A unique approach for protein secondary structure comparison under TOPS representation.

To unravel the intricate connection between protein function and protein structure, it is imperative to comprehensively evaluate protein secondary structure similarity from various perspectives. While numerous techniques have been suggested for comparing protein secondary structure elements (SSE), there continues to be a substantial need for finding alternative ways of comparing the same. In this paper, Topology of Protein Structure (TOPS) representations of protein secondary structures are considered to offer a new alignment-free method for evaluating similarities/dissimilarities of protein secondary structures. Initially, a two-dimensional numerical representation of the SSE is created, associating each point with a mass reflecting its frequency of occurrence. Then the means of coordinate values are determined by averaging weighted sums, and these mean values are subsequently used to calculate moments-of-inertia. Next, a four-component descriptor is generated out of the eigenvalues of the matrix and the mean values of the represented coordinates. Thereafter, Manhattan distance measure is used to obtain the distance matrix. This is finally applied to obtain the phylogenetic trees under the use of NJ method. SSE considered in the proposed method comprises 36-elements from the Chew-Kedem database giving five different taxa: globin, alpha-beta, tim-barrel, beta, and alpha. Phylogenetic trees were created for these SSE through the application of various methods: Clustal-Omega, LZ-Complexity, SED, TOPS + and TOC, to facilitate comparative analysis. Phylogenetic tree of the proposed method outperformed results of the previous methods when applied to the same SSE. Therefore, the method effectively constructs phylogenetic tree for analyzing protein secondary structure comparison.Communicated by Ramaswamy H. Sarma.

Choice of Metric Divergence in Genome Sequence Comparison.

The paper introduces a novel probability descriptor for genome sequence comparison, employing a generalized form of Jensen-Shannon divergence. This divergence metric stems from a one-parameter family, comprising fractions up to a maximum value of half. Utilizing this metric as a distance measure, a distance matrix is computed for the new probability descriptor, shaping Phylogenetic trees via the neighbor-joining method. Initial exploration involves setting the parameter at half for various species. Assessing the impact of parameter variation, trees drawn at different parameter values (half, one-fourth, one-eighth). However, measurement scales decrease with parameter value increments, with higher similarity accuracy corresponding to lower scale values. Ultimately, the highest accuracy aligns with the maximum parameter value of half. Comparative analyses against previous methods, evaluating via Symmetric Distance (SD) values and rationalized perception, consistently favor the present approach's results. Notably, outcomes at the maximum parameter value exhibit the most accuracy, validating the method's efficacy against earlier approaches.

MMV method: a new approach to compare protein sequences under binary representation.

In the present work, a new form of descriptor using minimal moment vector (MMV) is introduced to compare protein sequences in the frequency domain under their component wise binary representations. From every sequence, 20 different binary component sequences are formed, each corresponding to 20 amino acids. Each such vector is now shifted from the time domain to the frequency domain by applying the Fast Fourier Transform (FFT). Next, the power spectrum calculated from the FFT values for each component sequence is so normalized that the sum of the components equals 1. The descriptor is defined as a 20-component vector composed of the 20 second-order minimal moments calculated from the normalized spectrum of the 20 component sequences. Once the descriptor is known, the distance matrix is created by applying the Euclidean Distance measure. The phylogenetic tree is generated by applying the unweighted pair group method with the arithmetic mean (UPGMA) algorithm using Molecular Evolutionary Genetics Analysis11 (MEGA11) software. In this work, the datasets used for similarity studies are 9 NADH dehydrogenase 5 (ND5), 12 Baculoviruses, 24 Transferrins (TF) proteins, and 50 Spike Protein of coronavirus. A qualitative measure using rationalized perception is used to compare the effectiveness of the proposed method. Quantitative measure based on symmetric distance (SD) is used to compare the phylogenetic trees of the present method with those obtained by other methods. It is observed that the phylogenetic trees generated by the proposed technique are at par with their known biological references, and they produce results better than those of the earlier methods.Communicated by Ramaswamy H. Sarma.

Use of 2D FFT and DTW in Protein Sequence Comparison.

Protein sequence comparison remains a challenging work for the researchers owing to the computational complexity due to the presence of 20 amino acids compared with only four nucleotides in Genome sequences. Further, protein sequences of different species are of different lengths; it throws additional changes to the researchers to develop methods, specially alignment-free methods, to compare protein sequences. In this work, an efficient technique to compare protein sequences is developed by a graphical representation. First, the classified grouping of 20 amino acids with a cardinality of 4 based on polar class is considered to narrow down the representational range from 20 to 4. Then a unit vector technique based on a two-quadrant Cartesian system is proposed to provide a new two-dimensional graphical representation of the protein sequence. Now, two approaches are proposed to cope with the varying lengths of protein sequences from various species: one uses Dynamic Time Warping (DTW), while the other one uses a two-dimensional Fast Fourier Transform (2D FFT). Next, the effectiveness of these two techniques is analyzed using two evaluation criteria-quantitative measures based on symmetric distance (SD) and computational speed. An analysis is performed on five data sets of 9 ND4, 9 ND5, 9 ND6, 12 Baculovirus, and 24 TF proteins under the two methods. It is found that the FFT-based method produces the same results as DTW but in less computational time. It is found that the result of the proposed method agrees with the known biological reference. Further, the present method produces better clustering than the existing ones.

