Accuracy of sequence alignment and fold assessment using reduced amino acid alphabets

Reduced or simplified amino acid alphabets group the 20 naturally occurring amino acids into a smaller number of representative protein residues. To date, several reduced amino acid alphabets have been proposed, which have been derived and optimized by a variety of methods. The resulting reduced amino acid alphabets have been applied to pattern recognition, generation of consensus sequences from multiple alignments, protein folding, and protein structure prediction. In this work, amino acid substitution matrices and statistical potentials were derived based on several reduced amino acid alphabets and their performance assessed in a large benchmark for the tasks of sequence alignment and fold assessment of protein structure models, using as a reference frame the standard alphabet of 20 amino acids. The results showed that a large reduction in the total number of residue types does not necessarily translate into a significant loss of discriminative power for sequence alignment and fold assessment. Therefore, some definitions of a few residue types are able to encode most of the relevant sequence/structure information that is present in the 20 standard amino acids. Based on these results, we suggest that the use of reduced amino acid alphabets may allow to increasing the accuracy of current substitution matrices and statistical potentials for the prediction of protein structure of remote homologs.     

Prediction of ketoacyl synthase family using reduced amino acid alphabets

Ketoacyl synthases are enzymes involved in fatty acid synthesis and can be classified into five families based on primary sequence similarity. Different families have different catalytic mechanisms. Developing cost-effective computational models to identify the family of ketoacyl synthases will be helpful for enzyme engineering and in knowing individual enzymes’ catalytic mechanisms. In this work, a support vector machine-based method was developed to predict ketoacyl synthase family using the n-peptide composition of reduced amino acid alphabets. In jackknife cross-validation, the model based on the 2-peptide composition of a reduced amino acid alphabet of size 13 yielded the best overall accuracy of 96.44% with average accuracy of 93.36%, which is superior to other state-of-the-art methods. This result suggests that the information provided by n-peptide compositions of reduced amino acid alphabets provides efficient means for enzyme family classification and that the proposed model can be efficiently used for ketoacyl synthase family annotation.     

Reduction of protein sequence complexity by residue grouping

It is well known that there are some similarities among various naturally occurring amino acids. Thus, the complexity in protein systems could be reduced by sorting these amino acids with similarities into groups and then protein sequences can be simplified by reduced alphabets. This paper discusses how to group similar amino acids and whether there is a minimal amino acid alphabet by which proteins can be folded. Various reduced alphabets are obtained by reserving the maximal information for the simplified protein sequence compared with the parent sequence using global sequence alignment. With these reduced alphabets and simplified similarity matrices, we achieve recognition of the protein fold based on the similarity score of the sequence alignment. The coverage in dataset SCOP40 for various levels of reduction on the amino acid types is obtained, which is the number of homologous pairs detected by program BLAST to the number marked by SCOP40. For the reduced alphabets containing 10 types of amino acids, the ability to detect distantly related folds remains almost at the same level as that by the alphabet of 20 types of amino acids, which implies that 10 types of amino acids may be the degree of freedom for characterizing the complexity in proteins.     

Folding alphabets.

A new computational approach optimizes searches for reduced protein folding alphabets that use fewer than 20 types of amino acids. The predicted optimal five-letter alphabet happens to be in agreement with the suggestive results of a recent experiment, but whether highly reduced alphabets are sufficient for truly protein-like properties remains an open experimental question.     

Clustering of protein families into functional subtypes using Relative Complexity Measure with reduced amino acid alphabets

Background  

Phylogenetic analysis can be used to divide a protein family into subfamilies in the absence of experimental information. Most phylogenetic analysis methods utilize multiple alignment of sequences and are based on an evolutionary model. However, multiple alignment is not an automated procedure and requires human intervention to maintain alignment integrity and to produce phylogenies consistent with the functional splits in underlying sequences. To address this problem, we propose to use the alignment-free Relative Complexity Measure (RCM) combined with reduced amino acid alphabets to cluster protein families into functional subtypes purely on sequence criteria. Comparison with an alignment-based approach was also carried out to test the quality of the clustering.     

