NT4X and nT4M: Novel Time Non-reversible Mixture Amino Acid Substitution Models.

The single-matrix amino acid (AA) substitution models are widely used in phylogenetic analyses; however, they are unable to properly model the heterogeneity of AA substitution rates among sites. The multi-matrix mixture models can handle the site rate heterogeneity and outperform the single-matrix models. Estimating multi-matrix mixture models is a complex process and no computer program is available for this task. In this study, we implemented a computer program of the so-called QMix based on the algorithm of LG4X and LG4M with several enhancements to automatically estimate multi-matrix mixture models from large datasets. QMix employs QMaker algorithm instead of XRATE algorithm to accurately and rapidly estimate the parameters of models. It is able to estimate mixture models with different number of matrices and supports multi-threading computing to efficiently estimate models from thousands of genes. We re-estimate mixture models LG4X and LG4M from 1471 HSSP alignments. The re-estimated models (HP4X and HP4M) are slightly better than LG4X and LG4M in building maximum likelihood trees from HSSP and TreeBASE datasets. QMix program required about 10 hours on a computer with 18 cores to estimate a mixture model with four matrices from 200 HSSP alignments. It is easy to use and freely available for researchers.

Episodic evolution of RNA viruses.

Amino acid substitution matrices describe the rates by which amino acids are replaced during evolution. In contrast to nucleotide or codon models, amino acid substitution matrices are in general parameterless and empirically estimated, probably because there is no obvious parametrization for amino acid substitutions. Principal component analysis has previously been used to improve codon substitution models by empirically finding the most relevant parameters. Here, we apply the same method to amino acid substitution matrices, leading to a semiempirical substitution model that can adjust the transition rates to the protein sequences under investigation. Our new model almost invariably achieves the best likelihood values in large-scale comparisons with established amino acid substitution models (JTT, WAG, and LG). In particular for longer alignments, these likelihood gains are considerably larger than what could be expected from simply having more parameters. The application of our model differs from that of mixture models (such as UL2 or UL3), as we optimize one rate matrix per alignment, whereas mixture models apply the variation per alignments site. This makes our model computationally more efficient, while the performance is comparable to that of UL3. Applied to the phylogenetic problem of the origin of placental mammals, our new model and the UL3 mixed model are the only ones of the tested models that cluster Afrotheria and Xenarthra into a clade called Atlantogenata, which would be in correspondence with recent findings using more sophisticated phylogenetic methods.

In many multiple testing procedures, accurate modeling of the p-value distribution is a key issue. Mixture distributions have been shown to provide adequate models for p-value densities under the null and the alternative hypotheses. An important parameter of the mixture model that needs to be estimated is the proportion of true null hypotheses, which under the mixture formulation becomes the probability mass attached to the value associated with the null hypothesis. It is well known that in a general mixture model, especially when a scale parameter is present, the mixing distribution need not be identifiable. Nevertheless, under our setting for mixture model for p-values, we show that the weight attached to the null hypothesis is identifiable under two very different types of conditions. We consider several examples including univariate and multivariate mixture models for transformed p-values. Finally, we formulate an abstract theorem for general mixtures and present other examples.

A generalized bivariate mixture model for stock price volatility and trading volume

This paper considers the mixture model methodology for handling non-ignorable drop-outs in longitudinal studies with continuous outcomes. Recently, Hogan and Laird have developed a mixture model for non-ignorable drop-outs which is a standard linear mixed effects model except that the parameters which characterize change over time depend also upon time of drop-out. That is, the mean response is linear in time, other covariates and drop-out time, and their interactions. One of the key attractions of the mixture modelling approach to drop-outs is that it is relatively easy to explore the sensitivity of results to model specification. However, the main drawback of mixture models is that the parameters that are ordinarily of interest are not immediately available, but require marginalization of the distribution of outcome over drop-out times. Furthermore, although a linear model is assumed for the conditional mean of the outcome vector given time of drop out, after marginalization, the unconditional mean of the outcome vector is not, in general, linear in the regression parameters. As a result, it is not possible to parsimoniously describe the effects of covariates on the marginal distribution of the outcome in terms of regression coefficients. The need to explicitly average over the distribution of the drop-out times and the absence of regression coefficients that describe the effects of covariates on the outcome are two unappealing features of the mixture modelling approach. In this paper we describe a particular parameterization of the general linear mixture model that circumvents both of these problems.

