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Lineage selection in plasmid evolution

Lineage selection in plasmid evolution


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I've been reading through Paulsson (2002) and I am not sure what he means by "lineage selection" in the second to last section. The paper deals with plasmid replication, and mostly concentrates on the contrasting pressures from two levels of selection:

  1. intracell selection - competition between plasmids in a single cell. A plasmid can undergo a cis-mutation and over-replicate, resulting in a higher intracell fitness than the focal plasmid. The plasmids reproduce.
  2. intercell selection - competition between cells. Cells with a heavier load of plasmids will take longer to reproduce, and plasmids that produce a heavy load will have lower intercell fitness. The cells containing plasmids reproduce.

In this context, what does the third level of selection -- lineage selection -- mean? What reproduces? How do the lineages split or interact?

My guess

Does lineage selection simply mean group-selection on separate colonies of cells? In that case, how are new lineages formed? I would expect this group level to select for zero levels of plasmids (since they place no loads on the cells and thus these groups of cells will grow the fastest), but Paulsson (2002) suggests the opposite:

lineage selection could favor plasmid traits that help the population of plasmid-containing cells to fight plasmid-free cells.

Is there a more detailed discussions of this available than the one section in Paulsson (2002)? Neither the unit of selection nor either the evolutionary or genetic lineage Wikipedia articles address my question. The first only mentions lineage in passing, and the second two don't discuss models of selection.


References

Paulsson, J. (2002). Multileveled selection on plasmid replication. Genetics, 161(4): 1373-1384.


He defines lineage selection as selection for traits which increase the fitness of a group of plasmids, rather than an individual plasmid with in a cell or a particular cell containing plasmids. He says that the unit of selection are "plasmid-host clades" : in other words the unit of selection is the group of closely related plasmids in separate cells. It is an example of a kin-selection though I haven't seen the specific terminology in widespread use. He likely doesn't use kin selection because the plasmids don't have well defined offspring, so he uses a broader term for kin--lineage. I might have preferred clade selection, but this term has its own baggage. I'm not sure (and neither is Paulsson) that kin selection is need to explain 'spitefully low loss' rates, since intra-cellular and inter-cellular selection both favor lower loss rates.


Chromosomal barcoding of E. coli populations reveals lineage diversity dynamics at high resolution

Evolutionary dynamics in large asexual populations is strongly influenced by multiple competing beneficial lineages, most of which segregate at very low frequencies. However, technical barriers to tracking a large number of these rare lineages in bacterial populations have so far prevented a detailed elucidation of evolutionary dynamics. Here, we overcome this hurdle by developing a chromosomal-barcoding technique that allows simultaneous tracking of approximately 450,000 distinct lineages in Escherichia coli, which we use to test the effect of sub-inhibitory concentrations of common antibiotics on the evolutionary dynamics of low-frequency lineages. We find that populations lose lineage diversity at distinct rates that correspond to their antibiotic regimen. We also determine that some lineages have similar fates across independent experiments. By analysing the trajectory dynamics, we attribute the reproducible fates of these lineages to the presence of pre-existing beneficial mutations, and we demonstrate how the relative contribution of pre-existing and de novo mutations varies across drug regimens. Finally, we reproduce the observed lineage dynamics by simulations. Altogether, our results provide a valuable methodology for studying bacterial evolution as well as insights into evolution under sub-inhibitory antibiotic levels.


Introduction

Plasmids are accessory genetic elements able to transfer horizontally between bacteria. They carry genes that help their host adapt to new niches and stresses, playing a key role in bacterial evolution. 1 Plasmids frequently code for antibiotic resistance genes, being responsible for the spread of antibiotic resistance and multiresistance among pathogenic bacteria, which is currently a major concern for public health. 2,3

One of the central questions about plasmid biology is how plasmids can be stably maintained in bacterial populations in the long term. 4 This is challenging to understand due to factors that hinder plasmid survival. Specifically, (i) plasmids produce a cost to the host bacteria, 5 causing a competitive disadvantage and (ii) plasmids can be lost during cell division (even if it is at a very low rate). 6 Taken together, these 2򠾬tors predict a constant decline of the plasmid frequency in the population over time. 7 However, there are factors that counteract the effect of cost and segregational loss and contribute to plasmid maintenance in bacterial populations, such as (i) selection for plasmid-encoded traits, (ii) horizontal transfer of the plasmid between bacteria (mainly by conjugation) and (iii) compensatory mutations alleviating the cost produced by the plasmid. 4,8 The balance among all these factors determines the fate of a given plasmid in a bacterial population. 9

Previous theoretical studies have argued that plasmids can only be maintained in a bacterial population when they are able to conjugate. 8,10,11 However, recent advances in genome sequencing have shown that, paradoxically, a large fraction of plasmids seem to be “non-transmissible” by conjugation according to their sequence. 12 The mechanisms that allow non-transmissible plasmids to persist are poorly understood. In a recent study we used mathematical modeling, functional genomics and experimental evolution to investigate this problem. 13 We developed a model system based on the opportunistic pathogen Pseudomonas aeruginosa PAO1 carrying the small non-conjugative plasmid pNUK73, which produces a particularly big fitness cost in this strain (approximately 20% reduction in relative fitness). pNUK73 confers resistance to neomycin, producing an increase in the minimal inhibitory concentration (MIC) of approximately 60-fold in PAO1. After 30 daily passages (300 generations) the plasmid-bearing subpopulation presented compensatory mutations that completely compensated for the cost of plasmid carriage. These mutations putatively inactivated 3 particular chromosomal genes: a helicase carrying an UvrD-like helicase C-terminal domain (PA1372) and 2 contiguous putative serine/threonine protein kinases (PA4673.15 and PA4673.16).

However, the plasmid-free subpopulation was also adapting to the environmental conditions and therefore their fitness also increased relative to the parental strain. This was due to the acquisition of generally beneficial mutations for adaptation to the laboratory conditions. These mutations targeted primarily the diguanylate cyclase gene wspF (PA3703) in our experimental system. Thus, the plasmid-bearing lineage continued to go extinct, albeit at a slower rate. As a result, the population size of the plasmid-bearing lineage was too small for the generally beneficial mutations to fix. The plasmid-bearing populations could be rescued, however, by adding antibiotics. This led to an increase in plasmid-bearing cells population size which allowed generally beneficial mutations to fix. Therefore, we found that positive selection and compensatory adaptation interact to stabilize pNUK73: positive selection increases the probability of compensatory adaptation by increasing the population size of plasmid-bearing lineages, improving therefore the chances of new adaptive mutations in the plasmid-bearing cells. Compensatory adaptation, in turn, increases the effect of positive selection on plasmid stability by slowing the rate at which the plasmid is lost between episodes of positive selection.

Our previous results show that compensation and positive selection help stabilize non-transmissible plasmids over a few hundreds of generations. However, the long-term maintenance of these plasmids remains challenging to understand. 13 In this commentary we expand the results of our population genetics model to analyze the effects of different regimes of selection as well as the impact of horizontal gene transfer in the long-term stability of these plasmids.


Results

MODEL

We consider a population consisting of cells which can be either chromosomally resistant or chromosomally sensitive ( or ), with no plasmid, a resistant plasmid, or a sensitive plasmid (, , or ). This gives rise to six possible cell types: , , , , , and (the first letter denotes the chromosome, the second letter the plasmid).

We begin by developing a model of the dynamics of these cells (Fig. 1) and denote the density of each cell type by . Cells replicate at rate . Competition between cells is captured through a density-dependent death rate , where is the total cell density (). Plasmids spread through density-dependent transmission between cells at rate and are lost during cell replication with probability (segregation loss). Plasmid carriage is associated with a fitness cost , which reduces the replication rate by a factor of . We assume that cells can only be infected with one plasmid at a time. Cells with no resistance ( and ) experience an additional death rate from antibiotic exposure. Resistance is associated with a fitness cost, which reduces the replication rate by a factor of . We assume that resistance genes have the same fitness cost and the same effectiveness whether they are chromosomal or plasmid-borne. Cells that have both chromosomal and plasmid-borne resistance experience a dual fitness cost . The effect of modifying these assumptions is explored in the Supporting Information (Section 2). Our main results are generally robust, with sensitivities highlighted in the main text.

Schematic of the modeled dynamics (eq. 1). Each grey circle represents a cell type, with the interior circles representing the chromosome (large) and plasmid (small), with denoting resistance and sensitivity. The arrows indicate modeled processes: cell replication (dark blue), death (purple), plasmid transmission (orange), and segregation loss (light blue). The labels indicate the rate at which these processes occur. indicates the density of a cell type, so is the total cell density (), is the total density of cells with a resistant plasmid (), and is the total density of cells with a sensitive plasmid (). is the replication rate the density dependent death rate the antibiotic-associated death rate the plasmid transmission rate the probability of segregation loss the cost of plasmid carriage and the cost of carrying the resistance gene. (1)

The model parameters are summarized in Table 1. We expect parameter values (i.e., rates and costs) to differ considerably depending on, for example, bacterial species, type of plasmid, antibiotic, and environment. Our aim is to understand the behavior of a generalized system qualitatively, rather than make quantitative predictions about a specific system. We therefore explore a wide range of parameter values (Supporting Information Section 1) rather than choosing parameters to reflect a particular system.

