The dynamics of bacteria-plasmid systems

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.

DYNAMICAL BEHAVIOR OF STOCHASTIC COMPETITION BETWEEN PLASMID-BEARING AND PLASMID-FREE ORGANISMS IN A CHEMOSTAT MODEL

In this paper, a model of stochastic competition between plasmid-bearing and plasmid-free organisms in a chemostat is investigated. First, we show that there is a unique global positive solution for the stochastic system. Second, by employing stochastic Lyapunov functions, Itô formula, strong law of large number and some other important inequalities, stochastic characteristics of the stochastic competition chemostat model are studied such as the stochastic asymptotic behaviors of the system. Finally, some numerical simulations are given.

Competition in the chemostat with an undesirable lethal competitor

In this study, we compare the effects of competitors in a chemostat when one of the competitors is lethal to the other. The first competitor ("the mutant") is the desired organism because it provides a benefit, such as a substance that is harvested. However, when the mutant undergoes cell division the result may return to the original ("wild type") organism that produces a substance ("toxin") that is lethal to the mutant. We introduce an external inhibitor that negatively affects the growth of the wild type organism but that does not affect the mutant. The goal is for the mutant to dominate in the competition while co-existing with its wild type relative that is controlled. In this manner, we hope that understanding the dynamics of the system will help in designing methods to control the purity of the harvesting vessel without having to periodically restart the process more than necessary. We show that it is possible for co-existence in which the undesirable wild-type coexists with the mutant. However, it is also possible to destabilize the system and cause the extinction of the mutant.

Plasmid stability is enhanced by higher-frequency pulses of positive selection

Plasmids accelerate bacterial adaptation by sharing ecologically important traits between lineages. However, explaining plasmid stability in bacterial populations is challenging owing to their associated costs. Previous theoretical and experimental studies suggest that pulsed positive selection may explain plasmid stability by favouring gene mobility and promoting compensatory evolution to ameliorate plasmid cost. Here we test how the frequency of pulsed positive selection affected the dynamics of a mercury-resistance plasmid, pQBR103, in experimental populations of Pseudomonas fluorescens SBW25. Plasmid dynamics varied according to the frequency of Hg²⁺ positive selection: in the absence of Hg²⁺ plasmids declined to low frequency, whereas pulses of Hg²⁺ selection allowed plasmids to sweep to high prevalence. Compensatory evolution to ameliorate the cost of plasmid carriage was widespread across the entire range of Hg²⁺ selection regimes, including both constant and pulsed Hg²⁺ selection. Consistent with theoretical predictions, gene mobility via conjugation appeared to play a greater role in promoting plasmid stability under low-frequency pulses of Hg²⁺ selection. However, upon removal of Hg²⁺ selection, plasmids which had evolved under low-frequency pulse selective regimes declined over time. Our findings suggest that temporally variable selection environments, such as those created during antibiotic treatments, may help to explain the stability of mobile plasmid-encoded resistance.

Bacteriophages limit the existence conditions for conjugative plasmids

Bacteriophages are a major cause of bacterial mortality and impose strong selection on natural bacterial populations, yet their effects on the dynamics of conjugative plasmids have rarely been tested. We combined experimental evolution, mathematical modeling, and individual-based simulations to explain how the ecological and population genetics effects of bacteriophages upon bacteria interact to determine the dynamics of conjugative plasmids and their persistence. The ecological effects of bacteriophages on bacteria are predicted to limit the existence conditions for conjugative plasmids, preventing persistence under weak selection for plasmid accessory traits. Experiments showed that phages drove faster extinction of plasmids in environments where the plasmid conferred no benefit, but they also revealed more complex effects of phages on plasmid dynamics under these conditions, specifically, the temporary maintenance of plasmids at fixation followed by rapid loss. We hypothesized that the population genetic effects of bacteriophages, specifically, selection for phage resistance mutations, may have caused this. Further mathematical modeling and individual-based simulations supported our hypothesis, showing that conjugative plasmids may hitchhike with phage resistance mutations in the bacterial chromosome.

Conjugative plasmids are infectious loops of DNA capable of transmitting DNA between bacterial cells and between species. Because plasmids often carry extra genes that allow bacteria to live in otherwise-inhospitable environments, their dynamics are central to understanding bacterial adaptive evolution. The plasmid-bacterium interaction has typically been studied in isolation, but in natural bacterial communities, bacteriophages, viruses that infect bacteria, are ubiquitous. Using experiments, mathematical models, and computer simulations we show that bacteriophages drive plasmid dynamics through their ecological and evolutionary effects on bacteria and ultimately limit the conditions allowing plasmid existence. These results advance our understanding of bacterial adaptation and show that bacteriophages could be used to select against plasmids carrying undesirable traits, such as antibiotic resistance.

Competition between plasmid-bearing and plasmid-free organisms in a chemostat with nutrient recycling and an inhibitor

The asymptotic behavior of solutions of a model for competition between plasmid-bearing and plasmid-free organisms in the chemostat with two distributed delays and an external inhibitor is considered. The model presents a refinement of the one considered by Lu and Hadeler [Z. Lu, K.P. Hadeler, Model of plasmid-bearing plasmid-free competition in the chemostat with nutrient recycling and an inhibitor, Math. Biosci. 167 (2000) p. 177]. The delays model the fact that the nutrient is partially recycled after the death of the biomass by bacterial decomposition. Furthermore, it is assumed that there is inter-specific competition between the plasmid-bearing and plasmid-free organisms as well as intra-specific competition within each population. Conditions for boundedness of solutions and existence of non-negative equilibrium are given. Analysis of the extinction of the organisms, including plasmid-bearing and plasmid-free organisms, and the uniform persistence of the system are also carried out. By constructing appropriate Liapunov-like functionals, some sufficient conditions of global attractivity to the extinction equilibria are obtained and the combined effects of the delays and the inhibitor are studied.

