Epistasis for growth rate and total metabolic flux in yeast

Studies of interactions between gene deletions repeatedly show that the effect of epistasis on the growth of yeast cells is roughly null or barely positive. These observations relate generally to the pace of growth, its costs in terms of required metabolites and energy are unknown. We measured the maximum rate at which yeast cultures grow and amounts of glucose they consume per synthesized biomass for strains with none, single, or double gene deletions. Because all strains were maintained under a fermentative mode of growth and thus shared a common pattern of metabolic processes, we used the rate of glucose uptake as a proxy for the total flux of metabolites and energy. In the tested sample, the double deletions showed null or slightly positive epistasis both for the mean growth and mean flux. This concordance is explained by the fact that average efficiency of converting glucose into biomass was nearly constant, that is, it did not change with the strength of growth effect. Individual changes in the efficiency caused by gene deletions did have a genetic basis as they were consistent over several environments and transmitted between single and double deletion strains indicating that the efficiency of growth, although independent of its rate, was appreciably heritable. Together, our results suggest that data on the rate of growth can be used as a proxy for the rate of total metabolism when the goal is to find strong individual interactions or estimate the mean epistatic effect. However, it may be necessary to assay both growth and flux in order to detect smaller individual effects of epistasis.     

Effect of varying epistasis on the evolution of recombination

Whether recombination decelerates or accelerates a population's response to selection depends, at least in part, on how fitness-determining loci interact. Realistically, all genomes likely contain fitness interactions both with positive and with negative epistasis. Therefore, it is crucial to determine the conditions under which the potential beneficial effects of recombination with negative epistasis prevail over the detrimental effects of recombination with positive epistasis. Here, we examine the simultaneous effects of diverse epistatic interactions with different strengths and signs in a simplified model system with independent pairs of interacting loci and selection acting only on the haploid phase. We find that the average form of epistasis does not predict the average amount of linkage disequilibrium generated or the impact on a recombination modifier when compared to results using the entire distribution of epistatic effects and associated single-mutant effects. Moreover, we show that epistatic interactions of a given strength can produce very different effects, having the greatest impact when selection is weak. In summary, we observe that the evolution of recombination at mutation-selection balance might be driven by a small number of interactions with weak selection rather than by the average epistasis of all interactions. We illustrate this effect with an analysis of published data of Saccharomyces cerevisiae. Thus to draw conclusions on the evolution of recombination from experimental data, it is necessary to consider the distribution of epistatic interactions together with the associated selection coefficients.     

GENETIC LOAD OF THE YEAST SACCHAROMYCES CEREVISIAE UNDER DIVERSE ENVIRONMENTAL CONDITIONS

Fitness effect of spontaneous mutations accumulated in mismatch-repair deficient strains of yeast was estimated by measuring their maximum growth rate. Several environments with different energetic substrates, nutritional conditions, and temperature were tested. Genetic load of haploid strains was about 20–30% under most of these conditions. Because such a pronounced effect was caused by relatively small lesions (point mutations) affecting probably less than 1% of genes, resistance of the yeast genome to DNA damage appears to be rather limited. Fitness transitions among environments were orderly, in the sense that some strains tended to be more or less fit than others in all circumstances. One of the environments (an extremely high temperature, 38°C) was stressful to the strains that accumulated mutations, as some of them stopped to grow, whereas the mutation-free strains were only moderately affected. These results imply that the impact of random point mutations is substantial and generally not dependent on a particular environment. Under stressful conditions, however, natural selection may be especially effective in purging mutations that, if commonly met, could slow down the rate of mutation accumulation.     

