Evolution of catalytic proteins or on the origin of enzyme species by means of natural selection

On paradoxes between optimal growth, metabolic control analysis, and flux balance analysis

In Microbiology it is often assumed that growth rate is maximal. This may be taken to suggest that the dependence of the growth rate on every enzyme activity is at the top of an inverse-parabolic function, i.e. that all flux control coefficients should equal zero. This might seem to imply that the sum of these flux control coefficients equals zero. According to the summation law of Metabolic Control Analysis (MCA) the sum of flux control coefficients should equal 1 however. And in Flux Balance Analysis (FBA) catabolism is often limited by a hard bound, causing catabolism to fully control the fluxes, again in apparent contrast with a flux control coefficient of zero. Here we resolve these paradoxes (apparent contradictions) in an analysis that uses the 'Edinburgh pathway', the 'Amsterdam pathway', as well as a generic metabolic network providing the building blocks or Gibbs energy for microbial growth. We review and show that (i) optimization depends on so-called enzyme control coefficients rather than the 'catalytic control coefficients' of MCA's summation law, (ii) when optimization occurs at fixed total protein, the former differ from the latter to the extent that they may all become equal to zero in the optimum state, (iii) in more realistic scenarios of optimization where catalytically inert biomass is compensating or maintenance metabolism is taken into consideration, the optimum enzyme concentrations should not be expected to equal those that maximize the specific growth rate, (iv) optimization may be in terms of yield rather than specific growth rate, which resolves the paradox because the sum of catalytic control coefficients on yield equals 0, (v) FBA effectively maximizes growth yield, and for yield the summation law states 0 rather than 1, thereby removing the paradox, (vi) furthermore, FBA then comes more often to a 'hard optimum' defined by a maximum catabolic flux and a catabolic-enzyme control coefficient of 1. The trade-off between maintenance metabolism and growth is highlighted as worthy of further analysis.

Self-Organization of Enzyme-Catalyzed Reactions Studied by the Maximum Entropy Production Principle

The self-organization of open reaction systems is closely related to specific mechanisms that allow the export of internally generated entropy from systems to their environment. According to the second law of thermodynamics, systems with effective entropy export to the environment are better internally organized. Therefore, they are in thermodynamic states with low entropy. In this context, we study how self-organization in enzymatic reactions depends on their kinetic reaction mechanisms. Enzymatic reactions in an open system are considered to operate in a non-equilibrium steady state, which is achieved by satisfying the principle of maximum entropy production (MEPP). The latter is a general theoretical framework for our theoretical analysis. Detailed theoretical studies and comparisons of the linear irreversible kinetic schemes of an enzyme reaction in two and three states are performed. In both cases, in the optimal and statistically most probable thermodynamic steady state, a diffusion-limited flux is predicted by MEPP. Several thermodynamic quantities and enzymatic kinetic parameters, such as the entropy production rate, the Shannon information entropy, reaction stability, sensitivity, and specificity constants, are predicted. Our results show that the optimal enzyme performance may strongly depend on the number of reaction steps when linear reaction mechanisms are considered. Simple reaction mechanisms with a smaller number of intermediate reaction steps could be better organized internally and could allow fast and stable catalysis. These could be features of the evolutionary mechanisms of highly specialized enzymes.

Evolution of enzyme levels in metabolic pathways: A theoretical approach. Part 2

Metabolism is essential for cell function and adaptation. Because of their central role in metabolism, kinetic parameters and enzyme concentrations are under constant selective pressure to adapt the fluxes of the metabolic networks to the needs of the organism. In line with various studies dealing with enzyme evolution, we recently developed a model of the evolution of enzyme concentrations under selection for increased flux, considered as a proxy for fitness (Coton et al., 2022). With this model, taking into account two realistic cellular constraints, competition for resources and co-regulation, we determined the evolutionary equilibria and range of neutral variations of enzyme concentrations. In this article, we expanded this model by considering that the enzymes in a pathway can belong to different co-regulation groups. We determined the equilibria and showed that the constraints modify the adaptive landscape by limiting the number of independent dimensions. We also showed that any trade-off between enzyme concentrations is sufficient to limit the flux and relax selection for increasing the concentration of other enzymes. Even though this model is based on simplifying assumptions, the complexity of the relationship between enzyme concentrations prevents the formal analysis of the range of neutral variation of enzyme concentrations. However, we could show that selection for maximizing the flux results in selective neutrality for all enzymes regardless the constraints applied, giving generality to the prediction of Hartl et al. (1985).

Evolution of enzyme levels in metabolic pathways: A theoretical approach

The central role of metabolism in cell functioning and adaptation has given rise to countless studies on the evolution of enzyme-coding genes and network topology. However, very few studies have addressed the question of how enzyme concentrations change in response to positive selective pressure on the flux, considered a proxy of fitness. In particular, the way cellular constraints, such as resource limitations and co-regulation, affect the adaptive landscape of a pathway under selection has never been analyzed theoretically. To fill this gap, we developed a model of the evolution of enzyme concentrations that combines metabolic control theory and an adaptive dynamics approach, and integrates possible dependencies between enzyme concentrations. We determined the evolutionary equilibria of enzyme concentrations and their range of neutral variation, and showed that they differ with the properties of the enzymes, the constraints applied to the system and the initial enzyme concentrations. Simulations of long-term evolution confirmed all analytical and numerical predictions, even though we relaxed the simplifying assumptions used in the analytical treatment.

Adaptation dynamics between copy-number and point mutations

Together, copy-number and point mutations form the basis for most evolutionary novelty, through the process of gene duplication and divergence. While a plethora of genomic data reveals the long-term fate of diverging coding sequences and their cis-regulatory elements, little is known about the early dynamics around the duplication event itself. In microorganisms, selection for increased gene expression often drives the expansion of gene copy-number mutations, which serves as a crude adaptation, prior to divergence through refining point mutations. Using a simple synthetic genetic reporter system that can distinguish between copy-number and point mutations, we study their early and transient adaptive dynamics in real time in Escherichia coli. We find two qualitatively different routes of adaptation, depending on the level of functional improvement needed. In conditions of high gene expression demand, the two mutation types occur as a combination. However, under low gene expression demand, copy-number and point mutations are mutually exclusive; here, owing to their higher frequency, adaptation is dominated by copy-number mutations, in a process we term amplification hindrance. Ultimately, due to high reversal rates and pleiotropic cost, copy-number mutations may not only serve as a crude and transient adaptation, but also constrain sequence divergence over evolutionary time scales.

