On novel representation of proteins based on amino acid adjacency matrix

FFP: joint Fast Fourier transform and fractal dimension in amino acid property-aware phylogenetic analysis

Background

Amino acid property-aware phylogenetic analysis (APPA) refers to the phylogenetic analysis method based on amino acid property encoding, which is used for understanding and inferring evolutionary relationships between species from the molecular perspective. Fast Fourier transform (FFT) and Higuchi’s fractal dimension (HFD) have excellent performance in describing sequences’ structural and complexity information for APPA. However, with the exponential growth of protein sequence data, it is very important to develop a reliable APPA method for protein sequence analysis.

Results

Consequently, we propose a new method named FFP, it joints FFT and HFD. Firstly, FFP is used to encode protein sequences on the basis of the important physicochemical properties of amino acids, the dissociation constant, which determines acidity and basicity of protein molecules. Secondly, FFT and HFD are used to generate the feature vectors of encoded sequences, whereafter, the distance matrix is calculated from the cosine function, which describes the degree of similarity between species. The smaller the distance between them, the more similar they are. Finally, the phylogenetic tree is constructed. When FFP is tested for phylogenetic analysis on four groups of protein sequences, the results are obviously better than other comparisons, with the highest accuracy up to more than 97%.

Conclusion

FFP has higher accuracy in APPA and multi-sequence alignment. It also can measure the protein sequence similarity effectively. And it is hoped to play a role in APPA’s related research.

Prioritizing the candidate genes related to cervical cancer using the moment of inertia tensor

It is well known that cervical cancer poses the fourth most malignancy threat to women worldwide among all cancer types. There is a tremendous improvement in realizing the underlying molecular associations in cervical cancer. Several studies reported pieces of evidence for the involvement of various genes in the disease progression. However, with the ever-evolving bioinformatics tools, there has been an upsurge in predicting numerous genes responsible for cervical cancer progression and making it highly complex to target the genes for further evaluation. In this article, we prioritized the candidate genes based on the sequence similarity analysis with known cancer genes. For this purpose, we used the concept of the moment of inertia tensor, which reveals the similarities between the protein sequences more efficiently. Tensor for moment of inertia explores the similarity of the protein sequences based on the physicochemical properties of amino acids. From our analysis, we obtained 14 candidate cervical cancer genes, which are highly similar to known cervical cancer genes. Further, we analyzed the GO terms and prioritized these genes based on the number of hits with biological process, molecular functions, and their involvement in KEGG pathways. We also discussed the evidence-based involvement of the prioritized genes in other cancers and listed the available drugs for those genes.

A Statistical Similarity/Dissimilarity Analysis of Protein Sequences Based on a Novel Group Representative Vector

Similarity/dissimilarity analysis is a key way of understanding the biology of an organism by knowing the origin of the new genes/sequences. Sequence data are grouped in terms of biological relationships. The number of sequences related to any group is susceptible to be increased every day. All the present alignment-free methods approve the utility of their approaches by producing a similarity/dissimilarity matrix. Although this matrix is clear, it measures the degree of similarity among sequences individually. In our work, a representative of each of three groups of protein sequences is introduced. A similarity/dissimilarity vector is evaluated instead of the ordinary similarity/dissimilarity matrix based on the group representative. The approach is applied on three selected groups of protein sequences: beta globin, NADH dehydrogenase subunit 5 (ND5), and spike protein sequences. A cross-grouping comparison is produced to ensure the singularity of each group. A qualitative comparison between our approach, previous articles, and the phylogenetic tree of these protein sequences proved the utility of our approach.

Measuring Similarity among Protein Sequences Using a New Descriptor

The comparison of protein sequences according to similarity is a fundamental aspect of today's biomedical research. With the developments of sequencing technologies, a large number of protein sequences increase exponentially in the public databases. Famous sequences' comparison methods are alignment based. They generally give excellent results when the sequences under study are closely related and they are time consuming. Herein, a new alignment-free method is introduced. Our technique depends on a new graphical representation and descriptor. The graphical representation of protein sequence is a simple way to visualize protein sequences. The descriptor compresses the primary sequence into a single vector composed of only two values. Our approach gives good results with both short and long sequences within a little computation time. It is applied on nine beta globin, nine ND5 (NADH dehydrogenase subunit 5), and 24 spike protein sequences. Correlation and significance analyses are also introduced to compare our similarity/dissimilarity results with others' approaches, results, and sequence homology.

