Protein Contact Prediction Research Articles

PCP-GC-LM: single-sequence-based protein contact prediction using dual graph convolutional neural network and convolutional neural network

BackgroundRecently, the process of evolution information and the deep learning network has promoted the improvement of protein contact prediction methods. Nevertheless, still remain some bottleneck: (1) One of the bottlenecks is the prediction of orphans and other fewer evolution information proteins. (2) The other bottleneck is the method of predicting single-sequence-based proteins mainly focuses on selecting protein sequence features and tuning the neural network architecture, However, while the deeper neural networks improve prediction accuracy, there is still the problem of increasing the computational burden. Compared with other neural networks in the field of protein prediction, the graph neural network has the following advantages: due to the advantage of revealing the topology structure via graph neural network and being able to take advantage of the hierarchical structure and local connectivity of graph neural networks has certain advantages in capturing the features of different levels of abstraction in protein molecules. When using protein sequence and structure information for joint training, the dependencies between the two kinds of information can be better captured. And it can process protein molecular structures of different lengths and shapes, while traditional neural networks need to convert proteins into fixed-size vectors or matrices for processing.ResultsHere, we propose a single-sequence-based protein contact map predictor PCP-GC-LM, with dual-level graph neural networks and convolution networks. Our method performs better with other single-sequence-based predictors in different independent tests. In addition, to verify the validity of our method against complex protein structures, we will also compare it with other methods in two homodimers protein test sets (DeepHomo test dataset and CASP-CAPRI target dataset). Furthermore, we also perform ablation experiments to demonstrate the necessity of a dual graph network. In all, our framework presents new modules to accurately predict inter-chain contact maps in protein and it’s also useful to analyze interactions in other types of protein complexes.

Protein–protein contact prediction by geometric triangle-aware protein language models

Protein–protein contact prediction by geometric triangle-aware protein language models

ETLD: an encoder-transformation layer-decoder architecture for protein contact and mutation effects prediction.

The latent features extracted from the multiple sequence alignments (MSAs) of homologous protein families are useful for identifying residue-residue contacts, predicting mutation effects, shaping protein evolution, etc. Over the past three decades, a growing body of supervised and unsupervised machine learning methods have been applied to this field, yielding fruitful results. Here, we propose a novel self-supervised model, called encoder-transformation layer-decoder (ETLD) architecture, capable of capturing protein sequence latent features directly from MSAs. Compared to the typical autoencoder model, ETLD introduces a transformation layer with the ability to learn inter-site couplings, which can be used to parse out the two-dimensional residue-residue contacts map after a simple mathematical derivation or an additional supervised neural network. ETLD retains the process of encoding and decoding sequences, and the predicted probabilities of amino acids at each site can be further used to construct the mutation landscapes for mutation effects prediction, outperforming advanced models such as GEMME, DeepSequence and EVmutation in general. Overall, ETLD is a highly interpretable unsupervised model with great potential for improvement and can be further combined with supervised methods for more extensive and accurate predictions.

DeepHomo2.0: improved protein-protein contact prediction of homodimers by transformer-enhanced deep learning.

Protein-protein interactions play an important role in many biological processes. However, although structure prediction for monomer proteins has achieved great progress with the advent of advanced deep learning algorithms like AlphaFold, the structure prediction for protein-protein complexes remains an open question. Taking advantage of the Transformer model of ESM-MSA, we have developed a deep learning-based model, named DeepHomo2.0, to predict protein-protein interactions of homodimeric complexes by leveraging the direct-coupling analysis (DCA) and Transformer features of sequences and the structure features of monomers. DeepHomo2.0 was extensively evaluated on diverse test sets and compared with eight state-of-the-art methods including protein language model-based, DCA-based and machine learning-based methods. It was shown that DeepHomo2.0 achieved a high precision of >70% with experimental monomer structures and >60% with predicted monomer structures for the top 10 predicted contacts on the test sets and outperformed the other eight methods. Moreover, even the version without using structure information, named DeepHomoSeq, still achieved a good precision of >55% for the top 10 predicted contacts. Integrating the predicted contacts into protein docking significantly improved the structure prediction of realistic Critical Assessment of Protein Structure Prediction homodimeric complexes. DeepHomo2.0 and DeepHomoSeq are available at http://huanglab.phys.hust.edu.cn/DeepHomo2/.

