Plasmid co-infection: linking biological mechanisms to ecological and evolutionary dynamics

Abstract

As infectious agents of bacteria and vehicles of horizontal gene transfer, plasmids play a key role in bacterial ecology and evolution. Plasmid dynamics are shaped not only by plasmid-host interactions but also by ecological interactions between plasmid variants. These interactions are complex: plasmids can co-infect the same cell and the consequences for the co-resident plasmid can be either beneficial or detrimental. Many of the biological processes that govern plasmid co-infection-from systems that exclude infection by other plasmids to interactions in the regulation of plasmid copy number-are well characterized at a mechanistic level. Modelling plays a central role in translating such mechanistic insights into predictions about plasmid dynamics and the impact of these dynamics on bacterial evolution. Theoretical work in evolutionary epidemiology has shown that formulating models of co-infection is not trivial, as some modelling choices can introduce unintended ecological assumptions. Here, we review how the biological processes that govern co-infection can be represented in a mathematical model, discuss potential modelling pitfalls, and analyse this model to provide general insights into how co-infection impacts ecological and evolutionary outcomes. In particular, we demonstrate how beneficial and detrimental effects of co-infection give rise to frequency-dependent selection on plasmid variants. This article is part of the theme issue 'The secret lives of microbial mobile genetic elements'.

Keywords: ecological and evolutionary dynamics; frequency-dependent selection; mathematical modelling; plasmid co-infection; plasmids.

Figure 1.

Visualization of the modelled plasmid co-infection processes and the corresponding parameters. (a) Schematic diagram of the co-infection model given by equations (2.1). P₀ denotes plasmid-free cells, P_A and P_B are bacterial cells infected with plasmid variant A or B, respectively, and P_AB are cells co-infected with A and B. Arrows indicate the transition of cells between states. (b) Co-infection processes incorporated in the model, listed with their associated parameters and parameter descriptions.

Figure 2.

Parameter space exploration using linear discriminant analysis (LDA). (a) Probability of each class over all simulation outcomes. Frequencies of each class at the end of 500 time steps - ‘no plasmid’ (red), ‘high co-infection’ (green) or ‘low co-infection’ (blue)—are given for 6100 parameter sets randomly sampled over [0, 0.5] for m_i and [0, 1] for k_i,j (= 2k_i,AB), β_i and c_i. (b) LDA using the three classes shown in (a) (same colour scheme). Arrows show the magnitude and direction of the parameters varied (e.g. the shorter arrow of c_i indicates lower significance of this parameter in class separation, whereas m_i and k_i,j (k_i,AB) are most important in separating high from low co-infection areas).

Figure 3.

Co-infection affects evolutionary outcomes through frequency-dependent selection. (a) The effect of the co-infected state on the outcome of competition between two plasmid variants with identical properties. When the co-infected state is neither beneficial nor detrimental, there is no frequency-dependent selection and the plasmid variants remain at their initial frequencies. A co-infection related advantage for both variants introduces negative frequency-dependent selection (NFDS), which equalizes variant frequencies and leads to coexistence. A co-infection related disadvantage introduces positive frequency-dependent selection (PFDS), which leads to the exclusion of the variant with a lower initial frequency. (b) The effect of frequency-dependent selection on evolutionary outcomes in presence of fitness differences between otherwise identical plasmid variants. The figures show the equilibrium frequency of a variant with a fitness advantage but with low initial frequency (P_A = 0.001 and P_B = 1 at t = 0). The colour indicates the equilibrium frequency of variant A (here defined as P_A + P_AB/2 at t = 300 000). The x-axis captures the extent of the fitness difference. Here, we implement this as a difference in conjugation rate (β_i); fitness differences between variants could also arise from differences in e.g. segregation rate or cost. The y-axis captures the strength and direction of the frequency-dependent selection, here implemented by varying the death rate (γ_i) of the co-infected cells. For both plots, standard parameter values are: ρ₀ = 1, ρ_A = ρ_B = ρ_AB = 0.9, γ_i = 0.1, β_A = β_B = 0.2, β_AB = 0, m_i = 1/3, q_i = 1/2, s_i = 1/1000 k_A,B = k_B,A = 1/2, k_A,AB = k_B,AB = 1/4.