The secondary structure of folded RNA sequences is a good model to map phenotype onto genotype, as represented by the RNA sequence. Computational studies of the evolution of ensembles of RNA molecules towards target secondary structures yield valuable clues to the mechanisms behind adaptation of complex populations. The relationship between the space of sequences and structures, the organization of RNA ensembles at mutation-selection equilibrium, the time of adaptation as a function of the population parameters, the presence of collective effects in quasispecies, or the optimal mutation rates to promote adaptation all are issues that can be explored within this framework.in silico evolution and adaptation. We calculate the distribution of the effects of mutations on fitness, the relative fractions of beneficial and deleterious mutations and the corresponding selection coefficients for populations evolving under different mutation rates. Three different situations are explored: the mutation-selection equilibrium (optimized population) in three different fitness landscapes, the dynamics during adaptation towards a goal structure (adapting population), and the behavior under periodic population bottlenecks (perturbed population).We investigate the effect of microscopic mutations on the phenotype of RNA molecules during their μ at which evolution proceeds. In contrast, the selective value of mutations remains almost constant, independent of μ, indicating that adaptation occurs through an increase in the amount of beneficial mutations, with little variations in the average effect they have on fitness. Statistical analyses of the distribution of fitness effects reveal that small effects, either beneficial or deleterious, are well described by a Pareto distribution. These results are robust under changes in the fitness landscape, remarkably when, in addition to selecting a target secondary structure, specific subsequences or low-energy folds are required. A population perturbed by bottlenecks behaves similarly to an adapting population, struggling to return to the optimized state. Whether it can survive in the long run or whether it goes extinct depends critically on the length of the time interval between bottlenecks.The ratio between the number of beneficial and deleterious mutations experienced by a population of RNA sequences increases with the value of the mutation rate  The fate of evolving populations is determined by a number of intrinsic properties of the ensemble and extrinsic mechanisms that interact in a highly non-trivial manner. The natural mutation rate of populations and their size, the effect that such mutations have on fitness and how these effects vary with the state of the population, or the environmental perturbations they have to cope with, all are relevant variables conditioning long-term survivability .Populations evolving in constant environments eventually reach a fitness plateau, often interpreted as an optimum in the fitness landscape. The time required to reach the optimum and the structure of the population at the mutation-selection equilibrium corresponding to that environment depend, in addition to the factors listed above, on the environment and on the initial state of the population. During adaptation, the effect of mutations is different from their effect at equilibrium, probably due, among others, to differences in the fitness of populations and to changes in the genomic context ,3. ThougThe relationship between the mutation rate of a population and the variability of the environment where it evolves has been a matter of interest for a long time -12. In sSimple, computational models of evolution explicitly separating genotype and phenotype might be of great aid in bridging the gap between phenomenological theories and experimental observations. The former are built on empirical observations which, as of yet, are far from complete. Actually, most experimental observations deal with a relatively small number of cases and model organisms, such that generalization is still a difficult enterprise . AnotherThe computational study of random ensembles of RNA sequences folding into their minimum free energy secondary structure (a proxy for the phenotype) has permitted one to assess the role played by compensatory mutations . More reGenomes within a population have to be highly correlated, since they share a phylogenetic history and have experienced similar selection pressures.a priori. They depend on the specific change that they produce in the secondary structure of the evolving molecules, in particular subsequences, or in the energy of the folded state. Our model also permits us to analyze the multiple mutations simultaneously present in a population, independently of whether they become fixed or not. Thus, mutations with highly deleterious effects can be pinpointed and those with a very small effect can be distinguished from neutral changes.The aim of this contribution is to investigate the internal organization of optimized, adapting and perturbed populations of RNA molecules evolving under different genomic mutation rates, with the goal of quantifying the effect of mutations on fitness and establishing links between the state of the population and the effect of mutations. In the case of optimized populations, different fitness landscapes are used to probe the generality of our results. The model we use does not presuppose any underlying distribution of mutational effects. Mutations arise according to the established mutation rate and their effects are not selected l = 50 nucleotides (nt). We begin with an ensemble of N random sequences. The ensemble evolves through discrete generations and the population size is kept constant. An exception is the case of perturbations through population bottlenecks, to be discussed in detail below. At every generation, all the sequences in the population are folded into their minimum free energy secondary structure with help of the Vienna package (see Methods). We define a target secondary structure S  that a molecule i in the population replicates is larger the closer to S it folds. This probability is defined asOur model system consists of a population of replicating RNA sequences, each of length di is the distance between the structure corresponding to sequence i and the target structure S. As a measure of structural distance, we use the base-pair distance (see Definitions). The constant l is a scale factor, since the maximum base pair distance between two molecules of length l is proportional to l. The overall normalization factor is S-landscape).where s ≡ [p(di) - p(dj)]/p(dj) of a sequence i folding at distance di to the target with respect to a sequence j folding at distance dj = m + di is independent of di,With the above definition of replication probability, the selective advantage β determines the relative advantage between different sequences in the population. In the limit β → 0, s → 0 for any two sequences: the distinction between molecules folding closer or farther from S is lost and all have asymptotically the same probability to replicate. When β → ∞, only the sequence closest to the target is selected, the rest being eliminated in the next generation. The target structure S is found and fixed for most finite values of β, and only quantitative changes in the properties of the population are produced when it is varied. Increases in β can be compensated by decreases in μ, and vice versa. In this work, the value of this selection parameter will be fixed to β = 2.This result implies that the selective advantage of a structure depends on the populational context, and not on its absolute distance to the target. Further, it reveals that the selection parameter μ to be replaced by a nucleotide randomly chosen with equal probability among A, C, G, and U. In cases where the populations exceeds the maximum size N, we perform the usual Wright-Fisher sampling.When a molecule replicates, each nucleotide has a probability The Hamming distance between two RNA sequences or subsequences is given by the number of positions in which their nucleotides differ. Structural differences can be estimated by various means. In this work, we apply the base-pair distance, given by the number of base pairs that have to be opened and closed to transform one structure into the other .ρ of structures in the population folding into the target structure. This quantity is zero when our simulation starts: note that the probability that a random sequence of length l folds into an arbitrary secondary structure is negligibly small, of the order of 10-15 in the present case [ρ is attained at the statistically stationary state, once the target structure is fixed in the population. The process of fixation and the dependence of ρ with the mutation rate μ have been described in detail elsewhere [A relevant macroscopic quantity to characterize the degree of optimization of the population is the fraction ent case  (but seeent case ). The malsewhere .μ is quantified by comparing the secondary structures of the mother i and daughter j sequences. We calculate the distances di and dj, as described, and the difference Δij = di - dj. If Δij = Δ > 0 (meaning that the mother sequence was farther from the target structure than its mutated daughter), the mutations increased fitness and count in the total of beneficial changes. If Δij = Δ < 0, mutations have caused a negative change in fitness, and the daughter sequence is farther from the target than her mother was. When Δij = 0, either mutations had no effect on fitness or no mutation has occurred.The change in fitness of an RNA molecule under replication with mutation rate i, j), as we will specify, to obtain a probability distribution Π(Δ) of the changes in fitness. That distribution eventually yields the fraction of deleterious changes p and the fraction of beneficial changes q:This procedure is repeated over a large number of mother-daughter pairs (n' = Π(0)-regardless of whether no mutations occurred or because the ones occurring were neutral-, can be immediately obtained from p and q: n' = 1 - p - q.The fraction of replication events with no change in fitness, μ, the probability that a sequence of length l acquires k mutations upon replication follows a Poisson distribution of average μl,For a mutation rate P(0) = eμl-, which for μl ≪ 1 reduces to P(0) = 1 - μl. The fraction of truly neutral mutations is thus n = n' - P(0). If one wishes to calculate the fraction of deleterious, beneficial or neutral mutations conditional on at least one mutation having taken place, it suffices to divide the values of p, q, and n above by the expected number of sequences with one or more mutations, 1 - P(0). The effect of single mutations can be estimated in this way only for sufficiently small values of the mutation rate μ, since for relatively large values the probability of having two mutations in the same sequence becomes non-negligible. For example, for μ = 10-3, the probability that a sequence of length l = 50 is hit by two or more mutations is P(k ≥ 2) = 1 - P(0) - P(1) ≃ 0.00121, thus one in a thousand molecules gets more than one mutation under replication. At sufficiently low mutation rates, the distribution of effects of mutations on fitness thus corresponds to the distribution of the effect of single mutations. As μ increases, sequences at a distance of two and more mutations from the parental molecule can appear in a single replication event. This has implications in the mobility of the population in sequence space and in its evolutionary dynamics [The probability of incorporating no mutations is thus dynamics .