* Institute of Genetics, University of Nottingham, Queens Medical Centre, Nottingham, United Kingdom
Clinical Pharmacology, Royal College of Surgeons in Ireland, Dublin, Ireland
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Abstract |
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Key Words: transient insertion mutations transposable elements mobile DNA insertion sequences
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Introduction |
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The potential for successful mutator strains in bacteria is well documented (Chao and Cox 1983; Mao et al. 1997; Sniegowski, Gerrish, and Lenski 1997; Taddei et al. 1997; Tenaillon et al. 1999), and bacterial transposable elements can sometimes act as beneficial mutators (Chao et al. 1983; Chao and McBroom 1985; Modi et al. 1992; Blot 1994). In some situations, insertions of insertion sequences into functional genes create advantageous genotypes in laboratory environments (Zinser and Kolter 2000). We postulate that corresponding changes will be possible in the wild, given the great range of environments that bacterial populations encounter. However, if advantageous insertion mutations into functional genes maintain insertion sequences, selection for such insertions will, with time, inactivate all such genes whose loss is advantageous. Thus, one would expect that, in organisms selected for efficiency such as bacteria, these inactivated genes will be lost, the process will stop, and, ultimately, insertion sequences themselves will be lost. The only viable model for the maintenance of mobile DNAs through their ability to create advantageous null mutations requires the selective advantages of insertions to be environment-dependent, such that in a different, future environment there would be selection for reactivation of the gene. It follows, then, that these mobile DNA insertions must be capable of reversion by precise excision events. Such excisions are seen in nature (Kleckner 1981; Allgood and Silhavy 1988; Mills et al. 1992; Hammerschidt et al. 1996; Ziebuhr et al. 1999), and there is even some evidence that these excisions may be induced by environmental stress (Aleshkin, Kadzhaev, and Markov 1998). Many authors have identified reversible insertions of insertion sequences that are of benefit to adapting bacteria. Examples include colonial variation of Shigella flexneri (Mills et al. 1992), modulation of cell surface sialic acid expression in Neisseria meningitidis (Hammerschidt et al. 1996), and phase variation of biofilm formation in Staphylococcus epidermidis (Ziebuhr et al. 1999).
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Materials and Methods |
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Each generation the following events occur:
(A) Deletions. Each class [I, J] experiences deletion (precise excision) of elements at a rate of µ(I+J), and make contributions to new class frequencies as follows:
(B) Fitness. Each class [I, J] experiences selection of t per element and, depending on I and e, selection s at the site of interest:
(C) Transposition. Each class [I, J] experiences transposition of elements at a rate of (I + J). Transposition targets are the site of interest, i, neutral sites, n, or deleterious sites, (1 - i - n). Classes make contributions to new class frequencies as follows:
The remaining p[I, J](I + J)(1 - i - n) are lost through deleterious insertions and effectively add to the fitness cost, t.
(D) Normalization. Classes with a frequency under 10-20 are removed. The frequencies of the remaining classes are then divided by the sum of all classes to restore a total frequency of 1: p[I, J]/p[I, J].
Horizontal Transmission
For horizontal transmission, a certain proportion of transpositions h generate insertions in random members of the population, rather than the donor cell. In step (C), contributions (ii) and (iii) are altered by a factor (1 - h) giving a probability of receiving a horizontal transmitted element, H = p[I, J]
(I + J)h(i + n). Following an additional normalization step, p[I, J]/
p[I, J] and H/
p[I, J], this "pool" of insertions is then distributed among the population. Because lethal insertions will affect every class equally, these are ignored and H adjusted accordingly, H / (1 - H(1 - i - n)). Contributions to new class frequencies are then made:
The final normalization and class removal (step D) then occurs as before.
Finite Population Size Models
For finite population models, class frequencies are converted into numbers of cells during step (D). An expected number NE[I, J] is first determined by multiplying frequencies by the population size N, NE[I, J] = p[I, J]N. These are then converted to actual numbers NA[I, J]. For NE[I, J] > 100, NA[I, J] = NE[I, J]. For NE[I, J] 100, the model incorporates random genetic drift, where NA[I, J] is Poisson distributed with a mean given by NE[I, J]. The population is then returned to frequencies: p[I, J] = NA[I, J]/
NA[I, J].
Analytical Approximation of Minimum Cycle Length
The cycle length, T, allowing stability falls within a range determined by the parameters, s, n, i, t, , and µ. A simplified model can be considered in which there is never more than one element at the site of interest and never more than one element at a neutral site. We call an individual with no elements (0,0); one with an element only at the neutral site, (0,1); one with an element only at the site of interest, (1,0); and one at both sites, (1,1).
If the cycle time is short the element will not be eliminated from the site of interest during environment 2, nor will it spread to fixation during environment 1. The element at the site of interest is subject to selection of strength s - t during environment 1 and -s - t during environment 2, which lasts for an equal length. Without transposition or deletion the element would inexorably be lost at the site of interest. However, transposition into the site of interest may allow the element to persist stably. If we assume, for now, that throughout the cycle there is exactly one element present at a neutral site (i.e., all cells are of the (0,1) or (1,1) types) it is possible to model the cycling of the frequencies of these (0,1) and (1,1) cells. Cells with an insertion at the site of interest have frequency p and a selective advantage in environment 1, which we call . Cells of the (0,1) class receive transpositions into the site of interest at rate i
. We call ß the selective disadvantage of the element in the site of interest in environment 2.
