The population biology of bacterial plasmids: a hidden Markov model approach

Horizontal plasmid transfer plays a key role in bacterial adaptation. In harsh environments, bacterial populations adapt by sampling genetic material from a horizontal gene pool through self-transmissible plasmids, and that allows persistence of these mobile genetic elements. In the absence of selection for plasmid-encoded traits it is not well understood if and how plasmids persist in bacterial communities. Here we present three models of the dynamics of plasmid persistence in the absence of selection. The models consider plasmid loss (segregation), plasmid cost, conjugative plasmid transfer, and observation error. Also, we present a stochastic model in which the relative fitness of the plasmid-free cells was modeled as a random variable affected by an environmental process using a hidden Markov model (HMM). Extensive simulations showed that the estimates from the proposed model are nearly unbiased. Likelihood-ratio tests showed that the dynamics of plasmid persistence are strongly dependent on the host type. Accounting for stochasticity was necessary to explain four of seven time-series data sets, thus confirming that plasmid persistence needs to be understood as a stochastic process. This work can be viewed as a conceptual starting point under which new plasmid persistence hypotheses can be tested.     

Selection pressure required for long-term persistence of blaCMY-2-positive IncA/C plasmids

Multidrug resistance blaCMY-2 plasmids that confer resistance to expanded-spectrum cephalosporins have been found in multiple bacterial species collected from different hosts worldwide. The widespread distribution of blaCMY-2 plasmids may be driven by antibiotic use that selects for the dissemination and persistence of these plasmids. Alternatively, these plasmids may persist and spread in bacterial populations in the absence of selection pressure if a balance exists among conjugative transfer, segregation loss during cell division, and fitness cost to the host. We conducted a series of experiments (both in vivo and in vitro) to study these mechanisms for three blaCMY-2 plasmids, peH4H, pAR060302, and pAM04528. Results of filter mating experiments showed that the conjugation efficiency of blaCMY-2 plasmids is variable, from <10(-7) for pAM04528 and peH4H to ～10(-3) for pAR060302. Neither peH4H nor pAM04528 was transferred from Escherichia coli strain DH10B, but peH4H was apparently mobilized by the coresident trimethoprim resistance-encoding plasmid pTmpR. Competition studies showed that carriage of blaCMY-2 plasmids imposed a measurable fitness cost on the host bacteria both in vitro (0.095 to 0.25) and in vivo (dairy calf model). Long-term passage experiments in the absence of antibiotics demonstrated that plasmids with limited antibiotic resistance phenotypes arose, but eventually drug-sensitive, plasmid-free clones dominated the populations. Given that plasmid decay or loss is inevitable, we infer that some level of selection is required for the long-term persistence of blaCMY-2 plasmids in bacterial populations.     

The effect of seasonal host birth rates on disease persistence

In this paper, we add seasonality to the birth rate of an SIR model with density dependence in the death rate. We find that disease persistence can be explained by considering the average value of the seasonal term. If the basic reproductive ratio R(0)>1 with this average value then the disease will persist and if R(0)<1 with this average value then the disease will die out. However, if the underlying non-seasonal model displays oscillations towards the equilibrium then the dynamics of the seasonal model can become more complex. In this case, the seasonality can interact with the underlying oscillations, resonate and the population can display a range of complex behaviours including chaos. We discuss these results in terms of two examples, Cowpox in bank voles and Rabbit Haemorrhagic disease in rabbits.     

Positive epistasis between co-infecting plasmids promotes plasmid survival in bacterial populations