Effect of alphabet size and foldability requirements on protein structure designability.

A number of investigators have addressed the issue of why certain protein structures are especially common by considering structure designability, defined as the number of sequences that would successfully fold into any particular native structure. One such approach, based on foldability, suggested that structures could be classified according to their maximum possible foldability and that this optimal foldability would be highly correlated with structure designability. Other approaches have focused on computing the designability of lattice proteins written with reduced two-letter amino acid alphabets. These different approaches suggested contrasting characteristics of the most designable structures. This report compares the designability of lattice proteins over a wide range of amino acid alphabets and foldability requirements. While all alphabets have a wide distribution of protein designabilities, the form of the distribution depends on how protein "viability" is defined. Furthermore, under increasing foldability requirements, the change in designabilities for all alphabets are in good agreement with the previous conclusions of the foldability approach. Most importantly, it was noticed that those structures that were highly designable for the two-letter amino acid alphabets are not especially designable with higher-letter alphabets.     

Evaluation of local structure alphabets based on residue burial

Residue burial, which describes a protein residue's exposure to solvent and neighboring atoms, is key to protein structure prediction, modeling, and analysis. We assessed 21 alphabets representing residue burial, according to their predictability from amino acid sequence, conservation in structural alignments, and utility in one fold-recognition scenario. This follows upon our previous work in assessing nine representations of backbone geometry.1 The alphabet found to be most effective overall has seven states and is based on a count of C(beta) atoms within a 14 A-radius sphere centered at the C(beta) of a residue of interest. When incorporated into a hidden Markov model (HMM), this alphabet gave us a 38% performance boost in fold recognition and 23% in alignment quality.     

Amino acid alphabet reduction preserves fold information contained in contact interactions in proteins

To reduce complexity, understand generalized rules of protein folding, and facilitate de novo protein design, the 20‐letter amino acid alphabet is commonly reduced to a smaller alphabet by clustering amino acids based on some measure of similarity. In this work, we seek the optimal alphabet that preserves as much of the structural information found in long‐range (contact) interactions among amino acids in natively‐folded proteins. We employ the Information Maximization Device, based on information theory, to partition the amino acids into well‐defined clusters. Numbering from 2 to 19 groups, these optimal clusters of amino acids, while generated automatically, embody well‐known properties of amino acids such as hydrophobicity/polarity, charge, size, and aromaticity, and are demonstrated to maintain the discriminative power of long‐range interactions with minimal loss of mutual information. Our measurements suggest that reduced alphabets (of less than 10) are able to capture virtually all of the information residing in native contacts and may be sufficient for fold recognition, as demonstrated by extensive threading tests. In an expansive survey of the literature, we observe that alphabets derived from various approaches—including those derived from physicochemical intuition, local structure considerations, and sequence alignments of remote homologs—fare consistently well in preserving contact interaction information, highlighting a convergence in the various factors thought to be relevant to the folding code. Moreover, we find that alphabets commonly used in experimental protein design are nearly optimal and are largely coherent with observations that have arisen in this work. Proteins 2015; 83:2198–2216. © 2015 Wiley Periodicals, Inc.     

Using protein structural information in evolutionary inference: transmembrane proteins

We present a model of amino acid sequence evolution based on a hidden Markov model that extends to transmembrane proteins previous methods that incorporate protein structural information into phylogenetics. Our model aims to give a better understanding of processes of molecular evolution and to extract structural information from multiple alignments of transmembrane sequences and use such information to improve phylogenetic analyses. This should be of value in phylogenetic studies of transmembrane proteins: for example, mitochondrial proteins have acquired a special importance in phylogenetics and are mostly transmembrane proteins. The improvement in fit to example data sets of our new model relative to less complex models of amino acid sequence evolution is statistically tested. To further illustrate the potential utility of our method, phylogeny estimation is performed on primate CCR5 receptor sequences, sequences of l and m subunits of the light reaction center in purple bacteria, guinea pig sequences with respect to lagomorph and rodent sequences of calcitonin receptor and K-substance receptor, and cetacean sequences of cytochrome b.     

