Mutational robustness accelerates the origin of novel RNA phenotypes through phenotypic plasticity

The Boltzmann distributions of molecular structures predict likely changes through random mutations

New folded molecular structures can only evolve after arising through mutations. This aspect is modeled using genotype-phenotype maps, which connect sequence changes through mutations to changes in molecular structures. Previous work has shown that the likelihood of appearing through mutations can differ by orders of magnitude from structure to structure and that this can affect the outcomes of evolutionary processes. Thus, we focus on the phenotypic mutation probabilities φqp, i.e., the likelihood that a random mutation changes structure p into structure q. For both RNA secondary structures and the HP protein model, we show that a simple biophysical principle can explain and predict how this likelihood depends on the new structure q: φqp is high if sequences that fold into p as the minimum-free-energy structure are likely to have q as an alternative structure with high Boltzmann frequency. This generalizes the existing concept of plastogenetic congruence from individual sequences to the entire neutral spaces of structures. Our result helps us understand why some structural changes are more likely than others, may be useful for estimating these likelihoods via sampling and makes a connection to alternative structures with high Boltzmann frequency, which could be relevant in evolutionary processes.

The non-deterministic genotype-phenotype map of RNA secondary structure

Selection and variation are both key aspects in the evolutionary process. Previous research on the mapping between molecular sequence (genotype) and molecular fold (phenotype) has shown the presence of several structural properties in different biological contexts, implying that these might be universal in evolutionary spaces. The deterministic genotype-phenotype (GP) map that links short RNA sequences to minimum free energy secondary structures has been studied extensively because of its computational tractability and biologically realistic nature. However, this mapping ignores the phenotypic plasticity of RNA. We define a GP map that incorporates non-deterministic (ND) phenotypes, and take RNA as a case study; we use the Boltzmann probability distribution of folded structures and examine the structural properties of ND GP maps for RNA sequences of length 12 and coarse-grained RNA structures of length 30 (RNAshapes30). A framework is presented to study robustness, evolvability and neutral spaces in the ND map. This framework is validated by demonstrating close correspondence between the ND quantities and sample averages of their deterministic counterparts. When using the ND framework we observe the same structural properties as in the deterministic GP map, such as bias, negative correlation between genotypic robustness and evolvability, and positive correlation between phenotypic robustness and evolvability.

The simple emergence of complex molecular function

At odds with a traditional view of molecular evolution that seeks a descent-with-modification relationship between functional sequences, new functions can emerge de novo with relative ease. At early times of molecular evolution, random polymers could have sufficed for the appearance of incipient chemical activity, while the cellular environment harbours a myriad of proto-functional molecules. The emergence of function is facilitated by several mechanisms intrinsic to molecular organization, such as redundant mapping of sequences into structures, phenotypic plasticity, modularity or cooperative associations between genomic sequences. It is the availability of niches in the molecular ecology that filters new potentially functional proposals. New phenotypes and subsequent levels of molecular complexity could be attained through combinatorial explorations of currently available molecular variants. Natural selection does the rest. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.

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.

Insertions and deletions in the RNA sequence-structure map

Genotype-phenotype maps link genetic changes to their fitness effect and are thus an essential component of evolutionary models. The map between RNA sequences and their secondary structures is a key example and has applications in functional RNA evolution. For this map, the structural effect of substitutions is well understood, but models usually assume a constant sequence length and do not consider insertions or deletions. Here, we expand the sequence-structure map to include single nucleotide insertions and deletions by using the RNAshapes concept. To quantify the structural effect of insertions and deletions, we generalize existing definitions for robustness and non-neutral mutation probabilities. We find striking similarities between substitutions, deletions and insertions: robustness to substitutions is correlated with robustness to insertions and, for most structures, to deletions. In addition, frequent structural changes after substitutions also tend to be common for insertions and deletions. This is consistent with the connection between energetically suboptimal folds and possible structural transitions. The similarities observed hold both for genotypic and phenotypic robustness and mutation probabilities, i.e. for individual sequences and for averages over sequences with the same structure. Our results could have implications for the rate of neutral and non-neutral evolution.

From genotypes to organisms: State-of-the-art and perspectives of a cornerstone in evolutionary dynamics

Understanding how genotypes map onto phenotypes, fitness, and eventually organisms is arguably the next major missing piece in a fully predictive theory of evolution. We refer to this generally as the problem of the genotype-phenotype map. Though we are still far from achieving a complete picture of these relationships, our current understanding of simpler questions, such as the structure induced in the space of genotypes by sequences mapped to molecular structures, has revealed important facts that deeply affect the dynamical description of evolutionary processes. Empirical evidence supporting the fundamental relevance of features such as phenotypic bias is mounting as well, while the synthesis of conceptual and experimental progress leads to questioning current assumptions on the nature of evolutionary dynamics-cancer progression models or synthetic biology approaches being notable examples. This work delves with a critical and constructive attitude into our current knowledge of how genotypes map onto molecular phenotypes and organismal functions, and discusses theoretical and empirical avenues to broaden and improve this comprehension. As a final goal, this community should aim at deriving an updated picture of evolutionary processes soundly relying on the structural properties of genotype spaces, as revealed by modern techniques of molecular and functional analysis.

