Robust elastic network model: A general modeling for precise understanding of protein dynamics

In the study of protein dynamics relevant to functions, normal mode analysis based on elastic network models (ENMs) has become popular. These models are usually validated by comparing the calculated atomic fluctuation for a single protein in a vacuum to experimental temperature factors in the crystal packing state. Without reflecting the crystal packing effect, in addition, their arbitrary assignment of spring constants leads to inaccurate simulation results, yielding a low correlation of the B-factor. To overcome this limitation, we propose a robust elastic network model (RENM) that not only considers the crystalline effect by using symmetric constraint information but also uses lumped masses and specific spring constants based on the type of amino acids and chemical interactions, respectively. Simulation results with more than 500 protein structures verify qualitatively and quantitatively that one can obtain the better correlation of the B-factor by RENM without additional computational burden. Moreover, an optimal spring constant in physical units (dyne/cm) is quantitatively determined as a function of the temperature at 100 and 290. K, which enables us to predict the atomic fluctuations and vibrational density of states (VDOS) without a fitting process. The additional investigation of 80 high-resolution crystal structures with anisotropic displacement parameters (ADPs) indicates that RENM could give a full description of vibrational characteristics of individual residues in proteins.