The Ascent of the Abundant: How Mutational Networks Constrain Evolution

Evolution by natural selection is fundamentally shaped by the fitness landscapes in which it occurs. Yet fitness landscapes are vast and complex, and thus we know relatively little about the long-range constraints they impose on evolutionary dynamics. Here, we exhaustively survey the structural landscapes of RNA molecules of lengths 12 to 18 nucleotides, and develop a network model to describe the relationship between sequence and structure. We find that phenotype abundance—the number of genotypes producing a particular phenotype—varies in a predictable manner and critically influences evolutionary dynamics. A study of naturally occurring functional RNA molecules using a new structural statistic suggests that these molecules are biased toward abundant phenotypes. This supports an “ascent of the abundant” hypothesis, in which evolution yields abundant phenotypes even when they are not the most fit

Degeneracy: a link between evolvability, robustness and complexity in biological systems

A full accounting of biological robustness remains elusive; both in terms of the mechanisms by which robustness is achieved and the forces that have caused robustness to grow over evolutionary time. Although its importance to topics such as ecosystem services and resilience is well recognized, the broader relationship between robustness and evolution is only starting to be fully appreciated. A renewed interest in this relationship has been prompted by evidence that mutational robustness can play a positive role in the discovery of adaptive innovations (evolvability) and evidence of an intimate relationship between robustness and complexity in biology. This paper offers a new perspective on the mechanics of evolution and the origins of complexity, robustness, and evolvability. Here we explore the hypothesis that degeneracy, a partial overlap in the functioning of multi-functional components, plays a central role in the evolution and robustness of complex forms. In support of this hypothesis, we present evidence that degeneracy is a fundamental source of robustness, it is intimately tied to multi-scaled complexity, and it establishes conditions that are necessary for system evolvability

Efficient Algorithms for Probing the RNA Mutation Landscape

The diversity and importance of the role played by RNAs in the regulation and development of the cell are now well-known and well-documented. This broad range of functions is achieved through specific structures that have been (presumably) optimized through evolution. State-of-the-art methods, such as McCaskill's algorithm, use a statistical mechanics framework based on the computation of the partition function over the canonical ensemble of all possible secondary structures on a given sequence. Although secondary structure predictions from thermodynamics-based algorithms are not as accurate as methods employing comparative genomics, the former methods are the only available tools to investigate novel RNAs, such as the many RNAs of unknown function recently reported by the ENCODE consortium. In this paper, we generalize the McCaskill partition function algorithm to sum over the grand canonical ensemble of all secondary structures of all mutants of the given sequence. Specifically, our new program, RNAmutants, simultaneously computes for each integer k the minimum free energy structure MFE(k) and the partition function Z(k) over all secondary structures of all k-point mutants, even allowing the user to specify certain positions required not to mutate and certain positions required to base-pair or remain unpaired. This technically important extension allows us to study the resilience of an RNA molecule to pointwise mutations. By computing the mutation profile of a sequence, a novel graphical representation of the mutational tendency of nucleotide positions, we analyze the deleterious nature of mutating specific nucleotide positions or groups of positions. We have successfully applied RNAmutants to investigate deleterious mutations (mutations that radically modify the secondary structure) in the Hepatitis C virus cis-acting replication element and to evaluate the evolutionary pressure applied on different regions of the HIV trans-activation response element. In particular, we show qualitative agreement between published Hepatitis C and HIV experimental mutagenesis studies and our analysis of deleterious mutations using RNAmutants. Our work also predicts other deleterious mutations, which could be verified experimentally. Finally, we provide evidence that the 3′ UTR of the GB RNA virus C has been optimized to preserve evolutionarily conserved stem regions from a deleterious effect of pointwise mutations. We hope that there will be long-term potential applications of RNAmutants in de novo RNA design and drug design against RNA viruses. This work also suggests potential applications for large-scale exploration of the RNA sequence-structure network. Binary distributions are available at http://RNAmutants.csail.mit.edu/

The relationship between the error catastrophe, survival of the flattest, and natural selection

