Protein robustness promotes evolutionary innovations on large evolutionary time-scales

Evolution of the substrate specificity of an RNA ligase ribozyme from phosphorimidazole to triphosphate activation

The acquisition of new RNA functions through evolutionary processes was essential for the diversification of RNA-based primordial biology and its subsequent transition to modern biology. However, the mechanisms by which RNAs access new functions remain unclear. Do RNA enzymes need completely new folds to support new but related functions, or is reoptimization of the active site sufficient? What are the roles of neutral and adaptive mutations in evolutionary innovation? Here, we address these questions experimentally by focusing on the evolution of substrate specificity in RNA-catalyzed RNA assembly. We use directed in vitro evolution to show that a ligase ribozyme that uses prebiotically relevant 5'-phosphorimidazole-activated substrates can be evolved to catalyze ligation with substrates that are 5'-activated with the biologically relevant triphosphate group. Interestingly, despite catalyzing a related reaction, the new ribozyme folds into a completely new structure and exhibits promiscuity by catalyzing RNA ligation with both triphosphate and phosphorimidazole-activated substrates. Although distinct in sequence and structure, the parent phosphorimidazolide ligase and the evolved triphosphate ligase ribozymes can be connected by a series of point mutations where the intermediate sequences retain at least some ligase activity. The existence of a quasi-neutral pathway between these distinct ligase ribozymes suggests that neutral drift is sufficient to enable the acquisition of new substrate specificity, thereby providing opportunities for subsequent adaptive optimization. The transition from RNA-catalyzed RNA assembly using phosphorimidazole-activated substrates to triphosphate-activated substrates may have foreshadowed the later evolution of the protein enzymes that use monomeric triphosphates (nucleoside triphosphates, NTPs) for RNA synthesis.

Evo-devo beyond development: Generalizing evo-devo to all levels of the phenotypic evolution

A foundational idea of evo-devo is that morphological variation is not isotropic, that is, it does not occur in all directions. Instead, some directions of morphological variation are more likely than others from DNA-level variation and these largely depend on development. We argue that this evo-devo perspective should apply not only to morphology but to evolution at all phenotypic levels. At other phenotypic levels there is no development, but there are processes that can be seen, in analogy to development, as constructing the phenotype (e.g., protein folding, learning for behavior, etc.). We argue that to explain the direction of evolution two types of arguments need to be combined: generative arguments about which phenotypic variation arises in each generation and selective arguments about which of it passes to the next generation. We explain how a full consideration of the two types of arguments improves the explanatory power of evolutionary theory. Also see the video abstract here: https://youtu.be/Egbvma_uaKc.

A review of visualisations of protein fold networks and their relationship with sequence and function

Proteins form arguably the most significant link between genotype and phenotype. Understanding the relationship between protein sequence and structure, and applying this knowledge to predict function, is difficult. One way to investigate these relationships is by considering the space of protein folds and how one might move from fold to fold through similarity, or potential evolutionary relationships. The many individual characterisations of fold space presented in the literature can tell us a lot about how well the current Protein Data Bank represents protein fold space, how convergence and divergence may affect protein evolution, how proteins affect the whole of which they are part, and how proteins themselves function. A synthesis of these different approaches and viewpoints seems the most likely way to further our knowledge of protein structure evolution and thus, facilitate improved protein structure design and prediction.

Adaptive evolvability through direct selection instead of indirect, second-order selection

Can evolvability itself be the product of adaptive evolution? To answer this question is challenging, because any DNA mutation that alters only evolvability is subject to indirect, "second order" selection on the future effects of this mutation. Such indirect selection is weaker than "first-order" selection on mutations that alter fitness, in the sense that it can operate only under restrictive conditions. Here I discuss a route to adaptive evolvability that overcomes this challenge. Specifically, a recent evolution experiment showed that some mutations can enhance both fitness and evolvability through a combination of direct and indirect selection. Unrelated evidence from gene duplication and the evolution of gene regulation suggests that mutations with such dual effects may not be rare. Through such mutations, evolvability may increase at least in part because it provides an adaptive advantage. These observations suggest a research program on the adaptive evolution of evolvability, which aims to identify such mutations and to disentangle their direct fitness effects from their indirect effects on evolvability. If evolvability is itself adaptive, Darwinian evolution may have created more than life's diversity. It may also have helped create the very conditions that made the success of Darwinian evolution possible.

Fast free-energy-based neutral set size estimates for the RNA genotype-phenotype map

The genotype-phenotype (GP) map of RNA secondary structure links each RNA sequence to its corresponding secondary structure. Previous research has shown that the large-scale structural properties of GP maps, such as the size of neutral sets in genotype space, can influence evolutionary outcomes. In order to use neutral set sizes, efficient and accurate computational methods are needed to compute them. Here, we propose a new method, which is based on free energy estimates and is much faster than existing sample-based methods. Moreover, this approach can give insight into the reasons behind neutral set size variations, for example, why structures with fewer stacks tend to have larger neutral set sizes. In addition, we generalize neutral set size calculations from the previously studied many-to-one framework, where each sequence folds into a single energetically preferred structure, to a fuller many-to-many framework, where several low-energy structures are included. We find that structures with high neutral sets in one framework also tend to have large neutral sets in the other framework for a range of parameters and thus the choice of GP map does not fundamentally affect which structures have the largest neutral set sizes.

