A generalized mechanistic codon model.

Models of codon evolution have attracted particular interest because of their unique capabilities to detect selection forces and their high fit when applied to sequence evolution. We described here a novel approach for modeling codon evolution, which is based on Kronecker product of matrices. The 61 × 61 codon substitution rate matrix is created using Kronecker product of three 4 × 4 nucleotide substitution matrices, the equilibrium frequency of codons, and the selection rate parameter. The entities of the nucleotide substitution matrices and selection rate are considered as parameters of the model, which are optimized by maximum likelihood. Our fully mechanistic model allows the instantaneous substitution matrix between codons to be fully estimated with only 19 parameters instead of 3,721, by using the biological interdependence existing between positions within codons. We illustrate the properties of our models using computer simulations and assessed its relevance by comparing the AICc measures of our model and other models of codon evolution on simulations and a large range of empirical data sets. We show that our model fits most biological data better compared with the current codon models. Furthermore, the parameters in our model can be interpreted in a similar way as the exchangeability rates found in empirical codon models.

KCM, a general framework for codon-based model of evolution

With the advancement of high-throughput sequencing and dramatic increase of available genetic data, statistical modeling has become an essential part in the field of molecular evolution. Statistical modeling results in many interesting discoveries in the field, from detection of highly conserved or diverse regions in a genome to phylogenetic inference of species evolutionary history Among different types of genome sequences, protein coding regions are particularly interesting due to their impact on proteins. The building blocks of proteins, i.e. amino acids, are coded by triples of nucleotides, known as codons. Accordingly, studying the evolution of codons leads to fundamental understanding of how proteins function and evolve. The current codon models can be classified into three principal groups: mechanistic codon models, empirical codon models and hybrid ones. The mechanistic models grasp particular attention due to clarity of their underlying biological assumptions and parameters. However, they suffer from simplified assumptions that are required to overcome the burden of computational complexity. The main assumptions applied to the current mechanistic codon models are (a) double and triple substitutions of nucleotides within codons are negligible, (b) there is no mutation variation among nucleotides of a single codon and (c) assuming HKY nucleotide model is sufficient to capture essence of transition- transversion rates at nucleotide level. In this thesis, I develop a framework of mechanistic codon models, named KCM-based model family framework, based on holding or relaxing the mentioned assumptions. Accordingly, eight different models are proposed from eight combinations of holding or relaxing the assumptions from the simplest one that holds all the assumptions to the most general one that relaxes all of them. The models derived from the proposed framework allow me to investigate the biological plausibility of the three simplified assumptions on real data sets as well as finding the best model that is aligned with the underlying characteristics of the data sets. -- Avec l'avancement de séquençage à haut débit et l'augmentation dramatique des données géné¬tiques disponibles, la modélisation statistique est devenue un élément essentiel dans le domaine dé l'évolution moléculaire. Les résultats de la modélisation statistique dans de nombreuses découvertes intéressantes dans le domaine de la détection, de régions hautement conservées ou diverses dans un génome de l'inférence phylogénétique des espèces histoire évolutive. Parmi les différents types de séquences du génome, les régions codantes de protéines sont particulièrement intéressants en raison de leur impact sur les protéines. Les blocs de construction des protéines, à savoir les acides aminés, sont codés par des triplets de nucléotides, appelés codons. Par conséquent, l'étude de l'évolution des codons mène à la compréhension fondamentale de la façon dont les protéines fonctionnent et évoluent. Les modèles de codons actuels peuvent être classés en trois groupes principaux : les modèles de codons mécanistes, les modèles de codons empiriques et les hybrides. Les modèles mécanistes saisir une attention particulière en raison de la clarté de leurs hypothèses et les paramètres biologiques sous-jacents. Cependant, ils souffrent d'hypothèses simplificatrices qui permettent de surmonter le fardeau de la complexité des calculs. Les principales hypothèses retenues pour les modèles actuels de codons mécanistes sont : a) substitutions doubles et triples de nucleotides dans les codons sont négligeables, b) il n'y a pas de variation de la mutation chez les nucléotides d'un codon unique, et c) en supposant modèle nucléotidique HKY est suffisant pour capturer l'essence de taux de transition transversion au niveau nucléotidique. Dans cette thèse, je poursuis deux objectifs principaux. Le premier objectif est de développer un cadre de modèles de codons mécanistes, nommé cadre KCM-based model family, sur la base de la détention ou de l'assouplissement des hypothèses mentionnées. En conséquence, huit modèles différents sont proposés à partir de huit combinaisons de la détention ou l'assouplissement des hypothèses de la plus simple qui détient toutes les hypothèses à la plus générale qui détend tous. Les modèles dérivés du cadre proposé nous permettent d'enquêter sur la plausibilité biologique des trois hypothèses simplificatrices sur des données réelles ainsi que de trouver le meilleur modèle qui est aligné avec les caractéristiques sous-jacentes des jeux de données. Nos expériences montrent que, dans aucun des jeux de données réelles, tenant les trois hypothèses mentionnées est réaliste. Cela signifie en utilisant des modèles simples qui détiennent ces hypothèses peuvent être trompeuses et les résultats de l'estimation inexacte des paramètres. Le deuxième objectif est de développer un modèle mécaniste de codon généralisée qui détend les trois hypothèses simplificatrices, tandis que d'informatique efficace, en utilisant une opération de matrice appelée produit de Kronecker. Nos expériences montrent que sur un jeux de données choisis au hasard, le modèle proposé de codon mécaniste généralisée surpasse autre modèle de codon par rapport à AICc métrique dans environ la moitié des ensembles de données. En outre, je montre à travers plusieurs expériences que le modèle général proposé est biologiquement plausible.

