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.     

Filling-in Void and Sparse Regions in Protein Sequence Space by Protein-Like Artificial Sequences Enables Remarkable Enhancement in Remote Homology Detection Capability

Protein functional annotation relies on the identification of accurate relationships, sequence divergence being a key factor. This is especially evident when distant protein relationships are demonstrated only with three-dimensional structures. To address this challenge, we describe a computational approach to purposefully bridge gaps between related protein families through directed design of protein-like “linker” sequences. For this, we represented SCOP domain families, integrated with sequence homologues, as multiple profiles and performed HMM-HMM alignments between related domain families. Where convincing alignments were achieved, we applied a roulette wheel-based method to design 3,611,010 protein-like sequences corresponding to 374 SCOP folds. To analyze their ability to link proteins in homology searches, we used 3024 queries to search two databases, one containing only natural sequences and another one additionally containing designed sequences. Our results showed that augmented database searches showed up to 30% improvement in fold coverage for over 74% of the folds, with 52 folds achieving all theoretically possible connections. Although sequences could not be designed between some families, the availability of designed sequences between other families within the fold established the sequence continuum to demonstrate 373 difficult relationships. Ultimately, as a practical and realistic extension, we demonstrate that such protein-like sequences can be “plugged-into” routine and generic sequence database searches to empower not only remote homology detection but also fold recognition. Our richly statistically supported findings show that complementary searches in both databases will increase the effectiveness of sequence-based searches in recognizing all homologues sharing a common fold.     

Predicting substrate specificity of adenylation domains of nonribosomal peptide synthetases and other protein properties by latent semantic indexing

Successful genome mining is dependent on accurate prediction of protein function from sequence. This often involves dividing protein families into functional subtypes (e.g., with different substrates). In many cases, there are only a small number of known functional subtypes, but in the case of the adenylation domains of nonribosomal peptide synthetases (NRPS), there are >500 known substrates. Latent semantic indexing (LSI) was originally developed for text processing but has also been used to assign proteins to families. Proteins are treated as ‘‘documents’’ and it is necessary to encode properties of the amino acid sequence as ‘‘terms’’ in order to construct a term-document matrix, which counts the terms in each document. This matrix is then processed to produce a document-concept matrix, where each protein is represented as a row vector. A standard measure of the closeness of vectors to each other (cosines of the angle between them) provides a measure of protein similarity. Previous work encoded proteins as oligopeptide terms, i.e. counted oligopeptides, but used no information regarding location of oligopeptides in the proteins. A novel tokenization method was developed to analyze information from multiple alignments. LSI successfully distinguished between two functional subtypes in five well-characterized families. Visualization of different ‘‘concept’’ dimensions allows exploration of the structure of protein families. LSI was also used to predict the amino acid substrate of adenylation domains of NRPS. Better results were obtained when selected residues from multiple alignments were used rather than the total sequence of the adenylation domains. Using ten residues from the substrate binding pocket performed better than using 34 residues within 8 Å of the active site. Prediction efficiency was somewhat better than that of the best published method using a support vector machine.     

Improved sensitivity of profile searches through the use of sequence weights and gap excision

Position-specific substitution matrices, known as profiles,derived from multiple sequence alignments are currently usedto search sequence databases for distantly related members ofprotein families. The performance of the database searches isenhanced by using (i) a sequence weighting scheme which assignshigher weights to more distantly related sequences based onbranch lengths derived from phylogenetic trees, (ii) exclusionof positions with mainly padding characters at sites of insertionsor deletions and (iii) the BLOSUM62 residue comparison matrix.A natural consequence of these modifications is an improvementin the alignment of new sequences to the profiles. However,the accuracy of the alignments can be further increased by employinga similarity residue comparison matrix. These developments areimplemented in a program called PROFILEWEIGHT which runs onUnix and Vax computers. The only input required by the programis the multiple sequence alignment. The output from PROFILEWEIGHTis a profile designed to be used by existing searching and alignmentprograms. Test results from database searches with four differentfamilies of proteins show the improved sensitivity of the weightedprofiles.     

