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The past decade has witnessed the development and success of coarse-grainednetwork models of proteins for predicting many equilibrium properties relatedto collective modes of motion. Curiously, the results are usually robusttowards the different cutoff distances used for constructing the residuenetworks from the knowledge of the experimental coordinates. In this study, wepresent a systematical study of network construction, and their effect on thepredicted properties. Probing bond orientational order around each residue, wepropose a natural partitioning of the interactions into an essential and aresidual set. In this picture the robustness originates from the way with whichnew contacts are added so that an unusual local orientational order builds up.These residual interactions have a vanishingly small effect on the forcevectors on each residue. The stability of the overall force balance thentranslates into the Hessian as small shifts in the slow modes of motion and aninvariance of the corresponding eigenvectors. We introduce a rescaled versionof the Hessian matrix and point out a link between the matrix Frobenius normbased on spectral stability arguments. A recipe for the optimal choice ofpartitioning the interactions into essential and residual components isprescribed. Implications for the study of biologically relevant properties ofproteins are discussed with specific examples.

Orientational Order Governs Collectivity of Folded Proteins