Annonaceae substitution rates: a codon model perspective

The Annonaceae includes cultivated species of economic interest and represents an important source of information for better understanding the evolution of tropical rainforests. In phylogenetic analyses of DNA sequence data that are used to address evolutionary questions, it is imperative to use appropriate statistical models. Annonaceae are cases in point: Two sister clades, the subfamilies Annonoideae and Malmeoideae, contain the majority of Annonaceae species diversity. The Annonoideae generally show a greater degree of sequence divergence compared to the Malmeoideae, resulting in stark differences in branch lengths in phylogenetic trees. Uncertainty in how to interpret and analyse these differences has led to inconsistent results when estimating the ages of clades in Annonaceae using molecular dating techniques. We ask whether these differences may be attributed to inappropriate modelling assumptions in the phylogenetic analyses. Specifically, we test for (clade-specific) differences in rates of non-synonymous and synonymous substitutions. A high ratio of nonsynonymous to synonymous substitutions may lead to similarity of DNA sequences due to convergence instead of common ancestry, and as a result confound phylogenetic analyses. We use a dataset of three chloroplast genes (rbcL, matK, ndhF) for 129 species representative of the family. We find that differences in branch lengths between major clades are not attributable to different rates of non-synonymous and synonymous substitutions. The differences in evolutionary rate between the major clades of Annonaceae pose a challenge for current molecular dating techniques that should be seen as a warning for the interpretation of such results in other organisms.

Improving the performance of positive selection inference by filtering unreliable alignment regions.

Errors in the inferred multiple sequence alignment may lead to false prediction of positive selection. Recently, methods for detecting unreliable alignment regions were developed and were shown to accurately identify incorrectly aligned regions. While removing unreliable alignment regions is expected to increase the accuracy of positive selection inference, such filtering may also significantly decrease the power of the test, as positively selected regions are fast evolving, and those same regions are often those that are difficult to align. Here, we used realistic simulations that mimic sequence evolution of HIV-1 genes to test the hypothesis that the performance of positive selection inference using codon models can be improved by removing unreliable alignment regions. Our study shows that the benefit of removing unreliable regions exceeds the loss of power due to the removal of some of the true positively selected sites.

Evidence for an episodic model of protein sequence evolution.

The evolution of protein function appears to involve alternating periods of conservative evolution and of relatively rapid change. Evidence for such episodic evolution, consistent with some theoretical expectations, comes from the application of increasingly sophisticated models of evolution to large sequence datasets. We present here some of the recent methods to detect functional shifts, using amino acid or codon models. Both provide evidence for punctual shifts in patterns of amino acid conservation, including the fixation of key changes by positive selection. Although a link to gene duplication, a presumed source of functional changes, has been difficult to establish, this episodic model appears to apply to a wide variety of proteins and organisms.