σq and σp are calculated as the relative average change in fitness produced by all replication events affected by mutations with a beneficial or a deleterious effect on fitness, respectively:The average selection coefficients l corresponds to the maximum fitness change, such that 0 <  < 1. The fraction of deleterious and beneficial mutations and the corresponding average selection coefficients are calculated while keeping a fixed value of the genomic mutation rate μ.where μc, the population is able to climb up towards the optimum of the phenotype space. After the transient, if mutation-selection equilibrium is reached, the population sits around the optimum, with a fraction ρ of correctly folding sequences determined by μ: the error rate at which a population evolves determines the degree of adaptation reached at the equilibrium. The mutation rate also determines the spread of the population in sequence and structure spaces. Populations perturbed through bottlenecks are forced to recover starting with a single sequence. If the time between bottlenecks is long enough, beneficial mutations can be found and fixed, recovery is possible, and the population is to be located near the optimum most of the time. However, for frequent perturbations it is likely that suboptimal sequences are repeatedly chosen. This favours the accumulation of deleterious mutations that separate the population steadily from the optimum: recovery is not possible, and eventual extinction might supervene.In the following we investigate the response of populations of RNA sequences evolving under the situations described. The three different cases explored are schematically represented in Figure S (plots (a), (c), and (e)) and the corresponding Hamming distance between all possible pairs of molecules in the population (plots (b), (d), and (f)). This quantitative picture agrees with the phenomenological description represented in Figure In the three cases described, and for a fixed value of the mutation rate, the diversity of each population in sequence and structure differs notably. Figure N = 1000 random RNA sequences subject to selection as a function of their distance to the target structure S, Eq. (1). In the statistically stationary state, the population has attained its maximum degree of optimization and is located as close to the optimum (represented by the target structure) as allowed by the operating mutation rate μ. The fraction ρ of sequences folding into S is a decreasing function of μ for values of the mutation rate below the error threshold; ρ becomes strictly zero for μ > μc only for sequences of infinite length. In our case, where sequences are short, there is a non-zero probability that the target structure is found, even above the error threshold. However, it is rapidly lost due to the high mutation rate. Hence, though we sporadically see the appearance of S above threshold, it cannot be fixed in the population.We start the simulation as described, with μ = 0.004, which yields a fraction ρ ≃ 0.34 of correctly folded sequences. Larger values of μ would yield broader distributions and smaller values of μ, corresponding to larger values of ρ, would pack the population closer to the optimum. An important point is to notice that there is always place for improvement within the population for any μ > 0. Suboptimal sequences (with di ≥ 1) might incorporate mutations (mostly compensatory once at the mutation-selection equilibrium) that diminish their distance to S and thus increase their fitness, while optimal sequences (with di = 0) might be affected by mutations that change their folded state, and thus count as deleterious. At equilibrium, the two processes balance so as to maintain the fraction ρ constant. The situation is different regarding the genomic diversity of the population. Though at the first generations after fixation of the target structure all sequences are similar, in successive iterations the population explores the neutral network of genotypes. This permits the population to expand in sequence space, displaying broad variability in sequences while maintaining the optimized phenotype. Further, the topological properties of the neutral network allow a deep exploration of the space of configurations, a feature that has been shown to underly the extreme plasticity observed not only in RNA sequence evolution in silico [The distributions shown in Figure n silico , but alsn silico . The reoμ. Beneficial mutations are very rare at low values of μ, where the largest fractions ρ of correctly folded sequences occur. The fraction of mutations with deleterious effects is slightly larger, though it still has low absolute value. As could have been expected, most replication events do not change fitness, particularly because mutations are absent. As μ increases, mutations become more abundant, and changes of fitness upon replication increase in frequency. Simultaneously, the distribution becomes more symmetrical: the ratio between beneficial and deleterious mutations increases towards one. This analysis has been repeated for populations optimized at different values of μ. Figure p, q, and the selection coefficients σp and σq as a function of the mutation rate μ. We have indicated the approximate position of the error threshold μc. It is interesting to note that the effect of mutations on phenotype does not have any particular sensitivity to this important threshold. It only affects the probability of fixation of beneficial mutations, not their appearance, which increases monotonically with μ. This is consistent with previous observations of structural stability, a kind of collective effect in RNA populations, which still maintain a distributed signal of the target secondary structure despite the fact that no sequence in the population folds into it [At the mutation-selection equilibrium, the effect of deleterious mutations is compensated by the incorporation of compensatory mutations , together with the replicative advantage of correctly folding sequences. Several examples of probability distributions Π(Δ) are shown in Figure  into it .μ:Below the critical error threshold, the phenotypic mutation fractions seem to bear a simple functional relationship with q/p quantifies the number of compensatory mutations per deleterious mutation. Its dependence with μ is displayed in the inset of Figure q/p ≃ μξ, with ξ = γ - α = 0.87 ± 0.03.with exponents α ≃ 0.89 ± 0.01 and γ ≃ 1.77 ± 0.02, indicating that, as the degree of adaptation of a population reduces as a consequence of evolution at progressively increased mutation rates, compensatory mutations increase their frequency at a higher speed than do deleterious mutations. We expect the algebraic relationship between phenotypic and microscopic mutation rates to be generic, although the specific values of the exponents α and γ will depend on the length of the sequences and on the particular secondary structure chosen. The ratio μ, with σp taking about twice the value of σq. This relationship is dependent on sequence length and target structure.The average selection coefficients vary only slightly with N = 1000 random RNA sequences is the starting point, and we replicate and select sequences as described. Now, however, fitness changes are measured before the population has found the target structure, such that it is formed by a population of phylogenetically related, suboptimal structures. In practice, we measure the structure of the population and the effect of mutations during 50 generations after the initial random state. The average number of generations required to find and fix the target structure is well above this value.The study of adapting populations is performed in a way similar to that for optimized populations. An ensemble of d ≃ 9 to the target structure in Figure The internal structure of the population at generation 50 is illustrated through the representative example shown in Figure μ. The overall shape of Π(Δ) is similar to that obtained at the mutation-selection equilibrium: a larger amount of deleterious mutations and a tendency of the distribution to become symmetrical as μ grows.The distribution of changes in fitness along the first 50 generations of adaptation is shown in Figure μ. In comparison to an optimized population, the fraction of deleterious mutations is slightly smaller than in the optimized case, while the fraction of mutations with a positive effect on fitness  is significantly larger. This fact is explained by considering that there are many more possibilities of improvement in the suboptimal states visited by an adapting population. This difference is bigger in the case of populations that evolve at low μ than in populations evolving at high μ. For μ values above the error threshold, adapting and optimized populations behave similarly. The functional dependence of the phenotypic mutation fractions with μ is of the same type as observed in an optimized population, Eq. (6). The exponents take different values in this case: using a least squares fit to the numerical data we obtain α = 0.93 ± 0.01 and γ = 1.06 ± 0.01. Note the remarkable quantitative difference in the behaviour of the ratio q/p, represented in the inset. Though still increasing as a function of μ, its variation with the mutation rate is much milder than in the case of optimized populations, as the corresponding exponent ξ = 0.13 ± 0.04 indicates. This result suggests that in the first stages of adaptation, populations evolving at different error rates are more similar than the same populations when equilibrium has been attained. In this case, however, substantial deviations observed in the q/p curve suggest that the power-law is not a good fit in the whole range of μ. The selective value of mutations is, both for beneficial and deleterious changes, typically lower than in the optimized case. Adaptation takes place through an increase in the fraction of beneficial mutations. In natural systems, mutations with a large effect on fitness can mask beneficial mutations with a small effect, which are then not identified during evolution  replicate at a slower pace. Note that the relative advantage of sequences folding into structures at relative distance m is the same as for the case of constant populations, Eq. (2).This dynamical rule applies now to the case of a growing population and substitutes the definition of replicative ability given in Eq. (1), the latter applying to populations of constant size. If the sequence at the bottleneck folds into the target structure, then ⟨g of generations elapsed between bottlenecks is large enough, the population will be able to recover and again attain mutation-selection equilibrium. As g decreases, the time for optimization becomes shorter and, for g small enough, the total population will not be capable of achieving the optimum. Still, survival might be possible. At too low values of g, however, the perturbation becomes too strong and the few sequences after the bottleneck might be unable to replicate, in which case the population goes extinct.If the number μ is the main source of randomness in the system, permitting as well change and improvement. Population bottlenecks constitute an additional source of stochasticity and represent a stronger perturbation, since selecting a random sequence to found a new population implies choosing a suboptimal structure with a probability of at least 1 - ρ. In those cases, the population faces two important difficulties: first, it has to go again through the adapting transient, where the target structure has not yet been found; second, the reduction in the population size impairs the capability of the ensemble to generate beneficial variants.For optimized and adapting populations, the mutation rate Figure Qβ bacteriophage incorporated a lower amount of beneficial mutations than viruses isolated from a population previously displaced from mutation-selection equilibrium due to the application of successive bottlenecks [The dynamics of three populations under the action of bottlenecks with different periodicity is illustrated in Figure tlenecks .In the possible case that an optimal sequence is selected, it replicates fast and reaches high density in a small number of generations. In this case, almost all sequences in the first generations after the bottleneck fold into optimal structures, thus generating a superoptimal, unstable population that slowly relaxes towards the diversity characteristic of the mutation-selection equilibrium under the action of the mutation rate. Figure μ. Low values of μ correspond to a higher density ρ of correctly folded sequences, thus favouring selection of an optimal sequence at the bottleneck. However, a sufficiently low value of μ hinders the generation of diversity and with it the appearance of more optimal variants. Actually, when