Understanding on the residue contact network using the log-normal cluster model and the multilevel wheel diagram

Residue clusters play essential role in stabilizing protein structures in the form of complex networks. We show that the cluster sizes in a native protein follow the log-normal distribution for a dataset consisting of 424 proteins. To our knowledge, this is the first time of such fitting for the native structures. Based on log-normal model, the asymptotically increasing mean cluster sizes produce a critical protein chain length of about 200 amino acids, beyond which length most globular proteins have nearly the same mean cluster sizes. This suggests that the larger proteins use a different packing mechanism than the smaller proteins. We confirmed the scale-free property of the residue contact network for most of the protein structures in the dataset, although the violations were observed for the tightly packed proteins. Residue cluster network wheel (RCNW) is proposed to visualize the relationship between the multiple properties of the residue network such as the cluster size, the residue types and contacts, and the flexibility of the residue. We noticed that the residues with large cluster size have smaller Calpha displacement measured using the normal mode analysis.