Multi-locus interactions and the build-up of reproductive isolation

All genes interact with other genes, and their additive effects and epistatic interactions affect an organism's phenotype and fitness. Recent theoretical and empirical work has advanced our understanding of the role of multi-locus interactions in speciation. However, relating different models to one another and to empirical observations is challenging. This review focuses on multi-locus interactions that lead to reproductive isolation (RI) through reduced hybrid fitness. We first review theoretical approaches and show how recent work incorporating a mechanistic understanding of multi-locus interactions recapitulates earlier models, but also makes novel predictions concerning the build-up of RI. These include high variance in the build-up rate of RI among taxa, the emergence of strong incompatibilities producing localized barriers to introgression, and an effect of population size on the build-up of RI. We then review recent experimental approaches to detect multi-locus interactions underlying RI using genomic data. We argue that future studies would benefit from overlapping methods like ancestry disequilibrium scans, genome scans of differentiation and analyses of hybrid gene expression. Finally, we highlight a need for further overlap between theoretical and empirical work, and approaches that predict what kind of patterns multi-locus interactions resulting in incompatibilities will leave in genome-wide polymorphism data. This article is part of the theme issue 'Towards the completion of speciation: the evolution of reproductive isolation beyond the first barriers'.

Mutations in disordered proteins as early indicators of nucleic acid changes triggering speciation

In this study, we analyze the role of different structural variants of proteins in the speciation processes. We separate human and mouse proteomes (taken as a reference) into three previously defined variants of disorder: ordered proteins (ORDPs), structured proteins with intrinsically disordered protein regions (IDPRs), and intrinsically disordered proteins (IDPs). Then, using the representation we call here Forsdyke plot, we study the correlation of DNA divergence with the corresponding protein (phenotypic) divergence in the three variants, comparing human and mouse coding sequences with their homologs from 26 eukaryotes. The parameters of the correlation are related to the speciation process. We find that the three variants of disordered proteins are differently related to the speciation process. Specifically, IDPs phenotypically diverge earlier than ORDPs and IDPRs. ORDPs diverge later but are phenotypically more reactive to nucleotide mutations than IDPRs and IDPs. Finally, IDPRs appear to diverge phenotypically later than IDPs, like ORDPs, but they are prone to accept mutations with rates that are similar to those of IDPs. We conclude that IDPs are involved in the early stages of the speciation process, whereas mutations in ORDPs, once speciation is initiated, accelerate phenotypic divergence.

A Novel 'Candidatus Liberibacter asiaticus'-Encoded Sec-Dependent Secretory Protein Suppresses Programmed Cell Death in Nicotiana benthamiana

'Candidatus Liberibacter asiaticus' (CLas) is one of the causal agents of citrus Huanglongbing (HLB), a bacterial disease of citrus trees that greatly reduces fruit yield and quality. CLas strains produce an array of currently uncharacterized Sec-dependent secretory proteins. In this study, the conserved chromosomally encoded protein CLIBASIA_03875 was identified as a novel Sec-dependent secreted protein. We show that CLIBASIA_03875 contains a putative Sec- secretion signal peptide (SP), a 29 amino acid residue located at the N-terminus, with a mature protein (m3875) of 22 amino acids found to localize in multiple subcellular components of the leaf epidermal cells of Nicotiana benthamiana. When overexpressed via a Potato virus X (PVX)-based expression vector in N. benthamiana, m3875 suppressed programmed cell death (PCD) and the H2O2 accumulation triggered by the pro-apoptotic mouse protein BAX and the Phytophthora infestans elicitin INF1. Overexpression also resulted in a phenotype of dwarfing, leaf deformation and mosaics, suggesting that m3875 has roles in plant immune response, growth, and development. Substitution mutagenesis of the charged amino acid (D7, R9, R11, and K22) with alanine within m3875 did not recover the phenotypes for PCD and normal growth. In addition, the transiently overexpressed m3875 regulated the transcriptional levels of N. benthamiana orthologs of CNGCs (cyclic nucleotide-gated channels), BI-1 (Bax-inhibitor 1), and WRKY33 that are involved in plant defense mechanisms. To our knowledge, m3875 is the first PCD suppressor identified from CLas. Studying the function of this protein provides insight as to how CLas attenuates the host immune responses to proliferate and cause Huanglongbing disease in citrus plants.

Information theory, evolutionary innovations and evolvability

How difficult is it to 'discover' an evolutionary adaptation or innovation? I here suggest that information theory, in combination with high-throughput DNA sequencing, can help answer this question by quantifying a new phenotype's information content. I apply this framework to compute the phenotypic information associated with novel gene regulation and with the ability to use novel carbon sources. The framework can also help quantify how DNA duplications affect evolvability, estimate the complexity of phenotypes and clarify the meaning of 'progress' in Darwinian evolution.This article is part of the themed issue 'Process and pattern in innovations from cells to societies'.

Why Phenotype Robustness Promotes Phenotype Evolvability

Robustness and evolvability are fundamental characteristics of life whose relationship has intrigued generations of biologists. Studies of several genotype–phenotype maps (GPMs) such as the map between short DNA sequences and their bindings to transcription factors showed that phenotype robustness (PR) promotes phenotype evolvability (PE), but the underlying reason is unclear. Here, we show mathematically that the expected PE is a monotonically increasing function of the expected PR in random GPMs. Population genetic simulations confirm that increasing PR raises the probability that a target phenotype appears in a population within a given time, under empirical as well as randomly rewired GPMs. These and other results demonstrate that the positive correlation between PR and PE is mathematical rather than biological. Hence, it is unsurprising to observe this correlation in every empirical GPM investigated, although the magnitude of the correlation may vary due to influences of various biological factors.

How Many Protein Sequences Fold to a Given Structure? A Coevolutionary Analysis

Quantifying the relationship between protein sequence and structure is key to understanding the protein universe. A fundamental measure of this relationship is the total number of amino acid sequences that can fold to a target protein structure, known as the "sequence capacity," which has been suggested as a proxy for how designable a given protein fold is. Although sequence capacity has been extensively studied using lattice models and theory, numerical estimates for real protein structures are currently lacking. In this work, we have quantitatively estimated the sequence capacity of 10 proteins with a variety of different structures using a statistical model based on residue-residue co-evolution to capture the variation of sequences from the same protein family. Remarkably, we find that even for the smallest protein folds, such as the WW domain, the number of foldable sequences is extremely large, exceeding the Avogadro constant. In agreement with earlier theoretical work, the calculated sequence capacity is positively correlated with the size of the protein, or better, the density of contacts. This allows the absolute sequence capacity of a given protein to be approximately predicted from its structure. On the other hand, the relative sequence capacity, i.e., normalized by the total number of possible sequences, is an extremely tiny number and is strongly anti-correlated with the protein length. Thus, although there may be more foldable sequences for larger proteins, it will be much harder to find them. Lastly, we have correlated the evolutionary age of proteins in the CATH database with their sequence capacity as predicted by our model. The results suggest a trade-off between the opposing requirements of high designability and the likelihood of a novel fold emerging by chance.