bottlenecks are frequent a good evolutionary strategy is to replicate under a not too low mutation rate, such that, in the case that a suboptimal phenotype is the founder of a new population, the time to recover mutation-selection diversity is minimized [The critical frequency of bottleneck application for the population to survive depends on other model parameters, especially on the mutation rate inimized . This reAn important question is whether our results are robust when different definitions of fitness for the RNA molecules are used. Up to now, we have only considered that, the closer a sequence folds to the target structure, the fitter it is. In this section, we introduce two additional definitions of fitness and discuss how they affect the dynamics and organization of optimized populations. As will be shown, the system is able to find a remarkably large number of genotypes compatible with the new selection pressures applied to the system, and the collective statistical properties of the population are only weakly affected.Q of length ls nucleotides is required at a certain position for a sequence to have maximal fitness, and that deviations from that composition are penalized. A sensible way to add this requirement is the use of a fitness function of the formMany molecules require a specific sequence of nucleotides for their function to be properly performed. Conserved subsequences often correspond to active sites which cannot be mutated, so variations in that subsequence are selected against. As an example, suppose that a target sequence i and the target sequence Q, ls is the length of the target sequence, and βH is a selection parameter that measures the relative strength of selection for target sequence Q versus selection for target structure S. The landscape defined by Eq. (8) is the S + Q-landscape. In the examples to be shown, we have chosen a target sequence GUAUCUUCAC, with ls = 10, placed at the 5' end of molecules in the population, and a selection parameter βH = 1. As previously, β = 2.where Em for sequences of length l, and call Ei the energy of sequence i folded into its minimum free energy secondary structure. A suitable fitness function to favour low-energy configurations isA second important property of folded molecules is their thermodynamical stability. Usually, sequences folding into configurations of lower energy are at an advantage with respect to those of higher energy. Suppose that there is an absolute minimum energy i and the reference energy Em, and βE is a selection parameter that again measures the relative strength of selection for low energy versus selection for target structure S. Equation (9) defines the S + E-landscape. In the forthcoming examples, Em = -72 kcal/mol, which corresponds to the energy of a sequence of length l = 50 with 23 G=C pairs that contribute -3 kcal/mol each and where the positive contribution of the loop has been discarded. This value of Em is a lower bound to the energy of sequences of length l = 50. The selection parameter βE = 0.5, and β = 2. Let us compare the mutation-selection equilibria of three populations evolving on each of the landscapes described under a mutation rate μ = 0.003. In order to evaluate the degree of adaptation achieved for each of the traits under selection , three relevant quantities describing the macroscopic state of these populations are used: as before, the density of sequences correctly folding into the target sequence, the average energy ⟨E⟩ = N-1∑i Ei of the population, and the fraction ρH of sequences at distance Q. As previously performed, the simulation begins with an ensemble of N = 1000 random sequences. At each generation, the quantities id, Ei relevant in each landscape are evaluated. Substitution by a new generation of offspring sequences proceeds as described.where, analogous to previous definitions, S has ρ ≃ 0.43, its average energy is ⟨E⟩ ≃ -12.3 kcal/mol and ρH ≃ 0. That is, the required secondary structure has been successfully found but essentially none of the subsequences matches Q. The energy of the population is comparable to that of an ensemble of randomly chosen sequences folding into the target structure S. When selection for sequence is turned on in the S + Q landscape, there is a fraction ρ ≃ 0.45 of sequences correctly folding into the target structure. However, this occurs simultaneously with a fraction ρH ≃ 0.85 of molecules bearing the correct target sequence Q. The average energy in this case is comparable to that in the previous landscape, ⟨E⟩ ≃ -13.0 kcal/mol. Hence, the population has been completely displaced from its position in the space of sequences (compared to landscape S), allowing the optimization of a second trait (target sequence) while keeping other macroscopic values essentially unchanged. The third population, evolving on landscape S + E, is optimized at ρ ≃ 0.36 with ρH ≃ 0. However, its average energy has significantly decreased to ⟨E⟩ ≃ -28.4 kcal/mol. This again speaks for a major displacement in sequence space with respect to the two previous landscapes, favouring those sequences folding into S with minimum energy, and with a composition that does not match the target sequence Q.At the mutation-selection equilibrium, we observe the following. The population evolving in landscape S and the target sequence Q can be simultaneously (and partly independently) optimized since Q is compatible with folding into S. This is not a general situation, since demanding a target sequence too long or too biased in its composition might prevent the existence of solutions fulfilling both requirements. This is also the case for the selection of S together with the requirement of a low folding energy. If the parameter βE would take an exceedingly high value, structures of low energy (different from S) would dominate the population. This is probably the reason why ρ takes a value slightly lower in landscape S + E than in the two former landscapes. While it is important to take these possibilities into account, our results indicate that, in this model, the simultaneous optimization of two traits is possible for a broad range of selection parameters β, βH, and βE.The target structure μ the distribution of changes in μl, identical to Eq. (4). The landscape corresponding to selection for low energy shares characteristics with both. On the one hand, if mutations acquired through replication do not disrupt the folded state, changes in energy have to be small, since only the composition of the sequence is affected. However, if mutations lead to a different folded state, the minimum energy can suffer major changes, due to the appearance of a different distribution of structural motifs  having a major role in the folded energy.In addition to the different conceptual situations represented by the three landscapes introduced in this work, there are relevant geometrical differences among them. Selection for structure represents a rough landscape where changes in a single nucleotide can cause deep reorganizations in the folded configuration. On the contrary, selection for a specific sequence represents a smooth landscape where changes in the distance L) corresponding to landscapes S, S + Q, and S + E. The superindex L is generic and corresponds to a different variable ΔL for each landscape. To make the three distributions quantitatively comparable, we have to use rescaled variables in the x-axes, analogous to x = Δ/l, as introduced for landscape S. They are xQ = ΔQ/l for landscape S + Q and xE = ΔE/l for landscape S + E, withIn the next section, we study the distribution of fitness effects Π and of the corresponding cumulative probability function (CPF), R-squared values as shown. As a general trend, we observe that beneficial mutations typically have significantly smaller fitness effects than deleterious mutations - in agreement with the difference in the average selection coefficients calculated previously. This can be seen for instance in the λ parameter of exponential fits, in the consistent changes in the shape parameter b for Γ and β distributions, in the slope a of the Pareto distribution, or in the σ value of the Lognormal distribution.We have used five different probability density functions to fit the numerical, cumulative distributions of the effects of mutations on fitness. Table R-squared values corresponding to each fit as a measure of its goodness, we might conclude that most PDs represent the data reasonably well, though there is no function able to account for all numerical distributions. A closer inspection of the fits reveals systematic deviations from numerical results. Figure β distributions) underestimate the number of small effects and overestimate the number of average-to-large effects. In the case of the Γ and β distributions, the parameter a is in almost all cases close to 1 . This reveals that the fit to data is not improved by considering those two-parameter functions instead of the simpler, one parameter, exponential. The three functions are actually very similar. The Lognormal distribution slightly improves the fit in the region of small effects: It represents a best fit to beneficial distributions , though it systematically fails in the same regions as functions characterized by exponential decays.If we were only to consider None of the functions assayed are thus able to explain the shape of the distributions obtained in the whole domain of changes in fitness. One reason might be that our sequences are relatively short and thus fold into small secondary structures. We cannot discard that large effects on fitness could be affected by structural motifs of the particular target secondary structure studied in this work .R-squared coefficients are at least as good as the best fit in the whole range of fitness change, but now there are no systematic deviations from data. Two representative examples of Pareto distribution fits to numerical data are shown in the inserts of Figure The distribution of small effects on fitness, which considers mutations that slightly change the secondary structure of the parent sequence, should be much less affected by specific properties of the structure studied. We have thus conducted a systematic study of the distribution of small fitness effects, defined as those replication events affected by mutations where the change in the secondary structure was at most 22% with respect to the parent structure. This range is not too small: it can explain around 90% of the beneficial changes observed and around 70% of the deleterious changes (see Table Q(x ≤ Λ) for beneficial (B) and deleterious (D) changes in fitness and the three landscapes analysed. The visible similarity between the functional form in either case is supported by the quantitative analysis of the distribution of small effects, as summarized in Table Q(x ≤ Λ) for the landscapes and populations studied.Our analysis of optimized populations in different fitness landscapes agrees with the functional behaviour just described. Changes in the fitness landscape modify the distribution of effects on fitness, though only quantitatively. The three landscapes studied are compared in Figure S-landscape.In this section, we compare by means of explicit examples the overall effect of mutations, as obtained in our simulations with RNA sequences, with some measures performed in natural systems. Due to the important differences between populations, environments, and fitness definitions used in different works, the effect of mutations in those different systems should be compared with due care. Nevertheless, the values obtained might give clues about the degree of optimization of the population and about the likeliness that fitness is improved. In the following, the numerical results obtained in our simulations correspond to populations evolving on the μ = 0.001. As described, there is a fraction P(0) = 0.951 of replication events without mutations and an amount 1 - P(0) - P(1) = 1.209 × 10-3 of daughter sequences incorporating two or more mutations. Hence, in most cases where mutations occur, the replicated sequence is hit by a single mutation (P(1) = 0.047). Let us consider only those cases, where a mutation has been incorporated. Our simulations indicate