Genotype networks,innovation, and robustness in sulfur metabolism

Background  

A metabolism is a complex network of chemical reactions. This network synthesizes multiple small precursor molecules of biomass from chemicals that occur in the environment. The metabolic network of any one organism is encoded by a metabolic genotype, defined as the set of enzyme-coding genes whose products catalyze the network's reactions. Each metabolic genotype has a metabolic phenotype. We define this metabolic phenotype as the spectrum of different sources of a chemical element that a metabolism can use to synthesize biomass. We here focus on the element sulfur. We study properties of the space of all possible metabolic genotypes in sulfur metabolism by analyzing random metabolic genotypes that are viable on different numbers of sulfur sources.     

The potential for non-adaptive origins of evolutionary innovations in central carbon metabolism

Background

Biological systems are rife with examples of pre-adaptations or exaptations. They range from the molecular scale – lens crystallins, which originated from metabolic enzymes – to the macroscopic scale, such as feathers used in flying, which originally served thermal insulation or waterproofing. An important class of exaptations are novel and useful traits with non-adaptive origins. Whether such origins could be frequent cannot be answered with individual examples, because it is a question about a biological system’s potential for exaptation.We here take a step towards answering this question by analyzing central carbon metabolism, and novel traits that allow an organism to survive on novel sources of carbon and energy. We have previously applied flux balance analysis to this system and predicted the viability of 10¹⁵ metabolic genotypes on each of ten different carbon sources.

Results

We here use this exhaustive genotype-phenotype map to ask whether a central carbon metabolism that is viable on a given, focal carbon source C – the equivalent of an adaptation in our framework – is usually or rarely viable on one or more other carbon sources C _new – a potential exaptation. We show that most metabolic genotypes harbor potential exaptations, that is, they are viable on one or more carbon sources C _new . The nature and number of these carbon sources depends on the focal carbon source C itself, and on the biochemical similarity between C and C _new . Moreover, metabolisms that show a higher biomass yield on C, and that are more complex, i.e., they harbor more metabolic reactions, are viable on a greater number of carbon sources C _new .

Conclusions

A high potential for exaptation results from correlations between the phenotypes of different genotypes, and such correlations are frequent in central carbon metabolism. If they are similarly abundant in other metabolic or biological systems, innovations may frequently have non-adaptive (“exaptive”) origins.

     

The role of robustness in phenotypic adaptation and innovation

Phenotypes that vary in response to DNA mutations are essential for evolutionary adaptation and innovation. Therefore, it seems that robustness, a lack of phenotypic variability, must hinder adaptation. The main purpose of this review is to show why this is not necessarily correct. There are two reasons. The first is that robustness causes the existence of genotype networks--large connected sets of genotypes with the same phenotype. I discuss why genotype networks facilitate phenotypic variability. The second reason emerges from the evolutionary dynamics of evolving populations on genotype networks. I discuss how these dynamics can render highly robust phenotypes more variable, using examples from protein and RNA macromolecules. In addition, robustness can help avoid an important evolutionary conflict between the interests of individuals and populations-a conflict that can impede evolutionary adaptation.     

On the Accessibility of Adaptive Phenotypes of a Bacterial Metabolic Network

The mechanisms by which adaptive phenotypes spread within an evolving population after their emergence are understood fairly well. Much less is known about the factors that influence the evolutionary accessibility of such phenotypes, a pre-requisite for their emergence in a population. Here, we investigate the influence of environmental quality on the accessibility of adaptive phenotypes of Escherichia coli''s central metabolic network. We used an established flux-balance model of metabolism as the basis for a genotype-phenotype map (GPM). We quantified the effects of seven qualitatively different environments (corresponding to both carbohydrate and gluconeogenic metabolic substrates) on the structure of this GPM. We found that the GPM has a more rugged structure in qualitatively poorer environments, suggesting that adaptive phenotypes could be intrinsically less accessible in such environments. Nevertheless, on average ∼74% of the genotype can be altered by neutral drift, in the environment where the GPM is most rugged; this could allow evolving populations to circumvent such ruggedness. Furthermore, we found that the normalized mutual information (NMI) of genotype differences relative to phenotype differences, which measures the GPM''s capacity to transmit information about phenotype differences, is positively correlated with (simulation-based) estimates of the accessibility of adaptive phenotypes in different environments. These results are consistent with the predictions of a simple analytic theory that makes explicit the relationship between the NMI and the speed of adaptation. The results suggest an intuitive information-theoretic principle for evolutionary adaptation; adaptation could be faster in environments where the GPM has a greater capacity to transmit information about phenotype differences. More generally, our results provide insight into fundamental environment-specific differences in the accessibility of adaptive phenotypes, and they suggest opportunities for research at the interface between information theory and evolutionary biology.     