Aligning amino acid sequences: comparison of commonly used methods

We examined two extensive families of protein sequences using four different alignment schemes that employ various degrees of "weighting" in order to determine which approach is most sensitive in establishing relationships. All alignments used a similarity approach based on a general algorithm devised by Needleman and Wunsch. The approaches included a simple program, UM (unitary matrix), whereby only identities are scored; a scheme in which the genetic code is used as a basis for weighting (GC); another that employs a matrix based on structural similarity of amino acids taken together with the genetic basis of mutation (SG); and a fourth that uses the empirical log-odds matrix (LOM) developed by Dayhoff on the basis of observed amino acid replacements. The two sequence families examined were (a) nine different globins and (b) nine different tyrosine kinase-like proteins. It was assumed a priori that all members of a family share common ancestry. In cases where two sequences were more than 30% identical, alignments by all four methods were almost always the same. In cases where the percentage identity was less than 20%, however, there were often significant differences in the alignments. On the average, the Dayhoff LOM approach was the most effective in verifying distant relationships, as judged by an empirical "jumbling test." This was not universally the case, however, and in some instances the simple UM was actually as good or better. Trees constructed on the basis of the various alignments differed with regard to their limb lengths, but had essentially the same branching orders. We suggest some reasons for the different effectivenesses of the four approaches in the two different sequence settings, and offer some rules of thumb for assessing the significance of sequence relationships.     

Relationships between amino acid sequences determined through optimum alignments, clustering, and specific distance patterns: application to a group of scorpion toxins.

Optimum alignment in all pairwise combinations among a group of amino acid sequences generated a distance matrix. These distances were clustered to evaluate relationships among the sequences. The degree of relationship among sequences was also evaluated by calculating specific distances from the distance matrix and examining correlations between patterns of specific distances for pairs of sequences. The sequences examined were a group of 20 amino acid sequences of scorpion toxins originally published and analyzed by M.J. Dufton and H. Rochat in 1984. Alignment gap penalties were constant for all 190 pairwise sequence alignments and were chosen after assessing the impact of changing penalties on resultant distances. The total distances generated by the 190 pairwise sequence alignments were clustered using complete (farthest neighbour) linkage. The square, symmetrical input distance matrix is analogous to diallel cross data where reciprocal and parental values are absent. Diallel analysis methods provided analogues for the distance matrix to genetical specific combining abilities, namely specific distances between all sequence pairs that are independent of the average distances shown by individual sequences. Correlation of specific distance patterns, with transformation to modified z values and a stringent probability level, were used to delineate subgroups of related sequences. These were compared with complete linkage clustering results. Excellent agreement between the two approaches was found. Three originally outlying sequences were placed within the four new subgroups.     

Integrated gene and species phylogenies from unaligned whole genome protein sequences

MOTIVATION: Most molecular phylogenies are based on sequence alignments. Consequently, they fail to account for modes of sequence evolution that involve frequent insertions or deletions. Here we present a method for generating accurate gene and species phylogenies from whole genome sequence that makes use of short character string matches not placed within explicit alignments. In this work, the singular value decomposition of a sparse tetrapeptide frequency matrix is used to represent the proteins of organisms uniquely and precisely as vectors in a high-dimensional space. Vectors of this kind can be used to calculate pairwise distance values based on the angle separating the vectors, and the resulting distance values can be used to generate phylogenetic trees. Protein trees so derived can be examined directly for homologous sequences. Alternatively, vectors defining each of the proteins within an organism can be summed to provide a vector representation of the organism, which is then used to generate species trees. RESULTS: Using a large mitochondrial genome dataset, we have produced species trees that are largely in agreement with previously published trees based on the analysis of identical datasets using different methods. These trees also agree well with currently accepted phylogenetic theory. In principle, our method could be used to compare much larger bacterial or nuclear genomes in full molecular detail, ultimately allowing accurate gene and species relationships to be derived from a comprehensive comparison of complete genomes. In contrast to phylogenetic methods based on alignments, sequences that evolve by relative insertion or deletion would tend to remain recognizably similar.     

