Hydrophobic, hydrophilic, and charged amino acid networks within protein

Abstract

The native three-dimensional structure of a single protein is determined by the physicochemical nature of its constituent amino acids. The 20 different types of amino acids, depending on their physicochemical properties, can be grouped into three major classes: hydrophobic, hydrophilic, and charged. The anatomy of the weighted and unweighted networks of hydrophobic, hydrophilic, and charged residues separately for a large number of proteins were studied. Results showed that the average degree of the hydrophobic networks has a significantly larger value than that of hydrophilic and charged networks. The average degree of the hydrophilic networks is slightly higher than that of the charged networks. The average strength of the nodes of hydrophobic networks is nearly equal to that of the charged network, whereas that of hydrophilic networks has a smaller value than that of hydrophobic and charged networks. The average strength for each of the three types of networks varies with its degree. The average strength of a node in a charged network increases more sharply than that of the hydrophobic and hydrophilic networks. Each of the three types of networks exhibits the "small-world" property. Our results further indicate that the all-amino-acids networks and hydrophobic networks are of assortative type. Although most of the hydrophilic and charged networks are of the assortative type, few others have the characteristics of disassortative mixing of the nodes. We have further observed that all-amino-acids networks and hydrophobic networks bear the signature of hierarchy, whereas the hydrophilic and charged networks do not have any hierarchical signature.

FIGURE 1

Average strength 〈s〉(k) as a function of degree k of hydrophobic (BN), hydrophilic (IN), charged (CN), and all-amino-acids (AN) networks.

FIGURE 2

Ratios p (= 〈C〉/〈C_r〉) and q (= 〈L〉/〈L_r〉) as a function of network size N. The ratio p varies linearly with N, whereas the ratio q varies logarithmically with N. The best-fit curves are shown by lines for the two ratios. (A) All-amino-acids networks (AN). (B) Hydrophobic networks (BN). (C) Hydrophilic networks (IN). (D) Charged networks (CN).

FIGURE 3

Topological clustering coefficient C(k) and weighted clustering coefficient C^w(k) as a function of degree k for different types of networks: (A) all-amino-acids networks (AN), (B) hydrophobic networks (BN), (C) hydrophilic networks (IN), and (D) charged networks (CN) for a representative protein (PDB Id:8ACN). The best-fit curves are shown by lines.