Elastic Network Models, Rigidity, and Protein Dynamics

Coarse-grained normal mode analysis assumes that a protein's geometry contains sufficient information to describe its equilibrium fluctuations. This geometry is represented as a residue interaction network (RIN), in which residues are connected by edges. The protein's normal modes are then approximated by those of the RIN. Existing methods differ in how edges are defined and how their force constants are assigned. Here, we introduce a new framework for guiding the geometric construction of elastic networks. We establish an equivalence between the normal mode formalism and the graph-theoretic framework of anisotropic rigidity, which allows the use of constraint counting to filter RINs. In particular, we apply the pebble game algorithm to identify independent edges that preserve the network's flexibility. The resulting filtered RINs yield normal mode models that outperform unfiltered networks in predicting local atomic flexibility, representing conformational changes, and capturing molecular symmetries.