Maximum likelihood phylogenetic estimation from DNA sequences with variable rates over sites: approximate methods

Two approximate methods are proposed for maximum likelihood phylogenetic estimation, which allow variable rates of substitution across nucleotide sites. Three data sets with quite different characteristics were analyzed to examine empirically the performance of these methods. The first, called the "discrete gamma model," uses several categories of rates to approximate the gamma distribution, with equal probability for each category. The mean of each category is used to represent all the rates falling in the category. The performance of this method is found to be quite good, and four such categories appear to be sufficient to produce both an optimum, or near-optimum fit by the model to the data, and also an acceptable approximation to the continuous distribution. The second method, called "fixed-rates model", classifies sites into several classes according to their rates predicted assuming the star tree. Sites in different classes are then assumed to be evolving at these fixed rates when other tree topologies are evaluated. Analyses of the data sets suggest that this method can produce reasonable results, but it seems to share some properties of a least-squares pairwise comparison; for example, interior branch lengths in nonbest trees are often found to be zero. The computational requirements of the two methods are comparable to that of Felsenstein's (1981, J Mol Evol 17:368-376) model, which assumes a single rate for all the sites.

Codon-Substitution Models for Heterogeneous Selection Pressure at Amino Acid Sites

Comparison of relative fixation rates of synonymous (silent) and nonsynonymous (amino acid-altering) mutations provides a means for understanding the mechanisms of molecular sequence evolution. The nonsynonymous/synonymous rate ratio (ω = dN/dS) is an important indicator of selective pressure at the protein level, with ω = 1 meaning neutral mutations, ω < 1 purifying selection, and ω > 1 diversifying positive selection. Amino acid sites in a protein are expected to be under different selective pressures and have different underlying ω ratios. We develop models that account for heterogeneous ω ratios among amino acid sites and apply them to phylogenetic analyses of protein-coding DNA sequences. These models are useful for testing for adaptive molecular evolution and identifying amino acid sites under diversifying selection. Ten data sets of genes from nuclear, mitochondrial, and viral genomes are analyzed to estimate the distributions of ω among sites. In all data sets analyzed, the selective pressure indicated by the ω ratio is found to be highly heterogeneous among sites. Previously unsuspected Darwinian selection is detected in several genes in which the average ω ratio across sites is <1, but in which some sites are clearly under diversifying selection with ω > 1. Genes undergoing positive selection include the β-globin gene from vertebrates, mitochondrial protein-coding genes from hominoids, the hemagglutinin (HA) gene from human influenza virus A, and HIV-1 env, vif, and pol genes. Tests for the presence of positively selected sites and their subsequent identification appear quite robust to the specific distributional form assumed for ω and can be achieved using any of several models we implement. However, we encountered difficulties in estimating the precise distribution of ω among sites from real data sets.

Estimating synonymous and nonsynonymous substitution rates under realistic evolutionary models

Approximate methods for estimating the numbers of synonymous and nonsynonymous substitutions between two DNA sequences involve three steps: counting of synonymous and nonsynonymous sites in the two sequences, counting of synonymous and nonsynonymous differences between the two sequences, and correcting for multiple substitutions at the same site. We examine complexities involved in those steps and propose a new approximate method that takes into account two major features of DNA sequence evolution: transition/transversion rate bias and base/codon frequency bias. We compare the new method with maximum likelihood, as well as several other approximate methods, by examining infinitely long sequences, performing computer simulations, and analyzing a real data set. The results suggest that when there are transition/transversion rate biases and base/codon frequency biases, previously described approximate methods for estimating the nonsynonymous/synonymous rate ratio may involve serious biases, and the bias can be both positive and negative. The new method is, in general, superior to earlier approximate methods and may be useful for analyzing large data sets, although maximum likelihood appears to always be the method of choice.

