A comparison of three estimators of the population-scaled recombination rate: accuracy and robustness

We have performed simulations to assess the performance of three population genetics approximate-likelihood methods in estimating the population-scaled recombination rate from sequence data. We measured performance in two ways: accuracy when the sequence data were simulated according to the (simplistic) standard model underlying the methods and robustness to violations of many different aspects of the standard model. Although we found some differences between the methods, performance tended to be similar for all three methods. Despite the fact that the methods are not robust to violations of the underlying model, our simulations indicate that patterns of relative recombination rates should be inferred reasonably well even if the standard model does not hold. In addition, we assess various techniques for improving the performance of approximate-likelihood methods. In particular we find that the composite-likelihood method of Hudson (2001) can be improved by including log-likelihood contributions only for pairs of sites that are separated by some prespecified distance.     

Toward a detailed understanding of search trajectories in fragment assembly approaches to protein structure prediction

Energy functions, fragment libraries, and search methods constitute three key components of fragment‐assembly methods for protein structure prediction, which are all crucial for their ability to generate high‐accuracy predictions. All of these components are tightly coupled; efficient searching becomes more important as the quality of fragment libraries decreases. Given these relationships, there is currently a poor understanding of the strengths and weaknesses of the sampling approaches currently used in fragment‐assembly techniques. Here, we determine how the performance of search techniques can be assessed in a meaningful manner, given the above problems. We describe a set of techniques that aim to reduce the impact of the energy function, and assess exploration in view of the search space defined by a given fragment library. We illustrate our approach using Rosetta and EdaFold, and show how certain features of these methods encourage or limit conformational exploration. We demonstrate that individual trajectories of Rosetta are susceptible to local minima in the energy landscape, and that this can be linked to non‐uniform sampling across the protein chain. We show that EdaFold's novel approach can help balance broad exploration with locating good low‐energy conformations. This occurs through two mechanisms which cannot be readily differentiated using standard performance measures: exclusion of false minima, followed by an increasingly focused search in low‐energy regions of conformational space. Measures such as ours can be helpful in characterizing new fragment‐based methods in terms of the quality of conformational exploration realized. Proteins 2016; 84:411–426. © 2016 The Authors Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc.     

Confidence-Guided Local Structure Prediction with HHfrag

We present a method to assess the reliability of local structure prediction from sequence. We introduce a greedy algorithm for filtering and enrichment of dynamic fragment libraries, compiled with remote-homology detection methods such as HHfrag. After filtering false hits at each target position, we reduce the fragment library to a minimal set of representative fragments, which are guaranteed to have correct local structure in regions of detectable conservation. We demonstrate that the location of conserved motifs in a protein sequence can be predicted by examining the recurrence and structural homogeneity of detected fragments. The resulting confidence score correlates with the local RMSD of the representative fragments and allows us to predict torsion angles from sequence with better accuracy compared to existing machine learning methods.     

Confidence measures for protein fold recognition

MOTIVATION: We present an extensive evaluation of different methods and criteria to detect remote homologs of a given protein sequence. We investigate two associated problems: first, to develop a sensitive searching method to identify possible candidates and, second, to assign a confidence to the putative candidates in order to select the best one. For searching methods where the score distributions are known, p-values are used as confidence measure with great success. For the cases where such theoretical backing is absent, we propose empirical approximations to p-values for searching procedures. RESULTS: As a baseline, we review the performances of different methods for detecting remote protein folds (sequence alignment and threading, with and without sequence profiles, global and local). The analysis is performed on a large representative set of protein structures. For fold recognition, we find that methods using sequence profiles generally perform better than methods using plain sequences, and that threading methods perform better than sequence alignment methods. In order to assess the quality of the predictions made, we establish and compare several confidence measures, including raw scores, z-scores, raw score gaps, z-score gaps, and different methods of p-value estimation. We work our way from the theoretically well backed local scores towards more explorative global and threading scores. The methods for assessing the statistical significance of predictions are compared using specificity--sensitivity plots. For local alignment techniques we find that p-value methods work best, albeit computationally cheaper methods such as those based on score gaps achieve similar performance. For global methods where no theory is available methods based on score gaps work best. By using the score gap functions as the measure of confidence we improve the more powerful fold recognition methods for which p-values are unavailable. AVAILABILITY: The benchmark set is available upon request.     