Evolution of intrinsic disorder in eukaryotic proteins

Conformational flexibility conferred though regions of intrinsic structural disorder allows proteins to behave as dynamic molecules. While it is well-known that intrinsically disordered regions can undergo disorder-to-order transitions in real-time as part of their function, we also are beginning to learn more about the dynamics of disorder-to-order transitions along evolutionary time-scales. Intrinsically disordered regions endow proteins with functional promiscuity, which is further enhanced by the ability of some of these regions to undergo real-time disorder-to-order transitions. Disorder content affects gene retention after whole genome duplication, but it is not necessarily conserved. Altered patterns of disorder resulting from evolutionary disorder-to-order transitions indicate that disorder evolves to modify function through refining stability, regulation, and interactions. Here, we review the evolution of intrinsically disordered regions in eukaryotic proteins. We discuss the interplay between secondary structure and disorder on evolutionary time-scales, the importance of disorder for eukaryotic proteome expansion and functional divergence, and the evolutionary dynamics of disorder.

Alpha Helices Are More Robust to Mutations than Beta Strands

The rapidly increasing amount of data on human genetic variation has resulted in a growing demand to identify pathogenic mutations computationally, as their experimental validation is currently beyond reach. Here we show that alpha helices and beta strands differ significantly in their ability to tolerate mutations: helices can accumulate more mutations than strands without change, due to the higher numbers of inter-residue contacts in helices. This results in two patterns: a) the same number of mutations causes less structural change in helices than in strands; b) helices diverge more rapidly in sequence than strands within the same domains. Additionally, both helices and strands are significantly more robust than coils. Based on this observation we show that human missense mutations that change secondary structure are more likely to be pathogenic than those that do not. Moreover, inclusion of predicted secondary structure changes shows significant utility for improving upon state-of-the-art pathogenicity predictions.

The factors that determine the robustness and evolvability of proteins are still largely unknown. In this work the authors show that different secondary structure elements of proteins (helices and strands) differ in their ability to tolerate mutations, and demonstrate that it is caused by differences in the number of non-covalent residue interactions within these secondary structure units. The results suggest that engineering de novo all-alpha proteins should be easier than all-beta ones, as more sequences can to fold to the same topology. Additionally, secondary structure can be used to improve current methods of pathogenicity predictions; mutations that change secondary structure are more likely to be pathogenic than mutations that do not, due to their strong destabilizing effect on protein structure.

Evolutionary Genomics Suggests That CheV Is an Additional Adaptor for Accommodating Specific Chemoreceptors within the Chemotaxis Signaling Complex

Escherichia coli and Salmonella enterica are models for many experiments in molecular biology including chemotaxis, and most of the results obtained with one organism have been generalized to another. While most components of the chemotaxis pathway are strongly conserved between the two species, Salmonella genomes contain some chemoreceptors and an additional protein, CheV, that are not found in E. coli. The role of CheV was examined in distantly related species Bacillus subtilis and Helicobacter pylori, but its role in bacterial chemotaxis is still not well understood. We tested a hypothesis that in enterobacteria CheV functions as an additional adaptor linking the CheA kinase to certain types of chemoreceptors that cannot be effectively accommodated by the universal adaptor CheW. Phylogenetic profiling, genomic context and comparative protein sequence analyses suggested that CheV interacts with specific domains of CheA and chemoreceptors from an orthologous group exemplified by the Salmonella McpC protein. Structural consideration of the conservation patterns suggests that CheV and CheW share the same binding spot on the chemoreceptor structure, but have some affinity bias towards chemoreceptors from different orthologous groups. Finally, published experimental results and data newly obtained via comparative genomics support the idea that CheV functions as a “phosphate sink” possibly to off-set the over-stimulation of the kinase by certain types of chemoreceptors. Overall, our results strongly suggest that CheV is an additional adaptor for accommodating specific chemoreceptors within the chemotaxis signaling complex.

Due to the overwhelming complexity and diversity of biological systems, the functional roles of the majority of proteins encoded in sequenced genomes remain unknown or poorly understood. The multi-protein pathway controlling chemotaxis in bacteria and archaea is an example of such complexity and diversity. Chemotaxis pathway in E. coli is one of the best understood signal transduction networks in nature; however, this model organism lacks some of the system components, such as CheV, that are found in many other species. The biological role of CheV is still under avid debate. CheV is an auxiliary component of many chemotaxis systems and is present in important human pathogens, such as Salmonella and Helicobacter, where chemotaxis is being studied as an important virulence trait. Here we established the evolutionary history of the chemotaxis pathway in enterobacteria and combined a computational genomics approach with available structural information to propose a role for CheV. Our results show that CheV in enterics evolved as an adaptor for a specific type of chemoreceptors. Furthermore, we propose that some CheV-associated chemoreceptors might increase the kinase activity above the base level, and in these cases CheV acts as an attenuator.