Parameter Definition Dimensions Main text value (SI range) Bistability when
Replication rate Time −1 1 (0.5, 2) High
Death rate Volume cells −1 time −1 1 (0.5, 2) Low
Antibiotic-associated death rate Time −1 1 (0, 2) Low
Cost of antibiotic resistance Dimensionless 0.05 (0, 0.5) High
Cost of plasmid carriage Dimensionless 0.075 (0, 0.5) Low
Plasmid transmission rate Volume cells −1 time −1 0.2 (0, 0.25) High
Segregation loss Dimensionless 0.005 (0, 0.1) Low
  • Note: More specifically, the fifth column indicates whether the region of bistability (where resistance can be either plasmid-borne or chromosomal) occurs at high or low parameter values compared to the region where only chromosomal resistance is evolutionarily stable (see Supporting Information Section 1). The parameter units are arbitrary. The main text values are chosen to best illustrate the range of evolutionary stable outcomes.

EVOLUTIONARY STABILITY OF PLASMID-BORNE AND CHROMOSOMAL RESISTANCE

We are interested in the evolutionary stability of chromosomal and plasmid-borne resistance, that is, whether established chromosomal resistance can be displaced by plasmid-borne resistance and vice versa. We determine parameter regions in which each type of resistance is stable (Figs. 2, and S1 and S2) using linear stability analysis (see Methods). Under conditions selecting for resistance, we observe three behaviors: evolutionary stability of chromosomal—but not plasmid-borne—resistance evolutionary stability of plasmid-borne—but not chromosomal—resistance and evolutionary stability of both forms of resistance. In this third region, resistance occurs on either the plasmid or on the chromosome, but not both: having both chromosomal and plasmid-borne resistance increases the cost of resistance while providing no added benefit.

Evolutionary stability of plasmid-borne and chromosomal resistance. The colors indicate which form of resistance is evolutionarily stable: only chromosomal resistance (orange) only plasmid-borne resistance (blue) or either (purple). When resistance is chromosomal, the sensitive plasmid can either be present or absent from the population (dark vs light orange). In the white space in the left-hand panel, neither form of resistance is stable (the population is antibiotic-sensitive). Parameter values are: , , . For left-hand panel = 0.075 and . For right-hand panel and . Figures S1 and S2 show results for more parametrizations. Note that in the parameter space where resistance is beneficial, it can either be essential (: antibiotic susceptible cells are not viable, even in the absence of competition from resistant cells) or non-essential. This distinction does not impact our results (Figs. S1 and S2).

Chromosomal resistance only

When only chromosomal resistance is evolutionarily stable, resistance genes will always end up on the chromosome over an evolutionary time-scale. The plasmid will either be sensitive, or absent from the population. In general terms (Table 1 and Figs. S1 and S2), chromosomal resistance is the only evolutionarily stable outcome when the benefit from resistance is high (high antibiotic associated mortality, low cost of resistance) when the fitness of the plasmid is low (low plasmid transmission rate, high segregation loss, high plasmid cost) and when overall cell density is low (high death rate, low replication rate).

Plasmid-borne resistance only

When plasmid-borne resistance is evolutionary stable, resistance genes will always end up on the plasmid. Note that in this region, chromosomal resistance is not stable at all (Fig. S12): it represents a region in which resistance genes can only persist when horizontally transferred (van Dijk et al. 2020 ). This outcome arises only under very specific conditions (small parameter space, when resistance yields only a minor fitness benefit Fig. 2) and its presence is sensitive to model structure (e.g., how antibiotic effect is modeled see Fig. S7). We therefore do not consider this an ecologically plausible explanation for why resistance genes are on plasmids.

Bistability

When both equilibria are evolutionarily stable, resistance can be either chromosomal or plasmid-borne depending on initial conditions. Once one form of resistance has established, it can no longer be displaced by the other.

To further investigate the dependence on initial conditions, we simulate the system numerically, starting at different initial cell densities (see Methods). We consider a scenario with an initial population consisting of resistant cells and sensitive cells (Fig. 3). We vary (i) the initial frequency of the sensitive plasmid in the sensitive population (ii) the initial frequency of chromosomal versus plasmid-borne resistance in the resistant population and (iii) whether the chromosomally resistant cells carry the sensitive plasmid. The results of these simulations (Figs. 3 and S3 and S4) provide insight into the evolutionary pressures that determine the location of resistance genes in three ways.

The effect of initial conditions on the equilibrium location of the resistance gene, showing evolutionary outcome depends on both the initial frequencies of plasmid-borne and chromosomal resistance and the initial frequency of the sensitive plasmid. The left-hand panels illustrate variation in the initial conditions. The right-hand panels illustrate whether plasmid-borne (blue) or chromosomal resistance (orange) is observed at equilibrium. The x-axis indicates the frequency of the sensitive plasmid in the initial sensitive population . The y-axis indicates the frequency of the plasmid-borne resistance in the initial resistant population for panel A, for panel B. Plasmid-borne resistance is a more typical outcome in panels B than A because of the presence of the sensitive plasmid in the initial chromosomally resistant population in panel A. The total densities of the initial sensitive and resistant populations are both 1. (Varying the initial ratio of resistance to sensitivity does not affect qualitative results—Fig. S3). Parameter values are as follows: , , , = 0.075, , , and .

First, the presence of positive frequency-dependent selection: plasmid-borne resistance is a more typical outcome when the initial frequency of plasmid-borne resistance is high compared to the frequency of chromosomal resistance. Similarly, a high initial frequency of chromosomal resistance, compared to plasmid-borne resistance, leads to chromosomal resistance as the evolutionary outcome. The fitness of one type of resistance is therefore positively correlated with its frequency. This frequency dependence arises because dually resistant cells are less fit than cells with either form of single resistance: dual resistance incurs an additional fitness cost but provides no additional fitness benefit. The higher the frequency of chromosomal resistance is, the higher the probability that a resistant plasmid will infect a chromosomally resistant (rather than chromosomally sensitive) cell. This disadvantages the resistant plasmid. Similarly, the higher the frequency of the resistant plasmid is, the higher the probability that a chromosomally resistant cell will be infected with the resistant plasmid. This disadvantages the resistant chromosome. Thus, the more common the resistance form, the greater its fitness compared to the other form.

Second, the evolutionary outcome also depends on the frequency of the sensitive plasmid. Plasmid-borne resistance benefits from the sensitive plasmid being rare: plasmid-borne resistance is a more typical outcome when the initial chromosomally resistant population does not carry the sensitive plasmid and when the frequency of the plasmid in the sensitive population is low. This is because a low initial frequency of the sensitive plasmid means that plasmid-borne resistance can spread both vertically (cell replication) and horizontally (plasmid transmission), allowing it to increase in frequency more rapidly than chromosomal resistance.

Third, overall, chromosomal resistance is a more typical outcome in these simulations than plasmid-borne resistance. This is because plasmid-borne resistance, unlike chromosomal resistance, is subject to segregation loss: it is not always inherited during cell replication. Indeed, increasing the probability of segregation loss favors chromosomal resistance (Fig. S4).

ROBUSTNESS OF RESULTS

We test the robustness of these results to a number of assumptions about model structure (see Methods and Supporting Information Section 2). The general result is that the presence of bistability is robust, although the size of the region of bistability can change. The only crucial assumption for positive frequency dependence is that dual resistance is less beneficial than single resistance (Figs. S5 and S6). In other words, eliminating the additional cost from dual resistance, or increasing the benefit of dual resistance so much that it outweighs this additional cost, abolishes the region of bistability. Under these circumstances, dual resistance dominates (i.e., the population will consist of a resistant plasmid circulating in a chromosomally resistant population).

The results of two sensitivity analyses in particular are worth highlighting. First, our results are robust to inclusion of gene flow between the plasmid and chromosome (e.g., transposition of the resistance gene). Gene flow allows the otherwise excluded form of resistance to persist at low frequency (analogous to mutation-selection balance), and increases the range of initial conditions leading to chromosomal resistance (Fig. S8). However, these effects only become substantial for unrealistically high transposition rates (Supporting Information Section 2.4) (Sousa et al. 2013 ). Second, the presence of bistability is robust to modeling fluctuating, instead of constant, antibiotic pressure. Depending on its period, fluctuation can favor plasmid-borne resistance, increasing the size of the parameter space in which only plasmid-borne resistance is evolutionarily stable (Fig. S10).