Genotype networks shed light on evolutionary constraints

An evolutionary constraint is a bias or limitation in phenotypic variation that a biological system produces. One can distinguish physicochemical, selective, genetic and developmental causes of such constraints. Here, I discuss these causes in three classes of system that bring forth many phenotypic traits and evolutionary innovations: regulatory circuits, macromolecules and metabolic networks. In these systems, genotypes with the same phenotype form large genotype networks that extend throughout a vast genotype space. Such genotype networks can help unify different causes of evolutionary constraints. They can show that these causes ultimately emerge from the process of development; that is, how phenotypes form from genotypes. Furthermore, they can explain important consequences of constraints, such as punctuated stasis and canalization.     

Evolutionary innovations and the organization of protein functions in genotype space

The organization of protein structures in protein genotype space is well studied. The same does not hold for protein functions, whose organization is important to understand how novel protein functions can arise through blind evolutionary searches of sequence space. In systems other than proteins, two organizational features of genotype space facilitate phenotypic innovation. The first is that genotypes with the same phenotype form vast and connected genotype networks. The second is that different neighborhoods in this space contain different novel phenotypes. We here characterize the organization of enzymatic functions in protein genotype space, using a data set of more than 30,000 proteins with known structure and function. We show that different neighborhoods of genotype space contain proteins with very different functions. This property both facilitates evolutionary innovation through exploration of a genotype network, and it constrains the evolution of novel phenotypes. The phenotypic diversity of different neighborhoods is caused by the fact that some functions can be carried out by multiple structures. We show that the space of protein functions is not homogeneous, and different genotype neighborhoods tend to contain a different spectrum of functions, whose diversity increases with increasing distance of these neighborhoods in sequence space. Whether a protein with a given function can evolve specific new functions is thus determined by the protein's location in sequence space.     

Mutational Robustness Accelerates the Origin of Novel RNA Phenotypes through Phenotypic Plasticity

Novel phenotypes can originate either through mutations in existing genotypes or through phenotypic plasticity, the ability of one genotype to form multiple phenotypes. From molecules to organisms, plasticity is a ubiquitous feature of life, and a potential source of exaptations, adaptive traits that originated for nonadaptive reasons. Another ubiquitous feature is robustness to mutations, although it is unknown whether such robustness helps or hinders the origin of new phenotypes through plasticity. RNA is ideal to address this question, because it shows extensive plasticity in its secondary structure phenotypes, a consequence of their continual folding and unfolding, and these phenotypes have important biological functions. Moreover, RNA is to some extent robust to mutations. This robustness structures RNA genotype space into myriad connected networks of genotypes with the same phenotype, and it influences the dynamics of evolving populations on a genotype network. In this study I show that both effects help accelerate the exploration of novel phenotypes through plasticity. My observations are based on many RNA molecules sampled at random from RNA sequence space, and on 30 biological RNA molecules. They are thus not only a generic feature of RNA sequence space but are relevant for the molecular evolution of biological RNA.     

Mutational Robustness Accelerates the Origin of Novel RNA Phenotypes through Phenotypic Plasticity

Novel phenotypes can originate either through mutations in existing genotypes or through phenotypic plasticity, the ability of one genotype to form multiple phenotypes. From molecules to organisms, plasticity is a ubiquitous feature of life, and a potential source of exaptations, adaptive traits that originated for nonadaptive reasons. Another ubiquitous feature is robustness to mutations, although it is unknown whether such robustness helps or hinders the origin of new phenotypes through plasticity. RNA is ideal to address this question, because it shows extensive plasticity in its secondary structure phenotypes, a consequence of their continual folding and unfolding, and these phenotypes have important biological functions. Moreover, RNA is to some extent robust to mutations. This robustness structures RNA genotype space into myriad connected networks of genotypes with the same phenotype, and it influences the dynamics of evolving populations on a genotype network. In this study I show that both effects help accelerate the exploration of novel phenotypes through plasticity. My observations are based on many RNA molecules sampled at random from RNA sequence space, and on 30 biological RNA molecules. They are thus not only a generic feature of RNA sequence space but are relevant for the molecular evolution of biological RNA.     

