Table 1.

Dynamic residue network centrality metrics used to identify residues crucial for communication in FP-2 systems.

Centrality metric	Formula	Note
Averaged BC	$\overline{\mathit{BC}}\left(v\right)=\frac{1}{m}{\sum }_{i=1}^m{\sum }_{u=1}^{n-1}\frac{\delta \left(s_i,t_i|v_i\right)}{\delta \left(s_i,t_i\right)}$	V is the complete set of nodes; m is the number of frames; $\delta \left(s,t\right)$ is the number of shortest paths connecting nodes s and t; $\delta \left(s,t|v\right)$ is the number of these paths passing through another node v; and i is the frame number.
Averaged CC	$\overline{\mathit{CC}}\left(v\right)=\frac{n-1}{m}{\sum }_{i=1}^m{\sum }_{u=1}^{n-1}d\left(v,u\right)$	d(v, u) is the shortest-path distance between v and u, and n is the number of nodes in the graph.
Averaged DC	$\overline{\mathit{DC}}\left(k\right)=\frac{1}{m\left(n-1\right)}{\sum }_{i=1}^m{\sum }_{j=1,j\ne i}^n{A}_{\mathit{ijk}}$	n is the number of nodes; Aijk is the jkth adjacency for the ith frame.
Averaged EC	$A·\overrightarrow{\mathit{EC}}=\lambda ·\overrightarrow{\mathit{EC}}$(a)$\overline{\mathit{EC}}\left(i\right)=\frac{1}{m}{\sum }_{k=1}^m{\mathit{EC}}_{\mathit{ik}}$(b)	(a) EC is the eigenvector, and lambda is the eigenvalue for the eigen decomposition of adjacency matrix A. In NetworkX, this is obtained by power iteration. (b) Averaged EC is computed for ith residue by computing the vector for each MD frame and averaging.
Averaged KC	$KC\left(i\right)=\alpha {\sum }_{j=1}^n{A}_{\mathit{ij}}{\mathit{KC}}_j+\beta$(a)$\overline{\mathit{KC}}\left(i\right)=\frac{1}{m}{\sum }_{k=1}^m{\mathit{KC}}_{\mathit{ik}}$ (b)	KC is a modification of EC that employs a dampening coefficient and a constant in order to influence adjacency values.