RELATIONSHIP TO PREVIOUS MODELING RESULTS

Next, we revisit some previous modeling results. As discussed in the introduction, previous modeling predicts that locally beneficial traits will be plasmid-borne rather than chromosomal, thus providing a complementary hypothesis for why certain genes reside on plasmids (Bergstrom et al. 2000 ). However, the model from which this prediction is derived assumes absence of the plasmid outside the local niche. We therefore ask whether local adaptation favors plasmid-borne resistance if the sensitive plasmid can persist outside the local niche. We modify our model to include an influx of sensitive cells, and vary the frequency of the sensitive plasmid in these incoming cells (Supporting Information Section 3). This corresponds to a scenario in which resistance is locally beneficial in the modeled environment, but not selected for elsewhere. As shown in Figure 4, an influx of sensitive cells without the sensitive plasmid does indeed favor plasmid-borne resistance, as suggested previously (Bergstrom et al. 2000 ). However, an influx of sensitive cells with the sensitive plasmid favors chromosomal resistance. The strength of this effect depends on the rate of influx of sensitive cells. Thus, local adaptation only favors plasmid-borne resistance if the frequency of the sensitive plasmid is low outside the local niche.

The location (chromosomal or plasmid-borne) of a locally beneficial resistance gene depends on the presence of the sensitive plasmid in immigrant cells. The initial population is fully resistant (with chromosomally resistant cells carrying the sensitive plasmid, corresponding to panel A in Figure 3), with the y-axis indicating the frequency of plasmid-borne resistance in this initial population . The x-axis indicates the frequency of the sensitive plasmid in the immigrant cells. The presence of the plasmid in these immigrant cells favors chromosomal resistance. The high influx rate is , the low influx rate is . Other parameters values are: , , , = 0.075, , , and .

Second, we revisit results relating to plasmid persistence. Previous modeling work has suggested that if plasmid fitness is too low for plasmids to persist as pure parasites (i.e., without carrying genes beneficial to the host cell), beneficial genes will always locate on the chromosome rather than plasmid (in absence of local adaptation Bergstrom et al. 2000 ). Thus, the persistence of low transmissibility plasmids is a paradox: they cannot be maintained without beneficial genes, but beneficial genes cannot be maintained on these plasmids (Bergstrom et al. 2000 ).

We test this prediction in our model (as detailed in Supporting Information Section 4) by comparing the parameter space in which plasmid-borne resistance is evolutionarily stable (i.e., resistance genes can locate onto the plasmid even in the presence of competition from chromosomal resistance) with the parameter space in which a parasitic plasmid can persist (i.e., a sensitive plasmid can persist in a chromosomally sensitive population). We find that previous results do not hold for the model structure presented here: resistance genes can locate onto the plasmid instead of the chromosome even if the plasmid transmissibility is too low for the plasmid to persist as a parasite (Fig. S11). This implies that in theory, it is possible for there to be low transmissibility plasmids which persist purely because of the advantage they provide host cells. It is worth noting, however, that the parameter space in which this occurs is small (Fig. S11).

RATE OF ACQUISITION DETERMINES RESISTANCE GENE LOCATION

Thus far, our results show that for moderately beneficial genes (i.e., those in the bistable parameter region), the presence of positive frequency-dependent selection means that plasmid-borne resistance can be evolutionarily stable despite segregation loss. This frequency-dependent selection is not, in itself, a sufficient explanation for why resistance genes are plasmid-borne. However, it does suggest that whichever form of resistance (plasmid-borne or chromosomal) is acquired first is likely to establish in the population: if the first form of resistance has time to increase in density prior to the acquisition of the other form, its greater frequency will give it a fitness advantage. The first resistance type need not have reached fixation to preclude invasion by the other: the frequency-dependent advantage is sufficiently strong even at low overall resistance frequencies (Fig. S13). Therefore, when the rate of resistance acquisition is low compared to the rate of increase in resistance frequency once acquired, the first form of resistance will persist.

Thus, the presence of resistance genes on plasmids could be explained by the acquisition rate of plasmid-borne resistance being higher than the acquisition rate of chromosomal resistance. Indeed, rates of conjugative plasmid transfer are generally higher than rates of chromosomal horizontal gene transfer (one estimate, based on comparison of experimental measures, suggests of the order of higher, though this is probably highly context dependent Nazarian et al. 2018 ). Furthermore, for a number of bacterial species, the primary mechanism of resistance gene acquisition is indeed thought to be inter-species transfer of resistance-bearing plasmids (Baker et al. 2018 MacLean and San Millan 2019 ).

To formalize this idea, we develop a simple model of resistance acquisition in multiple species (Fig. 5 and “Methods” section). We model species a resistance gene which is beneficial in all species and a plasmid that can be transferred between and persist in all species (either because it has a broad host range or because its range can be shifted or expanded following transfer Loftie-Eaton et al. 2016 ). Resistance can be either plasmid-borne or chromosomal. Once a species acquires one form of resistance, this form of resistance becomes established and can no longer be replaced (due to positive frequency-dependent selection). We assume that resistance genes only emerge de novo on the chromosome (at rate ). The gene can spread through interspecies horizontal transfer of chromosomal resistance (e.g., transformation) (at rate ), or interspecies transfer of resistance plasmids (at rate ). We assume the gene can move between the plasmid and chromosome at low rates, which allows the otherwise excluded form of resistance to persist at low frequency. We do not explicitly model this coexistence, but do model the horizontal transfer of the low-frequency form (at rate for plasmid-borne resistance and rate for chromosomal resistance, where is the frequency of the low frequency form).

Prevalence of plasmid-borne resistance. Panel A: Representation of the model structure. represents species without the resistance gene species with the resistance gene on the plasmid species with the resistance gene on the chromosome. is the rate at which resistance arises through mutation the rate at which the plasmid-borne resistance is transferred between species the rate at which chromosomal resistance is transferred between species and captures gene flow between the plasmid and chromosome. Panel B: The proportion of plasmid-borne resistance depends on the number of simulated species and the ratio of the rate of interspecies transfer of the chromosomal () and plasmid-borne gene (). The horizontal dashed lines show the maximum proportion of plasmid resistance, given that resistance must first emerge on the chromosome (). The error bars represent 95% confidence intervals, based on 1000 realizations. Parameters were: , and . Results for alternative parameterizations are shown in Figure S14.

We simulate this system stochastically (see “Methods” section), starting from no species having the resistance gene. Figure 5 shows the proportion of species with plasmid-borne resistance once the gene has spread to all species. As expected, the proportion of species with plasmid-borne resistance increases with the rate of interspecies plasmid transfer. In addition, this proportion also increases with the number of modeled species. This effect arises for two reasons. First, the initial de novo appearance of the gene must be on the chromosome. Thus, for example, when only two species are modeled, plasmid-borne resistance can only occur in one of two species. Second, the impact of the rate of interspecies transfer increases with the number of potential donor species. These results are robust to different parametrization (Fig. S14).


Evolution in Bacterial Plasmids and Levels of Selection

Gene flow between different reproductive such as bacterial plasmids and chromosomes presents unusual problems for evolutionary analysis. Far more than in eukaryotes, reproductive advantages at several levels of selection-genes, transposons, plasmids, cells, and clones-must be considered simultaneously to understand plasmid evolution. No level consistently prevails in conflict situations, and some reproductive units carry genes that restrain their own reproduction or survival, apparently to enhance the reproduction or survival of the higher-level reproductive units that carry them. Despite gene flow between plasmids and chromosomes, genes for certain functions show strong tendencies to occur on plasmids while others consistently occur on chromosomes. Functions generally associated with plasmids are diverse, but all are useful only in locally restricted contexts it is argued that the selective consequences of the greater horizontal (within generation) transmission of plasmids are responsible for this pattern. The tendency for prokaryote transposons, which are also horizontally mobile, to carry genes similar to those commonly on plasmids supports this argument. The apparent trends in eukaryote plasmids and transposons to lack these same characters also accords with predictions of the local adaptation hypothesis, because genes on these genetic units are generally no more horizontally mobile than chromosomal genes. There are theoretical reasons to expect that plasmid genes tend to evolve more rapidly than chromosonal genes.


