Five Hierarchical Levels of Sequence-Structure Correlation in Proteins

This article reviews recent work towards modelling protein folding pathways using a bioinformatics approach. Statistical models have been developed for sequence-structure correlations in proteins at five levels of structural complexity: (i) short motifs; (ii) extended motifs; (iii) nonlocal pairs of motifs; (iv) 3-dimensional arrangements of multiple motifs; and (v) global structural homology. We review statistical models, including sequence profiles, hidden Markov models (HMMs) and interaction potentials, for the first four levels of structural detail. The I-sites (folding Initiation sites) Library models short local structure motifs. Each succeeding level has a statistical model, as follows: HMMSTR (HMM for STRucture) is an HMM for extended motifs; HMMSTR-CM (Contact Maps) is a model for pairwise interactions between motifs; and SCALI-HMM (HMMs for Structural Core ALIgnments) is a set of HMMs for the spatial arrangements of motifs. The parallels between the statistical models and theoretical models for folding pathways are discussed in this article; however, global sequence models are not discussed because they have been extensively reviewed elsewhere. The data used and algorithms presented in this article are available at http://www.bioinfo.rpi.edu/~bystrc/ (click on "servers" or "downloads") or by request to bystrc@rpi.edu .     

Improved pairwise alignments of proteins in the Twilight Zone using local structure predictions

MOTIVATION: In recent years, advances have been made in the ability of computational methods to discriminate between homologous and non-homologous proteins in the 'twilight zone' of sequence similarity, where the percent sequence identity is a poor indicator of homology. To make these predictions more valuable to the protein modeler, they must be accompanied by accurate alignments. Pairwise sequence alignments are inferences of orthologous relationships between sequence positions. Evolutionary distance is traditionally modeled using global amino acid substitution matrices. But real differences in the likelihood of substitutions may exist for different structural contexts within proteins, since structural context contributes to the selective pressure. RESULTS: HMMSUM (HMMSTR-based substitution matrices) is a new model for structural context-based amino acid substitution probabilities consisting of a set of 281 matrices, each for a different sequence-structure context. HMMSUM does not require the structure of the protein to be known. Instead, predictions of local structure are made using HMMSTR, a hidden Markov model for local structure. Alignments using the HMMSUM matrices compare favorably to alignments carried out using the BLOSUM matrices or structure-based substitution matrices SDM and HSDM when validated against remote homolog alignments from BAliBASE. HMMSUM has been implemented using local Dynamic Programming and with the Bayesian Adaptive alignment method.     

Fully automated ab initio protein structure prediction using I-SITES,HMMSTR and ROSETTA

MOTIVATION: The Monte Carlo fragment insertion method for protein tertiary structure prediction (ROSETTA) of Baker and others, has been merged with the I-SITES library of sequence structure motifs and the HMMSTR model for local structure in proteins, to form a new public server for the ab initio prediction of protein structure. The server performs several tasks in addition to tertiary structure prediction, including a database search, amino acid profile generation, fragment structure prediction, and backbone angle and secondary structure prediction. Meeting reasonable service goals required improvements in the efficiency, in particular for the ROSETTA algorithm. RESULTS: The new server was used for blind predictions of 40 protein sequences as part of the CASP4 blind structure prediction experiment. The results for 31 of those predictions are presented here. 61% of the residues overall were found in topologically correct predictions, which are defined as fragments of 30 residues or more with a root-mean-square deviation in superimposed alpha carbons of less than 6A. HMMSTR 3-state secondary structure predictions were 73% correct overall. Tertiary structure predictions did not improve the accuracy of secondary structure prediction.     

Comparing protein sequence-based and predicted secondary structure-based methods for identification of remote homologs.

We have compared a novel sequence-structure matching technique, FORESST, for detecting remote homologs to three existing sequence based methods, including local amino acid sequence similarity by BLASTP, hidden Markov models (HMMs) of sequences of protein families using SAM, HMMs based on sequence motifs identified using meta-MEME. FORESST compares predicted secondary structures to a library of structural families of proteins, using HMMs. Altogether 45 proteins from nine structural families in the database CATH were used in a cross-validated test of the fold assignment accuracy of each method. Local sequence similarity of a query sequence to a protein family is measured by the highest segment pair (HSP) score. Each of the HMM-based approaches (FORESST, MEME, amino acid sequence-based HMM) yielded log-odds score for the query sequence. In order to make a fair comparison among these methods, the scores for each method were converted to Z-scores in a uniform way by comparing the raw scores of a query protein with the corresponding scores for a set of unrelated proteins. Z-Scores were analyzed as a function of the maximum pairwise sequence identity (MPSID) of the query sequence to sequences used in training the model. For MPSID above 20%, the Z-scores increase linearly with MPSID for the sequence-based methods but remain roughly constant for FORESST. Below 15%, average Z-scores are close to zero for the sequence-based methods, whereas the FORESST method yielded average Z-scores of 1.8 and 1.1, using observed and predicted secondary structures, respectively. This demonstrates the advantage of the sequence-structure method for detecting remote homologs.     