The problem of whether mutations that increase a species' fitness are incorporated into the genome as a function of generation interval or as a function of absolute time is of some interest because of the clock-like nature of amino acid substitutions known to have occurred in the evolution of certain well studied proteins. The molecular clock features a rate of amino acid substitution that is relatively constant when averaged over a sufficiently long time, and the constant rate of substitution is independent of the generation interval of the species involved1,2. Furthermore, the variance in the rate of substitution is roughly twice the mean2. Some authors have argued that the very existence of a molecular clock implies that most amino acid substitutions must be selectively neutral or nearly neutral3. On the other hand, there is no compelling reason to assume that selectively driven gene substitutions would not also exhibit clock-like behaviour, in which case the rate of increase in fitness of a population should be a function of absolute time rather than generation interval. In this report, we have investigated the issue of rate of increase in fitness using initially isogeneic strains of Escherichia coli that had been allowed to evolve independently in glucose-limited chemostats4 for 500 h. The nutrient supply was adjusted in such a manner that some of the strains maintained a doubling time of 2.5 h and others a doubling time of 5.0 h, and the relative fitnesses of the evolving strains were measured periodically. Our main conclusions are that (1) selectively driven gene substitutions detectable as increases in fitness do exhibit clocklike behaviour, (2) when averaged over a sufficiently long time, the rate of increase in fitness is a function of absolute time and independent of generation interval, and (3) except for an initial period related to adjustment to chemostat conditions, the variance in the rate of increase in fitness is very nearly twice the mean.

Nonsynonymous substitutions in DNA cause amino acid substitutions while synonymous substitutions in DNA leave amino acids unchanged. The cause of the correlation between the substitution rates at nonsynonymous (K(A)) and synonymous (K(S)) sites in mammals is a contentious issue, and one that impacts on many aspects of molecular evolution. Here we use a large set of orthologous mammalian genes to investigate the causes of the K(A)-K(S) correlation in rodents. The strength of the K(A)-K(S) correlation exceeds the neutral theory expectation when substitution rates are estimated using algorithmic methods, but not when substitution rates are estimated by maximum likelihood. Irrespective of this methodological uncertainty the strength of the K(A)-K(S) correlation appears mostly due to tandem substitutions, an excess of which is generated by substitutional nonindependence. Doublet mutations cannot explain the excess of tandem synonymous-nonsynonymous substitutions, and substitution patterns indicate that selection on silent sites is the likely cause. We find no evidence for selection on codon usage. The nature of the relationship between synonymous divergence and base composition is unclear because we find a significant correlation if we use maximum-likelihood methods but not if we use algorithmic methods. Finally, we find that K(S) is reduced at the start of genes, which suggests that selection for RNA structure may affect silent sites in mammalian protein-coding genes.

Protein sites present different amino acids during their evolution, whose number reflects the selective constraints operating on them. This evolutionary variability is strongly influenced by the structural properties of the site in the native structure, and it is quantified either through sequence entropy or through substitution rates. However, while the sequence entropy only depends on the equilibrium frequencies of the amino acids, the substitution rate also depends on the exchangeability matrix that describes mutations in the mathematical model of the substitution process. Here we apply a mathematical model of protein evolution with selection for protein stability, both against unfolding and against misfolding, and find that sites with the same sequence entropy present different substitution rates depending on whether the site is prevalently hydrophobic or hydrophylic. For equal sequence entropy, polar sites evolve faster than hydrophobic sites. This is a consequence of the differential exchangeability associated with hydrophobic or polar amino acids. Accordingly, the model predicts that more polar proteins present, on the average, a faster substitution rate. However, these results change if we compare proteins that evolve under different mutation biases, such as orthologous proteins in different bacterial genomes. In this case, the substitution rates are faster in genomes that evolve under mutational bias that favour hydrophobic amino acids by preferentially incorporating the nucleotide Thymine that is more frequent in hydrophobic codons. In our model, the mutation bias influences both the sequence entropies and the substitution rates of protein sites. The sequence entropy is maximal for the mutational biases that reproduce the observed amino acid distributions and strongly decreases when extreme mutational biases are approached. The hydrophobicity for which the entropy is maximal is close to the mean hydrophobicity of the twenty amino acids and independent of the mutation bias. In contrast, the substitution rate and the hydrophobicity for which the substitution rate is maximal tend to increase when the mutation bias favours hydrophobic amino acids. Thus, changes of the mutational bias lead to deep effects on the biophysical properties of the protein (hydrophobicity) and on its evolutionary properties (sequence entropy and substitution rate) at the same time. The program Prot_evol is freely available for download at the url https://ub.cbm.uam.es/prot_fold_evol/prot_fold_evol_soft_main.php#Prot_Evol.[p]

