Condensed Representations of Protein Secondary Structure Sequences and Their Application

Abstract

In this paper, we propose a nongraphical representation for protein secondary structures. By counting the frequency of occurrence of all possible four-tuples (i.e., four-letter words) of a protein secondary structure sequence, we construct a set of 3 × 3 matrices for the corresponding protein secondary structure sequence. Furthermore, the leading eigenvalues of these matrices are computed and considered as invariants for the protein secondary structure sequences. To illustrate the utility of our approach, we apply it to a set of real data to distinguish protein structural classes. The result indicates that it can be used to complement the classification of protein secondary structures.     

On a seven-dimensional representation of RNA secondary structures

In this paper, we proposed a seven-dimensional (7D) representation of ribonucleic acid (RNA) secondary structures. The use of the 7D representation is illustrated by constructing structure invariants. Comparisons with the similarity/dissimilarity results based on 7D representation for a set of RNA 3 secondary structures at the 3′-terminus of different viruses, are considered to illustrate the use of our structure invariants based on the entries in derived sequence matrices restricted to a selected width of a band along the main diagonal.     

On a six-dimensional representation of RNA secondary structures

In this paper, we proposed a 6-D representation of RNA secondary structures. The use of the 6-D representation is illustrated by constructing structure invariants. Comparisons with the similarity/dissimilarity results based on 6-D representation for a set of RNA secondary structures, are considered to illustrate the use of our structure invariants based on the entries in derived sequence matrices restricted to a selected width of a band along the main diagonal.     

Recoverable one-dimensional encoding of three-dimensional protein structures

One-dimensional (1D) structures of proteins such as secondary structure and contact number provide intuitive pictures to understand how the native three-dimensional (3D) structure of a protein is encoded in the amino acid sequence. However, it is still not clear whether a given set of 1D structures contains sufficient information for recovering the underlying 3D structure. Here we show that the 3D structure of a protein can be recovered from a set of three types of 1D structures, namely, secondary structure, contact number and residue-wise contact order which is introduced here for the first time. Using simulated annealing molecular dynamics simulations, the structures satisfying the given native 1D structural restraints were sought for 16 proteins of various structural classes and of sizes ranging from 56 to 146 residues. By selecting the structures best satisfying the restraints, all the proteins showed a coordinate RMS deviation of <4 A from the native structure, and, for most of them, the deviation was even <2 A. The present result opens a new possibility to protein structure prediction and our understanding of the sequence-structure relationship.     

On A Six-Dimensional Representation of RNA Secondary Structures

Abstract

In this paper, we proposed a 6-D representation of RNA secondary structures. The use of the 6-D representation is illustrated by constructing structure invariants. Comparisons with the similarity/dissimilarity results based on 6-D representation for a set of RNA secondary structures, are considered to illustrate the use of our structure invariants based on the entries in derived sequence matrices restricted to a selected width of a band along the main diagonal.     

An algebraic representation of RNA secondary structures.

This paper develops mathematical methods for describing and analyzing RNA secondary structures. It was motivated by the need to develop rigorous yet efficient methods to treat transitions from one secondary structure to another, which we propose here may occur as motions of loops within RNAs having appropriate sequences. In this approach a molecular sequence is described as a vector of the appropriate length. The concept of symmetries between nucleic acid sequences is developed, and the 48 possible different types of symmetries are described. Each secondary structure possible for a particular nucleotide sequence determines a symmetric, signed permutation matrix. The collection of all possible secondary structures is comprised of all matrices of this type whose left multiplication with the sequence vector leaves that vector unchanged. A transition between two secondary structures is given by the product of the two corresponding structure matrices. This formalism provides an efficient method for describing nucleic acid sequences that allows questions relating to secondary structures and transitions to be addressed using the powerful methods of abstract algebra. In particular, it facilitates the determination of possible secondary structures, including those containing pseudoknots. Although this paper concentrates on RNA structure, this formalism also can be applied to DNA.     