A framework for direct locating and conformational sampling of protein structural motifs

A specific treatment of recurrent structural motifs that represent the local bias information has been proven to be an important ingredient in de novo protein structure predication. Significant majority of methods for local structure are based on building blocks, which still suffer from its inherent discrete nature. Instead of using building blocks, this work presents a new protocol framework for local structural motifs prediction based on the direct locating along protein sequence and probabilistic sampling in a continuous (φ, ψ) space. The protein sequence was first scanned by an algorithm of sliding window with variable length of 7 to 19 residues, to match local segments to one of 82 motifs patterns in the fragment library. Identified segments were then labeled and modeled as the correlations of backbone torsion angles with mixture of bivariate cosine distributions in continuous (φ, ψ) space. 3D conformations of corresponding segments were finally sampled by using a backtrack algorithm to the hidden Markov model with single output of (φ, ψ). For local motifs in 50 proteins of testing set, about 62% of eight-residue segments located with high confidence value were predicted within 1.5 ? of their native structures by the method. Majority of local structural motifs were identified and sampled, which indicates the proposed protocol may at least serve as the foundation to obtain better protein tertiary structure prediction.     

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.     

一种新的蛋白质结构编码方法及其应用

基于四肽构象的可视化聚类的结果,提出了一种新的编码方法,由此可将蛋白质三维构象空间映射到一维编码空间,将蛋白质三维结构空间中的模式搜索和模式发现问题转化为一维编码空间中的相应问题。通过两个算法从模式检索以及模式发现两方面验证了编码的有效性;同时利用熵的概念探讨了序列、结构之间的相关度,得到了一些重要的序列．结构模式．实验结果表明,该编码方法能更加准确地反映四肽构象空间中的分布情况,其结果可解释性更强．     

Simulating protein folding initiation sites using an alpha‐carbon‐only knowledge‐based force field

Protein folding is a hierarchical process where structure forms locally first, then globally. Some short sequence segments initiate folding through strong structural preferences that are independent of their three‐dimensional context in proteins. We have constructed a knowledge‐based force field in which the energy functions are conditional on local sequence patterns, as expressed in the hidden Markov model for local structure (HMMSTR). Carbon‐alpha force field (CALF) builds sequence specific statistical potentials based on database frequencies for α‐carbon virtual bond opening and dihedral angles, pair‐wise contacts and hydrogen bond donor‐acceptor pairs, and simulates folding via Brownian dynamics. We introduce hydrogen bond donor and acceptor potentials as α‐carbon probability fields that are conditional on the predicted local sequence. Constant temperature simulations were carried out using 27 peptides selected as putative folding initiation sites, each 12 residues in length, representing several different local structure motifs. Each 0.6 μs trajectory was clustered based on structure. Simulation convergence or representativeness was assessed by subdividing trajectories and comparing clusters. For 21 of the 27 sequences, the largest cluster made up more than half of the total trajectory. Of these 21 sequences, 14 had cluster centers that were at most 2.6 Å root mean square deviation (RMSD) from their native structure in the corresponding full‐length protein. To assess the adequacy of the energy function on nonlocal interactions, 11 full length native structures were relaxed using Brownian dynamics simulations. Equilibrated structures deviated from their native states but retained their overall topology and compactness. A simple potential that folds proteins locally and stabilizes proteins globally may enable a more realistic understanding of hierarchical folding pathways. Proteins 2009. © 2008 Wiley‐Liss, Inc.     

A dynamic Bayesian network approach to protein secondary structure prediction

Background  

Protein secondary structure prediction method based on probabilistic models such as hidden Markov model (HMM) appeals to many because it provides meaningful information relevant to sequence-structure relationship. However, at present, the prediction accuracy of pure HMM-type methods is much lower than that of machine learning-based methods such as neural networks (NN) or support vector machines (SVM).     

Discriminative motif finding for predicting protein subcellular localization

Many methods have been described to predict the subcellular location of proteins from sequence information. However, most of these methods either rely on global sequence properties or use a set of known protein targeting motifs to predict protein localization. Here, we develop and test a novel method that identifies potential targeting motifs using a discriminative approach based on hidden Markov models (discriminative HMMs). These models search for motifs that are present in a compartment but absent in other, nearby, compartments by utilizing an hierarchical structure that mimics the protein sorting mechanism. We show that both discriminative motif finding and the hierarchical structure improve localization prediction on a benchmark data set of yeast proteins. The motifs identified can be mapped to known targeting motifs and they are more conserved than the average protein sequence. Using our motif-based predictions, we can identify potential annotation errors in public databases for the location of some of the proteins. A software implementation and the data set described in this paper are available from http://murphylab.web.cmu.edu/software/2009_TCBB_motif/.     

