Multiscale Models for Nano-Bio Systems

We propose a differential geometry based multiscale paradigm for the description and analysis of aqueous chemical, biological systems, such as protein complex, molecular motors, ion channels, and PEM fuel cells. Our multiscale paradigm provides a macroscopic continuum description of the fluid or solvent, a microscopic discrete description of the macromolecule, a differential geometric formulation of the micro-macro interface, and a mixed micro-macro description of the electrostatic interaction. In the proposed framework, we have derived four types of governing equations for different parts of complex systems: fluid dynamics, molecular dynamics, electrostatic interactions, and surface dynamics. These four types of governing equations are generalized Navier–Stokes equations, Newton’s equations, generalized Poisson or Poisson–Boltzmann equations, and hypersurface evolution equations. For systems far from equilibrium, coupled geometric evolution equations, generalized Navier–Stokes equations, Newton’s equations, and Poisson–Nernst–Planck (PNP) equations are formulated. For excessively large chemical and biological systems, we replace the expensive molecular dynamics with a macroscopic elastic description and develop alternative differential geometry based fluid-electroelastic models.