The Relationship Between Low-Frequency Motions and Community Structure of Residue Network in Protein Molecules

The global shape of a protein molecule is believed to be dominant in determining low-frequency deformational motions. However, how structure dynamics relies on residue interactions remains largely unknown. The global residue community structure and the local residue interactions are two important coexisting factors imposing significant effects on low-frequency normal modes. In this work, an algorithm for community structure partition is proposed by integrating Miyazawa-Jernigan empirical potential energy as edge weight. A sensitivity parameter is defined to measure the effect of local residue interaction on low-frequency movement. We show that community structure is a more fundamental feature of residue contact networks. Moreover, we surprisingly find that low-frequency normal mode eigenvectors are sensitive to some local critical residue interaction pairs (CRIPs). A fair amount of CRIPs act as bridges and hold distributed structure components into a unified tertiary structure by bonding nearby communities. Community structure analysis and CRIP detection of 116 catalytic proteins reveal that breaking up of a CRIP can cause low-frequency allosteric movement of a residue at the far side of protein structure. The results imply that community structure and CRIP may be the structural basis for low-frequency motions.