Resource uptake and the evolution of moderately efficient enzymes

Enzymes speed up reactions that would otherwise be too slow to sustain the metabolism of selfreplicators. Yet, most enzymes seem only moderately efficient, exhibiting kinetic parameters orders of magnitude lower than their expected physically achievable maxima and spanning over surprisingly large ranges of values. Here, we question how these parameters evolve using a mechanistic model where enzyme efficiency is a key component of individual competition for resources. We show that kinetic parameters are under strong directional selection only up to a point, above which enzymes appear to evolve under near-neutrality, thereby confirming the qualitative observation of other modeling approaches. While the existence of a large fitness plateau could potentially explain the extensive variation in enzyme features reported, we show using a population genetics model that such a widespread distribution is an unlikely outcome of evolution on a common landscape, as mutation–selection–drift balance occupy a narrow area even when very moderate biases towards lower efficiency are considered. Instead, differences in the evolutionary context encountered by each enzyme should be involved, such that each evolves on an individual, unique landscape. Our results point to drift and effective population size playing an important role, along with the kinetics of nutrient transporters, the tolerance to high concentrations of intermediate metabolites, and the reversibility of reactions. Enzyme concentration also shapes selection on kinetic parameters, but we show that the joint evolution of concentration and efficiency does not yield extensive variance in evolutionary outcomes when documented costs to protein expression are applied.

The essence of life revisited: how theories can shed light on it

Disagreement over whether life is inevitable when the conditions can support life remains unresolved, but calculations show that self-organization can arise naturally from purely random effects. Closure to efficient causation, or the need for all specific catalysts used by an organism to be produced internally, implies that a true model of an organism cannot exist, though this does not exclude the possibility that some characteristics can be simulated. Such simulations indicate that there is a limit to how small a self-organizing system can be: much smaller than a bacterial cell, but around the size of a typical virus particle. All current theories of life incorporate, at least implicitly, the idea of catalysis, but they largely ignore the need for metabolic regulation.

Evolution of linkage and genome expansion in protocells: The origin of chromosomes

Chromosomes are likely to have assembled from unlinked genes in early evolution. Genetic linkage reduces the assortment load and intragenomic conflict in reproducing protocell models to the extent that chromosomes can go to fixation even if chromosomes suffer from a replicative disadvantage, relative to unlinked genes, proportional to their length. Here we numerically show that chromosomes spread within protocells even if recurrent deleterious mutations affecting replicating genes (as ribozymes) are considered. Dosage effect selects for optimal genomic composition within protocells that carries over to the genic composition of emerging chromosomes. Lacking an accurate segregation mechanism, protocells continue to benefit from the stochastic corrector principle (group selection of early replicators), but now at the chromosome level. A remarkable feature of this process is the appearance of multigene families (in optimal genic proportions) on chromosomes. An added benefit of chromosome formation is an increase in the selectively maintainable genome size (number of different genes), primarily due to the marked reduction of the assortment load. The establishment of chromosomes is under strong positive selection in protocells harboring unlinked genes. The error threshold of replication is raised to higher genome size by linkage due to the fact that deleterious mutations affecting protocells metabolism (hence fitness) show antagonistic (diminishing return) epistasis. This result strengthens the established benefit conferred by chromosomes on protocells allowing for the fixation of highly specific and efficient enzymes.

The emergence of chromosomes harboring several genes is a crucial ingredient of the major evolutionary transition from naked replicators to cells. Linkage of replicating genes reduces conflict between them and alleviates the problem of chance loss of genes upon stochastic protocell fission. The emerging organization of protocells maintaining several segregating chromosomes with balanced gene composition also allows for an increase in the number of gene types despite recurrent deleterious mutations. We suggest that this interim genomic organization enabled protocells to evolve specific and efficient enzymes and paved the way toward an accurate mechanism for chromosome segregation later in evolution.

Reduced alphabet of prebiotic amino acids optimally encodes the conformational space of diverse extant protein folds

Background

There is wide agreement that only a subset of the twenty standard amino acids existed prebiotically in sufficient concentrations to form functional polypeptides. We ask how this subset, postulated as {A,D,E,G,I,L,P,S,T,V}, could have formed structures stable enough to found metabolic pathways. Inspired by alphabet reduction experiments, we undertook a computational analysis to measure the structural coding behavior of sequences simplified by reduced alphabets. We sought to discern characteristics of the prebiotic set that would endow it with unique properties relevant to structure, stability, and folding.

Results

Drawing on a large dataset of single-domain proteins, we employed an information-theoretic measure to assess how well the prebiotic amino acid set preserves fold information against all other possible ten-amino acid sets. An extensive virtual mutagenesis procedure revealed that the prebiotic set excellently preserves sequence-dependent information regarding both backbone conformation and tertiary contact matrix of proteins. We observed that information retention is fold-class dependent: the prebiotic set sufficiently encodes the structure space of α/β and α + β folds, and to a lesser extent, of all-α and all-β folds. The prebiotic set appeared insufficient to encode the small proteins. Assessing how well the prebiotic set discriminates native vs. incorrect sequence-structure matches, we found that α/β and α + β folds exhibit more pronounced energy gaps with the prebiotic set than with nearly all alternatives.

Conclusions

The prebiotic set optimally encodes local backbone structures that appear in the folded environment and near-optimally encodes the tertiary contact matrix of extant proteins. The fold-class-specific patterns observed from our structural analysis confirm the postulated timeline of fold appearance in proteogenesis derived from proteomic sequence analyses. Polypeptides arising in a prebiotic environment will likely form α/β and α + β-like folds if any at all. We infer that the progressive expansion of the alphabet allowed the increased conformational stability and functional specificity of later folds, including all-α, all-β, and small proteins. Our results suggest that prebiotic sequences are amenable to mutations that significantly lower native conformational energies and increase discrimination amidst incorrect folds. This property may have assisted the genesis of functional proto-enzymes prior to the expansion of the full amino acid alphabet.

Evolutionary Innovations and Where to Find Them: Routes to Open-Ended Evolution in Natural and Artificial Systems

This article presents a high-level conceptual framework to help orient the discussion and implementation of open-endedness in evolutionary systems. Drawing upon earlier work by Banzhaf et al. (2016), three different kinds of open-endedness are identified: exploratory, expansive, and transformational. These are characterized in terms of their relationship to the search space of phenotypic behaviors. A formalism is introduced to describe three key processes required for an evolutionary process: the generation of a phenotype from a genetic description, the evaluation of that phenotype, and the reproduction with variation of individuals according to their evaluation. The formalism makes explicit various influences in each of these processes that can easily be overlooked. The distinction is made between intrinsic and extrinsic implementations of these processes. A discussion then investigates how various interactions between these processes, and their modes of implementation, can lead to open-endedness. However, an important contribution of the article is the demonstration that these considerations relate to exploratory open-endedness only. Conditions for the implementation of the more interesting kinds of open-endedness-expansive and transformational-are also discussed, emphasizing factors such as multiple domains of behavior, transdomain bridges, and non-additive compositional systems. In contrast to a traditional Darwinian analysis, these factors relate not to the generic evolutionary properties of individuals and populations, but rather to the nature of the building blocks out of which individual organisms are constructed, and the laws and properties of the environment in which they exist. The article ends with suggestions of how the framework can be used to categorize and compare the open-ended evolutionary potential of different systems, how it might guide the design of systems with greater capacity for open-ended evolution, and how it might be further improved.

