The Population Biology of Bacterial Plasmids: A Hidden Markov Model Approach

Abstract

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.

Stability of a promiscuous plasmid in different hosts: no guarantee for a long-term relationship

“…This variability was much higher than expected to arise from the observational error due to the sampling process alone. However, the non-deterministic VS model, which draws a selection coefficient from the distribution S~N(s,t 2 ) at each time step, provided a good fit for these datasets (Ponciano et al, 2007). Overall, these results show that different models may be required to adequately capture the observed plasmid loss dynamics in different bacterial hosts.…”

“…The experimental cost values for strains S34 and S55 were much higher than the mean (s) of the estimated probability distribution S (see Fig. 3), but still fell within the 95 % 1.04 (0.14-11.91) 11.5±0.6 % *Parameter estimates as obtained by using the best fitting model (Ponciano et al, 2007). DFor P21, H2 and R28, the 95 % confidence interval (CI) was calculated using parametric bootstrap; for P18, S34, S96 and S55, the 95 % credibility interval (CI) is the 2.5 and 97.5 percentiles of the estimated posterior distributions of the cost (Ponciano et al, 2007).…”

“…In these models, c was defined as the fraction of the encounters between donor cells and plasmid-free cells that result in a plasmid transfer; the units of c were ml per cell h 21 . In the difference equations used in our study, the conjugation frequency c actually represents the maximum fraction of the encounters per unit of time between plasmidfree cells and plasmid-carrying cells that results in plasmid transfer (Ponciano et al, 2007). Hence the discrete transfer frequency used here and the continuous transfer rate constant defined previously are different parameters, and their values cannot be compared.…”

“…The VS model adds just one extra parameter to the SS model: instead of using a fixed plasmid cost (s), it assumes that at each time step, the plasmid cost (S) is drawn from a normal probability distribution with mean (s) and variance (t 2 ). This model is described in detail in Ponciano et al (2007).Statistical analyses. The statistical analysis of these models is described in detail by Ponciano et al (2007).…”

“…3. For each of the seven strains that showed plasmid loss, the model that best captured the plasmid dynamics was first determined (see Table 1 in Ponciano et al, 2007). The SS model, which considered only segregational plasmid loss and a fixed plasmid cost, provided a good fit to the data for two strains (R28 and H2), and more complex models did not fit significantly better, as confirmed by the absolute goodness of fit P-values.…”