Types and concentrations of tire wear particles (TWPs) in road dust generated in slow lanes

Dual-band unidirectional reflectionlessness at exceptional points is investigated theoretically in a non-Hermitian plasmonic waveguide system, based on near-field coupling by using only two resonators. The system consists of a metal-insulator-metal waveguide end-coupled to two nanohole resonators. The reflectivity for the forward (backward) direction is ∼0 (∼0) at frequency 205.20 THz (194.56 THz), while for the backward (forward) direction it is ∼0.76 (∼0.78). Moreover, the quality factors of the dual-band unidirectional reflectionlessness for forward and backward directions can reach ∼132 and ∼137, respectively.

Adaptation of hepatitis C virus for persistent infection in patients with acute hepatitis

Amino acid substitutions at position 69 of the reverse transcriptase of human immunodeficiency virus type 1 are frequent in zalcitabine-naive antiretroviral-drug-experienced patients.

Fidelity of DNA synthesis, catalyzed by DNA polymerases, is critical for the maintenance of the integrity of the genome. Mutant polymerases with elevated accuracy (antimutators) have been observed, but these mainly involve increased exonuclease proofreading or large decreases in polymerase activity. We have determined the tolerance of DNA polymerase for amino acid substitutions in the active site and in different segments of E. coli DNA polymerase I and have determined the effects of these substitutions on the fidelity of DNA synthesis. We established a DNA polymerase I mutant library, with random substitutions throughout the polymerase domain. This random library was first selected for activity. The essentiality of DNA polymerases and their sequence and structural conservation suggests that few amino acid substitutions would be tolerated. However, we report that two-thirds of single base substitutions were tolerated without loss of activity, and plasticity often occurs at evolutionarily conserved regions. We screened 408 members of the active library for alterations in fidelity of DNA synthesis in Escherichia coli expressing the mutant polymerases and carrying a second plasmid containing a beta-lactamase reporter. Mutation frequencies varied from 1/1000- to 1000-fold greater compared with wild type. Mutations that produced an antimutator phenotype were distributed throughout the polymerase domain, with 12% clustered in the M-helix. We confirmed that a single mutation in this segment results in increased base discrimination. Thus, this work identifies the M-helix as a determinant of fidelity and suggests that polymerases can tolerate many substitutions that alter fidelity without incurring major changes in activity.

Do the properties of amino acids affect their rates of substitution? The neutral theory predicts that greater selective constraint leads to slower rates of evolution; similarly, we expect amino acids that are more different from each other to have lower rates of exchange because such changes are most likely to affect protein structure and function. Here, we test these predictions, using substitution rates estimated from empirical amino acid exchangeability matrices. To measure degree of amino acid difference, we focused on two physicochemical properties, charge and size, uncorrelated metrics that are known to have important implications for protein structure and function. We find that for both charge and size, amino acid pairs with large differences had lower rates of substitution. We also found that amino acids that differed in both properties had the lowest rates of substitution, suggesting that both physicochemical properties are under selective constraint. Mutation properties, such as the number of mutations or the number of transitions as opposed to transversions separating amino acid pairs, were also important predictors of substitution rates. The relationship between amino acid substitution rates and differences in their physiochemical properties holds across several taxonomically restricted datasets. This finding suggests that purifying selection affects amino acid substitution rates in a similar manner across taxonomic groups with different effective population sizes.