# Did group selection play a role in the evolution of plasmid endosymbiosis?

Bacterial plasmids are nucleotide sequences floating in the cytoplasm of bacteria. These molecules replicate independently from the main chromosomal DNA and are not essential to the survival or replication of their host. Plasmids are thought to be part of the bacterial domain’s mobilome (for overview, see Siefert, 2009), a sort of genetic commonwealth which most, if not all, bacterial cells can pull from, incorporate and express. Plasmids can replicate inside a host and then move to another cell via horizontal genetic transfer (HGT), a term denoting various mechanism of incorporation of exogenous genetic material.

Of these mechanisms, two are relevant to plasmids:

1. transformation – the uptake of genetic material in the cell’s surrounding environment through its membrane, and
2. conjugation – the direct transfer of genetic material via cell-to-cell contact.

Interestingly, in the case of conjugation, most plasmid-carrying cells have mechanisms to detect whether a potential recipient cell already carries the plasmid to be transferred, and initiate transfer only if it does not. Horizontal genetic transfer plays a role similar for bacteria as sexual reproduction does for sexually differentiated forms of life by increasing genetic variability and thus evolutive potential. Most plasmids are endosymbionts to their host cell and may serve, among other functions, to foster antibiotic resistance as well as cause benign bacterial strains to become virulent. Other plasmids, however, parasitize their host and degrade cell function and fitness.

### Endosymbionts: evolution of cooperation

Endosymbiotic plasmids provide an interesting case study for inquiring into the evolution of cooperation. For instance, in his 2002 paper that I mentioned earlier, Paulsson claims that replication control by plasmids is the product of group selection – if plasmids are seen as the individuals and the host cell as the group. If plasmids replicated up to the cell’s carrying capacity, they would increase their chance of fixing in the descendant cells relative to their cell mates but would significantly hamper their host. Viewed from a group selection standpoint, within-group selection should then favor “selfishness” –- high replication rate –- while between-group selection should favor limited replication — “altruism”. By controlling their replication below carrying capacity via a sophisticated feedback system involving plasmid-encoded replication activators and inhibitors, many plasmids have struck a balance between these opposite selection gradients. (Paulsson, 2002)

A few weeks ago I gave a presentation on Paulsson’s paper about plasmid group selection for the EGT group, at the end of which Artem suggested that we build a game theoretical model to better understand, and generalize, the mechanisms at play behind plasmid replication control. To be honest, I am only beginning to dabble with game theory, so I am unsure exactly where our work is leading to. But it is nevertheless clear to me that before building any such model, we should understand the basics of how plasmids replicate within a cell and how they split at cell division, for these two mechanisms — replication and partition — greatly influence plasmid fitness.

### Replication control

To be maintained across generations of bacterial cells, plasmids must ensure that they replicate at least once during the life cycle of their host. As a result, most plasmids have evolved systems to enable and control their replication. Some plasmids replicate only once at each cell cycle, as is the case of the prototypical plasmid, the F-plasmid; others replicate many times per cycle. Many plasmids control their replication via a feedback system in which activators promote replication and inhibitors contain it. In the case of two well-studied plasmids, R1 and ColE1, activators can act in cis – in which case the cis sequence is usually neighboring the replication initiation sequence and affects only that sequence – or in in trans – in which case the trans sequence affects the initiation sequences of all activator-sensitive plasmids in the cell (note that plasmids of different types are not necessarily insensitive to other plasmids’ activators/inhibitors; more about that in the penultimate paragraph). Inhibitors, by contrast, act only in trans. The distinction between cis and trans is an important one, because any mutation to a trans activator will be “public” to all activator-sensitive plasmids in the cell, whereas cis activators/inhibitors mutations will be private to the mutant. (Paulsson 2002)

### Partition control

Not only must plasmids secure their replication, they must also ensure that, once replicated, the plasmids will be split in the daughter cells in such a way that each daughter contains at least one plasmid copy. For instance, in the case of the F-plasmid, since the latter replicates only once, the partition control mechanism has to ensure, and does, that each daughter contains exactly one copy. Unlike the partitioning of chromosomal DNA during cell mitosis, which was first observed at the end of the nineteenth century and is now well understood, the precise mechanisms of plasmid partitioning largely remain a mystery. Some hints have recently been uncovered, however. A few studies have shown that some plasmids use a mechanical system similar to that which partitions chromosomes during mitosis. Where that is case, plasmids are tethered to each pole of the dividing cell with protein “strings” or tubular structures that pull sister plasmids apart as the host divides. But it has recently been suggested that the dominant mechanism for plasmid partitioning might be molecular rather than mechanical in nature. For low-copy number plasmids, especially, some authors have shown that plasmids encode Par ATPases, <proteins built around the Walker A amino-acid sequence motif that ensure effective partition (Sherratt 2013). I won’t delve into this further here, mostly because I know so little about the subject, and also because I intend to deepen this discussion in future posts.

