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Induction of natural competence in Streptococcus pneumoniae triggers lysis and DNA release from a subfraction of the cell population. Proceedings of the National Academy of Sciences , 99 11 , The Gel Phase. Transformation, B. The Heat Shock Method. The first protocol for artificial transformation of E. This method became the basis for chemical transformation. In , Douglas Hanahan published an improved method to prepare competent cells, where optimal conditions and media for bacterial growth and transformation were identified for higher transformation efficiency [4].
As an alternate approach to chemical transformation, an electrical field can be applied to the cells to enhance the uptake of DNA, a method known as electroporation Figure 2. In , Neumann et al. In , transformation of E. Figure 2. Chemical transformation vs. Since the development of artificial transformation of E.
Today, a variety of competent cells—made for different transformation methods, transformation efficiencies, genotypes, and packaging—are available in ready-to-use formats to propagate cloned plasmids in molecular biology experiments. Don't have an account? Create Account.
Sign in Quick Order. Search Thermo Fisher Scientific. Search All. See Navigation. This supports our hypothesis that phenotypic diversity for competence can be favored by natural selection, even in an unchanging environment.
If HGR is strong enough, the rate of adaptation is maximized when only a finite fraction of cells express competence at any moment left. Competent populations are favored because they perform HGR, but disfavored because of their longer generation time.
This latter effect is normalized out by considering the speed of evolution per generation right. The tradeoff then disappears and is maximized by a purely competent population. However, and not , is the evolutionarily relevant measure. Phenotypic diversity is maintained via the switching rates : The fraction of cells expressing competence at any moment was adjusted by varying the rate of competence initiation , while.
Error bars denote one standard error of the mean. Clonal initial conditions result in similar qualitative behavior and are explored in figure S8. This striking result has a simple conceptual explanation. Increasing causes both an increased effective level of HGR, which accelerates adaptation figure 2 , and an increased generation time, which acts to slow down adaptation. The fact that these forces oppose one another presents the possibility that there exists a nontrivial i.
An additional piece to the puzzle, evident in figure 4 , is that only when is large enough. This makes sense in light of the shape of figure 2 , which becomes flatter with increasing. We can think of the parameter as tuning the effective rate of HGR between the values zero and.
Consequently, for small figure 4. By constrast, for larger , figure 2 becomes flat, and the marginal benefits of HGR become overwhelmed by the indirect cost of persistence for some. The hypothesis that increased generation time is the relevant counterweight to the positive effects of HGR is supported by figure 4 right , which considers the speed of adaptation per generation. This measure naturally masks all generation time effects. We see that by this measure, i.
Of course, real competitions depend on fitness changes that occur in real time, and therefore , not is the better measure of success. Above, we discussed the speed of adaptation, which measures evolutionary success at the population level. We now turn our attention toward direct competitions which measure evolutionary success at the individual level.
For simplicity, we did not allow invaders to mutate into residents or vice versa. We did not observe stable coexistence between invaders and residents.
Rather, after a sufficiently long period of time elapsed, the invader's lineage either went extinct or, occasionally, conquered the entire population i. The probability of fixation was then compared to the expectation under selective neutrality, which is simply the initial fraction of invaders. Figure 5 left shows the results of competitions initiated as the resident population adapted up the fitness peak see Methods.
One set of invaders fully committed to competence whereas another favored set stochastically switched between the two phenotypes. We see that the fully competent invaders are favored, but the invaders that switch are even more highly favored. This supports our previous conclusion that stochastic switching is optimal during adaptation. When invading vegetative residents during adaptation, each stochastically switching cell leaves an average of descendants: 4 times as many as competent invaders.
Likewise, under equilibrium conditions, each stochastically switching cell leaves an average of descendants: again, 4 times as many as competent invaders.
Mixed populations are also able to directly invade competent residents during adaptation blue diamonds, left but not at equilibrium. The linear increase suggests that frequency-dependent selection is not operating see main text. The neutral expectation represents , where is the number of cells present at the beginning of competitions. Solid lines are the least squares linear fit. All other parameters are the same as above. Using -fold smaller mutation rates results in similar qualitative behavior for the adaptive case left , and is explored in figure S Figure 5 right shows that stochastically switching populations were more likely to conquer a vegetative resident than were purely competent cells.