An Algebraic Representation of RNA Secondary Structures

Abstract

This paper develops mathematical methods for describing and analyzing RNA secondary structures. It was motivated by the need to develop rigorous yet efficient methods to treat transitions from one secondary structure to another, which we propose here may occur as motions of loops within RNAs having appropriate sequences. In this approach a molecular sequence is described as a vector of the appropriate length. The concept of symmetries between nucleic acid sequences is developed, and the 48 possible different types of symmetries are described. Each secondary structure possible for a particular nucleotide sequence determines a symmetric, signed permutation matrix. The collection of all possible secondary structures is comprised of all matrices of this type whose left multiplication with the sequence vector leaves that vector unchanged. A transition between two secondary structures is given by the product of the two corresponding structure matrices. This formalism provides an efficient method for describing nucleic acid sequences that allows questions relating to secondary structures and transitions to be addressed using the powerful methods of abstract algebra. In particular, it facilitates the determination of possible secondary structures, including those containing pseudoknots. Although this paper concentrates on RNA structure, this formalism also can be applied to DNA     

Use of secondary structural information and C<Emphasis Type="Italic">α</Emphasis>-C<Emphasis Type="Italic">α</Emphasis> distance restraints to model protein structures with MODELLER

Protein secondary structure predictions and amino acid long range contact map predictions from primary sequence of proteins have been explored to aid in modelling protein tertiary structures. In order to evaluate the usefulness of secondary structure and 3D-residue contact prediction methods to model protein structures we have used the known Q3 (alpha-helix, beta-strands and irregular turns/loops) secondary structure information, along with residue-residue contact information as restraints for MODELLER. We present here results of our modelling studies on 30 best resolved single domain protein structures of varied lengths. The results shows that it is very difficult to obtain useful models even with 100% accurate secondary structure predictions and accurate residue contact predictions for up to 30% of residues in a sequence. The best models that we obtained for proteins of lengths 37, 70, 118, 136 and 193 amino acid residues are of RMSDs 4.17, 5.27, 9.12, 7.89 and 9.69, respectively. The results show that one can obtain better models for the proteins which have high percent of alpha-helix content. This analysis further shows that MODELLER restrain optimization program can be useful only if we have truly homologous structure(s) as a template where it derives numerous restraints, almost identical to the templates used. This analysis also clearly indicates that even if we satisfy several true residue-residue contact distances, up to 30% of their sequence length with fully known secondary structural information, we end up predicting model structures much distant from their corresponding native structures.     

Use of secondary structural information and C alpha-C alpha distance restraints to model protein structures with MODELLER

Protein secondary structure predictions and amino acid long range contact map predictions from primary sequence of proteins have been explored to aid in modelling protein tertiary structures. In order to evaluate the usefulness of secondary structure and 3D-residue contact prediction methods to model protein structures we have used the known Q3 (alpha-helix,beta-strands and irregular turns/loops) secondary structure information, along with residue-residue contact information as restraints for MODELLER. We present here results of our modelling studies on 30 best resolved single domain protein structures of varied lengths. The results shows that it is very difficult to obtain useful models even with 100% accurate secondary structure predictions and accurate residue contact predictions for up to 30% of residues in a sequence. The best models that we obtained for proteins of lengths 37, 70, 118, 136 and 193 amino acid residues are of RMSDs 4.17, 5.27, 9.12, 7.89 and 9.69,respectively. The results show that one can obtain better models for the proteins which have high percent of alpha-helix content. This analysis further shows that MODELLER restrain optimization program can be useful only if we have truly homologous structure(s) as a template where it derives numerous restraints, almost identical to the templates used. This analysis also clearly indicates that even if we satisfy several true residue-residue contact distances, up to 30%of their sequence length with fully known secondary structural information, we end up predicting model structures much distant from their corresponding native structures.     

Analogy-based protein structure prediction: III. Optimizing the combination of the substitution matrix and pseudopotentials used to align protein sequences with spatial structures

A general and fast method for maximizing the “recognition ability” of a linear combination of an arbitrary number of various methods used to recognize protein structures and produce sequence-to-structure alignments for the structurally analogous proteins is described. It is shown that, at a low level of sequence similarity, the optimal combination of methods displays a significantly higher recognition ability than each method alone; the leading role in this combination is played by (1) pseudopotentials of long-range interactions, (2) matrices of secondary structure similarity, and (3) amino acid substitution matrices. In the case of a high sequence similarity, substitution matrices play the leading and practically the sole role in the optimal combination, although the addition of pseudopotentials of long-range interactions and matrices of secondary structure similarity somewhat increases the recognition ability of the combined method.     

SPSSM8: An accurate approach for predicting eight-state secondary structures of proteins

Protein eight-state secondary structure prediction is challenging, but is necessary to determine protein structure and function. Here, we report the development of a novel approach, SPSSM8, to predict eight-state secondary structures of proteins accurately from sequences based on the structural position-specific scoring matrix (SPSSM). The SPSSM has been successfully utilized to predict three-state secondary structures. Now we employ an eight-state SPSSM as a feature that is obtained from sequence structure alignment against a large database of 9 million sequences with putative structural information. The SPSSM8 uses a low sequence identity dataset (9062 entries) as a training set and conditional random field for the classification algorithm. The SPSSM8 achieved an average eight-state secondary structure accuracy (Q8) of 71.7% (Q3, 81.6%) for an independent testing set (463 entries), which had an improved accuracy of 10.1% and 4.6% compared with SSPro8 and CNF, respectively, and significantly improved the accuracy of eight-state secondary structure prediction. For CASP 9 dataset (92 entries) the SPSSM8 achieved a Q8 accuracy of 80.1% (Q3, 83.0%). The SPSSM8 was confirmed as an outstanding predictor for eight-state secondary structures of proteins. SPSSM8 is freely available at http://cal.tongji.edu.cn/SPSSM8.     

