Scaling Behaviour of Conserved Sites in Protein Families

Base on the database of families of structurally similar proteins, a statistical study is made on the scaling behaviour of occupying probabilities of conserved sites (P_c) in various protein families. A power-law decrease of P_c with the increasing protein-chain length L_f is found. This is related to the power-law scaling behaviour of the occurring probabilities of local contact interactions (P_local) between residues. In addition, applying residue grouping, we find the same scaling behaviour when the number of residue types is more than 12, indicating that 12 residue types are enough to present the complexity of proteins.