Gaussian Network Model (Bahar et al.,1997)

The dynamics of the interactions is controlled by the connectivity (or Kirchhoff) matrix G, by analogy with the statistical mechanical theory of elasticity originally developed by Flory and coworkers for polymer networks.  The elements of G are defined as

• Here r_c is the cutoff distance defining the range of interaction of residues, each residue being represented by its a-carbon, and R_ij is the distance between ith and jth residues.
  

• The value of r_c = 7 Å includes the neighboring residues located in the first coordination shell near a central residue.
  

• The equilibrium correlations between the fluctuations DRi and DRj of residues i and j are given by

           < ΔR_i . ΔR_j > = (k_BT/ g) [ G^-1 ]_ij

 where l is the smallest nonzero eigenvalue of G and  u₁ is the corresponding eigenvector reflecting the global mode frequency and shape, respectively, the subscript 1 refers to mode 1 (global mode) and the subscript ii refers to the ith diagonal element of the N x N matrix enclosed in square brackets.

• Note that the columns (or rows) of G are interdependent (all sum up to zero), and thus G cannot be inverted; instead it is reconstructed after removal of its zero eigenvalue and corresponding eigenvector.