Multiscale continuum modeling of protein dynamics
Karlson, Kyle N.
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Two multiscale continuum models for simulating protein dynamics are developed which allow for resolution of protein peptide planes in a beam-like finite element. A curvature and strain based finite element formulation is utilized. This formulation is advantageous in simulating proteins since amino acid chains may be described by a single element, even when the protein segment considered exhibits large curvature and twist such as the alpha-helical shapes prominent in many proteins. Specifically, concurrent and hierarchical multiscale models are developed for the curvature and strain based beam formulation. The hierarchical multiscale continuum model utilizes a novel shooting method to calculate the deformed configuration of the protein. An optimization algorithm determines the requisite stiffness parameters by varying the beam stiffness used in the shooting method until deformed configurations of test cases correspond to those produced by the LAMMPS molecular dynamics software. Additionally, a concurrent multiscale method is detailed for evaluating protein inter-atomic potential parameters from the curvature and strain degrees of freedom employed in the model. This allows internal forces and moments to be calculated using nonlinear protein potentials. Proof of concept testing and model verification for both models includes comparing the multiscale techniques to all-atom molecular dynamics solutions. Specifically, the models are verified by simulating a polypeptide in a vacuum and comparing the predicted results to those computed using LAMMPS.