Iron-Sulfur Cluster Biogenesis Chaperones: Evidence for Emergence of Mutational Robustness of a Highly Specific Protein-Protein Interaction

Biogenesis of iron-sulfur clusters (FeS) is a highly conserved process involving Hsp70 and J-protein chaperones. However, Hsp70 specialization differs among species. In most eukaryotes, including Schizosaccharomyces pombe, FeS biogenesis involves interaction between the J-protein Jac1 and the multifunctional Hsp70 Ssc1. But, in Saccharomyces cerevisiae and closely related species, Jac1 interacts with the specialized Hsp70 Ssq1, which emerged through duplication of SSC1. As little is known about how gene duplicates affect the robustness of their protein interaction partners, we analyzed the functional and evolutionary consequences of Ssq1 specialization on the ubiquitous J-protein cochaperone Jac1, by comparing S. cerevisiae and S. pombe. Although deletion of JAC1 is lethal in both species, alanine substitutions within the conserved His-Pro-Asp (HPD) motif, which is critical for Jac1:Hsp70 interaction, have species-specific effects. They are lethal in S. pombe, but not in S. cerevisiae. These in vivo differences correlated with in vitro biochemical measurements. Charged residues present in the J-domain of S. cerevisiae Jac1, but absent in S. pombe Jac1, are important for tolerance of S. cerevisiae Jac1 to HPD alterations. Moreover, Jac1 orthologs from species that encode Ssq1 have a higher sequence divergence. The simplest interpretation of our results is that Ssq1's coevolution with Jac1 resulted in expansion of their binding interface, thus increasing the efficiency of their interaction. Such an expansion could in turn compensate for negative effects of HPD substitutions. Thus, our results support the idea that the robustness of Jac1 emerged as consequence of its highly efficient and specific interaction with Ssq1.

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.

Coming of age: orphan genes in plants

Sizable minorities of protein-coding genes from every sequenced eukaryotic and prokaryotic genome are unique to the species. These so-called ‘orphan genes’ may evolve de novo from non-coding sequence or be derived from older coding material. They are often associated with environmental stress responses and species-specific traits or regulatory patterns. However, difficulties in studying genes where comparative analysis is impossible, and a bias towards broadly conserved genes, have resulted in underappreciation of their importance. We review here the identification, possible origins, evolutionary trends, and functions of orphans with an emphasis on their role in plant biology. We exemplify several evolutionary trends with an analysis of Arabidopsis thaliana and present QQS as a model orphan gene.

The robustness and innovability of protein folds

Assignment of protein folds to functions indicates that >60% of folds carry out one or two enzymatic functions, while few folds, for example, the TIM-barrel and Rossmann folds, exhibit hundreds. Are there structural features that make a fold amenable to functional innovation (innovability)? Do these features relate to robustness--the ability to readily accumulate sequence changes? We discuss several hypotheses regarding the relationship between the architecture of a protein and its evolutionary potential. We describe how, in a seemingly paradoxical manner, opposite properties, such as high stability and rigidity versus conformational plasticity and structural order versus disorder, promote robustness and/or innovability. We hypothesize that polarity--differentiation and low connectivity between a protein's scaffold and its active-site--is a key prerequisite for innovability.

Robustness, evolvability, and the logic of genetic regulation

In gene regulatory circuits, the expression of individual genes is commonly modulated by a set of regulating gene products, which bind to a gene's cis-regulatory region. This region encodes an input-output function, referred to as signal-integration logic, that maps a specific combination of regulatory signals (inputs) to a particular expression state (output) of a gene. The space of all possible signal-integration functions is vast and the mapping from input to output is many-to-one: For the same set of inputs, many functions (genotypes) yield the same expression output (phenotype). Here, we exhaustively enumerate the set of signal-integration functions that yield identical gene expression patterns within a computational model of gene regulatory circuits. Our goal is to characterize the relationship between robustness and evolvability in the signal-integration space of regulatory circuits, and to understand how these properties vary between the genotypic and phenotypic scales. Among other results, we find that the distributions of genotypic robustness are skewed, so that the majority of signal-integration functions are robust to perturbation. We show that the connected set of genotypes that make up a given phenotype are constrained to specific regions of the space of all possible signal-integration functions, but that as the distance between genotypes increases, so does their capacity for unique innovations. In addition, we find that robust phenotypes are (i) evolvable, (ii) easily identified by random mutation, and (iii) mutationally biased toward other robust phenotypes. We explore the implications of these latter observations for mutation-based evolution by conducting random walks between randomly chosen source and target phenotypes. We demonstrate that the time required to identify the target phenotype is independent of the properties of the source phenotype.

Integration of new genes into cellular networks, and their structural maturation

It has been recently discovered that new genes can originate de novo from noncoding DNA, and several biological traits including expression or sequence composition form a continuum from noncoding sequences to conserved genes. In this article, using yeast genes I test whether the integration of new genes into cellular networks and their structural maturation shows such a continuum by analyzing their changes with gene age. I show that 1) The number of regulatory, protein-protein, and genetic interactions increases continuously with gene age, although with very different rates. New regulatory interactions emerge rapidly within a few million years, while the number of protein-protein and genetic interactions increases slowly, with a rate of 2-2.25 × 10(-8)/year and 4.8 × 10(-8)/year, respectively. 2) Gene essentiality evolves relatively quickly: the youngest essential genes appear in proto-genes ∼14 MY old. 3) In contrast to interactions, the secondary structure of proteins and their robustness to mutations indicate that new genes face a bottleneck in their evolution: proto-genes are characterized by high β-strand content, high aggregation propensity, and low robustness against mutations, while conserved genes are characterized by lower strand content and higher stability, most likely due to the higher probability of gene loss among young genes and accumulation of neutral mutations.

Stationary distribution of self-organized states and biological information generation

Self-organization, where spontaneous orderings occur under driven conditions, is one of the hallmarks of biological systems. We consider a statistical mechanical treatment of the biased distribution of such organized states, which become favored as a result of their catalytic activity under chemical driving forces. A generalization of the equilibrium canonical distribution describes the stationary state, which can be used to model shifts in conformational ensembles sampled by an enzyme in working conditions. The basic idea is applied to the process of biological information generation from random sequences of heteropolymers, where unfavorable Shannon entropy is overcome by the catalytic activities of selected genes. The ordering process is demonstrated with the genetic distance to a genotype with high catalytic activity as an order parameter. The resulting free energy can have multiple minima, corresponding to disordered and organized phases with first-order transitions between them.