Degeneracy and genetic assimilation in RNA evolution

BACKGROUND

The neutral theory of Motoo Kimura stipulates that evolution is mostly driven by neutral mutations. However adaptive pressure eventually leads to changes in phenotype that involve non-neutral mutations. The relation between neutrality and adaptation has been studied in the context of RNA before and here we further study transitional mutations in the context of degenerate (plastic) RNA sequences and genetic assimilation. We propose quasineutral mutations, i.e. mutations which preserve an element of the phenotype set, as minimal mutations and study their properties. We also propose a general probabilistic interpretation of genetic assimilation and specialize it to the Boltzmann ensemble of RNA sequences.

RESULTS

We show that degenerate sequences i.e. sequences with more than one structure at the MFE level have the highest evolvability among all sequences and are central to evolutionary innovation. Degenerate sequences also tend to cluster together in the sequence space. The selective pressure in an evolutionary simulation causes the population to move towards regions with more degenerate sequences, i.e. regions at the intersection of different neutral networks, and this causes the number of such sequences to increase well beyond the average percentage of degenerate sequences in the sequence space. We also observe that evolution by quasineutral mutations tends to conserve the number of base pairs in structures and thereby maintains structural integrity even in the presence of pressure to the contrary.

CONCLUSIONS

We conclude that degenerate RNA sequences play a major role in evolutionary adaptation.

On the networked architecture of genotype spaces and its critical effects on molecular evolution

Evolutionary dynamics is often viewed as a subtle process of change accumulation that causes a divergence among organisms and their genomes. However, this interpretation is an inheritance of a gradualistic view that has been challenged at the macroevolutionary, ecological and molecular level. Actually, when the complex architecture of genotype spaces is taken into account, the evolutionary dynamics of molecular populations becomes intrinsically non-uniform, sharing deep qualitative and quantitative similarities with slowly driven physical systems: nonlinear responses analogous to critical transitions, sudden state changes or hysteresis, among others. Furthermore, the phenotypic plasticity inherent to genotypes transforms classical fitness landscapes into multiscapes where adaptation in response to an environmental change may be very fast. The quantitative nature of adaptive molecular processes is deeply dependent on a network-of-networks multilayered structure of the map from genotype to function that we begin to unveil.

The architecture of an empirical genotype-phenotype map

Recent advances in high-throughput technologies are bringing the study of empirical genotype-phenotype (GP) maps to the fore. Here, we use data from protein-binding microarrays to study an empirical GP map of transcription factor (TF) -binding preferences. In this map, each genotype is a DNA sequence. The phenotype of this DNA sequence is its ability to bind one or more TFs. We study this GP map using genotype networks, in which nodes represent genotypes with the same phenotype, and edges connect nodes if their genotypes differ by a single small mutation. We describe the structure and arrangement of genotype networks within the space of all possible binding sites for 525 TFs from three eukaryotic species encompassing three kingdoms of life (animal, plant, and fungi). We thus provide a high-resolution depiction of the architecture of an empirical GP map. Among a number of findings, we show that these genotype networks are "small-world" and assortative, and that they ubiquitously overlap and interface with one another. We also use polymorphism data from Arabidopsis thaliana to show how genotype network structure influences the evolution of TF-binding sites in vivo. We discuss our findings in the context of regulatory evolution.

Robustness versus evolvability analysis for regulatory feed-forward loops

From the definition, it appears that phenotypic robustness and evolvability of an organism are inversely related to each other. However, a number of studies exploring this question have found conflicting evidences in this regard. This question motivated the current work where we explore the relationship between robustness and evolvability. As a model system, we pick the Feed Forward Loops (FFLs), and develop a framework to characterize their performance in terms of their ability to resist changes to steady state expression (robustness), and their ability to evolve towards novel phenotypes (evolvability). We demonstrate that robustness and evolvability are positively correlated in some FFL topologies. We compare this against other small regulatory topologies, and show that the same trend does not hold among them. We postulate that the ability to positively link robustness and evolvability could be an additional reason for over-representation of FFLs in living organisms, as compared to other regulatory topologies.

Protein structural robustness to mutations: an in silico investigation

Proteins possess qualities of robustness and adaptability to perturbations such as mutations, but occasionally fail to withstand them, resulting in loss of function. Herein, the structural impact of mutations is investigated independently of the functional impact. Primarily, we aim at understanding the mechanisms of structural robustness pre-requisite for functional integrity. The structural changes due to mutations propagate from the site of mutation to residues much more distant than typical scales of chemical interactions, following a cascade mechanism. This can trigger dramatic changes or subtle ones, consistent with a loss of function and disease or the emergence of new functions. Robustness is enhanced by changes producing alternative structures, in good agreement with the view that proteins are dynamic objects fulfilling their functions from a set of conformations. This result, robust alternative structures, is also coherent with epistasis or rescue mutations, or more generally, with non-additive mutational effects and compensatory mutations. To achieve this study, we developed the first algorithm, referred to as Amino Acid Rank (AAR), which follows the structural changes associated with mutations from the site of the mutation to the entire protein structure and quantifies the changes so that mutations can be ranked accordingly. Assessing the paths of changes opens the possibility of assuming secondary mutations for compensatory mechanisms.

