Population genetics without intraspecific data

A central goal of computational biology is the prediction of phenotype from DNA and protein sequence data. Recent models of sequence change use in silico prediction systems to incorporate the effects of phenotype on evolutionary rates. These models have been designed for analyzing sequence data from different species and have been accompanied by statistical techniques for estimating model parameters when the incorporation of phenotype induces dependent change among sequence positions. A difficulty with these efforts to link phenotype and interspecific evolution is that evolution occurs within populations, and parameters of interspecific models should have population genetic interpretations. We show, with two examples, how population genetic interpretations can be assigned to evolutionary models. The first example considers the impact of RNA secondary structure on sequence change, and the second reflects the tendency for protein tertiary structure to influence nonsynonymous substitution rates. We argue that statistical fit to data should not be the sole criterion for assessing models of sequence change. A good interspecific model should also yield a clear and biologically plausible population genetic interpretation.     

Novel strategies to study the role of mutation and nucleic acid structure in evolution

Natural selection processes tune genomes in the edge of the chaos imposed by mutation and drift, allowing an enduring exploration of fitter genetic networks within the constraints imposed by self-organization and the interactions of genotype and phenotype. Alternatively, evolution can be viewed from thermodynamic, kinetic or cybernetic perspectives. Regardless of insight, there is need to understand structure-function relationships at the molecular and holistic evolutionary levels. Strategies are here described that analyze genetic variation in time and trace the evolution of nucleic acid structure. Nucleic acid scanning techniques were used to measure sequence divergence and provide a direct inference of genome-wide mutation rate. This was tested for the first time in vegetatively propagating plants. The method is general and was also used in a study of mutational patterns in phytopathogenic fungi, showing there was a link between sequence and structural diversification of ribosomal gene spacers. In order to determine if this was a general phenomenon, the origin and diversification of nucleic acid secondary structure was traced using a cladistic method capable of producing rooted phylogenetic trees. Phylogenies reconstructed from primary and secondary RNA structure were congruent at all taxonomical levels, providing evidence of a strong link between phenotype and genotype favoring thermodynamic stability and dissipation of Gibbs free energy. Overall results suggest that thermodynamic principles are important driving forces of the evolutionary processes of the living world.     

Molecular phylogeny of protists: origin and evolution of the Dinoflagellates

Abstract

Molecular sequence data have become prominent tools for phylogenetic relationship inference, particularly useful in the analysis of highly diverse taxonomic orders. Ribosomal RNA sequences provide markers that can be used in the study of phylogeny, because their function and structure have been conserved to a large extent throughout the evolutionary history of organisms. These sequences are inferred from cloned or enzymatically amplified gene sequences, or determined by direct RNA sequencing. The first step of the phylogenetic interpretation of nucleic acid sequence variations implies proper alignment of corresponding sequences from various organisms. Best alignment based on similarity criteria is greatly reinforced, in the case of ribosomal RNAs, by secondary structure homologies. Distance matrix methods to infer evolutionary trees are based on the assumption that the phylogenetic distance between each pair of organisms is proportional to the number of nucleotide substitution events. Computed tree inference methods usually take into consideration the possibility of unequal mutation rates among lineages. Divergence times can be estimated on the tree, provided that at least one lineage has been dated by fossil records. We have utilized this approach based on ribosomal RNA sequence comparison to investigate the phylogenetic relationship between dinoflagellated and other eukaryote protists, and to refine controverse phylogenies of the class Dinophycae.     

Comparative study of the evolution of nuclear ribosomal spacers incorporating secondary structure analyzes within Dodonaeoideae,Hippocastanoideae and Xanthoceroideae (Sapindaceae)

Ribosomal DNA internal transcribed spacers (ITS) and partial external transcribed spacers (ETSf) are popularly used to infer evolutionary hypotheses. However, there is generally little consideration given to the secondary structures of these small RNA molecules and their potential effects on sequence alignment and phylogenetic analyzes. Intergeneric relationships amongst three of the four major lineages in the Sapindaceae, the Dodonaeoideae, Hippcastanoideae and Xanthoceroideae were assessed by firstly, generating secondary structure predictions for ITS and partial ETSf sequences, and then these predictions were used to assist alignment of the sequences. Secondly, the alignment was analyzed using RNA specific models of sequence evolution that account for the variation in nucleotide evolution in the independent loops and covariating stems regions of the ribosomal spacers. These models and phylogeny drawn from these analyzes were compared with that from analyzes using ‘traditional’ 4-state models and previous plastid analyzes. These analyzes identified that paired-site models developed to deal specifically with stem structures in RNA encoding sequences more appropriately account for the evolutionary history of the sequences than traditional 4-state substitution models.     