Identifying anticancer peptides by using a generalized chaos game representation

We generalize chaos game representation (CGR) to higher dimensional spaces while maintaining its bijection, keeping such method sufficiently representative and mathematically rigorous compare to previous attempts. We first state and prove the asymptotic property of CGR and our generalized chaos game representation (GCGR) method. The prediction follows that the dissimilarity of sequences which possess identical subsequences but distinct positions would be lowered exponentially by the length of the identical subsequence; this effect was taking place unbeknownst to researchers. By shining a spotlight on it now, we show the effect fundamentally supports (G)CGR as a similarity measure or feature extraction technique. We develop two feature extraction techniques: GCGR-Centroid and GCGR-Variance. We use the GCGR-Centroid to analyze the similarity between protein sequences by using the datasets 9 ND5, 24 TF and 50 beta-globin proteins. We obtain consistent results compared with previous studies which proves the significance thereof. Finally, by utilizing support vector machines, we train the anticancer peptide prediction model by using both GCGR-Centroid and GCGR-Variance, and achieve a significantly higher prediction performance by employing the 3 well-studied anticancer peptide datasets.

An efficient method for measuring the similarity of protein sequences

An accurate numerical descriptor for protein sequence is introduced. It is basically a set of each three successive amino acids in the sequence (triplet), starting from left to right, in addition to the distances between each two successive amino acids in the triplet such that the summation of these distances does not exceed 8. This numerical descriptor combines two features the amino acid composition and the position of each amino acid relative to the other nearby amino acids. This numerical descriptor is used to measure the similarity between protein sequences in three sets: NADH dehydrogenase subunit 5 (ND5) proteins of different species, 24 transferrin proteins from vertebrates and 12 proteins of baculoviruses. High correlation coefficient values between our results and the results of ClustalW program are obtained. These values are higher than the values obtained in many other related works.

PredβTM: A Novel β-Transmembrane Region Prediction Algorithm

Predicting the transmembrane regions is an important aspect of understanding the structures and architecture of different β-barrel membrane proteins. Despite significant efforts, currently available β-transmembrane region predictors are still limited in terms of prediction accuracy, especially in precision. Here, we describe PredβTM, a transmembrane region prediction algorithm for β-barrel proteins. Using amino acid pair frequency information in known β-transmembrane protein sequences, we have trained a support vector machine classifier to predict β-transmembrane segments. Position-specific amino acid preference data is incorporated in the final prediction. The predictor does not incorporate evolutionary profile information explicitly, but is based on sequence patterns generated implicitly by encoding the protein segments using amino acid adjacency matrix. With a benchmark set of 35 β-transmembrane proteins, PredβTM shows a sensitivity and precision of 83.71% and 72.98%, respectively. The segment overlap score is 82.19%. In comparison with other state-of-art methods, PredβTM provides a higher precision and segment overlap without compromising with sensitivity. Further, we applied PredβTM to analyze the β-barrel membrane proteins without defined transmembrane regions and the uncharacterized protein sequences in eight bacterial genomes and predict possible β-transmembrane proteins. PredβTM can be freely accessed on the web at http://transpred.ki.si/.

On the history of the connectivity index: from the connectivity index to the exact solution of the protein alignment problem

We briefly review the history of the connectivity index from 1975 to date. We hope to throw some light on why this unique, by its design, graph theoretical molecular descriptor continues to be of interest in QSAR, having wide use in applications in structure-property and structure-activity studies. We will elaborate on its generalizations and the insights it offered on applications in Multiple Regression Analysis (MRA). Going beyond the connectivity index we will outline several related developments in the development of molecular descriptors used in MRA, including molecular ID numbers (1986), the variable connectivity index (1991), orthogonal regression (1991), irrelevance of co-linearity of descriptors (1997), anti-connectivity (2006), and high discriminatory descriptors characterizing molecular similarity (2015). We will comment on beauty in QSAR and recent progress in searching for similarity of DNA, proteins and the proteome. This review reports on several results which are little known to the structure-property-activity community, the significance of which may surprise those unfamiliar with the application of discrete mathematics to chemistry. It tells the reader many unknown stories about the connectivity index, which may help the reader to better understand the meaning of this index. Readers are not required to be familiar with graph theory.

ADLD: a novel graphical representation of protein sequences and its application

To facilitate the intuitional analysis of protein sequences, a novel graphical representation of protein sequences called ADLD (Alignment Diagonal Line Diagram) is introduced in this paper first, and then a new ADLD based method is proposed and utilized to analyze the similarity/dissimilarity of protein sequences. Comparing with existing methods, our ADLD based method is proved to be effective in the similarity/dissimilarity analysis of protein sequences and have the merits of good intuition, visuality, and simplicity. The examinations of the similarities/dissimilarities for both the 16 different ND5 proteins and the 29 different spike proteins illustrate the utility of our ADLD based approach.