Improved protein contact prediction using dimensional hybrid residual networks and singularity enhanced loss function.

Deep residual learning has shown great success in protein contact prediction. In this study, a new deep residual learning-based protein contact prediction model was developed. Comparing with previous models, a new type of residual block hybridizing 1D and 2D convolutions was designed to increase the effective receptive field of the residual network, and a new loss function emphasizing the easily misclassified residue pairs was proposed to enhance the model training. The developed protein contact prediction model referred to as DRN-1D2D was first evaluated on 105 CASP11 targets, 76 CAMEO hard targets and 398 membrane proteins together with two in house-developed reference models based on either the standard 2D residual block or the traditional BCE loss function, from which we confirmed that both the dimensional hybrid residual block and the singularity enhanced loss function can be employed to improve the model performance for protein contact prediction. DRN-1D2D was further evaluated on 39 CASP13 and CASP14 free modeling targets together with the two reference models and six state-of-the-art protein contact prediction models including DeepCov, DeepCon, DeepConPred2, SPOT-Contact, RaptorX-Contact and TripleRes. The result shows that DRN-1D2D consistently achieved the best performance among all these models.

Protein inter-residue contact and distance prediction by coupling complementary coevolution features with deep residual networks in CASP14.

This article reports and analyzes the results of protein contact and distance prediction by our methods in the 14th Critical Assessment of techniques for protein Structure Prediction (CASP14). A new deep learning-based contact/distance predictor was employed based on the ensemble of two complementary coevolution features coupling with deep residual networks. We also improved our multiple sequence alignment (MSA) generation protocol with wholesale meta-genome sequence databases. On 22 CASP14 free modeling (FM) targets, the proposed model achieved a top-L/5 long-range precision of 63.8% and a mean distance bin error of 1.494. Based on the predicted distance potentials, 11 out of 22 FM targets and all of the 14 FM/template-based modeling (TBM) targets have correctly predicted folds (TM-score >0.5), suggesting that our approach can provide reliable distance potentials for ab initio protein folding.

Performance Analysis of Deep Learning Methods for Protein Contact Prediction in CASP13

Protein structure prediction is one of the most important problems in Computational Biology; and consists of determining the 3D structure of a protein given its amino acid sequence. A key component that has allowed considerable improvements in recent decades is the prediction of contacts in a protein, since it provides fundamental information about its three-dimensional structure. In the 13th edition of the CASP (Critical Assessment of protein Structure Prediction), a notable progress has been evidenced for both problems with the use of deep learning algorithms. For the contact prediction category, the best methods in CASP13 achieved an average precision of 70%. In the present work, the performance of these methods is analyzed using a larger data set, with 483 proteins from four families according to the structural classification of the SCOP database (Structural Classification of Proteins). The selected methods were evaluated using the CASP metrics, and their results indicate an average contact prediction precision greater than 90%. SPOT-Contact was the method with the best overall performance, and one of the methods with the best performance for each SCOP class. The set of proteins used for the experiments and the implementations made for the analysis are publicly available.

COMTOP: Protein Residue-Residue Contact Prediction through Mixed Integer Linear Optimization.

Protein contact prediction helps reconstruct the tertiary structure that greatly determines a protein’s function; therefore, contact prediction from the sequence is an important problem. Recently there has been exciting progress on this problem, but many of the existing methods are still low quality of prediction accuracy. In this paper, we present a new mixed integer linear programming (MILP)-based consensus method: a Consensus scheme based On a Mixed integer linear opTimization method for prOtein contact Prediction (COMTOP). The MILP-based consensus method combines the strengths of seven selected protein contact prediction methods, including CCMpred, EVfold, DeepCov, NNcon, PconsC4, plmDCA, and PSICOV, by optimizing the number of correctly predicted contacts and achieving a better prediction accuracy. The proposed hybrid protein residue–residue contact prediction scheme was tested in four independent test sets. For 239 highly non-redundant proteins, the method showed a prediction accuracy of 59.68%, 70.79%, 78.86%, 89.04%, 94.51%, and 97.35% for top-5L, top-3L, top-2L, top-L, top-L/2, and top-L/5 contacts, respectively. When tested on the CASP13 and CASP14 test sets, the proposed method obtained accuracies of 75.91% and 77.49% for top-L/5 predictions, respectively. COMTOP was further tested on 57 non-redundant α-helical transmembrane proteins and achieved prediction accuracies of 64.34% and 73.91% for top-L/2 and top-L/5 predictions, respectively. For all test datasets, the improvement of COMTOP in accuracy over the seven individual methods increased with the increasing number of predicted contacts. For example, COMTOP performed much better for large number of contact predictions (such as top-5L and top-3L) than for small number of contact predictions such as top-L/2 and top-L/5. The results and analysis demonstrate that COMTOP can significantly improve the performance of the individual methods; therefore, COMTOP is more robust against different types of test sets. COMTOP also showed better/comparable predictions when compared with the state-of-the-art predictors.

