New applications of maximum likelihood and Bayesian statistics in macromolecular crystallography

Maximum likelihood methods are well known to macromolecular crystallographers as the methods of choice for isomorphous phasing and structure refinement. Recently, the use of maximum likelihood and Bayesian statistics has extended to the areas of molecular replacement and density modification, placing these methods on a stronger statistical foundation and making them more accurate and effective.     

Malin: maximum likelihood analysis of intron evolution in eukaryotes

Malin is a software package for the analysis of eukaryotic gene structure evolution. It provides a graphical user interface for various tasks commonly used to infer the evolution of exon-intron structure in protein-coding orthologs. Implemented tasks include the identification of conserved homologous intron sites in protein alignments, as well as the estimation of ancestral intron content, lineage-specific intron losses and gains. Estimates are computed either with parsimony, or with a probabilistic model that incorporates rate variation across lineages and intron sites. Availability: Malin is available as a stand-alone Java application, as well as an application bundle for MacOS X, at the website http://www.iro.umontreal.ca/~csuros/introns/malin/. The software is distributed under a BSD-style license.     

TREE-PUZZLE: maximum likelihood phylogenetic analysis using quartets and parallel computing

SUMMARY: TREE-PUZZLE is a program package for quartet-based maximum-likelihood phylogenetic analysis (formerly PUZZLE, Strimmer and von Haeseler, Mol. Biol. Evol., 13, 964-969, 1996) that provides methods for reconstruction, comparison, and testing of trees and models on DNA as well as protein sequences. To reduce waiting time for larger datasets the tree reconstruction part of the software has been parallelized using message passing that runs on clusters of workstations as well as parallel computers. AVAILABILITY: http://www.tree-puzzle.de. The program is written in ANSI C. TREE-PUZZLE can be run on UNIX, Windows and Mac systems, including Mac OS X. To run the parallel version of PUZZLE, a Message Passing Interface (MPI) library has to be installed on the system. Free MPI implementations are available on the Web (cf. http://www.lam-mpi.org/mpi/implementations/).     

Stoichiometric identification with maximum likelihood principal component analysis

This study presents an effective procedure for the determination of a biologically inspired, black-box model of cultures of microorganisms (including yeasts, bacteria, plant and animal cells) in bioreactors. This procedure is based on sets of experimental data measuring the time-evolution of a few extracellular species concentrations, and makes use of maximum likelihood principal component analysis to determine, independently of the kinetics, an appropriate number of macroscopic reactions and their stoichiometry. In addition, this paper provides a discussion of the geometric interpretation of a stoichiometric matrix and the potential equivalent reaction schemes. The procedure is carefully evaluated within the stoichiometric identification framework of the growth of the yeast Kluyveromyces marxianus on cheese whey. Using Monte Carlo studies, it is also compared with two other previously published approaches.     

Addressing inter-gene heterogeneity in maximum likelihood phylogenomic analysis: yeasts revisited

Phylogenomic approaches to the resolution of inter-species relationships have become well established in recent years. Often these involve concatenation of many orthologous genes found in the respective genomes followed by analysis using standard phylogenetic models. Genome-scale data promise increased resolution by minimising sampling error, yet are associated with well-known but often inappropriately addressed caveats arising through data heterogeneity and model violation. These can lead to the reconstruction of highly-supported but incorrect topologies. With the aim of obtaining a species tree for 18 species within the ascomycetous yeasts, we have investigated the use of appropriate evolutionary models to address inter-gene heterogeneities and the scalability and validity of supermatrix analysis as the phylogenetic problem becomes more difficult and the number of genes analysed approaches truly phylogenomic dimensions. We have extended a widely-known early phylogenomic study of yeasts by adding additional species to increase diversity and augmenting the number of genes under analysis. We have investigated sophisticated maximum likelihood analyses, considering not only a concatenated version of the data but also partitioned models where each gene constitutes a partition and parameters are free to vary between the different partitions (thereby accounting for variation in the evolutionary processes at different loci). We find considerable increases in likelihood using these complex models, arguing for the need for appropriate models when analyzing phylogenomic data. Using these methods, we were able to reconstruct a well-supported tree for 18 ascomycetous yeasts spanning about 250 million years of evolution.     

Modelling balanced longitudinal data: maximum likelihood estimation and analysis of variance.

For linear models, assuming a within-experimental-units covariance structure that incorporates errors of measurement, serial correlation, and variation between units, results on explicit estimation of regression parameters are used to simplify maximum likelihood estimation of covariance parameters. The use of an analysis of variance table as a simpler alternative to likelihood inference is illustrated with two examples.     