Evolution in silico and in vitro: the RNA model.

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

Compositional statistics: An improvement of evolutionary parsimony and its application to deep branches in the tree of life

Summary We present compositional statistics, a new method of phylogenetic inference, which is an extension of evolutionary parsimony. Compositional statistics takes account of the base composition of the compared sequences by using nucleotide positions that evolutionary parsimony ignores. It shares with evolutionary parsimony the features of rate invariance and the fundamental distinction between transitions and transversions. Of the presently available methods of phylogenetic inference, compositional statistics is based on the fewest and mildest assumptions about the mode of DNA sequence evolution. It is therefore applicable to phylogenetic studies of the most distantly related organisms or molecules. This was illustrated by analyzing conservative positions in the DNA sequences of the large subunit of RNA polymerase from three archaebacterial groups, a eubacterium, a chloroplast, and the three eukaryotic polymerases. Internally consistent results, which are in accord with our knowledge of organelle origin and archaebacterial physiology, were achieved.     

Sampled ensemble neutrality as a feature to classify potential structured RNAs

Background

Structured RNAs have many biological functions ranging from catalysis of chemical reactions to gene regulation. Yet, many homologous structured RNAs display most of their conservation at the secondary or tertiary structure level. As a result, strategies for structured RNA discovery rely heavily on identification of sequences sharing a common stable secondary structure. However, correctly distinguishing structured RNAs from surrounding genomic sequence remains challenging, especially during de novo discovery. RNA also has a long history as a computational model for evolution due to the direct link between genotype (sequence) and phenotype (structure). From these studies it is clear that evolved RNA structures, like protein structures, can be considered robust to point mutations. In this context, an RNA sequence is considered robust if its neutrality (extent to which single mutant neighbors maintain the same secondary structure) is greater than that expected for an artificial sequence with the same minimum free energy structure.

Results

In this work, we bring concepts from evolutionary biology to bear on the structured RNA de novo discovery process. We hypothesize that alignments corresponding to structured RNAs should consist of neutral sequences. We evaluate several measures of neutrality for their ability to distinguish between alignments of structured RNA sequences drawn from Rfam and various decoy alignments. We also introduce a new measure of RNA structural neutrality, the structure ensemble neutrality (SEN). SEN seeks to increase the biological relevance of existing neutrality measures in two ways. First, it uses information from an alignment of homologous sequences to identify a conserved biologically relevant structure for comparison. Second, it only counts base-pairs of the original structure that are absent in the comparison structure and does not penalize the formation of additional base-pairs.

Conclusion

We find that several measures of neutrality are effective at separating structured RNAs from decoy sequences, including both shuffled alignments and flanking genomic sequence. Furthermore, as an independent feature classifier to identify structured RNAs, SEN yields comparable performance to current approaches that consider a variety of features including stability and sequence identity. Finally, SEN outperforms other measures of neutrality at detecting mutational robustness in bacterial regulatory RNA structures.

Electronic supplementary material

The online version of this article (doi:10.1186/s12864-014-1203-8) contains supplementary material, which is available to authorized users.     