Unlike the adaptive case, mixed invaders never beat competent residents in equilibrium, which is unsurprising since competent populations have higher equilibrium fitness figure 3. The competitive success of stochastically switching invaders can be rationalized by their optimal speed of adaptation figure 4. However, we do not have a corresponding simple explanation for the advantage of stochastic switching in equilibrium.
We hope to pursue this topic in future work. To put the data from figure 5 in perspective, consider the expected number of descendants left by each invader, which equals divided by the initial frequency of invaders.
A neutral allele, of course, produces just one descendant. During adaptation and invasion of vegetative residents, stochastic switchers have , whereas for purely competent invaders,. Stochastic switchers have when directly invading competent residents. In the equilibrium case, and , and so again. We anticipate that HGR will also confer a competitive advantage in other parameter regimes. We expect this same logic to apply to our somewhat different model of bacterial transformation.
Those authors, as well as others [48] , also found an increasing advantage to sex as population size increased, but only in the regime where. For we expect the opposite trend to occur, since the effect of Muller's ratchet is strongest in this regime. In figure S10 we explore the case of fold smaller mutation rates. In that case, mixed cells continue to invade adapting populations. However, in equilibrium populations with small mutation rates, we observed no fixations of invaders of any type, from which we conclude that the fixation probability of those invaders was less than or comparable to.
These results suggest an interesting dynamic in which a purely competent population displaced from its fitness peak by e. By contrast, frequency-dependent selection means that depends on. Figure 5 shows a clear linear increase of with , consistent with the null expectation. This linear trend continued for up to for clarity, data not shown. The authors from [23] concluded that frequency-dependent selection was present, based only in part on their observation that out of 50 replicate trials, was large when competitions were initiated with a ratio of resident to invader, but small or zero when, say, a ratio was used.
Our model would almost certainly exhibit this same qualitative behavior, but we emphasize that both our data and theirs is consistent with a simpler explanation, and neither data requires frequency-dependent selection. In order to fully explore frequency dependence in this system, one would need to measure for all and examine whether this function can be fit by the frequency-independent model.
In that regime, where invaders are initially abundant, HGR may well display some frequency dependence. Our proceeding results were based exclusively on computer simulations whose underlying Markov process cannot be solved analytically. Below, we develop a set of equations that approximate these simulations. The solutions display impressive qualitative agreement with the key conceptual findings discussed above, but the quantitative agreement is often weak compare symbols and solid curves in figures 2 , 4.
The utility of these equations is that they can be rapidly solved numerically, for arbitrary parameter values. This allows a qualitative exploration of regions in parameter space that are biologically relevant but consume prohibitively large amounts of CPU time. Below, we briefly present the finite- deterministic approach, the basis of which is treated in detail elsewhere [22] , [36]. Table 1 summarizes the notation used.
More detail can be found in Methods. This is determined by the processes of birth, death, mutation, and HGR, which we will consider in turn. The birthrate depends on both and the total number of cells , via a simple logistic factor see Methods.
By contrast, the death rate is a constant in our model. The term is the Heaviside step function which simply equals one if and zero otherwise. Now let us consider mutation in isolation from birth, death, and HGR. These mutations result in a flux of cells between fitness level and its neighboring fitness levels. The growth and mutation operators can be combined in a single equation that has proven qualitatively successful in describing asexual evolution dynamics [59] :.
This is essentially a quasi-species equation [60] , [61] , except for two non-traditional features: i distinct sequences are binned according to their fitness value and, ii the presence of the cutoff factor. We now include recombination, which is much more difficult to model. When an HGR event occurs, a consequential genomic change happens only if the donor allele differs from that of the acceptor.
Specifically, we assume that every genotype containing ones is uniformly represented in the population at all times. In other words, we assume a maximal level of genetic diversity within each fitness class [62]. We assume that this is true regardless of. This modification does not change our essential results. After assembling these dynamical ingredients, including the persistence factor , and allowing for phenotypic switching between and , we obtain the coupled set of equations 7 8.
