Predicting epistasis: an experimental test of metabolic control theory with bacterial transcription and translation

The genotype-phenotype relationship and evolutionary genetics in the light of the Metabolic Control Analysis

Metabolic control analysis has long been used as a systemic model of the genotype-phenotype (GP) relationship. By considering kinetic parameters and enzyme concentrations as reflecting the genotype level and metabolic fluxes or pools as phenotypes related to fitness, MCA has given a biological basis to the relationship between these two levels. The non-linear and concave relationship between enzymes and fluxes can account for common genetic effects that reductionist approaches have been powerless to explain, such as the dominance of active alleles over less active alleles, the various types of epistasis and heterosis, and reveals the structural links between these genetic effects. The summation property of the flux control coefficients accounts for the L-shaped distribution of Quantitative Trait Locus (QTL) effects, irrespective of other possible causes. Metabolic models of response to selection results in evolutionary scenarios that are markedly different from those derived from the classical infinitesimal model of quantitative genetics. In particular, evolution towards selective neutrality appears to be a consequence of the diminishing return of the flux-enzyme relationship. In this paper, we survey the historical and recent achievements of MCA in genetics, quantitative genetics and evolution, focusing on epistasis and the evolution of flux in relation to enzyme concentrations.

Epistasis and evolution: recent advances and an outlook for prediction

As organisms evolve, the effects of mutations change as a result of epistatic interactions with other mutations accumulated along the line of descent. This can lead to shifts in adaptability or robustness that ultimately shape subsequent evolution. Here, we review recent advances in measuring, modeling, and predicting epistasis along evolutionary trajectories, both in microbial cells and single proteins. We focus on simple patterns of global epistasis that emerge in this data, in which the effects of mutations can be predicted by a small number of variables. The emergence of these patterns offers promise for efforts to model epistasis and predict evolution.

Mutational robustness changes during long-term adaptation in laboratory budding yeast populations

As an adapting population traverses the fitness landscape, its local neighborhood (i.e., the collection of fitness effects of single-step mutations) can change shape because of interactions with mutations acquired during evolution. These changes to the distribution of fitness effects can affect both the rate of adaptation and the accumulation of deleterious mutations. However, while numerous models of fitness landscapes have been proposed in the literature, empirical data on how this distribution changes during evolution remains limited. In this study, we directly measure how the fitness landscape neighborhood changes during laboratory adaptation. Using a barcode-based mutagenesis system, we measure the fitness effects of 91 specific gene disruption mutations in genetic backgrounds spanning 8000–10,000 generations of evolution in two constant environments. We find that the mean of the distribution of fitness effects decreases in one environment, indicating a reduction in mutational robustness, but does not change in the other. We show that these distribution-level patterns result from differences in the relative frequency of certain patterns of epistasis at the level of individual mutations, including fitness-correlated and idiosyncratic epistasis.

Emergence and propagation of epistasis in metabolic networks

Epistasis is often used to probe functional relationships between genes, and it plays an important role in evolution. However, we lack theory to understand how functional relationships at the molecular level translate into epistasis at the level of whole-organism phenotypes, such as fitness. Here, I derive two rules for how epistasis between mutations with small effects propagates from lower- to higher-level phenotypes in a hierarchical metabolic network with first-order kinetics and how such epistasis depends on topology. Most importantly, weak epistasis at a lower level may be distorted as it propagates to higher levels. Computational analyses show that epistasis in more realistic models likely follows similar, albeit more complex, patterns. These results suggest that pairwise inter-gene epistasis should be common, and it should generically depend on the genetic background and environment. Furthermore, the epistasis coefficients measured for high-level phenotypes may not be sufficient to fully infer the underlying functional relationships.

