SynPAM—A Distance Measure Based on Synonymous Codon Substitutions

Measuring evolutionary distances between DNA or protein sequences forms the basis of many applications in computational biology and evolutionary studies. Of particular interest are distances based on synonymous substitutions since these substitutions are considered to be under very little selection pressure and therefore assumed to accumulate in an almost clock-like manner. SynPAM, the method presented here, allows the estimation of distances between coding DNA sequences based on synonymous codon substitutions. The problem of estimating an accurate distance from the observed substitution pattern is solved by maximum likelihood with empirical codon substitution matrices employed for the underlying Markov model. Comparisons with established measures of synonymous distance indicate that SynPAM has less variance and yields useful results over a longer time range.     

MC-Net: a method for the construction of phylogenetic networks based on the Monte-Carlo method

Background  

A phylogenetic network is a generalization of phylogenetic trees that allows the representation of conflicting signals or alternative evolutionary histories in a single diagram. There are several methods for constructing these networks. Some of these methods are based on distances among taxa. In practice, the methods which are based on distance perform faster in comparison with other methods. The Neighbor-Net (N-Net) is a distance-based method. The N-Net produces a circular ordering from a distance matrix, then constructs a collection of weighted splits using circular ordering. The SplitsTree which is a program using these weighted splits makes a phylogenetic network. In general, finding an optimal circular ordering is an NP-hard problem. The N-Net is a heuristic algorithm to find the optimal circular ordering which is based on neighbor-joining algorithm.     

SynPAM-a distance measure based on synonymous codon substitutions.

Measuring evolutionary distances between DNA or protein sequences forms the basis of many applications in computational biology and evolutionary studies. Of particular interest are distances based on synonymous substitutions, since these substitutions are considered to be under very little selection pressure and therefore assumed to accumulate in an almost clock-like manner. SynPAM, the method presented here, allows the estimation of distances between coding DNA sequences based on synonymous codon substitutions. The problem of estimating an accurate distance from the observed substitution pattern is solved by maximum-likelihood with empirical codon substitution matrices employed for the underlying Markov model. Comparisons with established measures of synonymous distance indicate that SynPAM has less variance and yields useful results over a longer time range.     

Phylogenetic Inference with Weighted Codon Evolutionary Distances

We develop a new approach to estimate a matrix of pairwise evolutionary distances from a codon-based alignment based on a codon evolutionary model. The method first computes a standard distance matrix for each of the three codon positions. Then these three distance matrices are weighted according to an estimate of the global evolutionary rate of each codon position and averaged into a unique distance matrix. Using a large set of both real and simulated codon-based alignments of nucleotide sequences, we show that this approach leads to distance matrices that have a significantly better treelikeness compared to those obtained by standard nucleotide evolutionary distances. We also propose an alternative weighting to eliminate the part of the noise often associated with some codon positions, particularly the third position, which is known to induce a fast evolutionary rate. Simulation results show that fast distance-based tree reconstruction algorithms on distance matrices based on this codon position weighting can lead to phylogenetic trees that are at least as accurate as, if not better, than those inferred by maximum likelihood. Finally, a well-known multigene dataset composed of eight yeast species and 106 codon-based alignments is reanalyzed and shows that our codon evolutionary distances allow building a phylogenetic tree which is similar to those obtained by non-distance-based methods (e.g., maximum parsimony and maximum likelihood) and also significantly improved compared to standard nucleotide evolutionary distance estimates.     

A transition probability model for amino acid substitutions from blocks.

Substitution matrices have been useful for sequence alignment and protein sequence comparisons. The BLOSUM series of matrices, which had been derived from a database of alignments of protein blocks, improved the accuracy of alignments previously obtained from the PAM-type matrices estimated from only closely related sequences. Although BLOSUM matrices are scoring matrices now widely used for protein sequence alignments, they do not describe an evolutionary model. BLOSUM matrices do not permit the estimation of the actual number of amino acid substitutions between sequences by correcting for multiple hits. The method presented here uses the Blocks database of protein alignments, along with the additivity of evolutionary distances, to approximate the amino acid substitution probabilities as a function of actual evolutionary distance. The PMB (Probability Matrix from Blocks) defines a new evolutionary model for protein evolution that can be used for evolutionary analyses of protein sequences. Our model is directly derived from, and thus compatible with, the BLOSUM matrices. The model has the additional advantage of being easily implemented.     