Plasmids have a key role in the horizontal transfer of genes among bacteria. Although plasmids are catalysts for bacterial evolution, it is challenging to understand how they can persist in bacterial populations over the long term because of the burden they impose on their hosts (the ‘plasmid paradox''). This paradox is especially perplexing in the case of ‘small'' plasmids, which are unable to self-transfer by conjugation. Here, for the first time, we investigate how interactions between co-infecting plasmids influence plasmid persistence. Using an experimental model system based on interactions between a diverse assemblage of ‘large'' plasmids and a single small plasmid, pNI105, in the pathogenic bacterium Pseudomonas aeruginosa, we demonstrate that positive epistasis minimizes the cost associated with carrying multiple plasmids over the short term and increases the stability of the small plasmid over a longer time scale. In support of these experimental data, bioinformatic analysis showed that associations between small and large plasmids are more common than would be expected owing to chance alone across a range of families of bacteria; more generally, we find that co-infection with multiple plasmids is more common than would be expected owing to chance across a wide range of bacterial phyla. Collectively, these results suggest that positive epistasis promotes plasmid stability in bacterial populations. These findings pave the way for future mechanistic studies aimed at elucidating the molecular mechanisms of plasmid–plasmid interaction, and evolutionary studies aimed at understanding how the coevolution of plasmids drives the spread of plasmid-encoded traits.     

Host-parasite interactions between the local and the mean-field: how and when does spatial population structure matter?

The assumption that populations are completely mixed is reasonable for many populations, but there is likely to be some degree of local interaction whether spatially or socially in many systems. An important question is therefore how strong these local interactions need to be before there are significant effects on the dynamics of the system. Here, our approach is to use a multi-scale pair-approximation model to move between completely local and completely mixed host-parasite interactions. We show that systems dominated by near neighbour effects have less persistence of disease, and a greater possibility of parasite driven extinction and limit cycles. Furthermore this reduction in persistence occurs over a wide range of infection scales and is still significant in predominantly mixed host populations. Deterministic extinctions are only likely in highly spatial SI systems while oscillations also persist over a wide range of infection ranges, but only in hosts that reproduce mostly locally. In general the mean-field may well be a good approximation for many systems, even when there are a significant proportion of near neighbour events, but this depends crucially on the ecological context.     

A Single-Amino-Acid Change in Murine Norovirus NS1/2 Is Sufficient for Colonic Tropism and Persistence

Human norovirus (HuNoV) is the major cause of acute nonbacterial gastroenteritis worldwide but has no clear animal reservoir. HuNoV can persist after the resolution of symptoms, and this persistence may be essential for viral maintenance within the population. Many strains of the related murine norovirus (MNV) also persist, providing a tractable animal model for studying norovirus (NoV) persistence. We have used recombinant cDNA clones of representative persistent (CR6) and nonpersistent (CW3) strains to identify a domain within the nonstructural gene NS1/2 that is necessary and sufficient for persistence. Furthermore, we found that a single change of aspartic acid to glutamic acid in CW3 NS1/2 was sufficient for persistence. This same conservative change also caused increased growth of CW3 in the proximal colon, which we found to be a major tissue reservoir of MNV persistence, suggesting that NS1/2 determines viral tropism that is necessary for persistence. These findings represent the first identified function for NoV NS1/2 during infection and establish a novel model system for the study of enteric viral persistence.     

Individual-based vs deterministic models for macroparasites: host cycles and extinction

Our understanding of the qualitative dynamics of host-macroparasite systems is mainly based on deterministic models. We study here an individual-based stochastic model that incorporates the same assumptions as the classical deterministic model. Stochastic simulations, using parameter values based on some case studies, preserve many features of the deterministic model, like the average value of the variables and the approximate length of the cycles.An important difference is that, even when deterministic models yield damped oscillations, stochastic simulations yield apparently sustained oscillations. The amplitude of such oscillations may be so large to threaten parasites' persistence.With density-dependence in parasite demographic traits, persistence increases somewhat. Allowing instead for infections from an external parasite reservoir, we found that host extinction may easily occur. However, the extinction probability is almost independent of the level of external infection over a wide intermediate parameter region.     