Integration of frequency changes in the two environments, and setting p at the end of environment 2 to be the same as at the start of environment 1 (defining an equilibrium cycle for p) requires p to be i(
eßT + ße
T)/ (
ß(eßT - e
T)) at the start of environment 1 and p to be given by
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As an approximation, we assume that, at the start of environment 1, one half of the cells lacking an element at the site of interest are (0,1) and the other half are (0,0). Selection against the former cells will mean that at the start of environment 2 a proportion 1/(1 + e(t+(1-n-i))T) of the cells lacking the element at the site of interest will be (0,1). Thus for an equilibrium cycle the frequency of (0,1) cells among the (0,0) and (0,1) cells has to be raised, at the time when the proportion of cells at the site of interest is high (at the end of environment 1 and the start of environment 2), from 1/(1 + e(t+(1-n-i)
)T) to e(t+(1-n-i)
)T/(1 + e(t+(1-n-i)
)T). This happens by deletion from the site of interest, which converts (1,1) cells, which have frequency p, to (0,1) cells. If p >> (1 - p) at the end of environment 1, even a low rate of deletion µ, changing (1,1) cells to (0,1) cells can greatly increase the relative proportion of (0,1) to (0,0) cells. To maintain the proportion of (0,1) relative to (0,0) cells,
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Because approximately one half of the cells lacking an element at the site of interest have no element at the neutral site, whereas almost all of the cells with an element at the site of interest have an element at the neutral site, the effective values for selection are = s -1.5 (t + (1 - n - i)
), ß = s + 1.5(t + (1 - n -i)
).
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Results and Discussion |
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The population is defined as a collection of cells that differ in the number of elements that they have at neutral sites and at the site of interest. The proportion of a given cell type changes each generation as a result of deletion, selection, and transposition. In the model there is the spread, during environment 1, of cells with an insertion at the site of interest. Then, during environment 2, there is selection in favor of cells that lack such insertions. Predictably, the frequency of cells with insertions at the site of interest cycles to track the changing environments. An example of an equilibrium cycle is shown in figure 1. We have explored the outcomes of such a model, concentrating in particular on the lengths of the cycles that allow the maintenance of the mobile elements in the population in an equilibrium cycle. Figure 2 shows the range of cycle lengths that permit the maintenance of the element for various parameter values.
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The maintenance of the elements under the model is quite robust to changes in the parameters. This is particularly true of the length of cycles, T, which permit maintenance. Parameter values have a greater effect on the mean number of elements at equilibrium. Figure 3 shows the equilibrium mean number of elements at the start of environment 1 under three different sets of parameters, with differing s and t values, across the range of T in which elements are maintained. None of the parameter sets in the models shown allow maintenance of the mobile element in the absence of favored insertions during environment 1. Further, the conditions for selfish spread are not met. Also, over the whole cycle, the geometrical mean fitness of cells with elements at the site of interest is less than that of cells without such elements. Thus the selection at the site of interest could not maintain the elements in the absence of elements at neutral sites.
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The model can also be applied to situations in which a low level of horizontal transfer is allowed. Figure 4 shows the impact of a level of horizontal transfer of elements where none, half, or all of the transpositions enter a cell different from the donor cell. Again, selection against the element is still too strong for selfish spread to maintain elements. The introduction of horizontal transfer reduces mean element number. The effect is small at low levels of horizontal transfer but becomes severe as the level of horizontal transfer approaches 50%. This is because insertions into the site of interest that are made as a result of a horizontal transfer, rather than by transposition from a linked neutral site, do not give the frequency of neutral insertions a boost due to "hitch-hiking." [An alternative model of horizontal gene transfer was also tested. This time, a proportion of the population replaced the site of interest with that from a random member of the population. The effects of gene transfer were similar to horizontal transmission of TEs, with an even greater reduction in mean element number (data not shown)].
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The model presented here involves some form of environmental cycling. There is no reason to expect the environmental cycles to be synchronized in remote locations. Rather we believe that the population structure of many bacteria will be a "metapopulation," with environmental fluctuations operating locally, maintaining mobile elements by this mechanism, but with low levels of gene flow between local populations. The gene flow has to be sufficiently low that the advantageous genotypes required at the starts of environment 1 and environment 2 are generated by transposition and deletion, respectively, rather than being introduced by migration from other populations.
