  The past decade has witnessed the development and success of coarse-grained
network models of proteins for predicting many equilibrium properties related
to collective modes of motion. Curiously, the results are usually robust
towards the different methodologies used for constructing the residue networks
from knowledge of the experimental coordinates. We present a systematical study
of network construction strategies, and their effect on the predicted
properties. The analysis is based on the radial distribution function and the
spectral dimensions of a large set of proteins as well as a newly defined
quantity, the angular distribution function. By partitioning the interactions
into an essential and a residual set, we show that the robustness originates
from a large number of long-distance interactions belonging to the latter.
These residuals have a vanishingly small effect on the force vectors on each
residue. The overall force balance then translates into the Hessian as small
shifts in the slow modes of motion and an invariance of the corresponding
eigenvectors. Implications for the study of biologically relevant properties of
proteins are discussed.