Higher-fitness yeast genotypes are less robust to deleterious mutations

Natural selection drives populations toward higher fitness, but second-order selection for adaptability and mutational robustness can also influence evolution. In many microbial systems, diminishing-returns epistasis contributes to a tendency for more-fit genotypes to be less adaptable, but no analogous patterns for robustness are known. To understand how robustness varies across genotypes, we measure the fitness effects of hundreds of individual insertion mutations in a panel of yeast strains. We find that more-fit strains are less robust: They have distributions of fitness effects with lower mean and higher variance. These differences arise because many mutations have more strongly deleterious effects in faster-growing strains. This negative correlation between fitness and robustness implies that second-order selection for robustness will tend to conflict with first-order selection for fitness.

Heterosis Is a Systemic Property Emerging From Non-linear Genotype-Phenotype Relationships: Evidence From in Vitro Genetics and Computer Simulations

Heterosis, the superiority of hybrids over their parents for quantitative traits, represents a crucial issue in plant and animal breeding as well as evolutionary biology. Heterosis has given rise to countless genetic, genomic and molecular studies, but has rarely been investigated from the point of view of systems biology. We hypothesized that heterosis is an emergent property of living systems resulting from frequent concave relationships between genotypic variables and phenotypes, or between different phenotypic levels. We chose the enzyme-flux relationship as a model of the concave genotype-phenotype (GP) relationship, and showed that heterosis can be easily created in the laboratory. First, we reconstituted in vitro the upper part of glycolysis. We simulated genetic variability of enzyme activity by varying enzyme concentrations in test tubes. Mixing the content of "parental" tubes resulted in "hybrids," whose fluxes were compared to the parental fluxes. Frequent heterotic fluxes were observed, under conditions that were determined analytically and confirmed by computer simulation. Second, to test this model in a more realistic situation, we modeled the glycolysis/fermentation network in yeast by considering one input flux, glucose, and two output fluxes, glycerol and acetaldehyde. We simulated genetic variability by randomly drawing parental enzyme concentrations under various conditions, and computed the parental and hybrid fluxes using a system of differential equations. Again we found that a majority of hybrids exhibited positive heterosis for metabolic fluxes. Cases of negative heterosis were due to local convexity between certain enzyme concentrations and fluxes. In both approaches, heterosis was maximized when the parents were phenotypically close and when the distributions of parental enzyme concentrations were contrasted and constrained. These conclusions are not restricted to metabolic systems: they only depend on the concavity of the GP relationship, which is commonly observed at various levels of the phenotypic hierarchy, and could account for the pervasiveness of heterosis.

Diminishing-returns epistasis decreases adaptability along an evolutionary trajectory

Populations evolving in constant environments exhibit declining adaptability. Understanding the basis of this pattern could reveal underlying processes determining the repeatability of evolutionary outcomes. In principle, declining adaptability can be due to a decrease in the effect size of beneficial mutations, a decrease in the rate at which they occur, or some combination of both. By evolving Escherichia coli populations started from different steps along a single evolutionary trajectory, we show that declining adaptability is best explained by a decrease in the size of available beneficial mutations. This pattern reflected the dominant influence of negative genetic interactions that caused new beneficial mutations to confer smaller benefits in fitter genotypes. Genome sequencing revealed that starting genotypes that were more similar to one another did not exhibit greater similarity in terms of new beneficial mutations, supporting the view that epistasis acts globally, having a greater influence on the effect than on the identity of available mutations along an adaptive trajectory. Our findings provide support for a general mechanism that leads to predictable phenotypic evolutionary trajectories.

The heterocyst regulatory protein HetP and its homologs modulate heterocyst commitment in Anabaena sp. strain PCC 7120