that, at equilibrium, 0.59% of such mutations have beneficial effects, while 46.34% diminish fitness. A large amount of mutations is neutral: 53.07%. Adapting populations suffer a similar amount of neutral mutations, 54.33% at the same mutation rate μ, but they substantially differ in the amount of mutations with an effect on fitness. Deleterious mutations represent 38.51%, and beneficial mutations increase to 7.16%. It would be difficult to evaluate the effect of single mutations at higher rates of μ. For example, if the average number of mutations per replication event is one per genome (μ = 0.02 in our case), over 26% of the daughter genomes incorporate two or more mutations, and epistatic effects should not be discarded. This might entail a difficulty when translating the results of controlled experiments to natural situations involving fast-mutating replicators.Let us illustrate, with an example, the overall relative fractions of beneficial, deleterious, and neutral mutations affecting optimized and adapting populations. Take the mutation rate Empirical results concerning the effect of mutations on fitness have been obtained in different contexts and for different model systems. Single nucleotide substitutions in vesicular stomatitis virus yielded complex distributions of fitness effects, with the functional form of those corresponding to beneficial mutations (Γ-distribution) differing from that of deleterious mutations , and both depending on how mutations were acquired . The oveWe have quantified the effect of mutations on fitness for populations of RNA sequences in different situations. Beneficial or compensatory mutations are systematically less probable than deleterious ones, the ratio between both types being strongly dependent on the degree of optimization of the population. Once the error threshold is crossed (at high error rates), optimized and adapted populations behave similarly. Selection coefficients are almost constant, regardless of the degree of adaptation of the population. They are only slightly lower in adapting populations than in optimized populations evolved at the same mutation rate, indicating that adaptation takes place through an increase in the fraction of beneficial mutations, preferably of those with small effect in fitness.Efforts to quantify the distribution of positive fitness effects rely on the interest to understand the dynamics of the adaptive process. Mutations of small effect are difficult to detect and quantify, so both theory and experiment have mainly addressed the tail of the distribution, where mutations with a large positive effect on fitness sit. Extreme value theory predicted an exponential shape for large effects . Howeverμ. In a first approximation, and in the absence of additional evidence, it would be advisable to maintain constant selection coefficients. As a consequence, at least in the system that we have studied, fitness equilibria are reached and maintained mainly through compensatory epistasis, and not through a variation in the average selective coefficients with fitness. This result is in good agreement with recent measurements of the same effects in populations of the bacteriophage ΦX174, where, moreover, the distributions of beneficial and deleterious fitness effects follow a single functional form [The results here presented could be used to design more realistic evolutionary models where an explicit representation of the microscopic mutation rate is not feasible. These suggest using phenotypic mutation fractions that increase algebraically with the genomic mutation rate nal form , as obtaS, S + Q, or S + E). One of our future objectives is to deepen the study of the universality of these and similar models, analyzing whether populations differing in their fitness values across environments, evolving towards different target structures, or incorporating a larger number of realistic phenotypic traits, still adapt through an increase in the amount of beneficial mutations with small effects on fitness, and whether the functional form of the distribution of fitness effects agrees with those obtained here.The restrictions imposed by the simultaneous selection of more than one phenotypic trait is an important subject worthy of additional analysis. Landscapes such as those introduced here could be a first step towards the quantification of constraints in evolution and adaptation of complex populations. Despite remarkable differences among the situations investigated, the distributions of effects on fitness are best explained by a unique functional form  irrespectively of the state of adaptation of the population (whether optimized or adapting) and of the fitness landscape on which the population evolves . For random number generation, we relied on the Mersenne Twister and Ziff's GFSR4 algorithms as provided by GNU Scientific Library (GSL), Version 1.7 . For secMS, EL, and SCM conceived and designed the research. MS performed the simulations. MS, EL, and SCM analyzed the data. EL and SCM performed the statistical analysis. SCM wrote the paper. All authors read and approved the final manuscript.


The ability for an evolving population to adapt to a novel environment is achieved through a balance of robustness and evolvability. Robustness is the invariance of phenotype in the face of perturbation and evolvability is the capacity to adapt in response to selection. Genetic robustness has been posited, depending on the underlying mechanism, to either decrease the efficacy of selection, or increase the possibility of future adaptation. However, the true effect of genetic robustness on evolvability in biological systems remains uncertain.Here we demonstrate that genetic robustness increases evolvability of thermotolerance in laboratory populations of the RNA virus φ6. We observed that populations founded by robust clones evolved greater resistance to heat shock, relative to populations founded by brittle (less-robust) clones. Thus, we provide empirical evidence for the idea that robustness can promote evolvability in this environment, and further suggest that evolvability can arise indirectly via selection for robustness, rather than through direct selective action.Our data imply that greater tolerance of mutational change is associated with virus adaptability in a new niche, a finding generally relevant to evolutionary biology, and informative for elucidating how viruses might evolve to emerge in new habitats and/or overcome novel therapies. Evolvability may be defined as the capacity to adapt in response to selection -3, or alUntil recently, it was controversial whether biological populations could evolve genetic robustness as posed by theory . HoweverPseudomonas syringae pathovar phaseolicola, under low versus high levels of virus co-infection , and gauging their relative ability to adapt to a novel environment. To do so, we tested whether populations founded by genetically-robust viruses were more evolvable than lineages founded by genetically-brittle viruses, in an environment that imposes strong directional selection. In particular, we explored whether robust virus lineages had the capacity to evolve faster than brittle populations, when viruses must adapt by evolving thermotolerance – resistance to the deleterious consequences of periodic heat shock.P. phaseolicola host bacteria. Bacteria-free lysates (~108 virus particles) of the wild type virus were subjected to thermal incubation at seven temperatures ranging between 35°C and 50°C, in repeated (3 <n < 5) assays. Results showed that temperatures increasingly higher than 40°C caused a progressively larger fraction of the virus population to become incapable of producing plaques on the host bacteria  of virus φ6 is adversely affected by virus exposure to temperatures above 45°C [10 W = log10 Wpost-bottleneck - log10 Wpre-bottleneck) was calculated for each lineage. The data revealed that variance in Δlog10 W for the 12 lineages founded by high co-infection viruses (σ2 = 0.046) was over twice that of the low co-infection derived lineages . Robustness of one group relative to another can be defined as lesser variance in fitness changes brought on by mutation(s) added to the genome [10 W following mutation accumulation for lineages founded by high co-infection viruses (mean = -0.168) was over three-fold greater than that of the low co-infection derived lineages . This outcome is consistent with theory suggesting that increased mutational robustness should cause mutations to have reduced effects on mean fitness [Our prior mutation-accumulation experiment revealed that viruses which were evolved for 300 generations under low and high levels of co-infection could be generally categorized as robust and brittle, respectively . Using t σ2 = 0.06 was ovee genome . Thus, t fitness . AlthougS) following 5 min exposure to 45°C for all 24 strains, using repeated (n = 6) survival assays. Results  strains was 14.899 ± 1.641 s.e.m, and that for the 12 high co-infection evolved (brittle) clones was 13.467 ± 3.312 s.e.m. The average of these data across all 24 strains was 14.182 ± 2.163 s.e.m., which did not differ according to robust versus brittle categorization . We concluded that the two groups of founding viruses were equivalent in average survival under heat shock at 45°C, regardless of their prior history of selection at low versus high co-infection.We then conducted preliminary assays to confirm that the two groups of strains  were equally poor at surviving the selective heat-shock environment. To do so, we measured the mean of percent survival (%P. phaseolicola) at low and high co-infection. Whereas the design of the original 300-generation experiment allowed pre-adsorption to cells to manipulate co-infection level  fitness assays. Consistent with earlier data for the entire 60-member collection [10 W at low MOI did not significantly differ according to prior adaptive history (low versus high co-infection) . We concluded that the intended thermal selection regime involving propagation in absence of co-infection would not bias in favor of viruses previously adapted to low co-infection conditions.We next conducted two preliminary experiments to determine whether the groups of viruses differed in fitness  fitness assays. Results showed that mean fitness did not significantly differ according to prior adaptive history (low versus high co-infection) . We concluded that the two groups of viruses were equivalent in fitness under low and high levels of co-infection (see further discussion below).For completeness, we also determined whether the two groups of founding viruses differed in performance at high co-infection, by estimating the mean logP. phaseolicola at 25°C. Thus, heat shock was imposed only every fifth generation of virus evolution. At the end of the experiment, we used replicated (n = 6) survival assays to measure mean %S at 45°C for each of the founding clones, and for each of their corresponding derived endpoint populations. Measurements of %S for a founding genotype and its evolved descendant population were conducted in parallel. The difference between the two mean values was then used to estimate Δ%S, the change in average percent survival at 45°C following 50 generations of viral evolution with periodic heat shock.To test the formal hypothesis that evolvability correlates with robustness we used the 12 robust and 12 brittle clones as founders of independent lineages in an experimental evolution study. The 24 lineages were subjected to 50 generations (10 days) of viral evolution, involving daily exposure to 5 min incubation at 45°C, followed by five generations of growth on S for lineages founded by the robust strains was a significantly larger value than that for the populations initiated by brittle strains . Although the founding clones showed no difference in heat-shock survival prior to selection . Overall, these data provided strong support for the hypothesis that genetic robustness promotes evolvability of virus φ6 in a novel habitat where heat shock imposes directional selection.Results Figure  showed tS at 45°C with three-fold replication, for the founding strains and their descendant populations in parallel. Results showed that the two groups of