What makes a protein fold amenable to functional innovation? Fold polarity and stability trade-offs

Protein evolvability includes two elements--robustness (or neutrality, mutations having no effect) and innovability (mutations readily inducing new functions). How are these two conflicting demands bridged? Does the ability to bridge them relate to the observation that certain folds, such as TIM barrels, accommodate numerous functions, whereas other folds support only one? Here, we hypothesize that the key to innovability is polarity--an active site composed of flexible, loosely packed loops alongside a well-separated, highly ordered scaffold. We show that highly stabilized variants of TEM-1 β-lactamase exhibit selective rigidification of the enzyme's scaffold while the active-site loops maintained their conformational plasticity. Polarity therefore results in stabilizing, compensatory mutations not trading off, but instead promoting the acquisition of new activities. Indeed, computational analysis indicates that in folds that accommodate only one function throughout evolution, for example, dihydrofolate reductase, ≥ 60% of the active-site residues belong to the scaffold. In contrast, folds associated with multiple functions such as the TIM barrel show high scaffold-active-site polarity (~20% of the active site comprises scaffold residues) and >2-fold higher rates of sequence divergence at active-site positions. Our work suggests structural measures of fold polarity that appear to be correlated with innovability, thereby providing new insights regarding protein evolution, design, and engineering.

Antibiotics as selectors and accelerators of diversity in the mechanisms of resistance: from the resistome to genetic plasticity in the β-lactamases world

Antibiotics and antibiotic resistance determinants, natural molecules closely related to bacterial physiology and consistent with an ancient origin, are not only present in antibiotic-producing bacteria. Throughput sequencing technologies have revealed an unexpected reservoir of antibiotic resistance in the environment. These data suggest that co-evolution between antibiotic and antibiotic resistance genes has occurred since the beginning of time. This evolutionary race has probably been slow because of highly regulated processes and low antibiotic concentrations. Therefore to understand this global problem, a new variable must be introduced, that the antibiotic resistance is a natural event, inherent to life. However, the industrial production of natural and synthetic antibiotics has dramatically accelerated this race, selecting some of the many resistance genes present in nature and contributing to their diversification. One of the best models available to understand the biological impact of selection and diversification are β-lactamases. They constitute the most widespread mechanism of resistance, at least among pathogenic bacteria, with more than 1000 enzymes identified in the literature. In the last years, there has been growing concern about the description, spread, and diversification of β-lactamases with carbapenemase activity and AmpC-type in plasmids. Phylogenies of these enzymes help the understanding of the evolutionary forces driving their selection. Moreover, understanding the adaptive potential of β-lactamases contribute to exploration the evolutionary antagonists trajectories through the design of more efficient synthetic molecules. In this review, we attempt to analyze the antibiotic resistance problem from intrinsic and environmental resistomes to the adaptive potential of resistance genes and the driving forces involved in their diversification, in order to provide a global perspective of the resistance problem.

Bringing molecules back into molecular evolution

Much molecular-evolution research is concerned with sequence analysis. Yet these sequences represent real, three-dimensional molecules with complex structure and function. Here I highlight a growing trend in the field to incorporate molecular structure and function into computational molecular-evolution work. I consider three focus areas: reconstruction and analysis of past evolutionary events, such as phylogenetic inference or methods to infer selection pressures; development of toy models and simulations to identify fundamental principles of molecular evolution; and atom-level, highly realistic computational modeling of molecular structure and function aimed at making predictions about possible future evolutionary events.

Structure and age jointly influence rates of protein evolution

What factors determine a protein's rate of evolution are actively debated. Especially unclear is the relative role of intrinsic factors of present-day proteins versus historical factors such as protein age. Here we study the interplay of structural properties and evolutionary age, as determinants of protein evolutionary rate. We use a large set of one-to-one orthologs between human and mouse proteins, with mapped PDB structures. We report that previously observed structural correlations also hold within each age group – including relationships between solvent accessibility, designabililty, and evolutionary rates. However, age also plays a crucial role: age modulates the relationship between solvent accessibility and rate. Additionally, younger proteins, despite being less designable, tend to evolve faster than older proteins. We show that previously reported relationships between age and rate cannot be explained by structural biases among age groups. Finally, we introduce a knowledge-based potential function to study the stability of proteins through large-scale computation. We find that older proteins are more stable for their native structure, and more robust to mutations, than younger ones. Our results underscore that several determinants, both intrinsic and historical, can interact to determine rates of protein evolution.

Rates of protein evolution vary dramatically within and between organisms. But the factors that determine a protein's evolutionary rate are still under debate, despite extensive studies over the past decade. Several determinants have been proposed, for example gene expression, the importance of the gene for the organism, the number of physical or genetic interactions it has, its structural characteristics, or when it originated. Here we study how age and structural characteristics interact with one another to influence evolutionary rates. We use a set of one-to-one orthologs of human and mouse proteins, with known crystal structures. We find that these two determinants interact: for example, the age of protein modulates how its structure correlates with evolutionary rate. Nonetheless, the influence of age on evolutionary rate cannot be explained by its interplay with structure.

The influence of assortativity on the robustness of signal-integration logic in gene regulatory networks

Gene regulatory networks (GRNs) drive the cellular processes that sustain life. To do so reliably, GRNs must be robust to perturbations, such as gene deletion and the addition or removal of regulatory interactions. GRNs must also be robust to genetic changes in regulatory regions that define the logic of signal-integration, as these changes can affect how specific combinations of regulatory signals are mapped to particular gene expression states. Previous theoretical analyses have demonstrated that the robustness of a GRN is influenced by its underlying topological properties, such as degree distribution and modularity. Another important topological property is assortativity, which measures the propensity with which nodes of similar connectivity are connected to one another. How assortativity influences the robustness of the signal-integration logic of GRNs remains an open question. Here, we use computational models of GRNs to investigate this relationship. We separately consider each of the three dynamical regimes of this model for a variety of degree distributions. We find that in the chaotic regime, robustness exhibits a pronounced increase as assortativity becomes more positive, while in the critical and ordered regimes, robustness is generally less sensitive to changes in assortativity. We attribute the increased robustness to a decrease in the duration of the gene expression pattern, which is caused by a reduction in the average size of a GRN's in-components. This study provides the first direct evidence that assortativity influences the robustness of the signal-integration logic of computational models of GRNs, illuminates a mechanistic explanation for this influence, and furthers our understanding of the relationship between topology and robustness in complex biological systems.