MEGA5: molecular evolutionary genetics analysis using maximum likelihood, evolutionary distance, and maximum parsimony methods

Comparative analysis of molecular sequence data is essential for reconstructing the evolutionary histories of species and inferring the nature and extent of selective forces shaping the evolution of genes and species. Here, we announce the release of Molecular Evolutionary Genetics Analysis version 5 (MEGA5), which is a user-friendly software for mining online databases, building sequence alignments and phylogenetic trees, and using methods of evolutionary bioinformatics in basic biology, biomedicine, and evolution. The newest addition in MEGA5 is a collection of maximum likelihood (ML) analyses for inferring evolutionary trees, selecting best-fit substitution models (nucleotide or amino acid), inferring ancestral states and sequences (along with probabilities), and estimating evolutionary rates site-by-site. In computer simulation analyses, ML tree inference algorithms in MEGA5 compared favorably with other software packages in terms of computational efficiency and the accuracy of the estimates of phylogenetic trees, substitution parameters, and rate variation among sites. The MEGA user interface has now been enhanced to be activity driven to make it easier for the use of both beginners and experienced scientists. This version of MEGA is intended for the Windows platform, and it has been configured for effective use on Mac OS X and Linux desktops. It is available free of charge from http://www.megasoftware.net.     

Methods for X-ray diffraction analysis of macromolecular structures.

A modern approach to protein crystallography relies as much on molecular biology as on the 'core' crystallographic disciplines. Some recent, biologically significant structure determinations have demonstrated this and show the importance of new third generation synchrotron sources. Novel uses of well known phasing techniques have also been valuable in these structure determinations. For the majority of structures, advances in phasing techniques, data collection and processing and the associated computer programs have led to more effective structure determinations.     

Targeted maximum likelihood estimation of effect modification parameters in survival analysis

The Cox proportional hazards model or its discrete time analogue, the logistic failure time model, posit highly restrictive parametric models and attempt to estimate parameters which are specific to the model proposed. These methods are typically implemented when assessing effect modification in survival analyses despite their flaws. The targeted maximum likelihood estimation (TMLE) methodology is more robust than the methods typically implemented and allows practitioners to estimate parameters that directly answer the question of interest. TMLE will be used in this paper to estimate two newly proposed parameters of interest that quantify effect modification in the time to event setting. These methods are then applied to the Tshepo study to assess if either gender or baseline CD4 level modify the effect of two cART therapies of interest, efavirenz (EFV) and nevirapine (NVP), on the progression of HIV. The results show that women tend to have more favorable outcomes using EFV while males tend to have more favorable outcomes with NVP. Furthermore, EFV tends to be favorable compared to NVP for individuals at high CD4 levels.     

DPRml: distributed phylogeny reconstruction by maximum likelihood

MOTIVATION: In recent years there has been increased interest in producing large and accurate phylogenetic trees using statistical approaches. However for a large number of taxa, it is not feasible to construct large and accurate trees using only a single processor. A number of specialized parallel programs have been produced in an attempt to address the huge computational requirements of maximum likelihood. We express a number of concerns about the current set of parallel phylogenetic programs which are currently severely limiting the widespread availability and use of parallel computing in maximum likelihood-based phylogenetic analysis. RESULTS: We have identified the suitability of phylogenetic analysis to large-scale heterogeneous distributed computing. We have completed a distributed and fully cross-platform phylogenetic tree building program called distributed phylogeny reconstruction by maximum likelihood. It uses an already proven maximum likelihood-based tree building algorithm and a popular phylogenetic analysis library for all its likelihood calculations. It offers one of the most extensive sets of DNA substitution models currently available. We are the first, to our knowledge, to report the completion of a distributed phylogenetic tree building program that can achieve near-linear speedup while only using the idle clock cycles of machines. For those in an academic or corporate environment with hundreds of idle desktop machines, we have shown how distributed computing can deliver a 'free' ML supercomputer.     

pIQPNNI: parallel reconstruction of large maximum likelihood phylogenies

SUMMARY: IQPNNI is a program to infer maximum-likelihood phylogenetic trees from DNA or protein data with a large number of sequences. We present an improved and MPI-parallel implementation showing very good scaling and speed-up behavior.     

Integrating functional genomics data using maximum likelihood based simultaneous component analysis

Background  

In contemporary biology, complex biological processes are increasingly studied by collecting and analyzing measurements of the same entities that are collected with different analytical platforms. Such data comprise a number of data blocks that are coupled via a common mode. The goal of collecting this type of data is to discover biological mechanisms that underlie the behavior of the variables in the different data blocks. The simultaneous component analysis (SCA) family of data analysis methods is suited for this task. However, a SCA may be hampered by the data blocks being subjected to different amounts of measurement error, or noise. To unveil the true mechanisms underlying the data, it could be fruitful to take noise heterogeneity into consideration in the data analysis. Maximum likelihood based SCA (MxLSCA-P) was developed for this purpose. In a previous simulation study it outperformed normal SCA-P. This previous study, however, did not mimic in many respects typical functional genomics data sets, such as, data blocks coupled via the experimental mode, more variables than experimental units, and medium to high correlations between variables. Here, we present a new simulation study in which the usefulness of MxLSCA-P compared to ordinary SCA-P is evaluated within a typical functional genomics setting. Subsequently, the performance of the two methods is evaluated by analysis of a real life Escherichia coli metabolomics data set.     

