models. In many applications and publications, including the original articles, it has been shown that expected residue fluctuations obtained by the GNM are in good agreement with the experimentally measured native state fluctuations. The relation between B-factors, for example, and expected residue fluctuations obtained from GNM is as follows Figure 3 shows an example of GNM calculation for the catalytic domain of the protein Cdc25B, a cell division cycle dual-specificity phosphatase. Physical meanings of slow and fast modes Diagonalization of the Kirchhoff matrix decomposes the conformational motions into a spectrum of collective modes. The expected values of fluctuations and cross-correlations are obtained from linear combinations of fluctuations along these normal modes. The contribution of each mode is scaled with the inverse of that modes frequency. Hence, slow (low frequency) modes contribute most to the expected fluctuations. Along the few slowest modes, motions are shown to be collective and global and potentially relevant to functionality of the biomolecules. Fast (high frequency) modes, on the other hand, describe uncorrelated motions not inducing notable changes in the structure. GNM-based methods do not provide real dynamics but only an approximation based on the combination and interpolation of normal modes. Their applicability strongly depends on how collective the motion is. Other specific applications There are several major areas in which the Gaussian network model and other elastic network models have proved to be useful. These include: Spring bead based network model: In spring-bead based network model, the springs and beads are used as components in the crosslinked network. Springs are cross-linked to represent mechanical behavior of the material and bridge molecular dynamics (MD) model and finite element (FE) model (see Figure. 5). The beads represent material mass of cluster bonds. Each spring is used to represent a cluster of polymer chains, instead of part of a single polymer chain. This simplification allows to bridge different models at multiple length scales and improves the simulation efficiency significantly. At each iteration step in the simulation, forces in the springs are applied to the nodes at the center of the beads, and the equilibrated nodal displacements throughout the system are calculated. Different from the traditional FE method for obtaining stress and strain, the spring–bead model provides the displacements of the nodes and forces in the springs. The equivalent strain and strain energy of spring–bead based network model can be defined and calculated using the displacements of nodes and