiotic-resistant bacteria reflects both, a gradual, completely Darwinian evolution, which mostly yields slight decreases in antibiotic susceptibility, along with phenotypes that are not precisely characterized as "resistance"; and sudden changes, from full susceptibility to full resistance, which are driven by a vast array of horizontal gene transfer mechanisms. Antibiotics select for more than just antibiotic resistance (i.e., increased virulence and enhanced gene exchange abilities); and many non-antibiotic agents or conditions select for or maintain antibiotic resistance traits as a result of a complex network of underlying and often overlapping mechanisms. Thus, the development of new antibiotics and thoughtful, integrated anti-infective strategies is needed to address the immediate and long-term threat of antibiotic resistance. Since the biology of resistance is complex, these new drugs and strategies will not come from free-market forces, or from "incentives" for pharmaceutical companies.

Measuring the rate of conjugal plasmid transfer in a bacterial population using quantitative PCR

Horizontal transfer of genes between species is an important mechanism for bacterial genome evolution. In Escherichia coli, conjugation is the transfer from a donor (F(+)) to a recipient (F(-)) cell through cell-to-cell contact. We demonstrate what we believe to be a novel qPCR method for quantifying the transfer kinetics of the F plasmid in a population by enumerating the relative abundance of genetic loci unique to the plasmid and the chromosome. This approach allows us to query the plasmid transfer rate without the need for selective culturing with unprecedented single locus resolution. We fit the results to a mass action model where the rate of plasmid growth includes the lag time of newly formed F(+) transconjugants and the recovery time between successive conjugation events of the F(+) donors. By assaying defined mixtures of genotypically identical donor and recipient cells at constant inoculation densities, we extract an F plasmid transfer rate of 5 × 10(-10) (cells/mL · min)(-1). We confirm a plasmid/chromosome ratio of 1:1 in homogenous F(+) populations throughout batch growth. Surprisingly, in some mixture experiments we observe an excess of F plasmid in the early saturation phase that equilibrates to a final ratio of one plasmid per chromosome.

The evolution of plasmid-carried antibiotic resistance

Background

Antibiotic resistance represents a significant public health problem. When resistance genes are mobile, being carried on plasmids or phages, their spread can be greatly accelerated. Plasmids in particular have been implicated in the spread of antibiotic resistance genes. However, the selective pressures which favour plasmid-carried resistance genes have not been fully established. Here we address this issue with mathematical models of plasmid dynamics in response to different antibiotic treatment regimes.

Results

We show that transmission of plasmids is a key factor influencing plasmid-borne antibiotic resistance, but the dosage and interval between treatments is also important. Our results also hold when plasmids carrying the resistance gene are in competition with other plasmids that do not carry the resistance gene. By altering the interval between antibiotic treatments, and the dosage of antibiotic, we show that different treatment regimes can select for either plasmid-carried, or chromosome-carried, resistance.

Conclusions

Our research addresses the effect of environmental variation on the evolution of plasmid-carried antibiotic resistance.

Population biological principles of drug-resistance evolution in infectious diseases

The emergence of resistant pathogens in response to selection pressure by drugs and their possible disappearance when drug use is discontinued are evolutionary processes common to many pathogens. Population biological models have been used to study the dynamics of resistance in viruses, bacteria, and eukaryotic microparasites both at the level of the individual treated host and of the treated host population. Despite the existence of generic features that underlie such evolutionary dynamics, different conclusions have been reached about the key factors affecting the rate of resistance evolution and how to best use drugs to minimise the risk of generating high levels of resistance. Improved understanding of generic versus specific population biological aspects will help to translate results between different studies, and allow development of a more rational basis for sustainable drug use than exists at present.

Modelling conjugation with stochastic differential equations

Conjugation is an important mechanism involved in the transfer of resistance between bacteria. In this article a stochastic differential equation based model consisting of a continuous time state equation and a discrete time measurement equation is introduced to model growth and conjugation of two Enterococcus faecium strains in a rich exhaustible media. The model contains a new expression for a substrate dependent conjugation rate. A maximum likelihood based method is used to estimate the model parameters. Different models including different noise structure for the system and observations are compared using a likelihood-ratio test and Akaike's information criterion. Experiments indicating conjugation on the agar plates selecting for transconjugants motivates the introduction of an extended model, for which conjugation on the agar plate is described in the measurement equation. This model is compared to the model without plate conjugation. The modelling approach described in this article can be applied generally when modelling dynamical systems.

Accounting for mating pair formation in plasmid population dynamics

Plasmids are important vehicles for horizontal gene transfer and rapid adaptation in bacteria, including the spread of antibiotic resistance genes. Conjugative transfer of a plasmid from a plasmid-bearing to a plasmid-free bacterial cell requires contact and attachment of the cells followed by plasmid DNA transfer prior to detachment. We introduce a system of differential equations for plasmid transfer in well-mixed populations that accounts for attachment, DNA transfer, and detachment dynamics. These equations offer advantages over classical mass-action models that combine these three processes into a single "bulk" conjugation rate. By decomposing the process of plasmid transfer into its constituent parts, this new model provides a framework that facilitates meaningful comparisons of plasmid transfer rates in surface and liquid environments. The model also allows one to account for experimental and environmental effects such as mixing intensity. To test the adequacy of the model and further explore the effects of mixing on plasmid transfer, we performed batch culture experiments using three different plasmids and a range of different mixing intensities. The results show that plasmid transfer is optimized at low to moderate shaking speeds and that vigorous shaking negatively affects plasmid transfer. Using reasonable assumptions on attachment and detachment rates, the mathematical model predicts the same behavior.

The persistence of parasitic plasmids

The conditions under which plasmids are predicted to persist remain controversial. Here, we reevaluate the ordinary differential equations used previously to model plasmid persistence and conclude that the parameter space required for maintenance is far less stringent than has been supposed. Strikingly, our model demonstrates that purely parasitic plasmids may persist, even in the absence of heterogeneity in the host population, and that this persistence is expressed by oscillations or damped oscillations between the plasmid-bearing and the plasmid-free class.