Identification of biophysical interaction patterns in direct coupling analysis.

Direct-coupling analysis is a statistical learning method for protein contact prediction based on sequence information alone. The maximum entropy principle leads to an effective inverse Potts model. Predictions on contacts are based on fitted local fields and couplings from an empirical multiple sequence alignment. Typically, the l_{2} norm of the resulting two-body couplings is used for contact prediction. However, this procedure discards important information. In this paper we show that the usage of the full fields and coupling information improves prediction accuracy.

Combination of deep neural network with attention mechanism enhances the explainability of protein contact prediction

Deep learning has emerged as a revolutionary technology for protein residue‐residue contact prediction since the 2012 CASP10 competition. Considerable advancements in the predictive power of the deep learning‐based contact predictions have been achieved since then. However, little effort has been put into interpreting the black‐box deep learning methods. Algorithms that can interpret the relationship between predicted contact maps and the internal mechanism of the deep learning architectures are needed to explore the essential components of contact inference and improve their explainability. In this study, we present an attention‐based convolutional neural network for protein contact prediction, which consists of two attention mechanism‐based modules: sequence attention and regional attention. Our benchmark results on the CASP13 free‐modeling targets demonstrate that the two attention modules added on top of existing typical deep learning models exhibit a complementary effect that contributes to prediction improvements. More importantly, the inclusion of the attention mechanism provides interpretable patterns that contain useful insights into the key fold‐determining residues in proteins. We expect the attention‐based model can provide a reliable and practically interpretable technique that helps break the current bottlenecks in explaining deep neural networks for contact prediction. The source code of our method is available at https://github.com/jianlin-cheng/InterpretContactMap.

Chasing coevolutionary signals in intrinsically disordered proteins complexes

Intrinsically disordered proteins/regions (IDPs/IDRs) are crucial components of the cell, they are highly abundant and participate ubiquitously in a wide range of biological functions, such as regulatory processes and cell signaling. Many of their important functions rely on protein interactions, by which they trigger or modulate different pathways. Sequence covariation, a powerful tool for protein contact prediction, has been applied successfully to predict protein structure and to identify protein–protein interactions mostly of globular proteins. IDPs/IDRs also mediate a plethora of protein–protein interactions, highlighting the importance of addressing sequence covariation-based inter-protein contact prediction of this class of proteins. Despite their importance, a systematic approach to analyze the covariation phenomena of intrinsically disordered proteins and their complexes is still missing. Here we carry out a comprehensive critical assessment of coevolution-based contact prediction in IDP/IDR complexes and detail the challenges and possible limitations that emerge from their analysis. We found that the coevolutionary signal is faint in most of the complexes of disordered proteins but positively correlates with the interface size and binding affinity between partners. In addition, we discuss the state-of-art methodology by biological interpretation of the results, formulate evaluation guidelines and suggest future directions of development to the field.

Mi3-GPU: MCMC-based inverse Ising inference on GPUs for protein covariation analysis