SlimCodeML: An Optimized Version of CodeML for the Branch-Site Model

CodeML (part of the PAML package) im- plements a maximum likelihood-based approach to de- tect positive selection on a specific branch of a given phylogenetic tree. While CodeML is widely used, it is very compute-intensive. We present SlimCodeML, an optimized version of CodeML for the branch-site model. Our performance analysis shows that SlimCodeML substantially outperforms CodeML (up to 9.38 times faster), especially for large-scale genomic analyses.

The branch-site test of positive selection is surprisingly robust but lacks power under synonymous substitution saturation and variation in GC

Positive selection is widely estimated from protein coding sequence alignments by the nonsynonymous-to-synonymous ratio omega. Increasingly elaborate codon models are used in a likelihood framework for this estimation. Although there is widespread concern about the robustness of the estimation of the omega ratio, more efforts are needed to estimate this robustness, especially in the context of complex models. Here, we focused on the branch-site codon model. We investigated its robustness on a large set of simulated data. First, we investigated the impact of sequence divergence. We found evidence of underestimation of the synonymous substitution rate for values as small as 0.5, with a slight increase in false positives for the branch-site test. When dS increases further, underestimation of dS is worse, but false positives decrease. Interestingly, the detection of true positives follows a similar distribution, with a maximum for intermediary values of dS. Thus, high dS is more of a concern for a loss of power (false negatives) than for false positives of the test. Second, we investigated the impact of GC content. We showed that there is no significant difference of false positives between high GC (up to similar to 80%) and low GC (similar to 30%) genes. Moreover, neither shifts of GC content on a specific branch nor major shifts in GC along the gene sequence generate many false positives. Our results confirm that the branch-site is a very conservative test.

ON AMINO ACID AND CODON ASSIGNMENT IN ALGEBRAIC MODELS FOR THE GENETIC CODE

We give a list of all possible schemes for performing amino acid and codon assignments in algebraic models for the genetic code, which are consistent with a few simple symmetry principles, in accordance with the spirit of the algebraic approach to the evolution of the genetic code proposed by Hornos and Hornos. Our results are complete in the sense of covering all the algebraic models that arise within this approach, whether based on Lie groups/Lie algebras, on Lie superalgebras or on finite groups.

Modeling sequencing errors by combining Hidden Markov models.

Among the largest resources for biological sequence data is the large amount of expressed sequence tags (ESTs) available in public and proprietary databases. ESTs provide information on transcripts but for technical reasons they often contain sequencing errors. Therefore, when analyzing EST sequences computationally, such errors must be taken into account. Earlier attempts to model error prone coding regions have shown good performance in detecting and predicting these while correcting sequencing errors using codon usage frequencies. In the research presented here, we improve the detection of translation start and stop sites by integrating a more complex mRNA model with codon usage bias based error correction into one hidden Markov model (HMM), thus generalizing this error correction approach to more complex HMMs. We show that our method maintains the performance in detecting coding sequences.

Large-scale analysis of orthologs and paralogs under covarion-like and constant-but-different models of amino acid evolution.

Functional divergence between homologous proteins is expected to affect amino acid sequences in two main ways, which can be considered as proxies of biochemical divergence: a "covarion-like" pattern of correlated changes in evolutionary rates, and switches in conserved residues ("conserved but different"). Although these patterns have been used in case studies, a large-scale analysis is needed to estimate their frequency and distribution. We use a phylogenomic framework of animal genes to answer three questions: 1) What is the prevalence of such patterns? 2) Can we link such patterns at the amino acid level with selection inferred at the codon level? 3) Are patterns different between paralogs and orthologs? We find that covarion-like patterns are more frequently detected than "constant but different," but that only the latter are correlated with signal for positive selection. Finally, there is no obvious difference in patterns between orthologs and paralogs.