Use of a database of structural alignments and phylogenetic trees in investigating the relationship between sequence and structural variability among homologous proteins

The database PALI (Phylogeny and ALIgnment of homologous protein structures) consists of families of protein domains of known three-dimensional (3D) structure. In a PALI family, every member has been structurally aligned with every other member (pairwise) and also simultaneous superposition (multiple) of all the members has been performed. The database also contains 3D structure-based and structure-dependent sequence similarity-based phylogenetic dendrograms for all the families. The PALI release used in the present analysis comprises 225 families derived largely from the HOMSTRAD and SCOP databases. The quality of the multiple rigid-body structural alignments in PALI was compared with that obtained from COMPARER, which encodes a procedure based on properties and relationships. The alignments from the two procedures agreed very well and variations are seen only in the low sequence similarity cases often in the loop regions. A validation of Direct Pairwise Alignment (DPA) between two proteins is provided by comparing it with Pairwise alignment extracted from Multiple Alignment of all the members in the family (PMA). In general, DPA and PMA are found to vary rarely. The ready availability of pairwise alignments allows the analysis of variations in structural distances as a function of sequence similarities and number of topologically equivalent Calpha atoms. The structural distance metric used in the analysis combines root mean square deviation (r.m.s.d.) and number of equivalences, and is shown to vary similarly to r.m.s.d. The correlation between sequence similarity and structural similarity is poor in pairs with low sequence similarities. A comparison of sequence and 3D structure-based phylogenies for all the families suggests that only a few families have a radical difference in the two kinds of dendrograms. The difference could occur when the sequence similarity among the homologues is low or when the structures are subjected to evolutionary pressure for the retention of function. The PALI database is expected to be useful in furthering our understanding of the relationship between sequences and structures of homologous proteins and their evolution.     

Sequence variations within protein families are linearly related to structural variations

It is commonly believed that similarities between the sequences of two proteins infer similarities between their structures. Sequence alignments reliably recognize pairs of protein of similar structures provided that the percentage sequence identity between their two sequences is sufficiently high. This distinction, however, is statistically less reliable when the percentage sequence identity is lower than 30% and little is known then about the detailed relationship between the two measures of similarity. Here, we investigate the inverse correlation between structural similarity and sequence similarity on 12 protein structure families. We define the structure similarity between two proteins as the cRMS distance between their structures. The sequence similarity for a pair of proteins is measured as the mean distance between the sequences in the subsets of sequence space compatible with their structures. We obtain an approximation of the sequence space compatible with a protein by designing a collection of protein sequences both stable and specific to the structure of that protein. Using these measures of sequence and structure similarities, we find that structural changes within a protein family are linearly related to changes in sequence similarity.     

A comprehensive vertebrate phylogeny using vector representations of protein sequences from whole genomes

We recently developed a method for producing comprehensive gene and species phylogenies from unaligned whole genome data using singular value decomposition (SVD) to analyze character string frequencies. This work provides an integrated gene and species phylogeny for 64 vertebrate mitochondrial genomes composed of 832 total proteins. In addition, to provide a theoretical basis for the method, we present a graphical interpretation of both the original frequency matrix and the SVD-derived matrix. These large matrices describe high-dimensional Euclidean spaces within which biomolecular sequences can be uniquely represented as vectors. In particular, the SVD-derived vector space describes each protein relative to a restricted set of newly defined, independent axes, each of which represents a novel form of conserved motif, termed a correlated peptide motif. A quantitative comparison of the relative orientations of protein vectors in this space provides accurate and straightforward estimates of sequence similarity, which can in turn be used to produce comprehensive gene trees. Alternatively, the vector representations of genes from individual species can be summed, allowing species trees to be produced.     

Refining multiple sequence alignments with conserved core regions

Accurate multiple sequence alignments of proteins are very important to several areas of computational biology and provide an understanding of phylogenetic history of domain families, their identification and classification. This article presents a new algorithm, REFINER, that refines a multiple sequence alignment by iterative realignment of its individual sequences with the predetermined conserved core (block) model of a protein family. Realignment of each sequence can correct misalignments between a given sequence and the rest of the profile and at the same time preserves the family's overall block model. Large-scale benchmarking studies showed a noticeable improvement of alignment after refinement. This can be inferred from the increased alignment score and enhanced sensitivity for database searching using the sequence profiles derived from refined alignments compared with the original alignments. A standalone version of the program is available by ftp distribution (ftp://ftp.ncbi.nih.gov/pub/REFINER) and will be incorporated into the next release of the Cn3D structure/alignment viewer.     