Prodepth: Predict Residue Depth by Support Vector Regression Approach from Protein Sequences Only

Residue depth (RD) is a solvent exposure measure that complements the information provided by conventional accessible surface area (ASA) and describes to what extent a residue is buried in the protein structure space. Previous studies have established that RD is correlated with several protein properties, such as protein stability, residue conservation and amino acid types. Accurate prediction of RD has many potentially important applications in the field of structural bioinformatics, for example, facilitating the identification of functionally important residues, or residues in the folding nucleus, or enzyme active sites from sequence information. In this work, we introduce an efficient approach that uses support vector regression to quantify the relationship between RD and protein sequence. We systematically investigated eight different sequence encoding schemes including both local and global sequence characteristics and examined their respective prediction performances. For the objective evaluation of our approach, we used 5-fold cross-validation to assess the prediction accuracies and showed that the overall best performance could be achieved with a correlation coefficient (CC) of 0.71 between the observed and predicted RD values and a root mean square error (RMSE) of 1.74, after incorporating the relevant multiple sequence features. The results suggest that residue depth could be reliably predicted solely from protein primary sequences: local sequence environments are the major determinants, while global sequence features could influence the prediction performance marginally. We highlight two examples as a comparison in order to illustrate the applicability of this approach. We also discuss the potential implications of this new structural parameter in the field of protein structure prediction and homology modeling. This method might prove to be a powerful tool for sequence analysis.     

Incorporating homologues into sequence embeddings for protein analysis

Statistical and learning techniques are becoming increasingly popular for different tasks in bioinformatics. Many of the most powerful statistical and learning techniques are applicable to points in a Euclidean space but not directly applicable to discrete sequences such as protein sequences. One way to apply these techniques to protein sequences is to embed the sequences into a Euclidean space and then apply these techniques to the embedded points. In this work we introduce a biologically motivated sequence embedding, the homology kernel, which takes into account intuitions from local alignment, sequence homology, and predicted secondary structure. This embedding allows us to directly apply learning techniques to protein sequences. We apply the homology kernel in several ways. We demonstrate how the homology kernel can be used for protein family classification and outperforms state-of-the-art methods for remote homology detection. We show that the homology kernel can be used for secondary structure prediction and is competitive with popular secondary structure prediction methods. Finally, we show how the homology kernel can be used to incorporate information from homologous sequences in local sequence alignment.     

Automating human intuition for protein design

In the design of new enzymes and binding proteins, human intuition is often used to modify computationally designed amino acid sequences prior to experimental characterization. The manual sequence changes involve both reversions of amino acid mutations back to the identity present in the parent scaffold and the introduction of residues making additional interactions with the binding partner or backing up first shell interactions. Automation of this manual sequence refinement process would allow more systematic evaluation and considerably reduce the amount of human designer effort involved. Here we introduce a benchmark for evaluating the ability of automated methods to recapitulate the sequence changes made to computer‐generated models by human designers, and use it to assess alternative computational methods. We find the best performance for a greedy one‐position‐at‐a‐time optimization protocol that utilizes metrics (such as shape complementarity) and local refinement methods too computationally expensive for global Monte Carlo (MC) sequence optimization. This protocol should be broadly useful for improving the stability and function of designed binding proteins. Proteins 2014; 82:858–866. © 2013 Wiley Periodicals, Inc.     

Spectral clustering of protein sequences

An important problem in genomics is automatically clustering homologous proteins when only sequence information is available. Most methods for clustering proteins are local, and are based on simply thresholding a measure related to sequence distance. We first show how locality limits the performance of such methods by analysing the distribution of distances between protein sequences. We then present a global method based on spectral clustering and provide theoretical justification of why it will have a remarkable improvement over local methods. We extensively tested our method and compared its performance with other local methods on several subsets of the SCOP (Structural Classification of Proteins) database, a gold standard for protein structure classification. We consistently observed that, the number of clusters that we obtain for a given set of proteins is close to the number of superfamilies in that set; there are fewer singletons; and the method correctly groups most remote homologs. In our experiments, the quality of the clusters as quantified by a measure that combines sensitivity and specificity was consistently better [on average, improvements were 84% over hierarchical clustering, 34% over Connected Component Analysis (CCA) (similar to GeneRAGE) and 72% over another global method, TribeMCL].     