HIV-specific probabilistic models of protein evolution

Comparative sequence analyses, including such fundamental bioinformatics techniques as similarity searching, sequence alignment and phylogenetic inference, have become a mainstay for researchers studying type 1 Human Immunodeficiency Virus (HIV-1) genome structure and evolution. Implicit in comparative analyses is an underlying model of evolution, and the chosen model can significantly affect the results. In general, evolutionary models describe the probabilities of replacing one amino acid character with another over a period of time. Most widely used evolutionary models for protein sequences have been derived from curated alignments of hundreds of proteins, usually based on mammalian genomes. It is unclear to what extent these empirical models are generalizable to a very different organism, such as HIV-1-the most extensively sequenced organism in existence. We developed a maximum likelihood model fitting procedure to a collection of HIV-1 alignments sampled from different viral genes, and inferred two empirical substitution models, suitable for describing between-and within-host evolution. Our procedure pools the information from multiple sequence alignments, and provided software implementation can be run efficiently in parallel on a computer cluster. We describe how the inferred substitution models can be used to generate scoring matrices suitable for alignment and similarity searches. Our models had a consistently superior fit relative to the best existing models and to parameter-rich data-driven models when benchmarked on independent HIV-1 alignments, demonstrating evolutionary biases in amino-acid substitution that are unique to HIV, and that are not captured by the existing models. The scoring matrices derived from the models showed a marked difference from common amino-acid scoring matrices. The use of an appropriate evolutionary model recovered a known viral transmission history, whereas a poorly chosen model introduced phylogenetic error. We argue that our model derivation procedure is immediately applicable to other organisms with extensive sequence data available, such as Hepatitis C and Influenza A viruses.     

Empirical models for substitution in ribosomal RNA

Empirical models of substitution are often used in protein sequence analysis because the large alphabet of amino acids requires that many parameters be estimated in all but the simplest parametric models. When information about structure is used in the analysis of substitutions in structured RNA, a similar situation occurs. The number of parameters necessary to adequately describe the substitution process increases in order to model the substitution of paired bases. We have developed a method to obtain substitution rate matrices empirically from RNA alignments that include structural information in the form of base pairs. Our data consisted of alignments from the European Ribosomal RNA Database of Bacterial and Eukaryotic Small Subunit and Large Subunit Ribosomal RNA ( Wuyts et al. 2001. Nucleic Acids Res. 29:175-177; Wuyts et al. 2002. Nucleic Acids Res. 30:183-185). Using secondary structural information, we converted each sequence in the alignments into a sequence over a 20-symbol code: one symbol for each of the four individual bases, and one symbol for each of the 16 ordered pairs. Substitutions in the coded sequences are defined in the natural way, as observed changes between two sequences at any particular site. For given ranges (windows) of sequence divergence, we obtained substitution frequency matrices for the coded sequences. Using a technique originally developed for modeling amino acid substitutions ( Veerassamy, Smith, and Tillier. 2003. J. Comput. Biol. 10:997-1010), we were able to estimate the actual evolutionary distance for each window. The actual evolutionary distances were used to derive instantaneous rate matrices, and from these we selected a universal rate matrix. The universal rate matrices were incorporated into the Phylip Software package ( Felsenstein 2002. http://evolution.genetics.washington.edu/phylip.html), and we analyzed the ribosomal RNA alignments using both distance and maximum likelihood methods. The empirical substitution models performed well on simulated data, and produced reasonable evolutionary trees for 16S ribosomal RNA sequences from sequenced Bacterial genomes. Empirical models have the advantage of being easily implemented, and the fact that the code consists of 20 symbols makes the models easily incorporated into existing programs for protein sequence analysis. In addition, the models are useful for simulating the evolution of RNA sequence and structure simultaneously.     

Phenotypic effect of mutations in evolving populations of RNA molecules

Background  

The secondary structure of folded RNA sequences is a good model to map phenotype onto genotype, as represented by the RNA sequence. Computational studies of the evolution of ensembles of RNA molecules towards target secondary structures yield valuable clues to the mechanisms behind adaptation of complex populations. The relationship between the space of sequences and structures, the organization of RNA ensembles at mutation-selection equilibrium, the time of adaptation as a function of the population parameters, the presence of collective effects in quasispecies, or the optimal mutation rates to promote adaptation all are issues that can be explored within this framework.     