Biophysical characterization of mutants of Bacillus subtilis lipase evolved for thermostability: factors contributing to increased activity retention

Previously, Lipase A from Bacillus subtilis was subjected to in vitro directed evolution using iterative saturation mutagenesis, with randomization sites chosen on the basis of the highest B-factors available from the crystal structure of the wild-type (WT) enzyme. This provided mutants that, unlike WT enzyme, retained a large part of their activity after heating above 65 °C and cooling down. Here, we subjected the three best mutants along with the WT enzyme to biophysical and biochemical characterization. Combining thermal inactivation profiles, circular dichroism, X-ray structure analyses and NMR experiments revealed that mutations of surface amino acid residues counteract the tendency of Lipase A to undergo precipitation under thermal stress. Reduced precipitation of the unfolding intermediates rather than increased conformational stability of the evolved mutants seems to be responsible for the activity retention.

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.

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.

Metabolic networks and their evolution

Since the last decade of the twentieth century, systems biology has gained the ability to study the structure and function of genome-scale metabolic networks. These are systems of hundreds to thousands of chemical reactions that sustain life. Most of these reactions are catalyzed by enzymes which are encoded by genes. A metabolic network extracts chemical elements and energy from the environment, and converts them into forms that the organism can use. The function of a whole metabolic network constrains evolutionary changes in its parts. I will discuss here three classes of such changes, and how they are constrained by the function of the whole. These are the accumulation of amino acid changes in enzyme-coding genes, duplication of enzyme-coding genes, and changes in the regulation of enzymes. Conversely, evolutionary change in network parts can alter the function of the whole network. I will discuss here two such changes, namely the elimination of reactions from a metabolic network through loss of function mutations in enzyme-coding genes, and the addition of metabolic reactions, for example through mechanisms such as horizontal gene transfer. Reaction addition also provides a window into the evolution of metabolic innovations, the ability of a metabolism to sustain life on new sources of energy and of chemical elements.

The Vein Patterning 1 (VEP1) gene family laterally spread through an ecological network

Lateral gene transfer (LGT) is a major evolutionary mechanism in prokaryotes. Knowledge about LGT— particularly, multicellular— eukaryotes has only recently started to accumulate. A widespread assumption sees the gene as the unit of LGT, largely because little is yet known about how LGT chances are affected by structural/functional features at the subgenic level. Here we trace the evolutionary trajectory of VEin Patterning 1, a novel gene family known to be essential for plant development and defense. At the subgenic level VEP1 encodes a dinucleotide-binding Rossmann-fold domain, in common with members of the short-chain dehydrogenase/reductase (SDR) protein family. We found: i) VEP1 likely originated in an aerobic, mesophilic and chemoorganotrophic α-proteobacterium, and was laterally propagated through nets of ecological interactions, including multiple LGTs between phylogenetically distant green plant/fungi-associated bacteria, and five independent LGTs to eukaryotes. Of these latest five transfers, three are ancient LGTs, implicating an ancestral fungus, the last common ancestor of land plants and an ancestral trebouxiophyte green alga, and two are recent LGTs to modern embryophytes. ii) VEP1's rampant LGT behavior was enabled by the robustness and broad utility of the dinucleotide-binding Rossmann-fold, which provided a platform for the evolution of two unprecedented departures from the canonical SDR catalytic triad. iii) The fate of VEP1 in eukaryotes has been different in different lineages, being ubiquitous and highly conserved in land plants, whereas fungi underwent multiple losses. And iv) VEP1-harboring bacteria include non-phytopathogenic and phytopathogenic symbionts which are non-randomly distributed with respect to the type of harbored VEP1 gene. Our findings suggest that VEP1 may have been instrumental for the evolutionary transition of green plants to land, and point to a LGT-mediated ‘Trojan Horse’ mechanism for the evolution of bacterial pathogenesis against plants. VEP1 may serve as tool for revealing microbial interactions in plant/fungi-associated environments.

Protein structural modularity and robustness are associated with evolvability

Theory suggests that biological modularity and robustness allow for maintenance of fitness under mutational change, and when this change is adaptive, for evolvability. Empirical demonstrations that these traits promote evolvability in nature remain scant however. This is in part because modularity, robustness, and evolvability are difficult to define and measure in real biological systems. Here, we address whether structural modularity and/or robustness confer evolvability at the level of proteins by looking for associations between indices of protein structural modularity, structural robustness, and evolvability. We propose a novel index for protein structural modularity: the number of regular secondary structure elements (helices and strands) divided by the number of residues in the structure. We index protein evolvability as the proportion of sites with evidence of being under positive selection multiplied by the average rate of adaptive evolution at these sites, and we measure this as an average over a phylogeny of 25 mammalian species. We use contact density as an index of protein designability, and thus, structural robustness. We find that protein evolvability is positively associated with structural modularity as well as structural robustness and that the effect of structural modularity on evolvability is independent of the structural robustness index. We interpret these associations to be the result of reduced constraints on amino acid substitutions in highly modular and robust protein structures, which results in faster adaptation through natural selection.