Is this a likely model for bacterial response to fluctuating environments? First, do environments change in ways that create fitness advantages for insertion mutations? The introduction gives examples of advantageous insertions, inactivating genes in some environments. In addition, the phenomenon of mutations showing a growth advantage in stationary phase ("GASP") in Escherichia coli (Vulic and Kolter 2001), some of which are null mutations (Zinser and Kolter 2000), suggests one possible type of transient insertion mutation whose advantage is environment-dependent. Furthermore, we have shown (Edwards, Sockett, and Brookfield 2002) that, in experimental shaking cultures of E. coli, insertions creating null mutations in flagella genes show considerable (10%20%) selective advantages over progenitor cells in which the pathway of flagella production is intact. One might expect that a regular cycle of environmental change would trigger the evolution of environmental sensing systems that would sequentially inactivate and reactivate the gene of interest in response to the cycles. Its greatly enhanced speed and efficiency would make the evolution of such a system of gene regulation probable if the population had a long history of exposure to two specific alternating environments. However, in our model, the gene of interest is restored to wild-type in the whole local population at the end of environment 2, and thus the model does not require that the gene of interest that is inactivated be the same in each cycle. Element maintenance in the model is also fairly robust to increases in the length of environment 2, and the regular periodicity of the cycling is not necessary. Thus, we have a model, not of a population in an environment that fluctuates regularly between two alternative states, but one in which a myriad of environments will successively select for insertions into, and reactivation of, different genes. For each transient beneficial insertion, elements will receive a boost in numbers, provided that the selection persists long enough for the insertion to reach fixation in the local population.
Mobile genetic elements are not the only source of mutation. In reality, base substitutions will also occur, and they may inactivate the gene of interest during environment 1. The frequency of such inactivating base substitutions may well approach the rate of insertion of elements into the gene of interest. If so, at the end of environment 1, when all cells have inactivating mutations in the site of interest, only about one half of the cells will have insertion mutations. However, during environment 2, the rate of excision of the element will be orders of magnitude higher than is the rate of back mutation to revert a base substitution mutation. Thus, at the end of environment 2, the proportion of cells that will have gone through the transposition-excision cycle will be orders of magnitude higher than the proportion of cells that have gone through a base substitution-reversion cycle, and the power of the former to maintain the elements will be little affected by the possibility of the latter.
Of course, mobile elements may be lost through processes other than precise excision, including imprecise excision or lack of function mutations. This will serve to increase the effective rate of deletion from neutral sites, and to reduce the maximum length T in which elements are maintained. The dynamics of elements at the site of interest would not be greatly affected, as only cells experiencing a precise excision here have any long-term future.
The model potentially applies to all bacterial species. In addition, it may have some relevance for other clonal groups, including some plants and animals, such as the Bdelloid rotifers, which are an anciently clonal group of animals. These have been found to lack retrotransposons (Archipova and Meselson 2000). The absence of retrotransposons would be consistent with the absence of a precise deletion process for these elements, and their inability to be maintained in a clonal host by the mechanism that we model here. The model explains the maintenance of mobile elements not by sex, but by selection for their transiently advantageous effects. Whether bacteria are effectively sexual depends on bacterial species studied (Maynard Smith et al. 1993; Guttman 1997; Maynard Smith and Smith 1998). In some species, there is little sign of the linkage disequilibrium expected under clonality. It is important to remember that the level of sex and recombination required to create linkage equilibrium is not the same as that required to allow transposable elements to persist. Escherichia coli, for example, despite manifesting strong evidence of some horizontal gene-transfer events with important evolutionary consequences, has a very low level of recombination per generation (Milkman and Bridges 1990; Guttman and Dykhuizen 1994). To be effectively sexual in terms of linkage disequilibria for neutral genes, the time to common ancestry of randomly chosen individuals must be ancient compared to the reciprocal of the rate of recombination between lineages. The time to common ancestry will be the reciprocal of the effective population size. For the sexual spread of transposable elements, however, the rate of sexuality has to be large relative to the strength of selection against the elements (which we model in the range from 0.001 to 0.01). A level of sex and recombination which is enough to create effective sexuality in terms of linkage equilibrium will be insufficient to allow selfish elements to spread by sex in the face of selection.
The common feature of transposable elements is their mobility, and this is the only attribute required by the model. Here, we have explicitly modeled unregulated replicative transposition. Regulation of transposition rates such that the number of transpositions per generation is independent of the number of elements in the cell (above zero) has the predictable affect of reducing TE number (not shown). As long as a cell has at least one element, there is no longer an advantage for having more copies. The range of parameter space that can maintain elements is largely unchanged because there is generally only one neutral insertion retained at the extremes of T, and so regulation of transposition here has no effect. Some bacterial transposable elements may increase rates of transposition (Kleckner 1981; Blot 1994; Mahillon and Chandler 1998) or precise excision (Aleshkin, Kadzhaev, and Markov 1998) in times of physiological stress. This has not been modeled but will intuitively benefit elements and the lower limit of their range by accelerating the time taken for advantageous insertions to spread through the population at the start of environment 1.
We have presented here a general model for the maintenance of mobile genetic elements through their ubiquitous capacity to generate insertion mutations. If such mutations experience transient positive selection, then linkage disequilibrium with neutral donor elements is sufficient to increase mean element number. A fluctuating environment of this kind would generate periodic selection but would not necessarily leave a legacy of amino acid substitutions as is seen following successive selective sweeps adapting to a stable environment. In direct contrast to the selfish DNA hypothesis, horizontal transfer weakens the maintenance of elements in this system.
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Acknowledgements |
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Footnotes |
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