Results

The Existence of Characteristic Copy Numbers

We begin by focusing our attention to a single cell that contains a population of plasmids that are identical with respect to their replication profile. We initially ignore the stochastic nature of replication and cell division and consider the copy number to be a continuous variable, with both the host growth and the copy number described by deterministic differential equations (see Equations 1 and 2 in Supplementary Text S1). Our model allows us to establish a relationship between the number of plasmids at the beginning of the cell cycle () and the number of plasmids at the end of the cell cycle at the time of cell division (), where represents the number of plasmids in the resulting daughter cells, assuming equipartitioning during cell division. Figure 2 demonstrates a typical relationship between and , which is dependent on the plasmid replication rate which is, in turn, a function of the plasmid parameters , and (see Equation 2). Subject to the initial number of plasmids in the parent cell , the resulting daughter cells will have either fewer (), more () or as many plasmids () as their parent cell initially contained. The latter case represents the cross-generational equilibrium of a particular copy number for a given set of plasmid parameter values. This equilibrium can be either stable or unstable, depending upon the response of the system to fluctuations in copy number. The conditions for a stable equilibrium where there is a stable characteristic copy number can be defined according to:

so that when a cell has fewer than plasmids at the beginning of the cell cycle, plasmids over-replicate and when it has more than plasmids, plasmids under-replicate. In both cases, which can emerge as a result of stochasticities in plasmid replication or segregation upon cell division, the tendency is towards an equilibrium future cell cycle with plasmids again. An example of a stable characteristic copy number is the point marked with a filled circle in Figure 2 . The point marked with an open circle on the same curve is an unstable equilibrium copy number, any perturbation to which will lead either to plasmid over-replication or under-replication, the latter case in this instance resulting in movement towards the stable equilibrium.

Each curve represents the deterministic relationship between the number of plasmids at the beginning of the parent cell cycle and the number of plasmids at the beginning of the daughter cell cycle (assuming equipartitioning during cell division), for a range of initial copy numbers and a fixed set of cell and plasmid parameters. The diagonal represents the consistency of copy numbers between parent and daughter cells points below the diagonal indicate plasmid under-replication, while points above the diagonal indicate plasmid over-replication. The curve's shape and its point(s) of intersection with the diagonal depend on the plasmid parameter values curves that do not intersect with the diagonal represent the case of consistent under- or over- replication of plasmids for any initial copy number (blue low curve and cyan high curve respectively). The high end of each curve corresponds to a limit beyond which the cell can not sustain its plasmid population due to a negative cell growth rate that leads to cell death. Points marked with circles on the medium curve (green) represent equilibrium copy numbers a filled circle indicates stability and the existence of a characteristic copy number, whereas an open circle indicates an unstable equilibrium. The critical curve (red), which is tangential to the diagonal, represents the limit (edge) of stability, in which the stable and unstable characteristic copy numbers collapse to a singular point.

The Boundaries of Plasmid Stability

For any configuration of plasmid replication parameters , and , we can determine whether a stable characteristic copy number exists, what its value is, and what is the corresponding cell fitness, which is defined as the reciprocal of the time required for a cell to divide. Figure 3 presents the results of exploring the space of plasmid parameters for two distinct CNC regimes. First, we consider the case in which plasmids have self-determined replication rates independent of the presence of other plasmids in the same host (, NO-CNC). In this case, the only mechanism of controlling the copy number is plasmid self-restraint (in the form of ), what early theoretical approaches termed “passive” copy number control [36]. Second, we consider the case of an active negative feedback loop between copy number and plasmid replication rate that is realized through the synthesis of trans-acting replication inhibitors (, with , CNC).

Stable (solid) and unstable (dashed) equilibrium copy numbers for a single cell as a function of basal plasmid replication rates for and various values of the binding affinity (blue for green for red for ). The values of cell fitness (calculated as the reciprocal of the cell division time ) that correspond to the stable characteristic copy numbers are shown in the bottom panel. The stable and unstable equilibrium copy numbers collapse to a singular point (the edge of copy number stability as demonstrated by the critical curve in Figure 2 ) that is marked by a colored vertical dotted line, beyond which there exist no characteristic copy numbers, i.e. plasmids over-replicate for any initial copy number. The limit below which the stable characteristic copy number becomes zero is . In the case where (blue lines), the edge of stability coincides with maximum cell fitness for (green, red lines), the host fitness peak is surrounded by suboptimal parameter configurations which are characterized by stability with respect to copy number.

In the former case (NO-CNC), we observe that the system has a stable non-zero characteristic copy number for an extremely limited region of basal plasmid replication rates . This stable region is surrounded by regions of plasmid instability characterized by consistent under- or over- replication of plasmids for any initial copy number (described by the low and high curves in Figure 2 ). Within the region of plasmid stability, cell fitness increases with until a critical point which marks the transition to instability where plasmids consistently over-replicate. Hence, under no CNC, inter-cellular selection would favor increasing values of the plasmid replication rate (), since this translates to higher cell fitness, until the critical point of plasmid instability is reached. This transition (denoted by a vertical dotted line in Figure 3 ) occurs at maximum cell fitness and is characterized by the collapse of the stable and unstable equilibrium copy numbers to a singular copy number (an event that is captured by the critical curve in Figure 2 ). Consistent over-replication results in future cell cycles with an increasing number of plasmids which leads, eventually, to plasmid explosion and cell death. The activation of the CNC system (, with ) effectively widens the range of plasmid stability and, crucially, decouples the point of transition to instability from the point of optimal cell growth. As a result, the configuration of plasmid replication parameters that yields optimal cell growth is now surrounded by suboptimal, yet also stable, regions. Under these conditions, inter-cellular selection for increased cell division rates would favor cells containing plasmids with stable copy numbers.

Plasmid Stability and Host Growth

Our previous simulations demonstrated that, when stochasticity is ignored, there is only a limited range of that allows for stability in plasmid replication. In the absence of CNC, optimization of the cell division rate would result in plasmid replication rates at the edge of stability, whereas the presence of CNC both broadens the range of stable replication rates, as well as creates a situation in which optimal cellular fitness is located in the interior of this region of stability. We now proceed by extending the deterministic unicellular framework we have considered so far in order to investigate plasmid stability and host performance in the context of stochastic multicellular simulations that describe the asynchronous growth and division (or death) of hosts and the autonomous replication of plasmids within such hosts. We introduce stochasticity in plasmid replication by considering the expected number of replication events for plasmids in each host at each discrete time point to be Poisson-distributed, as specified by Equation 2 (for more details see Supplementary Text S1).

The performance of a particular strain in such a stochastic simulation, in which hosts are infected by plasmids with identical replication parameter values, can be evaluated by calculating the average net host growth rate as the difference between the average host division and death rates. Figure 4 displays the resulting fitness landscape of independent strains as a function of the corresponding values of the plasmid replication parameters and given . We note that, due to the homogeneity of the plasmid population, parameters and are interchangeable (see also Equation 2) and, as such, the fitness landscape of and given is identical to the fitness landscape of and given . The region of plasmid stability in this landscape is dominated by the gradient of the net host growth rate leading to an area of optimal growth in which obedience to policing is maximally strong (). Just as in the unicellular deterministic case, the stable region is surrounded by regions of plasmid instability, in which plasmids are eliminated from the host population, due to the absence of a stable characteristic copy number and the consistent under- or over- replication of plasmids. Consistent under-replication leads to the gradual dilution and eventual disappearance of plasmids from the population (white area below the stable region in Figure 4 ). Consistent over-replication leads to an elevated copy number that slows down cellular growth (see also Equation 1), providing more time for plasmids to replicate, thereby further compromising cellular growth. As such, plasmid-free hosts, resulting from stochastic segregational errors, are able to outgrow over-infected hosts, until the population is completely plasmid-free (white area above the stable region in Figure 4 ). In the case of extreme plasmid selfishness (at high , low ), the host population collapses under the weight of excessive plasmid over-replication, before plasmid-free segregants are given the chance to outgrow over-infected hosts and form a plasmid-free population (black clusters in Figure 4 ).

The heatmap displays the population's net average growth rate (expressed as the difference between the average division and death rates) as a function of the plasmid replication parameters and , averaged across three independent stochastic multicellular simulations with plasmid homogeneity (no mutations) and a fixed rate of inhibitor production. The white areas below and above the stable region represent the regions of the plasmid parameter space in which plasmids are eliminated from the population due to consistent under- or over- replication respectively. The black clusters in the upper-left corner represent the collapse of the host population under the weight of excessive plasmid replication. The horizontal dashed line indicates the value of for which the system reaches optimal growth at (see Figure 5 ). Finally, the black ladder-like path outlines the evolution of CNC in a stochastic simulation where and are allowed to mutate with probability and a fixed rate of inhibitor production.