The relationship between relative solvent accessibility and evolutionary rate in protein evolution

Recent work with Saccharomyces cerevisiae shows a linear relationship between the evolutionary rate of sites and the relative solvent accessibility (RSA) of the corresponding residues in the folded protein. Here, we aim to develop a mathematical model that can reproduce this linear relationship. We first demonstrate that two models that both seem reasonable choices (a simple model in which selection strength correlates with RSA and a more complex model based on RSA-dependent amino acid distributions) fail to reproduce the observed relationship. We then develop a model on the basis of observed site-specific amino acid distributions and show that this model behaves appropriately. We conclude that evolutionary rates are directly linked to the distribution of amino acids at individual sites. Because of this link, any future insight into the biophysical mechanisms that determine amino acid distributions will improve our understanding of evolutionary rates.

Phenotypic robustness can increase phenotypic variability after nongenetic perturbations in gene regulatory circuits

Nongenetic perturbations, such as environmental change or developmental noise, can induce novel phenotypes. If an induced phenotype appears recurrently and confers a fitness advantage, selection may promote its genetic stabilization. Nongenetic perturbations can thus initiate evolutionary innovation. Genetic variation that is not usually phenotypically visible may play an important role in this process. Populations under stabilizing selection on a phenotype that is robust to mutations can accumulate such variation. After nongenetic perturbations, this variation can produce new phenotypes. We here study the relationship between a phenotype's mutational robustness and a population's potential to generate novel phenotypic variation. To this end, we use a well-studied model of transcriptional regulation circuits that are important in many evolutionary innovations. We find that phenotypic robustness promotes phenotypic variability in response to nongenetic perturbations, but not in response to mutation. Our work suggests that nongenetic perturbations may initiate innovation more frequently in mutationally robust gene expression traits.

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.

Results

We show that metabolic genotypes with the same phenotype form large connected genotype networks - networks of metabolic networks - that extend far through metabolic genotype space. How far they reach through this space depends linearly on the number of super-essential reactions. A super-essential reaction is an essential reaction that occurs in all networks viable in a given environment. Metabolic networks can differ in how robust their phenotype is to the removal of individual reactions. We find that this robustness depends on metabolic network size, and on other variables, such as the size of minimal metabolic networks whose reactions are all essential in a specific environment. We show that different neighborhoods of any genotype network harbor very different novel phenotypes, metabolic innovations that can sustain life on novel sulfur sources. We also analyze the ability of evolving populations of metabolic networks to explore novel metabolic phenotypes. This ability is facilitated by the existence of genotype networks, because different neighborhoods of these networks contain very different novel phenotypes.

Conclusions

We show that the space of metabolic genotypes involved in sulfur metabolism is organized similarly to that of carbon metabolism. We demonstrate that the maximum genotype distance and robustness of metabolic networks can be explained by the number of superessential reactions and by the sizes of minimal metabolic networks viable in an environment. In contrast to the genotype space of macromolecules, where phenotypic robustness may facilitate phenotypic innovation, we show that here the ability to access novel phenotypes does not monotonically increase with robustness.

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.

Phenotypic plasticity can facilitate adaptive evolution in gene regulatory circuits

BACKGROUND

Many important evolutionary adaptations originate in the modification of gene regulatory circuits to produce new gene activity phenotypes. How do evolving populations sift through an astronomical number of circuits to find circuits with new adaptive phenotypes? The answer may often involve phenotypic plasticity. Phenotypic plasticity allows a genotype to produce different - alternative - phenotypes after non-genetic perturbations that include gene expression noise, environmental change, or epigenetic modification.

RESULTS

We here analyze a well-studied model of gene regulatory circuits. A circuit's genotype encodes the regulatory interactions among circuit genes, and its phenotype corresponds to a stable gene activity pattern the circuit forms. For this model, we study how genotypes are arranged in genotype space, where the distance between two genotypes reflects the number of regulatory mutations that set those genotypes apart. Specifically, we address whether this arrangement favors adaptive evolution mediated by plasticity. We find that plasticity facilitates the origin of genotypes that produce a new phenotype in response to non-genetic perturbations. We also find that selection can then stabilize the new phenotype genetically, allowing it to become a circuit's dominant gene expression phenotype. These are generic properties of the circuits we study here.

CONCLUSIONS

Taken together, our observations suggest that phenotypic plasticity frequently facilitates the evolution of novel beneficial gene activity patterns in gene regulatory circuits.

Robustness and evolvability

Why isn't random variation always deleterious? Are there factors that sometimes make adaptation easier? Biological systems are extraordinarily robust to perturbation by mutations, recombination and the environment. It has been proposed that this robustness might make them more evolvable. Robustness to mutation allows genetic variation to accumulate in a cryptic state. Switching mechanisms known as evolutionary capacitors mean that the amount of heritable phenotypic variation available can be correlated to the degree of stress and hence to the novelty of the environment and remaining potential for adaptation. There have been two somewhat separate literatures relating robustness to evolvability. One has focused on molecular phenotypes and new mutations, the other on morphology and cryptic genetic variation. Here, we review both literatures, and show that the true distinction is whether recombination rates are high or low. In both cases, the evidence supports the claim that robustness promotes evolvability.

Positive selection differs between protein secondary structure elements in Drosophila

Different protein secondary structure elements have different physicochemical properties and roles in the protein, which may determine their evolutionary flexibility. However, it is not clear to what extent protein structure affects the way Darwinian selection acts at the amino acid level. Using phylogeny-based likelihood tests for positive selection, we have examined the relationship between protein secondary structure and selection across six species of Drosophila. We find that amino acids that form disordered regions, such as random coils, are far more likely to be under positive selection than expected from their proportion in the proteins, and residues in helices and β-structures are subject to less positive selection than predicted. In addition, it appears that sites undergoing positive selection are more likely than expected to occur close to one another in the protein sequence. Finally, on a genome-wide scale, we have determined that positively selected sites are found more frequently toward the gene ends. Our results demonstrate that protein structures with a greater degree of organization and strong hydrophobicity, represented here as helices and β-structures, are less tolerant to molecular adaptation than disordered, hydrophilic regions, across a diverse set of proteins.