Modeling genome-wide enzyme evolution predicts strong epistasis underlying catalytic turnover rates

Systems biology describes cellular phenotypes as properties that emerge from the complex interactions of individual system components. Little is known about how these interactions have affected the evolution of metabolic enzymes. Here, we combine genome-scale metabolic modeling with population genetics models to simulate the evolution of enzyme turnover numbers (k_cats) from a theoretical ancestor with inefficient enzymes. This systems view of biochemical evolution reveals strong epistatic interactions between metabolic genes that shape evolutionary trajectories and influence the magnitude of evolved k_cats. Diminishing returns epistasis prevents enzymes from developing higher k_cats in all reactions and keeps the organism far from the potential fitness optimum. Multifunctional enzymes cause synergistic epistasis that slows down adaptation. The resulting fitness landscape allows k_cat evolution to be convergent. Predicted k_cat parameters show a significant correlation with experimental data, validating our modeling approach. Our analysis reveals how evolutionary forces shape modern k_cats and the whole of metabolism.

The evolutionary dynamics of metabolic protocells

Protocell multilevel selection models have been proposed to study the evolutionary dynamics of vesicles encapsulating a set of replicating, competing and mutating sequences. The frequency of the different sequence types determines protocell survival through a fitness function. One of the defining features of these models is the genetic load generated when the protocell divides and its sequences are assorted between the offspring vesicles. However, these stochastic assortment effects disappear when the redundancy of each sequence type is sufficiently high. The fitness dependence of the vesicle with its sequence content is usually defined without considering a realistic account on how the lower level dynamics would specify the protocell fitness. Here, we present a protocell model with a fitness function determined by the output flux of a simple metabolic network with the aim of understanding how the evolution of both kinetic and topological features of metabolism would have been constrained by the particularities of the protocell evolutionary dynamics. In our model, the sequences inside the vesicle are both the carriers of information and Michaelis-Menten catalysts exhibiting saturation. We found that the saturation of the catalysts controlling the metabolic fluxes, achievable by modifying the kinetic or stoichiometric parameters, provides a mechanism to ameliorate the assortment load by increasing the redundancy of the catalytic sequences required to achieve the maximum flux. Regarding the network architecture, we conclude that combinations of parallel network motifs and bimolecular catalysts are a robust way to increase the complexity of the metabolism enclosed by the protocell.

The protocell hypothesis conjectures the existence of a vesicle containing catalytic and replicating sequences as the primordial cellular organization during the early stages of the evolution of life. Mathematical models of protocells traditionally consider RNA sequences being encapsulated and having both an informational and a catalytic role in the same molecule. Because of this dual function, the protocell sequences are evolutionarily constrained. Mathematical models have been extensively used to study the evolutionary dynamics of protocells with a focus on the processes, like mutation or stochastic sequence assortment upon division, that affect the protocell information capacity in terms of the coexistence of different sequence types. Here we introduce a simple model of metabolic networks whose output determines the survival of the protocell with the aim of studying the effect of modifying the kinetic and architectural properties of the network on sequence coexistence. We find that stochastic assortment and mutation limit the architectures able to be encapsulated by the protocell with a given fraction of the population harbouring all possible sequence types.

Evolution of new regulatory functions on biophysically realistic fitness landscapes

Gene expression is controlled by networks of regulatory proteins that interact specifically with external signals and DNA regulatory sequences. These interactions force the network components to co-evolve so as to continually maintain function. Yet, existing models of evolution mostly focus on isolated genetic elements. In contrast, we study the essential process by which regulatory networks grow: the duplication and subsequent specialization of network components. We synthesize a biophysical model of molecular interactions with the evolutionary framework to find the conditions and pathways by which new regulatory functions emerge. We show that specialization of new network components is usually slow, but can be drastically accelerated in the presence of regulatory crosstalk and mutations that promote promiscuous interactions between network components.Gene networks evolve by transcription factor (TF) duplication and divergence of their binding site specificities, but little is known about the global constraints at play. Here, the authors study the coevolution of TFs and binding sites using a biophysical-evolutionary approach, and show that the emerging complex fitness landscapes strongly influence regulatory evolution with a role for crosstalk.

Endoglucanase activity at a second site in Pyrococcus furiosus triosephosphate isomerase-Promiscuity or compensation for a metabolic handicap?

The eight‐stranded (β/α)₈ barrel fold known as the Triosephosphate isomerase (TIM) barrel is the most commonly observed fold in enzymes, displaying an eightfold structural symmetry. The sequences and structures of different TIM barrel enzymes suggest that nature exploits the modularity inherent in the eightfold symmetry to generate enzymes with diverse enzymatic activities and, in certain cases, more than one catalytic activity per enzyme. Here, we report the discovery, verification, and characterization of such an additional activity, a novel endoglucanase/cellulase activity in what is otherwise a triosephosphate isomerase from the hyperthermophile archaeon Pyrococcus furiosus (PfuTIM). The activity is seen in two different ranges of temperatures, with one maximum at 40 °C and a second maximum close to 100 °C. The endoglucanase/cellulase activity is inhibited by norharman, a TIM inhibitor, which is suspected to bind at a site different to that of the regular substrate, glyceraldehyde‐3‐phosphate (G3P). However, endoglucanase/cellulose activity is not inhibited either by G3P analogs or by glycine‐scanning mutations involving residues in loops 1, 4, and 6 of PfuTIM, which are known to be important for TIM activity. It appears, therefore, that two different sites on PfuTIM are responsible for the observed TIM and endoglucanase activities. We discuss possible correlations between this discovery and certain unusual features of the glycolytic pathway in P. furiosus.

Enzyme

Pyrococcus furiosus Triosephosphate isomerase (EC:5.3.1.1)

The natural history of molecular functions inferred from an extensive phylogenomic analysis of gene ontology data

The origin and natural history of molecular functions hold the key to the emergence of cellular organization and modern biochemistry. Here we use a genomic census of Gene Ontology (GO) terms to reconstruct phylogenies at the three highest (1, 2 and 3) and the lowest (terminal) levels of the hierarchy of molecular functions, which reflect the broadest and the most specific GO definitions, respectively. These phylogenies define evolutionary timelines of functional innovation. We analyzed 249 free-living organisms comprising the three superkingdoms of life, Archaea, Bacteria, and Eukarya. Phylogenies indicate catalytic, binding and transport functions were the oldest, suggesting a 'metabolism-first' origin scenario for biochemistry. Metabolism made use of increasingly complicated organic chemistry. Primordial features of ancient molecular functions and functional recruitments were further distilled by studying the oldest child terms of the oldest level 1 GO definitions. Network analyses showed the existence of an hourglass pattern of enzyme recruitment in the molecular functions of the directed acyclic graph of molecular functions. Older high-level molecular functions were thoroughly recruited at younger lower levels, while very young high-level functions were used throughout the timeline. This pattern repeated in every one of the three mappings, which gave a criss-cross pattern. The timelines and their mappings were remarkable. They revealed the progressive evolutionary development of functional toolkits, starting with the early rise of metabolic activities, followed chronologically by the rise of macromolecular biosynthesis, the establishment of controlled interactions with the environment and self, adaptation to oxygen, and enzyme coordinated regulation, and ending with the rise of structural and cellular complexity. This historical account holds important clues for dissection of the emergence of biomcomplexity and life.