Likelihood models for detecting positively selected amino acid sites and applications to the HIV-1 envelope gene

Several codon-based models for the evolution of protein-coding DNA sequences are developed that account for varying selection intensity among amino acid sites. The "neutral model" assumes two categories of sites at which amino acid replacements are either neutral or deleterious. The "positive-selection model" assumes an additional category of positively selected sites at which nonsynonymous substitutions occur at a higher rate than synonymous ones. This model is also used to identify target sites for positive selection. The models are applied to a data set of the V3 region of the HIV-1 envelope gene, sequenced at different years after the infection of one patient. The results provide strong support for variable selection intensity among amino acid sites The neutral model is rejected in favor of the positive-selection model, indicating the operation of positive selection in the region. Positively selected sites are found in both the V3 region and the flanking regions.

Likelihood ratio tests for detecting positive selection and application to primate lysozyme evolution

An excess of nonsynonymous substitutions over synonymous ones is an important indicator of positive selection at the molecular level. A lineage that underwent Darwinian selection may have a nonsynonymous/synonymous rate ratio (dN/dS) that is different from those of other lineages or greater than one. In this paper, several codon-based likelihood models that allow for variable dN/dS ratios among lineages were developed. They were then used to construct likelihood ratio tests to examine whether the dN/dS ratio is variable among evolutionary lineages, whether the ratio for a few lineages of interest is different from the background ratio for other lineages in the phylogeny, and whether the dN/dS ratio for the lineages of interest is greater than one. The tests were applied to the lysozyme genes of 24 primate species. The dN/dS ratios were found to differ significantly among lineages, indicating that the evolution of primate lysozymes is episodic, which is incompatible with the neutral theory. Maximum-likelihood estimates of parameters suggested that about nine nonsynonymous and zero synonymous nucleotide substitutions occurred in the lineage leading to hominoids, and the dN/dS ratio for that lineage is significantly greater than one. The corresponding estimates for the lineage ancestral to colobine monkeys were nine and one, and the dN/dS ratio for the lineage is not significantly greater than one, although it is significantly higher than the background ratio. The likelihood analysis thus confirmed most, but not all, conclusions Messier and Stewart reached using reconstructed ancestral sequences to estimate synonymous and nonsynonymous rates for different lineages.

Probability distribution of molecular evolutionary trees: a new method of phylogenetic inference

A new method is presented for inferring evolutionary trees using nucleotide sequence data. The birth-death process is used as a model of speciation and extinction to specify the prior distribution of phylogenies and branching times. Nucleotide substitution is modeled by a continuous-time Markov process. Parameters of the branching model and the substitution model are estimated by maximum likelihood. The posterior probabilities of different phylogenies are calculated and the phylogeny with the highest posterior probability is chosen as the best estimate of the evolutionary relationship among species. We refer to this as the maximum posterior probability (MAP) tree. The posterior probability provides a natural measure of the reliability of the estimated phylogeny. Two example data sets are analyzed to infer the phylogenetic relationship of human, chimpanzee, gorilla, and orangutan. The best trees estimated by the new method are the same as those from the maximum likelihood analysis of separate topologies, but the posterior probabilities are quite different from the bootstrap proportions. The results of the method are found to be insensitive to changes in the rate parameter of the branching process.

Present-day crustal deformation in China constrained by global positioning system measurements

Global Positioning System (GPS) measurements in China indicate that crustal shortening accommodates most of India's penetration into Eurasia. Deformation within the Tibetan Plateau and its margins, the Himalaya, the Altyn Tagh, and the Qilian Shan, absorbs more than 90% of the relative motion between the Indian and Eurasian plates. Internal shortening of the Tibetan plateau itself accounts for more than one-third of the total convergence. However, the Tibetan plateau south of the Kunlun and Ganzi-Mani faults is moving eastward relative to both India and Eurasia. This movement is accommodated through rotation of material around the eastern Syntaxis. The North China and South China blocks, east of the Tibetan Plateau, move coherently east-southeastward at rates of 2 to 8 millimeters per year and 6 to 11 millimeters per year, respectively, with respect to the stable Eurasia.

