In spite of the importance of plasmids in bacterial adaptation, we have a poor understanding of their dynamics. It is not known if or how plasmids persist in and spread through (invade) a bacterial population when there is no selection for plasmid-encoded traits. Moreover, the differences in dynamics between spatially structured and mixed populations are poorly understood. Through a joint experimental/theoretical approach, we tested the hypothesis that self-transmissible IncP-1 plasmids can invade a bacterial population in the absence of selection when initially very rare, but only in spatially structured habitats and when nutrients are regularly replenished. Using protocols that differed in the degree of spatial structure and nutrient levels, the invasiveness of plasmid pB10 in Escherichia coli was monitored during at least 15 days, with an initial fraction of plasmid-bearing (p þ ) cells as low as 10 À7 . To further explore the mechanisms underlying plasmid dynamics, we developed a spatially explicit mathematical model. When cells were grown on filters and transferred to fresh medium daily, the p þ fraction increased to 13%, whereas almost complete invasion occurred when the population structure was disturbed daily. The plasmid was unable to invade in liquid. When carbon source levels were lower or not replenished, plasmid invasion was hampered.Simulations of the mathematical model closely matched the experimental results and produced estimates of the effects of alternative experimental parameters. This allowed us to isolate the likely mechanisms most responsible for the observations. In conclusion, spatial structure and nutrient availability can be key determinants in the invasiveness of plasmids.

Bacterial plasmids are extra-chromosomal genetic elements that code for a wide variety of phenotypes in their bacterial hosts and are maintained in bacterial communities through both vertical and horizontal transfer. Current mathematical models of plasmid-bacteria dynamics, based almost exclusively on mass-action differential equations that describe these interactions in completely mixed environments, fail to adequately explain phenomena such as the long-term persistence of plasmids in natural and clinical bacterial communities. This failure is, at least in part, due to the absence of any spatial structure in these models, whereas most bacterial populations are spatially structured in microcolonies and biofilms. To help bridge the gap between theoretical predictions and observed patterns of plasmid spread and persistence, an individual-based lattice model (interacting particle system) that provides a predictive framework for understanding the dynamics of plasmid-bacteria interactions in spatially structured populations is presented here. To assess the accuracy and flexibility of the model, a series of experiments that monitored plasmid loss and horizontal transfer of the IncP-1b plasmid pB10 : : rfp in Escherichia coli K12 and other bacterial populations grown on agar surfaces were performed. The model-based visual patterns of plasmid loss and spread, as well as quantitative predictions of the effects of different initial parental strain densities and incubation time on densities of transconjugants formed on a 2D grid, were in agreement with this and previously published empirical data. These results include features of spatially structured populations that are not predicted by mass-action differential equation models.

Conjugative plasmid transfer is key to the ability of bacteria to rapidly adapt to new environments, but there is no agreement on a single quantitative measure of the rate of plasmid transfer. Some studies derive estimates of transfer rates from mass-action differential equation models of plasmid population biology. The often-used ‘endpoint method’ is such an example. Others report measures of plasmid transfer efficiency that simply represent ratios of plasmid-bearing and plasmid-free cell densities and do not correspond to parameters in any mathematical model. Unfortunately, these quantities do not measure the same thing – sometimes differing by orders of magnitude – and their use is often clouded by a lack of specificity. Moreover, they do not distinguish between bulk transfer rates that are only relevant in well-mixed populations and the ‘intrinsic’ rates between individual cells. This leads to problems for surface-associated populations, which are not well-mixed but spatially structured. We used simulations of a spatially explicit mathematical model to evaluate the effectiveness of these various plasmid transfer efficiency measures when they are applied to surface-associated populations. The simulation results, supported by some experimental findings, showed that these measures can be affected by initial cell densities, donor-to-recipient ratios and initial cell cluster size, and are therefore flawed as universal measures of plasmid transfer efficiency. The simulations also allowed us to formulate some guiding principles on when these estimates are appropriate for spatially structured populations and how to interpret the results. While we focus on plasmid transfer, the general lessons of this study should apply to any measures of horizontal spread (e.g., infection rates in epidemiology) that are based on simple mass-action models (e.g., SIR models in epidemiology) but applied to spatial settings.

IncP-1 plasmids are known to be promiscuous, but it is not understood if they are equally well adapted to various species within their host range. Moreover, little is known about their fate in bacterial communities. We determined if the IncP-1beta plasmid pB10 was unstable in some Proteobacteria, and whether plasmid stability was enhanced after long-term carriage in a single host and when regularly switched between isogenic hosts. Plasmid pB10 was found to be very unstable in Pseudomonas putida H2, and conferred a high cost (c. 20% decrease in fitness relative to the plasmid-free host). H2(pB10) was then evolved under conditions that selected for plasmid maintenance, with or without regular plasmid transfer (host-switching). When tested in the ancestral host, the evolved plasmids were more stable and their cost was significantly reduced (9% and 16% for plasmids from host-switched and nonswitched lineages, respectively). Our findings suggest that IncP-1 plasmids can rapidly adapt to an unfavorable host by improving their overall stability, and that regular conjugative transfer accelerates this process.