Combining protein evolution and secondary structure

An evolutionary model that combines protein secondary structure and amino acid replacement is introduced. It allows likelihood analysis of aligned protein sequences and does not require the underlying secondary (or tertiary) structures of these sequences to be known. One component of the model describes the organization of secondary structure along a protein sequence and another specifies the evolutionary process for each category of secondary structure. A database of proteins with known secondary structures is used to estimate model parameters representing these two components. Phylogeny, the third component of the model, can be estimated from the data set of interest. As an example, we employ our model to analyze a set of sucrose synthase sequences. For the evolution of sucrose synthase, a parametric bootstrap approach indicates that our model is statistically preferable to one that ignores secondary structure.      

Protein fold recognition using sequence-derived predictions.

In protein fold recognition, one assigns a probe amino acid sequence of unknown structure to one of a library of target 3D structures. Correct assignment depends on effective scoring of the probe sequence for its compatibility with each of the target structures. Here we show that, in addition to the amino acid sequence of the probe, sequence-derived properties of the probe sequence (such as the predicted secondary structure) are useful in fold assignment. The additional measure of compatibility between probe and target is the level of agreement between the predicted secondary structure of the probe and the known secondary structure of the target fold. That is, we recommend a sequence-structure compatibility function that combines previously developed compatibility functions (such as the 3D-1D scores of Bowie et al. [1991] or sequence-sequence replacement tables) with the predicted secondary structure of the probe sequence. The effect on fold assignment of adding predicted secondary structure is evaluated here by using a benchmark set of proteins (Fischer et al., 1996a). The 3D structures of the probe sequences of the benchmark are actually known, but are ignored by our method. The results show that the inclusion of the predicted secondary structure improves fold assignment by about 25%. The results also show that, if the true secondary structure of the probe were known, correct fold assignment would increase by an additional 8-32%. We conclude that incorporating sequence-derived predictions significantly improves assignment of sequences to known 3D folds. Finally, we apply the new method to assign folds to sequences in the SWISSPROT database; six fold assignments are given that are not detectable by standard sequence-sequence comparison methods; for two of these, the fold is known from X-ray crystallography and the fold assignment is correct.     

ChSeq: A database of chameleon sequences

Chameleon sequences (ChSeqs) refer to sequence strings of identical amino acids that can adopt different conformations in protein structures. Researchers have detected and studied ChSeqs to understand the interplay between local and global interactions in protein structure formation. The different secondary structures adopted by one ChSeq challenge sequence‐based secondary structure predictors. With increasing numbers of available Protein Data Bank structures, we here identify a large set of ChSeqs ranging from 6 to 10 residues in length. The homologous ChSeqs discovered highlight the structural plasticity involved in biological function. When compared with previous studies, the set of unrelated ChSeqs found represents an about 20‐fold increase in the number of detected sequences, as well as an increase in the longest ChSeq length from 8 to 10 residues. We applied secondary structure predictors on our ChSeqs and found that methods based on a sequence profile outperformed methods based on a single sequence. For the unrelated ChSeqs, the evolutionary information provided by the sequence profile typically allows successful prediction of the prevailing secondary structure adopted in each protein family. Our dataset will facilitate future studies of ChSeqs, as well as interpretations of the interplay between local and nonlocal interactions. A user‐friendly web interface for this ChSeq database is available at prodata.swmed.edu/chseq .     

A rapid protein structure alignment algorithm based on a text modeling technique

Structural alignment of proteins is widely used in various fields of structural biology. In order to further improve the quality of alignment, we describe an algorithm for structural alignment based on text modelling techniques. The technique firstly superimposes secondary structure elements of two proteins and then, models the 3D-structure of the protein in a sequence of alphabets. These sequences are utilized by a step-by-step sequence alignment procedure to align two protein structures. A benchmark test was organized on a set of 200 non-homologous proteins to evaluate the program and compare it to state of the art programs, e.g. CE, SAL, TM-align and 3D-BLAST. On average, the results of all-against-all structure comparison by the program have a competitive accuracy with CE and TM-align where the algorithm has a high running speed like 3D-BLAST.     