<p>Abstract</p> <p>Background</p> <p>The quasispecies model is a general model of evolution that is generally applicable to replication up to high mutation rates. It predicts that at a sufficiently high mutation rate, quasispecies with higher mutational robustness can displace quasispecies with higher replicative capacity, a phenomenon called "survival of the flattest". In some fitness landscapes it also predicts the existence of a maximum mutation rate, called the error threshold, beyond which the quasispecies enters into error catastrophe, losing its genetic information. The aim of this paper is to study the relationship between survival of the flattest and the transition to error catastrophe, as well as the connection between these concepts and natural selection.</p> <p>Results</p> <p>By means of a very simplified model, we show that the transition to an error catastrophe corresponds to a value of zero for the selective coefficient of the mutant phenotype with respect to the master phenotype, indicating that transition to the error catastrophe is in this case similar to the selection of a more robust species. This correspondence has been confirmed by considering a single-peak landscape in which sequences are grouped with respect to their Hamming distant from the master sequence. When the robustness of a classe is changed by modification of its quality factor, the distribution of the population changes in accordance with the new value of the robustness, although an error catastrophe can be detected at the same values as in the general case. When two quasispecies of different robustness competes with one another, the entry of one of them into error catastrophe causes displacement of the other, because of the greater robustness of the former. Previous works are explicitly reinterpreted in the light of the results obtained in this paper.</p> <p>Conclusions</p> <p>The main conclusion of this paper is that the entry into error catastrophe is a specific case of survival of the flattest acting on phenotypes that differ in the trade-off between replicative ability and mutational robustness. In fact, entry into error catastrophe occurs when the mutant phenotype acquires a selective advantage over the master phenotype. As both entry into error catastrophe and survival of the flattest are caused by natural selection when mutation rate is increased, we propose differentiating between them by the level of selection at which natural selection acts. So we propose to consider the transition to error catastrophe as a phenomenon of intra-quasispecies selection, and survival of the flattest as a phenomenon of inter-quasispecies selection.</p

Heterogeneous Adaptive Trajectories of Small Populations on Complex Fitness Landscapes

Background Small populations are thought to be adaptively handicapped, not only because they suffer more from deleterious mutations but also because they have limited access to new beneficial mutations, particularly those conferring large benefits. Methodology/Principal Findings Here, we test this widely held conjecture using both simulations and experiments with small and large bacterial populations evolving in either a simple or a complex nutrient environment. Consistent with expectations, we find that small populations are adaptively constrained in the simple environment; however, in the complex environment small populations not only follow more heterogeneous adaptive trajectories, but can also attain higher fitness than the large populations. Large populations are constrained to near deterministic fixation of rare large-benefit mutations. While such determinism speeds adaptation on the smooth adaptive landscape represented by the simple environment, it can limit the ability of large populations from effectively exploring the underlying topography of rugged adaptive landscapes characterized by complex environments. Conclusions Our results show that adaptive constraints often faced by small populations can be circumvented during evolution on rugged adaptive landscapes

Horizontal gene transfer dynamics and distribution of fitness effects during microbial in silico evolution

<p>Abstract</p> <p>Background</p> <p>Horizontal gene transfer (HGT) is a process that facilitates the transfer of genetic material between organisms that are not directly related, and thus can affect both the rate of evolution and emergence of traits. Recent phylogenetic studies reveal HGT events are likely ubiquitous in the Tree of Life. However, our knowledge of HGT's role in evolution and biological organization is very limited, mainly due to the lack of ancestral evolutionary signatures and the difficulty to observe complex evolutionary dynamics in a laboratory setting. Here, we utilize a multi-scale microbial evolution model to comprehensively study the effect of HGT on the evolution of complex traits and organization of gene regulatory networks.</p> <p>Results</p> <p>Large-scale simulations reveal a distinct signature of the Distribution of Fitness Effect (DFE) for HGT events: during evolution, while mutation fitness effects become more negative and neutral, HGT events result in a balanced effect distribution. In either case, lethal events are significantly decreased during evolution (33.0% to 3.2%), a clear indication of mutational robustness. Interestingly, evolution was accelerated when populations were exposed to correlated environments of increasing complexity, especially in the presence of HGT, a phenomenon that warrants further investigation. High HGT rates were found to be disruptive, while the average transferred fragment size was linked to functional module size in the underlying biological network. Network analysis reveals that HGT results in larger regulatory networks, but with the same sparsity level as those evolved in its absence. Observed phenotypic variability and co-existing solutions were traced to individual gain/loss of function events, while subsequent re-wiring after fragment integration was necessary for complex traits to emerge.</p

Does Mutational Robustness Inhibit Extinction by Lethal Mutagenesis in Viral Populations?