Multiple regression on distance matrices: a multivariate spatial analysis tool

I explore the use of multiple regression on distance matrices (MRM), an extension of partial Mantel analysis, in spatial analysis of ecological data. MRM involves a multiple regression of a response matrix on any number of explanatory matrices, where each matrix contains distances or similarities (in terms of ecological, spatial, or other attributes) between all pair-wise combinations of n objects (sample units); tests of statistical significance are performed by permutation. The method is flexible in terms of the types of data that may be analyzed (counts, presence–absence, continuous, categorical) and the shapes of response curves. MRM offers several advantages over traditional partial Mantel analysis: (1) separating environmental distances into distinct distance matrices allows inferences to be made at the level of individual variables; (2) nonparametric or nonlinear multiple regression methods may be employed; and (3) spatial autocorrelation may be quantified and tested at different spatial scales using a series of lag matrices, each representing a geographic distance class. The MRM lag matrices model may be parameterized to yield very similar inferences regarding spatial autocorrelation as the Mantel correlogram. Unlike the correlogram, however, the lag matrices model may also include environmental distance matrices, so that spatial patterns in species abundance distances (community similarity) may be quantified while controlling for the environmental similarity between sites. Examples of spatial analyses with MRM are presented.     

Fast computation of distance estimators

Background  

Some distance methods are among the most commonly used methods for reconstructing phylogenetic trees from sequence data. The input to a distance method is a distance matrix, containing estimated pairwise distances between all pairs of taxa. Distance methods themselves are often fast, e.g., the famous and popular Neighbor Joining (NJ) algorithm reconstructs a phylogeny of n taxa in time O(n ³). Unfortunately, the fastest practical algorithms known for Computing the distance matrix, from n sequences of length l, takes time proportional to l·n ². Since the sequence length typically is much larger than the number of taxa, the distance estimation is the bottleneck in phylogeny reconstruction. This bottleneck is especially apparent in reconstruction of large phylogenies or in applications where many trees have to be reconstructed, e.g., bootstrapping and genome wide applications.     

Bayesian refinement of protein functional site matching

Background  

Matching functional sites is a key problem for the understanding of protein function and evolution. The commonly used graph theoretic approach, and other related approaches, require adjustment of a matching distance threshold a priori according to the noise in atomic positions. This is difficult to pre-determine when matching sites related by varying evolutionary distances and crystallographic precision. Furthermore, sometimes the graph method is unable to identify alternative but important solutions in the neighbourhood of the distance based solution because of strict distance constraints. We consider the Bayesian approach to improve graph based solutions. In principle this approach applies to other methods with strict distance matching constraints. The Bayesian method can flexibly incorporate all types of prior information on specific binding sites (e.g. amino acid types) in contrast to combinatorial formulations.     

Accurate and robust phylogeny estimation based on profile distances: a study of the Chlorophyceae (Chlorophyta)

Background  

In phylogenetic analysis we face the problem that several subclade topologies are known or easily inferred and well supported by bootstrap analysis, but basal branching patterns cannot be unambiguously estimated by the usual methods (maximum parsimony (MP), neighbor-joining (NJ), or maximum likelihood (ML)), nor are they well supported. We represent each subclade by a sequence profile and estimate evolutionary distances between profiles to obtain a matrix of distances between subclades.     