Natural selection, infectious transfer and the existence conditions for bacterial plasmids

Despite the near-ubiquity of plasmids in bacterial populations and the profound contribution of infectious gene transfer to the adaptation and evolution of bacteria, the mechanisms responsible for the maintenance of plasmids in bacterial populations are poorly understood. In this article, we address the question of how plasmids manage to persist over evolutionary time. Empirical studies suggest that plasmids are not infectiously transmitted at a rate high enough to be maintained as genetic parasites. In part i, we present a general mathematical proof that if this is the case, then plasmids will not be able to persist indefinitely solely by carrying genes that are beneficial or sometimes beneficial to their host bacteria. Instead, such genes should, in the long run, be incorporated into the bacterial chromosome. If the mobility of host-adaptive genes imposes a cost, that mobility will eventually be lost. In part ii, we illustrate a pair of mechanisms by which plasmids can be maintained indefinitely even when their rates of transmission are too low for them to be genetic parasites. First, plasmids may persist because they can transfer locally adapted genes to newly arriving strains bearing evolutionary innovations, and thereby preserve the local adaptations in the face of background selective sweeps. Second, plasmids may persist because of their ability to shuttle intermittently favored genes back and forth between various (noncompeting) bacterial strains, ecotypes, or even species.     

Fate of exogenous recombinant plasmids introduced into mouse and human cells.

We have constructed a number of plasmids selectable in both E. coli and mouse or human cells. Human DNA sequences were inserted and the recombinant plasmids were used to transfect either mouse or human cells by the Ca-phosphate precipitation technique. We have observed that: (i) competent cells uptake large amounts of plasmid DNA; (ii) input plasmids persist in transformed mammalian cells as free unreplicating circular molecules for up to 20 generations; such persistence does not depend on the presence of selective markers; (iii) plasmids incorporated into mouse L-cells undergo widespread rearrangements (in the absence of replication) entailing mostly deletions of both human and bacterial sequences which yield smaller products; the latter appear to be more stable in a subsequent transformation cycle. Surprisingly such rearrangements are almost totally absent in transformed human KB-cells. This property of human KB-cells may prove useful for the development of a vector apt at cloning and expressing human DNA sequences. Unlike what has been observed in yeast, no "autonomously replicating sequence" can be detected in mammalian cells by randomly cloning human DNA sequences into a selectable plasmid and screening for an increased transformation efficiency.     

Persistence, spread and the drift paradox

We derive conditions for persistence and spread of a population where individuals are either immobile or dispersing by advection and diffusion through a one-dimensional medium with a unidirectional flow. Reproduction occurs only in the stationary phase. Examples of such systems are found in rivers and streams, marine currents, and areas with prevalent wind direction. In streams, a long-standing question, dubbed 'the drift paradox', asks why aquatic insects faced with downstream drift are able to persist in upper stream reaches. For our two-phase model, persistence of the population is guaranteed if, at low population densities, the local growth rate of the stationary component of the population exceeds the rate of entry of individuals into the drift. Otherwise the persistence condition involves all the model parameters, and persistence requires a critical (minimum) domain size. We calculate the rate at which invasion fronts propagate up- and downstream, and show that persistence and ability to spread are closely connected: if the population cannot advance upstream against the flow, it also cannot persist on any finite spatial domain. By studying two limiting cases of our model, we show that residence in the immobile state always enhances population persistence. We use our findings to evaluate a number of mechanisms previously proposed in the ecological literature as resolutions of the drift paradox.     

Mapping EBNA-1 domains involved in binding to metaphase chromosomes

The Epstein-Barr virus (EBV) genome can persist in dividing human B cells as multicopy circular episomes. Viral episomes replicate in synchrony with host cell DNA and are maintained at a relatively constant copy number for a long time. Only two viral elements, the replication origin OriP and the EBNA-1 protein, are required for the persistence of viral genomes during latency. EBNA-1 activates OriP during the S phase and may also contribute to the partition and/or retention of viral genomes during mitosis. Indeed, EBNA-1 has been shown to interact with mitotic chromatin. Moreover, viral genomes are noncovalently associated with metaphase chromosomes. This suggests that EBNA-1 may facilitate the anchorage of viral genomes on cellular chromosomes, thus ensuring proper partition and retention. In the present paper, we have investigated the chromosome-binding activity of EBV EBNA-1, herpesvirus papio (HVP) EBNA-1, and various derivatives of EBV EBNA-1, fused to a variant of the green fluorescent protein. The results show that binding to metaphase chromosomes is a common property of EBV and HVP EBNA-1. Further studies indicated that at least three independent domains (CBS-1, -2, and -3) mediate EBNA-1 binding to metaphase chromosomes. In agreement with the anchorage model, two of these domains mapped to a region that has been previously demonstrated to be required for the long-term persistence of OriP-containing plasmids.     

