A Finite Element Framework for Computation of Protein Normal Modes and Mechanical Response

A computational framework based on the Finite Element Method is presented to calculate the normal modes and mechanical response of proteins and their supramolecular assemblies. Motivated by elastic network models, proteins are treated as continuum elastic solids with molecular 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 a mutant of T4 phage lysozyme, G-actin, syntenin, cytochrome-c', beta-tubulin, and the supramolecular assembly filamentous actin (F-actin). Equilibrium thermal fluctuations of alpha-carbon atoms and their inter-residue correlations compare favorably with all-atom-based results, the Rotational-Translational Block procedure, and experiment. Additionally, the free vibration and compressive buckling responses of F-actin are in quantitative agreement with experiment. The proposed methodology is applicable to any protein or protein assembly and facilitates the incorporation of specific atomic-level interactions, including aqueous-electrolyte-mediated electrostatic effects and solvent damping. 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.