Evolutionary accessibility of mutational pathways

Functional effects of different mutations are known to combine to the total effect in highly nontrivial ways. For the trait under evolutionary selection (`fitness'), measured values over all possible combinations of a set of mutations yield a fitness landscape that determines which mutational states can be reached from a given initial genotype. Understanding the accessibility properties of fitness landscapes is conceptually important in answering questions about the predictability and repeatability of evolutionary adaptation. Here we theoretically investigate accessibility of the globally optimal state on a wide variety of model landscapes, including landscapes with tunable ruggedness as well as neutral `holey' landscapes. We define a mutational pathway to be accessible if it contains the minimal number of mutations required to reach the target genotype, and if fitness increases in each mutational step. Under this definition accessibility is high, in the sense that at least one accessible pathwayexists with a substantial probability that approaches unity as the dimensionality of the fitness landscape (set by the number of mutational loci) becomes large. At the same time the number of alternative accessible pathways grows without bound. We test the model predictions against an empirical 8-locus fitness landscape obtained for the filamentous fungus \textit{Aspergillus niger}. By analyzing subgraphs of the full landscape containing different subsets of mutations, we are able to probe the mutational distance scale in the empirical data. The predicted effect of high accessibility is supported by the empirical data and very robust, which we argue to reflect the generic topology of sequence spaces.Comment: 16 pages, 4 figures; supplementary material available on reques

Long-term experimental evolution in Escherichia coli. XI. Rejection of non-transitive interactions as cause of declining rate of adaptation

BACKGROUND: Experimental populations of Escherichia coli have evolved for 20,000 generations in a uniform environment. Their rate of improvement, as measured in competitions with the ancestor in that environment, has declined substantially over this period. This deceleration has been interpreted as the bacteria approaching a peak or plateau in a fitness landscape. Alternatively, this deceleration might be caused by non-transitive competitive interactions, in particular such that the measured advantage of later genotypes relative to earlier ones would be greater if they competed directly. RESULTS: To distinguish these two hypotheses, we performed a large set of competitions using one of the evolved lines. Twenty-one samples obtained at 1,000-generation intervals each competed against five genetically marked clones isolated at 5,000-generation intervals, with three-fold replication. The pattern of relative fitness values for these 315 pairwise competitions was compared with expectations under transitive and non-transitive models, the latter structured to produce the observed deceleration in fitness relative to the ancestor. In general, the relative fitness of later and earlier generations measured by direct competition agrees well with the fitness inferred from separately competing each against the ancestor. These data thus support the transitive model. CONCLUSION: Non-transitive competitive interactions were not a major feature of evolution in this population. Instead, the pronounced deceleration in its rate of fitness improvement indicates that the population early on incorporated most of those mutations that provided the greatest gains, and subsequently relied on beneficial mutations that were fewer in number, smaller in effect, or both

Environmental stress and the effects of mutation

Mutations are the ultimate fuel for evolution, but most mutations have a negative effect on fitness. It has been widely accepted that these deleterious fitness effects are, on average, magnified in stressful environments. Recent results suggest that the effects of deleterious mutations can, instead, sometimes be ameliorated in stressful environments

Quantitative analyses of empirical fitness landscapes

The concept of a fitness landscape is a powerful metaphor that offers insight into various aspects of evolutionary processes and guidance for the study of evolution. Until recently, empirical evidence on the ruggedness of these landscapes was lacking, but since it became feasible to construct all possible genotypes containing combinations of a limited set of mutations, the number of studies has grown to a point where a classification of landscapes becomes possible. The aim of this review is to identify measures of epistasis that allow a meaningful comparison of fitness landscapes and then apply them to the empirical landscapes to discern factors that affect ruggedness. The various measures of epistasis that have been proposed in the literature appear to be equivalent. Our comparison shows that the ruggedness of the empirical landscape is affected by whether the included mutations are beneficial or deleterious and by whether intra- or intergenic epistasis is involved. Finally, the empirical landscapes are compared to landscapes generated with the Rough Mt.\ Fuji model. Despite the simplicity of this model, it captures the features of the experimental landscapes remarkably well.Comment: 24 pages, 5 figures; to appear in Journal of Statistical Mechanics: Theory and Experimen