Interference and the persistence of vertically transmitted parasites

Given their ubiquity in nature, understanding the factors that allow the persistence of multiple enemies and in particular vertically transmitted parasites (VTPs) is of considerable importance. Here a model that allows a virulent VTP to be maintained in a system containing a host and a horizontally transmitted parasite (HTP) is analysed. The method of persistence relies on the VTP offering the host a level of protection from the HTP. The VTP is assumed to reduce the HTPs ability to transmit to the host through ecological interference. We show that VTPs are more likely to persist with HTPs that prevent host reproduction than with those that allow it. The VTP persists more easily in r-selected hosts and with highly transmittable HTPs. As the level of protection through interference increases the densities of the host also increase. We also show that VTPs when they do persist tend to stabilise the host population cycles produced by free-living HTPs. The study raised questions about persistence of diseases through interactions with others, and also the stabilising effects of VTPs on dynamical systems in a biological control context.     

Conjugation is necessary for a bacterial plasmid to survive under protozoan predation

Horizontal gene transfer by conjugative plasmids plays a critical role in the evolution of antibiotic resistance. Interactions between bacteria and other organisms can affect the persistence and spread of conjugative plasmids. Here we show that protozoan predation increased the persistence and spread of the antibiotic resistance plasmid RP4 in populations of the opportunist bacterial pathogen Serratia marcescens. A conjugation-defective mutant plasmid was unable to survive under predation, suggesting that conjugative transfer is required for plasmid persistence under the realistic condition of predation. These results indicate that multi-trophic interactions can affect the maintenance of conjugative plasmids with implications for bacterial evolution and the spread of antibiotic resistance genes.     

Habitat destruction in a simple predator-prey patch model: how predators enhance prey persistence and abundance

We model a metapopulation of predator-prey patches using both spatially implicit or mean-field (MF) and spatially explicit (SE) approaches. We show that in the MF model there are parameter regimes for which prey cannot persist in the absence of predators, but can in their presence. In addition, there are parameter regimes for which prey may persist in isolation, but the presence of predators will increase prey patch density. Predators may thus enhance prey persistence and overall abundance. The key mechanism responsible for this effect is the occurrence of prey dispersal from patches that are occupied by both prey and predators. In addition, these patches should be either long-lived, such as that occurs when predators keep prey from overexploiting its local resource, or the presence of a predator on a patch should significantly enhance the prey dispersal out of that patch. In the SE approach these positive effects of predators on prey persistence and abundance occur for even larger parameter ranges than in the MF model. Prey dispersal from predator-prey patches may thus be important for persistence of both species as a community, independent of the modeling framework studied. Comparison of the MF and SE approaches shows that local dispersal constraints can have the edge over global dispersal for the persistence of the metapopulation in regimes where the two species have a beneficial effect on each other. In general, our model provides an example of feedback in multiple-species metapopulations that can make the implementation of conservation schemes based on single-species arguments very risky.     

Backward bifurcation and oscillations in a nested immuno-eco-epidemiological model

This paper introduces a novel partial differential equation immuno-eco-epidemiological model of competition in which one species is affected by a disease while another can compete with it directly and by lowering the first species' immune response to the infection, a mode of competition termed stress-induced competition. When the disease is chronic, and the within-host dynamics are rapid, we reduce the partial differential equation model (PDE) to a three-dimensional ordinary differential equation (ODE) model. The ODE model exhibits backward bifurcation and sustained oscillations caused by the stress-induced competition. Furthermore, the ODE model, although not a special case of the PDE model, is useful for detecting backward bifurcation and oscillations in the PDE model. Backward bifurcation related to stress-induced competition allows the second species to persist for values of its invasion number below one. Furthermore, stress-induced competition leads to destabilization of the coexistence equilibrium and sustained oscillations in the PDE model. We suggest that complex systems such as this one may be studied by appropriately designed simple ODE models.     