Protein evolution with dependence among codons due to tertiary structure

Markovian models of protein evolution that relax the assumption of independent change among codons are considered. With this comparatively realistic framework, an evolutionary rate at a site can depend both on the state of the site and on the states of surrounding sites. By allowing a relatively general dependence structure among sites, models of evolution can reflect attributes of tertiary structure. To quantify the impact of protein structure on protein evolution, we analyze protein-coding DNA sequence pairs with an evolutionary model that incorporates effects of solvent accessibility and pairwise interactions among amino acid residues. By explicitly considering the relationship between nonsynonymous substitution rates and protein structure, this approach can lead to refined detection and characterization of positive selection. Analyses of simulated sequence pairs indicate that parameters in this evolutionary model can be well estimated. Analyses of lysozyme c and annexin V sequence pairs yield the biologically reasonable result that amino acid replacement rates are higher when the replacements lead to energetically favorable proteins than when they destabilize the proteins. Although the focus here is evolutionary dependence among codons that is associated with protein structure, the statistical approach is quite general and could be applied to diverse cases of evolutionary dependence where surrogates for sequence fitness can be measured or modeled.     

Evolutionary model selection with a genetic algorithm: a case study using stem RNA

The choice of a probabilistic model to describe sequence evolution can and should be justified. Underfitting the data through the use of overly simplistic models may miss out on interesting phenomena and lead to incorrect inferences. Overfitting the data with models that are too complex may ascribe biological meaning to statistical artifacts and result in falsely significant findings. We describe a likelihood-based approach for evolutionary model selection. The procedure employs a genetic algorithm (GA) to quickly explore a combinatorially large set of all possible time-reversible Markov models with a fixed number of substitution rates. When applied to stem RNA data subject to well-understood evolutionary forces, the models found by the GA 1) capture the expected overall rate patterns a priori; 2) fit the data better than the best available models based on a priori assumptions, suggesting subtle substitution patterns not previously recognized; 3) cannot be rejected in favor of the general reversible model, implying that the evolution of stem RNA sequences can be explained well with only a few substitution rate parameters; and 4) perform well on simulated data, both in terms of goodness of fit and the ability to estimate evolutionary rates. We also investigate the utility of several distance measures for comparing and contrasting inferred evolutionary models. Using widely available small computer clusters, our approach allows, for the first time, to evaluate the performance of existing RNA evolutionary models by comparing them with a large pool of candidate models and to validate common modeling assumptions. In addition, the new method provides the foundation for rigorous selection and comparison of substitution models for other types of sequence data.     

Evidence that microRNA precursors, unlike other non-coding RNAs, have lower folding free energies than random sequences

MOTIVATION: Most non-coding RNAs are characterized by a specific secondary and tertiary structure that determines their function. Here, we investigate the folding energy of the secondary structure of non-coding RNA sequences, such as microRNA precursors, transfer RNAs and ribosomal RNAs in several eukaryotic taxa. Statistical biases are assessed by a randomization test, in which the predicted minimum free energy of folding is compared with values obtained for structures inferred from randomly shuffling the original sequences. RESULTS: In contrast with transfer RNAs and ribosomal RNAs, the majority of the microRNA sequences clearly exhibit a folding free energy that is considerably lower than that for shuffled sequences, indicating a high tendency in the sequence towards a stable secondary structure. A possible usage of this statistical test in the framework of the detection of genuine miRNA sequences is discussed.     

Robustness and evolvability: a paradox resolved

Understanding the relationship between robustness and evolvability is key to understand how living things can withstand mutations, while producing ample variation that leads to evolutionary innovations. Mutational robustness and evolvability, a system's ability to produce heritable variation, harbour a paradoxical tension. On one hand, high robustness implies low production of heritable phenotypic variation. On the other hand, both experimental and computational analyses of neutral networks indicate that robustness enhances evolvability. I here resolve this tension using RNA genotypes and their secondary structure phenotypes as a study system. To resolve the tension, one must distinguish between robustness of a genotype and a phenotype. I confirm that genotype (sequence) robustness and evolvability share an antagonistic relationship. In stark contrast, phenotype (structure) robustness promotes structure evolvability. A consequence is that finite populations of sequences with a robust phenotype can access large amounts of phenotypic variation while spreading through a neutral network. Population-level processes and phenotypes rather than individual sequences are key to understand the relationship between robustness and evolvability. My observations may apply to other genetic systems where many connected genotypes produce the same phenotypes.     