Exploring the relationship between sequence similarity and accurate phylogenetic trees

We have characterized the relationship between accurate phylogenetic reconstruction and sequence similarity, testing whether high levels of sequence similarity can consistently produce accurate evolutionary trees. We generated protein families with known phylogenies using a modified version of the PAML/EVOLVER program that produces insertions and deletions as well as substitutions. Protein families were evolved over a range of 100-400 point accepted mutations; at these distances 63% of the families shared significant sequence similarity. Protein families were evolved using balanced and unbalanced trees, with ancient or recent radiations. In families sharing statistically significant similarity, about 60% of multiple sequence alignments were 95% identical to true alignments. To compare recovered topologies with true topologies, we used a score that reflects the fraction of clades that were correctly clustered. As expected, the accuracy of the phylogenies was greatest in the least divergent families. About 88% of phylogenies clustered over 80% of clades in families that shared significant sequence similarity, using Bayesian, parsimony, distance, and maximum likelihood methods. However, for protein families with short ancient branches (ancient radiation), only 30% of the most divergent (but statistically significant) families produced accurate phylogenies, and only about 70% of the second most highly conserved families, with median expectation values better than 10(-60), produced accurate trees. These values represent upper bounds on expected tree accuracy for sequences with a simple divergence history; proteins from 700 Giardia families, with a similar range of sequence similarities but considerably more gaps, produced much less accurate trees. For our simulated insertions and deletions, correct multiple sequence alignments did not perform much better than those produced by T-COFFEE, and including sequences with expressed sequence tag-like sequencing errors did not significantly decrease phylogenetic accuracy. In general, although less-divergent sequence families produce more accurate trees, the likelihood of estimating an accurate tree is most dependent on whether radiation in the family was ancient or recent. Accuracy can be improved by combining genes from the same organism when creating species trees or by selecting protein families with the best bootstrap values in comprehensive studies.     

Fast, optimal alignment of three sequences using linear gap costs

Alignment algorithms can be used to infer a relationship between sequences when the true relationship is unknown. Simple alignment algorithms use a cost function that gives a fixed cost to each possible point mutation-mismatch, deletion, insertion. These algorithms tend to find optimal alignments that have many small gaps. It is more biologically plausible to have fewer longer gaps rather than many small gaps in an alignment. To address this issue, linear gap cost algorithms are in common use for aligning biological sequence data. More reliable inferences are obtained by aligning more than two sequences at a time. The obvious dynamic programming algorithm for optimally aligning k sequences of length n runs in O(n(k)) time. This is impractical if k>/=3 and n is of any reasonable length. Thus, for this problem there are many heuristics for aligning k sequences, however, they are not guaranteed to find an optimal alignment. In this paper, we present a new algorithm guaranteed to find the optimal alignment for three sequences using linear gap costs. This gives the same results as the dynamic programming algorithm for three sequences, but typically does so much more quickly. It is particularly fast when the (three-way) edit distance is small. Our algorithm uses a speed-up technique based on Ukkonen's greedy algorithm (Ukkonen, 1983) which he presented for two sequences and simple costs.     

Omiga™: A PC-based sequence analysis tool

Computer-based sequence analysis, notation, and manipulation are a necessity for all molecular biologists working with any but the most simple DNA sequences. As sequence data become increasingly available, tools that can be used to manipulate and annotate individual sequences and sequence elements will become an even more vital implement in the molecular biologist's arsenal. The Omiga DNA and Protein Sequence Analysis Software tool, version 2.0 provides an effective and comprehensive tool for the analysis of both nucleic acid and protein sequences that runs on a standard PC available in every molecular biology laboratory. Omiga allows the import of sequences in several common formats. Upon importing sequences and assigning them to various projects, Omiga allows the user to produce, analyze, and edit sequence alignments. Sequences may also be queried for the presence of restriction sites, sequence motifs, and other sequence features, all of which can be added into the notations accompanying each sequence. This newest version of Omiga also allows for sequencing and polymerase chain reaction (PCR) primer prediction, a functionality missing in earlier versions. Finally, Omiga allows rapid searches for putative coding regions, and Basic Local Alignment Search Tool (BLAST) queries against public databases at the National Center for Biotechnology Information (NCBI).     