The molecular origins of evolutionary innovations

The history of life is a history of evolutionary innovations, qualitatively new phenotypic traits that endow their bearers with new, often game-changing abilities. We know many individual examples of innovations and their natural history, but we know little about the fundamental principles of phenotypic variability that permit new phenotypes to arise. Most phenotypic innovations result from changes in three classes of systems: metabolic networks, regulatory circuits, and macromolecules. I here highlight two important features that these classes of systems share. The first is the ubiquity of vast genotype networks - connected sets of genotypes with the same phenotype. The second is the great phenotypic diversity of small neighborhoods around different genotypes in genotype space. I here explain that both features are essential for the phenotypic variability that can bring forth qualitatively new phenotypes. Both features emerge from a common cause, the robustness of phenotypes to perturbations, whose origins are linked to life in changing environments.     

Metastable evolutionary dynamics: Crossing fitness barriers or escaping via neutral paths?

We analytically study the dynamics of evolving populations that exhibit metastability on the level of phenotype or fitness. In constant selective environments, such metastable behavior is caused by two qualitatively different mechanisms. On the one hand, populations may become pinned at a local fitness optimum, being separated from higher-fitness genotypes by a fitness barrier of low-fitness genotypes. On the other hand, the population may only be metastable on the level of phenotype or fitness while, at the same time, diffusing over neutral networks of selectively neutral genotypes. Metastability occurs in this case because the population is separated from higher-fitness genotypes by an entropy barrier: the population must explore large portions of these neutral networks before it discovers a rare connection to fitter phenotypes. We derive analytical expressions for the barrier crossing times in both the fitness barrier and entropy barrier regime. In contrast with ‘landscape’ evolutionary models, we show that the waiting times to reach higher fitness depend strongly on the width of a fitness barrier and much less on its height. The analysis further shows that crossing entropy barriers is faster by orders of magnitude than fitness barrier crossing. Thus, when populations are trapped in a metastable phenotypic state, they are most likely to escape by crossing an entropy barrier, along a neutral path in genotype space. If no such escape route along a neutral path exists, a population is most likely to cross a fitness barrier where the barrier is narrowest, rather than where the barrier is shallowest.     

Uncovering the gene knockout landscape for improved lycopene production in E. coli

Systematic and combinatorial genetic approaches for the identification of gene knockout and overexpression targets have been effectively employed in the improvement of cellular phenotypes. Previously, we demonstrated how two of these tools, metabolic modeling and transposon mutagenesis, can be combined to identify strains of interest spanning the metabolic landscape of recombinant lycopene production in Escherichia coli. However, it is unknown how to best select multiple-gene knockout targets. Hence, this study seeks to understand how the overall order of gene selection, or search trajectory, biases the exploration and topology of the metabolic landscape. In particular, transposon mutagenesis and selection were employed in the background of eight different knockout genotypes. Collectively, 800,000 mutants were analyzed in hopes of exhaustively identifying all advantageous gene knockout targets. Several interesting observations, including clusters of gene functions, recurrence, and divergent genotypes, demonstrate the complexity of mapping only one genotype to one phenotype. One particularly interesting mutant, the ΔhnrΔyliE genotype, exhibited a drastically improved lycopene production capacity in basic minimal medium in comparison to the best strains identified in previous studies.     

A European multicenter study of phenylalanine hydroxylase deficiency: classification of 105 mutations and a general system for genotype-based prediction of metabolic phenotype.