Likelihood-based inferences under isolation by distance: two-dimensional habitats and confidence intervals

Likelihood-based methods of inference of population parameters from genetic data in structured populations have been implemented but still little tested in large networks of populations. In this work, a previous software implementation of inference in linear habitats is extended to two-dimensional habitats, and the coverage properties of confidence intervals are analyzed in both cases. Both standard likelihood and an efficient approximation are considered. The effects of misspecification of mutation model and dispersal distribution, and of spatial binning of samples, are considered. In the absence of model misspecification, the estimators have low bias, low mean square error, and the coverage properties of confidence intervals are consistent with theoretical expectations. Inferences of dispersal parameters and of the mutation rate are sensitive to misspecification or to approximations inherent to the coalescent algorithms used. In particular, coalescent approximations are not appropriate to infer the shape of the dispersal distribution. However, inferences of the neighborhood parameter (or of the product of population density and mean square dispersal rate) are generally robust with respect to complicating factors, such as misspecification of the mutation process and of the shape of the dispersal distribution, and with respect to spatial binning of samples. Likelihood inferences appear feasible in moderately sized networks of populations (up to 400 populations in this work), and they are more efficient than previous moment-based spatial regression method in realistic conditions.     

Using substitution matrices to estimate probability distributions for biological sequences.

Accurately estimating probabilities from observations is important for probabilistic-based approaches to problems in computational biology. In this paper we present a biologically-motivated method for estimating probability distributions over discrete alphabets from observations using a mixture model of common ancestors. The method is an extension of substitution matrix-based probability estimation methods. In contrast to previous such methods, our method has a simple Bayesian interpretation and has the advantage over Dirichlet mixtures that it is both effective and simple to compute for large alphabets. The method is applied to estimate amino acid probabilities based on observed counts in an alignment and is shown to perform comparably to previous methods. The method is also applied to estimate probability distributions over protein families and improves protein classification accuracy.     

Elevated substitution rate estimates from ancient DNA: model violation and bias of Bayesian methods

The increasing ability to extract and sequence DNA from noncontemporaneous tissue offers biologists the opportunity to analyse ancient DNA (aDNA) together with modern DNA (mDNA) to address the taxonomy of extinct species, evolutionary origins, historical phylogeography and biogeography. Perhaps more exciting are recent developments in coalescence-based Bayesian inference that offer the potential to use temporal information from aDNA and mDNA for the estimation of substitution rates and divergence dates as an alternative to fossil and geological calibration. This comes at a time of growing interest in the possibility of time dependency for molecular rate estimates. In this study, we provide a critical assessment of Bayesian Markov chain Monte Carlo (MCMC) analysis for the estimation of substitution rate using simulated samples of aDNA and mDNA. We conclude that the current models and priors employed in Bayesian MCMC analysis of heterochronous mtDNA are susceptible to an upward bias in the estimation of substitution rates because of model misspecification when the data come from populations with less than simple demographic histories, including sudden short-lived population bottlenecks or pronounced population structure. However, when model misspecification is only mild, then the 95% highest posterior density intervals provide adequate frequentist coverage of the true rates.     

Using mixtures of common ancestors for estimating the probabilities of discrete events in biological sequences

Accurately estimating probabilities from observations is important for probabilistic-based approaches to problems in computational biology. In this paper we present a biologically-motivated method for estimating probability distributions over discrete alphabets from observations using a mixture model of common ancestors. The method is an extension of substitution matrix-based probability estimation methods. In contrast to previous such methods, our method has a simple Bayesian interpretation and has the advantage over Dirichlet mixtures that it is both effective and simple to compute for large alphabets. The method is applied to estimate amino acid probabilities based on observed counts in an alignment and is shown to perform comparably to previous methods. The method is also applied to estimate probability distributions over protein families and improves protein classification accuracy.     