On the accuracy of homology modeling and sequence alignment methods applied to membrane proteins

In this study, we investigate the extent to which techniques for homology modeling that were developed for water-soluble proteins are appropriate for membrane proteins as well. To this end we present an assessment of current strategies for homology modeling of membrane proteins and introduce a benchmark data set of homologous membrane protein structures, called HOMEP. First, we use HOMEP to reveal the relationship between sequence identity and structural similarity in membrane proteins. This analysis indicates that homology modeling is at least as applicable to membrane proteins as it is to water-soluble proteins and that acceptable models (with C alpha-RMSD values to the native of 2 A or less in the transmembrane regions) may be obtained for template sequence identities of 30% or higher if an accurate alignment of the sequences is used. Second, we show that secondary-structure prediction algorithms that were developed for water-soluble proteins perform approximately as well for membrane proteins. Third, we provide a comparison of a set of commonly used sequence alignment algorithms as applied to membrane proteins. We find that high-accuracy alignments of membrane protein sequences can be obtained using state-of-the-art profile-to-profile methods that were developed for water-soluble proteins. Improvements are observed when weights derived from the secondary structure of the query and the template are used in the scoring of the alignment, a result which relies on the accuracy of the secondary-structure prediction of the query sequence. The most accurate alignments were obtained using template profiles constructed with the aid of structural alignments. In contrast, a simple sequence-to-sequence alignment algorithm, using a membrane protein-specific substitution matrix, shows no improvement in alignment accuracy. We suggest that profile-to-profile alignment methods should be adopted to maximize the accuracy of homology models of membrane proteins.     

Accurate detection of very sparse sequence motifs.

Protein sequence alignments are more reliable the shorter the evolutionary distance. Here, we align distantly related proteins using many closely spaced intermediate sequences as stepping stones. Such transitive alignments can be generated between any two proteins in a connected set, whether they are direct or indirect sequence neighbors in the underlying library of pairwise alignments. We have implemented a greedy algorithm, MaxFlow, using a novel consistency score to estimate the relative likelihood of alternative paths of transitive alignment. In contrast to traditional profile models of amino acid preferences, MaxFlow models the probability that two positions are structurally equivalent and retains high information content across large distances in sequence space. Thus, MaxFlow is able to identify sparse and narrow active-site sequence signatures which are embedded in high-entropy sequence segments in the structure based multiple alignment of large diverse enzyme superfamilies. In a challenging benchmark based on the urease superfamily, MaxFlow yields better reliability and double coverage compared to available sequence alignment software. This promises to increase information returns from functional and structural genomics, where reliable sequence alignment is a bottleneck to transferring the functional or structural characterization of model proteins to entire protein superfamilies.     

GeneRAGE: a robust algorithm for sequence clustering and domain detection

MOTIVATION: Efficient, accurate and automatic clustering of large protein sequence datasets, such as complete proteomes, into families, according to sequence similarity. Detection and correction of false positive and negative relationships with subsequent detection and resolution of multi-domain proteins. RESULTS: A new algorithm for the automatic clustering of protein sequence datasets has been developed. This algorithm represents all similarity relationships within the dataset in a binary matrix. Removal of false positives is achieved through subsequent symmetrification of the matrix using a Smith-Waterman dynamic programming alignment algorithm. Detection of multi-domain protein families and further false positive relationships within the symmetrical matrix is achieved through iterative processing of matrix elements with successive rounds of Smith-Waterman dynamic programming alignments. Recursive single-linkage clustering of the corrected matrix allows efficient and accurate family representation for each protein in the dataset. Initial clusters containing multi-domain families, are split into their constituent clusters using the information obtained by the multi-domain detection step. This algorithm can hence quickly and accurately cluster large protein datasets into families. Problems due to the presence of multi-domain proteins are minimized, allowing more precise clustering information to be obtained automatically. AVAILABILITY: GeneRAGE (version 1.0) executable binaries for most platforms may be obtained from the authors on request. The system is available to academic users free of charge under license.     