An alignment-free method to find similarity among protein sequences via the general form of Chou's pseudo amino acid composition

In this paper, we propose a method to create the 60-dimensional feature vector for protein sequences via the general form of pseudo amino acid composition. The construction of the feature vector is based on the contents of amino acids, total distance of each amino acid from the first amino acid in the protein sequence and the distribution of 20 amino acids. The obtained cosine distance metric (also called the similarity matrix) is used to construct the phylogenetic tree by the neighbour joining method. In order to show the applicability of our approach, we tested it on three proteins: 1) ND5 protein sequences from nine species, 2) ND6 protein sequences from eight species, and 3) 50 coronavirus spike proteins. The results are in agreement with known history and the output from the multiple sequence alignment program ClustalW, which is widely used. We have also compared our phylogenetic results with six other recently proposed alignment-free methods. These comparisons show that our proposed method gives a more consistent biological relationship than the others. In addition, the time complexity is linear and space required is less as compared with other alignment-free methods that use graphical representation. It should be noted that the multiple sequence alignment method has exponential time complexity.

Mathematical characterization of protein transmembrane regions

Graphical bioinformatics has paved a unique way of mathematical characterization of proteins and proteomic maps. The graphics representations and the corresponding mathematical descriptors have proved to be useful and have provided unique solutions to problems related to identification, comparisons, and analyses of protein sequences and proteomics maps. Based on sequence information alone, these descriptors are independent from physiochemical properties of amino acids and evolutionary information. In this work, we have presented invariants from amino acid adjacency matrix and decagonal isometries matrix as potential descriptors of protein sequences. Encoding protein sequences into amino acid adjacency matrix is already well established. We have shown its application in classification of transmembrane and nontransmembrane regions of membrane protein sequences. We have introduced the dodecagonal isometries matrix, which is a novel method of encoding protein sequences based on decagonal isometries group.

On graphical representation of trans-membrane proteins

In the first part of this paper, we present a novel graphical representation of proteins, which starts with constructing a map of a protein that is obtained from a matrix, the elements of which record the adjacencies of pairs of amino acids in the primary structure of a protein. Starting with the novel protein map, one interprets its matrix elements as vertices of a graph, which are labelled in sequential order as in the protein sequence. The nearest vertices are connected to the nearest neighbour which has a smaller label. In the second part of this paper, we describe the construction of protein binary codes that can serve as protein descriptors. This novel graphical representation of proteins is illustrated on segments of trans-membrane proteins, which are embedded in the membrane.

Graphical representation and mathematical characterization of protein sequences and applications to viral proteins

Graphical representation and numerical characterization (GRANCH) of nucleotide and protein sequences is a new field that is showing a lot of promise in analysis of such sequences. While formulation and applications of GRANCH techniques for DNA/RNA sequences started just over a decade ago, analyses of protein sequences by these techniques are of more recent origin. The emphasis is still on developing the underlying technique, but significant results have been achieved in using these methods for protein phylogeny, mass spectral data of proteins and protein serum profiles in parasites, toxicoproteomics, determination of different indices for use in QSAR studies, among others. We briefly mention these in this chapter, with some details on protein phylogeny and viral diseases. In particular, we cover a systematic method developed in GRANCH to determine conserved surface exposed peptide segments in selected viral proteins that can be used for drug and vaccine targeting. The new GRANCH techniques and applications for DNAs and proteins are covered briefly to provide an overview to this nascent field.

The graphical representation of protein sequences based on the physicochemical properties and its applications

Based on the chaos game representation, a 2D graphical representation of protein sequences was introduced in which the 20 amino acids are rearranged in a cyclic order according to their physicochemical properties. The Euclidean distances between the corresponding amino acids from the 2-D graphical representations are computed to find matching (or conserved) fragments of amino acids between the two proteins. Again, the cumulative distance of the 2D-graphical representations is defined to compare the similarity of protein. And, the examination of the similarity among sequences of the ND5 proteins of nine species shows the utility of our approach.

Novel graph distance matrix

We have introduced novel distance matrix for graphs, which is based on interpretation of columns of the adjacency matrix of a graph as a set of points in n-dimensional space, n being the number of vertices in the graph. Numerical values for the distances are based on the Euclidean distance between n points in n-dimensional space. In this way, we have combined the traditional representation of graphs (drawn as 2D object of no fixed geometry) with their representation in n-dimensional space, defined by a set of n-points that lead to a representation of definite geometry. The novel distance matrix, referred to as natural distance matrix, shows some structural properties and offers novel graph invariants as molecular descriptors for structure-property-activity studies. One of the novel graph descriptors is the modified connectivity index in which the bond contribution for (m, n) bond-type is given by 1/ radical(m + n), where m and n are the valence of the end vertices of the bond. The novel distance matrix (ND) can be reduced to sparse distance-adjacency matrix (DA), which can be viewed as specially weighted adjacency matrix of a graph. The quotient of the leading eigenvalues of novel distance-adjacency matrix and novel distance matrix, as illustrated on a collection of graphs of chemical interest, show parallelism with a simple measure of graph density, based on the quotient of the number of edges in a graph and the maximal possible number of edges for graphs of the same size.