Factors affecting the errors in the estimation of evolutionary distances between sequences

Phylogenetic methods that use matrices of pairwise distances between sequences (e.g., neighbor joining) will only give accurate results when the initial estimates of the pairwise distances are accurate. For many different models of sequence evolution, analytical formulae are known that give estimates of the distance between two sequences as a function of the observed numbers of substitutions of various classes. These are often of a form that we call "log transform formulae". Errors in these distance estimates become larger as the time t since divergence of the two sequences increases. For long times, the log transform formulae can sometimes give divergent distance estimates when applied to finite sequences. We show that these errors become significant when t approximately 1/2 |lambda(max)|(-1) logN, where lambda(max) is the eigenvalue of the substitution rate matrix with the largest absolute value and N is the sequence length. Various likelihood-based methods have been proposed to estimate the values of parameters in rate matrices. If rate matrix parameters are known with reasonable accuracy, it is possible to use the maximum likelihood method to estimate evolutionary distances while keeping the rate parameters fixed. We show that errors in distances estimated in this way only become significant when t approximately 1/2 |lambda(1)|(-1) logN, where lambda(1) is the eigenvalue of the substitution rate matrix with the smallest nonzero absolute value. The accuracy of likelihood-based distance estimates is therefore much higher than those based on log transform formulae, particularly in cases where there is a large range of timescales involved in the rate matrix (e.g., when the ratio of transition to transversion rates is large). We discuss several practical ways of estimating the rate matrix parameters before distance calculation and hence of increasing the accuracy of distance estimates.     

Phylogenetic tree information aids supervised learning for predicting protein-protein interaction based on distance matrices

Background  

Protein-protein interactions are critical for cellular functions. Recently developed computational approaches for predicting protein-protein interactions utilize co-evolutionary information of the interacting partners, e.g., correlations between distance matrices, where each matrix stores the pairwise distances between a protein and its orthologs from a group of reference genomes.     

The sea urchin (<Emphasis Type="Italic">Strongylocentrotus purpuratus</Emphasis>) test and spine proteomes

Background  

The organic matrix of biominerals plays an important role in biomineral formation and in determining biomineral properties. However, most components of biomineral matrices remain unknown at present. In sea urchin, which is an important model organism for developmental biology and biomineralization, only few matrix components have been identified and characterized at the protein level. The recent publication of the Strongylocentrotus purpuratus genome sequence rendered possible not only the identification of possible matrix proteins at the gene level, but also the direct identification of proteins contained in matrices of skeletal elements by in-depth, high-accuracy, proteomic analysis.     

SDM: a fast distance-based approach for (super) tree building in phylogenomics

Phylogenomic studies aim to build phylogenies from large sets of homologous genes. Such "genome-sized" data require fast methods, because of the typically large numbers of taxa examined. In this framework, distance-based methods are useful for exploratory studies and building a starting tree to be refined by a more powerful maximum likelihood (ML) approach. However, estimating evolutionary distances directly from concatenated genes gives poor topological signal as genes evolve at different rates. We propose a novel method, named super distance matrix (SDM), which follows the same line as average consensus supertree (ACS; Lapointe and Cucumel, 1997) and combines the evolutionary distances obtained from each gene into a single distance supermatrix to be analyzed using a standard distance-based algorithm. SDM deforms the source matrices, without modifying their topological message, to bring them as close as possible to each other; these deformed matrices are then averaged to obtain the distance supermatrix. We show that this problem is equivalent to the minimization of a least-squares criterion subject to linear constraints. This problem has a unique solution which is obtained by resolving a linear system. As this system is sparse, its practical resolution requires O(naka) time, where n is the number of taxa, k the number of matrices, and a < 2, which allows the distance supermatrix to be quickly obtained. Several uses of SDM are proposed, from fast exploratory studies to more accurate approaches requiring heavier computing time. Using simulations, we show that SDM is a relevant alternative to the standard matrix representation with parsimony (MRP) method, notably when the taxa sets of the different genes have low overlap. We also show that SDM can be used to build an excellent starting tree for an ML approach, which both reduces the computing time and increases the topogical accuracy. We use SDM to analyze the data set of Gatesy et al. (2002, Syst. Biol. 51: 652-664) that involves 48 genes of 75 placental mammals. The results indicate that these genes have strong rate heterogeneity and confirm the simulation conclusions.     