Mathematical models for explaining the Warburg effect: a review focussed on ATP and biomass production

For producing ATP, tumour cells rely on glycolysis leading to lactate to about the same extent as on respiration. Thus, the ATP synthesis flux from glycolysis is considerably higher than in the corresponding healthy cells. This is known as the Warburg effect (named after German biochemist Otto H. Warburg) and also applies to striated muscle cells, activated lymphocytes, microglia, endothelial cells and several other cell types. For similar phenomena in several yeasts and many bacteria, the terms Crabtree effect and overflow metabolism respectively, are used. The Warburg effect is paradoxical at first sight because the molar ATP yield of glycolysis is much lower than that of respiration. Although a straightforward explanation is that glycolysis allows a higher ATP production rate, the question arises why cells do not re-allocate protein to the high-yield pathway of respiration. Mathematical modelling can help explain this phenomenon. Here, we review several models at various scales proposed in the literature for explaining the Warburg effect. These models support the hypothesis that glycolysis allows for a higher proliferation rate due to increased ATP production and precursor supply rates.

The minimotif synthesis hypothesis for the origin of life

Several theories for the origin of life have gained widespread acceptance, led by primordial soup, chemical evolution, metabolism first, and the RNA world. However, while new and existing theories often address a key step, there is less focus on a comprehensive abiogenic continuum leading to the last universal common ancestor. Herein, I present the "minimotif synthesis" hypothesis unifying select origin of life theories with new and revised steps. The hypothesis is based on first principles, on the concept of selection over long time scales, and on a stepwise progression toward complexity. The major steps are the thermodynamically-driven origination of extant molecular specificity emerging from primordial soup leading to the rise of peptide catalysts, and a cyclic feed-forward catalytic diversification of compound and peptides in the primordial soup. This is followed by degenerate, semi-partially conservative peptide replication to pass on catalytic knowledge to progeny protocells. At some point during this progression, the emergence of RNA and selection could drive the separation of catalytic and genetic functions, allowing peptides and proteins to permeate the catalytic space, and RNA to encode higher fidelity information transfer. Translation may have emerged from RNA template driven organization and successive ligation of activated amino acids as a predecessor to translation.

The steady-state assumption in oscillating and growing systems

The steady-state assumption, which states that the production and consumption of metabolites inside the cell are balanced, is one of the key aspects that makes an efficient analysis of genome-scale metabolic networks possible. It can be motivated from two different perspectives. In the time-scales perspective, we use the fact that metabolism is much faster than other cellular processes such as gene expression. Hence, the steady-state assumption is derived as a quasi-steady-state approximation of the metabolism that adapts to the changing cellular conditions. In this article we focus on the second perspective, stating that on the long run no metabolite can accumulate or deplete. In contrast to the first perspective it is not immediately clear how this perspective can be captured mathematically and what assumptions are required to obtain the steady-state condition. By presenting a mathematical framework based on the second perspective we demonstrate that the assumption of steady-state also applies to oscillating and growing systems without requiring quasi-steady-state at any time point. However, we also show that the average concentrations may not be compatible with the average fluxes. In summary, we establish a mathematical foundation for the steady-state assumption for long time periods that justifies its successful use in many applications. Furthermore, this mathematical foundation also pinpoints unintuitive effects in the integration of metabolite concentrations using nonlinear constraints into steady-state models for long time periods.

Computing the origin and evolution of the ribosome from its structure - Uncovering processes of macromolecular accretion benefiting synthetic biology

Accretion occurs pervasively in nature at widely different timeframes. The process also manifests in the evolution of macromolecules. Here we review recent computational and structural biology studies of evolutionary accretion that make use of the ideographic (historical, retrodictive) and nomothetic (universal, predictive) scientific frameworks. Computational studies uncover explicit timelines of accretion of structural parts in molecular repertoires and molecules. Phylogenetic trees of protein structural domains and proteomes and their molecular functions were built from a genomic census of millions of encoded proteins and associated terminal Gene Ontology terms. Trees reveal a ‘metabolic-first’ origin of proteins, the late development of translation, and a patchwork distribution of proteins in biological networks mediated by molecular recruitment. Similarly, the natural history of ancient RNA molecules inferred from trees of molecular substructures built from a census of molecular features shows patchwork-like accretion patterns. Ideographic analyses of ribosomal history uncover the early appearance of structures supporting mRNA decoding and tRNA translocation, the coevolution of ribosomal proteins and RNA, and a first evolutionary transition that brings ribosomal subunits together into a processive protein biosynthetic complex. Nomothetic structural biology studies of tertiary interactions and ancient insertions in rRNA complement these findings, once concentric layering assumptions are removed. Patterns of coaxial helical stacking reveal a frustrated dynamics of outward and inward ribosomal growth possibly mediated by structural grafting. The early rise of the ribosomal ‘turnstile’ suggests an evolutionary transition in natural biological computation. Results make explicit the need to understand processes of molecular growth and information transfer of macromolecules.

In silico ribozyme evolution in a metabolically coupled RNA population

BACKGROUND

The RNA World hypothesis offers a plausible bridge from no-life to life on prebiotic Earth, by assuming that RNA, the only known molecule type capable of playing genetic and catalytic roles at the same time, could have been the first evolvable entity on the evolutionary path to the first living cell. We have developed the Metabolically Coupled Replicator System (MCRS), a spatially explicit simulation modelling approach to prebiotic RNA-World evolution on mineral surfaces, in which we incorporate the most important experimental facts and theoretical considerations to comply with recent knowledge on RNA and prebiotic evolution. In this paper the MCRS model framework has been extended in order to investigate the dynamical and evolutionary consequences of adding an important physico-chemical detail, namely explicit replicator structure - nucleotide sequence and 2D folding calculated from thermodynamical criteria - and their possible mutational changes, to the assumptions of a previously less detailed toy model.

RESULTS

For each mutable nucleotide sequence the corresponding 2D folded structure with minimum free energy is calculated, which in turn is used to determine the fitness components (degradation rate, replicability and metabolic enzyme activity) of the replicator. We show that the community of such replicators providing the monomer supply for their own replication by evolving metabolic enzyme activities features an improved propensity for stable coexistence and structural adaptation. These evolutionary advantages are due to the emergent uniformity of metabolic replicator fitnesses imposed on the community by local group selection and attained through replicator trait convergence, i.e., the tendency of replicator lengths, ribozyme activities and population sizes to become similar between the coevolving replicator species that are otherwise both structurally and functionally different.

CONCLUSIONS

In the most general terms it is the surprisingly high extra viability of the metabolic replicator system that the present model adds to the MCRS concept of the origin of life. Surface-bound, metabolically coupled RNA replicators tend to evolve different, enzymatically active sites within thermodynamically stable secondary structures, and the system as a whole evolves towards the robust coexistence of a complete set of such ribozymes driving the metabolism producing monomers for their own replication.

Footprints of optimal protein assembly strategies in the operonic structure of prokaryotes

In this work, we investigate optimality principles behind synthesis strategies for protein complexes using a dynamic optimization approach. We show that the cellular capacity of protein synthesis has a strong influence on optimal synthesis strategies reaching from a simultaneous to a sequential synthesis of the subunits of a protein complex. Sequential synthesis is preferred if protein synthesis is strongly limited, whereas a simultaneous synthesis is optimal in situations with a high protein synthesis capacity. We confirm the predictions of our optimization approach through the analysis of the operonic organization of protein complexes in several hundred prokaryotes. Thereby, we are able to show that cellular protein synthesis capacity is a driving force in the dissolution of operons comprising the subunits of a protein complex. Thus, we also provide a tested hypothesis explaining why the subunits of many prokaryotic protein complexes are distributed across several operons despite the presumably less precise co-regulation.