Evolution of genetic architecture under directional selection

We investigate the multilinear epistatic model under mutation-limited directional selection. We confirm previous results that only directional epistasis, in which genes on average reinforce or diminish each other's effects, contribute to the initial evolution of mutational effects. Thus, either canalization or decanalization can occur under directional selection, depending on whether positive or negative epistasis is prevalent. We then focus on the evolution of the epistatic coefficients themselves. In the absence of higher-order epistasis, positive pairwise epistasis will tend to weaken relative to additive effects, while negative pairwise epistasis will tend to become strengthened. Positive third-order epistasis will counteract these effects, while negative third-order epistasis will reinforce them. More generally, gene interactions of all orders have an inherent tendency for negative changes under directional selection, which can only be modified by higher-order directional epistasis. We identify three types of nonadditive quasi-equilibrium architectures that, although not strictly stable, can be maintained for an extended time: (1) nondirectional epistatic architectures; (2) canalized architectures with strong epistasis; and (3) near-additive architectures in which additive effects keep increasing relative to epistasis.     

Epistatic interaction maps relative to multiple metabolic phenotypes

An epistatic interaction between two genes occurs when the phenotypic impact of one gene depends on another gene, often exposing a functional association between them. Due to experimental scalability and to evolutionary significance, abundant work has been focused on studying how epistasis affects cellular growth rate, most notably in yeast. However, epistasis likely influences many different phenotypes, affecting our capacity to understand cellular functions, biochemical networks adaptation, and genetic diseases. Despite its broad significance, the extent and nature of epistasis relative to different phenotypes remain fundamentally unexplored. Here we use genome-scale metabolic network modeling to investigate the extent and properties of epistatic interactions relative to multiple phenotypes. Specifically, using an experimentally refined stoichiometric model for Saccharomyces cerevisiae, we computed a three-dimensional matrix of epistatic interactions between any two enzyme gene deletions, with respect to all metabolic flux phenotypes. We found that the total number of epistatic interactions between enzymes increases rapidly as phenotypes are added, plateauing at approximately 80 phenotypes, to an overall connectivity that is roughly 8-fold larger than the one observed relative to growth alone. Looking at interactions across all phenotypes, we found that gene pairs interact incoherently relative to different phenotypes, i.e. antagonistically relative to some phenotypes and synergistically relative to others. Specific deletion-deletion-phenotype triplets can be explained metabolically, suggesting a highly informative role of multi-phenotype epistasis in mapping cellular functions. Finally, we found that genes involved in many interactions across multiple phenotypes are more highly expressed, evolve slower, and tend to be associated with diseases, indicating that the importance of genes is hidden in their total phenotypic impact. Our predictions indicate a pervasiveness of nonlinear effects in how genetic perturbations affect multiple metabolic phenotypes. The approaches and results reported could influence future efforts in understanding metabolic diseases and the role of biochemical regulation in the cell.     

Combinatorial Strategies for Improving Multiple-Stress Resistance in Industrially Relevant Escherichia coli Strains

High-cell-density fermentation for industrial production of chemicals can impose numerous stresses on cells due to high substrate, product, and by-product concentrations; high osmolarity; reactive oxygen species; and elevated temperatures. There is a need to develop platform strains of industrial microorganisms that are more tolerant toward these typical processing conditions. In this study, the growth of six industrially relevant strains of Escherichia coli was characterized under eight stress conditions representative of fed-batch fermentation, and strains W and BL21(DE3) were selected as platforms for transposon (Tn) mutagenesis due to favorable resistance characteristics. Selection experiments, followed by either targeted or genome-wide next-generation-sequencing-based Tn insertion site determination, were performed to identify mutants with improved growth properties under a subset of three stress conditions and two combinations of individual stresses. A subset of the identified loss-of-function mutants were selected for a combinatorial approach, where strains with combinations of two and three gene deletions were systematically constructed and tested for single and multistress resistance. These approaches allowed identification of (i) strain-background-specific stress resistance phenotypes, (ii) novel gene deletion mutants in E. coli that confer single and multistress resistance in a strain-background-dependent manner, and (iii) synergistic effects of multiple gene deletions that confer improved resistance over single deletions. The results of this study underscore the suboptimality and strain-specific variability of the genetic network regulating growth under stressful conditions and suggest that further exploration of the combinatorial gene deletion space in multiple strain backgrounds is needed for optimizing strains for microbial bioprocessing applications.     

