Do topological parameters of amino acids within protein contact networks depend on their physico-chemical properties?

The three dimensional structure of a protein is determined by the interactions of its constituent amino acids. Considering the amino acids as nodes and the non-bonded interactions among them in 3D space as edges, researchers have constructed protein contact networks and analyzed the values of several topological parameters to uncover different important aspects of proteins. Here, we have analyzed some of the topological parameters such as degree, strength, clustering coefficients, betweenness and closeness centrality of each of the twenty amino acids in a set of non-redundant proteins covering all classes and folds. The results show that the values of these topological parameters vary widely with different amino acids. Also, these values differ significantly with different length scales of proteins. Most of the hydrophobic residues along with Cys, Arg and His have larger contributions to the long range connectivities than short range. We have also studied whether the values of topological parameters have any significant dependency on the physico-chemical properties of the amino acids. While the clustering coefficients show a strong negative correlation with residual volumes, surface areas and number of atoms in the side chains of amino acids; the degrees, strengths and betweenness show positive correlations with the mentioned properties. All the topological parameters show high dependency on bulkiness and average area buried of the amino acid residues in all-range residue networks. The average degree shows higher dependency on hydrophobicity, while the average strength is more able to capture the essences of surface area, residual volume and number of atoms of amino acids. The hydrophobicities of the amino acids and their corresponding degrees show a higher positive correlation in long range networks (LRNs) than short range networks (SRNs). The closeness centrality shows high correlation with two hydrophobic scales and no correlation with surface area, residual volume or number of atoms in LRNs. We have further explored the relationship in hydrophobic, hydrophilic and charged residues separately. Interestingly, charged residues show a higher dependency on the number of atoms than their residual volumes and surface areas. Finally, we present a linear regression model relating the network parameters with physico-chemical properties of amino acids.