The commitment of differentiating cells to a specialized fate is fundamental to the correct assembly of tissues within a multicellular organism. Because commitment is often irreversible, entry into and progression through this phase of development must be tightly regulated. Under nitrogen-limiting conditions, the multicellular cyanobacterium Anabaena sp. strain PCC 7120 terminally commits ∼10% of its cells to become specialized nitrogen-fixing heterocysts. Although commitment is known to occur 9-14 h after the induction of differentiation, the factors that regulate the initiation and duration of this phase have yet to be elucidated. Here, we report the identification of four genes that share a functional domain and modulate heterocyst commitment: hetP (alr2818), asl1930, alr2902, and alr3234 Epistatic relationships between all four genes relating to commitment were revealed by deleting them individually and in combination; asl1930 and alr3234 acted most upstream to delay commitment, alr2902 acted next in the pathway to inhibit development, and hetP acted most downstream to drive commitment forward. Possible protein-protein interactions between HetP, its homologs, and the heterocyst master regulator, HetR, were assessed, and interaction partners were defined. Finally, patterns of gene expression for each homolog, as determined by promoter fusions to gfp and reverse transcription-quantitative PCR, were distinct from that of hetP in both spatiotemporal organization and regulation. We posit that a dynamic succession of protein-protein interactions modulates the timing and efficiency of the commitment phase of development and note that this work highlights the utility of a multicellular cyanobacterium as a model for the study of developmental processes.

Benefit of transferred mutations is better predicted by the fitness of recipients than by their ecological or genetic relatedness

The effect of a mutation depends on its interaction with the genetic background in which it is assessed. Studies in experimental systems have demonstrated that such interactions are common among beneficial mutations and often follow a pattern consistent with declining evolvability of more fit genotypes. However, these studies generally examine the consequences of interactions between a small number of focal mutations. It is not clear, therefore, that findings can be extrapolated to natural populations, where new mutations may be transferred between genetically divergent backgrounds. We build on work that examined interactions between four beneficial mutations selected in a laboratory-evolved population of Escherichia coli to test how they interact with the genomes of diverse natural isolates of the same species. We find that the fitness effect of transferred mutations depends weakly on the genetic and ecological similarity of recipient strains relative to the donor strain in which the mutations were selected. By contrast, mutation effects were strongly inversely correlated to the initial fitness of the recipient strain. That is, there was a pattern of diminishing returns whereby fit strains benefited proportionally less from an added mutation. Our results strengthen the view that the fitness of a strain can be a major determinant of its ability to adapt. They also support a role for barriers of transmission, rather than differential selection of transferred DNA, as an explanation of observed phylogenetically determined patterns of restricted recombination among E. coli strains.

Thousand and one ways to quantify and compare protein abundances in label-free bottom-up proteomics

How to process and analyze MS data to quantify and statistically compare protein abundances in bottom-up proteomics has been an open debate for nearly fifteen years. Two main approaches are generally used: the first is based on spectral data generated during the process of identification (e.g. peptide counting, spectral counting), while the second makes use of extracted ion currents to quantify chromatographic peaks and infer protein abundances based on peptide quantification. These two approaches actually refer to multiple methods which have been developed during the last decade, but were submitted to deep evaluations only recently. In this paper, we compiled these different methods as exhaustively as possible. We also summarized the way they address the different problems raised by bottom-up protein quantification such as normalization, the presence of shared peptides, unequal peptide measurability and missing data. This article is part of a Special Issue entitled: Plant Proteomics--a bridge between fundamental processes and crop production, edited by Dr. Hans-Peter Mock.

A Systems Approach to Elucidate Heterosis of Protein Abundances in Yeast

Heterosis is a universal phenomenon that has major implications in evolution and is of tremendous agro-economic value. To study the molecular manifestations of heterosis and to find factors that maximize its strength, we implemented a large-scale proteomic experiment in yeast. We analyzed the inheritance of 1,396 proteins in 55 inter- and intraspecific hybrids obtained from Saccharomyces cerevisiae and S. uvarum that were grown in grape juice at two temperatures. We showed that the proportion of heterotic proteins was highly variable depending on the parental strain and on the temperature considered. For intraspecific hybrids, this proportion was higher at nonoptimal temperature. Unexpectedly, heterosis for protein abundance was strongly biased toward positive values in interspecific hybrids but not in intraspecific hybrids. Computer modeling showed that this observation could be accounted for by assuming concave relationships between protein abundances and their controlling factors, in line with the metabolic model of heterosis. These results point to nonlinear processes that could play a central role in heterosis.

