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Numerical Evaluation of Protein Global Vibrations at Terahertz Frequencies by means of Elastic Lattice Models

Proteins represent one of the most important building blocks for most biological processes. Their biological mechanisms have been found to correlate significantly with their dynamics that is commonly investigated through Molecular Dynamics (MD) simulations. However, important insights on protein dynamics and biological mechanisms have also been obtained via much simpler and computationally efficient calculations based on Elastic Lattice Models (ELMs). Despite their simplification with respect to MD frameworks, the application of Structural Mechanics approaches, such as modal analysis, to the protein ELMs has allowed to find impressive results in terms of protein dynamics and vibrations. The low-frequency vibrations extracted from the protein ELM are usually found to occur within the Terahertz (THz) frequency range and correlate fairly accurately with the observed functional motions. In this contribution, the global vibrations of lysozyme will be investigated by means of a Finite Element (FE) truss model and we will show that there exists complete consistency between the proposed FE approach and one of the more well-known ELMs for protein dynamics, the Anisotropic Network Model (ANM). The proposed truss model can consequently be seen as a simple method, easily accessible to the Structural Mechanics community members, to analyze protein vibrations and their connections with the biological activity.

Keywords: Protein Vibrations; Elastic Lattice Model; Terahertz frequency; Lysozyme; B- factors