Parallel emergence of negative epistasis across experimental lineages

Epistatic interactions can greatly impact evolutionary phenomena, particularly the process of adaptation. Here, we leverage four parallel experimentally evolved lineages to study the emergence and trajectories of epistatic interactions in the social bacterium Myxococcus xanthus. A social gene (pilA) necessary for effective group swarming on soft agar had been deleted from the common ancestor of these lineages. During selection for competitiveness at the leading edge of growing colonies, two lineages evolved qualitatively novel mechanisms for greatly increased swarming on soft agar, whereas the other two lineages evolved relatively small increases in swarming. By reintroducing pilA into different genetic backgrounds along the four lineages, we tested whether parallel lineages showed similar patterns of epistasis. In particular, we tested whether a pattern of negative epistasis between accumulating mutations and pilA previously found in the fastest lineage would be found only in the two evolved lineages with the fastest and most striking swarming phenotypes, or rather was due to common epistatic structure across all lineages arising from the generic fixation of adaptive mutations. Our analysis reveals the emergence of negative epistasis across all four independent lineages. Further, we present results showing that the observed negative epistasis is not due exclusively to evolving populations approaching a maximum phenotypic value that inherently limits positive effects of pilA reintroduction, but rather involves direct antagonistic interactions between accumulating mutations and the reintroduced social gene.     

Epistasis and the mutation load: a measurement-theoretical approach

An approximate solution for the mean fitness in mutation-selection balance with arbitrary order of epistatic interaction is derived. The solution is based on the assumptions of coupling equilibrium and that the interaction effects are multilinear. We find that the effect of m-order epistatic interactions (i.e., interactions among groups of m loci) on the load is dependent on the total genomic mutation rate, U, to the mth power. Thus, higher-order gene interactions are potentially important if U is large and the interaction density among loci is not too low. The solution suggests that synergistic epistasis will decrease the mutation load and that variation in epistatic effects will elevate the load. Both of these results, however, are strictly true only if they refer to epistatic interaction strengths measured in the optimal genotype. If gene interactions are measured at mutation-selection equilibrium, only synergistic interactions among even numbers of genes will reduce the load. Odd-ordered synergistic interactions will then elevate the load. There is no systematic relationship between variation in epistasis and load at equilibrium. We argue that empirical estimates of gene interaction must pay attention to the genetic background in which the effects are measured and that it may be advantageous to refer to average interaction intensities as measured in mutation-selection equilibrium. We derive a simple criterion for the strength of epistasis that is necessary to overcome the twofold disadvantage of sex.     

Epistasis and its relationship to canalization in the RNA virus phi 6

Although deleterious mutations are believed to play a critical role in evolution, assessing their realized effect has been difficult. A key parameter governing the effect of deleterious mutations is the nature of epistasis, the interaction between the mutations. RNA viruses should provide one of the best systems for investigating the nature of epistasis because the high mutation rate allows a thorough investigation of mutational effects and interactions. Nonetheless, previous investigations of RNA viruses by S. Crotty and co-workers and by S. F. Elena have been unable to detect a significant effect of epistasis. Here we provide evidence that positive epistasis is characteristic of deleterious mutations in the RNA bacteriophage phi 6. We estimated the effects of deleterious mutations by performing mutation-accumulation experiments on five viral genotypes of decreasing fitness. We inferred positive epistasis because viral genotypes with low fitness were found to be less sensitive to deleterious mutations. We further examined environmental sensitivity in these genotypes and found that low-fitness genotypes were also less sensitive to environmental perturbations. Our results suggest that even random mutations impact the degree of canalization, the buffering of a phenotype against genetic and environmental perturbations. In addition, our results suggest that genetic and environmental canalization have the same developmental basis and finally that an understanding of the nature of epistasis may first require an understanding of the nature of canalization.     

