Calculation of centralities in protein kinase A

Abstract

Topological analysis of protein residue networks (PRNs) is a common method that can help to understand the roles of individual residues. Here, we used protein kinase A as a study object and asked what already known functionally important residues can be detected by network analysis. Along several traditional approaches to weight edges in PRNs we used local spatial pattern (LSP) alignment that assigns high weights to edges only if CαCβ vectors for the corresponding residues retain their mutual positions and orientation. Our results show that even short molecular dynamic simulations of 10 to 20 ns can give convergent values for betweenness and degree centralities calculated from the LSP-based PRNs. Using these centralities, we were able to clearly distinguish a group of residues that are highly conserved in protein kinases and play important functional and regulatory roles. In comparison, traditional methods based on cross-correlation and linear mutual information were much less efficient for this particular task. These results call for reevaluation of the current methods to generate PRNs.

Keywords: allostery; network analysis; protein kinases.

Fig. 1.

Conserved core of the eukaryotic protein kinases with the 26 preselected key residues (black spheres). The core consists of two lobes: N-lobe and C-lobe. ATP (shown as black sticks) is sandwiched between the lobes bound to two magnesium ions (teal spheres). Two hydrophobic ensembles C-spine (yellow surface) and R-spine (red surface) span the core, providing global connectivity within the molecule. The DFG motif and APE motif are flanking the activation segment (red ribbon). The HRD motif is a part of the catalytic loop (olive ribbon). Both spines are anchored to the αF-helix (dark red) that spans the C-lobe and serves as a foundation for the catalytic machinery of the kinase. Additional description of the selected key residues is provided in the Table 1.

Fig. 2.

Key scores calculated using four different centrality metrics, DC, BC, CL, and EG, for different types of PRNs, binary PRNs with no weights assigned to the edges (NW), and three different weighting methods, CC, LMI, and LSP alignment. Calculations were repeated five times using consecutive intervals of MD trajectory of varying length (x axis). SE values are shown. Key scores calculated from an SS are shown as red arrows.

Fig. 3.

Average correlation coefficients between centralities calculated for 336 residues of PKA from five consecutive intervals of varying length. DC, BC, CL, and EG are based on the first eigenvector for different types of PRNs, NW weighted by CC, LMI, and LSP alignment. SE values are shown.

Fig. 4.

EG and eigenvalues in the LSP-based PRNs. (A) Scatter plot of EG versus DC with 26 key residues shown as red dots. Calculations were made on five 16-ns consecutive intervals. SE bars are shown. (B) The top ten eigenvalues of a typical adjacency matrix taken from LSP-based PRN.

Fig. 5.

BC and DC distribution of 336 PKA residues in five different PRNs based on an SS (A) and NW (B) weighted by CC (C), LMI (D), and LSP alignment (E). For the MD simulation–based PRNs, 6-ns long trajectories were used; 26 key residues are shown in red. SEs for five replications values are shown.