Solutions to equations 7,8 are plotted as solid curves in figure 2 , 4. We see that the finite- deterministic equations reproduce the qualitative behavior of simulations, but, on a quantitative level, they always overestimate the speed of adaptive evolution.
However, this degree of diversity cannot be maintained by finite populations, resulting in an overestimate of the effects of HGR and hence the speed as well. The quantitative disagreement is large when simulations were founded with a single clone because, over the timescale of the population climbing the fitness peak, the population is unable to generate the neutral diversity assumed by the recombination operator.
However, our most important qualitative conclusion— that stochastic switching in and out of competence is evolutionarily optimal— remains true even if clonal conditions are used see figure S8. In the artificial case that that the carrying capacity , every possible genetic sequence exists for all , and recombination confers only a very small advantage.
Consequently, the optimal strategy in this case is for no cells to express competence pure vegetative growth see figure S9. Two very recent studies [37] , [63] develop a stochastic analytic approach to the dynamics of adapting sexual populations. Those authors calculate the fixation probability of new beneficial mutations as they continually recombine into different genetic backgrounds, then relate this fixation probability to the speed of adaptation.
The stochastic nature of these calculations is an improvement on our essentially deterministic equations, although, unlike our study, they neglect deleterious mutations. In addition to eukaryotic recombination, Neher et al. They consider an infinitely long genome where the number of segregating mutations is set by the balance between random drift, the rate of recombination, and the strength and production rate of beneficial mutations.
Recombination is assumed to shuffle these segregating mutations into all possible combinations, consistent with a Gaussian fitness distribution. These assumptions are superficially reminiscent of those we employ in constructing our recombination operator equation 6.
However, the assumptions are in fact quite different. Whereas they assume the occupation of all fitness classes consistent with combinations of newly segregating beneficial mutations, we assume the reverse— namely the occupation of all genotypes consistent with a given fitness distribution.
Whereas our methods overestimate the speed of adaptation from simulations, theirs yields an underestimate to the eventual steady state velocity.
Generally, their assumptions are much more reasonable than ours for the problem of steady-state adaptation, though ours may better approximate scenarios following a sudden environmental change, in which previously neutral or mildly deleterious polymorphisms are initially present [62] e.
Furthermore, it is worth reiterating that the eventual steady state considered in those studies is reached only after an extremely long transient, as evidenced by the sensitivity to initial conditions in figure 2.
We constructed a model of bacterial competence that includes both recombination throughout the entire genome and also a persister feature to the competent state. We found that HGR is indirectly favored in this model, even without the presence of epistasis see below. Persistence, on the other hand, is indirectly disfavored during adaptive evolution in our model. When we coupled persistence and HGR by allowing cells to stochastically switch between competent and vegetative phenotypes, we found that the optimal differentiation strategy often entailed a mixed population of the two phenotypes, reflecting a tradeoff between HGR and persistence.
Optimality of the mixed strategy during periods of adaptation i. However, there were some ambiguities and exceptions see Results. The more robust advantage to the mixed strategy during positive selection may reflect the fact that, in many species, the competence system is activated during stress [12] , i.
Below, we discuss this article's limitations and relate it to previous studies of recombination and phenotypic diversity. Our birth and death dynamics assume that the overall population size is at least approximately constant.
By contrast, previous models of persistence [6] , [21] , [64] focus on cycles of boom and bust resulting from environmental changes. During booms, the population expands and non-persisters exponentially outgrow persisters. Conversely, during busts, non-persisters die exponentially while the persisters remain intact. A modified version of these dynamics was recently applied to competitions between strains of B. Since a subpopulation of cells expresses competence, which includes persister effects, this strain is favored over the strain during busts mediated by antibiotics but disfavored during booms access to fresh media.
This observation was supported by experiments those authors performed on B. In stark contrast to our model, theirs does not include homologous recombination HGR. Rather, they include the effect of recombination only by allowing the occasional acquisition of strongly beneficial genes e.
Furthermore, they do not address the potential optimality of mixed competence expression. One straightforward way for a population to cope with uncertainty is by sensing the environment and then responding with the appropriate phenotype. The obvious cost to this strategy is that some cells invariably express the inappropriate phenotype.