Inverse Ising inference is a method for inferring the coupling parameters of a Potts/Ising model based on observed site-covariation, which has found important applications in protein physics for detecting interactions between residues in protein families. We introduce Mi3-GPU (“mee-three”, for MCMC Inverse Ising Inference) software for solving the inverse Ising problem for protein-sequence datasets with few analytic approximations, by parallel Markov-Chain Monte Carlo sampling on GPUs. We also provide tools for analysis and preparation of protein-family Multiple Sequence Alignments (MSAs) to account for finite-sampling issues, which are a major source of error or bias in inverse Ising inference. Our method is “generative” in the sense that the inferred model can be used to generate synthetic MSAs whose mutational statistics (marginals) can be verified to match the dataset MSA statistics up to the limits imposed by the effects of finite sampling. Our GPU implementation enables the construction of models which reproduce the covariation patterns of the observed MSA with a precision that is not possible with more approximate methods. The main components of our method are a GPU-optimized algorithm to greatly accelerate MCMC sampling, combined with a multi-step Quasi-Newton parameter-update scheme using a “Zwanzig reweighting” technique. We demonstrate the ability of this software to produce generative models on typical protein family datasets for sequence lengths L∼300 with 21 residue types with tens of millions of inferred parameters in short running times. Program summaryProgram Title: Mi3-GPUProgram Files doi:http://dx.doi.org/10.17632/ftbcfy2p35.1Licensing provisions: GPLv3Programming languages: Python3, OpenCL, CNature of problem: Mi3-GPU solves the inverse Ising problem for application in protein covariation analysis. The goal is to infer “coupling” parameters between positions in a Multiple Sequence Alignment of a protein family, with many applications including protein-contact prediction and fitness prediction.Solution method: Mi3-GPU solves the inverse Ising problem with few approximations using Markov-Chain Monte Carlo methods with Quasi-Newton optimization on GPUs. This problem previously has been approached by more approximate methods using analytic approximations including “message Passing”, “Susceptibility Propagation”, “mean-field” methods, pseudolikelihood approximations, and cluster expansion. The software leverages GPU to accelerate MCMC sampling and a histogram reweighting technique to accelerate parameter optimization.

DeepECA: an end-to-end learning framework for protein contact prediction from a multiple sequence alignment

BackgroundRecently developed methods of protein contact prediction, a crucially important step for protein structure prediction, depend heavily on deep neural networks (DNNs) and multiple sequence alignments (MSAs) of target proteins. Protein sequences are accumulating to an increasing degree such that abundant sequences to construct an MSA of a target protein are readily obtainable. Nevertheless, many cases present different ends of the number of sequences that can be included in an MSA used for contact prediction. The abundant sequences might degrade prediction results, but opportunities remain for a limited number of sequences to construct an MSA. To resolve these persistent issues, we strove to develop a novel framework using DNNs in an end-to-end manner for contact prediction.ResultsWe developed neural network models to improve precision of both deep and shallow MSAs. Results show that higher prediction accuracy was achieved by assigning weights to sequences in a deep MSA. Moreover, for shallow MSAs, adding a few sequential features was useful to increase the prediction accuracy of long-range contacts in our model. Based on these models, we expanded our model to a multi-task model to achieve higher accuracy by incorporating predictions of secondary structures and solvent-accessible surface areas. Moreover, we demonstrated that ensemble averaging of our models can raise accuracy. Using past CASP target protein domains, we tested our models and demonstrated that our final model is superior to or equivalent to existing meta-predictors.ConclusionsThe end-to-end learning framework we built can use information derived from either deep or shallow MSAs for contact prediction. Recently, an increasing number of protein sequences have become accessible, including metagenomic sequences, which might degrade contact prediction results. Under such circumstances, our model can provide a means to reduce noise automatically. According to results of tertiary structure prediction based on contacts and secondary structures predicted by our model, more accurate three-dimensional models of a target protein are obtainable than those from existing ECA methods, starting from its MSA. DeepECA is available from https://github.com/tomiilab/DeepECA.

Analysis of several key factors influencing deep learning-based inter-residue contact prediction.

MotivationDeep learning has become the dominant technology for protein contact prediction. However, the factors that affect the performance of deep learning in contact prediction have not been systematically investigated.ResultsWe analyzed the results of our three deep learning-based contact prediction methods (MULTICOM-CLUSTER, MULTICOM-CONSTRUCT and MULTICOM-NOVEL) in the CASP13 experiment and identified several key factors [i.e. deep learning technique, multiple sequence alignment (MSA), distance distribution prediction and domain-based contact integration] that influenced the contact prediction accuracy. We compared our convolutional neural network (CNN)-based contact prediction methods with three coevolution-based methods on 75 CASP13 targets consisting of 108 domains. We demonstrated that the CNN-based multi-distance approach was able to leverage global coevolutionary coupling patterns comprised of multiple correlated contacts for more accurate contact prediction than the local coevolution-based methods, leading to a substantial increase of precision by 19.2 percentage points. We also tested different alignment methods and domain-based contact prediction with the deep learning contact predictors. The comparison of the three methods showed deeper sequence alignments and the integration of domain-based contact prediction with the full-length contact prediction improved the performance of contact prediction. Moreover, we demonstrated that the domain-based contact prediction based on a novel ab initio approach of parsing domains from MSAs alone without using known protein structures was a simple, fast approach to improve contact prediction. Finally, we showed that predicting the distribution of inter-residue distances in multiple distance intervals could capture more structural information and improve binary contact prediction.Availability and implementation https://github.com/multicom-toolbox/DNCON2/.Supplementary information Supplementary data are available at Bioinformatics online.