Levels of Obedience and the Efficiency of Replication Control

The stochasticities in plasmid replication and segregation upon cell division give rise to a distribution of copy numbers in the population that occur across all plasmid-infected hosts over the course of a simulation. We explored the effects of obedience ( or policing , since these are interchangeable due to the homogeneity of the plasmid population) on the features of these distributions, by considering a cross-section of the fitness landscape for a fixed value of the plasmids' basal replication rate , which corresponds to the optimal net growth rate at maximal CNC (). The weak CNC regime along this cross-section of the fitness landscape () is unstable and plasmids are eventually eliminated from the population (see Figure 5 ). The broadness of the copy number distributions in this regime reflects the extensive variation and drift of copy numbers in the population, due to the amplification of stochastic copy number fluctuations [15]. The transformation of the distributions begins at the intermediate range of obedience (), with the emergence of a clear peak nevertheless, the presence of a heavy tail indicates the persistence of plasmid replication instabilities. These instabilities are minimized in the region of strong CNC () as the distributions become progressively less skewed, due to the increasing efficiency in controlling stochastic copy number fluctuations and the corresponding reduction in copy number variation. At the same time, the discrepancy between the distributions' average copy number and the copy number that is optimal for host growth (see also Equation 1) becomes lower with increasing obedience , thus inducing an acceleration of the net average host growth up to the optimal rate at maximal CNC ().

The effects of obedience (increasing copy number control ) on the distribution of plasmid copy numbers for a fixed value of the plasmids' basal replication rate , chosen so that the population fitness for this value is optimal at maximal CNC (see horizontal dashed line in Figure 4 ). The weak CNC regime () is unstable and plasmids are eventually eliminated from the population. Copy number distributions are given for different values of (top left blue for , green for , red for , cyan for and magenta for ). The distributions have been calculated by recording the copy numbers of all plasmid-infected hosts over the entire course of a multicellular stochastic simulation. The discrepancy between the average copy number and the copy number that is optimal for host growth is given as a function of (top right), as well as the standard deviation (bottom left) and skewness (bottom right) of the copy number distributions.

The Evolution of Collective Restraint

Having explored the effects of homogeneous plasmid cooperation on host growth and plasmid stability, we now ask how these effects influence the evolution of the plasmid replication parameters in the broader context of the conflict between the levels of selection. To this end, we introduce plasmid variation in our multicellular stochastic simulations: each plasmid replication event implies the possibility of mutation with probability , in which case the value of exactly one of the plasmid's replication parameters, chosen at random with equal probabilities, is modified.

Starting with an initial population of plasmids that do not respond to inhibitors (i.e. ), we allow and to evolve given a fixed rate of inhibitor production . The resulting evolutionary dynamics, shown in Figure 4 , demonstrate the emergence of efficient replication control as driven by the synergies between intra-cellular selection favoring immediate plasmid reproductive gains (higher selfishness , lower obedience ), and inter-cellular selection favoring evolutionary adjustments towards those regions of the plasmid parameter space where the net host growth rate increases. In effect, and due to the transient and epigenetic nature of stochastic copy number fluctuations, inter-cellular selection operates upon the net host growth rate accumulated over a few generations and, therefore, upon the copy number distributions associated with particular configurations of the plasmid replication parameters [27]. As such, the evolutionary adjustments favored by inter-cellular selection come in the form of cooperative plasmid parameter mutations, such as increased plasmid self-restraint (lower selfishness ) or increased sensitivity to the inhibitor (higher obedience ), which alter the mode of plasmid replication so as to ensure a reduction, first, in the discrepancy between the optimal and mean copy numbers, and, second, in the magnitude of copy number fluctuations (i.e. the variation of the copy number distribution). This way, the evolution of CNC unfolds with an escalating succession of selfish and cooperative plasmid parameter mutations that develops along the gradient of the host fitness landscape, leading the system towards the region of optimal host growth at maximal CNC. Further escalation is prevented due to the limits that are imposed on plasmid parameter values the absence of such limits would yield a ratcheting effect whereby the succession of selfish and cooperative mutations would continue indefinitely, limited only by the costs of producing the corresponding factors involved in plasmid replication (initiators and inhibitors).

The same cooperative outcome (evolution of an efficient CNC system) is obtained when we allow all three plasmid replication parameters , and to evolve from an initial state where plasmids neither produce () nor respond () to inhibitors (see Figure 6 ). In this case, cooperative mutations can be either cis-specific (higher obedience ) as before, or trans-specific (greater policing ), in which case a mutation that increases the rate of inhibitor production by an individual plasmid will influence not just the mutant but all plasmids in the intra-cellular replication pool (due to the term in Equation 2). The cis-specificity of implies that a cooperative mutation inducing a higher sensitivity to the inhibitor is costly at the intra-cellular level, since it decreases the mutant's chances of immediate reproductive success in the replication pool. The trans-specificity of introduces a coercive element to cooperation, because the production of inhibitors regulates the replication of all plasmids in the pool. It also creates the potential for subversive plasmid strategies according to which individual plasmids can gain an advantage in the replication pool by zealously producing the inhibitor (high policing ) while maintaining a low sensitivity (obedience ) to that inhibitor themselves. Nevertheless, this scope for opportunistic behavior does not prevent the emergence of the policing CNC mechanism. In fact, we find that plasmid parameter variation within cells is quite low (see Table 1 ), so that hosts are inhabited by a, more or less, homogeneous plasmid population (i.e. plasmids are highly related to their intra-cellular neighbors), due to the lack of plasmid migration (horizontal transmission) between hosts. The degree of plasmid homogeneity is reduced by approximately an order of magnitude between hosts, compared to its value within hosts, thus generating the host growth differential upon which inter-cellular selection operates by favoring stricter control over plasmid replication.

Average plasmid parameter values (blue), (green) and (red) over time, showing the evolution of the CNC mechanism in stochastic multicellular simulations, with mutation probability . Results have been averaged across 50 independent simulations with the same initial conditions.

Table 1

within hostsbetween hosts
The table summarizes the intra-cellular (within hosts) and inter-cellular (between hosts) variation of plasmid replication parameters, represented as the standard deviation , averaged over time and across 50 independent stochastic multicellular simulations (the corresponding plasmid parameter averages are shown in Figure 6 ). The intra-cellular variation is calculated for all plasmids within a host with respect to the host's intra-cellular mean and is averaged across all hosts in the population. The inter-cellular variation is calculated for the intra-cellular means of all hosts with respect to the population's (global) mean.

The Effects of Policing Costs on the Evolution of CNC

We also investigated the influence of policing costs to the evolution of collective restraint and the overall performance of the population, by introducing an additional cost term in Equation 1, where is the cost of production per unit of inhibitor paid by the host. This implies that there is now selection at the inter-cellular level against the production of policing resources, due to the associated policing costs that slow down host growth. Figure 7 shows that the increase in policing costs corresponds to a decrease in the production of policing resources (), but not a collapse of plasmid obedience () to policing. On the contrary, obedience is not only sustained but also slightly increases with rising policing costs. At the same time, the basal plasmid replication rate () decreases so as to compensate for the gradual reduction in the availability of policing resources (). As a result, the CNC system remains functional throughout (since there is still selection at the inter-cellular level for high obedience ) but becomes less efficient with increasing policing costs and the performance of the population deteriorates with lower division rates for hosts and higher rates of segregational loss for plasmids (see Figure 7 ).

Average values of the plasmid parameters (, , ), the rates of host division and segregational loss, as well as the fraction of plasmid-infected hosts in the population (plasmid spread) for varying costs of policing. The latter is expressed here as the production cost per unit of inhibitor relative to the constant general cost of maintenance per plasmid copy (e.g. the cost of gene expression, replication etc.).

Comparisons between Individual and Collective Restraint

The positive effects of CNC are not limited to hosts but extend to plasmids as well. We evaluated the advantages of CNC for hosts and plasmids by comparing the results of our multi-cellular stochastic CNC simulations (CNC evolve) to those of the baseline model where policing is absent and plasmids replicate independently of the presence of other plasmids in the same host (NO-CNC evolves, ). Host performance was evaluated in terms of the average division and death rates, while the performance of plasmids was assessed on the basis of the fidelity of vertical transmission and the spread of plasmids in the host population. Figure 8 demonstrates that all measures were significantly improved when CNC was functional (CNC simulations), compared to the case where the CNC mechanism was absent (NO-CNC simulations). As such, the beneficial effects of the CNC mechanism on plasmid stability, due to the stricter control of stochastic copy number fluctuations, allow for widespread host infection and the minimization of segregational losses within the margins allowed by inter-cellular selection, thus solidifying the persistence of the plasmid lineage in the population.

Host performance is measured in terms of the division (top left) and death rates (top right), while the performance of plasmids is measured in terms of the segregational losses (bottom left) and the fraction of plasmid-infected hosts in the population (bottom right). The rate of segregational loss is calculated by recording at every time step the instances of a plasmid-free daughter cell arising from a plasmid-infected parent cell among all divisions of plasmid-infected cells. Comparisons are drawn between the baseline model in which policing is absent (NO-CNC in blue color evolves, ) and the model in which policing and obedience are allowed to evolve (CNC in green color evolve). The distributions were calculated using the values of the last 100,000 steps of 50 independent stochastic multicellular simulations with the same initial conditions and mutation probability .

