On the meaning and estimation of plasmid transfer rates for surface-associated and well-mixed bacterial populations.

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.