Magnitude and sign epistasis among deleterious mutations in a positive-sense plant RNA virus

How epistatic interactions between mutations determine the genetic architecture of fitness is of central importance in evolution. The study of epistasis is particularly interesting for RNA viruses because of their genomic compactness, lack of genetic redundancy, and apparent low complexity. Moreover, interactions between mutations in viral genomes determine traits such as resistance to antiviral drugs, virulence and host range. In this study we generated 53 Tobacco etch potyvirus genotypes carrying pairs of single-nucleotide substitutions and measured their separated and combined deleterious fitness effects. We found that up to 38% of pairs had significant epistasis for fitness, including both positive and negative deviations from the null hypothesis of multiplicative effects. Interestingly, the sign of epistasis was correlated with viral protein-protein interactions in a model network, being predominantly positive between linked pairs of proteins and negative between unlinked ones. Furthermore, 55% of significant interactions were cases of reciprocal sign epistasis (RSE), indicating that adaptive landscapes for RNA viruses maybe highly rugged. Finally, we found that the magnitude of epistasis correlated negatively with the average effect of mutations. Overall, our results are in good agreement to those previously reported for other viruses and further consolidate the view that positive epistasis is the norm for small and compact genomes that lack genetic robustness.     

Small fitness effects and weak genetic interactions between deleterious mutations in heterozygous loci of the yeast Saccharomyces cerevisiae

Rare, random mutations were induced in budding yeast by ethyl methanesulfonate (EMS). Clones known to bear a single non-neutral mutation were used to obtain mutant heterozygotes and mutant homozygotes that were later compared with wild-type homozygotes. The average homozygous effect of mutation was an approximately 2% decrease in the growth rate. In heterozygotes, the harmful effect of these relatively mild mutations was reduced approximately fivefold. In a test of epistasis, two heterozygous mutant loci were paired at random. Fitness of the double mutants was best explained by multiplicative action of effects at single loci, with little evidence for epistasis and essentially excluding synergism. In other experiments, the same mutations in haploid and heterozygous diploid clones were compared. Regardless of the haploid phenotypes, mildly deleterious or lethal, fitness of the heterozygotes was decreased by less than half a per cent on average. In general, the results presented here suggest that most mutations tend to exhibit small and weakly interacting effects in heterozygous loci regardless of how harmful they are in haploids or homozygotes.     

Gene regulatory networks generating the phenomena of additivity, dominance and epistasis

We show how the phenomena of genetic dominance, overdominance, additivity, and epistasis are generic features of simple diploid gene regulatory networks. These regulatory network models are together sufficiently complex to catch most of the suggested molecular mechanisms responsible for generating dominant mutations. These include reduced gene dosage, expression or protein activity (haploinsufficiency), increased gene dosage, ectopic or temporarily altered mRNA expression, increased or constitutive protein activity, and dominant negative effects. As classical genetics regards the phenomenon of dominance to be generated by intralocus interactions, we have studied two one-locus models, one with a negative autoregulatory feedback loop, and one with a positive autoregulatory feedback loop. To include the phenomena of epistasis and downstream regulatory effects, a model of a three-locus signal transduction network is also analyzed. It is found that genetic dominance as well as overdominance may be an intra- as well as interlocus interaction phenomenon. In the latter case the dominance phenomenon is intimately connected to either feedback-mediated epistasis or downstream-mediated epistasis. It appears that in the intra- as well as the interlocus case there is considerable room for additive gene action, which may explain to some degree the predictive power of quantitative genetic theory, with its emphasis on this type of gene action. Furthermore, the results illuminate and reconcile the prevailing explanations of heterosis, and they support the old conjecture that the phenomenon of dominance may have an evolutionary explanation related to life history strategy.     