Replicational and transcriptional selection on codon usage in Borrelia burgdorferi

With more than 10 fully sequenced, publicly available prokaryotic genomes, it is now becoming possible to gain useful insights into genome evolution. Before the genome era, many evolutionary processes were evaluated from limited data sets and evolutionary models were constructed on the basis of small amounts of evidence. In this paper, I show that genes on the Borrelia burgdorferi genome have two separate, distinct, and significantly different codon usages, depending on whether the gene is transcribed on the leading or lagging strand of replication. Asymmetrical replication is the major source of codon usage variation. Replicational selection is responsible for the higher number of genes on the leading strands, and transcriptional selection appears to be responsible for the enrichment of highly expressed genes on these strands. Replicational–transcriptional selection, therefore, has an influence on the codon usage of a gene. This is a new paradigm of codon selection in prokaryotes.

Does recombination improve selection on codon usage? Lessons from nematode and fly complete genomes

Understanding the factors responsible for variations in mutation patterns and selection efficacy along chromosomes is a prerequisite for deciphering genome sequences. Population genetics models predict a positive correlation between the efficacy of selection at a given locus and the local rate of recombination because of Hill–Robertson effects. Codon usage is considered one of the most striking examples that support this prediction at the molecular level. In a wide range of species including Caenorhabditis elegans and Drosophila melanogaster, codon usage is essentially shaped by selection acting for translational efficiency. Codon usage bias correlates positively with recombination rate in Drosophila, apparently supporting the hypothesis that selection on codon usage is improved by recombination. Here we present an exhaustive analysis of codon usage in C. elegans and D. melanogaster complete genomes. We show that in both genomes there is a positive correlation between recombination rate and the frequency of optimal codons. However, we demonstrate that in both species, this effect is due to a mutational bias toward G and C bases in regions of high recombination rate, possibly as a direct consequence of the recombination process. The correlation between codon usage bias and recombination rate in these species appears to be essentially determined by recombination-dependent mutational patterns, rather than selective effects. This result highlights that it is necessary to take into account the mutagenic effect of recombination to understand the evolutionary role and impact of recombination.

Characterization Of Microsatellite Markers Developed From Prosopis Rubriflora And Prosopis Ruscifolia (leguminosae - Mimosoideae), Legume Species That Are Used As Models For Genetic Diversity Studies In Chaquenian Areas Under Anthropization In South America.

Prosopis rubriflora and Prosopis ruscifolia are important species in the Chaquenian regions of Brazil. Because of the restriction and frequency of their physiognomy, they are excellent models for conservation genetics studies. The use of microsatellite markers (Simple Sequence Repeats, SSRs) has become increasingly important in recent years and has proven to be a powerful tool for both ecological and molecular studies. In this study, we present the development and characterization of 10 new markers for P. rubriflora and 13 new markers for P. ruscifolia. The genotyping was performed using 40 P. rubriflora samples and 48 P. ruscifolia samples from the Chaquenian remnants in Brazil. The polymorphism information content (PIC) of the P. rubriflora markers ranged from 0.073 to 0.791, and no null alleles or deviation from Hardy-Weinberg equilibrium (HW) were detected. The PIC values for the P. ruscifolia markers ranged from 0.289 to 0.883, but a departure from HW and null alleles were detected for certain loci; however, this departure may have resulted from anthropic activities, such as the presence of livestock, which is very common in the remnant areas. In this study, we describe novel SSR polymorphic markers that may be helpful in future genetic studies of P. rubriflora and P. ruscifolia.

Censored Linear Regression Models For Irregularly Observed Longitudinal Data Using The Multivariate-t Distribution.

In acquired immunodeficiency syndrome (AIDS) studies it is quite common to observe viral load measurements collected irregularly over time. Moreover, these measurements can be subjected to some upper and/or lower detection limits depending on the quantification assays. A complication arises when these continuous repeated measures have a heavy-tailed behavior. For such data structures, we propose a robust structure for a censored linear model based on the multivariate Student's t-distribution. To compensate for the autocorrelation existing among irregularly observed measures, a damped exponential correlation structure is employed. An efficient expectation maximization type algorithm is developed for computing the maximum likelihood estimates, obtaining as a by-product the standard errors of the fixed effects and the log-likelihood function. The proposed algorithm uses closed-form expressions at the E-step that rely on formulas for the mean and variance of a truncated multivariate Student's t-distribution. The methodology is illustrated through an application to an Human Immunodeficiency Virus-AIDS (HIV-AIDS) study and several simulation studies.