Channelrhodopsins: A bioinformatics perspective

Channelrhodopsins are microbial-type rhodopsins that function as light-gated cation channels. Understanding how the detailed architecture of the protein governs its dynamics and specificity for ions is important, because it has the potential to assist in designing site-directed channelrhodopsin mutants for specific neurobiology applications. Here we use bioinformatics methods to derive accurate alignments of channelrhodopsin sequences, assess the sequence conservation patterns and find conserved motifs in channelrhodopsins, and use homology modeling to construct three-dimensional structural models of channelrhodopsins. The analyses reveal that helices C and D of channelrhodopsins contain Cys, Ser, and Thr groups that can engage in both intra- and inter-helical hydrogen bonds. We propose that these polar groups participate in inter-helical hydrogen-bonding clusters important for the protein conformational dynamics and for the local water interactions. This article is part of a Special Issue entitled: Retinal Proteins — You can teach an old dog new tricks.     

Structural Alphabets for Protein Structure Classification: A Comparison Study

Finding structural similarities between proteins often helps reveal shared functionality, which otherwise might not be detected by native sequence information alone. Such similarity is usually detected and quantified by protein structure alignment. Determining the optimal alignment between two protein structures, however, remains a hard problem. An alternative approach is to approximate each three-dimensional protein structure using a sequence of motifs derived from a structural alphabet. Using this approach, structure comparison is performed by comparing the corresponding motif sequences or structural sequences. In this article, we measure the performance of such alphabets in the context of the protein structure classification problem. We consider both local and global structural sequences. Each letter of a local structural sequence corresponds to the best matching fragment to the corresponding local segment of the protein structure. The global structural sequence is designed to generate the best possible complete chain that matches the full protein structure. We use an alphabet of 20 letters, corresponding to a library of 20 motifs or protein fragments having four residues. We show that the global structural sequences approximate well the native structures of proteins, with an average coordinate root mean square of 0.69 Å over 2225 test proteins. The approximation is best for all α-proteins, while relatively poorer for all β-proteins. We then test the performance of four different sequence representations of proteins (their native sequence, the sequence of their secondary-structure elements, and the local and global structural sequences based on our fragment library) with different classifiers in their ability to classify proteins that belong to five distinct folds of CATH. Without surprise, the primary sequence alone performs poorly as a structure classifier. We show that addition of either secondary-structure information or local information from the structural sequence considerably improves the classification accuracy. The two fragment-based sequences perform better than the secondary-structure sequence but not well enough at this stage to be a viable alternative to more computationally intensive methods based on protein structure alignment.     

MuGeN: simultaneous exploration of multiple genomes and computer analysis results

MOTIVATION: The availability of increasing amounts of sequence data about completely sequenced genomes spurs the development of new methods in the fields of automated annotation, and of comparative genomics. Tools allowing the visualization of results produced by analysis methods, superimposed on possibly annotated sequence data, and enabling synchronized navigation in multiple genomes, provide new means for interactive genome exploration. This kind of visual inspection can be used as a basis to assess the quality of new analysis algorithms, or to discover genome portions to be subjected to in-depth studies. RESULTS: We propose a software package, MuGeN, built for navigating through multiple annotated genomes. It is capable of retrieving annotated sequences in several formats, stored in local files, or available in databases over the network. From these, it then generates an interactive display, or an image file, in most common formats suitable for printing, further editing or integrating in Web pages. Genome maps may be mixed with computer analysis results loaded from XML files, whose format is generic enough to be adapted to a majority of sequence oriented analysis methods. AVAILABILITY: MuGeN is available at http://www-mig.jouy.inra.fr/bdsi/MuGeN.     

Non-sequential structure-based alignments reveal topology-independent core packing arrangements in proteins

MOTIVATION: Proteins of the same class often share a secondary structure packing arrangement but differ in how the secondary structure units are ordered in the sequence. We find that proteins that share a common core also share local sequence-structure similarities, and these can be exploited to align structures with different topologies. In this study, segments from a library of local sequence-structure alignments were assembled hierarchically, enforcing the compactness and conserved inter-residue contacts but not sequential ordering. Previous structure-based alignment methods often ignore sequence similarity, local structural equivalence and compactness. RESULTS: The new program, SCALI (Structural Core ALIgnment), can efficiently find conserved packing arrangements, even if they are non-sequentially ordered in space. SCALI alignments conserve remote sequence similarity and contain fewer alignment errors. Clustering of our pairwise non-sequential alignments shows that recurrent packing arrangements exist in topologically different structures. For example, the three-layer sandwich domain architecture may be divided into four structural subclasses based on internal packing arrangements. These subclasses represent an intermediate level of structure classification, more general than topology, but more specific than architecture as defined in CATH. A strategy is presented for developing a set of predictive hidden Markov models based on multiple SCALI alignments.     

