  A coarse-grained computational procedure based on the Finite Element Method
is proposed to calculate the normal modes and mechanical response of proteins
and their supramolecular assemblies. Motivated by the elastic network model,
proteins are modeled as homogeneous isotropic elastic solids with volume
defined by their solvent-excluded surface. The discretized Finite Element
representation is obtained using a surface simplification algorithm that
facilitates the generation of models of arbitrary prescribed spatial
resolution. The procedure is applied to compute the normal modes of a mutant of
T4 phage lysozyme and of filamentous actin, as well as the critical Euler
buckling load of the latter when subject to axial compression. Results compare
favorably with all-atom normal mode analysis, the Rotation Translation Blocks
procedure, and experiment. The proposed methodology establishes a computational
framework for the calculation of protein mechanical response that facilitates
the incorporation of specific atomic-level interactions into the model,
including aqueous-electrolyte-mediated electrostatic effects. The procedure is
equally applicable to proteins with known atomic coordinates as it is to
electron density maps of proteins, protein complexes, and supramolecular
assemblies of unknown atomic structure.
