Sociobiological control of plasmid copy number in bacteria

Abstract

All genes critical for plasmid replication regulation are located on the plasmid rather than on the host chromosome. It is possible therefore that there can be copy-up "cheater" mutants. In spite of this possibility, low copy number plasmids appear to exist stably in host populations. We examined this paradox using a multilevel selection model. Simulations showed that, a slightly higher copy number mutant could out-compete the wild type. Consequently, another mutant with still higher copy number could invade the first invader. However, the realized benefit of increasing intra-host fitness was saturating whereas that of inter-host fitness was exponential. As a result, above a threshold, intra-host selection was overcompensated by inter-host selection and the low copy number wild type plasmid could back invade a very high copy number plasmid. This led to a rock-paper-scissor (RPS) like situation that allowed the coexistence of plasmids with varied copy numbers. Furthermore, another type of cheater that had lost the genes required for conjugation but could hitchhike on a conjugal plasmid, could further reduce the advantage of copy-up mutants. These sociobiological interactions may compliment molecular mechanisms of replication regulation in stabilizing the copy numbers.

Figure 1. Transformations of cell types due to conjugation and segregation of plasmids.

Only one plasmid is assumed to get transferred or get cured at a time. Therefore x ₀ cannot be directly transformed into x_m and vice versa. Black arrows indicate conjugation and grey straight arrow indicates curing of plasmid. Curved grey arrows are intrinsic growth rates of respective cell types. Symbols used for the model are explained in Table 1.

Figure 2. Invasion by a mutant plasmid with higher fitness (hc plasmid).

(A) Populations of host cells and (B) proportions of plasmids in host cells with multiple infection. Parameter values for the figure are μ = 0.2, λ = 0.02, φ = 0.004, ε = 0.01, β_l = 0.05, β_h = 0.05, δ = 0.5.

Figure 3. Mutant plasmid with exorbitantly high copy number is invaded back by wild type plasmid.

(A) Populations of host cells and (B) proportions of plasmids in host cells with multiple infection. δ = 5 all other parameters as in Fig 2.

Figure 4. A conceptual diagram based on generalization from many numerical results, depicting the effect of intra and inter-host fitness on realized fitness.

(A) The realized fitness is a saturating function of intra-host fitness and an exponential function of inter-host fitness. As a result of the different nature of the two curves, RPS like dynamics results which is depicted schematically in (B). Arrows indicate the direction of evolutionary change. Mutants with slightly higher copy numbers can invade lower copy number plasmids owing to higher intra-host fitness. As a result the mean copy number increases, however the effect of intra-host fitness is saturating and therefore at a certain stage the reducing positive increment in realized fitness is over-compensated by increasing negative contribution of inter-host fitness difference. At this stage a low copy number plasmid can back invade resulting into a cyclic evolutionary dynamics.

Figure 5. The interaction of the two types of cheaters.

Successful invasion of hc plasmid by hn plasmid in cells with multiple infection brings the wild type back (A, B). Parameter values for the figure are as per Fig. 2. In the absence of hn plasmid, for the same parameters, hc plasmid dominates the population (C and D).

Figure 6. The maximum intra-host plasmid fitness as a function of plasmid cost.

The lines show the limit of intra-host fitness above which the wild type can back invade. In presence of the non-conjugal cheaters the limit is substantially reduced. All other parameters as in Fig 2.