A heat map showing the similarity of nine species in the ND5 dataset based on the 20-D amino acid content ratio vector.

<p>A heat map showing the similarity of nine species in the ND5 dataset based on the 20-D amino acid content ratio vector.</p

An Alignment-Free Algorithm in Comparing the Similarity of Protein Sequences Based on Pseudo-Markov Transition Probabilities among Amino Acids

<div><p>In this paper, we have proposed a novel alignment-free method for comparing the similarity of protein sequences. We first encode a protein sequence into a 440 dimensional feature vector consisting of a 400 dimensional Pseudo-Markov transition probability vector among the 20 amino acids, a 20 dimensional content ratio vector, and a 20 dimensional position ratio vector of the amino acids in the sequence. By evaluating the Euclidean distances among the representing vectors, we compare the similarity of protein sequences. We then apply this method into the ND5 dataset consisting of the ND5 protein sequences of 9 species, and the F10 and G11 datasets representing two of the xylanases containing glycoside hydrolase families, i.e., families 10 and 11. As a result, our method achieves a correlation coefficient of 0.962 with the canonical protein sequence aligner ClustalW in the ND5 dataset, much higher than those of other 5 popular alignment-free methods. In addition, we successfully separate the xylanases sequences in the F10 family and the G11 family and illustrate that the F10 family is more heat stable than the G11 family, consistent with a few previous studies. Moreover, we prove mathematically an identity equation involving the Pseudo-Markov transition probability vector and the amino acids content ratio vector.</p></div

A heat map showing the similarity of 20 xylanases in the F10 and G11 datasets.

<p>A heat map showing the similarity of 20 xylanases in the F10 and G11 datasets.</p

A heat map showing the similarity of nine species in the ND5 dataset.

<p>Red color indicates small distance and high similarity between the sequences and yellow color indicates large distance and low similarity, the same as below.</p

The distance matrix of nine species calculated by ClustalW (i.e. Table 4 in [31]).

<p>The distance matrix of nine species calculated by ClustalW (i.e. Table 4 in [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0167430#pone.0167430.ref031" target="_blank">31</a>]).</p

The position ratios of twenty amino acids in the ND5 dataset.

<p>The X axis denotes the 20 amino acids and the Y axis denotes the position ratios of each amino acid for 9 sequences.</p

Comparison of 6 alignment-free methods.

<p>Comparison of 6 alignment-free methods.</p

The distance matrix of nine species by our method.

<p>The distance matrix of nine species by our method.</p

The content ratios of twenty amino acids in the ND5 dataset.

<p>The X axis denotes the 20 amino acids and the Y axis denotes the content ratios of each amino acid for the 9 sequences.</p

A heat map showing the similarity of nine species in the ND5 dataset based on the 40-D amino acid position ratio and content ratio vector.

<p>A heat map showing the similarity of nine species in the ND5 dataset based on the 40-D amino acid position ratio and content ratio vector.</p