Inter-residue interactions in protein structures exhibit power-law behavior

Inter-residue interactions play an essential role in driving protein folding, and analysis of these interactions increases our understanding of protein folding and stability and facilitates the development of tools for protein structure and function prediction. In this work, we systematically characterized the change of inter-residue interactions at various sequence separation cutoffs using two protein datasets. The first set included 100 diverse, nonredundant and high-resolution soluble protein structures, covering all four major structural classes, all-alpha, alpha/beta, alpha+beta, and all-beta; and the second set included 20 diverse, nonredundant and high-resolution membrane protein structures, representing 19 unique superfamilies. It was shown that the average number of inter-residue interactions in structures of both datasets displays the power-law behavior. Fitting parameters of the power-law function are directly related to the structural classes analyzed. These findings provided further insight into the distribution of short-, medium-, and long-range inter-residue interactions in both soluble and membrane proteins and could be used for protein structure prediction.