evolved lineages in this control experiment did not statistically differ in Δ%S at 45°C . We therefore concluded that change in resistance to heat shock was indeed an adaptive trait, and not simply a consequential response to the general conditions manipulated in our experiment to address the formal hypothesis.Aside from the imposition of periodic heat-shock, the selection experiment was designed to be highly similar to the general culture conditions that the founding clones previously experienced during their 300 generations of evolution under low versus high co-infection . We observed that the robust viruses tended to generate much higher frequencies of mutants, which suggested that robustness coincided with a higher mutation rate [P. atrofaciens and were then forced to obtain an additional mutation that allowed infection of P. tomato [Our earlier work hinted that elevated mutation rate may be a characteristic of the virus φ6 strains which we defined as relatively robust . In partion rate . Howeverion rate -33. Furt. tomato . The latP. phaseolicola host cell [n = 24, P = 0.355). Because variability in mutant frequency was seen among strains in these assays, we surmised that subtle differences in BHT-mutant frequency (as a proxy for mutation rate) might be associated with the observed differences in evolvability. Thus, we also examined the relationship between BHT-mutant frequency and mean adaptive change in our heat-shock experiment (Δ%S) for the set of 24 clones. This analysis . In addition, correlation analyses conducted independently for the two groups were not significant either . These results strongly suggested that mutation rate differences among strains in our study did not influence their observed evolvability. Furthermore, these data for BHT mutant frequencies do not provide support for elevated mutation rate as the underlying mechanism governing the observed link between robustness and evolvability in virus φ6. However, although we cautioned against using host-range assays to discern mutation rate differences among robust and brittle clones [We identified a method for comparing mutant frequencies among robust and brittle strains of virus φ6 which should be less confounded by any of their underlying differences in genetic architecture in gene P3. The approach involved examining the frequency of mutants that are resistant to the chemical butylated hydroxytoluene (BHT). BHT is shown to be lethal to virus φ6 genotypes because it cleaves protein P3 from the virion, preventing attachment and subsequent entry of the virus into the ost cell . But oneost cell . Using ls Figure  showed ne clones , we note8 particles of a test clone to the challenge temperature (see Methods). These assayed lysates should be easily large enough to harbor rare spontaneous mutants; although the mutation rate and mutation spectrum for 45°C heat-shock resistance are unknown in φ6, we can expect between 10-4 and 10-6 particles should contain a point mutation for resistance to a selective challenge such as growth on a novel host [A somewhat related idea is that adaptation to the 45°C heat shock might require multiple mutational substitutions, and the robust clones evolved relatively faster because they happened to contain one or more of the needed mutations. We find this explanation unlikely, however. We observed that the initial survival of robust and brittle clones did not statistically differ at 45°C, using replicated survival assays which exposed lysates containing 10vel host ,35. ThusWe have yet to determine the exact molecular mechanism responsible for differences in genetic robustness among φ6 virus genotypes. However, data from other systems point to differences in protein stability as the responsible mechanism. In particular, it has been shown that proteins can be identical in shape, despite underlying sequence differences that impact protein sensitivity to the effects of mutations (i.e. robustness) . These rS at 45°C) in our selection experiment . Therefore, our data suggest that robust strains of φ6 are generally better at surviving moderate temperatures such as 42°C, but individual strain toleration of this temperature does not predict the adaptive success of its descendent lineage under 45°C selection. This analysis suggests that virus performance at moderate temperatures and evolvability under extreme temperature is not a trivial relationship, such as that resulting from a pre-existing mutation in a founding clone which places its descendent lineage closer to a selective optimum that is only two mutational steps away.We showed that the 12 robust and 12 brittle viruses used as founding genotypes in the current study were equally poor at surviving in the 45°C selective habitat  explanation for the transient nature of the trade-off suffered by high co-infection evolved viruses. The possibility exists that by generation 300 the high co-infection populations are no longer dominated by cheater viruses which present the trade-off; we discussed this possible outcome in a separate study . If the Genetic analyses should also prove useful for confirming the presumed role of latent genetic variation in our observed link between robustness and evolvability. Regardless of the molecular mechanism (e.g. protein stability) responsible for robustness in virus φ6, it is expected that a robust population should harbor more genetic diversity than its brittle counterpart. This assumption follows directly from the definition of robust genomes; i.e. they should be more easily capable of amassing neutral mutations because their robustness causes random mutations to be neutral in the current environment. All else being equal, we therefore might expect a larger number of molecular substitutions per genome in the generation-300 strains drawn from the low co-infection lineages, and a greater number of haplotypes per population in these treatment populations. Of course, the problem is that all else is not necessarily equal. Immediately above we discussed how cheaters might have been transiently successful in the high co-infection lineages, which suggests that virus-virus coevolution in these populations might have caused greater dynamic turnover of alleles and, hence, more extensive molecular evolution.Nevertheless, we acquired preliminary sequence data to examine the predicted larger number of substitutions/strain, and larger total number of haplotypes present (i.e. greater genetic diversity) in the generation-300 lineages evolved under low co-infection, which we defined as relatively robust. As part of a separate study , for all 24 strains we sequenced a 665 bp region on the large segment which is entirely protein-coding for the RNA-dependent RNA polymerase P2, a region that is thought to be highly conserved ,47. We aP0.05,4 = 0.007). We concluded that the φ6 populations evolved under low multiplicity showed greater genetic variability than the high MOI populations, on average, based on sequence data representing ~10% of the viral genome.As expected, very few changes were observed in the sequenced portion of the highly-conserved polymerase gene P2. Two synonymous substitutions were found in this protein-coding region of the large RNA segment: mutation N104N shared by clones L2.3 and L2.4, and mutation E255E shared by clones H1.1 and H1.7. Few changes were also observed in the coding region of the sequenced portion of gene P5 on the small segment. Here we observed two synonymous substitutions  and one non-synonymous change (A208E in clones H1.3 and H1.6). The sequenced non-coding region of gene P5 showed seven total mutations, all of which occurred in five clones drawn from populations in the low co-infection treatment: t2209c in L3.2, g2231a in L1.9, a2272g in L1.2, c2281t in L2.3 and L2.4, t2387c in L2.3 and L2.4. These five non-coding mutations explain the difference in the number of mutations observed in clones drawn from the two treatments . The data show that the low co-infection (robust) strains had an average of 1.08 substitutions/strain (13 mutations across 12 clones), compared to 0.58 substitutions/strain (7 mutations across 12 clones) for the high co-infection (brittle) strains. The sequence data also allowed us to estimate the inferred number of haplotypes per evolved population: L1, 3; L2, 3; L3, 3; H1, 2; H2, 1; H3, 1. The difference between robust and brittle populations in the inferred number of haplotypes was found to be statistically significant  was the host bacterium used in all experiments, and culture conditions are previously described [P. phaseolicola lawn for 24 hr; plaques were then collected and filtered  to remove bacteria. Virus lysates were stored at -20°C in 4:6 glycerol/LC (v/v).Virus φ6 is a lytic bacteriophage which contains a ~13 kb double-stranded RNA genome divided into three segments per particle . The curescribed ,55. Bact8 particles) in a PCR tube, followed by immediate sampling onto a host lawn to confirm the initial virus titer (Ni). The lysate was then placed in a preheated Eppendorf thermocycler for 5 min incubation, followed by sampling onto a host lawn to measure final titer (Nf). Percent survival (%S) equaled (Nf/Ni) * 100. Thus, survival at a test temperature was gauged through plaque-forming units (pfu), the phage particles that were viable for growth at 25°C.Temperature survival was assayed by placing 120 μl of a virus lysate  bacteria. This propagation scheme was repeated for 10 consecutive days. Because the overnight plaque growth corresponded to 5 viral generations [Virus lineage adaptation to heat shock occurred through experimental evolution involving periodic exposure to high temperature Figure . A lineaP. phaseolicola of a test genotype (or population) relative to a common competitor of φ6 bearing a genetic marker. In some assays the marked competitor was a host-range mutant containing a substitution in gene P3 of the medium RNA segment, allowing infection of P. pseudoalcaligenes bacteria. In other assays the competitor was an engineered mutant bearing the alpha subunit of the Escherichia coli beta-galactosidase  gene on the large RNA segment [P. phaseolicola lawn. Pre-adsorption to cells before plating was only allowed if the fitness assay examined impact of co-infection on relative fitness. After 24 hr incubation, the ~400 plaques were harvested and filtered to obtain a cell free lysate. When the common competitor was a host-range mutant, the ratios of competing genotypes in the starting mixture (R0) and in the harvested lysate (R1) were obtained by plating on mixed lawns of P. phaseolicola and P. pseudoalcaligenes (200:1 mixture), where ordinary and host-range genotypes form turbid and clear plaques, respectively. When the common competitor contained the β-gal gene insertion, ratios were tracked by plating on lawns of P. phaseolicola bacteria containing the beta subunit of the β-gal gene, allowing the marked competitor to produce blue plaques on agar containing X-gal (0.4% w/v). Fitness (W) was defined as the relative change in ratio of ordinary to marked virus, or W = R1/R0.Fitness assays consisted of paired-growth experiments , which c segment ; fitness10 viruses per mL) of a virus genotype was grown and titered on P. phaseolicola, and a sample of the lysate was then placed in 0.12 mM BHT for 5 min. Mutant frequency was calculated as the number of plaque-forming mutants per viruses in the inoculum following BHT exposure.We measured the frequency of spontaneous BHT-resistant mutants that occurred within virus populations grown in the absence of the chemical. A high-titer lysate .Genomic extraction was performed using QIAamp Viral RNA minikits (Qiagen). The dsRNA genome was reverse transcribed using random hexamer primers  and resultant cDNA was used as PCR template (primers available on request). PCR products were purified using the QIAquick PCR Purification kit (Qiagen) or ExoSAP-It . Sequencing was performed using the BigDye Terminator reaction v3.1 on an ABI 3100. Sequence reads were curated by eye using Sequencher software  and compared using ClustalX RCMcB, CBO and PET were involved in the conception, design and writing of this study. RCMcB conducted the experiments and analyses. All authors read and approved of the final manuscript.