The evolution and adaptive potential of transcriptional variation in sticklebacks--signatures of selection and widespread heritability

Evidence implicating differential gene expression as a significant driver of evolutionary novelty continues to accumulate, but our understanding of the underlying sources of variation in expression, both environmental and genetic, is wanting. Heritability in particular may be underestimated when inferred from genetic mapping studies, the predominant "genetical genomics" approach to the study of expression variation. Such uncertainty represents a fundamental limitation to testing for adaptive evolution at the transcriptomic level. By studying the inheritance of expression levels in 10,495 genes (10,527 splice variants) in a threespine stickleback pedigree consisting of 563 individuals, half of which were subjected to a thermal treatment, we show that 74-98% of transcripts exhibit significant additive genetic variance. Dominance variance is also prevalent (41-99% of transcripts), and genetic sources of variation seem to play a more significant role in expression variance in the liver than a key environmental variable, temperature. Among-population comparisons suggest that the majority of differential expression in the liver is likely due to neutral divergence; however, we also show that signatures of directional selection may be more prevalent than those of stabilizing selection. This predominantly aligns with the neutral model of evolution for gene expression but also suggests that natural selection may still act on transcriptional variation in the wild. As genetic variation both within- and among-populations ultimately defines adaptive potential, these results indicate that broad adaptive potential may be found within the transcriptome.

Genetic Interaction Scoring Procedure for Bacterial Species

A genetic interaction occurs when the phenotype of an organism carrying two mutant genes differs from what should have been observed given their independent influence. Such unexpected outcome indicates a mechanistic connection between the perturbed genes, providing a key source of functional information about the cell. Large-scale screening for genetic interactions involves measuring phenotypes of single and double mutants, which for microorganisms is usually done by automated analysis of images of ordered colonies. Obtaining accurate colony sizes, and using them to identify genetic interactions from such screens remains a challenging and time-consuming task. Here, we outline steps to compute genetic interaction scores in E. coli by measuring colony sizes from plate images, performing normalisation, and quantifying the strength of the effect.

A criticism of the value of midparent in polyploidization

The hypothesis of genetic additivity states that the effects of different alleles, or different genes, add up to produce the phenotype. When considering the F1 progeny of a cross, the hypothesis of additivity of the genetic dosages provided by the parents is tested against the mid-parent value (MPV), which is the average of parental phenotypes and represents the reference value for genetic additivity. Non-additive effects (genetic interactions) are typically measured as deviations from MPV. Recently, however, the use of MPV has been directly transposed to the study of genetic additivity in newly synthesized plant polyploids, assuming that they should as well display mid-parent expression patterns for additive traits. It is shown here that this direct transposition is incorrect. It is suggested that, in neo-polyploids, mid-parent expression has to be reconsidered in terms of reduced genetic additivity. Homeostatic mechanisms are deemed to be the obvious ones responsible for this effect. Genomes are therefore ruled by negative epistasis, and heterosis in allopolyploids is due to a decreased interaction of the parental repressive systems. It is contended that focalizing on the right perspective has relevant theoretical consequences and makes the studies of neo-polyploids very important for our understanding of how genomes work.

Patterns of Epistasis between beneficial mutations in an antibiotic resistance gene

Understanding epistasis is central to biology. For instance, epistatic interactions determine the topography of the fitness landscape and affect the dynamics and determinism of adaptation. However, few empirical data are available, and comparing results is complicated by confounding variation in the system and the type of mutations used. Here, we take a systematic approach by quantifying epistasis in two sets of four beneficial mutations in the antibiotic resistance enzyme TEM-1 β-lactamase. Mutations in these sets have either large or small effects on cefotaxime resistance when present as single mutations. By quantifying the epistasis and ruggedness in both landscapes, we find two general patterns. First, resistance is maximal for combinations of two mutations in both fitness landscapes and declines when more mutations are added due to abundant sign epistasis and a pattern of diminishing returns with genotype resistance. Second, large-effect mutations interact more strongly than small-effect mutations, suggesting that the effect size of mutations may be an organizing principle in understanding patterns of epistasis. By fitting the data to simple phenotype resistance models, we show that this pattern may be explained by the nonlinear dependence of resistance on enzyme stability and an unknown phenotype when mutations have antagonistically pleiotropic effects. The comparison to a previously published set of mutations in the same gene with a joint benefit further shows that the enzyme's fitness landscape is locally rugged but does contain adaptive pathways that lead to high resistance.