Finally, we also investigated the persistence and stability of an established policing mechanism among plasmids against invasion by selfish individuals, i.e. plasmids that are insensitive to replication inhibitors and replicate independently of the presence of other plasmids in the same host. More specifically, we simulated the competition between the NO-CNC ( only with ) and the CNC () types (a) by mixing both types equally within hosts (within-host heterogeneity) and (b) by distributing the two types separately and equally among different hosts in the population (between-host heterogeneity). In every case that we examined, we observed the rapid displacement of the selfish type from the population. The complete prevalence of the CNC type demonstrates the robustness and stability of the mechanism of collective restraint in the face of invasion by selfish elements that bypass the policing mechanism in order to gain a relative advantage in the intra-cellular replication pool.


Materials and Methods

Reagents and Tools Table

Reagent/Resource Reference or Source Identifier/ Catalog No
Media
Luria-Bertani (LB) BD Difco from Fisher Scientific DF0446 07 5
M9CA Amresco M9CA medium broth powder lot no. 2055C146
Plasmids
Donors and recipients
Strain Genotype
RP4 donor (Lopatkin et al, 2016 ) DA32838 Eco galK::cat-J23101-dTomato
pR donor (Lopatkin et al, 2016 ) DA26735 Eco lacIZYA::FRT, galK::mTagBFP2-amp
p41 donor (Lopatkin et al, 2016 ) E. coli isolate number 41
p168 donor (Lopatkin et al, 2016 ) E. coli isolate number 168
p193 donor (Lopatkin et al, 2016 ) E. coli isolate number 193
p283 donor (Händel et al, 2015 ) ESBL 242
R6K donor (Lopatkin et al, 2016 ) E. coli C600
R6Kdrd donor Generous gift from D. Mazel (Baharoglu et al, 2010 ) E. coli Dh5a
R1 donor Generous gift from F. Dionisio and J. Alves Gama (Gama et al, 2020 ) E. coli MG1655 Dara
R1drd donor Generous gift from F. Dionisio and J. Alves Gama (Gama et al, 2020 ) E. coli MG1655 Dara
pRK100 donor Generous gift from T. Sysoeva E. coli HB101
RIP113 donor Generous gift from D. Mazel (Baharoglu et al, 2010 ) E. coli Dh5a
RB933 recipient Generous gift from I. Gordo (Leónidas Cardoso et al, 2020 ) E. coli lacIZYA::scar galK::cat-YFP ∆gatZ::FRT-aph-FRT rpoB H526Y
MG1655 (Lopatkin et al, 2016 ) E. coli MG1655 (K-12 F – λ – ilvGrfb-50 rph-1)
DA838F (Lopatkin et al, 2016 ) DA32838 Eco galK::cat-J23101-dTomato
DA838 (Lopatkin et al, 2016 ) DA32838 Eco galK::cat-J23101-dTomato
P (recipient for p41, p193, and p168) This study, lab stock E. coli MG1655 (K-12 F – λ – ilvGrfb-50 rph-1)
KPN recipient (Gomez-Simmonds et al, 2015) Klebsiella pnseumoniae isolate KP0064, ST17
Software
MATLAB v. R2020a https://www.mathworks.com/products/matlab.html N/A
Tools
Tecan infinite Mplex plate reader Tecan N/A

Methods and Protocols

Strains, media, and growth conditions

Experiments were initiated with single clones picked from agar plates, inoculated in 2 ml Luria-Bertani (LB) media, and incubated overnight at 37°C for exactly 16 h while shaking at 250 rpm. When applicable, LB media was supplemented with specific antibiotics. For example, to measure the acquisition cost of RP4, D, R, and adapted T were grown with 50 μg/ml kanamycin (Kan), 50 µg/ml spectinomycin (Spec), or both, respectively (Appendix Table S1A). For all other donor and recipient combinations, the respective antibiotics and concentrations can be found in Appendix Table S1B. All experiments were performed in M9 medium (M9CA medium broth powder from Amresco, lot no. 2055C146, containing 2 mg/ml casamino acid, supplemented with 2 mM MgSO4, 0.1 mM CaCl2 and 0.4% w/v glucose.)

Generating adapted RP4 transconjugants

To generate adapted T, individual clones of D and R were grown overnight according to the previous description. After 16 hours, all cultures were resuspended 1:1 in M9CA. Equal volumes (400 µl each) of D and R were mixed in an Eppendorf tube and incubated for 1 h in a cooling incubator at 25°C. Following the conjugation period, mixtures were streaked onto Spec-Kan plates and grown for 16 h at 37°C this is sufficiently long to enable physiological adaptation (Erickson et al, 2017 ) without genetic mutations (Harrison et al, 2016 Lopatkin et al, 2017 ) and is consistent with previous protocols for establishing transconjugants for fitness cost estimates (Buckner et al, 2018 Dimitriu et al, 2019 ).

Quantifying the acquisition cost for RP4

To generate de novo T, individual clones of D and R were grown overnight and conjugated as described above. In parallel, adapted T colonies were grown overnight to establish the standard curve. During the conjugation period of D and R, 800 µl of adapted T were also aliquoted into an Eppendorf tube and placed in the 25°C cooling incubator. Following the conjugation period, de novo T was quantified from the mixture of D and R using either colony forming units (CFU) or via dilution into the plate reader. For CFU, the D and R mixture was serially diluted in 10-fold dilution increments. 10 µl of all dilution factors (10 0 –10 7 ) were spotted onto Spec-Kan agar plates, then incubated for 16 h at 37°C and counted. For the plate reader, the D and R mixture was diluted into M9CA media containing Spec-Kan, and 200 µl were aliquoted into wells of a 96-well plate in technical triplicates. As determined by pilot experiments, de novo T was diluted at 1,000× to result in approximately 2,000 cells per well, which was found to be low enough to prevent background growth or conjugation.

CFU of adapted T was also quantified at this time using the same protocol as described above. The standard curve was generated using seven dilution factors of adapted T (Fig 2B). Adapted T cells were diluted in M9CA medium with Spec-Kan, and then, 200 µl aliquots of each dilution factor were plated on the same 96-well plate, also in technical triplicate. All wells were then covered in 50 µl of mineral oil to prevent evaporation and immediately placed into a Tecan plate reader. In all cases, absorbance readings at 600 nm were taken every 15 min for at least 24 h until all cells reached stationary phase. All RP4 data were conducted in at least biological triplicates.

Generality of acquisition costs with other plasmids

The same conjugation protocol described above was used for all additional plasmids with few modifications. First, the antibiotics used to select for transconjugants in each case depended on the plasmid-encoded resistance genes and the compatible recipient strain (Appendix Table S1B). Also, out of the seven dilution factors used for the RP4 and pR standard curves, we found the subset of dilution factors at 10 2 X, 10 4 X, and 10 6 X sufficient to accurately quantify both plasmids’ acquisition costs (as when determined with all dilutions). Thus, these three dilution factors were used to generate standard curves for the remainder of the experiments. The maximum cell density (defined by OD600) and growth rates differed depending on the strain and plasmid, based on conjugation efficiency. In all cases, the dilution factor into the plate reader was determined based on pilot experiments to identify the highest initial density in the wells without observable background conjugation. In cases where background conjugation could not be eliminated entirely, growth was subtracted such that the exponential phase remained. To remain consistently within exponential phase, the threshold cell density was set to be equal to 50% of the maximum density achieved for each experiment this value appeared to most consistently select the region indicated in Fig 2A as described in the Results. Altering the threshold within the exponential growth phase does not qualitatively impact our conclusions. Finally, we note that acquisition costs were highly reproducible between biological replicates (see Appendix Fig S10A) in many cases, variability was greater among individual wells on a given day rather than between intra-day mean values, likely due to the low number of cells per well once diluted into 96-well plates. Where biological duplicate results were reproducible and did not lead to different statistical conclusions, we instead focused on technical variability within a representative replicate. Therefore, by utilizing the most variable data in any given case, we maximize the rigor of associated statistical conclusions. In each case, the replicate types used to generate statistics are shown in Appendix Table S3A (Fig 3H). We note that regardless of the replicates used to generate statistics, specific acquisition costs remain identical. Furthermore, the relationship between acquisition and fitness cost did not change depending on whether biological replicate averages were used instead (Appendix Fig S10B).

Calculating growth rate

where y2 > y1, where y2 and y1 are the OD600 at times t+2 and t−2, respectively. The Prensky lag time was found by the x-intercept of the tangent line passing through the maximum growth rate, consistent with the geometric lag time in Fig 2A.

Competition experiments

All competition experiments were performed in a previous publication and the data were reproduced with permission from Nature Communications (Lopatkin et al, 2017 ), which is licensed under the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/). Briefly, plasmid-free and plasmid-carrying populations were mixed in a 1:1 ratio and grown over successive generations for between 14-21 days. Every 24 h, the populations were diluted 10,000×, and CFU was monitored at regular intervals on double-selective agar.