DEEPCON: protein contact prediction using dilated convolutional neural networks with dropout.

Exciting new opportunities have arisen to solve the protein contact prediction problem from the progress in neural networks and the availability of a large number of homologous sequences through high-throughput sequencing. In this work, we study how deep convolutional neural networks (ConvNets) may be best designed and developed to solve this long-standing problem. With publicly available datasets, we designed and trained various ConvNet architectures. We tested several recent deep learning techniques including wide residual networks, dropouts and dilated convolutions. We studied the improvements in the precision of medium-range and long-range contacts, and compared the performance of our best architectures with the ones used in existing state-of-the-art methods. The proposed ConvNet architectures predict contacts with significantly more precision than the architectures used in several state-of-the-art methods. When trained using the DeepCov dataset consisting of 3456 proteins and tested on PSICOV dataset of 150 proteins, our architectures achieve up to 15% higher precision when L/2 long-range contacts are evaluated. Similarly, when trained using the DNCON2 dataset consisting of 1426 proteins and tested on 84 protein domains in the CASP12 dataset, our single network achieves 4.8% higher precision than the ensembled DNCON2 method when top L long-range contacts are evaluated. DEEPCON is available at https://github.com/badriadhikari/DEEPCON/.

Protein contact prediction using metagenome sequence data and residual neural networks.

Almost all protein residue contact prediction methods rely on the availability of deep multiple sequence alignments (MSAs). However, many proteins from the poorly populated families do not have sufficient number of homologs in the conventional UniProt database. Here we aim to solve this issue by exploring the rich sequence data from the metagenome sequencing projects. Based on the improved MSA constructed from the metagenome sequence data, we developed MapPred, a new deep learning-based contact prediction method. MapPred consists of two component methods, DeepMSA and DeepMeta, both trained with the residual neural networks. DeepMSA was inspired by the recent method DeepCov, which was trained on 441 matrices of covariance features. By considering the symmetry of contact map, we reduced the number of matrices to 231, which makes the training more efficient in DeepMSA. Experiments show that DeepMSA outperforms DeepCov by 10-13% in precision. DeepMeta works by combining predicted contacts and other sequence profile features. Experiments on three benchmark datasets suggest that the contribution from the metagenome sequence data is significant with P-values less than 4.04E-17. MapPred is shown to be complementary and comparable the state-of-the-art methods. The success of MapPred is attributed to three factors: the deeper MSA from the metagenome sequence data, improved feature design in DeepMSA and optimized training by the residual neural networks. http://yanglab.nankai.edu.cn/mappred/. Supplementary data are available at Bioinformatics online.

ResPRE: high-accuracy protein contact prediction by coupling precision matrix with deep residual neural networks.

Contact-map of a protein sequence dictates the global topology of structural fold. Accurate prediction of the contact-map is thus essential to protein 3D structure prediction, which is particularly useful for the protein sequences that do not have close homology templates in the Protein Data Bank. We developed a new method, ResPRE, to predict residue-level protein contacts using inverse covariance matrix (or precision matrix) of multiple sequence alignments (MSAs) through deep residual convolutional neural network training. The approach was tested on a set of 158 non-homologous proteins collected from the CASP experiments and achieved an average accuracy of 50.6% in the top-L long-range contact prediction with L being the sequence length, which is 11.7% higher than the best of other state-of-the-art approaches ranging from coevolution coupling analysis to deep neural network training. Detailed data analyses show that the major advantage of ResPRE lies at the utilization of precision matrix that helps rule out transitional noises of contact-maps compared with the previously used covariance matrix. Meanwhile, the residual network with parallel shortcut layer connections increases the learning ability of deep neural network training. It was also found that appropriate collection of MSAs can further improve the accuracy of final contact-map predictions. The standalone package and online server of ResPRE are made freely available, which should bring important impact on protein structure and function modeling studies in particular for the distant- and non-homology protein targets. https://zhanglab.ccmb.med.umich.edu/ResPRE and https://github.com/leeyang/ResPRE. Supplementary data are available at Bioinformatics online.