E. coli requires the accumulation of multiple mutations, including those that alter target genes and genes regulating drug efflux. Previous studies have shown some drug-resistance mutations reduce bacterial fitness, leading to the selection of fitness-compensatory mutations. The impact of fluoroquinolone-resistance on bacterial fitness was analyzed in constructed isogenic strains carrying up to 5 resistance mutations. Some mutations significantly decreased bacterial fitness both in vitro and in vivo. We identified low-fitness triple-mutants where the acquisition of a fourth resistance mutation significantly increased fitness in vitro and in vivo while at the same time dramatically decreasing drug susceptibility. The largest effect occurred with the addition of a parC mutation (Topoisomerase IV) to a low-fitness strain carrying resistance mutations in gyrA (DNA Gyrase) and marR (drug efflux regulation). Increased fitness was accompanied by a significant change in the level of gyrA promoter activity as measured in an assay of DNA supercoiling. In selection and competition experiments made in the absence of drug, parC mutants that improved fitness and reduced susceptibility were selected. These data suggest that natural selection for improved growth in bacteria with low-level resistance to fluoroquinolones could in some cases select for further reductions in drug susceptibility. Thus, increased resistance to fluoroquinolones could be selected even in the absence of further exposure to the drug.Fluoroquinolones are antibacterial drugs that inhibit DNA Gyrase and Topoisomerase IV. These essential enzymes facilitate chromosome replication and RNA transcription by regulating chromosome supercoiling. High-level resistance to fluoroquinolones in  The increasing frequency of human pathogens resistant to important classes of antibiotics poses a serious and growing challenge for medicine and society. We need improved strategies to reduce the rate of resistance development, for established and novel drugs, based on knowledge of the factors that drive the increase in resistance. Resistance to fluoroquinolones in most bacteria develops via a series of sequential genetic changes affecting several different genes. These are selected and enriched in bacterial populations by exposure to the drug. Relevant factors driving this increase include overuse, and inappropriate use, of these drugs. In this paper we show that mutant bacteria with low-level resistance (not itself a problem to treat with standard drug doses) can evolve by natural selection (for improved growth rate) to acquire mutations that dramatically increase their level of drug resistance. This means that we may need to consider how to reduce inappropriate drug use that can enrich for bacteria with low-levels of resistance, because at that stage some of the mutant bacteria in the population may continue to evolve higher level resistance even in the absence of any further drug exposure. E. coli, but resistance is increasing with 28 of 29 countries in Europe reporting a significant rise between 2001–2007 E. coli require multiple genetic changes, including mutations altering topoisomerases and up-regulating drug efflux in vitro and in vivoE. coli increased from ∼7–19% between 2001 and 2007 in the UK Fluoroquinolones are potent antibacterial drugs E. coli for decreased susceptibility to fluoroquinolones most lineages (16/18) suffered reduced growth competitiveness after only two or three selection steps Streptococcus pneumoniae carrying one or two resistance mutations in vivo in not clear. To examine the phenomenon we constructed isogenic strains carrying various combinations of five resistance mutations found commonly in fluoroquinolone-resistant clinical E. coli, and measured their drug-susceptibility and fitness. The relationships between the number of resistance mutations and bacterial fitness were complex and the addition of a resistance mutation was shown in some cases to improve bacterial fitness. These findings have implications for the evolution of fluoroquinolone resistance in the absence of antibiotic exposure.The fitness costs of drug resistance can be reduced by selection of low-cost mutations or by the accumulation of secondary fitness-compensating mutations that do not reduce resistance. During experimental evolution of clinical isolates of E. coli urinary tract infection isolate C1186 gyrA Ser83→Leu, Asp87→Asn; parC Ser80→Ile), and up-regulating drug efflux . These 5 mutations are typical of highly resistant clinical isolates gyrA, parC) or constructed by λ-red recombineering  and then separately introduced into MG1655 by P1 transduction. The gyrA and parC mutations were transduced by selection for a linked genetic marker , and all strains with 4 or 5 mutations had MIC's above the 1 µg/ml breakpoint that defines clinical resistance in Europe MIC for ciprofloxacin was measured for each strain . The margyrA S83L, gyrA D87N, and parC S80I) were statistically neutral whereas others (ΔmarR and ΔacrR) caused a significant reduction in fitness . Strains carrying three resistance mutations had fitness values that ranged from ∼1 down to as low as 0.60, with 8/9 strains suffering a fitness deficit of ≥5% per generation. Interestingly, the addition of a fourth resistance mutation to these strains restricted the minimum fitness value to 0.66 per generation, higher than that measured with three mutations  has high level resistance (MIC 32) with no significant reduction in fitness relative to the wild-type  in two of the three cases, LM695>LM707 and LM882→LM707 , and the average fitness of all strains carrying marR is 0.76 (SD 0.08). MarR protein regulates, directly and indirectly, transcription of many genes mar is most likely because of disruption of gene regulation. This suggests a possible mechanism of fitness compensation associated with resistance mutations in topoisomerase genes. Thus, some topoisomerase mutations that alter chromosomal supercoiling levels may partially restore expression of growth-limiting gene(s) regulated by mar, reversing the fitness deficit. This hypothesis predicts that the improvement in fitness measured in LM695→LM707 should be associated with a change in global supercoiling level. This was tested by electrophoresis of pUC18 and pUC19 plasmids purified from MG1655, LM695 and LM707 in chloroquine-agarose gels topA and pgyrA) whose expression is sensitive to, respectively, increased or decreased supercoiling levels topA / pgyrA) of reporter gene expression from these two promoters, defined as the quotient of supercoiling (Qsc), is a measure of the relative level of negative supercoiling in isogenic strains gyrA promoter construct in LM707 relative to LM695. Thus the introduction of the parC S80I mutation to make strain LM707 caused a significant increase in the Qsc, coincident with the improvement in fitness. Although we cannot explain the absence of an effect in the chloroquine-agarose assay, the reporter gene assay suggests that some changes in chromosomal supercoiling associated with the acquisition of topoisomerase mutations may provide a mechanism linking bacterial fitness and decreased susceptibility to fluoroquinolones. However, an alternative explanation is that the combination of mutations in LM707 reduces expression of gyrA by a mechanism that does not change global supercoiling levels, and that it is a consequence of the reduced expression of gyrA that causes the increase in growth fitness. Additional experiments will be required to distinguish between these models.The  strains . The marparC S80I mutation into LM695 increased its MIC for ciprofloxacin and its competitive growth fitness versus the wild-type. This predicted that the resulting constructed strain, LM707, should outcompete LM695 in a head-to-head competition, and also raised the following questions: (i) could a mutant with an increased MIC for ciprofloxacin and a higher growth fitness be selected spontaneously from LM695 in the absence of drug; and (ii) would such a mutant be exclusively associated with of the acquisition of the parC S80I mutation. These predictions and questions were addressed experimentally. First, in head-to-head growth competition experiments in LB medium with no drug, LM707 (four resistance mutations) outcompeted LM695 (three resistance mutations), gaining ∼8% per generation, in good agreement with the relative differences in growth fitness of each strain versus the wild-type  in a volume of 200 µL. An aliquot of 5×106 cfu from each lineage was tested, after the completion of 2, 3, and 4 cycles of growth, for the presence of resistant mutants on solid medium . Growth of LM695 is completely inhibited on 3 µg/mL ciprofloxacin and the spontaneous mutation rate to resistance on this media, measured in fluctuation tests, is 2×10−8. Accordingly, we expected that virtually none of the 96 independent lineages would contain a resistant mutant at the initiation of the experiment, but that a small number of resistant mutants would arise in each lineage during each growth cycle. If these mutants out-competed the parental LM695 they would be expected to increase relative to LM695, and thus have a greater probability of being transferred to the next growth cycle. The number of lineages from which resistant mutants were obtained was found to increase with successive growth cycles: from 2/96 (cycle 2)→8/96 (cycle 3)→15/96 (cycle 4). Because the spontaneous mutation rate to resistance (2×10−8) if much lower than the number of cells being tested from each lineage (5×106) it is very unlikely that these mutants arose on the selective media. Instead, the most reasonable conclusion is that the resistant mutants arose spontaneously and randomly during the growth of lineages in the absence of drug and were enriched because they out-competed the parent population. Three random drug-resistant mutants were chosen from independent lineages and tested by DNA sequencing for the presence of mutations in gyrA and B, in parC and E, and in marR and acrR. In each case the mutations originally present in LM695 were confirmed and in addition each of the mutants was found to have acquired a new mutation in parC . The MIC CIP of each of the mutants had increased from 0.75 to >32 µg/mL, and the exponential doubling time in rich medium had increased significantly, by ∼10% per generation  could also be generated by a variety of spontaneous mutations, and that the growth advantage phenotype could be enriched by growth selection in the absence of drug.In the sections above it was shown that the transfer of the ild-type . Second,neration . Thus, tE. coli strains was constructed and used to measure the relationship between the accumulation of fluoroquinolone resistance mutations, drug susceptibility, and growth fitness. The question was whether the accumulation of up to five resistance mutations, commonly found in resistant clinical isolates, would progressively reduce bacterial fitness. Most of the published data on the relationship between drug resistance and bacterial fitness would predict two possibilities: (i) that these mutations would cause little or no fitness cost, explaining their high frequency among resistant isolates; or (ii) that their accumulation would cause a progressive decrease in bacterial fitness, and require additional fitness-compensating mutations to restore fitness A set of 28 isogenic The main conclusions from the data set were the following:marR mutation had the largest negative effect on fitness.Some resistance mutations, individually or when incorporated in an already mutant strain, reduced