Assessing a novel approach for predicting local 3D protein structures from sequence

We developed a novel approach for predicting local protein structure from sequence. It relies on the Hybrid Protein Model (HPM), an unsupervised clustering method we previously developed. This model learns three-dimensional protein fragments encoded into a structural alphabet of 16 protein blocks (PBs). Here, we focused on 11-residue fragments encoded as a series of seven PBs and used HPM to cluster them according to their local similarities. We thus built a library of 120 overlapping prototypes (mean fragments from each cluster), with good three-dimensional local approximation, i.e., a mean accuracy of 1.61 A Calpha root-mean-square distance. Our prediction method is intended to optimize the exploitation of the sequence-structure relations deduced from this library of long protein fragments. This was achieved by setting up a system of 120 experts, each defined by logistic regression to optimize the discrimination from sequence of a given prototype relative to the others. For a target sequence window, the experts computed probabilities of sequence-structure compatibility for the prototypes and ranked them, proposing the top scorers as structural candidates. Predictions were defined as successful when a prototype <2.5 A from the true local structure was found among those proposed. Our strategy yielded a prediction rate of 51.2% for an average of 4.2 candidates per sequence window. We also proposed a confidence index to estimate prediction quality. Our approach predicts from sequence alone and will thus provide valuable information for proteins without structural homologs. Candidates will also contribute to global structure prediction by fragment assembly.     

Quasi-consensus-based comparison of profile hidden Markov models for protein sequences

A simple approach for the sensitive detection of distant relationships among protein families and for sequence-structure alignment via comparison of hidden Markov models based on their quasi-consensus sequences is presented. Using a previously published benchmark dataset, the approach is demonstrated to give better homology detection and yield alignments with improved accuracy in comparison to an existing state-of-the-art dynamic programming profile-profile comparison method. This method also runs significantly faster and is therefore suitable for a server covering the rapidly increasing structure database. A server based on this method is available at http://liao.cis.udel.edu/website/servers/modmod     

Detecting DNA-binding helix-turn-helix structural motifs using sequence and structure information

In this work, we analyse the potential for using structural knowledge to improve the detection of the DNA-binding helix–turn–helix (HTH) motif from sequence. Starting from a set of DNA-binding protein structures that include a functional HTH motif and have no apparent sequence similarity to each other, two different libraries of hidden Markov models (HMMs) were built. One library included sequence models of whole DNA-binding domains, which incorporate the HTH motif, the second library included shorter models of ‘partial’ domains, representing only the fraction of the domain that corresponds to the functionally relevant HTH motif itself. The libraries were scanned against a dataset of protein sequences, some containing the HTH motifs, others not. HMM predictions were compared with the results obtained from a previously published structure-based method and subsequently combined with it. The combined method proved more effective than either of the single-featured approaches, showing that information carried by motif sequences and motif structures are to some extent complementary and can successfully be used together for the detection of DNA-binding HTHs in proteins of unknown function.     

A Bayesian network model for protein fold and remote homologue recognition

MOTIVATION: The Bayesian network approach is a framework which combines graphical representation and probability theory, which includes, as a special case, hidden Markov models. Hidden Markov models trained on amino acid sequence or secondary structure data alone have been shown to have potential for addressing the problem of protein fold and superfamily classification. RESULTS: This paper describes a novel implementation of a Bayesian network which simultaneously learns amino acid sequence, secondary structure and residue accessibility for proteins of known three-dimensional structure. An awareness of the errors inherent in predicted secondary structure may be incorporated into the model by means of a confusion matrix. Training and validation data have been derived for a number of protein superfamilies from the Structural Classification of Proteins (SCOP) database. Cross validation results using posterior probability classification demonstrate that the Bayesian network performs better in classifying proteins of known structural superfamily than a hidden Markov model trained on amino acid sequences alone.     

Contingency Table Browser ? prediction of early stage protein structure

The Early Stage (ES) intermediate represents the starting structure in protein folding simulations based on the Fuzzy Oil Drop (FOD) model. The accuracy of FOD predictions is greatly dependent on the accuracy of the chosen intermediate. A suitable intermediate can be constructed using the sequence-structure relationship information contained in the so-called contingency table − this table expresses the likelihood of encountering various structural motifs for each tetrapeptide fragment in the amino acid sequence. The limited accuracy with which such structures could previously be predicted provided the motivation for a more indepth study of the contingency table itself. The Contingency Table Browser is a tool which can visualize, search and analyze the table. Our work presents possible applications of Contingency Table Browser, among them − analysis of specific protein sequences from the point of view of their structural ambiguity.     

