A framework of finite element procedures for the analysis of proteins

•A finite element framework for the analysis of proteins in solvent is newly developed.•The effect of solvent damping is considered.•The computational cost of this method is not dependent on the molecular size.•Through numerical examples, the effectiveness of the method is demonstrated. Large-scale, functional collective motions of proteins and their supra-molecular assemblies occur in a physiological solvent environment at finite temperatures. The solution of these motions with standard molecular dynamics algorithms is computationally hardly possible when considering macromolecules. Much research has focused on alternative approaches that use coarse-graining to model proteins, but mostly in vacuum. In this paper, we incorporate realistically the physical effects of solvent damping into the finite element model of proteins. The proposed framework is based on Brownian dynamics and shown to be effective. An important advantage of the approach is that the computational cost is not dependent on the molecular size, which makes the long-time simulation of macromolecules possible. Using the proposed procedure, we demonstrate the analysis of a macromolecule in solvent—an analysis that has not been achieved before and could not be performed with a molecular dynamics algorithm.