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. Steps 1. Coordinates (x,y and z) were extracted from the PDB file and saved as an Excel file. 2. Calculations for the matrix were done in MATLAB with code written by our team. The program uses the math described above. The output of the program is a matrix that has fluctuations that correspond to each node. 3. Fluctuation data, with corresponding node number, was again saved as an Excel file. 4. Coloration of the data was done in MATLAB. The output is an image of the structure with colors that corresponded to the fluctuation of the node. Dark blue was used for nodes with the least amount of flexibility. Red was used for nodes with the most flexibility. In between colors were used to represent that correct fluctuation.