Interestingly, this cost is minimized by a level of diversity, and underlying switching rates, that mirror the frequency of environmental change [21] , [64]. Bet-hedging can be favored over a sense-and-response strategy when environments change infrequently and the sensing apparatus imposes a large enough cost [21]. In the context of B. However, this seems inconsistent with the well known fact that competence in B. Thus, bet-hedging seems unlikely to explain diverse competence expression because B.
Furthermore, the competence system involves a large number of genes [66] , suggesting that it did not evolve primarily as a persistence system, which would presumably require far fewer genetic components. The apparent failure of bet-hedging explanations in this context motivates the central hypothesis of this article— that diversity in competence expression is itself optimal in a population-genetic sense.
A recent study [16] used the bet-hedging framework to address a related but distinct aspect of competence expression in B. In particular, they investigated the optimal distribution of competence duration times, finding that a broad distribution is best able to hedge against uncertain concentrations of extracellular DNA.
Their underlying assumption is that the ideal strategy for the cell is to remain competent for long enough to encounter sufficient DNA, and then return to vegetative growth. The purpose of our article is precisely to understand the basis of this assumption. Our results have some bearing on the evolutionary advantage of sex and recombination. There is an enormous amount of literature covering this topic, most of which is oriented toward diploid eukaryotes.
Although there are non-trivial differences between meiotic crossing over and bacterial transformation, models of the former provide insight to competence. Below, we touch upon some of this literature. The essential effect of recombination is to reduce the correlations between alleles at different loci.
Without these correlations, recombination can have at most a tiny effect. Our parameter values correspond to this regime. In asexual populations, these concurrently spreading beneficial mutations most likely originate and remain in different backgrounds. Therefore, in the absence of recombination, the presence of one beneficial mutation is anti-correlated with the presence of the other, i. LD is negative. Recombination brings the mutations together in a common chromosome, which pushes LD closer to zero and accelerates adaptive evolution.
The Fisher-Muller effect underlies the advantage to recombination seen in figures 2 and 5 left , and also in previous studies of HGR [22] , [23]. Consequently, sequences carrying multiple deleterious mutations are under-represented in the population, as compared to the case with no epistasis.
Thus, synergistic epistasis generates negative LD between deleterious mutations. Recombination decreases the extent of this LD and, under certain restrictions on the strength of epistasis [69] , [70] , can be favored. While correct in the infinite limit, this prediction does not apply to moderately size populations, as can be seen in figures 3 and 5 right and previous studies [48] , [50]. In fact [48] , [50] , show an increasing advantage to recombination as increases from to when. We expect the prediction to hold when the number of cells is much larger than the number of combinations of loci under consideration.
When the number of genotypes is large e. Three previous studies [23] — [25] explicitly consider HGR in bacteria, but not phenotypic switching into competence. Redfield and co-workers studied the equilibrium level of fitness achieved by infinite populations [24] , [25] , finding that synergistic epistasis is required in order to confer an equilibrium advantage to HGR, in accord with and subject to the same limitations as the aforementioned theory.
However, they do not consider the important case in which beneficial mutations are available and the population is adapting i. A major strength of that study is that they consider interesting issues that our work largely neglects, such as recombination of genes responsible for HGR and the possibility that alleles in the extracellular pool may tend to be loaded with deleterious mutations although see figure S1 and text S1. Future work could reconsider these important complications in our stochastic, finite context.
Recently, Levin and Cornejo [23] devised an HGR model that bears many similarities with ours, although they do not consider phenotypic switching. In rough agreement with our results, those authors found that HGR accelerates adaptation and that HGR can invade asexual residents although, see commentary surrounding frequency-dependent selection in Results and also figure 5. The most important difference between our approach and theirs is that they included only five loci with small fitness effects.
Each of these loci had a very small mutation rate , suggesting that they represent perhaps nucleotides each. Thus, their approach neglects the vast majority of genotypic diversity present throughout the rest of the genome. This is especially important in the context of recombination because the frequent mutations in this region generate sequence diversity upon which recombination will act. A prominent feature of our model is cell death during competence inducing conditions. Cell death is usually not explicitly measured during laboratory experiments unless killing agents e.