Genonets server-a web server for the construction, analysis and visualization of genotype networks

A genotype network is a graph in which vertices represent genotypes that have the same phenotype. Edges connect vertices if their corresponding genotypes differ in a single small mutation. Genotype networks are used to study the organization of genotype spaces. They have shed light on the relationship between robustness and evolvability in biological systems as different as RNA macromolecules and transcriptional regulatory circuits. Despite the importance of genotype networks, no tool exists for their automatic construction, analysis and visualization. Here we fill this gap by presenting the Genonets Server, a tool that provides the following features: (i) the construction of genotype networks for categorical and univariate phenotypes from DNA, RNA, amino acid or binary sequences; (ii) analyses of genotype network topology and how it relates to robustness and evolvability, as well as analyses of genotype network topography and how it relates to the navigability of a genotype network via mutation and natural selection; (iii) multiple interactive visualizations that facilitate exploratory research and education. The Genonets Server is freely available at http://ieu-genonets.uzh.ch.

Biophysics of protein evolution and evolutionary protein biophysics

The study of molecular evolution at the level of protein-coding genes often entails comparing large datasets of sequences to infer their evolutionary relationships. Despite the importance of a protein's structure and conformational dynamics to its function and thus its fitness, common phylogenetic methods embody minimal biophysical knowledge of proteins. To underscore the biophysical constraints on natural selection, we survey effects of protein mutations, highlighting the physical basis for marginal stability of natural globular proteins and how requirement for kinetic stability and avoidance of misfolding and misinteractions might have affected protein evolution. The biophysical underpinnings of these effects have been addressed by models with an explicit coarse-grained spatial representation of the polypeptide chain. Sequence-structure mappings based on such models are powerful conceptual tools that rationalize mutational robustness, evolvability, epistasis, promiscuous function performed by 'hidden' conformational states, resolution of adaptive conflicts and conformational switches in the evolution from one protein fold to another. Recently, protein biophysics has been applied to derive more accurate evolutionary accounts of sequence data. Methods have also been developed to exploit sequence-based evolutionary information to predict biophysical behaviours of proteins. The success of these approaches demonstrates a deep synergy between the fields of protein biophysics and protein evolution.

Revisiting robustness and evolvability: evolution in weighted genotype spaces

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

Preservation of genetic and regulatory robustness in ancient gene duplicates of Saccharomyces cerevisiae

Biological systems remain robust against certain genetic and environmental challenges. Robustness allows the exploration of ecological adaptations. It is unclear what factors contribute to increasing robustness. Gene duplication has been considered to increase genetic robustness through functional redundancy, accelerating the evolution of novel functions. However, recent findings have questioned the link between duplication and robustness. In particular, it remains elusive whether ancient duplicates still bear potential for innovation through preserved redundancy and robustness. Here we have investigated this question by evolving the yeast Saccharomyces cerevisiae for 2200 generations under conditions allowing the accumulation of deleterious mutations, and we put mechanisms of mutational robustness to a test. S. cerevisiae declined in fitness along the evolution experiment, but this decline decelerated in later passages, suggesting functional compensation of mutated genes. We resequenced 28 genomes from experimentally evolved S. cerevisiae lines and found more mutations in duplicates—mainly small-scale duplicates—than in singletons. Genetically interacting duplicates evolved similarly and fixed more amino acid–replacing mutations than expected. Regulatory robustness of the duplicates was supported by a larger enrichment for mutations at the promoters of duplicates than at those of singletons. Analyses of yeast gene expression conditions showed a larger variation in the duplicates’ expression than that of singletons under a range of stress conditions, sparking the idea that regulatory robustness allowed a wider range of phenotypic responses to environmental stresses, hence faster adaptations. Our data support the persistence of genetic and regulatory robustness in ancient duplicates and its role in adaptations to stresses.

Latent phenotypes pervade gene regulatory circuits

BACKGROUND

Latent phenotypes are non-adaptive byproducts of adaptive phenotypes. They exist in biological systems as different as promiscuous enzymes and genome-scale metabolic reaction networks, and can give rise to evolutionary adaptations and innovations. We know little about their prevalence in the gene expression phenotypes of regulatory circuits, important sources of evolutionary innovations.

RESULTS

Here, we study a space of more than sixteen million three-gene model regulatory circuits, where each circuit is represented by a genotype, and has one or more functions embodied in one or more gene expression phenotypes. We find that the majority of circuits with single functions have latent expression phenotypes. Moreover, the set of circuits with a given spectrum of functions has a repertoire of latent phenotypes that is much larger than that of any one circuit. Most of this latent repertoire can be easily accessed through a series of small genetic changes that preserve a circuit's main functions. Both circuits and gene expression phenotypes that are robust to genetic change are associated with a greater number of latent phenotypes.

CONCLUSIONS

Our observations suggest that latent phenotypes are pervasive in regulatory circuits, and may thus be an important source of evolutionary adaptations and innovations involving gene regulation.