Model calculations

Simulations were run to calculate the observed growth rate, μobs, and the maximum specific growth rate, μ, for a range of α and β values (Fig 4A). μobs was calculated as described in Appendix equation S6. μobs was determined to be numerically different from μ based on any observed growth rate that fell below 98% of the maximum value (e.g., if μobs < 0.98*μ). In all cases for data fitting, was calculated using the fminsearch function in MATLAB. fminsearch is an optimization function that minimizes any user-specified objective function, and requires an initial estimate of the parameter(s) to be fitted. In our case, we implemented this fitting by minimizing the difference between the ODE solution of S D + S A , and the raw data curves as shown in Appendix Fig S7 since ρ was constrained by experimentally estimating the ratio of growth rates between adapted and de novo populations, β was the only remaining free parameter to be fitted. Thus, for each plasmid, the initial β estimate was set to be the geometric lag time of the corresponding growth curve, and the output of the fminsearch optimization was an estimated β that best fit our experimental data.


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Vehicles, Replicators, and Intercellular Movement of Genetic Information: Evolutionary Dissection of a Bacterial Cell

Prokaryotic biosphere is vastly diverse in many respects. Any given bacterial cell may harbor in different combinations viruses, plasmids, transposons, and other genetic elements along with their chromosome(s). These agents interact in complex environments in various ways causing multitude of phenotypic effects on their hosting cells. In this discussion I perform a dissection for a bacterial cell in order to simplify the diversity into components that may help approach the ocean of details in evolving microbial worlds. The cell itself is separated from all the genetic replicators that use the cell vehicle for preservation and propagation. I introduce a classification that groups different replicators according to their horizontal movement potential between cells and according to their effects on the fitness of their present host cells. The classification is used to discuss and improve the means by which we approach general evolutionary tendencies in microbial communities. Moreover, the classification is utilized as a tool to help formulating evolutionary hypotheses and to discuss emerging bacterial pathogens as well as to promote understanding on the average phenotypes of different replicators in general. It is also discussed that any given biosphere comprising prokaryotic cell vehicles and genetic replicators may naturally evolve to have horizontally moving replicators of various types.

1. Introduction

Viruses that infect prokaryotic cells are known to be enormously diverse in terms of genetic information [1, 2]. Most novel viral isolates are likely to have at least some genes that have no homologues among any of the previously known genes, including those in the genomes of related viruses [3]. Yet, there has been a dispute whether or not new genes may actually emerge in viruses [3]. Viruses are dependent on cellular resources such as nucleotides, amino acids, and lipids for producing more viruses therefore it seems justified to ask whether they also use cellular genes for their genetic information. Yet, when viral genes are compared to other genes in databases, it often appears that they have no cellular counterparts [2]. Where then do these viral genes come from? Have they been acquired from a cellular host that we simply have not sequenced before? Or alternatively, are the cellular genes perhaps just evolving rapidly in viral genomes so that their common ancestry with the host genes can no longer be derived? Or perhaps, is it indeed possible that new genes actually emerge in viruses themselves?

Forterre and Prangishvili from Pasteur Institute argued that the core of the dispute appears to be in the notion that viruses are often considered to be just their protein-encapsulated extracellular forms [4] that are only stealing cellular resources (including genes) for their own purposes [3, 5, 6]. Take any textbook on viruses and majority of the pictures representing viruses are of the various types of viral shells composed of proteins (and sometimes lipids) that enclose the viral genome. But these infectious virus particles, or virions, are inert in all respects unless they encounter a susceptible host cell [7]. And due to this inertness of virions it is difficult to understand how a virus could ever come up with completely new genes.

The answer is, naturally, that viruses cannot produce new genes during their extracellular state, and thus any potential event for the emergence of a new viral gene must still occur within a cell during the replication cycle of a virus [5]. But if the gene emerges in the genome of a virus, then would it rather be the virus, and not the cell, that was the originator of that gene? Or, to put it differently, was it not the virus that benefited from the emergence of new genetic information? The actual process that causes the genetic information to acquire the status of a gene would still be due to similar processes as the origin of genes within chromosomes (these being different types of genetic changes, such as point mutations, insertions, deletions, gene duplications, etc.), but these changes would be selected due to their improvements on the fitness of the virus. This reasoning has made Forterre to propose a model where viruses are seen essentially as a cellular life form that can also have an extracellular state [7, 8]. Virus is not strictly equivalent to the protein-enclosed viral genome. Rather, the extracellular form of a virus should be denoted as a virion, and this virion should not be mistaken for a virus. Viruses, in a complete sense, are organisms that live within cells (i.e., ribosome-encoding organisms) and can transform other cells into virus-cell organisms by producing more virions. In other words, viruses can utilize an extracellular encapsulated form to transfer its genetic information from one cell to another. Forterre coined a term virocell, which refers to the stage of viral life during which the virus is within a cell [7]. The virocell organism is indeed both a (capsid encoding) virus and a (ribosome encoding) chromosome, and the actual phenotype of the virocell is encoded by both of these genetic entities. The virocells are entirely capable of coming up with novel genetic information just as cells are, and thus approaching viruses from this perspective should clear any controversies about the emergence of new genetic information in viruses.

Forterre’s line of reasoning along with my own studies on various different genetic elements (including characterization of temperate and virulent viruses [9, 10] determination of common ancestor between plasmids, viruses and chromosomal elements [11] conduction of evolution experiments with bacteria, viruses, and plasmids [12, 13] as well as more theoretical work on horizontal movement of genetic information [14, 15]) has served as an inspiration for this paper. Indeed, it could be argued in more general terms what it means that prokaryotic cells can be (and often are) chimeras of various types of genetically reproducing elements. Virocell concept clears effectively many of the confusions between viruses and virions and their relationship with cells. Nonetheless, virocell is only a special case among all the possible types of prokaryotic organisms. Bacterial and archaeal cells can also contain conjugative plasmids, various types of transposons, defective prophages, and many other independent replicators that are distinct from the ribosome encoding prokaryotic chromosome. Together these replicators can produce organisms in all possible combinations. In order for the arguments about virocells to be consistent with the other potential chimeras of genetic replicators, the cell itself must be considered as a separate entity from all the genetic replicators (including chromosomes) that exploit the cell structure for replication. In the following chapters I will perform an evolutionary dissection to a bacterial cell. This will lead into the separation of cell vehicles and replicators from each other and thus provide one potential way to approach the evolution of bacterial organisms.

2. Vehicles and Replicators

A vehicle is any unit, discrete enough to seem worth naming, which houses a collection of replicators and which works as a unit for the preservation and propagation of those replicators”, Richard Dawkins wrote in Extended Phenotype. Dawkins utilized the concepts of replicators and vehicles in an argument which stated that evolution ultimately operated on the level of genetic information and not on the level of populations of organisms, species, or even cells. Replicators refer to packages of genetic information that are responsible for any effective phenotype of the vehicle. Vehicle itself can be a cell, a multicellular organism, or, for example, the host organism of a parasite. “A vehicle is not a replicator”, argued Dawkins in an attempt to underline that it is the replicator (like the chromosome of a parasite) and not the vehicle (like the parasitized cell) that evolves. This difference, however, may sometimes be seemingly trivial, which is why it has caused some dissonance among evolutionary biologists.

Nevertheless, Dawkins’ work focused mostly on explaining evolutionary issues of eukaryotic organisms, but the replicator-centered evolution naturally operates also within and between prokaryotic cells. Indeed, there is a vast diversity of different forms of genetic replicators that use prokaryotic cell vehicles for their preservation and propagation. Any particular prokaryote that lives in this biosphere, being that a bacterium on your forehead or an archaeon in the bottom of Pacific Ocean, harbors a chromosome but may also host a collection of other replicators, including plasmids, transposons, and viruses. Some of the replicators, like conjugative plasmids and viruses, are able to actively move between available vehicles in its environment, thus making these replicators less dependent on the survival of any particular lineage of cell vehicles. Therefore they are not an inherent part of any particular bacterium and may thus be considered as distinct forms of genetically replicating entities that utilize cells for their propagation and survival (similarly with the viruses in Forterre’s virocell concept).

The continuous struggle for existence within and between prokaryotic vehicles modifies the phenotypes of the replicators. A lot of theoretical and experimental work has been done in order to clarify the functions and the evolutionary trajectories of viruses, bacterial cells, and plasmids in different ecological contexts and under various selection pressures. However, in this discussion I take a step away from any particular type of a replicator or an organism and explore from a general perspective whether the lateral movement potential (or lack of it) of the replicators could help illuminate some evolutionary aspects of the prokaryotic biosphere. This discussion attempts to provide an intuitive view on the selfish genes and various types of replicators in bacterial and archaeal cells. It is my intention to keep the text simple and readable regardless of the reader’s expertise on bacteria, viruses, plasmids, or, for that matter, evolutionary theory. Moreover, given the vast amount of details in microbial world, I hope that the readers realize that certain corners had to be cut in various places in order to keep the text within realistic length.