Sequence ordinations: a multivariate analysis approach to analysing large sequence data sets

Ordination is a powerful method for analysing complex data setsbut has been largely ignored in sequence analysis. This papershows how to use principal coordinates analysis to find low–dimensionalrepresentations of distance matrices derived from aligned setsof sequences. The method takes a matrix of Euclidean distancesbetween all pairs of sequence and finds a coordinate space wherethe distances are exactly preserved The main problem is to finda measure of distance between aligned sequences that is Euclidean.The simplest distance function is the square root of the percentagedifference (as measured by identities) between two sequences,where one ignores any positions in the alignment where thereis a gap in any sequence. If one does not ignore positions witha gap, the distances cannot be guaranteed to be Euclidean butthe deleterious effects are trivial. Two examples of using themethod are shown. A set of 226 aligned globins were analysedand the resulting ordination very successfully represents theknown patterns of relationship between the sequences. In theother example, a set of 610 aligned 5S rRNA sequences were analysed.Sequence ordinations complement phylogenetic analyses. Theyshould not be viewed as a complete alternative.     

Pfam: A comprehensive database of protein domain families based on seed alignments

Databases of multiple sequence alignments are a valuable aid to protein sequence classification and analysis. One of the main challenges when constructing such a database is to simultaneously satisfy the conflicting demands of completeness on the one hand and quality of alignment and domain definitions on the other. The latter properties are best dealt with by manual approaches, whereas completeness in practice is only amenable to automatic methods. Herein we present a database based on hidden Markov model profiles (HMMs), which combines high quality and completeness. Our database, Pfam, consists of parts A and B. Pfam-A is curated and contains well-characterized protein domain families with high quality alignments, which are maintained by using manually checked seed alignments and HMMs to find and align all members. Pfam-B contains sequence families that were generated automatically by applying the Domainer algorithm to cluster and align the remaining protein sequences after removal of Pfam-A domains. By using Pfam, a large number of previously unannotated proteins from the Caenorhabditis elegans genome project were classified. We have also identified many novel family memberships in known proteins, including new kazal, Fibronectin type III, and response regulator receiver domains. Pfam-A families have permanent accession numbers and form a library of HMMs available for searching and automatic annotation of new protein sequences. Proteins: 28:405–420, 1997. © 1997 Wiley-Liss, Inc.     

Empirical models for substitution in ribosomal RNA

Empirical models of substitution are often used in protein sequence analysis because the large alphabet of amino acids requires that many parameters be estimated in all but the simplest parametric models. When information about structure is used in the analysis of substitutions in structured RNA, a similar situation occurs. The number of parameters necessary to adequately describe the substitution process increases in order to model the substitution of paired bases. We have developed a method to obtain substitution rate matrices empirically from RNA alignments that include structural information in the form of base pairs. Our data consisted of alignments from the European Ribosomal RNA Database of Bacterial and Eukaryotic Small Subunit and Large Subunit Ribosomal RNA ( Wuyts et al. 2001. Nucleic Acids Res. 29:175-177; Wuyts et al. 2002. Nucleic Acids Res. 30:183-185). Using secondary structural information, we converted each sequence in the alignments into a sequence over a 20-symbol code: one symbol for each of the four individual bases, and one symbol for each of the 16 ordered pairs. Substitutions in the coded sequences are defined in the natural way, as observed changes between two sequences at any particular site. For given ranges (windows) of sequence divergence, we obtained substitution frequency matrices for the coded sequences. Using a technique originally developed for modeling amino acid substitutions ( Veerassamy, Smith, and Tillier. 2003. J. Comput. Biol. 10:997-1010), we were able to estimate the actual evolutionary distance for each window. The actual evolutionary distances were used to derive instantaneous rate matrices, and from these we selected a universal rate matrix. The universal rate matrices were incorporated into the Phylip Software package ( Felsenstein 2002. http://evolution.genetics.washington.edu/phylip.html), and we analyzed the ribosomal RNA alignments using both distance and maximum likelihood methods. The empirical substitution models performed well on simulated data, and produced reasonable evolutionary trees for 16S ribosomal RNA sequences from sequenced Bacterial genomes. Empirical models have the advantage of being easily implemented, and the fact that the code consists of 20 symbols makes the models easily incorporated into existing programs for protein sequence analysis. In addition, the models are useful for simulating the evolution of RNA sequence and structure simultaneously.