Unimodal diversity-productivity relationship emerged under stressful environment through sampling effect

Researches on the context dependence of biodiversity and ecosystem functioning (BEF) reveal the variation of diversity-productivity relationship (DPR) under stressful environment. The “habitat sampling effect” (HSE) is proposed as the dominant species interaction mechanism at stressful environment, whereas its potential role in driving the DPR has never been testified before. We constructed an individual-based simulation model to explore the variation of DPR along environmental stress gradient, and evaluated the contribution of HSE in explaining this variation. Our results indicated that DPR changed from positive to negative along environmental stress gradients. An unimodal DPR curve emerged at stressful environment, which was caused by the counterbalance of two opposite impacts of HSE on community productivity. At low richness level, the positive impact of HSE on community productivity dominated through the promotion of community size, which resulted in the positive DPR. Whereas with the increase of richness, the negative impact of HSE dominated instead through the reducing of individual productivity, which caused the decreasing part of unimodal curve. Our results highlight the complex characteristic of BEF relationship at stressful environment, and emphasize the necessity of biodiversity in maintaining community's functioning at stressful environment which are often sparse in species richness.     

Size and growth relationships in juvenile steelhead: The advantage of large relative size diminishes with increasing water temperatures

In territorial stream salmonids, asymmetric competition can perpetuate individual size differences over time, but the extent to which this is manifested can be environmentally mediated. Here we study the variation in juvenile steelhead (Oncorhynchus mykiss) growth rates to identify the conditions (population density and water temperature) under which an individual’s size relative to its conspecifics conferred an advantage. Among steelhead rearing in the same stream section we found that relatively larger individuals on average grew faster than smaller conspecifics. However, comparing across stream sections there was a negative interaction between relative size and water temperature. The effect of an individual’s relative size on its growth rate decreased as temperatures were increasing, indicating that the advantages of being large diminished during periods of high temperatures or in locations with relatively higher temperatures. Compared to temperature, the effects of population density on the growth rate were less substantial. The results suggest that larger individuals on average acquire more resources than smaller individuals, and demonstrate that water temperature exerts an important, modulating control over growth performance in heterogeneous environments.     

Balance of Competitive and Facilitative Effects of Exotic Trees on a Native Patagonian Grass

The balance between facilitation and competition in plants changes with species characteristics and environmental conditions. Facilitative effects are common in natural ecosystems, particularly in stressful environments or years. Contrarily, in artificial associations of plants, such as agroforestry systems, some authors have suggested that even when facilitative effects may occur, net balance of tree effects on grasses is usually negative, particularly in dry environments. The aim of this study was to determine the net effect of the exotic ponderosa pine on the native grass Festuca pallescens (St. Ives) Parodi in agroforestry systems in Patagonia. Soil water content, plant water status, and relative growth were measured in the grass growing in different treatments (determined by tree cover level) during two growing seasons with contrasting climatic conditions. Facilitative effects of trees over grass water status were recorded only when water availability was high. A net negative effect was detected on dates when soil water content was very low and evaporative demand was high. The strength of these negative effects depended on tree density and climatic conditions, being higher in treatments with lower tree canopy cover. These results indicate that the positive effect of trees could only be expected under relatively low stress conditions. However, relative growth of grasses was always similar in plants growing in forested plots than in open grassland. Differences in biomass allocation for grasses growing in shade and open habitats may reconcile these contrary results. Our results highlight the importance of the physiology of a species (relative drought and shade tolerance) in determining the response of a plant to a particular interacting species.     

From classical genetics to quantitative genetics to systems biology: modeling epistasis

Gene expression data has been used in lieu of phenotype in both classical and quantitative genetic settings. These two disciplines have separate approaches to measuring and interpreting epistasis, which is the interaction between alleles at different loci. We propose a framework for estimating and interpreting epistasis from a classical experiment that combines the strengths of each approach. A regression analysis step accommodates the quantitative nature of expression measurements by estimating the effect of gene deletions plus any interaction. Effects are selected by significance such that a reduced model describes each expression trait. We show how the resulting models correspond to specific hierarchical relationships between two regulator genes and a target gene. These relationships are the basic units of genetic pathways and genomic system diagrams. Our approach can be extended to analyze data from a variety of experiments, multiple loci, and multiple environments.     