Furthermore, in an attempt to maintain the simplicity, the following nomenclature and definitions are used throughout this paper. A cell vehicle denotes a prokaryotic cell with membranes, resources, and everything else but excludes any genetic material. Cell-vehicle lineage indicates a single vehicle and its direct descendant that emerge by cell division. A replicator is any discrete enough collection of genetic material (that seems worth naming), which utilizes the cell vehicle for its preservation and propagation. Replicators are replicated as distinct units forming a coherent collection of genetic material that can be separated with reasonable effort from other replicators. Replicators may be replicated as a part of the replication of other replicators, as integrative viruses are replicated along with host-chromosome multiplication, but essentially these two replicators can be denoted as two distinct entities given that the integrative virus can replicate its genetic information also separately from the replication of the chromosome. The mean by which the genetic information of a replicator is replicated is not relevant. However, I prefer to not make a too strict definition for a replicator as it is likely to lead to unproductive hair-splitting arguments. Yet, it must be noted that replicators do not include ribosomes or other nucleic acids containing molecules that essentially have an enzymatic function but that are not used as template for their own replication. Vertical relationship or vertical inheritance of a replicator indicates that this genetic replicator preserves itself within a dividing lineage of cell vehicles. Horizontal movement potential denotes that the replicator is able to introduce itself into a cell-vehicle lineage where the replicator was previously absent. Any feature that is encoded or induced by a replicator is denoted as a phenotype. Figure 1 links these terms with their biological counterparts.


APPENDIX D

We calculate Tp, the expected persistence time of a plasmid in a population with selective sweeps. We do so by calculating in turn the elements of Equation 11 in the text, which defines Tp. Most of the effort (up through Equation D13) is in calculating PR we then give expressions for Ta and Tf.

First, we calculate PR, the probability that, following the appearance of a chromosomal variant, the plasmid is rescued by a selective sweep before it goes extinct. Initially, let us assume that the chromosomal variant arises at time t = 0.

Then, note that PR is given by P R = ∫ 0 ∞ P M ( t ) P X ( t ) d t , (D1) where PM(t) is the probability that the first mutant appears during the interval [t,t + dt) following the appearance of the chromosomal, and PX(t) is the probability that a plasmid is transferred into the mutant lineage during its selective sweep, given that the sweep began in the interval [t,t + dt).

Lacking a good reason to make a more complex assumption, we assume that new mutations arrive in the population as a Poisson process with a constant rate σ. Then P M ( t ) = σ e − σ t . (D2)

To calculate PX(t) we use the following model. Consider a locally adapted population of fixed density N in a volume V, so that there are NV bacteria present. The population consists initially of bacteria bearing the focal gene on a plasmid, which have density P(t) at time t, and bacteria bearing the focal gene on their chromosome, which have density C(t). We assume that all fitness effects are multiplicative, that the fitness advantage of the focal gene is β, and that the fitness cost of the plasmid is α. Then the chromosomal and plasmid-bearing populations have growth rates ψ(1 + β) and ψ(1 + β)(1 − α), respectively. Following the appearance of a mutant, we track the density of mutants in the population as M(t), and we assume that the mutation it bears carries fitness advantage b, giving it a growth rate of ψ(1 + b), since it bears neither the focal gene nor the plasmid. For mathematical simplicity, we neglect segregation, which does not change the qualitative results. The values of these parameters are constrained by the following assumptions:

The fitness benefit of the focal gene is greater than the fitness cost of the plasmid: β > α/(1 − α).

The fitness benefit of the new mutation is greater than that of the focal gene (so that the focal gene will go to fixation): b > β.

The consequence of the Stewart and Levin criterion: the plasmid could not persist in competition with the chromosomal version by making up for its fitness burden by transfer: γN < ψα(1 + β).

To model changes in the densities (tracked by capital letters) of plasmid-bearers, chromosomals, and mutants (ignoring transconjugants for the moment), imposing a constraint of constant population size, we have d P ( t ) d t = [ Ψ ( 1 − α ) ( 1 + β ) − Ψ ¯ ] P + γ P C (D3) d C ( t ) d t = [ Ψ ( 1 + β ) − Ψ ¯ ] C − γ P C (D4) d M ( t ) d t = [ Ψ ( 1 + b ) − Ψ ¯ ] M , (D5) where Ψ ¯ ( t ) = Ψ [ ( 1 − α ) ( 1 + β ) P ( t ) + ( 1 + β ) C ( t ) + ( 1 + b ) M ( t ) ] ∕ N is the weighted average growth rate in the population at time t and is subtracted from the individual growth rates to maintain constant population size.

We assume that the chromosomal appears at t = 0 in a single bacterium this corresponds to an initial density of C(0) = 1/V. Following the appearance of the chromosomal, but before a mutant enters the population, we consider only the frequencies of chromosomal and plasmid-bearing types. During this period, we track the frequency of the plasmid-bearing type, p = P/(P + C), which can be calculated from (D3) and (D4) as d p ( t ) d t = [ γ N − Ψ α ( 1 + β ) ] p ( 1 − p ) . (D6)

This has the solution p ( t ) = ( N V − 1 ) e [ γ N − Ψ α ( 1 + β ) ] t 1 + ( N V − 1 ) e [ γ N − Ψ α ( 1 + β ) ] t . (D7)

Assume the mutant appears at a particular time t = t*. At the time of the appearance of the mutant, the densities of plasmid-bearers, chromosomals, and mutants, respectively, in the population are given by P ( t ∗ ) = ( N − 1 ∕ V ) p ( t ∗ ) (D8) C ( t ∗ ) = ( N − 1 ∕ V ) ( 1 − p ( t ∗ ) ) (D9) M ( t ∗ ) = 1 ∕ V , (D10) where p(t*) is given by (D7). Following the appearance of the mutant, the dynamics of these three populations are given by Equations D3, D4 and D5 these dynamics consist of an increase in the number of mutants (the selective sweep) while the number of plasmid-bearers and chromosomals declines.

We want to calculate PX, the probability that the plasmid is transferred at least once to the mutant population, creating a transconjugant, before the plasmid-bearers go extinct. We use the expected number of transconjugants created during the sweep to calculate the probability of producing at least one transconjugant during the sweep. The instantaneous rate of appearance of transconjugants during this sweep is γP(t)M(t), so X(t*), the expected number of transconjugants in a selective sweep beginning at time t = t*, is given by X ( t ∗ ) = γ ∫ t ∗ ∞ P ( s ) M ( s ) d s , (D11) where P(s) and M(s) are calculated by integrating Equations D3, D4 and D5, starting at t*, with the initial conditions given by Equations D8, D9 and D10. The probability PX(t*) that at least one transconjugant will appear, then, in a selective sweep beginning at time t*, is given by P X ( t ∗ ) = 1 − e − X ( t ∗ ) . (D12)

Substituting from (D2) and (D12) into (D1), we have P R = ∫ 0 ∞ σ e − σ t [ 1 − e − X ( t ) ] d t = ∫ 0 ∞ σ e − σ t [ 1 − e − γ ∫ t ∞ P ( s ) M ( s ) d s ] d t . (D13)

Finally, to calculate Tp from Equation 11, we need expressions for Ta and Tf. Assuming that in a population fixed for the plasmid-borne version of the gene, chromosomals appear as a Poisson process with rate χ, Ta = 1/χ. Tf can be approximated by assuming that the chromosome fixes because no selective sweep occurs in this case, Tf is simply the time required for the number of chromosomals to go from 1 to > N − 1, or equivalently, for the frequency of plasmid-bearers to go from 1 − 1/N to <1/N. This can be calculated from (D7) by setting p(Tf) = 1/N in (D7) and solving for Tf. This yields T f = 2 ln ( N V − 1 ) Ψ α ( 1 + β ) − γ N . (D14)

A note on computation: (D3, D4 and D5) cannot be solved analytically (H ofbauer and S igmund 1988). However, it is straightforward to solve them by numerical integration. The frequency of plasmid-bearing cells will always be declining at least as fast as in (D7), since mutants, if they appear, will only hasten the decline of the plasmid (ignoring transconjugants).

Therefore, it is reasonable to end the integration at Tf, the time at which the number of plasmid-bearing cells is <1. Thus, for computational purposes, Tf can safely be used as the upper limit of both integrals (replacing ∞) in (D13).


Watch the video: What is a Plasmid? - Plasmids 101 (May 2022).


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