Pervasive sign epistasis between conjugative plasmids and drug-resistance chromosomal mutations

Multidrug-resistant bacteria arise mostly by the accumulation of plasmids and chromosomal mutations. Typically, these resistant determinants are costly to the bacterial cell. Yet, recently, it has been found that, in Escherichia coli bacterial cells, a mutation conferring resistance to an antibiotic can be advantageous to the bacterial cell if another antibiotic-resistance mutation is already present, a phenomenon called sign epistasis. Here we study the interaction between antibiotic-resistance chromosomal mutations and conjugative (i.e., self-transmissible) plasmids and find many cases of sign epistasis (40%)—including one of reciprocal sign epistasis where the strain carrying both resistance determinants is fitter than the two strains carrying only one of the determinants. This implies that the acquisition of an additional resistance plasmid or of a resistance mutation often increases the fitness of a bacterial strain already resistant to antibiotics. We further show that there is an overall antagonistic interaction between mutations and plasmids (52%). These results further complicate expectations of resistance reversal by interdiction of antibiotic use.

Bacteria can become resistant to antibiotics by spontaneous mutation of chromosomal genes or through the acquisition of horizontally mobile genetic elements, mainly conjugative plasmids. Plasmid-borne resistance is widespread among bacterial pathogens. Plasmids generally entail a cost to the host, associated with the replication and maintenance of the genetic element and with the expression of its genes. Therefore, in the absence of antibiotic, both plasmids and resistance mutations are often deleterious and confer a fitness cost to the cell. Here we studied epistatic interactions between five natural conjugative plasmids and ten chromosomal mutations conferring resistance to three types of antibiotics, making a total of 50 different combinations of chromosomal mutations and conjugative plasmids. We show that sometimes plasmids confer an advantage to bacterial strains carrying resistance mutations in their chromosome. This occurs in 32% (16 out of 50) of tested combinations. Furthermore, in 5 out of 50 plasmid-mutations combinations studied (10%), we observed an increased fitness when a plasmid-bearing bacterial cell acquires a drug-resistant mutation. These examples of sign epistasis are highly unexpected. This work explains, at least in part, how multidrug resistance evolved so rapidly.

The fitness cost of rifampicin resistance in Pseudomonas aeruginosa depends on demand for RNA polymerase

Bacterial resistance to antibiotics usually incurs a fitness cost in the absence of selecting drugs, and this cost of resistance plays a key role in the spread of antibiotic resistance in pathogen populations. Costs of resistance have been shown to vary with environmental conditions, but the causes of this variability remain obscure. In this article, we show that the average cost of rifampicin resistance in the pathogenic bacterium Pseudomonas aeruginosa is reduced by the addition of ribosome inhibitors (chloramphenicol or streptomycin) that indirectly constrain transcription rate and therefore reduce demand for RNA polymerase activity. This effect is consistent with predictions from metabolic control theory. We also tested the alternative hypothesis that the observed trend was due to a general effect of environmental quality on the cost of resistance. To do this we measured the fitness of resistant mutants in the presence of other antibiotics (ciprofloxacin and carbenicillin) that have similar effects on bacterial growth rate but bind to different target enzymes (DNA gyrase and penicillin-binding proteins, respectively) and in 41 single-carbon source environments of varying quality. We find no consistent effect of environmental quality on the average cost of resistance in these treatments. These results show that the cost of rifampicin resistance varies with demand for the mutated target enzyme, rather than as a simple function of bacterial growth rate or stress.