The Bio3D packages for structural bioinformatics

Bio3D is a family of R packages for the analysis of biomolecular sequence, structure, and dynamics. Major functionality includes biomolecular database searching and retrieval, sequence and structure conservation analysis, ensemble normal mode analysis, protein structure and correlation network analysis, principal component, and related multivariate analysis methods. Here, we review recent package developments, including a new underlying segregation into separate packages for distinct analysis, and introduce a new method for structure analysis named ensemble difference distance matrix analysis (eDDM). The eDDM approach calculates and compares atomic distance matrices across large sets of homologous atomic structures to help identify the residue wise determinants underlying specific functional processes. An eDDM workflow is detailed along with an example application to a large protein family. As a new member of the Bio3D family, the Bio3D‐eddm package supports both experimental and theoretical simulation‐generated structures, is integrated with other methods for dissecting sequence‐structure–function relationships, and can be used in a highly automated and reproducible manner. Bio3D is distributed as an integrated set of platform independent open source R packages available from: http://thegrantlab.org/bio3d/ .     

Consensus Data Mining (CDM) Protein Secondary Structure Prediction Server: combining GOR V and Fragment Database Mining (FDM)

One of the challenges in protein secondary structure prediction is to overcome the cross-validated 80% prediction accuracy barrier. Here, we propose a novel approach to surpass this barrier. Instead of using a single algorithm that relies on a limited data set for training, we combine two complementary methods having different strengths: Fragment Database Mining (FDM) and GOR V. FDM harnesses the availability of the known protein structures in the Protein Data Bank and provides highly accurate secondary structure predictions when sequentially similar structural fragments are identified. In contrast, the GOR V algorithm is based on information theory, Bayesian statistics, and PSI-BLAST multiple sequence alignments to predict the secondary structure of residues inside a sliding window along a protein chain. A combination of these two different methods benefits from the large number of structures in the PDB and significantly improves the secondary structure prediction accuracy, resulting in Q3 ranging from 67.5 to 93.2%, depending on the availability of highly similar fragments in the Protein Data Bank.     

Using RNA secondary structures to guide sequence motif finding towards single-stranded regions

RNA binding proteins recognize RNA targets in a sequence specific manner. Apart from the sequence, the secondary structure context of the binding site also affects the binding affinity. Binding sites are often located in single-stranded RNA regions and it was shown that the sequestration of a binding motif in a double-strand abolishes protein binding. Thus, it is desirable to include knowledge about RNA secondary structures when searching for the binding motif of a protein. We present the approach MEMERIS for searching sequence motifs in a set of RNA sequences and simultaneously integrating information about secondary structures. To abstract from specific structural elements, we precompute position-specific values measuring the single-strandedness of all substrings of an RNA sequence. These values are used as prior knowledge about the motif starts to guide the motif search. Extensive tests with artificial and biological data demonstrate that MEMERIS is able to identify motifs in single-stranded regions even if a stronger motif located in double-strand parts exists. The discovered motif occurrences in biological datasets mostly coincide with known protein-binding sites. This algorithm can be used for finding the binding motif of single-stranded RNA-binding proteins in SELEX or other biological sequence data.     

Prediction of alpha-turns in proteins using PSI-BLAST profiles and secondary structure information

In this paper a systematic attempt has been made to develop a better method for predicting alpha-turns in proteins. Most of the commonly used approaches in the field of protein structure prediction have been tried in this study, which includes statistical approach "Sequence Coupled Model" and machine learning approaches; i) artificial neural network (ANN); ii) Weka (Waikato Environment for Knowledge Analysis) Classifiers and iii) Parallel Exemplar Based Learning (PEBLS). We have also used multiple sequence alignment obtained from PSIBLAST and secondary structure information predicted by PSIPRED. The training and testing of all methods has been performed on a data set of 193 non-homologous protein X-ray structures using five-fold cross-validation. It has been observed that ANN with multiple sequence alignment and predicted secondary structure information outperforms other methods. Based on our observations we have developed an ANN-based method for predicting alpha-turns in proteins. The main components of the method are two feed-forward back-propagation networks with a single hidden layer. The first sequence-structure network is trained with the multiple sequence alignment in the form of PSI-BLAST-generated position specific scoring matrices. The initial predictions obtained from the first network and PSIPRED predicted secondary structure are used as input to the second structure-structure network to refine the predictions obtained from the first net. The final network yields an overall prediction accuracy of 78.0% and MCC of 0.16. A web server AlphaPred (http://www.imtech.res.in/raghava/alphapred/) has been developed based on this approach.