Learning cellular sorting pathways using protein interactions and sequence motifs

Proper subcellular localization is critical for proteins to perform their roles in cellular functions. Proteins are transported by different cellular sorting pathways, some of which take a protein through several intermediate locations until reaching its final destination. The pathway a protein is transported through is determined by carrier proteins that bind to specific sequence motifs. In this article, we present a new method that integrates protein interaction and sequence motif data to model how proteins are sorted through these sorting pathways. We use a hidden Markov model (HMM) to represent protein sorting pathways. The model is able to determine intermediate sorting states and to assign carrier proteins and motifs to the sorting pathways. In simulation studies, we show that the method can accurately recover an underlying sorting model. Using data for yeast, we show that our model leads to accurate prediction of subcellular localization. We also show that the pathways learned by our model recover many known sorting pathways and correctly assign proteins to the path they utilize. The learned model identified new pathways and their putative carriers and motifs and these may represent novel protein sorting mechanisms. Supplementary results and software implementation are available from http://murphylab.web.cmu.edu/software/2010_RECOMB_pathways/.     

Clustering of amino acids for protein secondary structure prediction

Simple hidden Markov models are proposed for predicting secondary structure of a protein from its amino acid sequence. Since the length of protein conformation segments varies in a narrow range, we ignore the duration effect of length distribution, and focus on inclusion of short range correlations of residues and of conformation states in the models. Conformation-independent and -dependent amino acid coarse-graining schemes are designed for the models by means of proper mutual information. We compare models of different level of complexity, and establish a practical model with a high prediction accuracy.     

Bayesian restoration of a hidden Markov chain with applications to DNA sequencing.

Hidden Markov models (HMMs) are a class of stochastic models that have proven to be powerful tools for the analysis of molecular sequence data. A hidden Markov model can be viewed as a black box that generates sequences of observations. The unobservable internal state of the box is stochastic and is determined by a finite state Markov chain. The observable output is stochastic with distribution determined by the state of the hidden Markov chain. We present a Bayesian solution to the problem of restoring the sequence of states visited by the hidden Markov chain from a given sequence of observed outputs. Our approach is based on a Monte Carlo Markov chain algorithm that allows us to draw samples from the full posterior distribution of the hidden Markov chain paths. The problem of estimating the probability of individual paths and the associated Monte Carlo error of these estimates is addressed. The method is illustrated by considering a problem of DNA sequence multiple alignment. The special structure for the hidden Markov model used in the sequence alignment problem is considered in detail. In conclusion, we discuss certain interesting aspects of biological sequence alignments that become accessible through the Bayesian approach to HMM restoration.     

Structure of the adenovirus E4 Orf6 protein predicted by fold recognition and comparative protein modeling

To facilitate investigation of the molecular and biochemical functions of the adenovirus E4 Orf6 protein, we sought to derive three-dimensional structural information using computational methods, particularly threading and comparative protein modeling. The amino acid sequence of the protein was used for secondary structure and hidden Markov model (HMM) analyses, and for fold recognition by the ProCeryon program. Six alternative models were generated from the top-scoring folds identified by threading. These models were examined by 3D-1D analysis and evaluated in the light of available experimental evidence. The final model of the E4 protein derived from these and additional threading calculations was a chimera, with the tertiary structure of its C-terminal 226 residues derived from a TIM barrel template and a mainly alpha-nonbundle topology for its poorly conserved N-terminal 68 residues. To assess the accuracy of this model, additional threading calculations were performed with E4 Orf6 sequences altered as in previous experimental studies. The proposed structural model is consistent with the reported secondary structure of a functionally important C-terminal sequence and can account for the properties of proteins carrying alterations in functionally important sequences or of those that disrupt an unusual zinc-coordination motif.     

MUMMALS: multiple sequence alignment improved by using hidden Markov models with local structural information

We have developed MUMMALS, a program to construct multiple protein sequence alignment using probabilistic consistency. MUMMALS improves alignment quality by using pairwise alignment hidden Markov models (HMMs) with multiple match states that describe local structural information without exploiting explicit structure predictions. Parameters for such models have been estimated from a large library of structure-based alignments. We show that (i) on remote homologs, MUMMALS achieves statistically best accuracy among several leading aligners, such as ProbCons, MAFFT and MUSCLE, albeit the average improvement is small, in the order of several percent; (ii) a large collection (>10000) of automatically computed pairwise structure alignments of divergent protein domains is superior to smaller but carefully curated datasets for estimation of alignment parameters and performance tests; (iii) reference-independent evaluation of alignment quality using sequence alignment-dependent structure superpositions correlates well with reference-dependent evaluation that compares sequence-based alignments to structure-based reference alignments.