Competition between plasmid-bearing and plasmid-free organisms in the host: population dynamics and antibiotic resistance

OBJECTIVE

To clarify the effects of antibiotic exposure on bacterial antibiotic resistance.

MATERIALS AND METHODS

A competitive population dynamics model for plasmid-bearing organisms and plasmid-free organisms in the host was established. The Poincaré-Bendixson theorem was used for analysis.

RESULTS

All possible results of the competition dependent on biologically meaningful parameters were obtained, which can be classified into eight categories. With the outcomes of the plasmid model, we discussed the sterilizing effect if an antibiotic was added to the host.

CONCLUSION

When antibiotic-resistant bacteria existed in a host, a higher dosage of antibiotics was needed with an increased risk of survival of plasmid-bearing organisms and greater danger of resistance to antibiotics.

Plasmid-bearing, plasmid-free organisms competing for two complementary nutrients in a chemostat

A model of competition for two complementary nutrients between plasmid-bearing and plasmid-free organisms in a chemostat is proposed. A rigorous mathematical analysis of the global asymptotic behavior of the model is presented. The work extends the model of competition for a single-limited nutrient studied by Stephanopoulos and Lapidus [Chem. Engng. Sci. 443 (1988) 49] and Hsu, Waltman and Wolkowicz [J. Math. Biol. 32 (1994) 731].

Multileveled selection on plasmid replication

The replication control genes of bacterial plasmids face selection at two conflicting levels. Plasmid copies that systematically overreplicate relative to their cell mates have a higher chance of fixing in descendant cells, but these cells typically have a lower chance of fixing in the population. Apart from identifying the conflict, this mathematical discussion characterizes the efficiency of the selection levels and suggests how they drive the evolution of kinetic mechanisms. In particular it is hypothesized that: (1) tighter replication control is more vulnerable to selfishness; (2) cis-acting replication activators are relics of a conflict where a plasmid outreplicated its intracellular competitors by monopolizing activators; (3) high-copy plasmids with sloppy replication control arise because intracellular selection favors overreplication, thereby relieving intercellular selection for lower loss rates; (4) the excessive synthesis of cis-acting replication activators and trans-acting inhibitors is the result of an arms race between cis selfishness and trans retaliations; (5) site-specific recombination of plasmid dimers is equivalent to self-policing; and (6) plasmids modify their horizontal transfer to spread without promoting selfishness. It is also discussed how replication control may be subject to a third level of selection acting on the entire population of plasmid-containing cells.

Model of plasmid-bearing, plasmid-free competition in the chemostat with nutrient recycling and an inhibitor

In this paper, we consider competition between plasmid-bearing and plasmid-free organisms with nutrient recycling and an inhibitor in a chemostat-type systems. We discuss the cases where the nutrient is supplied at a constant rate and the nutrient supply is time-dependent. For each case, we obtain criteria for the boundedness of solutions and persistence.

A computer simulation model for the spread of nosocomial infections caused by multidrug-resistant pathogens

A Monte Carlo simulation model was developed for the spread of antibiotic-resistant bacteria in hospital units. The model allows for the representation of every patient and staff member. Staff-patient interactions, staff handwashing compliance, admission of colonized patients, and antibiotic use are included in the model. The simulation model provides colonization curves for patients and staff and offers the possibility of simulating different kinds of hospital units. Simulation of the spread of an antibiotic-resistant pathogen in an intensive care unit was performed. We studied the impact of handwashing compliance on colonization. The importance of handwashing in preventing colonization and the influence of admission of colonized patients in perpetuating an epidemic were confirmed by the model. The model offers a new approach to modeling the spread of nosocomial pathogens in hospital units. It allows one to study the impact of infection control measures and represents a valuable educational tool for staff.

The acquisition of indigenous plasmids by a genetically marked pseudomonad population colonizing the sugar beet phytosphere is related to local environmental conditions

The transfer of naturally occurring conjugative plasmids from the indigenous microflora to a genetically modified population of bacteria colonizing the phytospheres of plants has been observed. The marked strain (Pseudomonas fluorescens SBW25EeZY6KX) was introduced as a seed dressing to sugar beets (Beta vulgaris var. Amethyst) as part of a field experiment to assess the ecology and genetic stability of deliberately released bacterial inocula. The sustained populations of the introduced strain, which colonized the phytosphere, were assessed throughout the growing season for the acquisition of plasmids conferring mercury resistance (Hg(supr)). Transconjugants were isolated only from root and leaf samples collected within a narrow temporal window coincident with the midseason maturation of the crop. Conjugal-transfer events were recorded during this defined period in two separate field release experiments conducted over consecutive years. On one occasion seven of nine individual plants sampled supported transconjugant P. fluorescens SBW25EeZY6KX, demonstrating that conjugative gene transfer between bacterial populations in the phytosphere may be a common event under specific environmental conditions. The plasmids acquired in situ by the colonizing inocula were identified as natural variants of restriction digest pattern group I, III, or IV plasmids from five genetically distinct groups of large, conjugative mercury resistance plasmids known to persist in the phytospheres of sugar beets at the field site. These data demonstrate not only that gene transfer may be a common event but also that the genetic and phenotypic stability of inocula released into the natural environment cannot be predicted.