drug susceptibility without significantly reducing fitness. Other mutations were individually or in combination associated with significant fitness costs. This suggests that selection for low-cost mutations, and/or compensating mutations could be selective forces determining the frequency of particular mutations individually or in combination. The and an increase in relative fitness . Thus, the combination of target mutations studied here is typical of resistant clinical isolates. As measured by organic solvent tolerance, drug efflux was phenotypically up-regulated in 15/30 of these resistant isolates, associated in most cases with mutations in acrR and/or marORThe particular How fluoroquinolone resistance evolves in nature will depend on the genotype being selected and on the selective environment E. coli K12 MG1655 wild-type was the starting strain for all constructions (C1186 is a multiply mutant fluoroquinolone resistant UTI isolate previously described ructions . Liquid www.clsi.org).MIC was determined by Etest  on Mueller-Hinton agar plates incubated for 16 to 18 h at 37°C with quality control reference strains gyrA and parC were selected sequentially in E. coli MG1655 in LB with ciprofloxacin at 2–8-fold MIC and mutations were identified by DNA sequencing. Individual mutations were always moved into a clean genetic background (MG1655) after initial selection. Deletion-replacement mutations in marR, acrR, yfaH, metC and araB were made by λ-red recombineering + Nad+ derivative of DY329) using PCR amplified linear DNA from pCP16 with an FRT-bounded TcR cassette Spontaneous resistance mutations in marR and acrR was selected directly on LA+Tc. When transducing the gyrA and parC mutations selection was made for the linked markers, yfaH<>Frt::TcR::Frt and metC<>Frt::TcR::Frt, each ∼10 kb from gyrA and parC, respectively. Note that we are using the symbol <> to indicate a replacement generated by λ red homologous recombination technology. After transduction the TcR marker was removed by Flp-catalyzed excision expressed following transformation with pCP20 Isogenic derivatives of MG1655 were constructed by phage P1-mediated transduction. Transduction of the deletion-replacement mutations in araB<>FRT) was used as the standard wild type strain in growth competitions against which each of the constructed mutant strains was competed. This strain was tested against its parent MG1655 showing that the ΔaraB mutation was neutral (relative growth rate 1.002±0.005). To support statistical analysis each competition was tested in at least 5 independent experiments  was made the number of times indicated in ara+) and white (ΔaraB) colonies were scored. The change in the ratio of mutant/wild-type was used to estimate the selection coefficient per generation of each of the constructed strains according to the formula: S = ln2 (mutant/wild-type) / generation S+1. Note that the fitness defects could be due to defects at any stage of the growth cycle .LM347  at 10-min intervals, using a BioscreenC machine .Exponential doubling times were calculated by measuring the increase in optical density at 600 nm  is 2×10topA-luc, and, pgyrA-luc, The relative supercoiling degree was determined using a published assay. The quotient of supercoiling, Qsc Table S1Oligonucleotides used to amplify linear PCR fragments for λ-red recombineering(0.03 MB DOC)Click here for additional data file.Text S1The ascending urinary tract infection model in mice.(0.03 MB DOC)Click here for additional data file.Text S2Supercoiling assay.(0.03 MB DOC)Click here for additional data file.


The role of mutation rate in optimizing key features of evolutionary dynamics has recently been investigated in various computational models. Here, we address the related question of how maximum mutation size affects the formation of species in a simple computational evolutionary model. We find that the number of species is maximized for intermediate values of a mutation size parameter μ; the result is observed for evolving organisms on a randomly changing landscape as well as in a version of the model where negative feedback exists between the local population size and the fitness provided by the landscape. The same result is observed for various distributions of mutation values within the limits set by μ. When organisms with various values of μ compete against each other, those with intermediate μ values are found to survive. The surviving values of μ from these competition simulations, however, do not necessarily coincide with the values that maximize the number of species. These results suggest that various complex factors are involved in determining optimal mutation parameters for any population, and may also suggest approaches for building a computational bridge between the (micro) dynamics of mutations at the level of individual organisms and (macro) evolutionary dynamics at the species level. H. Sturtevant posed this question from above are perhaps harder to untangle. A source of variation is obviously necessary for the process of natural selection. On the other hand, too high a mutation rate has obvious negative consequences optimum amount of variability?The origins of limits on mutation rates Drake's studies of microbial genetics showed similar mutation rates across a wide range of genome sizes current organism on the basis of that organism's descendants' increased ability to radiate into new ecological niches. In other words, the fact that a higher mutation rate will help later generations does not explain how it can be selected for in the current generation, for which it does not have a clear advantage. As a result, mutations in genes that control mutation rate may often hitchhike along with other mutations that confer immediate selective advantage The question of mutation rate optimization is compounded by the problem of causality, to the extent that an increased mutation rate cannot be selected for in a whether an intermediate mutation rate can optimize fitness. In the present paper, we investigate a closely related problem, the optimization of the number of species as a function of maximum mutation size. Since we pose similar questions and take a similar approach to those of the three papers just cited – though in the context of speciation rather than of individual fitness – we briefly review each of those works.Several recent computational studies have addressed the problem of optimum mutation rate. Three of these studies, Bedau and Packard novelty (adaptability) and evolutionary memory (adaptedness). They explored the optimization of fitness as a function of mutation rate in a model of reproducing agents on a toroidal lattice; the agents consumed energy from a “continually augmented external source”, and reproduced when they had accumulated sufficient resources to split into two organisms. The organisms were characterized by their strategies of interacting with the environment and gathering resources; their fitness, defined as the amount of food gathered, was found to be optimized for an intermediate mutation rate, where the mutation rate represented the rate at which strategy elements were selected from a pool of possible behaviors. Bedau and Packard also performed simulations in which agents with different mutation rates competed against each other; they found that those with a specific intermediate mutation rate were the most successful. Using measures of diversity, they also demonstrated that “the mutation rate governs a transition between two qualitatively different phases of evolutionary dynamics”, namely a more ordered state characterized by long periods of stasis for low mutation rates, and highly disordered dynamics where “the gene pool tends to be a continually changing plethora” of strategies at high mutation rates Bedau and Packard different evolvability characteristics can be optimal under different circumstances. This result was already suggested by the bacteriophage and Drosophila studies cited above; it appears again in another computational evolutionary model, that of Clune et al. Earl and Deem is optimal, it may not be reachable via a natural selection algorithm operating on a highly rugged landscape. The authors interpret this in terms of the short term vs. long term cost of mutation rates: a high mutation rate would provide the benefit of rare large mutations that could “carry the organism over a valley to the next fitness peak”, but would also exact a high energetic cost due to the occurrence of mutations that are “not quite large enough”, costing the organism dearly, but leaving it stranded in the valley it was trying to escape. Clune et al. contrast their results with studies suggesting that high mutation rates can be optimal in all circumstances, commenting that “it seems unlikely that stably high mutation rates, such as those for RNA viruses, are maintained primarily because of the rapid adaptive capacity they bestow, as has sometimes been argued” Clune et al. The three studies summarized above address the optimization of a measure of individual organismal fitness. However, individual fitness is not the only quantity that can be optimized by natural selection. Darwin himself explored the idea that diversity itself may be selected for, and that phyla that are better at radiating may also be better at flourishing. This can be envisioned as an optimal filling of morphospace or, in more nineteenth-century terms, as a “Benthamite optimization calculus” variability, heritability and overpopulation, in the simplest possible manner. Organisms exist in a two-dimensional morphospace, where each axis represents a hypothetical phenotype. At each time step, a new generation of organisms is produced via an assortative mating algorithm. The number of new organisms depends on an underlying fitness landscape; the locations of new organisms in the morphospace are determined by the locations of their parent organisms, as well as by the mutation size. We investigate the clustering of organisms, where clusters are defined as reproductively isolated groups and serve as an analogue of species, as a function of maximum mutation size.The motivation for the design of the present model, implemented in MATLAB, was to incorporate the three fundamental aspects of Darwinian evolution, Simulated organisms exist on a landscape in a two-dimensional morphospace, with the x- and y-coordinates corresponding, respectively, to a given organism's two traits. This is illustrated in The model uses assortative mating, whereby, in each generation, every organism picks the nearest other organism in the landscape and mates with it to produce new organisms for the next generation. The choice of an assortative mating scheme is motivated at once by its simplicity and its realism. Recalling that the organisms exist in a morphospace rather than a physical space, it should be immediately apparent that the simplest realistic mating scheme is one in which phenotypically similar organisms mate with each other rather than with more phenotypically distant organisms.Assortative mating schemes have been extensively used in various studies, such as investigations of the mechanisms of sympatric cx1,cy1) and  are the morphospace coordinates of the two parent organisms, the coordinates  of a next-generation organism are given byuniform distribution between 0 and 1, and where μ represents the maximum possible mutation size.If  of a new organism are calculated as follows:normal distribution with zero mean, and b = 0.1581. Again, μ represents the maximum mutation size. Thus, for both versions of the model, the coordinates