Phenylketonuria (PKU) and mild hyperphenylalaninemia (MHP) are allelic disorders caused by mutations in the gene encoding phenylalanine hydroxylase (PAH). Previous studies have suggested that the highly variable metabolic phenotypes of PAH deficiency correlate with PAH genotypes. We identified both causative mutations in 686 patients from seven European centers. On the basis of the phenotypic characteristics of 297 functionally hemizygous patients, 105 of the mutations were assigned to one of four arbitrary phenotype categories. We proposed and tested a simple model for correlation between genotype and phenotypic outcome. The observed phenotype matched the predicted phenotype in 79% of the cases, and in only 5 of 184 patients was the observed phenotype more than one category away from that expected. Among the seven contributing centers, the proportion of patients for whom the observed phenotype did not match the predicted phenotype was 4%-23% (P<.0001), suggesting that differences in methods used for mutation detection or phenotype classification may account for a considerable proportion of genotype-phenotype inconsistencies. Our data indicate that the PAH-mutation genotype is the main determinant of metabolic phenotype in most patients with PAH deficiency. In the present study, the classification of 105 PAH mutations may allow the prediction of the biochemical phenotype in >10,000 genotypes, which may be useful for the management of hyperphenylalaninemia in newborns.     

Intrapopulation foraging niche variation between phenotypes and genotypes of Spirit bear populations

Foraging niche variation within a species can contribute to the maintenance of phenotypic diversity. The multiniche model posits that phenotypes occupying different niches can contribute to the maintenance of balanced polymorphisms. Using coastal populations of black bears (Ursus americanus kermodei) from British Columbia, Canada, we examined potential foraging niche divergence between phenotypes (black and white “Spirit” coat color) and between genotypes (black‐coated homozygote and heterozygous). We applied the Bayesian multivariate models, with biotracers of diet (δ¹³C and δ¹⁵N) together comprising the response variable, to draw inference about foraging niche variation. Variance–covariance matrices from multivariate linear mixed‐effect models were visualized as the Bayesian standard ellipses in δ¹³C and δ¹⁵N isotopic space to assess potential seasonal and annual niche variation between phenotypes and genotypes. We did not detect a difference in annual isotopic foraging niche area in comparisons between genotypes or phenotypes. Consistent with previous field experimental and isotopic analyses, however, we found that white phenotype Spirit bears were modestly more enriched in δ¹⁵N during the fall foraging season, though with our modest sample sizes these results were not significant. Although also not statistically significant, variation in isotopic niches between genotypes revealed that heterozygotes were moderately more enriched in δ¹³C along hair segments grown during fall foraging compared with black‐coated homozygotes. To the extent to which the pattern of elevated δ¹⁵N and δ¹³C may signal the consumption of salmon (Oncorhynchus spp.), as well as the influence of salmon consumption on reproductive fitness, these results suggest that black‐coated heterozygotes could have a minor selective advantage in the fall compared with black‐coated homozygotes. More broadly, our multivariate approach, coupled with knowledge of genetic variation underlying a polymorphic trait, provides new insight into the potential role of a multiniche mechanism in maintaining this rare morph of conservation priority in Canada''s Great Bear Rainforest and could offer new understanding into polymorphisms in other systems.     

Adenosine deaminase deficiency: genotype-phenotype correlations based on expressed activity of 29 mutant alleles.

Adenosine deaminase (ADA) deficiency causes lymphopenia and immunodeficiency due to toxic effects of its substrates. Most patients are infants with severe combined immunodeficiency disease (SCID), but others are diagnosed later in childhood (delayed onset) or as adults (late onset); healthy individuals with "partial" ADA deficiency have been identified. More than 50 ADA mutations are known; most patients are heteroallelic, and most alleles are rare. To analyze the relationship of genotype to phenotype, we quantitated the expression of 29 amino acid sequence-altering alleles in the ADA-deleted Escherichia coli strain SO3834. Expressed ADA activity of wild-type and mutant alleles ranged over five orders of magnitude. The 26 disease-associated alleles expressed 0.001%-0.6% of wild-type activity, versus 5%-28% for 3 alleles from "partials." We related these data to the clinical phenotypes and erythrocyte deoxyadenosine nucleotide (dAXP) levels of 52 patients (49 immunodeficient and 3 with partial deficiency) who had 43 genotypes derived from 42 different mutations, including 28 of the expressed alleles. We reduced this complexity to 13 "genotype categories," ranked according to the potential of their constituent alleles to provide ADA activity. Of 31 SCID patients, 28 fell into 3 genotype categories that could express <=0.05% of wild-type ADA activity. Only 2 of 21 patients with delayed, late-onset, or partial phenotypes had one of these "severe" genotypes. Among 37 patients for whom pretreatment metabolic data were available, we found a strong inverse correlation between red-cell dAXP level and total ADA activity expressed by each patient's alleles in SO3834. Our system provides a quantitative framework and ranking system for relating genotype to phenotype.     