PROCOV: maximum likelihood estimation of protein phylogeny under covarion models and site-specific covarion pattern analysis

Background  

The covarion hypothesis of molecular evolution holds that selective pressures on a given amino acid or nucleotide site are dependent on the identity of other sites in the molecule that change throughout time, resulting in changes of evolutionary rates of sites along the branches of a phylogenetic tree. At the sequence level, covarion-like evolution at a site manifests as conservation of nucleotide or amino acid states among some homologs where the states are not conserved in other homologs (or groups of homologs). Covarion-like evolution has been shown to relate to changes in functions at sites in different clades, and, if ignored, can adversely affect the accuracy of phylogenetic inference.     

Targeted maximum likelihood based causal inference: Part II

In this article, we provide a template for the practical implementation of the targeted maximum likelihood estimator for analyzing causal effects of multiple time point interventions, for which the methodology was developed and presented in Part I. In addition, the application of this template is demonstrated in two important estimation problems: estimation of the effect of individualized treatment rules based on marginal structural models for treatment rules, and the effect of a baseline treatment on survival in a randomized clinical trial in which the time till event is subject to right censoring.     

Bayesian and maximum likelihood estimation of genetic maps

There has recently been increased interest in the use of Markov Chain Monte Carlo (MCMC)-based Bayesian methods for estimating genetic maps. The advantage of these methods is that they can deal accurately with missing data and genotyping errors. Here we present an extension of the previous methods that makes the Bayesian method applicable to large data sets. We present an extensive simulation study examining the statistical properties of the method and comparing it with the likelihood method implemented in Mapmaker. We show that the Maximum A Posteriori (MAP) estimator of the genetic distances, corresponding to the maximum likelihood estimator, performs better than estimators based on the posterior expectation. We also show that while the performance is similar between Mapmaker and the MCMC-based method in the absence of genotyping errors, the MCMC-based method has a distinct advantage in the presence of genotyping errors. A similar advantage of the Bayesian method was not observed for missing data. We also re-analyse a recently published set of data from the eggplant and show that the use of the MCMC-based method leads to smaller estimates of genetic distances.     

LAMARC 2.0: maximum likelihood and Bayesian estimation of population parameters

We present a Markov chain Monte Carlo coalescent genealogy sampler, LAMARC 2.0, which estimates population genetic parameters from genetic data. LAMARC can co-estimate subpopulation Theta = 4N(e)mu, immigration rates, subpopulation exponential growth rates and overall recombination rate, or a user-specified subset of these parameters. It can perform either maximum-likelihood or Bayesian analysis, and accomodates nucleotide sequence, SNP, microsatellite or elecrophoretic data, with resolved or unresolved haplotypes. It is available as portable source code and executables for all three major platforms. AVAILABILITY: LAMARC 2.0 is freely available at http://evolution.gs.washington.edu/lamarc     

On the maximum likelihood method for estimating molecular trees: Uniqueness of the likelihood point

Summary Studies are carried out on the uniqueness of the stationary point on the likelihood function for estimating molecular phylogenetic trees, yielding proof that there exists at most one stationary point, i.e., the maximum point, in the parameter range for the one parameter model of nucleotide substitution. The proof is simple yet applicable to any type of tree topology with an arbitrary number of operational taxonomic units (OTUs). The proof ensures that any valid approximation algorithm be able to reach the unique maximum point under the conditions mentioned above. An algorithm developed incorporating Newton's approximation method is then compared with the conventional one by means of computers simulation. The results show that the newly developed algorithm always requires less CPU time than the conventional one, whereas both algorithms lead to identical molecular phylogenetic trees in accordance with the proof. Contribution No. 1780 from the National Institute of Genetics, Mishima 411, Japan     

Neurofibromatosis-1: a maximum likelihood estimation of mutation rate

Summary Methods of classical segregation analysis were applied to a sample of 129 sibships with one or more individuals affected by neurofibromatosis-1 (NF-1). The sample consists only of subjects with NF-1; all the probands had been referred for genetic counselling because of café-au-lait spots, and a diagnostic protocol was invariably applied. No deviation from the segregation ratio expected for a fully penetrant Mendelian dominant gene was observed. A maximum likelihood estimate of the proportion of sporadic cases was obtained, and the mutation rate was estimated to be 6.5×10^-5 gametes per generation (95% CI 5.0–8.1).