3-D maps and coupling numbers for protein sequences

3D graphical representation of protein sequences and their statistical characterization

“…Graphical representation of proteins emerged only recently [13][14][15][16][17][18][19][20][21]. A protein sequence consists of twenty different amino acids while a DNA sequence consists of only four bases.…”

“…A modification of this work was done by representing the x-coordinate as pKa (NH3 + ) and the y-coordinate as the difference between each pKa (COOH) of each amino acid and the average of all pKa (COOH) of all twenty amino acids [20]. A 3D graphical representation of proteins was proposed based on five-letter model of amino acids which converts the twenty letters of amino acids to only five letters [21]. Then a vector of three components was assigned to each letter in the sequence as a point P i (x i , y i , z i ).…”

“…Examples of matrices of DNA sequences are euclidean distance matrix (ED), graph theoretical distance matrix (GD), path distance matrix (PD), L/L matrix and M/M matrix [7,22]. Matrix invariants are graph radius, normalized geometrical centers [12], leading eigenvalues of L/L matrix, M/M matrix [7], 2D coupling numbers [17] and 3D coupling numbers [21]. In this paper, we proposed a novel 3D graphical representation based on physicochemical properties of amino acids side chains.…”

Representation of protein sequences on latitude-like circles and longitude-like semi-circles

“…There is a delay in protein graphical representations because its sequence consists of 20 amino acids while DNA sequence consists of only four bases. The graphical representations of protein sequences emerged recently [18][19][20][21][22][23][24][25][26][27][28][29][30]. Graphical representations can be associated with mathematical objects such as matrices.…”

“…It is highly compact and was constructed in the interior of a unit _magic_ circle, on the circumference of which at equal distances are positioned 20 amino acids. A 3-D graphical representation of protein sequence was proposed [29]. It was based on the five-letter model of the 20 amino acids.…”