A codon-based model of nucleotide substitution for protein-coding DNA sequences

A codon-based model for the evolution of protein-coding DNA sequences is presented for use in phylogenetic estimation. A Markov process is used to describe substitutions between codons. Transition/transversion rate bias and codon usage bias are allowed in the model, and selective restraints at the protein level are accommodated using physicochemical distances between the amino acids coded for by the codons. Analyses of two data sets suggest that the new codon-based model can provide a better fit to data than can nucleotide-based models and can produce more reliable estimates of certain biologically important measures such as the transition/transversion rate ratio and the synonymous/nonsynonymous substitution rate ratio.

Total synthesis of taxol

Taxol, a substance originally isolated from the Pacific yew tree (Taxus brevifolia) more than two decades ago, has recently been approved for the clinical treatment of cancer patients. Hailed as having provided one of the most significant advances in cancer therapy, this molecule exerts its anticancer activity by inhibiting mitosis through enhancement of the polymerization of tubulin and consequent stabilization of microtubules. The scarcity of taxol and the ecological impact of harvesting it have prompted extension searches for alternative sources including semisynthesis, cellular culture production and chemical synthesis. The latter has been attempted for almost two decades, but these attempts have been thwarted by the magnitude of the synthetic challenge. Here we report the total synthesis of taxol by a convergent strategy, which opens a chemical pathway for the production of both the natural product itself and a variety of designed taxoids.

Among-site rate variation and its impact on phylogenetic analyses

Although several decades of study have revealed the ubiquity of variation of evolutionary rates among sites, reliable methods for studying rate variation were not developed until very recently. Early methods fit theoretical distributions to the numbers of changes at sites inferred by parsimony and substantially underestimate the rate variation. Recent analyses show that failure to account for rate variation can have drastic effects, leading to biased dating of speciation events, biased estimation of the transition:transversion rate ratio, and incorrect reconstruction of phylogenies.

Bayesian phylogenetic inference using DNA sequences: a Markov Chain Monte Carlo Method

An improved Bayesian method is presented for estimating phylogenetic trees using DNA sequence data. The birth-death process with species sampling is used to specify the prior distribution of phylogenies and ancestral speciation times, and the posterior probabilities of phylogenies are used to estimate the maximum posterior probability (MAP) tree. Monte Carlo integration is used to integrate over the ancestral speciation times for particular trees. A Markov Chain Monte Carlo method is used to generate the set of trees with the highest posterior probabilities. Methods are described for an empirical Bayesian analysis, in which estimates of the speciation and extinction rates are used in calculating the posterior probabilities, and a hierarchical Bayesian analysis, in which these parameters are removed from the model by an additional integration. The Markov Chain Monte Carlo method avoids the requirement of our earlier method for calculating MAP trees to sum over all possible topologies (which limited the number of taxa in an analysis to about five). The methods are applied to analyze DNA sequences for nine species of primates, and the MAP tree, which is identical to a maximum-likelihood estimate of topology, has a probability of approximately 95%.

Locally resonant sonic materials

We have fabricated sonic crystals, based on the idea of localized resonant structures, that exhibit spectral gaps with a lattice constant two orders of magnitude smaller than the relevant wavelength. Disordered composites made from such localized resonant structures behave as a material with effective negative elastic constants and a total wave reflector within certain tunable sonic frequency ranges. A 2-centimeter slab of this composite material is shown to break the conventional mass-density law of sound transmission by one or more orders of magnitude at 400 hertz.

Advanced glycosylation end products in patients with diabetic nephropathy

BACKGROUND

Glucose reacts nonenzymatically with proteins in vivo, chemically forming covalently attached glucose-addition products and cross-links between proteins. The excessive accumulation of rearranged late-glucose-addition products, or advanced glycosylation end products (AGEs), is believed to contribute to the chronic complications of diabetes mellitus.

