Amino acid contact energy networks impact protein structure and evolution

One of the most challenging tasks in structural proteomics is to understand the relationship between protein structure, biological function, and evolution. An understanding of amino acid networks based on protein topology has an important role in the study of this relationship; however, the relationship between network parameters underlying protein topology with structural properties or evolutionary rate is still unknown. To investigate this further, we modeled the three dimensional structure of proteins as amino acid contact energy networks (AACENs) with nodes represented as amino acid residues and edges established according to environment-dependent residue-residue contact energies. Five other types of networks were also constructed to investigate their topological parameters and compare their effect on protein structure and evolution: (1) a random contact network (RCN), (2) a rewiring network with the same degree of distribution as AACEN (RNDD), (3) long-range contact energy networks with and without the backbone connectivity (LCEN_BBs and LCENs), and (4) short range contact energy networks (SCENs). The results indicated that the long-range link percentage and the network clustering coefficient showed a significantly positive and negative correlation, respectively, with protein secondary structure density. In addition, the long-range link percentage and network diameter had a significantly positive and negative correlation, respectively, with evolutionary rate. According to our knowledge, this is the first study to identify the potential role of long-range links and network diameter in protein evolution.