Protein sequence comparison based on representation on a finite dimensional unit hypercube.

Numerous techniques are used to compare protein sequences based on the values of the physiochemical properties of amino acids. In this work, a single physical/chemical property value based non-binary representation of protein sequences is obtained on a 20 × 20-dimensional unit hypercube. The represented vector expressed in the matrix form is taken as the descriptor. The generalized NTV metric, which is an extension of the NTV metric used for polynucleotide space is taken as a distance measure. Based on this distance measure, a distance matrix is obtained for protein sequence comparison. Using this distance matrix, phylogenetic trees are drawn by using Molecular Evolutionary Genetics Analysis 11 (MEGA11) software applying the neighbor-joining method. Data sets used in this current work are 9-ND4, 9-ND5, 9-ND6, 24 TF-LF proteins, 27 different viruses and 127 proteins from the protein kinase C (PKC) family. Two sets of phylogenetic trees are obtained - one based on property value of polarity and the other based on property value of molecular weight. They are found to be exactly the same. Similar results also hold for other single property value based representation. The present trees are individually tested for efficiency based on the criterion of rationalized perception and computational time. The results of the present method are compared with those obtained earlier by other methods on the same protein sequences using assessment criteria of Symmetric distance (SD), Correlation coefficient, and Rationalized perception. In all the cases, the present results are found to be better than the results of other methods under comparison.Communicated by Ramaswamy H. Sarma.

PTGAC Model: A machine learning approach for constructing phylogenetic tree to compare protein sequences.

This work proposes a machine learning-based phylogenetic tree generation model based on agglomerative clustering (PTGAC) that compares protein sequences considering all known chemical properties of amino acids. The proposed model can serve as a suitable alternative to the Unweighted Pair Group Method with Arithmetic Mean (UPGMA), which is inherently time-consuming in nature. Initially, principal component analysis (PCA) is used in the proposed scheme to reduce the dimensions of 20 amino acids using seven known chemical characteristics, yielding 20 TP (Total Points) values for each amino acid. The approach of cumulative summing is then used to give a non-degenerate numeric representation of the sequences based on these 20 TP values. A special kind of three-component vector is proposed as a descriptor, which consists of a new type of non-central moment of orders one, two, and three. Subsequently, the proposed model uses Euclidean Distance measures among the descriptors to create a distance matrix. Finally, a phylogenetic tree is constructed using hierarchical agglomerative clustering based on the distance matrix. The results are compared with the UPGMA and other existing methods in terms of the quality and time of constructing the phylogenetic tree. Both qualitative and quantitative analysis are performed as key assessment criteria for analyzing the performance of the proposed model. The qualitative analysis of the phylogenetic tree is performed by considering rationalized perception, while the quantitative analysis is performed based on symmetric distance (SD). On both criteria, the results obtained by the proposed model are more satisfactory than those produced earlier on the same species by other methods. Notably, this method is found to be efficient in terms of both time and space requirements and is capable of dealing with protein sequences of varying lengths.

Mathematical Approach to Protein Sequence Comparison Based on Physiochemical Properties.

The difficult aspect of developing new protein sequence comparison techniques is coming up with a method that can quickly and effectively handle huge data sets of various lengths in a timely manner. In this work, we first obtain two numerical representations of protein sequences separately based on one physical property and one chemical property of amino acids. The lengths of all the sequences under comparison are made equal by appending the required number of zeroes. Then, fast Fourier transform is applied to this numerical time series to obtain the corresponding spectrum. Next, the spectrum values are reduced by the standard inter coefficient difference method. Finally, the corresponding normalized values of the reduced spectrum are selected as the descriptors for protein sequence comparison. Using these descriptors, the distance matrices are obtained using Euclidian distance. They are subsequently used to draw the phylogenetic trees using the UPGMA algorithm. Phylogenetic trees are first constructed for 9 ND4, 9 ND5, and 9 ND6 proteins using the polarity value as the chemical property and the molecular weight as the physical property. They are compared, and it is seen that polarity is a better choice than molecular weight in protein sequence comparison. Next, using the polarity property, phylogenetic trees are obtained for 12 baculovirus and 24 transferrin proteins. The results are compared with those obtained earlier on the identical sequences by other methods. Three assessment criteria are considered for comparison of the results-quality based on rationalized perception, quantitative measures based on symmetric distance, and computational speed. In all the cases, the results are found to be more satisfactory.