Flow Cytometry and Real-Time Quantitative PCR as Tools for Assessing Plasmid Persistence

The maintenance of a plasmid in the absence of selection for plasmid-borne genes is not guaranteed. However, plasmid persistence can evolve under selective conditions. Studying the molecular mechanisms behind the evolution of plasmid persistence is key to understanding how plasmids are maintained under nonselective conditions. Given the current crisis of rapid antibiotic resistance spread by multidrug resistance plasmids, this insight is of high medical relevance. The conventional method for monitoring plasmid persistence (i.e., the fraction of plasmid-containing cells in a population over time) is based on cultivation and involves differentiating colonies of plasmid-containing and plasmid-free cells on agar plates. However, this technique is time-consuming and does not easily lend itself to high-throughput applications. Here, we present flow cytometry (FCM) and real-time quantitative PCR (qPCR) as alternative tools for monitoring plasmid persistence. For this, we measured the persistence of a model plasmid, pB10::gfp, in three Pseudomonas hosts and in known mixtures of plasmid-containing and -free cells. We also compared three performance criteria: dynamic range, resolution, and variance. Although not without exceptions, both techniques generated estimates of overall plasmid loss rates that were rather similar to those generated by the conventional plate count (PC) method. They also were able to resolve differences in loss rates between artificial plasmid persistence assays. Finally, we briefly discuss the advantages and disadvantages for each technique and conclude that, overall, both FCM and real-time qPCR are suitable alternatives to cultivation-based methods for routine measurement of plasmid persistence, thereby opening avenues for high-throughput analyses.     

具有分离扩散的两种群Lotka—Volterra模型的持久性

本文考虑具有分离扩散的捕食-被捕食系统的持续性。此模型由两种群组成，其中被捕食种群可在两个生态环境中生存，而捕食种群仅能在一个生态环境中生存，两种群的动态行为都用Lotka－Volterra模型来描述。得到了系统强持续的充分必要条件，并证明了无论无扩散时系统是共存的，还是主导的都可以适当选择分离扩散系数使整个系统强持续。     

Genetic characterization of high-level gentamicin-resistant strains of Enterococcus faecalis in Iran

The prevalence of resistance to high levels of gentamicin among 182 isolates of Enterococcus faecalis from 2 Iranian hospitals was 42%. Gentamicin resistance was associated with conjugative plasmids (>70 kb) in most strains. Fingerprinting using EcoRI and HindIII showed genetic variation among these plasmids and gave evidence of nosocomial outbreaks and persistence of infection in different wards of the study hospitals, as well as transfer of plasmids between genetically diverse isolates. Using EcoRI, hospital-based specific plasmid fingerprints were detected for the isolates that had previously proved to be unrelated by multilocus enzyme electrophoresis, suggesting the persistence of related plasmids at each hospital, though minor changes in these related plasmids could be detected with HindIII.     

基于反馈控制离散Lotka-Volterra竞争模型的持续生存和稳定性

针对一类具有偏离自变量的离散Lotka-Volterra竞争模型,考虑到不可避免的外界扰动,通过引入反馈控制,基于一定的分析技巧得到该系统持久性与全局稳定性的充分条件.生态意义上表明:在外界扰动下,具有偏离自变量的离散Lotka-Volterra竞争模型仍能持续生存并保持全局稳定发展.     

Transitory Derepression and the Maintenance of Conjugative Plasmids

It has been proposed that bacterial plasmids cannot be maintained by infectious transfer alone and that their persistence requires positive selection for plasmid-borne genes. To test this hypothesis, the population dynamics of two laboratory and five naturally occurring conjugative plasmids were examined in chemostat cultures of E. coli K-12. Both laboratory plasmids and three of the five wild plasmids failed to increase in frequency when introduced at low frequencies. However, two of the naturally occurring plasmids rapidly increased in frequency, and bacteria carrying them achieved dominance in the absence of selection for known plasmid-borne genes. Three hypotheses for the invasion and persistence of these two plasmids were examined. It is concluded that although these two extrachromosomal genetic elements are repressed for conjugative pili synthesis, as a consequence of high rates of transfer during periods of transitory derepression in newly formed transconjugants, they become established and are maintained by infectious transfer alone. The implications of these observations to the theory of plasmid maintenance and the evolution of repressible conjugative pili synthesis are discussed.