Problems in the genetics of stress. I. Genetic analysis of the behavior of mice in a stressful situation]

Behavior of progeny of complete diallel crossing between 4 inbred strains of mice (BALB/c, C3H/He, C57BL/6, AKR/J) in a stressful situation was studied. As a model of stressful situation, the open field test was used. A statistically significant influence of genotype on the variability of the behaviour characteristics is found. On the basis of analysis of general combining ability of the strains, a hypothesis is made that in the gene pool of BALB/c and C3H/He strains there are concentrated some genes of additive effect, which increase the strength of emotional reactions of mice in a stressful situation, while in the gene pool of C57BL/6 and AKR/J there are genes of opposite effect. An analysis of the specific combining ability demonstrates that an important role in the control of features characterizing the exploratory activity of mice is played by non-additive gene effects, in particular, the effects of over-dominance. Significant genotypic correlations between the rate of sexual maturation of female mice and their behaviour in stressful situation were observed. The mice which mature earlier are more reactive to the stressing effect of a strange environment.     

水稻株高上位性效应和ＱＥ互作效应的ＱＴＬ遗传研究

利用基因混合模型的ＱＴＬ定位方法研究了由籼稻品种ＩＲ６４和粳稻品种Ａzucena杂交衍生的ＤＨ群体在４个环境中的ＱＴＬ上位性效应和环境互作效应,结果表明,上位性是数量性状的重要遗传基础,并揭示了上位性的几个重要特点,所有的ＱＴＬ都参与了上位性效应的形成,６４％的ＱＴＬ还具有本身的加性效应,因此传统方法对ＱＴＬ加性效应的估算会由于上位性的影响而有偏,其他３６％的ＱＴＬ没有本身的加性效应,却参与了４８％的上位性互作用,这些位点可能通过诱发和修饰其他位点而起作用,上位性的特点还包括,经常发现了一个ＱＴＬ与多个ＱＴＬ发生互作;大效应的ＱＴＬ也参与上位性互作;上位性互作受环境影响,ＱＴＬ与环境的互效应比ＱＴＬ的主效应更多地被检测到,表明数量性状基因的表达易受环境影响。     

Muller''s Ratchet, Epistasis and Mutation Effects

In this study, computer simulation is used to show that despite synergistic epistasis for fitness, Muller's ratchet can lead to lethal fitness loss in a population of asexuals through the accumulation of deleterious mutations. This result contradicts previous work that indicated that epistasis will halt the ratchet. The present results show that epistasis will not halt the ratchet provided that rather than a single deleterious mutation effect, there is a distribution of deleterious mutation effects with sufficient density near zero. In addition to epistasis and mutation distribution, the ability of Muller's ratchet to lead to the extinction of an asexual population under epistasis for fitness depends strongly on the expected number of offspring that survive to reproductive age. This strong dependence is not present in the nonepistatic model and suggests that interpreting the population growth parameter as fecundity is inadequate. Because a continuous distribution of mutation effects is used in this model, an emphasis is placed on the dynamics of the mutation effect distribution rather than on the dynamics of the number of least mutation loaded individuals. This perspective suggests that current models of gene interaction are too simple to apply directly to long-term prediction for populations undergoing the ratchet.     

EPISTASIS AS A SOURCE OF INCREASED ADDITIVE GENETIC VARIANCE AT POPULATION BOTTLENECKS

The role of epistasis in evolution and speciation has remained controversial. We use a new parameterization of physiological epistasis to examine the effects of epistasis on levels of additive genetic variance during a population bottleneck. We found that all forms of epistasis increase average additive genetic variance in finite populations derived from initial populations with intermediate allele frequencies. Average additive variance continues to increase over many generations, especially at larger population sizes (N = 32 to 64). Additive-by-additive epistasis is the most potent source of additive genetic variance in this situation, whereas dominance-by-dominance epistasis contributes smaller amounts of additive genetic variance. With additive-by-dominance epistasis, additive genetic variance decreases at a relatively high rate immediately after a population bottleneck, rebounding to higher levels after several generations. Empirical examples of epistasis for murine adult body weight based on measured genotypes are provided illustrating the varying effects of epistasis on additive genetic variance during population bottlenecks.