METHODS

To elucidate the relation of AGEs to diabetic complications, we used a radioreceptor assay to measure serum and tissue AGEs in diabetic (Types I and Type II) and nondiabetic patients with different levels of renal function. Serum AGEs were measured as a low-molecular-weight (less than or equal to 10 kd) peptide fraction and a high-molecular-weight (greater than 10 kd) protein fraction.

RESULTS

The mean (+/- SD) AGE content of samples of arterial-wall collagen from 9 diabetic patients was significantly higher than that of samples from 18 nondiabetic patients (14.5 +/- 5.2 vs. 3.6 +/- 1.5 AGE units per milligram, P less than 0.001). Moreover, diabetic patients with end-stage renal disease had almost twice as much AGE in tissue as diabetic patients without renal disease (21.3 +/- 2.8 vs. 11.5 +/- 1.9 AGE units per milligram, P less than 0.001). The AGE levels in both serum fractions were elevated in the patients with diabetes, and the levels of AGE peptides correlated directly with serum creatinine (P less than 0.001) and inversely with creatinine clearance (P less than 0.005), suggesting that levels of AGE peptides increased with the severity of diabetic nephropathy. In six patients with diabetes who required hemodialysis, the levels of AGE peptides were five times higher than in eight normal subjects (82.8 +/- 9.4 vs. 15.6 +/- 3.4 AGE units per milliliter, P less than 0.001). In another group of diabetic patients the mean serum creatinine level, which decreased by 75 percent during a session of hemodialysis, whereas the level of AGE peptides decreased by only 24 percent. Serum levels of AGE peptides were normal in two patients with normal serum creatinine levels after renal transplantation.

CONCLUSIONS

AGEs accumulate at a faster-than-normal rate in arteries and the circulation of patients with diabetes; the increase in circulating AGE peptides parallels the severity of renal functional impairment in diabetic nephropathy.

Mass screening for lung cancer with mobile spiral computed tomography scanner

BACKGROUND

The incidence of and mortality from lung cancer have increased steadily. Most lung cancers are not localised when first detected, but early detection is mandatory to improve prognosis. Since curable early cases are hard to visualise with conventional chest radiography, a new diagnostic means must be found. We assessed whether population-based mass screening with a spiral computed tomography scanner could contribute substantially to detection of smaller cancers, and decrease mortality.

METHODS

In 1996, we screened in a mobile unit 5483 individuals from the general population of Matsumoto, Japan, aged between 40 years and 74 years who had undergone annual chest radiography (miniature fluorophotography) and cytological assessment of sputum. All participants had a low-dose X-ray spiral computed tomography (CT) scan of the thorax; 3967 also underwent miniature fluorophotography. We compared smokers and non-smokers. Further assessments were done for probably benign but suspicious lesions; suspicion of cancer; and indeterminate small nodules by chest radiography and conventional CT, with additional transbronchial biopsy when possible. Thoracotomy was recommended when it was strongly suspected that the patients had lung cancer.

FINDINGS

19 patients were diagnosed as having lung cancer--14 with suspicion of lung cancer, three with benign but suspicious lesions, and two with indeterminate small nodules. 18 cases were surgically confirmed, and one was clinically diagnosed. The mean size of lesions was 17 mm (range 6-47). In four of 19 patients, lung abnormality was seen on CT and miniature fluorophotography. The lung-cancer detection rate with CT was 0.48%, significantly higher than the 0.03-0.05% for standard mass assessments done previously in the same area. CT missed one case that was found solely on a sputum cytology examination.

INTERPRETATION

Our results show that miniature fluorophotography or conventional chest radiography, which have been the main diagnostic techniques for lung cancer, showed few small cancers. CT was more accurate in mass screening for lung cancer and led to early detection and an accurate diagnosis of lung cancer, and should be considered in future health plans.