The dynamics of the RNA world: insights and challenges

The RNA world hypothesis of the origin of life, in which RNA emerged as both enzyme and information carrier, is receiving solid experimental support. The prebiotic synthesis of biomolecules, the catalytic aid offered by mineral surfaces, and the vast enzymatic repertoire of ribozymes are only pieces of the origin of life puzzle; the full picture can only emerge if the pieces fit together by either following from one another or coexisting with each other. Here, we review the theory of the origin, maintenance, and enhancement of the RNA world as an evolving population of dynamical systems. The dynamical view of the origin of life allows us to pinpoint the missing and the not fitting pieces: (1) How can the first self-replicating ribozyme emerge in the absence of template-directed information replication? (2) How can nucleotide replicators avoid competitive exclusion despite utilizing the very same resources (nucleobases)? (3) How can the information catastrophe be avoided? (4) How can enough genes integrate into a cohesive system in order to transition to a cellular stage? (5) How can the way information is stored and metabolic complexity coevolve to pave to road leading out of the RNA world to the present protein-DNA world?

A phylogenomic census of molecular functions identifies modern thermophilic archaea as the most ancient form of cellular life

The origins of diversified life remain mysterious despite considerable efforts devoted to untangling the roots of the universal tree of life. Here we reconstructed phylogenies that described the evolution of molecular functions and the evolution of species directly from a genomic census of gene ontology (GO) definitions. We sampled 249 free-living genomes spanning organisms in the three superkingdoms of life, Archaea, Bacteria, and Eukarya, and used the abundance of GO terms as molecular characters to produce rooted phylogenetic trees. Results revealed an early thermophilic origin of Archaea that was followed by genome reduction events in microbial superkingdoms. Eukaryal genomes displayed extraordinary functional diversity and were enriched with hundreds of novel molecular activities not detected in the akaryotic microbial cells. Remarkably, the majority of these novel functions appeared quite late in evolution, synchronized with the diversification of the eukaryal superkingdom. The distribution of GO terms in superkingdoms confirms that Archaea appears to be the simplest and most ancient form of cellular life, while Eukarya is the most diverse and recent.

Dynamic optimization identifies optimal programmes for pathway regulation in prokaryotes

To survive in fluctuating environmental conditions, microorganisms must be able to quickly react to environmental challenges by upregulating the expression of genes encoding metabolic pathways. Here we show that protein abundance and protein synthesis capacity are key factors that determine the optimal strategy for the activation of a metabolic pathway. If protein abundance relative to protein synthesis capacity increases, the strategies shift from the simultaneous activation of all enzymes to the sequential activation of groups of enzymes and finally to a sequential activation of individual enzymes along the pathway. In the case of pathways with large differences in protein abundance, even more complex pathway activation strategies with a delayed activation of low abundance enzymes and an accelerated activation of high abundance enzymes are optimal. We confirm the existence of these pathway activation strategies as well as their dependence on our proposed constraints for a large number of metabolic pathways in several hundred prokaryotes.

pH feedback and phenotypic diversity within bacterial functional groups of the human gut

Microbial diversity in the human colon is very high with apparently large functional redundancy such that within each bacterial functional group there are many coexisting strains. Modelling this mathematically is problematic since strains within a functional group are often competing for the same limited number of resources and therefore competitive exclusion theory predicts a loss of diversity over time. Here we investigate, through computer simulation, a fluctuation dependent mechanism for the promotion of diversity. A variable pH environment caused by acidic by-products of bacterial growth on a fluctuating substrate coupled with small differences in acid tolerance between strains promotes diversity under both equilibrium and far-from-equilibrium conditions. Under equilibrium conditions pH fluctuations and relative nonlinearity in pH limitation among strains combine to prevent complete competitive exclusion. Under far-from-equilibrium conditions, loss of diversity through extinctions is made more difficult because pH cycling leads to fluctuations in the competitive ranking of strains, thereby helping to equalise fitness. We assume a trade-off between acid tolerance and maximum growth rate so that our microbial system consists of strains ranging from specialists to generalists. By altering the magnitude of the effect of the system on its pH environment (e.g. the buffering capacity of the colon) and the pattern of incoming resource we explore the conditions that promote diversity.

Structural phylogenomics retrodicts the origin of the genetic code and uncovers the evolutionary impact of protein flexibility

The genetic code shapes the genetic repository. Its origin has puzzled molecular scientists for over half a century and remains a long-standing mystery. Here we show that the origin of the genetic code is tightly coupled to the history of aminoacyl-tRNA synthetase enzymes and their interactions with tRNA. A timeline of evolutionary appearance of protein domain families derived from a structural census in hundreds of genomes reveals the early emergence of the 'operational' RNA code and the late implementation of the standard genetic code. The emergence of codon specificities and amino acid charging involved tight coevolution of aminoacyl-tRNA synthetases and tRNA structures as well as episodes of structural recruitment. Remarkably, amino acid and dipeptide compositions of single-domain proteins appearing before the standard code suggest archaic synthetases with structures homologous to catalytic domains of tyrosyl-tRNA and seryl-tRNA synthetases were capable of peptide bond formation and aminoacylation. Results reveal that genetics arose through coevolutionary interactions between polypeptides and nucleic acid cofactors as an exacting mechanism that favored flexibility and folding of the emergent proteins. These enhancements of phenotypic robustness were likely internalized into the emerging genetic system with the early rise of modern protein structure.

Structural phylogenomics reveals gradual evolutionary replacement of abiotic chemistries by protein enzymes in purine metabolism

The origin of metabolism has been linked to abiotic chemistries that existed in our planet at the beginning of life. While plausible chemical pathways have been proposed, including the synthesis of nucleobases, ribose and ribonucleotides, the cooption of these reactions by modern enzymes remains shrouded in mystery. Here we study the emergence of purine metabolism. The ages of protein domains derived from a census of fold family structure in hundreds of genomes were mapped onto enzymes in metabolic diagrams. We find that the origin of the nucleotide interconversion pathway benefited most parsimoniously from the prebiotic formation of adenine nucleosides. In turn, pathways of nucleotide biosynthesis, catabolism and salvage originated ∼300 million years later by concerted enzymatic recruitments and gradual replacement of abiotic chemistries. Remarkably, this process led to the emergence of the fully enzymatic biosynthetic pathway ∼3 billion years ago, concurrently with the appearance of a functional ribosome. The simultaneous appearance of purine biosynthesis and the ribosome probably fulfilled the expanding matter-energy and processing needs of genomic information.

Early evolution of efficient enzymes and genome organization

Background

Cellular life with complex metabolism probably evolved during the reign of RNA, when it served as both information carrier and enzyme. Jensen proposed that enzymes of primordial cells possessed broad specificities: they were generalist. When and under what conditions could primordial metabolism run by generalist enzymes evolve to contemporary-type metabolism run by specific enzymes?