Markov chain Monte Carlo segregation and linkage analysis for oligogenic models.

A new method for segregation and linkage analysis, with pedigree data, is described. Reversible jump Markov chain Monte Carlo methods are used to implement a sampling scheme in which the Markov chain can jump between parameter subspaces corresponding to models with different numbers of quantitative-trait loci (QTL's). Joint estimation of QTL number, position, and effects is possible, avoiding the problems that can arise from misspecification of the number of QTL's in a linkage analysis. The method is illustrated by use of a data set simulated for the 9th Genetic Analysis Workshop; this data set had several oligogenic traits, generated by use of a 1,497-member pedigree. The mixing characteristics of the method appear to be good, and the method correctly recovers the simulated model from the test data set. The approach appears to have great potential both for robust linkage analysis and for the answering of more general questions regarding the genetic control of complex traits.     

An information-theoretic classification of amino acids for the assessment of interfaces in protein–protein docking

Docking represents a versatile and powerful method to predict the geometry of protein–protein complexes. However, despite significant methodical advances, the identification of good docking solutions among a large number of false solutions still remains a difficult task. We have previously demonstrated that the formalism of mutual information (MI) from information theory can be adapted to protein docking, and we have now extended this approach to enhance its robustness and applicability. A large dataset consisting of 22,934 docking decoys derived from 203 different protein–protein complexes was used for an MI-based optimization of reduced amino acid alphabets representing the protein–protein interfaces. This optimization relied on a clustering analysis that allows one to estimate the mutual information of whole amino acid alphabets by considering all structural features simultaneously, rather than by treating them individually. This clustering approach is fast and can be applied in a similar fashion to the generation of reduced alphabets for other biological problems like fold recognition, sequence data mining, or secondary structure prediction. The reduced alphabets derived from the present work were converted into a scoring function for the evaluation of docking solutions, which is available for public use via the web service score-MI: http://score-MI.biochem.uni-erlangen.de     

Models of amino acid substitution and applications to mitochondrial protein evolution

Models of amino acid substitution were developed and compared using maximum likelihood. Two kinds of models are considered. "Empirical" models do not explicitly consider factors that shape protein evolution, but attempt to summarize the substitution pattern from large quantities of real data. "Mechanistic" models are formulated at the codon level and separate mutational biases at the nucleotide level from selective constraints at the amino acid level. They account for features of sequence evolution, such as transition-transversion bias and base or codon frequency biases, and make use of physicochemical distances between amino acids to specify nonsynonymous substitution rates. A general approach is presented that transforms a Markov model of codon substitution into a model of amino acid replacement. Protein sequences from the entire mitochondrial genomes of 20 mammalian species were analyzed using different models. The mechanistic models were found to fit the data better than empirical models derived from large databases. Both the mutational distance between amino acids (determined by the genetic code and mutational biases such as the transition-transversion bias) and the physicochemical distance are found to have strong effects on amino acid substitution rates. A significant proportion of amino acid substitutions appeared to have involved more than one codon position, indicating that nucleotide substitutions at neighboring sites may be correlated. Rates of amino acid substitution were found to be highly variable among sites.      