A new graphical representation of similarity/dissimilarity studies of protein sequences

Based on chaos game representation, a two-dimensional-graphical representation of protein sequences is described in which 20 amino acids are rearranged in a cyclic order using a PAM250 substitution matrix. A numerical characterisation has been developed as a descriptor to compare protein sequences. Finally, an example is given in which the dehydrogenase subunit 5 (ND5) protein sequences of nine species are compared.

Computational analysis and determination of a highly conserved surface exposed segment in H5N1 avian flu and H1N1 swine flu neuraminidase

Background

Catalytic activity of influenza neuraminidase (NA) facilitates elution of progeny virions from infected cells and prevents their self-aggregation mediated by the catalytic site located in the body region. Research on the active site of the molecule has led to development of effective inhibitors like oseltamivir, zanamivir etc, but the high rate of mutation and interspecies reassortment in viral sequences and the recent reports of oseltamivir resistant strains underlines the importance of determining additional target sites for developing future antiviral compounds. In a recent computational study of 173 H5N1 NA gene sequences we had identified a 50-base highly conserved region in 3'-terminal end of the NA gene.

Results

We extend the graphical and numerical analyses to a larger number of H5N1 NA sequences (514) and H1N1 swine flu sequences (425) accessed from GenBank. We use a 2D graphical representation model for the gene sequences and a Graphical Sliding Window Method (GSWM) for protein sequences scanning the sequences as a block of 16 amino acids at a time. Using a protein sequence descriptor defined in our model, the protein sliding scan method allowed us to compare the different strains for block level variability, which showed significant statistical correlation to average solvent accessibility of the residue blocks; single amino acid position variability results in no correlation, indicating the impact of stretch variability in chemical environment. Close to the C-terminal end the GSWM showed less descriptor-variability with increased average solvent accessibility (ASA) that is also supported by conserved predicted secondary structure of 3' terminal RNA and visual evidence from 3D crystallographic structure.

Conclusion

The identified terminal segment, strongly conserved in both RNA and protein sequences, is especially significant as it is surface exposed and structural chemistry reveals the probable role of this stretch in tetrameric stabilization. It could also participate in other biological processes associated with conserved surface residues. A RNA double hairpin secondary structure found in this segment in a majority of the H5N1 strains also supports this observation. In this paper we propose this conserved region as a probable site for designing inhibitors for broad-spectrum pandemic control of flu viruses with similar NA structure.

Data-driven model for the prediction of protein transmembrane regions

We present a novel approach combining mathematical methods and artificial neural networks to predict the transmembrane regions of transmembrane proteins, considering protein sequence information alone. We have focused on developing a data-driven model based on a non-linear modelling method, the counter-propagation artificial neural network, and on mathematical descriptors defining the sequence information of transmembrane proteins with known three-dimensional structures. The developed model has proven to be promising in predicting protein transmembrane regions, with an error below 10% for the external validation set. In combination with available experimental data the model can give us a better understanding of transmembrane proteins.

Generalized lattice graphs for 2D-visualization of biological information

Several graph representations have been introduced for different data in theoretical biology. For instance, complex networks based on Graph theory are used to represent the structure and/or dynamics of different large biological systems such as protein–protein interaction networks. In addition, Randic, Liao, Nandy, Basak, and many others developed some special types of graph-based representations. This special type of graph includes geometrical constrains to node positioning in space and adopts final geometrical shapes that resemble lattice-like patterns. Lattice networks have been used to visually depict DNA and protein sequences but they are very flexible. However, despite the proved efficacy of new lattice-like graph/networks to represent diverse systems, most works focus on only one specific type of biological data. This work proposes a generalized type of lattice and illustrates how to use it in order to represent and compare biological data from different sources. We exemplify the following cases: protein sequence; mass spectra (MS) of protein peptide mass fingerprints (PMF); molecular dynamic trajectory (MDTs) from structural studies; mRNA microarray data; single nucleotide polymorphisms (SNPs); 1D or 2D-Electrophoresis study of protein polymorphisms and protein-research patent and/or copyright information. We used data available from public sources for some examples but for other, we used experimental results reported herein for the first time. This work may break new ground for the application of Graph theory in theoretical biology and other areas of biomedical sciences.