Results

Here we show by numerical simulation of an enzyme-catalyzed reaction chain that specialist enzymes spread after the invention of the chromosome because protocells harbouring unlinked genes maintain largely non-specific enzymes to reduce their assortment load. When genes are linked on chromosomes, high enzyme specificity evolves because it increases biomass production, also by reducing taxation by side reactions.

Conclusion

The constitution of the genetic system has a profound influence on the limits of metabolic efficiency. The major evolutionary transition to chromosomes is thus proven to be a prerequisite for a complex metabolism. Furthermore, the appearance of specific enzymes opens the door for the evolution of their regulation.

Reviewers

This article was reviewed by Sándor Pongor, Gáspár Jékely, and Rob Knight.

Escape from Adaptive Conflict follows from weak functional trade-offs and mutational robustness

A fundamental question in molecular evolution is how proteins can adapt to new functions while being conserved for an existing function at the same time. Several theoretical models have been put forward to explain this apparent paradox. The most popular models include neofunctionalization, subfunctionalization (SUBF) by degenerative mutations, and dosage models. All of these models focus on adaptation after gene duplication. A newly proposed model named "Escape from Adaptive Conflict" (EAC) includes adaptive processes before and after gene duplication that lead to multifunctional proteins, and divergence (SUBF). Support for the importance of multifunctionality for the evolution of new protein functions comes from two experimental observations. First, many enzymes have highly evolvable promiscuous side activities. Second, different structural states of the same protein can be associated with different functions. How these observations may be related to the EAC model, under which conditions EAC is possible, and how the different models relate to each other is still unclear. Here, we present a theoretical framework that uses biophysical principles to infer the roles of functional promiscuity, gene dosage, gene duplication, point mutations, and selection pressures in the evolution of proteins. We find that selection pressures can determine whether neofunctionalization or SUBF is the more likely evolutionary process. Multifunctional proteins, arising during EAC evolution, allow rapid adaptation independent of gene duplication. This becomes a crucial advantage when gene duplications are rare. Finally, we propose that an increase in mutational robustness, not necessarily functional optimization, can be the sole driving force behind SUBF.

Biphasic patterns of diversification and the emergence of modules

The intricate molecular and cellular structure of organisms converts energy to work, which builds and maintains structure. Evolving structure implements modules, in which parts are tightly linked. Each module performs characteristic functions. In this work we propose that a module can emerge through two phases of diversification of parts. Early in the first phase of this biphasic pattern, the parts have weak linkage-they interact weakly and associate variously. The parts diversify and compete. Under selection for performance, interactions among the parts increasingly constrain their structure and associations. As many variants are eliminated, parts self-organize into modules with tight linkage. Linkage may increase in response to exogenous stresses as well as endogenous processes. In the second phase of diversification, variants of the module and its functions evolve and become new parts for a new cycle of generation of higher-level modules. This linkage hypothesis can interpret biphasic patterns in the diversification of protein domain structure, RNA and protein shapes, and networks in metabolism, codes, and embryos, and can explain hierarchical levels of structural organization that are widespread in biology.

Out of fuzzy chemistry: from prebiotic chemistry to metabolic networks

The origin of life on Earth was a chemical affair. So how did primitive biochemical systems originate from geochemical and cosmochemical processes on the young planet? Contemporary research into the origins of life subscribes to the Darwinian principle of material causes operating in an evolutionary context, as advocated by A. I. Oparin and J. B. S. Haldane in the 1920s. In its simplest form (e.g., a bacterial cell) extant biological complexity relies on the functional integration of metabolic networks and replicative genomes inside a lipid boundary. Different research programmes have explored the prebiotic plausibility of each of these autocatalytic subsystems and combinations thereof: self-maintained networks of small molecules, template chemistry, and self-reproductive vesicles. This tutorial review focuses on the debates surrounding the origin of metabolism and offers a brief overview of current studies on the evolution of metabolic networks. I suggest that a leitmotif in the origin and evolution of metabolism is the role played by catalysers' substrate ambiguity and multifunctionality.

The phylogenomic roots of modern biochemistry: origins of proteins, cofactors and protein biosynthesis

The complexity of modern biochemistry developed gradually on early Earth as new molecules and structures populated the emerging cellular systems. Here, we generate a historical account of the gradual discovery of primordial proteins, cofactors, and molecular functions using phylogenomic information in the sequence of 420 genomes. We focus on structural and functional annotations of the 54 most ancient protein domains. We show how primordial functions are linked to folded structures and how their interaction with cofactors expanded the functional repertoire. We also reveal protocell membranes played a crucial role in early protein evolution and show translation started with RNA and thioester cofactor-mediated aminoacylation. Our findings allow elaboration of an evolutionary model of early biochemistry that is firmly grounded in phylogenomic information and biochemical, biophysical, and structural knowledge. The model describes how primordial α-helical bundles stabilized membranes, how these were decorated by layered arrangements of β-sheets and α-helices, and how these arrangements became globular. Ancient forms of aminoacyl-tRNA synthetase (aaRS) catalytic domains and ancient non-ribosomal protein synthetase (NRPS) modules gave rise to primordial protein synthesis and the ability to generate a code for specificity in their active sites. These structures diversified producing cofactor-binding molecular switches and barrel structures. Accretion of domains and molecules gave rise to modern aaRSs, NRPS, and ribosomal ensembles, first organized around novel emerging cofactors (tRNA and carrier proteins) and then more complex cofactor structures (rRNA). The model explains how the generation of protein structures acted as scaffold for nucleic acids and resulted in crystallization of modern translation.

Toward a theory of multilevel evolution: long-term information integration shapes the mutational landscape and enhances evolvability

Most of evolutionary theory has abstracted away from how information is coded in the genome and how this information is transformed into traits on which selection takes place. While in the earliest stages of biological evolution, in the RNA world, the mapping from the genotype into function was largely predefined by the physical-chemical properties of the evolving entities (RNA replicators, e.g. from sequence to folded structure and catalytic sites), in present-day organisms, the mapping itself is the result of evolution. I will review results of several in silico evolutionary studies which examine the consequences of evolving the genetic coding, and the ways this information is transformed, while adapting to prevailing environments. Such multilevel evolution leads to long-term information integration. Through genome, network, and dynamical structuring, the occurrence and/or effect of random mutations becomes nonrandom, and facilitates rapid adaptation. This is what does happen in the in silico experiments. Is it also what did happen in biological evolution? I will discuss some data that suggest that it did. In any case, these results provide us with novel search images to tackle the wealth of biological data.

Evolutionary principles underlying structure and response dynamics of cellular networks

The network view in systems biology, in conjunction with the continuing development of experimental technologies, is providing us with the key structural and dynamical features of both cell-wide and pathway-level regulatory, signaling and metabolic systems. These include for example modularity and presence of hub proteins at the structural level and ultrasensitivity and feedback control at the level of dynamics. The uncovering of such features, and the seeming commonality of some of them, makes many systems biologists believe that these could represent design principles that underpin cellular systems across organisms. Here, we argue that such claims on any observed feature requires an understanding of how it has emerged in evolution and how it can shape subsequent evolution. We review recent and past studies that aim to achieve such evolutionary understanding for observed features of cellular networks. We argue that this evolutionary framework could lead to deciphering evolutionary origin and relevance of proposed design principles, thereby allowing to predict their presence or absence in an organism based on its environment and biochemistry and their effect on its future evolution.