HoDCA: higher order direct-coupling analysis

BackgroundDirect-coupling analysis (DCA) is a method for protein contact prediction from sequence information alone. Its underlying principle is parameter estimation for a Hamiltonian interaction function stemming from a maximum entropy model with one- and two-point interactions. Vastly growing sequence databases enable the construction of large multiple sequence alignments (MSA). Thus, enough data exists to include higher order terms, such as three-body correlations.ResultsWe present an implementation of hoDCA, which is an extension of DCA by including three-body interactions into the inverse Ising problem posed by parameter estimation. In a previous study, these three-body-interactions improved contact prediction accuracy for the PSICOV benchmark dataset. Our implementation can be executed in parallel, which results in fast runtimes and makes it suitable for large-scale application.ConclusionOur hoDCA software allows improved contact prediction using the Julia language, leveraging power of multi-core machines in an automated fashion.

PredMP: a web server for de novo prediction and visualization of membrane proteins

PredMP is the first web service, to our knowledge, that aims at de novo prediction of the membrane protein (MP) 3D structure followed by the embedding of the MP into the lipid bilayer for visualization. Our approach is based on a high-throughput Deep Transfer Learning (DTL) method that first predicts MP contacts by learning from non-MPs and then predicts the 3D model of the MP using the predicted contacts as distance restraints. This algorithm is derived from our previous Deep Learning (DL) method originally developed for soluble protein contact prediction, which has been officially ranked No. 1 in CASP12. The DTL framework in our approach overcomes the challenge that there are only a limited number of solved MP structures for training the deep learning model. There are three modules in the PredMP server: (i) The DTL framework followed by the contact-assisted folding protocol has already been implemented in RaptorX-Contact, which serves as the key module for 3D model generation; (ii) The 1D annotation module, implemented in RaptorX-Property, is used to predict the secondary structure and disordered regions; and (iii) the visualization module to display the predicted MPs embedded in the lipid bilayer guided by the predicted transmembrane topology. Tested on 510 non-redundant MPs, our server predicts correct folds for ∼290 MPs, which significantly outperforms existing methods. Tested on a blind and live benchmark CAMEO from September 2016 to January 2018, PredMP can successfully model all 10 MPs belonging to the hard category. PredMP is freely accessed on the web at http://www.predmp.com. Supplementary data are available at Bioinformatics online.

High precision in protein contact prediction using fully convolutional neural networks and minimal sequence features.

In addition to substitution frequency data from protein sequence alignments, many state-of-the-art methods for contact prediction rely on additional sources of information, or features, of protein sequences in order to predict residue-residue contacts, such as solvent accessibility, predicted secondary structure, and scores from other contact prediction methods. It is unclear how much of this information is needed to achieve state-of-the-art results. Here, we show that using deep neural network models, simple alignment statistics contain sufficient information to achieve state-of-the-art precision. Our prediction method, DeepCov, uses fully convolutional neural networks operating on amino-acid pair frequency or covariance data derived directly from sequence alignments, without using global statistical methods such as sparse inverse covariance or pseudolikelihood estimation. Comparisons against CCMpred and MetaPSICOV2 show that using pairwise covariance data calculated from raw alignments as input allows us to match or exceed the performance of both of these methods. Almost all of the achieved precision is obtained when considering relatively local windows (around 15 residues) around any member of a given residue pairing; larger window sizes have comparable performance. Assessment on a set of shallow sequence alignments (fewer than 160 effective sequences) indicates that the new method is substantially more precise than CCMpred and MetaPSICOV2 in this regime, suggesting that improved precision is attainable on smaller sequence families. Overall, the performance of DeepCov is competitive with the state of the art, and our results demonstrate that global models, which employ features from all parts of the input alignment when predicting individual contacts, are not strictly needed in order to attain precise contact predictions. DeepCov is freely available at https://github.com/psipred/DeepCov. Supplementary data are available at Bioinformatics online.