Analysis on the reconstruction accuracy of the Fitch method for inferring ancestral states

Background  

As one of the most widely used parsimony methods for ancestral reconstruction, the Fitch method minimizes the total number of hypothetical substitutions along all branches of a tree to explain the evolution of a character. Due to the extensive usage of this method, it has become a scientific endeavor in recent years to study the reconstruction accuracies of the Fitch method. However, most studies are restricted to 2-state evolutionary models and a study for higher-state models is needed since DNA sequences take the format of 4-state series and protein sequences even have 20 states.     

Sequence alignment with an appropriate substitution matrix.

A widely used algorithm for computing an optimal local alignment between two sequences requires a parameter set with a substitution matrix and gap penalties. It is recognized that a proper parameter set should be selected to suit the level of conservation between sequences. We describe an algorithm for selecting an appropriate substitution matrix at given gap penalties for computing an optimal local alignment between two sequences. In the algorithm, a substitution matrix that leads to the maximum alignment similarity score is selected among substitution matrices at various evolutionary distances. The evolutionary distance of the selected substitution matrix is defined as the distance of the computed alignment. To show the effects of gap penalties on alignments and their distances and help select appropriate gap penalties, alignments and their distances are computed at various gap penalties. The algorithm has been implemented as a computer program named SimDist. The SimDist program was compared with an existing local alignment program named SIM for finding reciprocally best-matching pairs (RBPs) of sequences in each of 100 protein families, where RBPs are commonly used as an operational definition of orthologous sequences. SimDist produced more accurate results than SIM on 50 of the 100 families, whereas both programs produced the same results on the other 50 families. SimDist was also used to compare three types of substitution matrices in scoring 444,461 pairs of homologous sequences from the 100 families.     

Evolutionary distance estimation and fidelity of pair wise sequence alignment

Background  

Evolutionary distances are a critical measure in comparative genomics and molecular evolutionary biology. A simulation study was used to examine the effect of alignment accuracy of DNA sequences on evolutionary distance estimation.     

Determining evolutionary distances from highly diverged nucleic acid sequences: Operator metrics

Summary Operator metrics are explicity designed to measure evolutionary distances from nucleic acid sequences when substitution rates differ greatly among the organisms being compared, or when substitutions have been extensive. Unlike lengths calculated by the distance matrix and parsimony methods, in which substitutions in one branch of a tree can alter the measured length of another branch, lengths determined by operator metrics are not affected by substitutions outside the branch.In the method, lengths (operator metrics) corresponding to each of the branches of an unrooted tree are calculated. The metric length of a branch reconstructs the number of (transversion) differences between sequences at a tip and a node (or between nodes) of a tree. The theory is general and is fundamentally independent of differences in substitution rates among the organisms being compared. Mathematically, the independence has been obtained becuase the metrics are eigen vectors of fundamental equations which describe the evolution of all unrooted trees.Even under conditions when both the distance matrix method or a simple parsimony length method are show to indicate lengths than are an order of magnitude too large or too small, the operator metrics are accurate. Examples, using data calculated with evolutionary rates and branchings designed to confuse the measurement of branch lengths and to camouflage the topology of the true tree, demonstrate the validity of operator metrics. The method is robust. Operator metric distances are easy to calculated, can be extended to any number of taxa, and provide a statistical estimate of their variances.The utility of the method is demonstrated by using it to analyze the origins and evolutionary of chloroplasts, mitochondria, and eubacteria.     

Assessment of methods for amino acid matrix selection and their use on empirical data shows that ad hoc assumptions for choice of matrix are not justified

Background  

In recent years, model based approaches such as maximum likelihood have become the methods of choice for constructing phylogenies. A number of authors have shown the importance of using adequate substitution models in order to produce accurate phylogenies. In the past, many empirical models of amino acid substitution have been derived using a variety of different methods and protein datasets. These matrices are normally used as surrogates, rather than deriving the maximum likelihood model from the dataset being examined. With few exceptions, selection between alternative matrices has been carried out in an ad hoc manner.