The evolution of enzyme specificity in the metabolic replicator model of prebiotic evolution

The chemical machinery of life must have been catalytic from the outset. Models of the chemical origins have attempted to explain the ecological mechanisms maintaining a minimum necessary diversity of prebiotic replicator enzymes, but little attention has been paid so far to the evolutionary initiation of that diversity. We propose a possible first step in this direction: based on our previous model of a surface-bound metabolic replicator system we try to explain how the adaptive specialization of enzymatic replicator populations might have led to more diverse and more efficient communities of cooperating replicators with two different enzyme activities. The key assumptions of the model are that mutations in the replicator population can lead towards a) both of the two different enzyme specificities in separate replicators: efficient “specialists” or b) a “generalist” replicator type with both enzyme specificities working at less efficiency, or c) a fast-replicating, non-enzymatic “parasite”. We show that under realistic trade-off constraints on the phenotypic effects of these mutations the evolved replicator community will be usually composed of both types of specialists and of a limited abundance of parasites, provided that the replicators can slowly migrate on the mineral surface. It is only at very weak trade-offs that generalists take over in a phase-transition-like manner. The parasites do not seriously harm the system but can freely mutate, therefore they can be considered as pre-adaptations to later, useful functions that the metabolic system can adopt to increase its own fitness.

The roots of bioinformatics in theoretical biology

From the late 1980s onward, the term "bioinformatics" mostly has been used to refer to computational methods for comparative analysis of genome data. However, the term was originally more widely defined as the study of informatic processes in biotic systems. In this essay, I will trace this early history (from a personal point of view) and I will argue that the original meaning of the term is re-emerging.

Sex linkage, sex-specific selection, and the role of recombination in the evolution of sexually dimorphic gene expression

Sex-biased genes--genes that are differentially expressed within males and females--are nonrandomly distributed across animal genomes, with sex chromosomes and autosomes often carrying markedly different concentrations of male- and female-biased genes. These linkage patterns are often gene- and lineage-dependent, differing between functional genetic categories and between species. Although sex-specific selection is often hypothesized to shape the evolution of sex-linked and autosomal gene content, population genetics theory has yet to account for many of the gene- and lineage-specific idiosyncrasies emerging from the empirical literature. With the goal of improving the connection between evolutionary theory and a rapidly growing body of genome-wide empirical studies, we extend previous population genetics theory of sex-specific selection by developing and analyzing a biologically informed model that incorporates sex linkage, pleiotropy, recombination, and epistasis, factors that are likely to vary between genes and between species. Our results demonstrate that sex-specific selection and sex-specific recombination rates can generate, and are compatible with, the gene- and species-specific linkage patterns reported in the genomics literature. The theory suggests that sexual selection may strongly influence the architectures of animal genomes, as well as the chromosomal distribution of fixed substitutions underlying sexually dimorphic traits.

Modeling the complex dynamics of enzyme-pathway coevolution

Metabolic pathways must have coevolved with the corresponding enzyme gene sequences. However, the evolutionary dynamics ensuing from the interplay between metabolic networks and genomes is still poorly understood. Here, we present a computational model that generates putative evolutionary walks on the metabolic network using a parallel evolution of metabolic reactions and their catalyzing enzymes. Starting from an initial set of compounds and enzymes, we expand the metabolic network iteratively by adding new enzymes with a probability that depends on their sequence-based similarity to already present enzymes. Thus, we obtain simulated time courses of chemical evolution in which we can monitor the appearance of new metabolites, enzyme sequences, or even entire organisms. We observe that new enzymes do not appear gradually but rather in clusters which correspond to enzyme classes. A comparison with Brownian motion dynamics indicates that our system displays biased random walks similar to diffusion on the metabolic network with long-range correlations. This suggests that a quantitative molecular principle may underlie the appearance of punctuated equilibrium dynamics, whereby enzymes occur in bursts rather than by phyletic gradualism. Moreover, the simulated time courses lead to a putative time-order of enzyme and organism appearance. Among the patterns we detect in these evolutionary trends is a significant correlation between the time of appearance and their enzyme repertoire size. Hence, our approach to metabolic evolution may help understand the rise in complexity at the biochemical and genomic levels.

Proteome evolution and the metabolic origins of translation and cellular life

The origin of life has puzzled molecular scientists for over half a century. Yet fundamental questions remain unanswered, including which came first, the metabolic machinery or the encoding nucleic acids. In this study we take a protein-centric view and explore the ancestral origins of proteins. Protein domain structures in proteomes are highly conserved and embody molecular functions and interactions that are needed for cellular and organismal processes. Here we use domain structure to study the evolution of molecular function in the protein world. Timelines describing the age and function of protein domains at fold, fold superfamily, and fold family levels of structural complexity were derived from a structural phylogenomic census in hundreds of fully sequenced genomes. These timelines unfold congruent hourglass patterns in rates of appearance of domain structures and functions, functional diversity, and hierarchical complexity, and revealed a gradual build up of protein repertoires associated with metabolism, translation and DNA, in that order. The most ancient domain architectures were hydrolase enzymes and the first translation domains had catalytic functions for the aminoacylation and the molecular switch-driven transport of RNA. Remarkably, the most ancient domains had metabolic roles, did not interact with RNA, and preceded the gradual build-up of translation. In fact, the first translation domains had also a metabolic origin and were only later followed by specialized translation machinery. Our results explain how the generation of structure in the protein world and the concurrent crystallization of translation and diversified cellular life created further opportunities for proteomic diversification.

Revisiting the thermodynamic theory of optimal ATP stoichiometries by analysis of various ATP-producing metabolic pathways

The stoichiometry of ATP-producing metabolic pathways had been analysed theoretically by several authors by using evolutionary arguments and optimality principles. Waddell et al. (Biochem Educ 27:12-13, 1999) analysed (lactate-producing) glycolysis and used linear irreversible thermodynamics. The result was that half of the free-energy difference should be converted into free-energy of ATP and the remaining half should be used to drive the pathway. The calculated stoichiometry is in agreement with the observed yield of two moles of ATP per mole of glucose. Using the same approach, we here analyse eight other metabolic pathways. Although the deviation is not very large, the calculated values do not fit as nicely as for glycolysis as leading to lactate. For example, for O₂ respiration, the theoretical ATP yield equals 27.9. The real value varies among organisms between 26 and 38. For mixed-acid fermentation in Escherichia coli, the theoretical and experimental values are 2.24 and 2, respectively. For arginine degradation in M. pneumoniae, the calculated value is 2.43 mol of ATP, while in vivo only one mole is produced. During evolution, some pathways may not have reached their optimal ATP net production because energy yield is not their only function. Moreover, it should be acknowledged that the approach by linear irreversible thermodynamics is a rough approximation.

