Large Protein dynamics described by hierarchical-component mode synthesis

Protein dynamics has played a pivotal role in understanding the biological function of protein. For investigation of such dynamics, normal-mode analysis (NMA) has been broadly employed with atomistic model and/or coarse-grained models such as elastic network model (ENM). For large protein complexes, NMA with even ENM encounters the expensive computational process such as diagonalization of Hessian (stiffness) matrix. Here, we suggest the hierarchical-component mode synthesis (hCMS), which allows the fast computation of lowfrequency normal modes related to conformational change. Specifically, a large protein structure is regarded as a combination of several structural units, for which the eigen-value problem is utilized for obtaining the frequencies and their normal modes for each structural unit, and consequently, such frequencies and normal modes are assembled with geometrical constraint for interface between structural units in order to find the low-frequency normal modes of a large protein complex. It is shown that hCMS is able to provide the normal modes with accuracy, quantitatively comparable to those of original NMA. This implies that hCMS may enable the computationally efficient analysis of large protein dynamics.