Modeling the ecology of parasitic plasmids

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.

Plasmids Increase the Competitive Ability of Plasmid-Bearing Cells Even When Transconjugants Are Poor Donors, as Shown by Computer Simulations

Bacterial cells often suffer a fitness cost after conjugative plasmids' entry because these cells replicate slower than plasmid-free cells. Compensatory mutations may appear after tens of or a few hundred generations, reducing or eliminating this cost. A previous work based on a mathematical model and computer simulations has shown that plasmid-bearing cells already adapted to the plasmid may gain a fitness advantage when plasmids transfer into neighboring plasmid-free cells because these cells are still unadapted to the plasmid. These slow-growing transconjugants use fewer resources, which can benefit donor cells. However, opportunities for compensatory mutations in transconjugants increase if these cells become numerous (through replication or conjugation). Moreover, transconjugants also gain an advantage when transferring the plasmid, but the original donors may be too distant from conjugation events to gain an advantage. To understand which consequence prevails, we performed further computer simulations allowing versus banning transfer from transconjugants. The advantage to donors is higher if transconjugants do not transfer plasmids, mainly when donors are rare and when the plasmid transfer rate (from donors) is high. These results show that conjugative plasmids are efficient biological weapons even if the transconjugant cells are poor plasmid donors. After some time, conjugative plasmids gain other host-benefit genes, such as virulence and drug-resistance.

Conceptualizing microbe-plasmid communities as complex adaptive systems

Plasmids shape microbial communities' diversity, structure, and function. Nevertheless, we lack a mechanistic understanding of how community structure and dynamics emerge from local microbe-plasmid interactions and coevolution. Addressing this gap is challenging because multiple processes operate simultaneously at multiple levels of organization. For example, immunity operates between a plasmid and a cell, but incompatibility mechanisms regulate coexistence between plasmids. Conceptualizing microbe-plasmid communities as complex adaptive systems is a promising approach to overcoming these challenges. I illustrate how agent-based evolutionary modeling, extended by network analysis, can be used to quantify the relative importance of local processes governing community dynamics. These theoretical developments can advance our understanding of plasmid ecology and evolution, especially when combined with empirical data.

Segregational instability of multicopy plasmids: A population genetics approach

Plasmids are extra-chromosomal genetic elements that encode a wide variety of phenotypes and can be maintained in bacterial populations through vertical and horizontal transmission, thus increasing bacterial adaptation to hostile environmental conditions like those imposed by antimicrobial substances. To circumvent the segregational instability resulting from randomly distributing plasmids between daughter cells upon division, nontransmissible plasmids tend to be carried in multiple copies per cell, with the added benefit of exhibiting increased gene dosage and resistance levels. But carrying multiple copies also results in a high metabolic burden to the bacterial host, therefore reducing the overall fitness of the population. This trade-off poses an existential question for plasmids: What is the optimal plasmid copy number? In this manuscript, we address this question by postulating and analyzing a population genetics model to evaluate the interaction between selective pressure, the number of plasmid copies carried by each cell, and the metabolic burden associated with plasmid bearing in the absence of selection for plasmid-encoded traits. Parameter values of the model were estimated experimentally using Escherichia coli K12 carrying a multicopy plasmid encoding for a fluorescent protein and bla _TEM-1, a gene conferring resistance to β-lactam antibiotics. By numerically determining the optimal plasmid copy number for constant and fluctuating selection regimes, we show that plasmid copy number is a highly optimized evolutionary trait that depends on the rate of environmental fluctuation and balances the benefit between increased stability in the absence of selection with the burden associated with carrying multiple copies of the plasmid.

A PDE Model for Protocell Evolution and the Origin of Chromosomes via Multilevel Selection

The evolution of complex cellular life involved two major transitions: the encapsulation of self-replicating genetic entities into cellular units and the aggregation of individual genes into a collectively replicating genome. In this paper, we formulate a minimal model of the evolution of proto-chromosomes within protocells. We model a simple protocell composed of two types of genes: a "fast gene" with an advantage for gene-level self-replication and a "slow gene" that replicates more slowly at the gene level, but which confers an advantage for protocell-level reproduction. Protocell-level replication capacity depends on cellular composition of fast and slow genes. We use a partial differential equation to describe how the composition of genes within protocells evolves over time under within-cell and between-cell competition, considering an infinite population of protocells that each contain infinitely many genes. We find that the gene-level advantage of fast replicators casts a long shadow on the multilevel dynamics of protocell evolution: no level of between-protocell competition can produce coexistence of the fast and slow replicators when the two genes are equally needed for protocell-level reproduction. By introducing a "dimer replicator" consisting of a linked pair of the slow and fast genes, we show analytically that coexistence between the two genes can be promoted in pairwise multilevel competition between fast and dimer replicators, and provide numerical evidence for coexistence in trimorphic competition between fast, slow, and dimer replicators. Our results suggest that dimerization, or the formation of a simple chromosome-like dimer replicator, can help to overcome the shadow of lower-level selection and work in concert with deterministic multilevel selection in protocells featuring high gene copy number to allow for the coexistence of two genes that are complementary at the protocell level but compete at the level of individual gene-level replication. These results for the PDE model complement existing results on the benefits of dimerization in the case of low genetic copy number, for which it has been shown that genetic linkage can help to overcome the stochastic loss of necessary genetic templates.

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.