Lethal mutagenesis is a promising new antiviral therapy that kills a virus by raising its mutation rate. One potential shortcoming of lethal mutagenesis is that viruses may resist the treatment by evolving genomes with increased robustness to mutations. Here, we investigate to what extent mutational robustness can inhibit extinction by lethal mutagenesis in viruses, using both simple toy models and more biophysically realistic models based on RNA secondary-structure folding. We show that although the evolution of greater robustness may be promoted by increasing the mutation rate of a viral population, such evolution is unlikely to greatly increase the mutation rate required for certain extinction. Using an analytic multi-type branching process model, we investigate whether the evolution of robustness can be relevant on the time scales on which extinction takes place. We find that the evolution of robustness matters only when initial viral population sizes are small and deleterious mutation rates are only slightly above the level at which extinction can occur. The stochastic calculations are in good agreement with simulations of self-replicating RNA sequences that have to fold into a specific secondary structure to reproduce. We conclude that the evolution of mutational robustness is in most cases unlikely to prevent the extinction of viruses by lethal mutagenesis

Topological Structure of the Space of Phenotypes: The Case of RNA Neutral Networks

The evolution and adaptation of molecular populations is constrained by the diversity accessible through mutational processes. RNA is a paradigmatic example of biopolymer where genotype (sequence) and phenotype (approximated by the secondary structure fold) are identified in a single molecule. The extreme redundancy of the genotype-phenotype map leads to large ensembles of RNA sequences that fold into the same secondary structure and can be connected through single-point mutations. These ensembles define neutral networks of phenotypes in sequence space. Here we analyze the topological properties of neutral networks formed by 12-nucleotides RNA sequences, obtained through the exhaustive folding of sequence space. A total of 412 sequences fragments into 645 subnetworks that correspond to 57 different secondary structures. The topological analysis reveals that each subnetwork is far from being random: it has a degree distribution with a well-defined average and a small dispersion, a high clustering coefficient, and an average shortest path between nodes close to its minimum possible value, i.e. the Hamming distance between sequences. RNA neutral networks are assortative due to the correlation in the composition of neighboring sequences, a feature that together with the symmetries inherent to the folding process explains the existence of communities. Several topological relationships can be analytically derived attending to structural restrictions and generic properties of the folding process. The average degree of these phenotypic networks grows logarithmically with their size, such that abundant phenotypes have the additional advantage of being more robust to mutations. This property prevents fragmentation of neutral networks and thus enhances the navigability of sequence space. In summary, RNA neutral networks show unique topological properties, unknown to other networks previously described

Redundancy and the Evolution of Cis-Regulatory Element Multiplicity

The promoter regions of many genes contain multiple binding sites for the same transcription factor (TF). One possibility is that this multiplicity evolved through transitional forms showing redundant cis-regulation. To evaluate this hypothesis, we must disentangle the relative contributions of different evolutionary mechanisms to the evolution of binding site multiplicity. Here, we attempt to do this using a model of binding site evolution. Our model considers binding sequences and their interactions with TFs explicitly, and allows us to cast the evolution of gene networks into a neutral network framework. We then test some of the model's predictions using data from yeast. Analysis of the model suggested three candidate nonadaptive processes favoring the evolution of cis-regulatory element redundancy and multiplicity: neutral evolution in long promoters, recombination and TF promiscuity. We find that recombination rate is positively associated with binding site multiplicity in yeast. Our model also indicated that weak direct selection for multiplicity (partial redundancy) can play a major role in organisms with large populations. Our data suggest that selection for changes in gene expression level may have contributed to the evolution of multiple binding sites in yeast. We conclude that the evolution of cis-regulatory element redundancy and multiplicity is impacted by many aspects of the biology of an organism: both adaptive and nonadaptive processes, both changes in cis to binding sites and in trans to the TFs that interact with them, both the functional setting of the promoter and the population genetic context of the individuals carrying them

Neutrality and Robustness in Evo-Devo: Emergence of Lateral Inhibition

Embryonic development is defined by the hierarchical dynamical process that translates genetic information (genotype) into a spatial gene expression pattern (phenotype) providing the positional information for the correct unfolding of the organism. The nature and evolutionary implications of genotype–phenotype mapping still remain key topics in evolutionary developmental biology (evo-devo). We have explored here issues of neutrality, robustness, and diversity in evo-devo by means of a simple model of gene regulatory networks. The small size of the system allowed an exhaustive analysis of the entire fitness landscape and the extent of its neutrality. This analysis shows that evolution leads to a class of robust genetic networks with an expression pattern characteristic of lateral inhibition. This class is a repertoire of distinct implementations of this key developmental process, the diversity of which provides valuable clues about its underlying causal principles