Numerical Treatment of Stokes Solvent Flow and Solute–Solvent Interfacial Dynamics for Nonpolar Molecules
We design and implement numerical methods for the incompressible Stokes solvent flow and solute–solvent interface motion for nonpolar molecules in aqueous solvent. The balance of viscous force, surface tension, and van der Waals type dispersive force leads to a traction boundary condition on the solute–solvent interface. To allow the change of solute volume, we design special numerical boundary conditions on the boundary of a computational domain through a consistency condition. We use a finite difference ghost fluid scheme to discretize the Stokes equation with such boundary conditions. The method is tested to have a second-order accuracy. We combine this ghost fluid method with the level-set method to simulate the motion of the solute–solvent interface that is governed by the solvent fluid velocity. Numerical examples show that our method can predict accurately the blow up time for a test example of curvature flow and reproduce the polymodal (e.g., dry and wet) states of hydration of some simple model molecular systems.
KeywordsNonpolar molecules Solute–solvent interface The Stokes equation Ghost fluid method Level-set method Interface motion Change of volume Traction boundary conditions
This work was supported by the US National Science Foundation (NSF) through grant DMS-1319731 and the US National Institutes of Health (NIH) through grant R01GM096188. Work in McCammon’s group is supported in part by NSF, NIH, HHMI, and NBCR. The authors thank Dr. Robert Krasny, Dr. Ray Luo, and Mr. Li Xiao for helpful discussions.
- 19.Siedlecki, C.A., Lestini, B.J., Kottke-Marchant, K.K., Eppell, S.J., Wilson, D.L., Marchant, R.E.: Shear-dependent changes in the three-dimensional structure of human von Willebrand factor. Blood 88, 2939–2950 (1996)Google Scholar
- 21.Szymczak, P., Cieplak, M.: Hydrodynamic effects in proteins. J. Phys.: Condens. Matter 23, 033102 (2011)Google Scholar
- 22.Tanford, C.: The Hydrophobic Effect: Formation of Micelles and Biological Membranes. Wiley, New York (1973)Google Scholar
- 26.White, M.: Mathematical Theory and Numerical Methods for Biomolecular Modeling. PhD thesis, University of California, San Diego (2015)Google Scholar