The evolvability of programmable hardware

In biological systems, individual phenotypes are typically adopted by multiple genotypes. Examples include protein structure phenotypes, where each structure can be adopted by a myriad individual amino acid sequence genotypes. These genotypes form vast connected 'neutral networks' in genotype space. The size of such neutral networks endows biological systems not only with robustness to genetic change, but also with the ability to evolve a vast number of novel phenotypes that occur near any one neutral network. Whether technological systems can be designed to have similar properties is poorly understood. Here we ask this question for a class of programmable electronic circuits that compute digital logic functions. The functional flexibility of such circuits is important in many applications, including applications of evolutionary principles to circuit design. The functions they compute are at the heart of all digital computation. We explore a vast space of 10(45) logic circuits ('genotypes') and 10(19) logic functions ('phenotypes'). We demonstrate that circuits that compute the same logic function are connected in large neutral networks that span circuit space. Their robustness or fault-tolerance varies very widely. The vicinity of each neutral network contains circuits with a broad range of novel functions. Two circuits computing different functions can usually be converted into one another via few changes in their architecture. These observations show that properties important for the evolvability of biological systems exist in a commercially important class of electronic circuitry. They also point to generic ways to generate fault-tolerant, adaptable and evolvable electronic circuitry.

On the possible role of robustness in the evolution of infectious diseases

Robustness describes the capacity for a biological system to remain canalized despite perturbation. Genetic robustness affords maintenance of phenotype despite mutational input, necessarily involving the role of epistasis. Environmental robustness is phenotypic constancy in the face of environmental variation, where epistasis may be uninvolved. Here we discuss genetic and environmental robustness, from the standpoint of infectious disease evolution, and suggest that robustness may be a unifying principle for understanding how different disease agents evolve. We focus especially on viruses with RNA genomes due to their importance in the evolution of emerging diseases and as model systems to test robustness theory. We present new data on adaptive constraints for a model RNA virus challenged to evolve in response to UV radiation. We also draw attention to other infectious disease systems where robustness theory may prove useful for bridging evolutionary biology and biomedicine, especially the evolution of antibiotic resistance in bacteria, immune evasion by influenza, and malaria parasite infections.

Protein dynamism and evolvability

The traditional view that proteins possess absolute functional specificity and a single, fixed structure conflicts with their marked ability to adapt and evolve new functions and structures. We consider an alternative, "avant-garde view" in which proteins are conformationally dynamic and exhibit functional promiscuity. We surmise that these properties are the foundation stones of protein evolvability; they facilitate the divergence of new functions within existing folds and the evolution of entirely new folds. Packing modes of proteins also affect their evolvability, and poorly packed, disordered, and conformationally diverse proteins may exhibit high evolvability. This dynamic view of protein structure, function, and evolvability is extrapolated to describe hypothetical scenarios for the evolution of the early proteins and future research directions in the area of protein dynamism and evolution.

Evolutionary consequences of cryptic genetic variation

Phenotypic evolution depends on heritable variation in phenotypes. A central aim of evolutionary biology, therefore, is to understand how processes generating phenotypic variation interact with selection and drift to result in phenotypic evolution. Recent studies have highlighted the propensity for populations to harbor genetic variation that contributes to phenotypic variation only after some environmental or genetic change. Many authors have suggested that release of this cryptic genetic variation by stressful or novel environments can facilitate phenotypic adaptation. However, there is little empirical evidence that stressful or novel environments release cryptic genetic variation, or that, once released, it contributes to phenotypic evolution. We argue that empirical studies are needed to answer these questions, and identify the empirical approaches needed to study the relationship between environment, released cryptic genetic variation and phenotypic evolution.

Neutralism and selectionism: a network-based reconciliation

Neutralism and selectionism are extremes of an explanatory spectrum for understanding patterns of molecular evolution and the emergence of evolutionary innovation. Although recent genome-scale data from protein-coding genes argue against neutralism, molecular engineering and protein evolution data argue that neutral mutations and mutational robustness are important for evolutionary innovation. Here I propose a reconciliation in which neutral mutations prepare the ground for later evolutionary adaptation. Key to this perspective is an explicit understanding of molecular phenotypes that has only become accessible in recent years.

Do viral proteins possess unique biophysical features?

Natural selection shapes the sequence, structure and biophysical properties of proteins to fit their environment. We hypothesize that highly thermostable proteins and viral proteins represent two opposing adaptation strategies. Thermostable proteins are highly compact and possess well-packed hydrophobic cores and intensely charged surfaces. By contrast, viral proteins, and RNA viral proteins in particular, display a high occurrence of disordered segments and loosely packed cores. These features might endow viral proteins with increased structural flexibility and effective ways to interact with the components of the host. They could also be related to high adaptability levels and mutation rates observed in viruses, thus, representing a unique strategy for buffering the deleterious effects of mutations, such that those that have little (interactions), have little to lose.

Neutral network sizes of biological RNA molecules can be computed and are not atypically small

Background

Neutral networks or sets consist of all genotypes with a given phenotype. The size and structure of these sets has a strong influence on a biological system's robustness to mutations, and on its evolvability, the ability to produce phenotypic variation; in the few studied cases of molecular phenotypes, the larger this set, the greater both robustness and evolvability of phenotypes. Unfortunately, any one neutral set contains generally only a tiny fraction of genotype space. Thus, current methods cannot measure neutral set sizes accurately, except in the smallest genotype spaces.

Results

Here we introduce a generalized Monte Carlo approach that can measure neutral set sizes in larger spaces. We apply our method to the genotype-to-phenotype mapping of RNA molecules, and show that it can reliably measure neutral set sizes for molecules up to 100 bases. We also study neutral set sizes of RNA structures in a publicly available database of functional, noncoding RNAs up to a length of 50 bases. We find that these neutral sets are larger than the neutral sets in 99.99% of random phenotypes. Software to estimate neutral network sizes is available at .

Conclusion

The biological RNA structures we examined are more abundant than random structures. This indicates that their robustness and their ability to produce new phenotypic variants may also be high.