of each new organism are randomly chosen to lie within a range defined by the coordinates of the parents, but with the boundaries of the range extended by the parameter μ. Note that μ can be easily related to a mutation rate M by integrating the rate over (generation) time. Thus,M is constant, then the maximum mutation size μ will be directly proportional to the mutation rate M.In another version of the experiment, the coordinates  shifting gradually or (2) being altered by feedback from the local density of organisms.n+1 position, leaving a “hole” at the first column of the matrix, which is replaced by 12 new, randomly-generated values, after which interpolation is performed again to generate a 45×45 landscape. These operations have the effect of shifting the landscape gradually to the right. The parameter λ was set at 2 throughout the simulations shown here.For the randomly shifting landscape, every λ generations, the last column is deleted from the 12×12 random matrix underlying the fitness landscape. The other n columns are shifted to the For landscapes modulated by feedback, in every generation, the fitness value at each location in the landscape grid was decreased by an amount proportional to the number of organisms living in the region. For the models implemented here, the proportionality was set at 0.0071. These reactive changes in the landscape symbolize the depletion by over-use of the available resources in a given ecological niche. The total summation of fitness values available across the entire landscape was conserved in each generation; this was done by adding back the entire subtracted quantity after dividing it equally amongst each of the 144 elements of the fitness landscape matrix (before interpolation). Through this method, areas in the morphospace which were unaffected by the subtraction (areas whose resources were not depleted) become increasingly advantageous for reproduction.In order to introduce further randomness into the model, a fraction ρ of the new organisms are randomly eliminated before the start of the new generation, where, for each generation, ρ is a random number selected from a uniform distribution between 0 and 0.70. The effects of overpopulation are implemented by setting a distance limit within which only one organism can exist. In all the implementations of the model shown here, the overpopulation limit is set at 0.25.In order to investigate the interactions between organisms with different mutation parameters, the model was modified so that each organism was assigned not only coordinates in the morphospace, but also a distinct value of μ . The mutation parameter μ for each individual in the initial population was selected randomly from a uniform distribution between 0 and 1. Note that the choice of a maximum value of μ = 1 is motivated solely by the range of μ values used in other simulations shown here; there is no a priori limit for the value of μ.The simulation was performed identically to the other simulations , except that each new organism takes the μ value of one of its parents.biological species, in which species are defined as reproductively isolated groups, i.e., groups with the ability to interbreed, developed by Dobzhansky, Mayr and others in the early days of the modern synthesis Clusters, the analog of species in our model, are determined by who mates with whom. The development of this algorithm was motivated by the concept of As implemented here, the clustering algorithm is carried out as follows. For a given organism in a given generation, a search is performed to find all the organisms that it, as well as its nearest neighbor (its mate) and its second-nearest neighbor, have mated with. Then a similar search is performed for each of the organisms found during this first search. This iterative search continues until a closed set – a cluster – is obtained, where all organisms within the set have mated, in that generation, only within the set. This algorithm assigns each organism to one, and only one, cluster, and arrives at a unique solution for each generation.inspired by, rather than being an explicit implementation of, the biological species concept. Several points need to be mentioned in this regard.It should be clarified that the definition of clusters implemented here is based on “who does mate with whom” rather than “who can mate with whom”, and thus we have described it as being can be interpreted as defining “who can mate with whom”. Consider one individual in the cluster, and its mate. A third organism which mates with the mate is also included in the cluster, and therefore the first individual chosen to seed the cluster could presumably mate with this third individual, under an expanded version of our assortative mating criterion. To this extent, we do indeed implement a criterion of “who could mate with whom”.First, let us consider the extent to which our cluster definition top-down definition of clusters . Such a top-down definition would undermine the crux of the approach taken here, which is to capture fundamental dynamical features which emerge naturally from a model satisfying certain basic criteria of evolving systems.A second point to be emphasized is that a more explicit implementation of the rigorous definition of biological species would necessitate a After all the parent organisms in a given generation have produced a new generation of organisms and some of the new organisms have been culled, the parent organisms vanish and a new generation begins, with the previous offspring now playing the role of parents. In the implementation of the model used here, the initial generation consisted of 300 individuals randomly placed within the landscape; during subsequent generations the population fluctuated between several hundred and nearly ten thousand organisms.Five experiments were performed: (1) uniformly distributed mutations with shifting fitness landscape, (2) uniformly distributed mutations with feedback-modulated landscape, (3) normally distributed mutations with shifting fitness landscape, (4) normally distributed mutations with feedback-modulated landscape, and (5) competition between organisms with different maximum mutation parameters (μ) on a shifting fitness landscape with uniformly distributed mutation values within the limits set by μ.Experiments (1)–(4) were run for a range of values of μ, with all other parameters held constant. For each experiment and at each value of μ, the simulation was allowed to run for 1000 generations; in some cases, the population became extinct before 1000 generations were reached. Over the course of each simulation, various parameters were recorded at each generation, such as the total population size, the number of clusters, the mean distance between individuals in a cluster, etc. For each experiment, five runs were performed at each value of μ.The results of a typical simulation after 1000 generations are shown in In some cases, simulations with identical parameters exhibited a high degree of historical contingency, as illustrated in In In order to obtain a measure of the diversity within species/clusters, we calculated the mean Euclidean distance in the morphospace between individuals in a cluster. This value was averaged over all clusters and all generations to give the within-cluster diversity at a given μ. This diversity measure is shown, averaged over five realizations of the model at each value of μ, in the time series of the population size and the time series of the number of clusters. At values of μ for which the population size and number of clusters sharply increase, however, the correlation coefficient drops, and also shows an increase in variability from one simulation run to another, indicated by the increased standard deviation. For some runs, there is a positive correlation between population and clusters; for others, a negative correlation. As μ reaches values corresponding to the population plateau, a consistent anticorrelation is observed between the two quantities.does not preclude others from doing the same. A traced organism has the original labeled organism as one of its ancestors, but this does not imply that this was its only ancestor. The fact that the final fraction of traced organisms increases with μ is likely a result of the increased mixing of the population as μ increases.In order to investigate the spread of an organism's descendents through the population, a random organism of the initial generation was labeled, and its descendents traced through subsequent generations. The maximum ratio of labeled organisms to total organisms is illustrated in different values of μ dominate in different runs of the simulation, and the surviving μ  that gives a maximal number of species for the shifting landscape model with uniformly distributed mutations  will increase the width of the normal distribution of mutation sizes, shifting the plots to the left.The model studied here is remarkably robust across various modifications, including changes in how the landscape varies  and in the distribution of mutation sizes . However, some differences do occur between the various implementations of the model. For example, the cases where mutation sizes are normally distributed  and 6 exA second difference among the different versions of the model concerns the sharpness in the drop of the correlation between population size and number of clusters. For the models without feedback  and 5d torder parameters characterizing the system. Not only do these parameters exhibit sharp changes in their mean values as a function of μ, but they also exhibit large fluctuations  during the transition, another characteristic of phase transitions. It is possible that further investigation of this and related models from such a statistical physics perspective may be of critical importance in understanding the role of mutation rate and mutation size in modulating speciation. Moreover, such models may eventually begin to touch upon a fundamental problem of evolutionary biology: the bridge between micro  and macro  levels. The phase transition behavior observed here is particularly tantalizing in this regard, since a key characteristic of phase transitions is the co-existence of multiple scales of behavior. Further, in the model presented here, properties at the individual level (such as the parameter μ) affect the global dynamics of the entire population, both by modulating the formation of clusters, and modulating the average properties of these clusters. It should be emphasized that this relation between scales is fundamentally in the spirit of statistical physics, where microscopic dynamics determine global, macroscopic behavior.For all versions of the model, sharp changes are observed in various quantities characterizing the system as μ is varied. These sharp changes are strongly reminiscent of phase transitions, with population size, number of clusters and population-cluster correlation serving as If an intermediate mutation parameter maximizes the number of clusters, does this mean that this value of μ is optimal? The competition experiment illustrated in It is striking that multiple stable populations with different values of μ have not been found to coexist in this model. However, the simulations did not allow for the reemergence of extinct mutation values, and thus perhaps the eventual dominance of a single value of μ may be inevitable, especially given the system's tendency in the limit of a large number of generations to exhibit a fully mixed population where all organisms share at least one common ancestor (as shown in