Biomod/2011/PSU/BlueGenes/method

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GNM Gaussian Network Model (GNM) predicts the flexibility of the structure by reducing it to be a set of certain atoms. The interactions of these atoms depend solely on their location. This representative set of atoms is known as nodes. Then a cutoff distance is defined such that outside of this distance, there are no interactions between nodes. The bonds between the atoms are estimated as a spring, with spring constant k=1. For a network of N nodes with given coordinates, the cutoff distnace is rc. The fundamental NxN Kirchhoff matrix, Γ, has elements: where rij is the distance between node i and node j. H(x) is the Heaviside step function where H(x)=1 for x>0 and H(x)=0 for x≤0. The elements of the covariance matrix predicted by the GNM are related to the inverse of the Kirchhoff matrix (Γ-1). The covariance matrix is defined as: kB is Boltzmann constant, T is temperature in Kelvins, γ is the force constant of the imaginary spring between two nodes. The diagonal elements of the covariance matrix are autocorrelations of the nodes and can be treated as fluctuations after normalized.