Application of coalescent methods to reveal fine-scale rate variation and recombination hotspots

There has been considerable recent interest in understanding the way in which recombination rates vary over small physical distances, and the extent of recombination hotspots, in various genomes. Here we adapt, apply, and assess the power of recently developed coalescent-based approaches to estimating recombination rates from sequence polymorphism data. We apply full-likelihood estimation to study rate variation in and around a well-characterized recombination hotspot in humans, in the beta-globin gene cluster, and show that it provides similar estimates, consistent with those from sperm studies, from two populations deliberately chosen to have different demographic and selectional histories. We also demonstrate how approximate-likelihood methods can be used to detect local recombination hotspots from genomic-scale SNP data. In a simulation study based on 80 100-kb regions, these methods detect 43 out of 60 hotspots (ranging from 1 to 2 kb in size), with only two false positives out of 2000 subregions that were tested for the presence of a hotspot. Our study suggests that new computational tools for sophisticated analysis of population diversity data are valuable for hotspot detection and fine-scale mapping of local recombination rates.     

Optimized representations and maximal information in proteins

In an effort to quantify loss of information in the processing of protein bioinformatic data, we examine how representations of amino acid sequence and backbone conformation affect the quantity of accessible structural information from local sequence. We propose a method to extract the maximum amount of peptide backbone structural information available in local sequence fragments, given a finite structural data set. Using methods of information theory, we develop an unbiased measure of local structural information that gauges changes in structural distributions when different representations of secondary structure and local sequence are used. We find that the manner in which backbone structure is represented affects the amount and quality of structural information that may be extracted from local sequence. Representations based on virtual bonds capture more structural information from local sequence than a three-state assignment scheme (helix/strand/loop). Furthermore, we find that amino acids show significant kinship with respect to the backbone structural information they carry, so that a collapse of the amino acid alphabet can be accomplished without severely affecting the amount of extractable information. This strategy is critical in optimizing the utility of a limited database of experimentally solved protein structures. Finally, we discuss the similarities within and differences between groups of amino acids in their roles in the local folding code and recognize specific amino acids critical in the formation of local structure.     

A new approach to the design of a sequence with the highest affinity for a molecular surface.

We describe an algorithm to design the primary structures for peptides which must have the strongest binding to a given molecular surface. This problem cannot be solved by a direct combinatorial sorting, because of an enormous number of possible primary and spatial structures. The approach to solve this problem is to describe a state of each residue by two variables: (i) amino acid type and (ii) 3-D coordinate, and to minimize binding energy over all these variables simultaneously. For short chains which have no long-range interactions within themselves, this minimization can be done easily and efficiently by dynamic programming. We also discuss the problem of how to estimate specificity of binding and how to deduce a sequence with maximal specificity for a given surface. We show that this sequence can be deduced by the same algorithm after some modification of energetic parameters.     

Efficient remote homology detection using local structure

MOTIVATION: The function of an unknown biological sequence can often be accurately inferred if we are able to map this unknown sequence to its corresponding homologous family. At present, discriminative methods such as SVM-Fisher and SVM-pairwise, which combine support vector machine (SVM) and sequence similarity, are recognized as the most accurate methods, with SVM-pairwise being the most accurate. However, these methods typically encode sequence information into their feature vectors and ignore the structure information. They are also computationally inefficient. Based on these observations, we present an alternative method for SVM-based protein classification. Our proposed method, SVM-I-sites, utilizes structure similarity for remote homology detection. RESULT: We run experiments on the Structural Classification of Proteins 1.53 data set. The results show that SVM-I-sites is more efficient than SVM-pairwise. Further, we find that SVM-I-sites outperforms sequence-based methods such as PSI-BLAST, SAM, and SVM-Fisher while achieving a comparable performance with SVM-pairwise. AVAILABILITY: I-sites server is accessible through the web at http://www.bioinfo.rpi.edu. Programs are available upon request for academics. Licensing agreements are available for commercial interests. The framework of encoding local structure into feature vector is available upon request.