CodonTest: Modeling Amino Acid Substitution Preferences in Coding Sequences

Codon models of evolution have facilitated the interpretation of selective forces operating on genomes. These models, however, assume a single rate of non-synonymous substitution irrespective of the nature of amino acids being exchanged. Recent developments have shown that models which allow for amino acid pairs to have independent rates of substitution offer improved fit over single rate models. However, these approaches have been limited by the necessity for large alignments in their estimation. An alternative approach is to assume that substitution rates between amino acid pairs can be subdivided into rate classes, dependent on the information content of the alignment. However, given the combinatorially large number of such models, an efficient model search strategy is needed. Here we develop a Genetic Algorithm (GA) method for the estimation of such models. A GA is used to assign amino acid substitution pairs to a series of rate classes, where is estimated from the alignment. Other parameters of the phylogenetic Markov model, including substitution rates, character frequencies and branch lengths are estimated using standard maximum likelihood optimization procedures. We apply the GA to empirical alignments and show improved model fit over existing models of codon evolution. Our results suggest that current models are poor approximations of protein evolution and thus gene and organism specific multi-rate models that incorporate amino acid substitution biases are preferred. We further anticipate that the clustering of amino acid substitution rates into classes will be biologically informative, such that genes with similar functions exhibit similar clustering, and hence this clustering will be useful for the evolutionary fingerprinting of genes.     

Gaussian binning: a new kernel-based method for processing NMR spectroscopic data for metabolomics

In many metabolomics studies, NMR spectra are divided into bins of fixed width. This spectral quantification technique, known as uniform binning, is used to reduce the number of variables for pattern recognition techniques and to mitigate effects from variations in peak positions; however, shifts in peaks near the boundaries can cause dramatic quantitative changes in adjacent bins due to non-overlapping boundaries. Here we describe a new Gaussian binning method that incorporates overlapping bins to minimize these effects. A Gaussian kernel weights the signal contribution relative to distance from bin center, and the overlap between bins is controlled by the kernel standard deviation. Sensitivity to peak shift was assessed for a series of test spectra where the offset frequency was incremented in 0.5 Hz steps. For a 4 Hz shift within a bin width of 24 Hz, the error for uniform binning increased by 150%, while the error for Gaussian binning increased by 50%. Further, using a urinary metabolomics data set (from a toxicity study) and principal component analysis (PCA), we showed that the information content in the quantified features was equivalent for Gaussian and uniform binning methods. The separation between groups in the PCA scores plot, measured by the J ₂ quality metric, is as good or better for Gaussian binning versus uniform binning. The Gaussian method is shown to be robust in regards to peak shift, while still retaining the information needed by classification and multivariate statistical techniques for NMR-metabolomics data.     

Property-based sequence representations do not adequately encode local protein folding information

We examine the informatic characteristics of amino acid representations based on physical properties. We demonstrate that sequences rewritten using contracted alphabets based on physical properties do not encode local folding information well. The best four-character alphabet can only encode approximately 57% of the maximum possible amount of structural information. This result suggests that property-based representations that operate on a local length scale are not likely to be useful in homology searches and fold-recognition exercises.     

Constraining protein sequence space: four amino acid alphabets are sufficient to recapitulate lambda repressor multimerization

Nucleic acid polymers selected from random sequence space constitute an enormous array of catalytic, diagnostic and therapeutic molecules. Despite the fact that proteins are robust polymers with far greater chemical and physical diversity, success in unlocking protein sequence space remains elusive. We have devised a combinatorial strategy for accessing nucleic acid sequence space corresponding to proteins comprising selected amino acid alphabets. Using the SynthOMIC approach (synthesis of ORFs by multimerizing in-frame codons), representative libraries comprising four amino acid alphabets were fused in-frame to the lambda repressor DNA-binding domain to provide an in vivo selection for self-interacting proteins that re-constitute lambda repressor function. The frequency of self-interactors as a function of amino acid composition ranged over five orders of magnitude, from ∼6% of clones in a library comprising the amino acid residues LARE to ∼0.6 in 10⁶ in the MASH library. Sequence motifs were evident by inspection in many cases, and individual clones from each library presented substantial sequence identity with translated proteins by BLAST analysis. We posit that the SynthOMIC approach represents a powerful strategy for creating combinatorial libraries of open reading frames that distils protein sequence space on the basis of three inherent properties: it supports the use of selected amino acid alphabets, eliminates redundant sequences and locally constrains amino acids.