### Incompatibility

Many plasmids are incompatible with each other, meaning that when both are present in a given host, one of the two will fixate at the expense of the other. It is now known that such incompatibility is mainly due to mutual susceptibility to each plasmid’s replication and partition control system. Let us take the simple example of two plasmids, each of which has a characteristic copy number $m$ of 1. If the two plasmids share the same replication control mechanism, the latter will allow one of the two plasmids to replicate, but will then prevent any further replication. The losing plasmid will not be replicated, and will thus be found in only one of the daughter cells. (Novick, 1987)

This post was meant to sketch the very basics of the dynamics affecting plasmid replication and partition. Plasmids have sophisticated mechanisms for controlling replication and partition and ensuring their viability down bacterial cell lines. Although the details of these control systems are often still shrouded in mystery, the little we know of them should enable us to sketch a simple yet plausible model of plasmid cooperation.

### References

Novick, R.P. (1987) Plasmid incompatibility. Microbiological Reviews, 51-4: 381-395

Paulsson J (2002). Multileveled selection on plasmid replication. Genetics, 161 (4), 1373-84 PMID: 12238464

Siefert, J. L. (2009). Defining the mobilome. In Horizontal Gene Transfer (pp. 13-27). Humana Press.

Sherratt, D. (2013) Plasmid partition: sisters drifing apart. The EMBO Journal, 32:1208-1210

### 12 Responses to Did group selection play a role in the evolution of plasmid endosymbiosis?

1. The plasmid partitioning is very surprising to me. I would have expected the stochastic partitioning mechanism, that would lead to an average difference of around $\sqrt{N}$ soread in the plasmid population of daughter cells if te mother had $N$ plasmids. Without this stochasticity we lose a known mechanism for promotion cooperation in public goods games (Killingback, Bieri, & Flatt, 2006), but at a potential simplification in modeling.

The simple fixation competition in a single cell should simplify life for us, since we can use results like Traulsen, Nowak, & Pacheco (2006) to model the dynamics as a generalized Moran process. For the special case of where replication is possible only once, we can do an even closer analysis by writing down the explicit master equation.

Killingback, T., Bieri, J., & Flatt, T. (2006). Evolution in group-structured populations can resolve the tragedy of the commons. Proceedings of the Royal Society B: Biological Sciences, 273(1593), 1477-1481.

Traulsen, A., Nowak, M. A., & Pacheco, J. M. (2006). Stochastic dynamics of invasion and fixation. Physical Review E, 74(1), 011909.

• Terrific T says:

This is probably a stupid question – by why the root of N, not N/2? I can hardly remember how cell division works and must be forgetting something here. Also went to your question for stack exchange and would like to know if you read the JL Spudich & DE Koshland Jr. 1976 paper recommended in one of the answers.

• First, make sure that we are talking about the same thing: I am talking about the spread or difference between the two cells. Each cell will contain about $N/2$ of the molecules, but the difference between the two cells will be on the order of $\sqrt{N}$, i.e. one of the cells will have about $\sqrt{N}$ of the molecule than the other. The $\sqrt{N}$ result is not specific to cell-division, but is a general result that comes from random walks.

Imagine that there are $N$ molecules with each one having a 50% chance to go to the left daughter and 50% change to go to the right daughter. We will number these $N$ molecules arbitrarily as $1, 2, ..., k, ..., N$ and consider a random walk on the line where at step $k$ the walker moves one spot to the left if the $k$-th molecule went to the left daughter cell, and moves one spot to the right if the molecule went to the right daughter cell. Since each molecule ‘decides’ independently of all other molecules if it will belong to the left or right daughter (in an inviscid setting), the result is an unbiased random walk of length $N$. If we start the walker at 0 then the walker’s current position corresponds to the difference in molecules between the cells (if the number is negative then the left cell has more, if positive then the right cell has more).

It is a standard result that a one dimensional random walk gets about $\sqrt{N}$ steps away from zero after a total of $N$ steps. Of course, the expected position is zero (i.e. $\mathbb{E}(X_N) = 0$), but that just tells us that there is no bias between the two cells. What we care about is the difference, i.e. $\mathbb{E}(|X_N|)$ — notice the absolute values. Since abs is hard to work with, look at the $\sqrt{\mathbb{E}(X^2_N)}$ this is just the standard deviation of a $N$ independent Bernoulli distributions and is equal to $\sqrt{N}$. With the proper treatment of absolute value, the math becomes a little bit more hairy, and that is why I say it is on the order of (and not exactly) $\sqrt{N}$, more precisely, we have the limit: $\lim_{N \rightarrow \infty} \frac{\mathbb{E}(|X_N|)}{\sqrt{N}} = \sqrt{\frac{2}{\pi}}$.

• For your second question, I glimpsed at SK76, but mostly concentrated on more recent papers citing it. In fact, it is how I found out about Paulsson and why I recommended him to Eric. Most people use the model I describe (random partitioning) for most macro-molecules. Of course, for essential pieces like the chromosomes, an active process is used by the cell to ensure that the difference between the two copies is zero and not on the order of $\sqrt{N}$. The main question addressed in this post was: is there such an active process used for plasmids? They are inessential, so at first glimpse it seems that such a process is not necessary, but it seems such a process still occurs, at least for the F-plasmids.

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