Mutation supply and the repeatability of selection for antibiotic resistance

Whether evolution can be predicted is a key question in evolutionary biology. Here we set out to better understand the repeatability of evolution. We explored experimentally the effect of mutation supply and the strength of selective pressure on the repeatability of selection from standing genetic variation. Different sizes of mutant libraries of an antibiotic resistance gene, TEM-1 $\beta$-lactamase in Escherichia coli, were subjected to different antibiotic concentrations. We determined whether populations went extinct or survived, and sequenced the TEM gene of the surviving populations. The distribution of mutations per allele in our mutant libraries- generated by error-prone PCR- followed a Poisson distribution. Extinction patterns could be explained by a simple stochastic model that assumed the sampling of beneficial mutations was key for survival. In most surviving populations, alleles containing at least one known large-effect beneficial mutation were present. These genotype data also support a model which only invokes sampling effects to describe the occurrence of alleles containing large-effect driver mutations. Hence, evolution is largely predictable given cursory knowledge of mutational fitness effects, the mutation rate and population size. There were no clear trends in the repeatability of selected mutants when we considered all mutations present. However, when only known large-effect mutations were considered, the outcome of selection is less repeatable for large libraries, in contrast to expectations. Furthermore, we show experimentally that alleles carrying multiple mutations selected from large libraries confer higher resistance levels relative to alleles with only a known large-effect mutation, suggesting that the scarcity of high-resistance alleles carrying multiple mutations may contribute to the decrease in repeatability at large library sizes.Comment: 31pages, 9 figure

When should root remnants and unrestorable broken teeth be extracted in frail older adults?

BACKGROUND: Many frail older adults have an unhealthy dentition; unrestorable broken teeth and root remnants with open root canals, commonly accompanied by periapical and periodontal inflammation, are often seen. Improving oral health in the growing group of frail older adults with remaining teeth is a considerable challenge for dental care professionals. Dentists are often uncertain how to deal with root remnants and unrestorable broken teeth in frail older adults. METHODS: The authors aim was to provide recommendations to dentists to help in their clinical decision making about the extraction or retention of roots remnants and broken teeth in frail older adults. CONCLUSIONS: Decisions about the extraction or retention of root remnants should made on the basis of preventing pain and oral discomfort, preventing severe inflammation, and preventing additional decline in oral health. Both root-related and patient-related factors are considered. PRACTICAL IMPLICATIONS: Decision-making trees can help dentists decide whether to extract root remnants and unrestorable broken teeth in frail older adults

Power provides protection : genetic robustness in yeast depends on the capacity to generate energy

The functional basis of genetic robustness, the ability of organisms to suppress the effects of mutations, remains incompletely understood. We exposed a set of 15 strains of Saccharomyces cerevisiae form diverse environments to increasing doses of the chemical mutagen EMS. The number of the resulting random mutations was similar for all tested strains. However, there were differences in immediate mortality after the mutagenic treatment and in defective growth of survivors. An analysis of gene expression revealed that immediate mortality was lowest in strains with lowest expression of transmembrane proteins, which are rich in thiol groups and thus vulnerable to EMS. A signal of genuine genetic robustness was detected for the other trait, the ability to grow well despite bearing non-lethal mutations. Increased tolerance of such mutations correlated with high expression of genes responsible for the oxidative energy metabolism, suggesting that the negative effect of mutations can be buffered if enough energy is available. We confirmed this finding in three additional tests of the ability to grow on (i) fermentable or non-fermentable sources of carbon, (ii) under chemical inhibition of the electron transport chain and (iii) during overexpression of its key component, cytochrome c. Our results add the capacity to generate energy as a general mechanism of genetic robustness