Estimating the pattern of nucleotide substitution

Knowledge of the pattern of nucleotide substitution is important both to our understanding of molecular sequence evolution and to reliable estimation of phylogenetic relationships. The method of parsimony analysis, which has been used to estimate substitution patterns in real sequences, has serious drawbacks and leads to results difficult to interpret. In this paper a model-based maximum likelihood approach is proposed for estimating substitution patterns in real sequences. Nucleotide substitution is assumed to follow a homogeneous Markov process, and the general reversible process model (REV) and the unrestricted model without the reversibility assumption are used. These models are also applied to examine the adequacy of the model of Hasegawa et al. (J. Mol. Evol. 1985;22:160-174) (HKY85). Two data sets are analyzed. For the psi eta-globin pseudogenes of six primate species, the REV models fits the data much better than HKY85, while, for a segment of mtDNA sequences from nine primates, REV cannot provide a significantly better fit than HKY85 when rate variation over sites is taken into account in the models. It is concluded that the use of the REV model in phylogenetic analysis can be recommended, especially for large data sets or for sequences with extreme substitution patterns, while HKY85 may be expected to provide a good approximation. The use of the unrestricted model does not appear to be worthwhile.

Accuracy and power of the likelihood ratio test in detecting adaptive molecular evolution

The selective pressure at the protein level is usually measured by the nonsynonymous/synonymous rate ratio (omega = dN/dS), with omega < 1, omega = 1, and omega > 1 indicating purifying (or negative) selection, neutral evolution, and diversifying (or positive) selection, respectively. The omega ratio is commonly calculated as an average over sites. As every functional protein has some amino acid sites under selective constraints, averaging rates across sites leads to low power to detect positive selection. Recently developed models of codon substitution allow the omega ratio to vary among sites and appear to be powerful in detecting positive selection in empirical data analysis. In this study, we used computer simulation to investigate the accuracy and power of the likelihood ratio test (LRT) in detecting positive selection at amino acid sites. The test compares two nested models: one that allows for sites under positive selection (with omega > 1), and another that does not, with the chi2 distribution used for significance testing. We found that use of the chi(2) distribution makes the test conservative, especially when the data contain very short and highly similar sequences. Nevertheless, the LRT is powerful. Although the power can be low with only 5 or 6 sequences in the data, it was nearly 100% in data sets of 17 sequences. Sequence length, sequence divergence, and the strength of positive selection also were found to affect the power of the LRT. The exact distribution assumed for the omega ratio over sites was found not to affect the effectiveness of the LRT.

The 7SK small nuclear RNA inhibits the CDK9/cyclin T1 kinase to control transcription

The human positive transcription elongation factor P-TEFb, consisting of a CDK9/cyclin T1 heterodimer, functions as both a general and an HIV-1 Tat-specific transcription factor. P-TEFb activates transcription by phosphorylating RNA polymerase (Pol) II, leading to the formation of processive elongation complexes. As a Tat cofactor, P-TEFb stimulates HIV-1 transcription by interacting with Tat and the transactivating responsive (TAR) RNA structure located at the 5' end of the nascent viral transcript. Here we identified 7SK, an abundant and evolutionarily conserved small nuclear RNA (snRNA) of unknown function, as a specific P-TEFb-associated factor. 7SK inhibits general and HIV-1 Tat-specific transcriptional activities of P-TEFb in vivo and in vitro by inhibiting the kinase activity of CDK9 and preventing recruitment of P-TEFb to the HIV-1 promoter. 7SK is efficiently dissociated from P-TEFb by treatment of cells with ultraviolet irradiation and actinomycin D. As these two agents have been shown to significantly enhance HIV-1 transcription and phosphorylation of Pol II (refs 6,7,8), our data provide a mechanistic explanation for their stimulatory effects. The 7SK/P-TEFb interaction may serve as a principal control point for the induction of cellular and HIV-1 viral gene expression during stress-related responses. Our studies demonstrate the involvement of an snRNA in controlling the activity of a Cdk-cyclin kinase.