Evolutionary models accounting for layers of selection in protein-coding genes and their impact on the inference of positive selection

The selective forces acting on a protein-coding gene are commonly inferred using evolutionary codon models by contrasting the rate of nonsynonymous substitutions to the rate of synonymous substitutions. These models usually assume that the synonymous substitution rate, Ks, is homogenous across all sites, which is justified if synonymous sites are free from selection. However, a growing body of evidence indicates that the DNA and RNA levels of protein-coding genes are subject to varying degrees of selective constraints due to various biological functions encoded at these levels. In this paper, we develop evolutionary models that account for these layers of selection by allowing for both among-site variability of substitution rates at the DNA/RNA level (which leads to Ks variability among protein-coding sites) and among-site variability of substitution rates at the protein level (Ka variability). These models are constructed so that positive selection is either allowed or not. This enables statistical testing of positive selection when variability at the DNA/RNA substitution rate is accounted for. Using this methodology, we show that variability of the baseline DNA/RNA substitution rate is a widespread phenomenon in coding sequence data of mammalian genomes, most likely reflecting varying degrees of selection at the DNA and RNA levels. Additionally, we use simulations to examine the impact that accounting for the variability of the baseline DNA/RNA substitution rate has on the inference of positive selection. Our results show that ignoring this variability results in a high rate of erroneous positive-selection inference. Our newly developed model, which accounts for this variability, does not suffer from this problem and hence provides a likelihood framework for the inference of positive selection on a background of variability in the baseline DNA/RNA substitution rate.     

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 4(12) 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.     

Phylogenetic relationships among Myrceugenia, Blepharocalyx, and Luma (Myrtaceae) based on paired-sites models and the secondary structures of ITS and ETS sequences

To establish relationships among the genera Blepharocalyx, Luma, and Myrceugenia, the phylogeny of tribe Myrteae was reconstructed based on secondary structures of the sequences of ITS (ITS1-5.8S-ITS2) and ETS regions from 93 taxa belonging to 29 genera. The DNA sequences were aligned according to their secondary structure and analysed with Bayesian inference (BI) using base substitution models for RNA, which can differentiate between the regions consisting of base pairs (helices) and unpaired bases (loops). The best-fit models were RNA7C for ITS and RNA7B for ETS, which differ in how they predict double substitutions and symmetry of the frequency of base pairs. The phylogenetic hypothesis was compared with results obtained using classical 4-state models, the results of maximum parsimony, and using sequence alignment without considering the secondary structure. Analyses show low support along the backbone of the consensus trees, those using substitution models of paired sites showing more highly supported derived clades than substitution models of independent sites. All tests were consistent and differed in the positioning of certain groups, but they also showed that Blepharocalyx, Luma, and Myrceugenia arise from three independent lineages that are not closely related. The substitution model for RNA shows that Luma is a monophyletic group and sister to the other genera of Myrteae, except for Myrtus communis. Myrceugenia appears as a monophyletic group, except for M. fernandeziana, which is related to Blepharocalyx, a genus that appears to be biphyletic.     

The nucleotide sequence of phenylalanine tRNA and 5S RNA from Rhodospirillum rubrum

The complete nucleotide sequence of tRNAPhe and 5S RNA from the photosynthetic bacterium Rhodospirillum rubrum has been elucidated. A combination of in vitro and in vivo labelling techniques was used. The tRNAPhe sequence is 76 nucleotides long, 7 of which are modified. The primary structure is typically prokaryotic and is most similar to the tRNAPhe of Escherichia coli and Anacystis nidulans (14 differences of 76 positions). The 5S ribosomal RNA sequence is 120 nucleotides long and again typical of other prokaryotic 5S RNAs. The invariable GAAC sequence is found starting at position 45. When aligned with other prokaryotic 5S RNA sequences, a surprising amount of nucleotide substitution is noted in the prokaryotic loop region of the R. rubrum 5S RNA. However, nucleotide complementarity is maintained reinforcing the hypothesis that this loop is an important aspect of prokaryotic 5S RNA secondary structure. The 5S and tRNAPhe are the first complete RNA sequences available from the photosynthetic bacteria.