Selfishness versus functional cooperation in a stochastic protocell model

How to design an "evolvable" artificial system capable to increase in complexity? Although Darwin's theory of evolution by natural selection obviously offers a firm foundation, little hope of success seems to be expected from the explanatory adequacy of modern evolutionary theory, which does a good job at explaining what has already happened but remains practically helpless at predicting what will occur. However, the study of the major transitions in evolution clearly suggests that increases in complexity have occurred on those occasions when the conflicting interests between competing individuals were partly subjugated. This immediately raises the issue about "levels of selection" in evolutionary biology, and the idea that multi-level selection scenarios are required for complexity to emerge. After analyzing the dynamical behaviour of competing replicators within compartments, we show here that a proliferation of differentiated catalysts and/or improvement of catalytic efficiency of ribozymes can potentially evolve in properly designed artificial cells where the strong internal competition between the different species of replicators is somewhat prevented (i.e., by choosing them with equal probability). Experimental evolution in these systems will likely stand as beautiful examples of artificial adaptive systems, and will provide new insights to understand possible evolutionary paths to the evolution of metabolic complexity.

Evolution under fluctuating environments explains observed robustness in metabolic networks

A high level of robustness against gene deletion is observed in many organisms. However, it is still not clear which biochemical features underline this robustness and how these are acquired during evolution. One hypothesis, specific to metabolic networks, is that robustness emerges as a byproduct of selection for biomass production in different environments. To test this hypothesis we performed evolutionary simulations of metabolic networks under stable and fluctuating environments. We find that networks evolved under the latter scenario can better tolerate single gene deletion in specific environments. Such robustness is underlined by an increased number of independent fluxes and multifunctional enzymes in the evolved networks. Observed robustness in networks evolved under fluctuating environments was “apparent,” in the sense that it decreased significantly as we tested effects of gene deletions under all environments experienced during evolution. Furthermore, when we continued evolution of these networks under a stable environment, we found that any robustness they had acquired was completely lost. These findings provide evidence that evolution under fluctuating environments can account for the observed robustness in metabolic networks. Further, they suggest that organisms living under stable environments should display lower robustness in their metabolic networks, and that robustness should decrease upon switching to more stable environments.

One of the most surprising recent biological findings is the high level of tolerance organisms show towards loss of single genes. This observation suggests that there are certain features of biological systems that give them a high tolerance (i.e. robustness) towards gene loss. We still lack an exact understanding of what these features might be and how they could have been acquired during evolution. Here, we offer a possible answer for these questions in the context of metabolic networks. Using mathematical models capturing the structure and dynamics of metabolic networks, we simulate their evolution under stable and fluctuating environments (i.e., available metabolites). We find that the latter scenario leads to evolution of metabolic networks that display high robustness against gene loss. This robustness of in silico evolved networks is underlined by an increased number of multifunctional enzymes and independent paths leading from initial metabolites to biomass. These findings provide evidence that fluctuating environments can be a major evolutionary force leading to the emergence of robustness as a side effect. A direct prediction resulting from this study is that organisms living in stable and fluctuating environments should display differing levels of robustness against gene loss.

Modelling the optimal timing in metabolic pathway activation-use of Pontryagin's Maximum Principle and role of the Golden section

The time course of enzyme concentrations in metabolic pathways can be predicted on the basis of the optimality criterion of minimizing the time period in which an essential product is generated. This criterion is in line with the widely accepted view that high fitness requires high pathway flux. Here, based on Pontryagin's Maximum Principle, a method is developed to solve the corresponding constrained optimal control problem in an almost exclusively analytical way and, thus, to calculate optimal enzyme profiles, when linear, irreversible rate laws are assumed. Three different problem formulations are considered and the corresponding optimization results are derived. Besides the minimization of transition time, we consider an operation time in which 90% of the substrate has been converted into product. In that case, only the enzyme at the lower end of the pathway rather than all enzymes are active in the last phase. In all cases, biphasic or multiphasic time courses are obtained. The biological meaning of the results in terms of a consecutive just-in-time expression of metabolic genes is discussed. For the special case of two-enzyme systems, the role of the Golden section in the solution is outlined.

Emergence and evolution of modern molecular functions inferred from phylogenomic analysis of ontological data

The biological processes that characterize the phenotypes of a living system are embodied in the function of molecules and hold the key to evolutionary history, delimiting natural selection and change. These processes and functions provide direct insight into the emergence, development, and organization of cellular life. However, detailed molecular functions make up a network-like hierarchy of relationships that tells little of evolutionary links between structure and function in biology. For example, Gene Ontology terms represent widely-used vocabularies of processes and functions with evolutionary relationships that are implicit but not defined. Here, we uncover patterns of global evolutionary history in ontological terms associated with the sequence of 38 genomes. These patterns unfold the metabolic origins of modern molecular functions and major biological transitions in evolution toward complex life. Phylogenies reveal the primordial appearance of hydrolases and transferases, with ATPase, GTPase, and helicase activities being the most ancient. This indicates that ancient catalysts were crucial for binding and transport, the emergence of nucleic acids and protein biopolymers, and the communication of primordial cells with the environment. Finally, the history of biological processes showed that cellular biopolymer metabolic processes preceded biopolymer biosynthesis and essential processes related to macromolecular formation, directly challenging the existence of an RNA world. Phylogenomic systematization of biological function takes the structure and function paradigm to a completely new level of abstraction, demonstrating a "metabolic first" origin of life. The approach uncovers patterns in the morphing of function that are unprecedented and necessary for systematic views in biology.

Pathway evolution by horizontal transfer and positive selection is accommodated by relaxed negative selection upon upstream pathway genes in purple bacterial carotenoid biosynthesis

Horizontal gene transfer and selection are major forces driving microbial evolution. However, interactions between them are rarely studied. Phylogenetic analyses of purple bacterial carotenoid biosynthesis genes suggest two lineages: one producing spheroidenone and the other producing spirilloxanthin. Of the latter lineage, Rubrivivax gelatinosus S1 and Hoeflea phototrophica DFL-43 also or instead produce spheroidenone. Evolution of the spheroidenone pathway from that producing spirilloxanthin theoretically requires changes in the substrate specificity of upstream pathway enzymes and acquisition of a terminal ketolase (CrtA). In R. gelatinosus and likely also in H. phototrophica, CrtA was acquired from the Bacteroidetes, in which it functions as a hydroxylase. Estimation of nonsynonymous and synonymous mutations using several pairwise methods indicated positive selection upon both genes, consistent with their functional changes from hydroxylases to ketolases. Relaxed negative selection upon all other carotenoid biosynthetic genes in these organisms was also apparent, likely facilitating changes in their substrate specificities. Furthermore, all genes responsible for terminal carotenoid biosynthetic pathway steps were under reduced negative selection compared to those known to govern biosynthetic pathway specificity. Horizontal transfer of crtA into R. gelatinosus and H. phototrophica has therefore likely been promoted by (i) the apparent selective advantage of spheroidenone production relative to spirilloxanthin production, (ii) reduced negative selection upon other carotenoid biosynthetic genes, facilitating changes in their substrate specificities, and (iii) preexisting low enzyme substrate specificities due to relaxed negative selection. These results highlight the importance and complexity of selection acting upon both a horizontally transferred gene and the biochemical network into which it is integrating.