A new method of inference of ancestral nucleotide and amino acid sequences

A statistical method was developed for reconstructing the nucleotide or amino acid sequences of extinct ancestors, given the phylogeny and sequences of the extant species. A model of nucleotide or amino acid substitution was employed to analyze data of the present-day sequences, and maximum likelihood estimates of parameters such as branch lengths were used to compare the posterior probabilities of assignments of character states (nucleotides or amino acids) to interior nodes of the tree; the assignment having the highest probability was the best reconstruction at the site. The lysozyme c sequences of six mammals were analyzed by using the likelihood and parsimony methods. The new likelihood-based method was found to be superior to the parsimony method. The probability that the amino acids for all interior nodes at a site reconstructed by the new method are correct was calculated to be 0.91, 0.86, and 0.73 for all, variable, and parsimony-informative sites, respectively, whereas the corresponding probabilities for the parsimony method were 0.84, 0.76, and 0.51, respectively. The probability that an amino acid in an ancestral sequence is correctly reconstructed by the likelihood analysis ranged from 91.3 to 98.7% for the four ancestral sequences.

Synonymous and nonsynonymous rate variation in nuclear genes of mammals

A maximum likelihood approach was used to estimate the synonymous and nonsynonymous substitution rates in 48 nuclear genes from primates, artiodactyls, and rodents. A codon-substitution model was assumed, which accounts for the genetic code structure, transition/transversion bias, and base frequency biases at codon positions. Likelihood ratio tests were applied to test the constancy of nonsynonymous to synonymous rate ratios among branches (evolutionary lineages). It is found that at 22 of the 48 nuclear loci examined, the nonsynonymous/synonymous rate ratio varies significantly across branches of the tree. The result provides strong evidence against a strictly neutral model of molecular evolution. Our likelihood estimates of synonymous and nonsynonymous rates differ considerably from previous results obtained from approximate pairwise sequence comparisons. The differences between the methods are explored by detailed analyses of data from several genes. Transition/transversion rate bias and codon frequency biases are found to have significant effects on the estimation of synonymous and nonsynonymous rates, and approximate methods do not adequately account for those factors. The likelihood approach is preferable, even for pairwise sequence comparison, because more realistic models about the mutation and substitution processes can be incorporated in the analysis.

Axonal transport of amyloid precursor protein is mediated by direct binding to the kinesin light chain subunit of kinesin-I

We analyzed the mechanism of axonal transport of the amyloid precursor protein (APP), which plays a major role in the development of Alzheimer's disease. Coimmunoprecipitation, sucrose gradient, and direct in vitro binding demonstrated that APP forms a complex with the microtubule motor, conventional kinesin (kinesin-I), by binding directly to the TPR domain of the kinesin light chain (KLC) subunit. The estimated apparent Kd for binding is 15-20 nM, with a binding stoichiometry of two APP per KLC. In addition, association of APP with microtubules and axonal transport of APP is greatly decreased in a gene-targeted mouse mutant of the neuronally enriched KLC1 gene. We propose that one of the normal functions of APP may be as a membrane cargo receptor for kinesin-I and that KLC is important for kinesin-I-driven transport of APP into axons.

Microtubule-based transport systems in neurons: the roles of kinesins and dyneins

The large size and extreme polarization of neurons is crucial to their ability to communicate at long distances and to form the complex cellular networks of the nervous system. The size, shape, and compartmentalization of these specialized cells must be generated and supported by the cytoskeletal systems of intracellular transport. One of the major systems is the microtubule-based transport system along which kinesin and dynein motor proteins generate force and drive the traffic of many cellular components. This review describes our current understanding of the functions of kinesins and dyneins and how these motor proteins may be harnessed to generate some of the unique properties of neuronal cells.