Genetic basis for correction of very-long-chain acyl-coenzyme A dehydrogenase deficiency by bezafibrate in patient fibroblasts: toward a genotype-based therapy

Very-long-chain acyl–coenzyme A dehydrogenase (VLCAD) deficiency is an inborn mitochondrial fatty-acid β-oxidation (FAO) defect associated with a broad mutational spectrum, with phenotypes ranging from fatal cardiopathy in infancy to adolescent-onset myopathy, and for which there is no established treatment. Recent data suggest that bezafibrate could improve the FAO capacities in β-oxidation–deficient cells, by enhancing the residual level of mutant enzyme activity via gene-expression stimulation. Since VLCAD-deficient patients frequently harbor missense mutations with unpredictable effects on enzyme activity, we investigated the response to bezafibrate as a function of genotype in 33 VLCAD-deficient fibroblasts representing 45 different mutations. Treatment with bezafibrate (400 μM for 48 h) resulted in a marked increase in FAO capacities, often leading to restoration of normal values, for 21 genotypes that mainly corresponded to patients with the myopathic phenotype. In contrast, bezafibrate induced no changes in FAO for 11 genotypes corresponding to severe neonatal or infantile phenotypes. This pattern of response was not due to differential inductions of VLCAD messenger RNA, as shown by quantitative real-time polymerase chain reaction, but reflected variable increases in measured VLCAD residual enzyme activity in response to bezafibrate. Genotype cross-analysis allowed the identification of alleles carrying missense mutations, which could account for these different pharmacological profiles and, on this basis, led to the characterization of 9 mild and 11 severe missense mutations. Altogether, the responses to bezafibrate reflected the severity of the metabolic blockage in various genotypes, which appeared to be correlated with the phenotype, thus providing a new approach for analysis of genetic heterogeneity. Finally, this study emphasizes the potential of bezafibrate, a widely prescribed hypolipidemic drug, for the correction of VLCAD deficiency and exemplifies the integration of molecular information in a therapeutic strategy.     

Evolution in silico and in vitro: the RNA model.

Theoretical concepts and experiments dealing with the evolution of molecules in vitro reached a state that allows for direct applications to the design of biomolecules with predefined properties. RNA evolution in vitro represents a basis for the development of a new and comprehensive model of evolution, focusing on the phenotype and its fitness relevant properties. Relations between genotypes and phenotypes are described by mappings from genotype space onto a space of phenotypes, which are many-to-one and thus give ample room for neutrality as expressed by the existence of extended neutral networks in genotype space. The RNA model reduces genotype-phenotype relations to mappings from sequences into secondary structures of minimal free energies and allows for derivation of otherwise inaccessible quantitative results. Continuity and discontinuity in evolution are defined through a new notion of accessibility in phenotype space that provides a basis for straight forward interpretation of computer simulations on RNA optimization; furthermore, it reveals the constructive role of random genomic drift in the search for phenotypes of higher fitness. The effects of population size on the course of evolutionary optimization can be predicted quantitatively by means of a simple stochastic model based on a birth-anddeath process with immigration.     

The curious consistency of carbon biosignatures over billions of years of Earth-life coevolution