Additionally, in B. Competence and sporulation are distinct stress responses in B. Spore formation involves asymmetric cell division in which the eventual products are a spore and a lysed non-competent cell see, e. Together, these observations suggest that cell death, particularly among non-competent cells, is both important and commonplace under conditions relevant to the evolution of competence. Careful treatment of these phenomena, and their interrelationships, is beyond the scope of the relatively simple model presented here, but could be pursued in future work.
In this article we make several assumptions that could be relaxed in future work. First, our model neglects sporulation, which may be inherently coupled to the competence system in B. Secondly, we have not directly represented the genes responsible for recombination in cells i. Since bacterial transformation is non-reciprocal, this modifier locus can exchange itself for a non-functional homologue in the extracellular pool, thereby becoming.
However, the reverse process required to replenish the number cells cannot occur, and thus the number of cells should decrease under this influence. This process cannot alter our results concerning the rate of adaptation figure 2 , 4 because all cells in those populations carry the modifier locus.
However, this effect will to some extent impact our results concerning competition experiments figure 5. This issue should lead to an effective selection coefficient against cells. Based on our parameter estimation see Methods , this implies a — effective disadvantage to.
Since we have estimated for recombining invaders figure 5 , we can very roughly estimate a selection coefficient of in favor of. This indirect benefit may or may not be sufficient to overcome the — decay caused by non-reciprocal exchange. Of course, it is important to remember that genes enabling a phenotype are obviously somehow maintained in many real bacterial populations.
It has been pointed out by other researchers that many genes enabling have other important functions, and that the capacity for HGR might only be maintained as a by-product see [76] for a review. In this article, we do not take a position on whether HGR is the dominant reason that these genes exist. Exploration of that topic requires detailed experimental knowledge of the pleiotropic effects of these genes, as well as estimates of their fitness consequences.
Rather, we have merely isolated, quantified, and attempted to deepen understanding of the population genetic aspects to competence. Relative to some previous studies [24] , [25] , our stochastic treatment reveals that HGR can be favored strongly and broadly e. Thirdly, we have assumed that competence does not entail a direct fitness dis advantage. Along these same lines, one could allow the overall population size to either grow directly favoring the vegetative phenotype or shrink directly favoring the persistence phenotype.
Fourthly, we have assumed that all mutations have the same effect on fitness, which is obviously not true in real populations.
A step toward greater realism could be made by incorporating a set of loci that become lethal if mutated. Fifthly, our fitness function equation 1 is non-epistatic; in other words, different loci make independent contributions toward organismal fitness. Indeed, as discussed above, population genetic theory predicts neither an advantage nor a disadvantage to recombination in the absence of epistasis.
Additionally, the experimental data is mixed and inconclusive e. Given this set of facts, our assumption of no inter-locus epistasis seems fair. Nevertheless, future work could investigate our model under various epistatic fitness functions. Finally, we point out an empirical shortcoming of our theory: Figure 4 predicts that the speed of evolution is optimized when of cells express competence, which is significantly larger than the observed in the laboratory.
This quantitative discrepancy could be due to any or all of the limitations listed above. A fundamental prediction of our theory is that, if total population size is approximately constant, cells which stochastically switch between the competent and vegetative phenotypes will prevail in competition experiments against otherwise isogenic cells that are either or that fully commit to competence. Thus, in principle, the fraction of competent cells can be experimentally adjusted equation 3 while holding constant the time spent in competence.
Although conceptually straightforward, there are potential complications to these experiments. An alternative that circumvents this problem is long-term batch culture [71]. However, in this case metabolic waste products accumulate and the environment is not constant. A second complication to this suggested experiment involves the possibly bizarre behavior of cells engineered to fully commit to competence.
Recall that normal B. Thus, if exit never occurs, these cells might not ever divide. In this case, our simple, continuous growth model completely misrepresents the strange behavior of the engineered cells. However, this does not at all change our central conclusion that phenotypic diversity for competence is evolutionarily favored over total commitment to competence, since non-dividing cells will obviously lose the competition.
Although we constructed our model with the behavior of B. First, we followed Johnsen et al.
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