The oldest and most wide-ranging signal of biological activity (biosignature) on our planet is the carbon isotope composition of organic materials preserved in rocks. These biosignatures preserve the long-term evolution of the microorganism-hosted metabolic machinery responsible for producing deviations in the isotopic compositions of inorganic and organic carbon. Despite billions of years of ecosystem turnover, evolutionary innovation, organismic complexification, and geological events, the organic carbon that is a residuum of the global marine biosphere in the rock record tells an essentially static story. The ~25‰ mean deviation between inorganic and organic ¹³C/¹²C values has remained remarkably unchanged over >3.5 billion years. The bulk of this record is conventionally attributed to early-evolved, RuBisCO-mediated CO₂ fixation that, in extant oxygenic phototrophs, produces comparable isotopic effects and dominates modern primary production. However, billions of years of environmental transition, for example, in the progressive oxygenation of the Earth’s atmosphere, would be expected to have accompanied shifts in the predominant RuBisCO forms as well as enzyme-level adaptive responses in RuBisCO CO₂-specificity. These factors would also be expected to result in preserved isotopic signatures deviating from those produced by extant RuBisCO in oxygenic phototrophs. Why does the bulk carbon isotope record not reflect these expected environmental transitions and evolutionary innovations? Here, we discuss this apparent discrepancy and highlight the need for greater quantitative understanding of carbon isotope fractionation behavior in extant metabolic pathways. We propose novel, laboratory-based approaches to reconstructing ancestral states of carbon metabolisms and associated enzymes that can constrain isotopic biosignature production in ancient biological systems. Together, these strategies are crucial for integrating the complementary toolsets of biological and geological sciences and for interpretation of the oldest record of life on Earth.Subject terms: Bacterial evolution, Applied microbiology, Biogeochemistry     

Revisiting Robustness and Evolvability: Evolution in Weighted Genotype Spaces

Robustness and evolvability are highly intertwined properties of biological systems. The relationship between these properties determines how biological systems are able to withstand mutations and show variation in response to them. Computational studies have explored the relationship between these two properties using neutral networks of RNA sequences (genotype) and their secondary structures (phenotype) as a model system. However, these studies have assumed every mutation to a sequence to be equally likely; the differences in the likelihood of the occurrence of various mutations, and the consequence of probabilistic nature of the mutations in such a system have previously been ignored. Associating probabilities to mutations essentially results in the weighting of genotype space. We here perform a comparative analysis of weighted and unweighted neutral networks of RNA sequences, and subsequently explore the relationship between robustness and evolvability. We show that assuming an equal likelihood for all mutations (as in an unweighted network), underestimates robustness and overestimates evolvability of a system. In spite of discarding this assumption, we observe that a negative correlation between sequence (genotype) robustness and sequence evolvability persists, and also that structure (phenotype) robustness promotes structure evolvability, as observed in earlier studies using unweighted networks. We also study the effects of base composition bias on robustness and evolvability. Particularly, we explore the association between robustness and evolvability in a sequence space that is AU-rich – sequences with an AU content of 80% or higher, compared to a normal (unbiased) sequence space. We find that evolvability of both sequences and structures in an AU-rich space is lesser compared to the normal space, and robustness higher. We also observe that AU-rich populations evolving on neutral networks of phenotypes, can access less phenotypic variation compared to normal populations evolving on neutral networks.     

Evolvability and robustness in a complex signalling circuit

Biological systems at various levels of organisation exhibit robustness, as well as phenotypic variability or evolvability, the ability to evolve novel phenotypes. We still know very little about the relationship between robustness and phenotypic variability at levels of organisation beyond individual macromolecules, and especially for signalling circuits. Here, we examine multiple alternate topologies of the Saccharomyces cerevisiae target-of-rapamycin (TOR) signalling circuit, in order to understand the circuit's robustness and phenotypic variability. We consider each of the topological variants a genotype, a set of alternative interactions between TOR circuit components. Two genotypes are neighbours in genotype space if they can be reached from each other by a single small genetic change. Each genotype (topology) has a signalling phenotype, which we define via the concentration trajectories of key signalling molecules. We find that the circuits we study can produce almost 300 different phenotypes. The number of genotypes with a given phenotype varies very widely among these phenotypes. Some phenotypes have few associated genotypes. Others have many genotypes that form genotype networks extending far through genotype space. A minority of phenotypes accounts for the vast majority of genotypes. Importantly, we find that these phenotypes tend to have large genotype networks, greater robustness and a greater ability to produce novel phenotypes. Thus, over a broad range of phenotypic robustness, robustness facilitates phenotypic variability in our study system. Our observations show parallels to studies on macromolecules, suggesting that similar principles might govern robustness and phenotypic variability in biological systems. Our approach points a way towards mapping genotype spaces in complex circuitry, and it exposes some challenges such mapping faces.